******************************************************************************************** ***** Complete list of all connected edge-transitive graphs on up to 47 vertices ***** ******************************************************************************************** This file gives the edge-sets of the connected edge-transitive graphs on up to 47 vertices, which are summarised at www.math.auckland.ac.nz/~conder/AllSmallETgraphs-upto47-summary.txt. These graphs were found in June & July 2017 by Marston Conder & Gabriel Verret, with the help of the Magma system, and in particular, using its databases of transitive groups of degree up to 47. (Note that any edge-transitive graph that is not vertex-transitive is bipartite, with the two parts being the orbits of its automorphism group on vertices.) The file is formatted for ease of input into the Magma system. The graphs are listed in ascending order, and ascending maximum valency for given order. The j-th edge-transitive graph of order n is labelled as "ETn.j". The notation Bipartite(k,m) indicates that the graph is bipartite, with parts A and B of sizes k and m, and in each such case, the valencies given are the valencies of vertices of A and B respectively. Every non-bipartite edge-transitive graph is regular. The term "twin-free" (introduced by Kotlov and Lovász (1996)) means that no two vertices of the graph have exactly the same neighbours. Another term used for this is "worthy". The terms "VT" and "AT" are abbreviations for "vertex-transitive" and "arc-transitive". The edge-set of the graph ETn.j is given as "EdgePairs[n][j]", for ease of input into the Magma system. Also a list of all all connected edge-transitive bipartite graphs on up to 63 vertices is given at www.math.auckland.ac.nz/~conder/AllSmallETBgraphs-upto63-summary.txt, with the edges given at www.math.auckland.ac.nz/~conder/AllSmallETBgraphs-upto63-full.txt. Marston Conder 25 May 2019 // ******************************************************************************************** // Order 1 // ET1.1 // Non-bipartite Valency 0 // Diameter 0 No cycles // Twin-free VT AT // Automorphism group of order 1 EdgePairs[1][1]:={ }; // Total number of connected ET graphs of order 1 is 1 // ******************************************************************************************** // Order 2 // ET2.1 // Bipartite(1,1) Valencies [1,1] // Diameter 1 No cycles // Twin-free VT AT // Automorphism group of order 2 EdgePairs[2][1]:={ {1,2} }; // Total number of connected ET graphs of order 2 is 1 // ******************************************************************************************** // Order 3 // ET3.1 // Bipartite(1,2) Valencies [2,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 2 EdgePairs[3][1]:={ {1,3}, {1,2} }; // ET3.2 // Non-bipartite Valency 2 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 6 EdgePairs[3][2]:={ {1,3}, {2,3}, {1,2} }; // Total number of connected ET graphs of order 3 is 2 // ******************************************************************************************** // Order 4 // ET4.1 // Bipartite(2,2) Valencies [2,2] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 8 EdgePairs[4][1]:={ {1,3}, {1,4}, {2,4}, {2,3} }; // ET4.2 // Bipartite(1,3) Valencies [3,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 6 EdgePairs[4][2]:={ {1,3}, {1,4}, {1,2} }; // ET4.3 // Non-bipartite Valency 3 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 24 EdgePairs[4][3]:={ {1,3}, {1,4}, {2,4}, {2,3}, {1,2}, {3,4} }; // Total number of connected ET graphs of order 4 is 3 // ******************************************************************************************** // Order 5 // ET5.1 // Non-bipartite Valency 2 // Diameter 2 Girth 5 // Twin-free VT AT // Automorphism group of order 10 EdgePairs[5][1]:={ {2,5}, {1,3}, {1,4}, {2,4}, {3,5} }; // ET5.2 // Bipartite(2,3) Valencies [3,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12 EdgePairs[5][2]:={ {1,5}, {2,5}, {1,3}, {1,4}, {2,4}, {2,3} }; // ET5.3 // Bipartite(1,4) Valencies [4,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 24 EdgePairs[5][3]:={ {1,5}, {1,3}, {1,4}, {1,2} }; // ET5.4 // Non-bipartite Valency 4 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 120 EdgePairs[5][4]:={ {1,3}, {1,5}, {2,5}, {1,4}, {4,5}, {2,4}, {1,2}, {2,3}, {3,4}, {3,5} }; // Total number of connected ET graphs of order 5 is 4 // ******************************************************************************************** // Order 6 // ET6.1 // Bipartite(3,3) Valencies [2,2] // Diameter 3 Girth 6 // Twin-free VT AT // Automorphism group of order 12 EdgePairs[6][1]:={ {2,5}, {3,6}, {1,4}, {2,4}, {3,5}, {1,6} }; // ET6.2 // Bipartite(3,3) Valencies [3,3] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 72 EdgePairs[6][2]:={ {1,5}, {2,5}, {2,6}, {1,6}, {1,4}, {2,4}, {3,5}, {3,4}, {3,6} }; // ET6.3 // Bipartite(2,4) Valencies [4,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 48 EdgePairs[6][3]:={ {1,5}, {2,5}, {1,3}, {2,6}, {1,4}, {2,4}, {2,3}, {1,6} }; // ET6.4 // Non-bipartite Valency 4 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 48 EdgePairs[6][4]:={ {4,6}, {3,5}, {2,6}, {2,3}, {4,5}, {5,6}, {3,4}, {1,3}, {1,2}, {1,5}, {1,6}, {2,4} }; // ET6.5 // Bipartite(1,5) Valencies [5,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 120 EdgePairs[6][5]:={ {1,5}, {1,3}, {1,4}, {1,2}, {1,6} }; // ET6.6 // Non-bipartite Valency 5 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[6][6]:={ {4,6}, {3,5}, {2,6}, {2,3}, {3,6}, {4,5}, {5,6}, {3,4}, {1,3}, {1,4}, {1,2}, {2,5}, {1,5}, {1,6}, {2,4} }; // Total number of connected ET graphs of order 6 is 6 // ******************************************************************************************** // Order 7 // ET7.1 // Non-bipartite Valency 2 // Diameter 3 Girth 7 // Twin-free VT AT // Automorphism group of order 14 EdgePairs[7][1]:={ {1,3}, {4,6}, {1,6}, {2,4}, {5,7}, {2,7}, {3,5} }; // ET7.2 // Bipartite(3,4) Valencies [4,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 144 EdgePairs[7][2]:={ {1,5}, {2,5}, {2,6}, {1,7}, {1,6}, {1,4}, {2,4}, {2,7}, {3,7}, {3,5}, {3,4}, {3,6} }; // ET7.3 // Bipartite(2,5) Valencies [5,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 240 EdgePairs[7][3]:={ {1,5}, {2,5}, {1,3}, {2,6}, {1,4}, {2,4}, {2,7}, {1,7}, {2,3}, {1,6} }; // ET7.4 // Bipartite(1,6) Valencies [6,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 720 EdgePairs[7][4]:={ {1,5}, {1,3}, {1,4}, {1,7}, {1,2}, {1,6} }; // ET7.5 // Non-bipartite Valency 6 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 5040 EdgePairs[7][5]:={ {4,6}, {3,5}, {2,6}, {2,3}, {6,7}, {3,6}, {4,5}, {5,6}, {3,4}, {1,3}, {1,4}, {1,2}, {2,5}, {4,7}, {5,7}, {1,5}, {2,7}, {1,6}, {3,7}, {2,4}, {1,7} }; // Total number of connected ET graphs of order 7 is 5 // ******************************************************************************************** // Order 8 // ET8.1 // Bipartite(4,4) Valencies [2,2] // Diameter 4 Girth 8 // Twin-free VT AT // Automorphism group of order 16 EdgePairs[8][1]:={ {2,8}, {1,5}, {2,6}, {4,7}, {1,6}, {3,8}, {4,5}, {3,7} }; // ET8.2 // Bipartite(4,4) Valencies [3,3] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 48 EdgePairs[8][2]:={ {1,8}, {1,5}, {2,5}, {2,6}, {4,7}, {4,8}, {1,6}, {3,8}, {4,5}, {2,7}, {3,7}, {3,6} }; // ET8.3 // Bipartite(4,4) Valencies [4,4] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 1152 EdgePairs[8][3]:={ {4,6}, {3,5}, {2,6}, {3,6}, {4,5}, {4,8}, {1,8}, {2,5}, {4,7}, {1,5}, {2,7}, {1,6}, {3,7}, {3,8}, {1,7}, {2,8} }; // ET8.4 // Bipartite(3,5) Valencies [5,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 720 EdgePairs[8][4]:={ {2,8}, {1,8}, {1,5}, {2,5}, {2,6}, {1,7}, {1,6}, {1,4}, {3,8}, {2,4}, {2,7}, {3,7}, {3,4}, {3,5}, {3,6} }; // ET8.5 // Bipartite(2,6) Valencies [6,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1440 EdgePairs[8][5]:={ {1,3}, {2,8}, {1,8}, {1,5}, {2,5}, {2,6}, {1,7}, {1,6}, {1,4}, {2,4}, {2,7}, {2,3} }; // ET8.6 // Non-bipartite Valency 6 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 384 EdgePairs[8][6]:={ {3,4}, {1,4}, {1,7}, {1,2}, {6,7}, {1,3}, {5,6}, {4,5}, {6,8}, {3,5}, {2,4}, {1,6}, {5,7}, {5,8}, {2,5}, {3,6}, {4,7}, {2,7}, {1,8}, {2,3}, {4,6}, {7,8}, {2,8}, {3,8} }; // ET8.7 // Bipartite(1,7) Valencies [7,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 5040 EdgePairs[8][7]:={ {1,5}, {1,3}, {1,4}, {1,7}, {1,2}, {1,6}, {1,8} }; // ET8.8 // Non-bipartite Valency 7 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 40320 EdgePairs[8][8]:={ {3,4}, {1,5}, {1,4}, {1,7}, {1,2}, {1,3}, {6,7}, {5,6}, {4,5}, {6,8}, {3,7}, {3,5}, {2,4}, {1,6}, {5,7}, {2,5}, {5,8}, {3,6}, {4,7}, {2,7}, {1,8}, {2,3}, {4,6}, {7,8}, {2,8}, {2,6}, {3,8}, {4,8} }; // Total number of connected ET graphs of order 8 is 8 // ******************************************************************************************** // Order 9 // ET9.1 // Non-bipartite Valency 2 // Diameter 4 Girth 9 // Twin-free VT AT // Automorphism group of order 18 EdgePairs[9][1]:={ {7,8}, {1,9}, {5,6}, {6,7}, {4,5}, {1,2}, {2,3}, {3,4}, {8,9} }; // ET9.2 // Bipartite(3,6) Valencies [4,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 48 EdgePairs[9][2]:={ {2,8}, {1,8}, {1,5}, {2,5}, {2,6}, {1,7}, {3,9}, {1,4}, {2,9}, {3,7}, {3,4}, {3,6} }; // ET9.3 // Non-bipartite Valency 4 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 72 EdgePairs[9][3]:={ {4,6}, {2,6}, {2,3}, {4,8}, {5,6}, {1,3}, {5,9}, {1,8}, {4,9}, {5,7}, {1,5}, {2,7}, {1,6}, {7,9}, {3,7}, {3,8}, {2,4}, {8,9} }; // ET9.4 // Bipartite(4,5) Valencies [5,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2880 EdgePairs[9][4]:={ {4,6}, {3,5}, {2,6}, {3,6}, {3,9}, {4,5}, {4,8}, {1,9}, {1,8}, {2,5}, {4,9}, {4,7}, {1,5}, {2,7}, {1,6}, {3,7}, {3,8}, {1,7}, {2,8}, {2,9} }; // ET9.5 // Bipartite(3,6) Valencies [6,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4320 EdgePairs[9][5]:={ {3,5}, {2,6}, {3,6}, {3,9}, {3,4}, {1,4}, {1,9}, {1,8}, {2,5}, {1,5}, {2,7}, {1,6}, {3,7}, {2,4}, {3,8}, {1,7}, {2,8}, {2,9} }; // ET9.6 // Non-bipartite Valency 6 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1296 EdgePairs[9][6]:={ {3,4}, {1,5}, {4,9}, {8,9}, {1,2}, {1,3}, {6,7}, {5,6}, {4,5}, {6,8}, {3,7}, {5,9}, {3,5}, {2,4}, {1,6}, {7,9}, {5,7}, {2,7}, {1,8}, {2,3}, {2,9}, {4,6}, {1,9}, {7,8}, {2,6}, {3,8}, {4,8} }; // ET9.7 // Bipartite(2,7) Valencies [7,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10080 EdgePairs[9][7]:={ {1,3}, {2,8}, {1,8}, {1,5}, {2,5}, {2,6}, {1,7}, {1,9}, {1,6}, {1,4}, {2,4}, {2,7}, {2,9}, {2,3} }; // ET9.8 // Bipartite(1,8) Valencies [8,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 40320 EdgePairs[9][8]:={ {1,5}, {1,3}, {1,4}, {1,9}, {1,7}, {1,2}, {1,6}, {1,8} }; // ET9.9 // Non-bipartite Valency 8 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 362880 EdgePairs[9][9]:={ {1,4}, {6,7}, {1,3}, {4,6}, {4,5}, {4,7}, {7,8}, {1,7}, {3,8}, {1,5}, {3,6}, {6,8}, {4,8}, {3,4}, {5,6}, {5,8}, {2,7}, {6,9}, {4,9}, {2,3}, {1,2}, {2,4}, {3,9}, {8,9}, {5,7}, {2,6}, {2,8}, {1,9}, {7,9}, {2,5}, {3,5}, {5,9}, {2,9}, {3,7}, {1,6}, {1,8} }; // Total number of connected ET graphs of order 9 is 9 // ******************************************************************************************** // Order 10 // ET10.1 // Bipartite(5,5) Valencies [2,2] // Diameter 5 Girth 10 // Twin-free VT AT // Automorphism group of order 20 EdgePairs[10][1]:={ {1,8}, {1,6}, {3,9}, {4,6}, {3,8}, {5,9}, {5,7}, {2,7}, {2,10}, {4,10} }; // ET10.2 // Bipartite(4,6) Valencies [3,2] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 24 EdgePairs[10][2]:={ {2,8}, {1,5}, {2,5}, {2,6}, {1,7}, {4,8}, {3,9}, {1,10}, {4,9}, {3,7}, {3,6}, {4,10} }; // ET10.3 // Non-bipartite Valency 3 // Diameter 2 Girth 5 // Twin-free VT AT // Automorphism group of order 120 EdgePairs[10][3]:={ {3,5}, {6,10}, {2,6}, {4,8}, {1,3}, {4,10}, {1,9}, {4,9}, {5,7}, {2,7}, {1,6}, {7,9}, {3,8}, {2,8}, {5,10} }; // ET10.4 // Bipartite(5,5) Valencies [4,4] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 240 EdgePairs[10][4]:={ {4,6}, {5,8}, {2,6}, {3,6}, {4,8}, {5,9}, {1,9}, {1,8}, {4,9}, {4,7}, {5,7}, {2,7}, {1,10}, {2,10}, {1,6}, {3,7}, {3,8}, {2,9}, {3,10}, {5,10} }; // ET10.5 // Non-bipartite Valency 4 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 320 EdgePairs[10][5]:={ {4,6}, {3,5}, {5,8}, {3,6}, {8,10}, {1,3}, {1,4}, {6,8}, {1,9}, {1,8}, {2,5}, {4,7}, {5,7}, {2,10}, {7,10}, {6,9}, {7,9}, {2,4}, {2,9}, {3,10} }; // ET10.6 // Bipartite(5,5) Valencies [5,5] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 28800 EdgePairs[10][6]:={ {4,6}, {5,8}, {2,6}, {3,6}, {3,9}, {4,8}, {5,6}, {4,10}, {5,9}, {1,9}, {1,8}, {4,9}, {4,7}, {5,7}, {2,7}, {1,10}, {2,10}, {1,6}, {3,7}, {3,8}, {1,7}, {2,8}, {2,9}, {3,10}, {5,10} }; // ET10.7 // Bipartite(4,6) Valencies [6,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 17280 EdgePairs[10][7]:={ {1,5}, {4,10}, {1,7}, {4,9}, {3,10}, {1,10}, {4,5}, {3,7}, {2,10}, {3,5}, {1,6}, {3,9}, {2,5}, {3,6}, {4,7}, {2,7}, {1,8}, {2,9}, {4,6}, {1,9}, {2,8}, {2,6}, {3,8}, {4,8} }; // ET10.8 // Non-bipartite Valency 6 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 120 EdgePairs[10][8]:={ {1,4}, {6,7}, {7,10}, {4,6}, {3,10}, {4,5}, {4,7}, {7,8}, {1,7}, {1,5}, {6,8}, {3,6}, {3,4}, {1,10}, {8,10}, {5,6}, {5,8}, {6,9}, {2,3}, {1,2}, {8,9}, {3,9}, {2,4}, {9,10}, {2,5}, {2,10}, {5,9}, {2,9}, {3,7}, {1,8} }; // ET10.9 // Bipartite(3,7) Valencies [7,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 30240 EdgePairs[10][9]:={ {3,5}, {2,6}, {3,6}, {3,9}, {3,4}, {1,4}, {1,9}, {1,8}, {2,5}, {1,5}, {2,7}, {1,10}, {2,10}, {1,6}, {3,7}, {2,4}, {3,8}, {1,7}, {2,8}, {2,9}, {3,10} }; // ET10.10 // Bipartite(2,8) Valencies [8,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 80640 EdgePairs[10][10]:={ {2,6}, {2,3}, {1,3}, {1,4}, {1,9}, {1,8}, {2,5}, {1,5}, {2,7}, {1,10}, {2,10}, {1,6}, {2,4}, {1,7}, {2,8}, {2,9} }; // ET10.11 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 3840 EdgePairs[10][11]:={ {3,4}, {1,5}, {4,10}, {6,10}, {1,4}, {1,7}, {8,9}, {1,2}, {1,3}, {3,10}, {6,7}, {1,10}, {5,6}, {4,5}, {6,8}, {3,7}, {5,9}, {2,10}, {3,5}, {2,4}, {7,9}, {8,10}, {6,9}, {7,10}, {5,7}, {3,9}, {2,5}, {5,8}, {3,6}, {4,7}, {1,8}, {2,3}, {2,9}, {4,6}, {1,9}, {7,8}, {9,10}, {2,8}, {2,6}, {4,8} }; // ET10.12 // Bipartite(1,9) Valencies [9,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 362880 EdgePairs[10][12]:={ {1,5}, {1,3}, {1,4}, {1,9}, {1,10}, {1,7}, {1,2}, {1,6}, {1,8} }; // ET10.13 // Non-bipartite Valency 9 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 3628800 EdgePairs[10][13]:={ {1,4}, {6,7}, {7,10}, {1,3}, {4,6}, {3,10}, {4,5}, {4,7}, {7,8}, {1,7}, {3,8}, {1,5}, {3,6}, {6,8}, {4,8}, {3,4}, {6,10}, {1,10}, {8,10}, {5,6}, {5,8}, {2,7}, {6,9}, {2,3}, {4,9}, {1,2}, {2,4}, {3,9}, {8,9}, {5,7}, {2,6}, {2,8}, {9,10}, {1,9}, {7,9}, {2,5}, {2,10}, {3,5}, {4,10}, {5,9}, {2,9}, {3,7}, {1,6}, {1,8}, {5,10} }; // Total number of connected ET graphs of order 10 is 13 // ******************************************************************************************** // Order 11 // ET11.1 // Non-bipartite Valency 2 // Diameter 5 Girth 11 // Twin-free VT AT // Automorphism group of order 22 EdgePairs[11][1]:={ {1,3}, {9,11}, {6,8}, {4,6}, {1,10}, {8,10}, {2,4}, {5,7}, {7,9}, {2,11}, {3,5} }; // ET11.2 // Bipartite(5,6) Valencies [6,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 86400 EdgePairs[11][2]:={ {4,10}, {5,11}, {1,7}, {4,9}, {3,10}, {1,10}, {5,6}, {3,11}, {2,11}, {3,7}, {5,9}, {2,10}, {1,11}, {1,6}, {4,11}, {5,7}, {3,9}, {5,8}, {5,10}, {3,6}, {4,7}, {2,7}, {1,8}, {2,9}, {4,6}, {1,9}, {2,8}, {2,6}, {3,8}, {4,8} }; // ET11.3 // Bipartite(4,7) Valencies [7,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 120960 EdgePairs[11][3]:={ {1,5}, {4,10}, {1,7}, {4,9}, {3,10}, {1,10}, {4,5}, {3,7}, {2,11}, {3,11}, {2,10}, {3,5}, {1,11}, {1,6}, {4,11}, {3,9}, {2,5}, {3,6}, {4,7}, {2,7}, {1,8}, {2,9}, {1,9}, {4,6}, {2,8}, {2,6}, {3,8}, {4,8} }; // ET11.4 // Bipartite(3,8) Valencies [8,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 241920 EdgePairs[11][4]:={ {3,4}, {1,5}, {1,4}, {1,7}, {3,10}, {1,10}, {3,7}, {2,11}, {3,11}, {2,10}, {3,5}, {2,4}, {1,11}, {1,6}, {2,5}, {3,9}, {3,6}, {2,7}, {1,8}, {2,9}, {1,9}, {2,8}, {2,6}, {3,8} }; // ET11.5 // Bipartite(2,9) Valencies [9,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 725760 EdgePairs[11][5]:={ {1,3}, {2,8}, {1,8}, {1,5}, {1,11}, {2,5}, {2,6}, {1,7}, {1,9}, {1,6}, {1,4}, {1,10}, {2,4}, {2,7}, {2,9}, {2,3}, {2,10}, {2,11} }; // ET11.6 // Bipartite(1,10) Valencies [10,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 3628800 EdgePairs[11][6]:={ {1,5}, {1,3}, {1,4}, {1,9}, {1,10}, {1,11}, {1,7}, {1,2}, {1,6}, {1,8} }; // ET11.7 // Non-bipartite Valency 10 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 39916800 EdgePairs[11][7]:={ {2,11}, {4,8}, {4,9}, {7,11}, {7,9}, {2,10}, {8,9}, {1,10}, {1,2}, {8,11}, {4,11}, {4,10}, {5,10}, {7,8}, {1,6}, {3,5}, {2,6}, {1,4}, {5,11}, {6,10}, {4,7}, {3,8}, {9,11}, {3,9}, {6,7}, {2,4}, {5,8}, {4,6}, {5,9}, {8,10}, {5,7}, {1,7}, {3,4}, {7,10}, {2,7}, {3,11}, {3,7}, {9,10}, {2,3}, {10,11}, {5,6}, {2,5}, {1,3}, {4,5}, {1,5}, {3,6}, {1,8}, {2,9}, {6,11}, {1,9}, {2,8}, {1,11}, {6,8}, {3,10}, {6,9} }; // Total number of connected ET graphs of order 11 is 7 // ******************************************************************************************** // Order 12 // ET12.1 // Bipartite(6,6) Valencies [2,2] // Diameter 6 Girth 12 // Twin-free VT AT // Automorphism group of order 24 EdgePairs[12][1]:={ {2,8}, {5,10}, {6,11}, {6,12}, {1,7}, {3,9}, {3,8}, {4,9}, {2,7}, {5,11}, {1,12}, {4,10} }; // ET12.2 // Bipartite(4,8) Valencies [4,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 128 EdgePairs[12][2]:={ {4,6}, {2,6}, {4,11}, {4,10}, {1,9}, {1,8}, {2,5}, {4,7}, {1,5}, {3,11}, {2,10}, {3,12}, {3,7}, {3,8}, {1,12}, {2,9} }; // ET12.3 // Bipartite(6,6) Valencies [4,4] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 768 EdgePairs[12][3]:={ {4,10}, {5,11}, {1,7}, {4,9}, {1,12}, {1,10}, {6,12}, {6,8}, {3,11}, {2,11}, {2,10}, {4,12}, {6,9}, {5,7}, {5,8}, {3,9}, {5,10}, {6,11}, {4,7}, {2,7}, {1,9}, {3,12}, {2,8}, {3,8} }; // ET12.4 // Non-bipartite Valency 4 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 48 EdgePairs[12][4]:={ {4,6}, {2,3}, {6,11}, {4,5}, {8,10}, {7,12}, {5,6}, {3,4}, {1,3}, {5,12}, {11,12}, {1,8}, {5,7}, {2,7}, {1,6}, {10,12}, {7,9}, {1,11}, {9,10}, {3,8}, {2,4}, {2,9}, {8,9}, {10,11} }; // ET12.5 // Bipartite(6,6) Valencies [5,5] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[12][5]:={ {4,10}, {5,11}, {1,7}, {1,12}, {3,10}, {6,7}, {1,10}, {6,12}, {6,8}, {3,11}, {2,11}, {3,7}, {5,9}, {2,10}, {4,11}, {4,12}, {6,9}, {5,7}, {5,8}, {3,9}, {5,10}, {6,11}, {4,7}, {1,8}, {2,9}, {1,9}, {3,12}, {2,8}, {2,12}, {4,8} }; // ET12.6 // Non-bipartite Valency 5 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 120 EdgePairs[12][6]:={ {1,4}, {7,10}, {1,3}, {4,6}, {3,10}, {2,11}, {3,8}, {6,8}, {3,6}, {8,12}, {8,11}, {1,10}, {5,12}, {5,8}, {2,7}, {4,9}, {6,11}, {2,4}, {4,11}, {5,7}, {9,10}, {7,12}, {7,9}, {1,9}, {3,5}, {2,12}, {11,12}, {2,9}, {1,6}, {5,10} }; // ET12.7 // Bipartite(3,9) Valencies [6,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1296 EdgePairs[12][7]:={ {2,8}, {1,8}, {1,5}, {1,11}, {2,5}, {2,6}, {1,7}, {3,10}, {3,9}, {1,4}, {1,10}, {2,12}, {3,12}, {2,9}, {3,7}, {2,11}, {3,4}, {3,6} }; // ET12.8 // Bipartite(4,8) Valencies [6,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 384 EdgePairs[12][8]:={ {1,5}, {4,9}, {1,12}, {3,10}, {1,10}, {4,5}, {3,11}, {2,11}, {3,7}, {2,10}, {1,6}, {4,11}, {4,12}, {2,5}, {3,6}, {4,7}, {2,7}, {1,8}, {2,9}, {1,9}, {3,12}, {2,6}, {3,8}, {4,8} }; // ET12.9 // Bipartite(6,6) Valencies [6,6] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 1036800 EdgePairs[12][9]:={ {6,7}, {3,10}, {4,7}, {1,7}, {3,8}, {2,11}, {6,8}, {4,8}, {6,12}, {6,10}, {1,10}, {5,12}, {5,8}, {3,11}, {2,7}, {1,12}, {6,9}, {4,9}, {6,11}, {4,11}, {3,9}, {1,11}, {5,7}, {5,11}, {2,8}, {3,12}, {1,9}, {2,10}, {2,12}, {4,10}, {5,9}, {2,9}, {3,7}, {4,12}, {5,10}, {1,8} }; // ET12.10 // Non-bipartite Valency 6 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 144 EdgePairs[12][10]:={ {6,7}, {1,3}, {4,6}, {3,10}, {4,5}, {7,8}, {3,8}, {10,12}, {6,8}, {3,4}, {9,11}, {8,10}, {5,6}, {5,12}, {2,7}, {1,12}, {4,9}, {2,3}, {1,2}, {6,11}, {2,4}, {4,11}, {8,9}, {1,11}, {5,7}, {10,11}, {9,10}, {7,12}, {7,9}, {3,5}, {2,12}, {11,12}, {2,9}, {1,6}, {1,8}, {5,10} }; // ET12.11 // Bipartite(5,7) Valencies [7,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 604800 EdgePairs[12][11]:={ {4,6}, {3,10}, {4,7}, {1,7}, {3,8}, {2,11}, {3,6}, {4,8}, {1,10}, {5,6}, {5,8}, {5,12}, {3,11}, {2,7}, {1,12}, {4,9}, {4,11}, {3,9}, {1,11}, {5,7}, {5,11}, {2,6}, {2,8}, {3,12}, {1,9}, {2,10}, {2,12}, {4,10}, {5,9}, {2,9}, {3,7}, {4,12}, {1,6}, {1,8}, {5,10} }; // ET12.12 // Bipartite(4,8) Valencies [8,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 967680 EdgePairs[12][12]:={ {4,6}, {3,10}, {4,5}, {4,7}, {1,7}, {3,8}, {2,11}, {1,5}, {3,6}, {4,8}, {1,10}, {3,11}, {2,7}, {1,12}, {4,9}, {3,9}, {4,11}, {1,11}, {2,6}, {2,8}, {3,12}, {1,9}, {2,5}, {2,10}, {2,12}, {3,5}, {4,10}, {2,9}, {3,7}, {4,12}, {1,6}, {1,8} }; // ET12.13 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 82944 EdgePairs[12][13]:={ {5,12}, {4,8}, {4,9}, {7,11}, {7,9}, {8,9}, {2,10}, {7,12}, {1,2}, {4,11}, {5,10}, {7,8}, {1,6}, {3,5}, {2,6}, {6,10}, {1,12}, {3,8}, {9,11}, {10,12}, {2,12}, {6,7}, {2,4}, {4,6}, {5,9}, {8,10}, {4,12}, {5,7}, {3,4}, {2,7}, {3,11}, {3,7}, {11,12}, {9,10}, {2,3}, {10,11}, {5,6}, {8,12}, {1,3}, {4,5}, {1,5}, {1,8}, {2,9}, {6,11}, {1,9}, {1,11}, {6,8}, {3,10} }; // ET12.14 // Bipartite(3,9) Valencies [9,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2177280 EdgePairs[12][14]:={ {3,5}, {2,6}, {3,6}, {3,9}, {3,4}, {1,4}, {1,9}, {1,8}, {2,5}, {1,5}, {2,7}, {1,10}, {2,10}, {3,11}, {1,6}, {2,12}, {3,12}, {1,11}, {3,7}, {2,4}, {1,12}, {3,8}, {1,7}, {2,11}, {2,8}, {2,9}, {3,10} }; // ET12.15 // Non-bipartite Valency 9 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 31104 EdgePairs[12][15]:={ {2,11}, {5,12}, {4,9}, {3,12}, {7,9}, {8,9}, {7,12}, {1,10}, {1,2}, {8,11}, {4,11}, {4,10}, {5,10}, {7,8}, {1,6}, {6,12}, {3,5}, {1,4}, {5,11}, {4,7}, {1,12}, {3,8}, {9,11}, {10,12}, {3,9}, {2,12}, {6,7}, {2,4}, {5,8}, {4,6}, {8,10}, {5,7}, {1,7}, {3,4}, {7,10}, {2,7}, {11,12}, {9,10}, {9,12}, {2,3}, {10,11}, {5,6}, {2,5}, {1,3}, {4,5}, {3,6}, {1,8}, {2,9}, {6,11}, {2,8}, {1,11}, {6,8}, {3,10}, {6,9} }; // ET12.16 // Bipartite(2,10) Valencies [10,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7257600 EdgePairs[12][16]:={ {1,3}, {2,8}, {1,8}, {1,5}, {1,11}, {2,5}, {2,6}, {1,7}, {1,9}, {1,6}, {1,4}, {1,10}, {2,12}, {2,4}, {2,7}, {2,9}, {2,3}, {1,12}, {2,10}, {2,11} }; // ET12.17 // Non-bipartite Valency 10 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 46080 EdgePairs[12][17]:={ {2,11}, {5,12}, {4,8}, {4,9}, {7,11}, {3,12}, {7,9}, {2,10}, {7,12}, {1,10}, {1,2}, {8,11}, {4,11}, {4,10}, {5,10}, {7,8}, {1,6}, {6,12}, {3,5}, {2,6}, {1,4}, {5,11}, {6,10}, {4,7}, {3,8}, {9,11}, {10,12}, {3,9}, {2,12}, {2,4}, {5,8}, {4,6}, {5,9}, {8,10}, {4,12}, {5,7}, {1,7}, {3,4}, {7,10}, {2,7}, {3,11}, {3,7}, {11,12}, {9,10}, {9,12}, {5,6}, {8,12}, {2,5}, {1,3}, {1,5}, {3,6}, {1,8}, {2,9}, {6,11}, {1,9}, {2,8}, {1,11}, {6,8}, {3,10}, {6,9} }; // ET12.18 // Bipartite(1,11) Valencies [11,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 39916800 EdgePairs[12][18]:={ {1,5}, {1,3}, {1,12}, {1,4}, {1,9}, {1,10}, {1,11}, {1,7}, {1,2}, {1,6}, {1,8} }; // ET12.19 // Non-bipartite Valency 11 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 479001600 EdgePairs[12][19]:={ {2,11}, {5,12}, {4,8}, {4,9}, {7,11}, {3,12}, {7,9}, {2,10}, {8,9}, {7,12}, {1,10}, {1,2}, {8,11}, {4,11}, {4,10}, {5,10}, {1,6}, {7,8}, {3,5}, {6,12}, {2,6}, {1,4}, {5,11}, {6,10}, {4,7}, {1,12}, {3,8}, {9,11}, {10,12}, {3,9}, {2,12}, {6,7}, {2,4}, {5,8}, {4,6}, {5,9}, {8,10}, {4,12}, {5,7}, {1,7}, {3,4}, {2,7}, {7,10}, {3,11}, {3,7}, {11,12}, {9,10}, {9,12}, {2,3}, {10,11}, {5,6}, {8,12}, {2,5}, {1,3}, {4,5}, {1,5}, {3,6}, {1,8}, {2,9}, {6,11}, {1,9}, {2,8}, {1,11}, {6,8}, {3,10}, {6,9} }; // Total number of connected ET graphs of order 12 is 19 // ******************************************************************************************** // Order 13 // ET13.1 // Non-bipartite Valency 2 // Diameter 6 Girth 13 // Twin-free VT AT // Automorphism group of order 26 EdgePairs[13][1]:={ {2,8}, {1,8}, {6,12}, {5,12}, {3,10}, {1,7}, {3,9}, {4,11}, {2,9}, {5,11}, {6,13}, {7,13}, {4,10} }; // ET13.2 // Non-bipartite Valency 4 // Diameter 2 Girth 4 // Twin-free VT AT // Automorphism group of order 52 EdgePairs[13][2]:={ {5,12}, {1,5}, {4,10}, {6,10}, {5,11}, {1,7}, {9,13}, {7,11}, {3,10}, {1,10}, {7,13}, {6,12}, {4,13}, {2,11}, {3,7}, {8,12}, {5,9}, {4,11}, {3,9}, {1,8}, {2,9}, {3,12}, {2,8}, {2,6}, {4,8}, {6,13} }; // ET13.3 // Non-bipartite Valency 6 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 78 EdgePairs[13][3]:={ {1,3}, {4,6}, {6,13}, {3,10}, {5,13}, {1,7}, {3,8}, {10,12}, {11,13}, {6,8}, {9,11}, {6,12}, {8,10}, {5,12}, {3,11}, {2,7}, {1,12}, {2,13}, {4,9}, {6,11}, {2,4}, {3,9}, {4,11}, {5,7}, {5,11}, {8,13}, {7,13}, {2,8}, {7,12}, {7,9}, {1,9}, {2,10}, {3,5}, {4,10}, {2,9}, {4,12}, {1,6}, {1,8}, {5,10} }; // ET13.4 // Bipartite(6,7) Valencies [7,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3628800 EdgePairs[13][4]:={ {6,7}, {6,13}, {3,10}, {5,13}, {4,7}, {1,7}, {3,8}, {2,11}, {6,8}, {4,8}, {6,12}, {6,10}, {1,10}, {5,12}, {5,8}, {3,11}, {2,7}, {1,12}, {2,13}, {1,13}, {6,9}, {4,9}, {6,11}, {4,11}, {3,9}, {1,11}, {5,7}, {5,11}, {2,8}, {3,12}, {1,9}, {3,13}, {4,13}, {2,12}, {2,10}, {4,10}, {5,9}, {2,9}, {3,7}, {4,12}, {5,10}, {1,8} }; // ET13.5 // Bipartite(5,8) Valencies [8,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4838400 EdgePairs[13][5]:={ {4,6}, {3,10}, {5,13}, {4,7}, {1,7}, {3,8}, {2,11}, {3,6}, {4,8}, {1,10}, {5,6}, {5,8}, {5,12}, {3,11}, {2,7}, {1,12}, {2,13}, {1,13}, {4,9}, {4,11}, {3,9}, {1,11}, {5,7}, {5,11}, {2,6}, {2,8}, {3,12}, {1,9}, {3,13}, {2,10}, {2,12}, {4,13}, {4,10}, {5,9}, {2,9}, {3,7}, {4,12}, {1,6}, {1,8}, {5,10} }; // ET13.6 // Bipartite(4,9) Valencies [9,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8709120 EdgePairs[13][6]:={ {4,6}, {3,10}, {4,5}, {4,7}, {1,7}, {3,8}, {2,11}, {1,5}, {3,6}, {4,8}, {1,10}, {3,11}, {2,7}, {1,12}, {2,13}, {1,13}, {4,9}, {3,9}, {4,11}, {1,11}, {2,6}, {2,8}, {3,12}, {1,9}, {3,13}, {2,5}, {2,10}, {2,12}, {3,5}, {4,13}, {4,10}, {2,9}, {3,7}, {4,12}, {1,6}, {1,8} }; // ET13.7 // Bipartite(3,10) Valencies [10,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 21772800 EdgePairs[13][7]:={ {3,4}, {1,5}, {1,4}, {1,7}, {1,12}, {3,10}, {1,13}, {1,10}, {2,13}, {3,11}, {2,11}, {3,7}, {2,10}, {3,5}, {2,4}, {1,11}, {1,6}, {3,9}, {2,5}, {3,6}, {2,7}, {1,8}, {2,9}, {1,9}, {3,12}, {2,8}, {2,6}, {3,8}, {2,12}, {3,13} }; // ET13.8 // Bipartite(2,11) Valencies [11,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 79833600 EdgePairs[13][8]:={ {1,13}, {2,6}, {2,3}, {1,3}, {1,4}, {1,9}, {1,8}, {2,5}, {1,5}, {2,7}, {1,10}, {2,10}, {1,6}, {2,12}, {2,13}, {1,11}, {2,4}, {1,12}, {1,7}, {2,11}, {2,8}, {2,9} }; // ET13.9 // Bipartite(1,12) Valencies [12,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 479001600 EdgePairs[13][9]:={ {1,3}, {1,8}, {1,5}, {1,11}, {1,7}, {1,9}, {1,6}, {1,4}, {1,10}, {1,2}, {1,13}, {1,12} }; // ET13.10 // Non-bipartite Valency 12 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 6227020800 EdgePairs[13][10]:={ {2,11}, {5,12}, {4,8}, {4,13}, {4,9}, {7,11}, {3,12}, {7,9}, {2,10}, {8,9}, {7,12}, {1,10}, {1,2}, {8,11}, {4,11}, {4,10}, {5,10}, {1,6}, {7,8}, {3,5}, {6,12}, {7,13}, {2,6}, {1,4}, {5,11}, {6,10}, {4,7}, {1,12}, {3,8}, {9,11}, {10,12}, {3,9}, {2,12}, {2,4}, {6,7}, {5,8}, {4,6}, {5,9}, {8,10}, {4,12}, {5,7}, {10,13}, {1,7}, {3,4}, {2,7}, {7,10}, {3,11}, {3,7}, {11,12}, {9,10}, {9,12}, {2,3}, {10,11}, {8,13}, {5,6}, {8,12}, {2,5}, {1,3}, {4,5}, {12,13}, {1,5}, {9,13}, {11,13}, {3,6}, {3,13}, {1,8}, {1,13}, {2,9}, {5,13}, {6,11}, {1,9}, {2,13}, {2,8}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // Total number of connected ET graphs of order 13 is 10 // ******************************************************************************************** // Order 14 // ET14.1 // Bipartite(7,7) Valencies [2,2] // Diameter 7 Girth 14 // Twin-free VT AT // Automorphism group of order 28 EdgePairs[14][1]:={ {1,8}, {7,11}, {6,8}, {3,10}, {2,12}, {1,10}, {5,14}, {7,9}, {4,12}, {3,14}, {2,9}, {5,11}, {6,13}, {4,13} }; // ET14.2 // Bipartite(7,7) Valencies [3,3] // Diameter 3 Girth 6 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[14][2]:={ {1,13}, {6,14}, {4,11}, {6,10}, {3,13}, {3,9}, {4,8}, {6,12}, {7,11}, {2,14}, {5,12}, {4,10}, {5,9}, {1,8}, {7,14}, {5,11}, {1,12}, {7,13}, {2,8}, {2,9}, {3,10} }; // ET14.3 // Bipartite(6,8) Valencies [4,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 48 EdgePairs[14][3]:={ {6,10}, {5,11}, {1,7}, {6,14}, {1,10}, {4,14}, {6,8}, {3,11}, {3,7}, {4,13}, {2,14}, {2,10}, {4,11}, {4,12}, {5,7}, {5,8}, {5,13}, {3,9}, {1,8}, {2,9}, {1,9}, {3,12}, {2,12}, {6,13} }; // ET14.4 // Bipartite(6,8) Valencies [4,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 384 EdgePairs[14][4]:={ {4,10}, {6,10}, {1,7}, {5,14}, {1,12}, {6,14}, {6,7}, {4,14}, {2,13}, {3,11}, {3,7}, {5,9}, {1,11}, {4,12}, {3,9}, {5,13}, {5,10}, {6,11}, {1,8}, {2,9}, {2,8}, {3,13}, {2,12}, {4,8} }; // ET14.5 // Bipartite(7,7) Valencies [4,4] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[14][5]:={ {5,8}, {6,14}, {1,14}, {3,14}, {4,11}, {6,10}, {6,11}, {3,13}, {4,8}, {7,11}, {7,12}, {2,14}, {5,12}, {5,9}, {1,8}, {4,9}, {2,12}, {2,13}, {7,10}, {4,13}, {6,9}, {1,11}, {3,8}, {1,12}, {7,13}, {2,9}, {3,10}, {5,10} }; // ET14.6 // Non-bipartite Valency 4 // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 1792 EdgePairs[14][6]:={ {10,14}, {4,14}, {5,8}, {2,6}, {3,14}, {6,10}, {3,6}, {3,13}, {4,8}, {7,11}, {8,12}, {1,4}, {5,9}, {9,13}, {10,13}, {2,5}, {4,7}, {1,5}, {2,12}, {2,13}, {7,10}, {6,9}, {1,11}, {3,7}, {9,12}, {1,12}, {11,14}, {8,11} }; // ET14.7 // Bipartite(7,7) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 10080 EdgePairs[14][7]:={ {7,10}, {6,13}, {7,14}, {3,10}, {5,13}, {1,14}, {2,11}, {3,8}, {3,14}, {6,8}, {4,8}, {6,10}, {1,10}, {4,14}, {5,12}, {5,8}, {1,12}, {6,9}, {2,13}, {1,13}, {4,9}, {6,14}, {6,11}, {4,11}, {3,9}, {1,11}, {5,11}, {7,11}, {7,13}, {2,8}, {3,12}, {7,12}, {3,13}, {7,9}, {2,12}, {4,10}, {5,9}, {2,9}, {4,12}, {2,14}, {1,8}, {5,10} }; // ET14.8 // Bipartite(7,7) Valencies [7,7] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 50803200 EdgePairs[14][8]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {3,12}, {7,9}, {2,10}, {7,12}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {7,8}, {6,12}, {7,13}, {6,10}, {5,11}, {1,12}, {3,8}, {3,9}, {2,12}, {5,8}, {5,9}, {4,12}, {7,10}, {3,11}, {3,14}, {5,14}, {3,13}, {1,8}, {1,13}, {5,13}, {2,9}, {6,11}, {1,9}, {2,13}, {4,14}, {2,8}, {7,14}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET14.9 // Bipartite(6,8) Valencies [8,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 29030400 EdgePairs[14][9]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {6,12}, {5,11}, {6,10}, {4,7}, {1,12}, {3,8}, {3,9}, {2,12}, {6,7}, {5,8}, {5,9}, {4,12}, {5,7}, {1,7}, {2,7}, {3,11}, {3,7}, {3,14}, {5,14}, {3,13}, {1,8}, {1,13}, {5,13}, {2,9}, {6,11}, {1,9}, {2,13}, {4,14}, {2,8}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET14.10 // Bipartite(5,9) Valencies [9,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 43545600 EdgePairs[14][10]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {5,10}, {1,6}, {2,6}, {5,11}, {4,7}, {1,12}, {3,8}, {3,9}, {2,12}, {5,8}, {4,6}, {5,9}, {4,12}, {5,7}, {1,7}, {2,7}, {3,11}, {3,7}, {5,6}, {3,14}, {3,6}, {5,14}, {3,13}, {1,8}, {1,13}, {2,9}, {5,13}, {1,9}, {2,13}, {4,14}, {2,8}, {1,11}, {3,10} }; // ET14.11 // Bipartite(4,10) Valencies [10,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 87091200 EdgePairs[14][11]:={ {4,6}, {3,10}, {4,5}, {1,14}, {4,7}, {1,7}, {3,8}, {3,14}, {2,11}, {1,5}, {3,6}, {4,8}, {1,10}, {4,14}, {3,11}, {2,7}, {1,12}, {2,13}, {1,13}, {4,9}, {3,9}, {4,11}, {1,11}, {2,6}, {2,8}, {3,12}, {1,9}, {3,13}, {2,5}, {2,10}, {2,12}, {3,5}, {4,13}, {4,10}, {2,9}, {3,7}, {4,12}, {2,14}, {1,8}, {1,6} }; // ET14.12 // Bipartite(3,11) Valencies [11,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 239500800 EdgePairs[14][12]:={ {1,4}, {3,10}, {1,14}, {1,7}, {3,8}, {2,11}, {3,14}, {1,5}, {3,6}, {3,4}, {1,10}, {3,11}, {2,7}, {1,12}, {2,13}, {1,13}, {2,4}, {3,9}, {1,11}, {2,6}, {2,8}, {3,12}, {1,9}, {3,13}, {2,5}, {2,10}, {2,12}, {3,5}, {2,9}, {3,7}, {2,14}, {1,8}, {1,6} }; // ET14.13 // Bipartite(2,12) Valencies [12,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 958003200 EdgePairs[14][13]:={ {1,13}, {1,14}, {2,3}, {2,6}, {2,14}, {1,3}, {1,4}, {1,9}, {1,8}, {2,5}, {1,5}, {2,7}, {1,10}, {2,10}, {1,6}, {2,12}, {2,13}, {1,11}, {2,4}, {1,12}, {1,7}, {2,11}, {2,8}, {2,9} }; // ET14.14 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 645120 EdgePairs[14][14]:={ {2,11}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {3,12}, {7,9}, {2,10}, {8,9}, {7,12}, {1,10}, {1,2}, {6,14}, {8,11}, {4,10}, {5,10}, {1,6}, {7,8}, {3,5}, {6,12}, {7,13}, {2,6}, {1,4}, {5,11}, {6,10}, {4,7}, {1,12}, {3,8}, {9,11}, {10,12}, {3,9}, {2,12}, {13,14}, {2,4}, {6,7}, {5,8}, {4,6}, {5,9}, {8,10}, {4,12}, {5,7}, {10,13}, {1,7}, {3,4}, {2,7}, {7,10}, {3,11}, {3,7}, {11,12}, {9,10}, {9,12}, {2,3}, {10,11}, {8,13}, {10,14}, {5,6}, {3,14}, {8,12}, {12,14}, {2,5}, {1,3}, {4,5}, {12,13}, {1,5}, {9,13}, {11,13}, {3,6}, {5,14}, {9,14}, {3,13}, {1,13}, {8,14}, {5,13}, {6,11}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {11,14}, {6,8}, {6,9} }; // ET14.15 // Bipartite(1,13) Valencies [13,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 6227020800 EdgePairs[14][15]:={ {1,3}, {1,8}, {1,5}, {1,11}, {1,14}, {1,7}, {1,9}, {1,6}, {1,4}, {1,10}, {1,2}, {1,13}, {1,12} }; // ET14.16 // Non-bipartite Valency 13 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 87178291200 EdgePairs[14][16]:={ {9,13}, {13,14}, {6,12}, {5,14}, {6,10}, {4,14}, {1,11}, {6,14}, {4,8}, {3,7}, {2,11}, {2,3}, {9,12}, {6,13}, {12,14}, {1,9}, {4,5}, {1,5}, {6,7}, {5,7}, {4,6}, {5,13}, {3,10}, {9,10}, {6,9}, {8,14}, {8,13}, {7,11}, {5,9}, {1,2}, {4,12}, {5,6}, {7,10}, {2,14}, {3,11}, {1,3}, {2,10}, {6,11}, {1,10}, {4,7}, {3,13}, {10,12}, {10,13}, {8,10}, {3,14}, {2,13}, {1,12}, {3,9}, {6,8}, {7,13}, {7,14}, {8,11}, {2,9}, {3,5}, {1,4}, {11,14}, {2,4}, {11,13}, {4,11}, {7,8}, {3,4}, {11,12}, {1,7}, {5,8}, {8,9}, {2,12}, {10,14}, {3,12}, {2,6}, {1,14}, {7,9}, {2,8}, {9,11}, {5,11}, {1,13}, {5,10}, {3,8}, {5,12}, {9,14}, {3,6}, {4,9}, {2,7}, {1,8}, {7,12}, {4,13}, {10,11}, {1,6}, {4,10}, {2,5}, {12,13}, {8,12} }; // Total number of connected ET graphs of order 14 is 16 // ******************************************************************************************** // Order 15 // ET15.1 // Non-bipartite Valency 2 // Diameter 7 Girth 15 // Twin-free VT AT // Automorphism group of order 30 EdgePairs[15][1]:={ {9,10}, {13,14}, {1,15}, {7,8}, {5,6}, {10,11}, {6,7}, {4,5}, {11,12}, {14,15}, {1,2}, {12,13}, {2,3}, {3,4}, {8,9} }; // ET15.2 // Bipartite(6,9) Valencies [3,2] // Diameter 4 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 72 EdgePairs[15][2]:={ {1,8}, {6,12}, {6,8}, {3,10}, {1,7}, {4,7}, {2,14}, {1,9}, {5,13}, {2,15}, {4,11}, {5,15}, {3,12}, {2,9}, {3,14}, {5,11}, {6,13}, {4,10} }; // ET15.3 // Bipartite(5,10) Valencies [4,2] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[15][3]:={ {4,10}, {3,15}, {5,14}, {1,13}, {2,13}, {3,11}, {1,6}, {4,11}, {4,12}, {1,14}, {5,7}, {5,15}, {3,9}, {5,10}, {2,7}, {4,6}, {1,9}, {2,8}, {2,12}, {3,8} }; // ET15.4 // Bipartite(5,10) Valencies [4,2] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 320 EdgePairs[15][4]:={ {1,14}, {5,14}, {3,6}, {3,13}, {4,8}, {5,12}, {4,10}, {5,9}, {1,9}, {5,7}, {2,7}, {3,11}, {2,10}, {1,6}, {2,12}, {4,13}, {1,11}, {2,15}, {3,8}, {4,15} }; // ET15.5 // Non-bipartite Valency 4 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 60 EdgePairs[15][5]:={ {3,4}, {1,5}, {6,10}, {10,11}, {1,12}, {9,13}, {8,9}, {1,2}, {7,11}, {6,7}, {5,6}, {4,5}, {2,13}, {1,15}, {3,7}, {8,12}, {14,15}, {5,9}, {4,15}, {13,14}, {3,14}, {11,15}, {10,14}, {2,3}, {7,8}, {9,10}, {11,12}, {2,6}, {12,13}, {4,8} }; // ET15.6 // Non-bipartite Valency 4 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 120 EdgePairs[15][6]:={ {4,6}, {6,13}, {3,10}, {5,13}, {1,14}, {1,7}, {10,12}, {3,14}, {4,15}, {1,15}, {3,6}, {8,12}, {8,11}, {6,10}, {5,8}, {2,3}, {4,11}, {5,7}, {7,13}, {9,10}, {2,8}, {7,9}, {1,9}, {11,15}, {2,5}, {4,13}, {11,12}, {14,15}, {9,12}, {2,14} }; // ET15.7 // Bipartite(5,10) Valencies [6,3] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[15][7]:={ {5,12}, {4,10}, {5,11}, {3,15}, {1,7}, {4,9}, {3,10}, {1,13}, {1,10}, {5,6}, {2,13}, {2,11}, {4,13}, {2,14}, {5,9}, {4,15}, {1,11}, {2,15}, {3,14}, {1,14}, {5,7}, {5,8}, {3,6}, {4,7}, {1,8}, {2,9}, {4,6}, {3,12}, {2,12}, {3,8} }; // ET15.8 // Bipartite(6,9) Valencies [6,4] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 72 EdgePairs[15][8]:={ {6,13}, {6,15}, {3,10}, {5,13}, {1,14}, {4,7}, {1,7}, {3,14}, {2,11}, {6,8}, {3,15}, {4,8}, {6,12}, {1,10}, {5,15}, {5,8}, {3,11}, {2,7}, {1,12}, {6,9}, {6,14}, {4,11}, {5,7}, {5,11}, {3,12}, {2,15}, {1,9}, {3,13}, {4,13}, {2,10}, {4,10}, {5,9}, {2,9}, {4,12}, {2,14}, {1,8} }; // ET15.9 // Bipartite(6,9) Valencies [6,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10368 EdgePairs[15][9]:={ {6,7}, {6,13}, {6,15}, {3,10}, {5,14}, {1,14}, {4,7}, {1,7}, {2,11}, {3,15}, {4,8}, {6,12}, {6,10}, {1,10}, {4,14}, {5,12}, {5,8}, {5,15}, {1,13}, {6,9}, {4,11}, {3,9}, {1,11}, {5,11}, {2,8}, {3,12}, {2,15}, {3,13}, {4,13}, {2,12}, {4,10}, {5,9}, {2,9}, {3,7}, {2,14}, {1,8} }; // ET15.10 // Non-bipartite Valency 6 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[15][10]:={ {1,4}, {1,3}, {12,13}, {4,7}, {7,8}, {2,11}, {6,8}, {10,14}, {7,15}, {13,15}, {8,15}, {6,12}, {1,10}, {5,6}, {8,14}, {5,12}, {5,15}, {3,11}, {1,13}, {2,13}, {4,9}, {6,11}, {8,9}, {3,9}, {2,4}, {7,11}, {10,11}, {13,14}, {2,6}, {9,14}, {10,15}, {2,15}, {7,12}, {3,13}, {3,5}, {4,10}, {5,9}, {2,9}, {3,7}, {11,14}, {12,14}, {4,12}, {1,6}, {1,8}, {5,10} }; // ET15.11 // Non-bipartite Valency 6 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 77760 EdgePairs[15][11]:={ {2,11}, {4,8}, {4,13}, {7,11}, {11,15}, {3,12}, {8,9}, {1,10}, {1,2}, {4,10}, {7,8}, {6,12}, {7,13}, {2,6}, {6,10}, {5,11}, {9,15}, {1,12}, {3,9}, {13,14}, {6,7}, {6,15}, {5,9}, {1,7}, {3,4}, {1,15}, {3,7}, {11,12}, {9,10}, {2,3}, {10,11}, {10,14}, {5,6}, {3,14}, {8,12}, {4,5}, {12,13}, {1,5}, {4,15}, {9,13}, {5,14}, {8,14}, {2,13}, {2,8}, {14,15} }; // ET15.12 // Bipartite(3,12) Valencies [8,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 82944 EdgePairs[15][12]:={ {3,4}, {1,5}, {1,4}, {1,7}, {3,15}, {3,10}, {1,13}, {1,10}, {3,7}, {2,11}, {2,14}, {1,11}, {2,15}, {1,14}, {3,9}, {2,5}, {3,6}, {1,8}, {2,9}, {3,12}, {2,8}, {2,6}, {2,12}, {3,13} }; // ET15.13 // Bipartite(5,10) Valencies [8,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3840 EdgePairs[15][13]:={ {4,6}, {3,10}, {5,13}, {1,14}, {4,7}, {1,7}, {3,8}, {3,14}, {4,15}, {3,6}, {3,15}, {4,14}, {5,6}, {5,8}, {5,12}, {5,15}, {3,11}, {2,7}, {1,12}, {2,13}, {1,13}, {4,9}, {4,11}, {3,9}, {1,11}, {5,7}, {5,11}, {2,8}, {2,15}, {1,9}, {3,13}, {2,10}, {2,12}, {4,10}, {2,9}, {4,12}, {2,14}, {1,8}, {1,6}, {5,10} }; // ET15.14 // Bipartite(7,8) Valencies [8,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 203212800 EdgePairs[15][14]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {3,12}, {7,9}, {2,10}, {7,12}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {7,8}, {6,12}, {7,13}, {5,11}, {6,10}, {1,12}, {5,15}, {3,8}, {3,9}, {2,12}, {6,15}, {5,8}, {5,9}, {4,12}, {1,15}, {7,10}, {3,11}, {3,15}, {7,15}, {2,15}, {3,14}, {4,15}, {5,14}, {3,13}, {1,8}, {1,13}, {5,13}, {2,9}, {6,11}, {1,9}, {2,13}, {4,14}, {2,8}, {7,14}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET15.15 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[15][15]:={ {5,12}, {4,8}, {1,14}, {7,11}, {11,15}, {7,9}, {8,9}, {2,10}, {1,2}, {6,14}, {4,11}, {7,8}, {8,15}, {3,5}, {2,6}, {6,10}, {1,12}, {9,11}, {10,12}, {13,14}, {6,7}, {2,4}, {4,6}, {5,9}, {8,10}, {4,12}, {5,7}, {3,4}, {1,15}, {3,11}, {3,7}, {11,12}, {9,10}, {2,3}, {10,11}, {7,15}, {10,14}, {5,6}, {2,15}, {3,14}, {8,12}, {12,14}, {1,3}, {4,5}, {12,13}, {1,5}, {4,15}, {9,13}, {11,13}, {13,15}, {1,8}, {5,13}, {2,9}, {1,9}, {2,13}, {7,14}, {14,15}, {6,13}, {6,8}, {3,10} }; // ET15.16 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[15][16]:={ {4,8}, {2,14}, {4,13}, {1,14}, {11,15}, {3,12}, {7,9}, {2,10}, {8,11}, {6,14}, {1,2}, {4,11}, {7,13}, {6,10}, {5,11}, {9,15}, {1,12}, {3,8}, {9,11}, {10,12}, {2,12}, {6,7}, {6,15}, {5,8}, {4,6}, {8,10}, {5,7}, {10,13}, {1,7}, {3,4}, {7,10}, {2,7}, {1,15}, {3,15}, {11,12}, {9,10}, {9,12}, {2,3}, {8,13}, {3,14}, {8,12}, {2,5}, {4,5}, {1,5}, {4,15}, {9,13}, {11,13}, {3,6}, {5,14}, {5,13}, {1,9}, {4,14}, {2,8}, {12,15}, {7,14}, {14,15}, {1,11}, {6,13}, {3,10}, {6,9} }; // ET15.17 // Bipartite(6,9) Valencies [9,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 261273600 EdgePairs[15][17]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {6,12}, {5,11}, {6,10}, {4,7}, {1,12}, {5,15}, {3,8}, {3,9}, {2,12}, {6,7}, {6,15}, {5,8}, {5,9}, {4,12}, {5,7}, {1,7}, {1,15}, {2,7}, {3,11}, {3,7}, {3,15}, {2,15}, {3,14}, {4,15}, {5,14}, {3,13}, {1,8}, {1,13}, {2,9}, {5,13}, {6,11}, {1,9}, {2,13}, {4,14}, {2,8}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET15.18 // Bipartite(5,10) Valencies [10,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 435456000 EdgePairs[15][18]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {5,10}, {1,6}, {2,6}, {5,11}, {4,7}, {1,12}, {5,15}, {3,8}, {3,9}, {2,12}, {5,8}, {4,6}, {5,9}, {4,12}, {5,7}, {1,7}, {1,15}, {2,7}, {3,11}, {3,7}, {3,15}, {5,6}, {2,15}, {3,14}, {4,15}, {3,6}, {5,14}, {3,13}, {1,8}, {1,13}, {2,9}, {5,13}, {1,9}, {2,13}, {4,14}, {2,8}, {1,11}, {3,10} }; // ET15.19 // Non-bipartite Valency 10 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 10368000 EdgePairs[15][19]:={ {5,12}, {4,8}, {4,9}, {10,15}, {1,14}, {7,11}, {11,15}, {7,9}, {2,10}, {8,9}, {7,12}, {1,2}, {6,14}, {4,11}, {5,10}, {1,6}, {7,8}, {8,15}, {3,5}, {2,6}, {6,10}, {5,15}, {1,12}, {3,8}, {9,11}, {10,12}, {2,12}, {13,14}, {6,7}, {2,4}, {4,6}, {5,9}, {8,10}, {4,12}, {5,7}, {3,4}, {1,15}, {2,7}, {3,11}, {3,7}, {11,12}, {9,10}, {2,3}, {10,11}, {7,15}, {8,13}, {10,14}, {5,6}, {2,15}, {3,14}, {8,12}, {12,14}, {1,3}, {4,5}, {12,13}, {1,5}, {4,15}, {9,13}, {11,13}, {13,15}, {9,14}, {3,13}, {1,8}, {5,13}, {2,9}, {6,11}, {1,9}, {2,13}, {4,14}, {7,14}, {14,15}, {1,11}, {6,13}, {6,8}, {3,10} }; // ET15.20 // Bipartite(4,11) Valencies [11,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 958003200 EdgePairs[15][20]:={ {2,11}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {1,6}, {3,5}, {2,6}, {4,7}, {1,12}, {3,8}, {3,9}, {2,12}, {4,6}, {4,12}, {1,7}, {1,15}, {2,7}, {3,11}, {3,7}, {3,15}, {2,15}, {3,14}, {2,5}, {4,5}, {1,5}, {4,15}, {3,6}, {3,13}, {1,8}, {1,13}, {2,9}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {3,10} }; // ET15.21 // Bipartite(3,12) Valencies [12,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2874009600 EdgePairs[15][21]:={ {3,4}, {1,5}, {1,4}, {1,7}, {3,15}, {1,12}, {3,10}, {1,13}, {1,10}, {2,13}, {1,15}, {2,11}, {3,7}, {3,11}, {2,14}, {2,10}, {3,5}, {2,4}, {2,15}, {1,11}, {1,6}, {3,14}, {1,14}, {2,5}, {3,9}, {3,6}, {2,7}, {1,8}, {2,9}, {1,9}, {3,12}, {2,8}, {2,6}, {2,12}, {3,8}, {3,13} }; // ET15.22 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 933120 EdgePairs[15][22]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {1,14}, {11,15}, {3,12}, {7,9}, {2,10}, {8,9}, {7,12}, {1,10}, {1,2}, {6,14}, {8,11}, {4,11}, {4,10}, {7,8}, {8,15}, {3,5}, {6,12}, {7,13}, {2,6}, {1,4}, {5,11}, {6,10}, {9,15}, {4,7}, {1,12}, {3,8}, {9,11}, {10,12}, {3,9}, {2,12}, {6,7}, {6,15}, {5,8}, {4,6}, {5,9}, {8,10}, {4,12}, {5,7}, {10,13}, {1,7}, {3,4}, {1,15}, {2,7}, {7,10}, {3,15}, {11,12}, {9,10}, {9,12}, {2,3}, {10,11}, {7,15}, {8,13}, {10,14}, {5,6}, {2,15}, {3,14}, {8,12}, {2,5}, {1,3}, {4,5}, {1,5}, {4,15}, {9,13}, {11,13}, {3,6}, {13,15}, {5,14}, {9,14}, {3,13}, {1,13}, {8,14}, {5,13}, {6,11}, {1,9}, {2,13}, {2,8}, {4,14}, {12,15}, {7,14}, {14,15}, {1,11}, {11,14}, {6,13}, {3,10}, {6,9} }; // ET15.23 // Bipartite(2,13) Valencies [13,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12454041600 EdgePairs[15][23]:={ {1,13}, {1,14}, {2,3}, {2,6}, {2,14}, {1,3}, {1,4}, {1,9}, {1,8}, {2,5}, {1,15}, {1,5}, {2,7}, {1,10}, {2,10}, {1,6}, {2,12}, {2,13}, {1,11}, {2,15}, {2,4}, {1,12}, {1,7}, {2,11}, {2,8}, {2,9} }; // ET15.24 // Bipartite(1,14) Valencies [14,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 87178291200 EdgePairs[15][24]:={ {1,3}, {1,8}, {1,5}, {1,11}, {1,14}, {1,15}, {1,7}, {1,9}, {1,6}, {1,4}, {1,10}, {1,2}, {1,13}, {1,12} }; // ET15.25 // Non-bipartite Valency 14 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 1307674368000 EdgePairs[15][25]:={ {1,15}, {9,13}, {13,14}, {6,12}, {11,15}, {5,14}, {3,15}, {6,10}, {4,14}, {1,11}, {6,14}, {4,8}, {3,7}, {2,11}, {2,3}, {9,12}, {6,13}, {12,15}, {12,14}, {1,9}, {4,5}, {1,5}, {6,7}, {5,7}, {7,15}, {4,6}, {5,13}, {3,10}, {9,10}, {2,15}, {6,9}, {8,14}, {8,13}, {7,11}, {5,9}, {1,2}, {4,12}, {5,6}, {8,15}, {7,10}, {2,14}, {3,11}, {1,3}, {2,10}, {6,11}, {1,10}, {4,7}, {3,13}, {10,12}, {10,13}, {8,10}, {3,14}, {2,13}, {10,15}, {1,12}, {3,9}, {5,15}, {6,8}, {7,13}, {7,14}, {6,15}, {8,11}, {4,15}, {2,9}, {3,5}, {9,15}, {1,4}, {11,14}, {2,4}, {11,13}, {4,11}, {7,8}, {3,4}, {11,12}, {1,7}, {5,8}, {8,9}, {2,12}, {10,14}, {3,12}, {2,6}, {1,14}, {7,9}, {2,8}, {14,15}, {9,11}, {5,11}, {1,13}, {5,10}, {3,8}, {13,15}, {5,12}, {9,14}, {3,6}, {4,9}, {2,7}, {1,8}, {7,12}, {4,13}, {10,11}, {1,6}, {4,10}, {2,5}, {12,13}, {8,12} }; // Total number of connected ET graphs of order 15 is 25 // ******************************************************************************************** // Order 16 // ET16.1 // Bipartite(8,8) Valencies [2,2] // Diameter 8 Girth 16 // Twin-free VT AT // Automorphism group of order 32 EdgePairs[16][1]:={ {6,14}, {6,11}, {7,15}, {3,10}, {1,9}, {5,13}, {1,16}, {3,12}, {8,16}, {8,15}, {4,12}, {2,9}, {5,11}, {2,10}, {4,13}, {7,14} }; // ET16.2 // Bipartite(8,8) Valencies [3,3] // Diameter 4 Girth 6 // Twin-free VT AT // Automorphism group of order 96 EdgePairs[16][2]:={ {1,13}, {4,14}, {1,14}, {4,11}, {6,13}, {3,9}, {7,11}, {7,12}, {2,14}, {8,12}, {5,16}, {1,9}, {3,15}, {6,16}, {2,10}, {2,12}, {5,11}, {6,15}, {8,16}, {7,13}, {4,15}, {8,9}, {5,10}, {3,10} }; // ET16.3 // Bipartite(8,8) Valencies [4,4] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 384 EdgePairs[16][3]:={ {6,15}, {5,14}, {1,14}, {7,16}, {2,11}, {3,15}, {8,12}, {7,15}, {8,15}, {6,10}, {1,16}, {1,10}, {6,16}, {8,10}, {4,14}, {5,12}, {3,11}, {2,13}, {4,9}, {6,11}, {8,9}, {5,11}, {7,13}, {2,16}, {3,12}, {7,9}, {3,13}, {1,9}, {4,13}, {4,12}, {2,14}, {5,10} }; // ET16.4 // Bipartite(8,8) Valencies [4,4] // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 4096 EdgePairs[16][4]:={ {8,13}, {6,10}, {3,15}, {5,14}, {4,9}, {7,16}, {7,15}, {8,9}, {6,14}, {7,11}, {8,15}, {1,13}, {1,10}, {3,16}, {6,12}, {6,16}, {3,11}, {4,13}, {2,14}, {5,9}, {2,10}, {4,15}, {4,11}, {1,14}, {8,11}, {5,13}, {5,10}, {2,16}, {1,9}, {3,12}, {7,12}, {2,12} }; // ET16.5 // Bipartite(6,10) Valencies [5,3] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 60 EdgePairs[16][5]:={ {6,15}, {5,13}, {4,7}, {1,7}, {3,14}, {2,11}, {4,15}, {6,8}, {4,8}, {1,16}, {1,10}, {6,16}, {5,12}, {5,15}, {2,13}, {6,9}, {6,14}, {4,11}, {3,9}, {1,11}, {5,16}, {2,8}, {3,12}, {1,9}, {3,13}, {2,10}, {3,7}, {4,12}, {2,14}, {5,10} }; // ET16.6 // Non-bipartite Valency 5 // Diameter 2 Girth 4 // Twin-free VT AT // Automorphism group of order 1920 EdgePairs[16][6]:={ {7,10}, {1,3}, {4,6}, {7,14}, {6,15}, {3,10}, {5,13}, {9,16}, {2,11}, {3,14}, {6,8}, {1,15}, {9,11}, {7,15}, {8,16}, {13,15}, {8,10}, {13,16}, {5,12}, {5,8}, {3,11}, {1,12}, {4,9}, {6,14}, {6,11}, {5,7}, {5,11}, {2,16}, {2,15}, {7,9}, {3,13}, {1,9}, {4,13}, {2,12}, {2,10}, {4,10}, {14,16}, {12,14}, {4,12}, {1,8} }; // ET16.7 // Bipartite(4,12) Valencies [6,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10368 EdgePairs[16][7]:={ {1,5}, {4,10}, {3,15}, {1,16}, {1,12}, {1,13}, {3,16}, {4,14}, {2,13}, {3,11}, {3,7}, {2,14}, {2,10}, {4,15}, {4,11}, {2,5}, {4,7}, {1,8}, {2,9}, {4,6}, {3,12}, {1,9}, {2,6}, {3,8} }; // ET16.8 // Bipartite(4,12) Valencies [6,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1536 EdgePairs[16][8]:={ {1,5}, {4,10}, {3,15}, {1,7}, {1,16}, {4,9}, {1,13}, {1,10}, {4,14}, {3,7}, {2,11}, {2,14}, {4,15}, {1,11}, {3,9}, {2,5}, {3,6}, {4,16}, {3,12}, {2,8}, {2,6}, {2,12}, {3,13}, {4,8} }; // ET16.9 // Bipartite(8,8) Valencies [6,6] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 12288 EdgePairs[16][9]:={ {7,10}, {3,16}, {6,13}, {7,14}, {6,15}, {3,10}, {5,13}, {5,14}, {1,14}, {7,16}, {2,11}, {3,14}, {4,15}, {3,15}, {8,11}, {8,12}, {4,16}, {7,15}, {8,16}, {8,15}, {6,10}, {1,16}, {1,10}, {5,12}, {3,11}, {1,12}, {2,13}, {1,13}, {6,9}, {4,9}, {6,14}, {6,11}, {4,11}, {8,9}, {7,11}, {5,16}, {8,13}, {3,12}, {2,15}, {7,12}, {1,9}, {4,13}, {2,10}, {5,9}, {2,9}, {4,12}, {2,14}, {5,10} }; // ET16.10 // Non-bipartite Valency 6 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 192 EdgePairs[16][10]:={ {3,16}, {4,6}, {6,13}, {11,16}, {5,13}, {9,16}, {5,14}, {12,13}, {1,14}, {7,16}, {10,13}, {1,7}, {1,5}, {4,15}, {1,15}, {4,8}, {8,11}, {7,15}, {8,16}, {8,15}, {6,12}, {1,10}, {8,10}, {4,14}, {3,11}, {2,13}, {6,9}, {6,14}, {4,11}, {5,11}, {2,6}, {9,14}, {10,15}, {2,8}, {2,16}, {3,12}, {7,12}, {12,15}, {1,9}, {3,13}, {7,9}, {2,10}, {3,5}, {2,9}, {3,7}, {11,14}, {4,12}, {5,10} }; // ET16.11 // Non-bipartite Valency 6 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1152 EdgePairs[16][11]:={ {3,16}, {4,6}, {6,13}, {7,14}, {6,15}, {3,10}, {9,16}, {5,14}, {12,13}, {4,5}, {1,14}, {10,16}, {7,16}, {1,7}, {2,11}, {9,15}, {11,13}, {4,15}, {1,15}, {3,6}, {8,11}, {8,15}, {6,12}, {1,10}, {8,10}, {4,14}, {2,7}, {1,12}, {6,9}, {2,13}, {4,9}, {4,11}, {5,11}, {5,16}, {8,13}, {10,15}, {2,8}, {2,16}, {3,12}, {7,12}, {7,9}, {3,13}, {3,5}, {2,9}, {11,14}, {12,14}, {5,10}, {1,8} }; // ET16.12 // Bipartite(8,8) Valencies [7,7] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 80640 EdgePairs[16][12]:={ {5,12}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {3,12}, {7,9}, {2,10}, {7,12}, {8,16}, {8,11}, {6,14}, {4,11}, {4,10}, {5,10}, {8,15}, {6,12}, {7,13}, {6,10}, {5,11}, {5,15}, {1,12}, {4,16}, {3,9}, {2,12}, {5,9}, {5,16}, {6,16}, {8,10}, {2,16}, {7,10}, {1,15}, {3,11}, {3,16}, {1,16}, {3,15}, {7,15}, {8,13}, {2,15}, {3,14}, {8,12}, {4,15}, {1,13}, {8,14}, {5,13}, {2,9}, {6,11}, {1,9}, {2,13}, {4,14}, {7,14}, {1,11}, {6,13}, {3,10}, {6,9} }; // ET16.13 // Bipartite(8,8) Valencies [8,8] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 3251404800 EdgePairs[16][13]:={ {2,11}, {5,12}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {7,16}, {3,12}, {7,9}, {2,10}, {8,9}, {7,12}, {8,16}, {1,10}, {6,14}, {8,11}, {4,11}, {4,10}, {5,10}, {8,15}, {6,12}, {7,13}, {6,10}, {5,11}, {5,15}, {1,12}, {4,16}, {3,9}, {2,12}, {6,15}, {5,9}, {5,16}, {6,16}, {8,10}, {4,12}, {2,16}, {1,15}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {7,15}, {8,13}, {2,15}, {3,14}, {8,12}, {4,15}, {5,14}, {3,13}, {1,13}, {8,14}, {5,13}, {2,9}, {6,11}, {1,9}, {2,13}, {4,14}, {7,14}, {1,11}, {6,13}, {3,10}, {6,9} }; // ET16.14 // Bipartite(4,12) Valencies [9,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31104 EdgePairs[16][14]:={ {3,16}, {3,10}, {4,5}, {1,14}, {4,7}, {2,11}, {3,8}, {3,14}, {1,5}, {4,15}, {3,6}, {3,15}, {4,8}, {4,16}, {1,16}, {1,10}, {3,11}, {2,7}, {1,12}, {2,13}, {1,13}, {4,9}, {4,11}, {2,6}, {3,12}, {2,15}, {1,9}, {2,5}, {4,13}, {2,10}, {2,9}, {3,7}, {4,12}, {2,14}, {1,8}, {1,6} }; // ET16.15 // Bipartite(7,9) Valencies [9,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1828915200 EdgePairs[16][15]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {7,16}, {3,12}, {7,9}, {2,10}, {7,12}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {7,8}, {6,12}, {7,13}, {5,11}, {6,10}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,15}, {5,8}, {5,9}, {5,16}, {6,16}, {4,12}, {2,16}, {1,15}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {7,15}, {2,15}, {3,14}, {4,15}, {5,14}, {3,13}, {1,8}, {1,13}, {2,9}, {5,13}, {6,11}, {1,9}, {2,13}, {4,14}, {2,8}, {7,14}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET16.16 // Non-bipartite Valency 9 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1152 EdgePairs[16][16]:={ {2,11}, {5,12}, {4,13}, {4,9}, {10,15}, {11,16}, {1,14}, {7,16}, {3,12}, {7,9}, {8,9}, {9,16}, {7,12}, {1,10}, {8,11}, {4,11}, {4,10}, {5,10}, {1,6}, {8,15}, {3,5}, {6,12}, {7,13}, {5,11}, {9,15}, {4,7}, {1,12}, {5,15}, {3,8}, {3,9}, {2,12}, {6,15}, {4,6}, {5,16}, {6,16}, {8,10}, {10,13}, {2,16}, {1,7}, {10,16}, {1,15}, {2,7}, {7,10}, {3,16}, {1,16}, {8,13}, {2,15}, {3,14}, {12,14}, {2,5}, {4,5}, {12,13}, {4,15}, {11,13}, {3,6}, {5,14}, {9,14}, {3,13}, {1,8}, {8,14}, {2,9}, {6,11}, {2,13}, {4,14}, {2,8}, {12,15}, {7,14}, {1,11}, {11,14}, {6,13}, {3,10}, {6,9} }; // ET16.17 // Bipartite(6,10) Valencies [10,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2612736000 EdgePairs[16][17]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {6,12}, {5,11}, {6,10}, {4,7}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {5,8}, {5,9}, {5,16}, {6,16}, {4,12}, {5,7}, {2,16}, {1,7}, {1,15}, {2,7}, {3,11}, {3,16}, {3,7}, {1,16}, {3,15}, {2,15}, {3,14}, {4,15}, {5,14}, {3,13}, {1,8}, {1,13}, {2,9}, {5,13}, {6,11}, {1,9}, {2,13}, {4,14}, {2,8}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET16.18 // Non-bipartite Valency 10 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1920 EdgePairs[16][18]:={ {2,11}, {5,12}, {4,13}, {4,9}, {11,16}, {11,15}, {7,9}, {2,10}, {9,16}, {7,12}, {13,16}, {8,16}, {1,10}, {1,2}, {6,14}, {8,11}, {4,10}, {3,5}, {6,12}, {7,13}, {2,6}, {5,11}, {9,15}, {4,7}, {5,15}, {1,12}, {3,8}, {9,11}, {4,16}, {10,12}, {3,9}, {2,12}, {13,14}, {2,4}, {6,15}, {5,8}, {4,6}, {6,16}, {8,10}, {4,12}, {5,7}, {2,16}, {1,7}, {10,16}, {1,15}, {7,10}, {3,11}, {3,16}, {3,7}, {9,10}, {7,15}, {10,14}, {5,6}, {2,15}, {3,14}, {8,12}, {12,14}, {1,3}, {1,5}, {4,15}, {9,13}, {11,13}, {13,15}, {5,14}, {3,13}, {1,8}, {8,14}, {5,13}, {2,9}, {6,11}, {1,9}, {4,14}, {2,8}, {12,15}, {7,14}, {1,11}, {14,16}, {6,13}, {6,8}, {3,10} }; // ET16.19 // Bipartite(5,11) Valencies [11,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4790016000 EdgePairs[16][19]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {5,10}, {1,6}, {2,6}, {5,11}, {4,7}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {5,8}, {4,6}, {5,9}, {5,16}, {4,12}, {5,7}, {2,16}, {1,7}, {1,15}, {2,7}, {3,11}, {3,16}, {3,7}, {1,16}, {3,15}, {5,6}, {2,15}, {3,14}, {4,15}, {3,6}, {5,14}, {3,13}, {1,8}, {1,13}, {2,9}, {5,13}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {3,10} }; // ET16.20 // Bipartite(4,12) Valencies [12,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 11496038400 EdgePairs[16][20]:={ {2,11}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {1,6}, {3,5}, {2,6}, {4,7}, {1,12}, {3,8}, {4,16}, {3,9}, {2,12}, {4,6}, {4,12}, {2,16}, {1,7}, {1,15}, {2,7}, {3,11}, {3,16}, {3,7}, {1,16}, {3,15}, {2,15}, {3,14}, {2,5}, {4,5}, {1,5}, {4,15}, {3,6}, {3,13}, {1,8}, {1,13}, {2,9}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {3,10} }; // ET16.21 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 7962624 EdgePairs[16][21]:={ {1,15}, {9,13}, {11,15}, {6,12}, {5,14}, {3,15}, {6,10}, {4,14}, {1,11}, {6,14}, {4,8}, {3,7}, {12,16}, {2,11}, {4,16}, {6,13}, {12,15}, {12,14}, {1,9}, {4,5}, {1,5}, {11,16}, {7,15}, {4,6}, {5,13}, {3,10}, {2,15}, {6,9}, {8,14}, {8,13}, {7,11}, {5,9}, {4,12}, {8,15}, {7,10}, {2,14}, {3,11}, {2,10}, {6,11}, {1,10}, {4,7}, {3,13}, {2,16}, {1,16}, {10,13}, {8,10}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {3,9}, {5,15}, {7,13}, {7,14}, {6,15}, {8,11}, {4,15}, {2,9}, {3,5}, {9,15}, {11,14}, {11,13}, {4,11}, {1,7}, {8,9}, {2,12}, {10,14}, {8,16}, {3,12}, {7,16}, {6,16}, {2,6}, {1,14}, {7,9}, {2,8}, {5,11}, {3,16}, {1,13}, {5,10}, {3,8}, {5,12}, {9,14}, {3,6}, {4,9}, {2,7}, {9,16}, {1,8}, {7,12}, {5,16}, {4,13}, {1,6}, {4,10}, {2,5}, {12,13}, {8,12} }; // ET16.22 // Bipartite(3,13) Valencies [13,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 37362124800 EdgePairs[16][22]:={ {2,11}, {2,14}, {1,14}, {3,12}, {2,10}, {1,10}, {1,6}, {3,5}, {2,6}, {1,4}, {1,12}, {3,8}, {3,9}, {2,12}, {2,4}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {3,16}, {3,15}, {2,15}, {3,14}, {2,5}, {1,5}, {3,6}, {3,13}, {1,8}, {1,13}, {2,9}, {1,9}, {2,13}, {2,8}, {1,11}, {3,10} }; // ET16.23 // Bipartite(2,14) Valencies [14,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 174356582400 EdgePairs[16][23]:={ {1,13}, {1,16}, {1,14}, {2,3}, {2,6}, {2,14}, {1,3}, {1,4}, {1,9}, {1,8}, {2,5}, {1,15}, {1,5}, {2,7}, {1,10}, {2,10}, {1,6}, {2,12}, {2,13}, {1,11}, {2,15}, {2,16}, {2,4}, {1,12}, {1,7}, {2,11}, {2,8}, {2,9} }; // ET16.24 // Non-bipartite Valency 14 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 10321920 EdgePairs[16][24]:={ {1,15}, {9,13}, {6,12}, {11,15}, {5,14}, {3,15}, {6,10}, {4,14}, {1,11}, {6,14}, {4,8}, {3,7}, {12,16}, {2,11}, {2,3}, {4,16}, {6,13}, {9,12}, {12,15}, {12,14}, {1,9}, {4,5}, {1,5}, {6,7}, {11,16}, {5,7}, {7,15}, {4,6}, {5,13}, {3,10}, {2,15}, {6,9}, {8,14}, {8,13}, {7,11}, {5,9}, {4,12}, {8,15}, {13,16}, {7,10}, {2,14}, {3,11}, {1,3}, {2,10}, {6,11}, {1,10}, {4,7}, {14,16}, {3,13}, {10,12}, {2,16}, {1,16}, {10,13}, {8,10}, {3,14}, {2,13}, {10,15}, {1,12}, {3,9}, {10,16}, {5,15}, {6,8}, {7,13}, {7,14}, {6,15}, {8,11}, {4,15}, {2,9}, {3,5}, {9,15}, {1,4}, {11,14}, {2,4}, {11,13}, {4,11}, {1,7}, {5,8}, {8,9}, {2,12}, {10,14}, {8,16}, {3,12}, {7,16}, {6,16}, {2,6}, {1,14}, {7,9}, {2,8}, {14,15}, {9,11}, {5,11}, {3,16}, {1,13}, {5,10}, {3,8}, {13,15}, {5,12}, {9,14}, {3,6}, {4,9}, {2,7}, {9,16}, {1,8}, {7,12}, {5,16}, {4,13}, {10,11}, {1,6}, {4,10}, {2,5}, {12,13}, {8,12} }; // ET16.25 // Bipartite(1,15) Valencies [15,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 1307674368000 EdgePairs[16][25]:={ {1,3}, {1,8}, {1,5}, {1,11}, {1,14}, {1,15}, {1,7}, {1,9}, {1,6}, {1,4}, {1,10}, {1,2}, {1,16}, {1,13}, {1,12} }; // ET16.26 // Non-bipartite Valency 15 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 20922789888000 EdgePairs[16][26]:={ {1,15}, {9,13}, {13,14}, {6,12}, {11,15}, {5,14}, {3,15}, {6,10}, {4,14}, {1,11}, {6,14}, {4,8}, {3,7}, {12,16}, {2,11}, {2,3}, {4,16}, {6,13}, {9,12}, {12,15}, {12,14}, {1,9}, {4,5}, {1,5}, {6,7}, {11,16}, {5,7}, {7,15}, {4,6}, {5,13}, {3,10}, {9,10}, {2,15}, {6,9}, {8,14}, {8,13}, {7,11}, {5,9}, {1,2}, {4,12}, {5,6}, {8,15}, {13,16}, {7,10}, {2,14}, {3,11}, {1,3}, {2,10}, {6,11}, {1,10}, {4,7}, {14,16}, {3,13}, {2,16}, {10,12}, {1,16}, {10,13}, {8,10}, {3,14}, {2,13}, {10,15}, {1,12}, {3,9}, {10,16}, {5,15}, {6,8}, {7,13}, {7,14}, {6,15}, {8,11}, {4,15}, {2,9}, {3,5}, {1,4}, {9,15}, {11,14}, {2,4}, {11,13}, {4,11}, {7,8}, {3,4}, {11,12}, {1,7}, {5,8}, {8,9}, {2,12}, {10,14}, {8,16}, {3,12}, {15,16}, {7,16}, {6,16}, {2,6}, {1,14}, {7,9}, {2,8}, {14,15}, {9,11}, {5,11}, {3,16}, {1,13}, {5,10}, {3,8}, {13,15}, {5,12}, {3,6}, {9,14}, {4,9}, {2,7}, {9,16}, {1,8}, {7,12}, {5,16}, {4,13}, {10,11}, {1,6}, {4,10}, {2,5}, {12,13}, {8,12} }; // Total number of connected ET graphs of order 16 is 26 // ******************************************************************************************** // Order 17 // ET17.1 // Non-bipartite Valency 2 // Diameter 8 Girth 17 // Twin-free VT AT // Automorphism group of order 34 EdgePairs[17][1]:={ {2,8}, {8,14}, {6,12}, {1,7}, {11,17}, {3,9}, {5,16}, {10,16}, {2,13}, {4,15}, {6,17}, {3,14}, {5,11}, {1,12}, {7,13}, {4,10}, {9,15} }; // ET17.2 // Non-bipartite Valency 4 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 68 EdgePairs[17][2]:={ {11,17}, {7,14}, {6,13}, {3,10}, {9,16}, {10,16}, {1,7}, {3,14}, {9,15}, {4,15}, {7,17}, {8,15}, {6,12}, {6,16}, {4,14}, {8,14}, {5,12}, {5,15}, {1,12}, {2,13}, {6,17}, {4,11}, {3,9}, {1,11}, {5,11}, {5,16}, {7,13}, {2,8}, {3,13}, {2,12}, {10,17}, {4,10}, {2,9}, {1,8} }; // ET17.3 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 136 EdgePairs[17][3]:={ {5,12}, {2,14}, {4,9}, {10,15}, {11,16}, {11,17}, {9,16}, {7,12}, {13,16}, {8,11}, {4,11}, {4,10}, {5,10}, {1,6}, {8,15}, {6,12}, {7,13}, {1,4}, {5,11}, {9,15}, {4,7}, {5,15}, {1,12}, {3,8}, {4,16}, {3,9}, {2,12}, {5,8}, {5,16}, {6,16}, {10,13}, {2,16}, {1,7}, {10,16}, {7,10}, {2,7}, {1,15}, {3,15}, {3,17}, {9,12}, {5,17}, {8,13}, {3,14}, {2,5}, {4,15}, {3,6}, {10,17}, {9,14}, {3,13}, {6,17}, {1,8}, {1,13}, {8,14}, {2,9}, {7,17}, {6,11}, {2,13}, {4,14}, {2,8}, {12,15}, {7,14}, {12,17}, {1,11}, {11,14}, {14,17}, {6,13}, {3,10}, {6,9} }; // ET17.4 // Bipartite(8,9) Valencies [9,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14631321600 EdgePairs[17][4]:={ {2,11}, {5,12}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {7,16}, {3,12}, {7,9}, {2,10}, {8,9}, {7,12}, {8,16}, {1,10}, {6,14}, {8,11}, {4,11}, {4,10}, {5,10}, {8,15}, {6,12}, {7,13}, {5,11}, {6,10}, {1,12}, {5,15}, {4,16}, {3,9}, {2,12}, {6,15}, {5,9}, {5,16}, {6,16}, {8,10}, {4,12}, {2,16}, {1,15}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {3,17}, {5,17}, {7,15}, {8,13}, {2,15}, {3,14}, {8,12}, {4,17}, {4,15}, {1,17}, {5,14}, {2,17}, {3,13}, {6,17}, {1,13}, {8,14}, {5,13}, {2,9}, {7,17}, {6,11}, {1,9}, {2,13}, {4,14}, {7,14}, {1,11}, {8,17}, {6,13}, {3,10}, {6,9} }; // ET17.5 // Bipartite(7,10) Valencies [10,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 18289152000 EdgePairs[17][5]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {7,16}, {3,12}, {7,9}, {2,10}, {7,12}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {7,8}, {6,12}, {7,13}, {5,11}, {6,10}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,15}, {5,8}, {5,9}, {5,16}, {6,16}, {4,12}, {2,16}, {1,15}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {3,17}, {5,17}, {7,15}, {2,15}, {3,14}, {4,17}, {4,15}, {1,17}, {5,14}, {2,17}, {3,13}, {6,17}, {1,8}, {1,13}, {2,9}, {5,13}, {7,17}, {6,11}, {1,9}, {2,13}, {4,14}, {2,8}, {7,14}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET17.6 // Bipartite(6,11) Valencies [11,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 28740096000 EdgePairs[17][6]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {6,12}, {5,11}, {6,10}, {4,7}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {5,8}, {5,9}, {5,16}, {6,16}, {4,12}, {5,7}, {2,16}, {1,7}, {1,15}, {2,7}, {3,11}, {3,16}, {3,7}, {1,16}, {3,15}, {3,17}, {5,17}, {2,15}, {3,14}, {4,17}, {4,15}, {1,17}, {5,14}, {2,17}, {3,13}, {6,17}, {1,8}, {1,13}, {2,9}, {5,13}, {6,11}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET17.7 // Bipartite(5,12) Valencies [12,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 57480192000 EdgePairs[17][7]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {5,10}, {1,6}, {2,6}, {5,11}, {4,7}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {5,8}, {4,6}, {5,9}, {5,16}, {4,12}, {5,7}, {2,16}, {1,7}, {1,15}, {2,7}, {3,11}, {3,16}, {3,7}, {1,16}, {3,15}, {3,17}, {5,17}, {5,6}, {2,15}, {3,14}, {4,17}, {4,15}, {1,17}, {3,6}, {5,14}, {2,17}, {3,13}, {1,8}, {1,13}, {2,9}, {5,13}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {3,10} }; // ET17.8 // Bipartite(4,13) Valencies [13,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 149448499200 EdgePairs[17][8]:={ {2,11}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {1,6}, {3,5}, {2,6}, {4,7}, {1,12}, {3,8}, {4,16}, {3,9}, {2,12}, {4,6}, {4,12}, {2,16}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {3,16}, {3,15}, {3,17}, {2,15}, {3,14}, {2,5}, {4,5}, {4,17}, {1,5}, {4,15}, {1,17}, {3,6}, {2,17}, {3,13}, {1,8}, {1,13}, {2,9}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {3,10} }; // ET17.9 // Bipartite(3,14) Valencies [14,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 523069747200 EdgePairs[17][9]:={ {2,11}, {2,14}, {1,14}, {3,12}, {2,10}, {1,10}, {1,6}, {3,5}, {2,6}, {1,4}, {1,12}, {3,8}, {3,9}, {2,12}, {2,4}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {3,16}, {3,15}, {3,17}, {2,15}, {3,14}, {2,5}, {1,5}, {1,17}, {3,6}, {2,17}, {3,13}, {1,8}, {1,13}, {2,9}, {1,9}, {2,13}, {2,8}, {1,11}, {3,10} }; // ET17.10 // Bipartite(2,15) Valencies [15,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2615348736000 EdgePairs[17][10]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,12}, {1,3}, {1,17}, {1,13}, {1,10}, {2,13}, {1,15}, {2,11}, {2,14}, {2,10}, {1,11}, {2,4}, {2,15}, {1,6}, {1,14}, {2,5}, {2,17}, {2,16}, {2,7}, {1,8}, {2,3}, {2,9}, {1,9}, {2,8}, {2,6}, {2,12} }; // ET17.11 // Bipartite(1,16) Valencies [16,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 20922789888000 EdgePairs[17][11]:={ {1,3}, {1,8}, {1,5}, {1,11}, {1,14}, {1,15}, {1,7}, {1,9}, {1,6}, {1,4}, {1,10}, {1,2}, {1,16}, {1,13}, {1,17}, {1,12} }; // ET17.12 // Non-bipartite Valency 16 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 355687428096000 EdgePairs[17][12]:={ {11,17}, {1,11}, {5,17}, {6,16}, {7,15}, {8,12}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {8,9}, {3,9}, {3,6}, {3,13}, {3,15}, {2,15}, {7,8}, {2,4}, {2,9}, {11,14}, {8,10}, {6,7}, {11,12}, {2,14}, {8,15}, {6,11}, {3,5}, {13,16}, {9,11}, {10,15}, {15,16}, {3,17}, {3,7}, {8,16}, {7,12}, {4,10}, {1,17}, {1,7}, {7,11}, {3,14}, {12,17}, {4,8}, {1,5}, {5,11}, {2,5}, {2,10}, {8,14}, {6,8}, {11,15}, {11,13}, {3,12}, {7,13}, {9,14}, {6,12}, {12,13}, {12,16}, {1,2}, {2,13}, {14,16}, {8,17}, {2,16}, {7,16}, {1,12}, {3,4}, {14,15}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {1,9}, {9,10}, {5,14}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {4,9}, {12,14}, {2,7}, {9,12}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {2,11}, {10,11}, {4,5}, {16,17}, {3,16}, {11,16}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {7,9}, {13,14}, {6,10}, {5,10}, {5,9}, {1,4}, {4,11}, {1,8}, {4,12}, {5,13}, {7,10}, {5,6}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {10,14}, {9,15}, {13,17}, {6,13}, {4,17}, {9,16}, {10,16}, {5,16} }; // Total number of connected ET graphs of order 17 is 12 // ******************************************************************************************** // Order 18 // ET18.1 // Bipartite(9,9) Valencies [2,2] // Diameter 9 Girth 18 // Twin-free VT AT // Automorphism group of order 36 EdgePairs[18][1]:={ {4,14}, {6,18}, {8,10}, {9,11}, {2,14}, {4,18}, {5,16}, {9,13}, {8,15}, {1,10}, {5,17}, {3,12}, {6,15}, {3,16}, {1,12}, {7,17}, {7,13}, {2,11} }; // ET18.2 // Bipartite(9,9) Valencies [3,3] // Diameter 4 Girth 6 // Twin-free VT AT // Automorphism group of order 216 EdgePairs[18][2]:={ {5,12}, {4,10}, {5,11}, {6,17}, {1,16}, {1,12}, {9,13}, {8,15}, {9,15}, {1,10}, {5,18}, {3,16}, {6,12}, {2,11}, {2,14}, {4,15}, {3,14}, {8,11}, {7,10}, {2,17}, {8,16}, {4,17}, {7,14}, {9,18}, {7,18}, {3,13}, {6,13} }; // ET18.3 // Bipartite(6,12) Valencies [4,2] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 48 EdgePairs[18][3]:={ {5,12}, {6,10}, {4,10}, {1,7}, {6,14}, {1,17}, {1,13}, {5,18}, {3,16}, {3,11}, {2,14}, {4,11}, {4,18}, {6,15}, {5,7}, {5,15}, {3,9}, {2,17}, {2,16}, {1,9}, {3,12}, {2,8}, {4,8}, {6,13} }; // ET18.4 // Bipartite(6,12) Valencies [4,2] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 768 EdgePairs[18][4]:={ {5,12}, {4,10}, {5,11}, {3,15}, {1,7}, {5,17}, {6,7}, {3,10}, {1,13}, {6,18}, {5,18}, {3,16}, {6,12}, {2,14}, {2,15}, {4,11}, {1,14}, {3,9}, {4,16}, {1,8}, {4,17}, {2,9}, {2,8}, {6,13} }; // ET18.5 // Bipartite(9,9) Valencies [4,4] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 144 EdgePairs[18][5]:={ {7,10}, {3,16}, {6,13}, {9,16}, {5,14}, {2,11}, {3,14}, {4,15}, {3,18}, {8,11}, {9,11}, {7,15}, {4,16}, {8,15}, {6,18}, {4,18}, {9,13}, {1,16}, {1,10}, {8,10}, {5,12}, {5,15}, {3,17}, {1,12}, {1,13}, {6,17}, {6,11}, {7,18}, {8,17}, {5,17}, {9,14}, {7,13}, {2,10}, {2,12}, {4,12}, {2,14} }; // ET18.6 // Non-bipartite Valency 4 // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 9216 EdgePairs[18][6]:={ {6,15}, {3,10}, {12,13}, {2,17}, {7,16}, {1,7}, {3,14}, {11,13}, {7,15}, {8,16}, {8,15}, {6,12}, {6,16}, {4,14}, {5,12}, {5,15}, {2,7}, {1,17}, {4,9}, {2,18}, {6,11}, {3,9}, {5,11}, {5,16}, {1,18}, {2,8}, {3,13}, {4,13}, {9,18}, {10,17}, {4,10}, {9,17}, {10,18}, {11,14}, {12,14}, {1,8} }; // ET18.7 // Bipartite(6,12) Valencies [6,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31104 EdgePairs[18][7]:={ {6,7}, {6,15}, {5,13}, {5,14}, {5,18}, {2,17}, {1,7}, {1,15}, {3,15}, {4,8}, {4,16}, {6,18}, {4,18}, {6,10}, {1,16}, {4,14}, {3,17}, {3,11}, {1,12}, {2,13}, {6,14}, {6,11}, {3,9}, {1,11}, {5,17}, {2,8}, {2,16}, {3,13}, {2,12}, {4,10}, {5,9}, {2,9}, {3,7}, {4,12}, {5,10}, {1,8} }; // ET18.8 // Bipartite(9,9) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 216 EdgePairs[18][8]:={ {2,11}, {5,12}, {2,14}, {4,13}, {7,11}, {7,16}, {2,10}, {8,16}, {8,11}, {6,14}, {1,10}, {4,11}, {5,10}, {8,15}, {6,12}, {6,10}, {9,15}, {5,15}, {1,12}, {9,11}, {4,16}, {5,16}, {4,12}, {4,18}, {2,16}, {7,10}, {1,15}, {3,11}, {1,16}, {3,15}, {7,18}, {3,17}, {9,12}, {7,15}, {5,17}, {8,13}, {8,12}, {3,18}, {1,18}, {6,18}, {9,18}, {5,14}, {2,17}, {9,14}, {3,13}, {6,17}, {1,13}, {2,13}, {4,14}, {7,14}, {8,17}, {6,13}, {9,17}, {3,10} }; // ET18.9 // Bipartite(9,9) Valencies [6,6] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 559872 EdgePairs[18][9]:={ {2,11}, {2,14}, {4,13}, {7,16}, {3,12}, {2,10}, {7,12}, {8,16}, {8,11}, {6,14}, {1,10}, {4,10}, {5,10}, {6,12}, {7,13}, {5,11}, {9,15}, {1,12}, {9,11}, {4,16}, {6,15}, {5,16}, {8,10}, {4,12}, {4,18}, {2,16}, {7,10}, {1,15}, {3,11}, {1,16}, {3,15}, {7,18}, {3,17}, {9,12}, {7,15}, {5,17}, {8,13}, {3,14}, {3,18}, {1,18}, {4,15}, {6,18}, {9,18}, {5,14}, {2,17}, {9,14}, {6,17}, {1,13}, {8,14}, {5,13}, {6,11}, {2,13}, {8,17}, {9,17} }; // ET18.10 // Bipartite(6,12) Valencies [8,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 663552 EdgePairs[18][10]:={ {6,7}, {3,16}, {6,13}, {6,15}, {3,10}, {4,17}, {5,14}, {1,14}, {4,7}, {5,18}, {2,17}, {1,7}, {2,11}, {3,18}, {3,15}, {4,8}, {4,16}, {6,18}, {6,12}, {6,10}, {1,16}, {1,10}, {6,16}, {4,14}, {5,8}, {5,12}, {5,15}, {1,17}, {1,13}, {6,9}, {2,18}, {4,11}, {3,9}, {1,11}, {5,11}, {5,17}, {2,8}, {3,12}, {2,15}, {3,13}, {4,13}, {2,12}, {4,10}, {5,9}, {2,9}, {3,7}, {2,14}, {1,8} }; // ET18.11 // Bipartite(9,9) Valencies [8,8] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 725760 EdgePairs[18][11]:={ {2,11}, {5,12}, {2,14}, {4,13}, {1,14}, {7,11}, {7,16}, {2,10}, {9,16}, {7,12}, {8,16}, {1,10}, {6,14}, {8,11}, {4,11}, {4,10}, {5,10}, {6,12}, {7,13}, {6,10}, {5,11}, {9,15}, {5,15}, {1,12}, {9,11}, {4,16}, {2,12}, {6,15}, {5,16}, {8,10}, {4,12}, {4,18}, {2,16}, {7,10}, {1,15}, {3,11}, {3,16}, {1,16}, {3,15}, {3,17}, {2,18}, {9,12}, {7,15}, {8,13}, {2,15}, {3,14}, {8,12}, {3,18}, {4,17}, {1,18}, {4,15}, {9,13}, {1,17}, {6,18}, {9,18}, {5,14}, {2,17}, {5,18}, {9,14}, {3,13}, {6,17}, {1,13}, {8,14}, {8,18}, {5,13}, {7,17}, {6,11}, {7,14}, {8,17}, {6,13}, {9,17}, {3,10} }; // ET18.12 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 36864 EdgePairs[18][12]:={ {5,12}, {4,13}, {4,9}, {10,15}, {11,16}, {11,15}, {3,12}, {12,18}, {11,17}, {2,10}, {9,16}, {1,10}, {6,14}, {4,11}, {12,16}, {4,10}, {6,12}, {7,13}, {5,11}, {9,15}, {5,15}, {3,9}, {6,7}, {6,15}, {5,8}, {5,16}, {6,16}, {4,12}, {5,7}, {10,13}, {4,18}, {2,16}, {1,7}, {10,16}, {1,15}, {2,7}, {3,11}, {1,16}, {7,18}, {3,17}, {2,18}, {8,13}, {10,14}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {9,13}, {1,17}, {5,14}, {2,17}, {9,14}, {3,13}, {1,8}, {8,14}, {8,18}, {5,13}, {2,9}, {7,17}, {6,11}, {1,9}, {4,14}, {2,8}, {12,15}, {7,14}, {11,18}, {12,17}, {8,17}, {6,13}, {6,8}, {3,10} }; // ET18.13 // Bipartite(9,9) Valencies [9,9] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 263363788800 EdgePairs[18][13]:={ {2,11}, {5,12}, {2,14}, {4,13}, {1,14}, {7,11}, {7,16}, {3,12}, {2,10}, {9,16}, {7,12}, {8,16}, {1,10}, {6,14}, {8,11}, {4,11}, {4,10}, {5,10}, {8,15}, {6,12}, {7,13}, {5,11}, {6,10}, {9,15}, {5,15}, {1,12}, {9,11}, {4,16}, {2,12}, {6,15}, {5,16}, {6,16}, {8,10}, {4,12}, {4,18}, {2,16}, {1,15}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {9,10}, {7,18}, {3,17}, {2,18}, {9,12}, {5,17}, {7,15}, {8,13}, {2,15}, {3,14}, {8,12}, {3,18}, {4,17}, {1,18}, {4,15}, {9,13}, {1,17}, {6,18}, {9,18}, {5,14}, {2,17}, {5,18}, {9,14}, {3,13}, {6,17}, {1,13}, {8,14}, {8,18}, {5,13}, {7,17}, {6,11}, {2,13}, {4,14}, {7,14}, {1,11}, {8,17}, {6,13}, {9,17}, {3,10} }; // ET18.14 // Bipartite(3,15) Valencies [10,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10368000 EdgePairs[18][14]:={ {1,4}, {3,16}, {3,10}, {1,14}, {2,17}, {1,7}, {2,11}, {1,5}, {3,6}, {3,18}, {3,15}, {3,4}, {1,16}, {1,10}, {1,17}, {1,13}, {2,18}, {3,9}, {1,11}, {2,6}, {2,8}, {3,12}, {2,15}, {3,13}, {2,5}, {2,12}, {2,9}, {3,7}, {2,14}, {1,8} }; // ET18.15 // Bipartite(6,12) Valencies [10,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 46080 EdgePairs[18][15]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {3,12}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {6,12}, {5,11}, {6,10}, {4,7}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {5,8}, {5,9}, {5,16}, {6,16}, {2,16}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {3,15}, {3,17}, {2,18}, {5,17}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {6,18}, {5,14}, {2,17}, {5,18}, {3,13}, {1,13}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {6,13}, {6,8}, {6,9} }; // ET18.16 // Bipartite(8,10) Valencies [10,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 146313216000 EdgePairs[18][16]:={ {2,11}, {5,12}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {7,16}, {3,12}, {7,9}, {2,10}, {8,9}, {7,12}, {8,16}, {1,10}, {6,14}, {8,11}, {4,11}, {4,10}, {5,10}, {8,15}, {6,12}, {7,13}, {5,11}, {6,10}, {1,12}, {5,15}, {4,16}, {3,9}, {2,12}, {6,15}, {5,9}, {5,16}, {6,16}, {8,10}, {4,12}, {4,18}, {2,16}, {1,15}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {7,18}, {3,17}, {2,18}, {5,17}, {7,15}, {8,13}, {2,15}, {3,14}, {8,12}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {6,18}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,13}, {8,14}, {8,18}, {2,9}, {5,13}, {7,17}, {6,11}, {1,9}, {2,13}, {4,14}, {7,14}, {1,11}, {8,17}, {6,13}, {3,10}, {6,9} }; // ET18.17 // Non-bipartite Valency 10 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 4320 EdgePairs[18][17]:={ {2,11}, {5,12}, {4,8}, {4,13}, {4,9}, {10,15}, {11,16}, {1,14}, {7,11}, {3,12}, {14,18}, {9,16}, {7,12}, {13,16}, {8,16}, {1,10}, {6,14}, {4,11}, {12,16}, {5,10}, {7,13}, {2,6}, {1,4}, {6,10}, {9,15}, {9,11}, {3,9}, {2,12}, {6,7}, {6,15}, {5,9}, {5,16}, {6,16}, {8,10}, {4,12}, {5,7}, {10,13}, {4,18}, {1,7}, {3,4}, {1,15}, {3,16}, {3,7}, {1,16}, {9,10}, {7,18}, {2,18}, {7,15}, {8,13}, {2,15}, {3,14}, {8,12}, {12,14}, {3,18}, {2,5}, {15,16}, {4,17}, {1,5}, {4,15}, {11,13}, {1,17}, {3,6}, {10,17}, {5,14}, {2,17}, {5,18}, {9,14}, {3,13}, {6,17}, {1,8}, {8,14}, {8,18}, {5,13}, {2,9}, {7,17}, {6,11}, {2,13}, {2,8}, {12,15}, {11,18}, {12,17}, {1,11}, {11,14}, {14,17}, {15,18}, {13,17}, {9,17}, {10,18}, {6,8}, {3,10} }; // ET18.18 // Bipartite(7,11) Valencies [11,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 201180672000 EdgePairs[18][18]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {7,16}, {3,12}, {7,9}, {2,10}, {7,12}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {7,8}, {6,12}, {7,13}, {5,11}, {6,10}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,15}, {5,8}, {5,9}, {5,16}, {6,16}, {4,12}, {2,16}, {4,18}, {1,15}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {7,18}, {3,17}, {2,18}, {5,17}, {7,15}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {6,18}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,8}, {1,13}, {2,9}, {5,13}, {7,17}, {6,11}, {1,9}, {2,13}, {2,8}, {4,14}, {7,14}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET18.19 // Bipartite(6,12) Valencies [12,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 344881152000 EdgePairs[18][19]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {6,12}, {5,11}, {6,10}, {4,7}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {5,8}, {5,9}, {5,16}, {6,16}, {4,12}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {3,16}, {3,7}, {1,16}, {3,15}, {3,17}, {2,18}, {5,17}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {6,18}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,8}, {1,13}, {2,9}, {5,13}, {6,11}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET18.20 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 2239488000 EdgePairs[18][20]:={ {1,15}, {9,13}, {6,12}, {11,15}, {5,14}, {3,15}, {11,17}, {6,10}, {6,18}, {4,14}, {1,11}, {6,14}, {4,8}, {6,17}, {3,7}, {12,16}, {2,11}, {4,16}, {6,13}, {12,15}, {12,17}, {12,14}, {1,9}, {6,7}, {11,16}, {12,18}, {5,7}, {7,15}, {5,13}, {3,10}, {2,18}, {6,9}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {5,9}, {4,12}, {3,18}, {8,15}, {2,14}, {3,11}, {2,10}, {6,11}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,16}, {10,13}, {2,17}, {8,18}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {3,9}, {5,15}, {6,8}, {7,13}, {8,17}, {7,14}, {6,15}, {11,18}, {4,17}, {4,15}, {2,9}, {9,15}, {11,14}, {11,13}, {4,11}, {1,7}, {5,8}, {7,18}, {2,12}, {10,14}, {8,16}, {5,17}, {3,12}, {7,16}, {6,16}, {1,14}, {9,18}, {10,17}, {2,8}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,8}, {5,12}, {9,14}, {3,17}, {4,9}, {2,7}, {5,18}, {9,16}, {7,17}, {1,8}, {5,16}, {4,13}, {1,18}, {4,10}, {12,13} }; // ET18.21 // Bipartite(5,13) Valencies [13,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 747242496000 EdgePairs[18][21]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {5,10}, {1,6}, {2,6}, {5,11}, {4,7}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {5,8}, {4,6}, {5,9}, {5,16}, {4,12}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {3,16}, {3,7}, {1,16}, {3,15}, {3,17}, {2,18}, {5,17}, {5,6}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {3,6}, {5,14}, {2,17}, {5,18}, {3,13}, {1,8}, {1,13}, {2,9}, {5,13}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {3,10} }; // ET18.22 // Bipartite(4,14) Valencies [14,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2092278988800 EdgePairs[18][22]:={ {2,11}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {1,6}, {3,5}, {2,6}, {4,7}, {1,12}, {3,8}, {4,16}, {3,9}, {2,12}, {4,6}, {4,12}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {1,5}, {4,15}, {1,17}, {3,6}, {2,17}, {3,13}, {1,8}, {1,13}, {2,9}, {1,9}, {2,13}, {2,8}, {4,14}, {1,11}, {3,10} }; // ET18.23 // Bipartite(3,15) Valencies [15,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7846046208000 EdgePairs[18][23]:={ {2,11}, {2,14}, {1,14}, {3,12}, {2,10}, {1,10}, {1,6}, {3,5}, {2,6}, {1,4}, {1,12}, {3,8}, {3,9}, {2,12}, {2,4}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {1,5}, {1,17}, {3,6}, {2,17}, {3,13}, {1,8}, {1,13}, {2,9}, {1,9}, {2,13}, {2,8}, {1,11}, {3,10} }; // ET18.24 // Non-bipartite Valency 15 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 33592320 EdgePairs[18][24]:={ {11,17}, {1,11}, {5,17}, {6,16}, {7,15}, {8,12}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {3,9}, {3,6}, {3,13}, {3,15}, {2,15}, {2,4}, {2,9}, {11,14}, {8,10}, {6,7}, {2,14}, {8,15}, {6,11}, {3,5}, {13,16}, {9,11}, {10,15}, {15,16}, {3,18}, {3,17}, {3,7}, {8,16}, {7,12}, {4,10}, {1,17}, {1,7}, {1,18}, {7,11}, {3,14}, {12,17}, {4,8}, {1,5}, {5,11}, {2,5}, {2,10}, {8,14}, {6,8}, {11,15}, {11,13}, {3,12}, {7,13}, {9,14}, {6,12}, {12,13}, {12,16}, {2,13}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {7,16}, {1,12}, {3,4}, {5,18}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {1,9}, {9,10}, {5,14}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {3,10}, {6,15}, {2,17}, {9,13}, {5,12}, {14,17}, {4,9}, {14,18}, {12,14}, {2,7}, {9,12}, {6,9}, {1,15}, {12,15}, {6,14}, {2,11}, {3,16}, {15,18}, {11,16}, {9,18}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {10,18}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {1,4}, {4,11}, {1,8}, {4,12}, {5,13}, {7,10}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {10,14}, {9,15}, {13,17}, {6,13}, {2,18}, {4,17}, {9,16}, {12,18}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET18.25 // Bipartite(2,16) Valencies [16,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 41845579776000 EdgePairs[18][25]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,12}, {1,3}, {1,17}, {1,13}, {1,10}, {2,18}, {2,13}, {1,15}, {2,11}, {2,14}, {2,10}, {1,11}, {2,4}, {2,15}, {1,6}, {1,14}, {2,5}, {1,18}, {2,17}, {2,16}, {2,7}, {1,8}, {2,3}, {2,9}, {1,9}, {2,8}, {2,6}, {2,12} }; // ET18.26 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 185794560 EdgePairs[18][26]:={ {11,17}, {1,11}, {5,17}, {6,16}, {7,15}, {8,12}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {8,9}, {3,9}, {3,6}, {3,13}, {3,15}, {2,15}, {2,4}, {16,18}, {2,9}, {11,14}, {8,10}, {6,7}, {2,14}, {8,15}, {6,11}, {3,5}, {9,11}, {13,16}, {10,15}, {3,18}, {3,17}, {3,7}, {8,16}, {7,12}, {4,10}, {1,17}, {1,7}, {1,18}, {7,11}, {3,14}, {12,17}, {4,8}, {1,5}, {5,11}, {2,5}, {2,10}, {8,14}, {6,8}, {11,15}, {11,13}, {3,12}, {7,13}, {9,14}, {6,12}, {12,13}, {12,16}, {2,13}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {7,16}, {1,12}, {5,18}, {14,15}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {1,9}, {5,14}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {4,9}, {14,18}, {12,14}, {2,7}, {9,12}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {2,11}, {10,11}, {4,5}, {16,17}, {3,16}, {15,18}, {11,16}, {9,18}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {10,18}, {7,9}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {1,4}, {4,11}, {1,8}, {4,12}, {5,13}, {7,10}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {10,14}, {9,15}, {13,17}, {6,13}, {2,18}, {4,17}, {9,16}, {12,18}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET18.27 // Bipartite(1,17) Valencies [17,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 355687428096000 EdgePairs[18][27]:={ {1,3}, {1,8}, {1,5}, {1,11}, {1,14}, {1,15}, {1,7}, {1,9}, {1,6}, {1,4}, {1,10}, {1,2}, {1,16}, {1,13}, {1,17}, {1,18}, {1,12} }; // ET18.28 // Non-bipartite Valency 17 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 6402373705728000 EdgePairs[18][28]:={ {11,17}, {1,11}, {5,17}, {6,16}, {7,15}, {8,12}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {8,9}, {3,9}, {3,6}, {3,13}, {3,15}, {2,15}, {7,8}, {2,4}, {16,18}, {2,9}, {11,14}, {8,10}, {6,7}, {11,12}, {2,14}, {8,15}, {6,11}, {3,5}, {9,11}, {13,16}, {10,15}, {15,16}, {3,18}, {3,17}, {3,7}, {8,16}, {7,12}, {4,10}, {1,17}, {1,7}, {1,18}, {7,11}, {3,14}, {12,17}, {4,8}, {1,5}, {5,11}, {2,5}, {2,10}, {8,14}, {6,8}, {11,15}, {11,13}, {3,12}, {7,13}, {9,14}, {6,12}, {12,13}, {12,16}, {1,2}, {2,13}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {7,16}, {1,12}, {3,4}, {5,18}, {14,15}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {1,9}, {9,10}, {17,18}, {5,14}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {4,9}, {14,18}, {12,14}, {2,7}, {9,12}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {2,11}, {10,11}, {4,5}, {16,17}, {3,16}, {15,18}, {11,16}, {9,18}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {10,18}, {7,9}, {13,14}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {1,4}, {4,11}, {1,8}, {4,12}, {5,13}, {7,10}, {5,6}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {10,14}, {9,15}, {13,17}, {6,13}, {2,18}, {4,17}, {9,16}, {12,18}, {11,18}, {7,18}, {10,16}, {5,16} }; // Total number of connected ET graphs of order 18 is 28 // ******************************************************************************************** // Order 19 // ET19.1 // Non-bipartite Valency 2 // Diameter 9 Girth 19 // Twin-free VT AT // Automorphism group of order 38 EdgePairs[19][1]:={ {2,8}, {8,14}, {6,19}, {1,14}, {6,12}, {1,7}, {11,17}, {3,9}, {2,15}, {10,16}, {5,18}, {13,19}, {12,18}, {4,17}, {3,16}, {5,11}, {7,13}, {4,10}, {9,15} }; // ET19.2 // Non-bipartite Valency 6 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 114 EdgePairs[19][2]:={ {2,11}, {4,8}, {4,13}, {13,19}, {9,19}, {1,14}, {7,11}, {11,15}, {7,16}, {3,12}, {12,18}, {14,18}, {11,17}, {1,10}, {12,16}, {4,10}, {6,12}, {7,13}, {2,6}, {6,10}, {5,11}, {9,15}, {5,15}, {3,9}, {2,12}, {6,15}, {5,9}, {6,16}, {1,7}, {10,16}, {3,16}, {3,7}, {1,16}, {15,19}, {10,14}, {2,15}, {8,12}, {3,18}, {4,17}, {1,5}, {9,13}, {6,19}, {10,19}, {9,18}, {5,14}, {2,17}, {5,18}, {3,13}, {8,18}, {8,14}, {7,17}, {4,14}, {2,8}, {4,19}, {1,11}, {8,17}, {13,17} }; // ET19.3 // Bipartite(9,10) Valencies [10,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1316818944000 EdgePairs[19][3]:={ {2,11}, {5,12}, {2,14}, {4,13}, {8,19}, {9,19}, {1,14}, {7,11}, {7,16}, {3,12}, {2,10}, {9,16}, {7,12}, {8,16}, {1,10}, {6,14}, {8,11}, {4,11}, {4,10}, {5,10}, {8,15}, {6,12}, {7,13}, {5,11}, {6,10}, {9,15}, {1,12}, {5,15}, {9,11}, {4,16}, {2,12}, {6,15}, {5,16}, {6,16}, {8,10}, {4,12}, {4,18}, {2,16}, {1,15}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {9,10}, {7,18}, {3,17}, {5,19}, {2,18}, {9,12}, {3,19}, {5,17}, {7,15}, {8,13}, {2,15}, {3,14}, {8,12}, {3,18}, {4,17}, {1,18}, {4,15}, {9,13}, {1,17}, {7,19}, {6,18}, {6,19}, {2,19}, {9,18}, {5,14}, {2,17}, {5,18}, {9,14}, {3,13}, {6,17}, {1,13}, {8,14}, {8,18}, {5,13}, {1,19}, {7,17}, {6,11}, {2,13}, {4,14}, {4,19}, {7,14}, {1,11}, {8,17}, {6,13}, {9,17}, {3,10} }; // ET19.4 // Bipartite(8,11) Valencies [11,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1609445376000 EdgePairs[19][4]:={ {2,11}, {5,12}, {2,14}, {4,13}, {4,9}, {8,19}, {1,14}, {7,11}, {7,16}, {3,12}, {7,9}, {2,10}, {8,9}, {7,12}, {8,16}, {1,10}, {6,14}, {8,11}, {4,11}, {4,10}, {5,10}, {8,15}, {6,12}, {7,13}, {5,11}, {6,10}, {1,12}, {5,15}, {4,16}, {3,9}, {2,12}, {6,15}, {5,9}, {5,16}, {6,16}, {8,10}, {4,12}, {4,18}, {2,16}, {1,15}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {7,18}, {3,17}, {5,19}, {2,18}, {3,19}, {5,17}, {7,15}, {8,13}, {2,15}, {3,14}, {8,12}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {7,19}, {6,18}, {6,19}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,13}, {8,14}, {8,18}, {1,19}, {2,9}, {5,13}, {7,17}, {6,11}, {1,9}, {2,13}, {4,14}, {4,19}, {7,14}, {1,11}, {8,17}, {6,13}, {3,10}, {6,9} }; // ET19.5 // Bipartite(7,12) Valencies [12,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2414168064000 EdgePairs[19][5]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {7,11}, {7,16}, {3,12}, {7,9}, {2,10}, {7,12}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {7,8}, {6,12}, {7,13}, {5,11}, {6,10}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,15}, {5,8}, {5,9}, {5,16}, {6,16}, {4,12}, {2,16}, {4,18}, {1,15}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {7,18}, {3,17}, {5,19}, {2,18}, {3,19}, {5,17}, {7,15}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {7,19}, {6,18}, {6,19}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {7,17}, {6,11}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {7,14}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET19.6 // Bipartite(6,13) Valencies [13,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4483454976000 EdgePairs[19][6]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {6,12}, {5,11}, {6,10}, {4,7}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {5,8}, {5,9}, {5,16}, {6,16}, {4,12}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {3,16}, {3,7}, {1,16}, {3,15}, {3,17}, {5,19}, {2,18}, {3,19}, {5,17}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {6,18}, {6,19}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {6,11}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET19.7 // Bipartite(5,14) Valencies [14,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10461394944000 EdgePairs[19][7]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {5,10}, {1,6}, {2,6}, {5,11}, {4,7}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {5,8}, {4,6}, {5,9}, {5,16}, {4,12}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {3,16}, {3,15}, {3,17}, {5,19}, {2,18}, {3,19}, {5,17}, {5,6}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {3,6}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {3,10} }; // ET19.8 // Bipartite(4,15) Valencies [15,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31384184832000 EdgePairs[19][8]:={ {2,11}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {1,6}, {3,5}, {2,6}, {4,7}, {1,12}, {3,8}, {4,16}, {3,9}, {2,12}, {4,6}, {4,12}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {1,5}, {4,15}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {3,10} }; // ET19.9 // Bipartite(3,16) Valencies [16,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 125536739328000 EdgePairs[19][9]:={ {2,11}, {2,14}, {1,14}, {3,12}, {2,10}, {1,10}, {1,6}, {3,5}, {2,6}, {1,4}, {1,12}, {3,8}, {3,9}, {2,12}, {2,4}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {1,5}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {2,13}, {2,8}, {1,11}, {3,10} }; // ET19.10 // Bipartite(2,17) Valencies [17,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 711374856192000 EdgePairs[19][10]:={ {1,4}, {1,3}, {1,14}, {2,17}, {1,7}, {2,11}, {2,19}, {1,5}, {1,15}, {1,16}, {1,10}, {2,7}, {1,12}, {2,13}, {1,13}, {1,17}, {2,3}, {2,18}, {2,4}, {1,11}, {1,19}, {1,18}, {2,6}, {2,8}, {2,16}, {2,15}, {1,9}, {2,5}, {2,10}, {2,12}, {2,9}, {2,14}, {1,8}, {1,6} }; // ET19.11 // Bipartite(1,18) Valencies [18,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 6402373705728000 EdgePairs[19][11]:={ {1,3}, {1,8}, {1,5}, {1,11}, {1,19}, {1,14}, {1,15}, {1,7}, {1,9}, {1,6}, {1,4}, {1,10}, {1,2}, {1,16}, {1,13}, {1,17}, {1,18}, {1,12} }; // ET19.12 // Non-bipartite Valency 18 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 121645100408832000 EdgePairs[19][12]:={ {11,17}, {1,11}, {5,17}, {6,16}, {7,15}, {8,12}, {14,19}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {8,9}, {3,9}, {3,6}, {3,13}, {3,15}, {2,15}, {4,19}, {16,19}, {2,19}, {7,8}, {1,19}, {2,4}, {16,18}, {2,9}, {11,14}, {8,10}, {6,7}, {11,12}, {2,14}, {8,15}, {6,11}, {3,5}, {9,11}, {13,16}, {10,15}, {15,16}, {3,18}, {3,17}, {3,7}, {8,16}, {7,12}, {4,10}, {1,17}, {1,7}, {8,19}, {1,18}, {7,11}, {3,14}, {12,17}, {4,8}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {6,8}, {11,15}, {11,13}, {3,12}, {7,13}, {9,14}, {6,12}, {12,13}, {12,16}, {1,2}, {15,19}, {2,13}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {7,16}, {1,12}, {3,4}, {5,18}, {14,15}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {1,9}, {9,10}, {17,18}, {5,14}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {3,19}, {4,9}, {14,18}, {12,19}, {18,19}, {12,14}, {17,19}, {2,7}, {9,12}, {6,19}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {2,11}, {10,11}, {4,5}, {16,17}, {3,16}, {15,18}, {11,16}, {13,19}, {9,18}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {10,18}, {7,9}, {13,14}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {10,19}, {1,4}, {4,11}, {1,8}, {4,12}, {5,13}, {7,10}, {5,6}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {10,14}, {5,19}, {9,15}, {13,17}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {12,18}, {11,18}, {7,18}, {10,16}, {5,16} }; // Total number of connected ET graphs of order 19 is 12 // ******************************************************************************************** // Order 20 // ET20.1 // Bipartite(10,10) Valencies [2,2] // Diameter 10 Girth 20 // Twin-free VT AT // Automorphism group of order 40 EdgePairs[20][1]:={ {4,14}, {3,14}, {10,19}, {6,18}, {1,20}, {9,19}, {4,17}, {9,16}, {10,20}, {8,13}, {5,18}, {2,12}, {5,17}, {3,12}, {1,11}, {6,15}, {8,16}, {7,13}, {2,11}, {7,15} }; // ET20.2 // Bipartite(8,12) Valencies [3,2] // Diameter 6 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 48 EdgePairs[20][2]:={ {4,10}, {6,17}, {7,15}, {6,14}, {7,11}, {3,17}, {2,19}, {5,18}, {3,16}, {2,13}, {1,15}, {3,11}, {7,19}, {5,9}, {5,16}, {8,14}, {8,10}, {4,12}, {1,20}, {8,18}, {4,20}, {1,9}, {2,12}, {6,13} }; // ET20.3 // Bipartite(10,10) Valencies [3,3] // Diameter 5 Girth 6 // Twin-free VT AT // Automorphism group of order 240 EdgePairs[20][3]:={ {6,20}, {3,20}, {3,19}, {10,16}, {10,13}, {2,19}, {9,15}, {8,12}, {10,14}, {6,12}, {4,18}, {1,16}, {8,14}, {4,19}, {5,15}, {1,17}, {6,11}, {7,18}, {4,11}, {5,11}, {8,17}, {1,18}, {5,17}, {9,14}, {7,13}, {2,16}, {2,15}, {7,12}, {3,13}, {9,20} }; // ET20.4 // Non-bipartite Valency 3 // Diameter 5 Girth 5 // Twin-free VT AT // Automorphism group of order 120 EdgePairs[20][4]:={ {8,20}, {14,17}, {2,17}, {7,16}, {3,14}, {1,5}, {7,17}, {3,15}, {10,14}, {4,16}, {8,15}, {9,13}, {8,18}, {6,16}, {5,15}, {6,9}, {10,19}, {12,20}, {13,18}, {4,11}, {1,11}, {1,18}, {2,6}, {3,12}, {9,20}, {11,19}, {2,12}, {4,13}, {7,19}, {5,10} }; // ET20.5 // Bipartite(10,10) Valencies [4,4] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 80 EdgePairs[20][5]:={ {6,20}, {3,16}, {6,13}, {6,15}, {3,20}, {4,17}, {9,19}, {5,18}, {10,16}, {10,13}, {3,14}, {4,15}, {7,17}, {3,15}, {8,12}, {8,11}, {10,14}, {7,15}, {4,16}, {5,20}, {4,18}, {9,13}, {1,16}, {1,12}, {2,20}, {2,18}, {1,11}, {8,17}, {7,11}, {10,11}, {1,18}, {5,17}, {8,19}, {9,14}, {7,13}, {6,19}, {2,12}, {5,19}, {2,14}, {9,12} }; // ET20.6 // Bipartite(10,10) Valencies [4,4] // Diameter 5 Girth 4 // Has twins VT AT // Automorphism group of order 20480 EdgePairs[20][6]:={ {4,20}, {6,13}, {9,16}, {5,14}, {3,19}, {2,17}, {3,14}, {9,15}, {10,12}, {7,20}, {4,15}, {3,18}, {7,17}, {9,11}, {10,14}, {4,16}, {7,15}, {6,18}, {1,16}, {8,18}, {6,16}, {8,14}, {5,12}, {1,13}, {2,20}, {10,19}, {6,11}, {4,11}, {1,11}, {1,18}, {5,17}, {8,13}, {8,19}, {2,15}, {7,12}, {3,13}, {9,20}, {2,12}, {10,17}, {5,19} }; // ET20.7 // Bipartite(10,10) Valencies [4,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3840 EdgePairs[20][7]:={ {5,12}, {6,19}, {8,13}, {6,14}, {10,15}, {10,19}, {5,20}, {6,18}, {9,15}, {7,13}, {3,16}, {2,18}, {2,13}, {4,15}, {3,20}, {5,19}, {8,14}, {1,11}, {4,11}, {7,17}, {8,20}, {9,16}, {3,14}, {10,20}, {1,14}, {5,15}, {2,17}, {1,18}, {6,11}, {8,16}, {1,19}, {4,16}, {9,17}, {4,17}, {10,12}, {9,11}, {7,18}, {3,13}, {2,12}, {7,12} }; // ET20.8 // Non-bipartite Valency 4 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 320 EdgePairs[20][8]:={ {1,4}, {7,10}, {1,20}, {4,6}, {5,13}, {5,14}, {12,19}, {7,16}, {4,15}, {16,18}, {6,8}, {3,6}, {3,15}, {9,11}, {7,15}, {8,10}, {13,16}, {5,8}, {3,11}, {15,18}, {1,13}, {2,13}, {6,17}, {12,20}, {17,20}, {2,4}, {10,11}, {1,19}, {5,17}, {8,19}, {18,20}, {3,12}, {2,10}, {9,18}, {2,9}, {14,16}, {9,17}, {11,14}, {12,14}, {7,19} }; // ET20.9 // Bipartite(5,15) Valencies [6,2] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 77760 EdgePairs[20][9]:={ {4,20}, {3,16}, {5,14}, {1,14}, {2,17}, {3,8}, {4,15}, {3,6}, {3,18}, {4,8}, {4,18}, {1,16}, {5,12}, {3,11}, {2,7}, {2,20}, {1,11}, {5,7}, {1,19}, {5,17}, {2,15}, {1,9}, {3,13}, {4,13}, {2,12}, {2,10}, {4,10}, {5,9}, {5,19}, {1,6} }; // ET20.10 // Bipartite(8,12) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 192 EdgePairs[20][10]:={ {6,20}, {8,20}, {4,20}, {7,10}, {3,16}, {6,13}, {6,15}, {3,10}, {5,14}, {3,19}, {5,18}, {2,17}, {7,16}, {2,11}, {3,14}, {4,15}, {1,15}, {7,17}, {3,15}, {4,18}, {8,18}, {6,16}, {8,10}, {8,14}, {3,11}, {1,12}, {1,13}, {6,9}, {2,20}, {6,14}, {4,11}, {5,11}, {8,17}, {1,19}, {1,18}, {5,17}, {8,13}, {7,13}, {2,16}, {7,12}, {1,9}, {2,12}, {4,10}, {5,9}, {2,9}, {5,19}, {4,12}, {7,19} }; // ET20.11 // Bipartite(8,12) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 165888 EdgePairs[20][11]:={ {1,20}, {3,16}, {6,13}, {3,20}, {5,13}, {3,19}, {2,17}, {7,16}, {7,20}, {4,15}, {3,15}, {8,11}, {5,20}, {7,15}, {6,18}, {8,15}, {4,18}, {6,10}, {1,16}, {8,18}, {8,10}, {4,14}, {8,14}, {5,12}, {4,19}, {3,11}, {1,12}, {2,13}, {1,13}, {1,17}, {6,9}, {6,17}, {6,14}, {2,18}, {4,11}, {7,11}, {5,16}, {5,17}, {8,19}, {3,12}, {7,12}, {1,9}, {2,10}, {4,10}, {5,9}, {2,9}, {7,19}, {2,14} }; // ET20.12 // Bipartite(8,12) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 24576 EdgePairs[20][12]:={ {8,20}, {4,20}, {7,10}, {1,20}, {3,16}, {6,15}, {3,10}, {5,14}, {1,14}, {3,19}, {7,16}, {1,15}, {7,17}, {8,12}, {5,20}, {6,18}, {6,12}, {6,10}, {4,18}, {8,18}, {6,16}, {4,14}, {8,14}, {4,19}, {5,15}, {3,17}, {3,11}, {1,17}, {6,9}, {2,18}, {1,11}, {5,11}, {7,11}, {5,17}, {8,13}, {8,19}, {7,13}, {2,16}, {2,15}, {1,9}, {3,13}, {4,13}, {2,12}, {2,10}, {5,9}, {2,9}, {7,19}, {4,12} }; // ET20.13 // Bipartite(8,12) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3072 EdgePairs[20][13]:={ {8,20}, {4,20}, {3,16}, {7,14}, {3,10}, {5,13}, {5,18}, {2,19}, {7,20}, {4,15}, {1,15}, {3,15}, {8,12}, {4,16}, {8,16}, {6,18}, {6,12}, {6,10}, {8,18}, {6,16}, {8,10}, {4,14}, {8,14}, {5,12}, {3,17}, {3,11}, {1,17}, {2,13}, {1,13}, {4,9}, {6,17}, {2,20}, {6,11}, {7,18}, {3,9}, {1,11}, {5,11}, {1,19}, {5,17}, {7,13}, {2,15}, {7,12}, {1,9}, {4,10}, {5,19}, {2,9}, {7,19}, {2,14} }; // ET20.14 // Bipartite(10,10) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 240 EdgePairs[20][14]:={ {2,11}, {5,12}, {2,14}, {4,13}, {10,15}, {9,19}, {1,14}, {7,11}, {8,20}, {7,16}, {3,12}, {9,16}, {8,16}, {8,11}, {6,14}, {8,15}, {1,12}, {9,11}, {4,16}, {10,12}, {6,15}, {5,16}, {5,20}, {4,12}, {1,15}, {3,11}, {3,16}, {2,20}, {3,15}, {5,19}, {2,18}, {9,12}, {4,20}, {8,13}, {3,14}, {3,18}, {4,17}, {4,15}, {7,20}, {9,13}, {7,19}, {6,18}, {6,19}, {10,19}, {10,17}, {5,14}, {2,17}, {5,18}, {6,17}, {1,13}, {8,18}, {7,17}, {1,19}, {2,13}, {7,14}, {10,20}, {1,11}, {6,13}, {9,17}, {10,18} }; // ET20.15 // Bipartite(10,10) Valencies [6,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3840 EdgePairs[20][15]:={ {5,12}, {2,14}, {8,19}, {8,20}, {7,16}, {9,20}, {8,11}, {4,11}, {8,15}, {6,12}, {5,11}, {9,15}, {1,12}, {9,11}, {10,12}, {6,15}, {3,20}, {5,16}, {6,16}, {4,12}, {10,13}, {4,18}, {2,16}, {10,16}, {1,15}, {3,11}, {1,16}, {2,20}, {3,15}, {7,18}, {3,17}, {2,18}, {9,12}, {4,20}, {10,11}, {3,19}, {5,17}, {8,13}, {10,14}, {1,18}, {4,15}, {7,20}, {7,19}, {6,18}, {6,19}, {2,19}, {9,18}, {10,17}, {5,14}, {2,17}, {9,14}, {3,13}, {1,13}, {5,13}, {1,19}, {7,17}, {4,14}, {7,14}, {8,17}, {6,13} }; // ET20.16 // Non-bipartite Valency 6 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 240 EdgePairs[20][16]:={ {2,11}, {4,13}, {4,9}, {8,19}, {9,19}, {1,14}, {7,16}, {3,12}, {12,18}, {9,20}, {11,17}, {1,10}, {4,11}, {4,10}, {8,15}, {11,20}, {7,13}, {5,15}, {1,12}, {3,9}, {2,12}, {6,15}, {5,16}, {6,16}, {5,20}, {2,16}, {1,15}, {3,16}, {1,16}, {7,18}, {6,20}, {5,19}, {8,13}, {2,15}, {3,14}, {12,19}, {4,15}, {7,20}, {6,19}, {10,19}, {9,18}, {10,17}, {5,14}, {5,18}, {3,13}, {6,17}, {8,18}, {8,14}, {7,17}, {2,9}, {2,13}, {4,14}, {7,14}, {10,20}, {11,18}, {12,17}, {1,11}, {8,17}, {6,13}, {3,10} }; // ET20.17 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 240 EdgePairs[20][17]:={ {2,14}, {4,9}, {10,15}, {11,16}, {7,11}, {14,19}, {9,16}, {8,9}, {13,16}, {15,20}, {1,10}, {6,12}, {3,5}, {1,4}, {5,11}, {4,7}, {3,8}, {6,7}, {3,20}, {5,8}, {4,6}, {4,18}, {2,16}, {7,10}, {2,7}, {1,15}, {2,20}, {6,20}, {17,19}, {3,17}, {5,19}, {9,12}, {2,3}, {10,11}, {8,13}, {8,12}, {12,14}, {13,20}, {11,13}, {16,19}, {9,18}, {10,17}, {5,14}, {5,18}, {6,17}, {1,8}, {1,13}, {1,19}, {2,9}, {16,17}, {18,20}, {12,15}, {7,14}, {4,19}, {14,15}, {11,18}, {12,17}, {15,18}, {6,13}, {3,10} }; // ET20.18 // Non-bipartite Valency 6 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 122880 EdgePairs[20][18]:={ {2,11}, {4,13}, {12,20}, {8,19}, {9,19}, {8,20}, {7,16}, {3,12}, {14,18}, {9,20}, {8,16}, {4,11}, {5,10}, {8,15}, {1,6}, {11,20}, {2,6}, {6,10}, {5,15}, {1,12}, {4,16}, {2,12}, {6,15}, {13,18}, {5,9}, {5,16}, {6,16}, {4,12}, {10,13}, {3,11}, {3,16}, {3,15}, {7,18}, {2,18}, {7,15}, {10,14}, {3,14}, {2,5}, {12,19}, {1,18}, {1,5}, {4,15}, {7,20}, {9,13}, {1,17}, {7,19}, {10,19}, {2,17}, {9,14}, {3,13}, {8,18}, {7,17}, {4,14}, {11,19}, {10,20}, {1,11}, {14,17}, {8,17}, {13,17}, {6,9} }; // ET20.19 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 240 EdgePairs[20][19]:={ {5,12}, {4,8}, {2,14}, {4,9}, {7,11}, {11,15}, {14,19}, {8,9}, {2,10}, {13,16}, {12,16}, {7,13}, {3,5}, {1,4}, {9,15}, {1,20}, {9,11}, {10,12}, {6,7}, {3,20}, {5,8}, {4,6}, {5,20}, {10,16}, {7,10}, {2,7}, {1,16}, {3,7}, {15,19}, {17,19}, {2,3}, {2,15}, {8,12}, {12,14}, {3,18}, {13,20}, {4,17}, {11,13}, {16,20}, {6,19}, {2,19}, {9,18}, {10,17}, {5,14}, {5,18}, {6,17}, {1,8}, {1,13}, {8,14}, {6,11}, {16,17}, {1,9}, {18,20}, {4,19}, {14,15}, {11,18}, {12,17}, {15,18}, {6,13}, {3,10} }; // ET20.20 // Bipartite(4,16) Valencies [8,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2654208 EdgePairs[20][20]:={ {1,20}, {3,16}, {4,6}, {3,20}, {3,19}, {4,7}, {2,17}, {3,8}, {1,5}, {4,15}, {3,15}, {4,18}, {1,16}, {4,14}, {4,19}, {3,11}, {1,12}, {2,13}, {1,13}, {1,17}, {2,18}, {4,11}, {2,6}, {3,12}, {1,9}, {2,5}, {2,10}, {4,10}, {2,9}, {3,7}, {2,14}, {1,8} }; // ET20.21 // Bipartite(10,10) Valencies [8,8] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 245760 EdgePairs[20][21]:={ {2,11}, {5,12}, {2,14}, {4,13}, {10,15}, {9,19}, {1,14}, {7,11}, {7,16}, {8,20}, {3,12}, {9,16}, {7,12}, {8,16}, {6,14}, {8,11}, {4,11}, {8,15}, {1,20}, {5,15}, {9,11}, {4,16}, {10,12}, {2,12}, {6,15}, {3,20}, {6,16}, {5,20}, {4,12}, {10,13}, {4,18}, {2,16}, {1,15}, {3,11}, {3,16}, {2,20}, {1,16}, {3,15}, {6,20}, {3,17}, {5,19}, {9,12}, {7,15}, {5,17}, {8,13}, {10,14}, {2,15}, {8,12}, {3,18}, {4,17}, {1,18}, {7,20}, {9,13}, {7,19}, {6,18}, {6,19}, {10,19}, {2,19}, {9,18}, {10,17}, {5,14}, {2,17}, {5,18}, {9,14}, {3,13}, {1,13}, {8,18}, {5,13}, {1,19}, {7,17}, {6,11}, {4,14}, {7,14}, {4,19}, {10,20}, {1,11}, {8,17}, {6,13}, {9,17}, {10,18} }; // ET20.22 // Non-bipartite Valency 8 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 79626240 EdgePairs[20][22]:={ {5,12}, {4,8}, {4,9}, {10,15}, {11,16}, {13,19}, {7,11}, {11,15}, {14,19}, {12,18}, {14,18}, {11,17}, {9,16}, {7,12}, {15,20}, {8,11}, {12,16}, {4,10}, {5,10}, {1,6}, {6,12}, {7,13}, {2,6}, {6,10}, {5,11}, {9,15}, {4,7}, {3,8}, {3,9}, {3,20}, {13,18}, {5,9}, {5,20}, {10,13}, {4,18}, {2,16}, {1,7}, {10,16}, {1,15}, {2,7}, {1,16}, {3,7}, {15,19}, {6,20}, {3,17}, {5,19}, {2,18}, {4,20}, {3,19}, {8,13}, {10,14}, {2,15}, {8,12}, {3,18}, {2,5}, {13,20}, {4,17}, {1,18}, {1,5}, {9,13}, {16,19}, {1,17}, {16,20}, {6,19}, {2,17}, {9,14}, {1,8}, {14,20}, {8,14}, {6,11}, {2,8}, {12,15}, {7,14}, {4,19}, {11,18}, {12,17}, {14,17}, {13,17}, {3,10}, {6,9} }; // ET20.23 // Bipartite(8,12) Valencies [9,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 497664 EdgePairs[20][23]:={ {2,11}, {5,12}, {2,14}, {4,13}, {4,9}, {8,19}, {1,14}, {7,11}, {7,16}, {8,20}, {3,12}, {2,10}, {8,9}, {7,12}, {8,16}, {1,10}, {6,14}, {8,11}, {4,11}, {5,10}, {8,15}, {6,10}, {1,20}, {1,12}, {4,16}, {6,15}, {3,20}, {5,9}, {5,16}, {5,20}, {4,12}, {7,10}, {3,11}, {3,16}, {1,16}, {3,15}, {7,18}, {2,18}, {4,20}, {3,19}, {5,17}, {7,15}, {8,13}, {2,15}, {3,14}, {8,12}, {3,18}, {4,17}, {1,18}, {4,15}, {7,20}, {1,17}, {7,19}, {6,18}, {6,19}, {2,19}, {5,14}, {2,17}, {5,18}, {6,17}, {1,13}, {5,13}, {2,9}, {6,11}, {1,9}, {2,13}, {4,19}, {7,14}, {8,17}, {6,13}, {3,10}, {6,9} }; // ET20.24 // Bipartite(10,10) Valencies [9,9] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 7257600 EdgePairs[20][24]:={ {5,12}, {2,14}, {4,13}, {8,19}, {10,15}, {9,19}, {7,11}, {8,20}, {3,12}, {9,20}, {9,16}, {7,12}, {8,16}, {6,14}, {8,11}, {4,11}, {8,15}, {6,12}, {7,13}, {5,11}, {1,20}, {1,12}, {5,15}, {9,11}, {4,16}, {2,12}, {6,15}, {3,20}, {5,16}, {6,16}, {4,12}, {10,13}, {4,18}, {2,16}, {10,16}, {1,15}, {3,11}, {3,16}, {2,20}, {1,16}, {3,15}, {7,18}, {6,20}, {5,19}, {2,18}, {9,12}, {4,20}, {10,11}, {3,19}, {5,17}, {7,15}, {8,13}, {10,14}, {2,15}, {3,14}, {8,12}, {3,18}, {4,17}, {1,18}, {4,15}, {7,20}, {9,13}, {1,17}, {7,19}, {6,18}, {6,19}, {10,19}, {2,19}, {9,18}, {10,17}, {5,14}, {2,17}, {5,18}, {9,14}, {3,13}, {6,17}, {1,13}, {8,14}, {5,13}, {1,19}, {7,17}, {6,11}, {2,13}, {4,14}, {7,14}, {10,20}, {1,11}, {8,17}, {9,17}, {10,18} }; // ET20.25 // Non-bipartite Valency 9 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[20][25]:={ {4,8}, {12,20}, {8,19}, {11,16}, {9,19}, {1,14}, {14,19}, {12,18}, {14,18}, {11,17}, {8,9}, {7,12}, {13,16}, {8,16}, {1,10}, {8,11}, {4,10}, {5,10}, {6,12}, {3,5}, {7,13}, {2,6}, {5,11}, {9,15}, {1,20}, {5,15}, {9,11}, {4,16}, {10,12}, {3,9}, {2,12}, {2,4}, {3,20}, {4,6}, {6,16}, {4,12}, {5,7}, {10,16}, {7,10}, {2,7}, {3,11}, {1,16}, {3,7}, {15,19}, {3,15}, {6,20}, {17,19}, {5,19}, {5,17}, {7,15}, {10,14}, {2,15}, {12,14}, {3,18}, {1,3}, {13,20}, {4,17}, {1,18}, {1,5}, {7,20}, {9,13}, {11,13}, {16,20}, {6,18}, {2,19}, {9,18}, {10,17}, {5,14}, {2,17}, {3,13}, {1,8}, {8,14}, {8,18}, {2,9}, {7,17}, {16,17}, {18,20}, {2,13}, {4,14}, {12,15}, {4,19}, {11,19}, {14,15}, {10,20}, {1,11}, {15,18}, {13,17}, {6,13}, {6,8}, {6,9} }; // ET20.26 // Bipartite(10,10) Valencies [10,10] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 26336378880000 EdgePairs[20][26]:={ {1,15}, {9,13}, {10,19}, {7,19}, {6,12}, {5,14}, {3,15}, {6,18}, {4,14}, {1,11}, {6,14}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {7,11}, {3,19}, {4,12}, {3,18}, {8,15}, {2,14}, {3,11}, {4,20}, {6,11}, {1,17}, {3,13}, {10,12}, {2,16}, {1,16}, {10,13}, {2,17}, {8,18}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {5,19}, {5,15}, {7,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,17}, {4,15}, {9,15}, {8,19}, {4,11}, {6,19}, {7,18}, {2,12}, {5,20}, {10,14}, {8,16}, {5,17}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {1,14}, {9,18}, {10,17}, {1,20}, {9,11}, {5,11}, {3,16}, {1,13}, {4,18}, {3,20}, {5,12}, {9,14}, {3,17}, {10,20}, {5,18}, {9,16}, {7,17}, {7,12}, {5,16}, {4,13}, {10,11}, {1,18}, {4,19}, {9,20}, {8,12} }; // ET20.27 // Bipartite(9,11) Valencies [11,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14485008384000 EdgePairs[20][27]:={ {1,15}, {9,13}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {6,14}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {7,15}, {5,13}, {3,10}, {9,10}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {7,11}, {3,19}, {4,12}, {3,18}, {8,15}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {1,10}, {1,17}, {3,13}, {2,16}, {1,16}, {8,10}, {8,18}, {2,17}, {3,14}, {2,13}, {1,12}, {5,19}, {5,15}, {7,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,17}, {4,15}, {9,15}, {8,19}, {4,11}, {6,19}, {7,18}, {2,12}, {5,20}, {8,16}, {5,17}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {1,14}, {9,18}, {1,20}, {9,11}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {5,12}, {9,14}, {3,17}, {5,18}, {9,16}, {7,17}, {7,12}, {5,16}, {4,13}, {1,18}, {4,19}, {4,10}, {8,12}, {9,20} }; // ET20.28 // Bipartite(4,16) Valencies [12,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7962624 EdgePairs[20][28]:={ {2,11}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {1,6}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {4,16}, {3,20}, {4,12}, {2,7}, {3,11}, {3,16}, {3,7}, {1,16}, {3,15}, {2,18}, {4,20}, {3,19}, {2,15}, {3,14}, {3,18}, {2,5}, {4,5}, {4,17}, {1,18}, {1,5}, {4,15}, {1,17}, {3,6}, {2,19}, {2,17}, {1,8}, {1,13}, {2,9}, {1,9}, {2,13}, {4,19}, {3,10} }; // ET20.29 // Bipartite(5,15) Valencies [12,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 933120 EdgePairs[20][29]:={ {5,12}, {2,14}, {4,9}, {1,14}, {2,10}, {4,11}, {4,10}, {5,10}, {1,6}, {5,11}, {4,7}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {3,20}, {5,8}, {4,6}, {5,16}, {4,12}, {5,20}, {5,7}, {1,7}, {2,7}, {3,11}, {3,16}, {2,20}, {1,16}, {3,15}, {2,18}, {4,20}, {3,19}, {5,17}, {5,6}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {3,6}, {2,19}, {2,17}, {5,18}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {3,10} }; // ET20.30 // Bipartite(8,12) Valencies [12,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 19313344512000 EdgePairs[20][30]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {6,14}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {1,9}, {7,15}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {8,14}, {8,13}, {7,11}, {5,9}, {3,19}, {4,12}, {3,18}, {8,15}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {1,10}, {1,17}, {3,13}, {2,16}, {1,16}, {8,10}, {8,18}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {5,19}, {5,15}, {7,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,17}, {4,15}, {2,9}, {8,19}, {4,11}, {6,19}, {7,18}, {8,9}, {2,12}, {5,20}, {8,16}, {5,17}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {1,14}, {7,9}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {5,12}, {3,17}, {4,9}, {5,18}, {7,17}, {7,12}, {5,16}, {4,13}, {1,18}, {4,19}, {4,10}, {8,12} }; // ET20.31 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 2880 EdgePairs[20][31]:={ {1,15}, {10,19}, {6,12}, {5,14}, {11,17}, {4,14}, {1,11}, {12,19}, {6,17}, {13,18}, {2,11}, {2,20}, {14,19}, {6,13}, {12,15}, {12,17}, {12,14}, {16,18}, {4,5}, {9,19}, {11,16}, {12,18}, {4,6}, {3,10}, {14,20}, {2,19}, {2,15}, {6,9}, {8,14}, {8,13}, {13,20}, {3,18}, {8,15}, {7,10}, {6,11}, {1,10}, {4,7}, {3,13}, {2,16}, {1,16}, {16,17}, {10,13}, {8,10}, {8,18}, {2,17}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {3,9}, {16,19}, {5,19}, {5,15}, {7,20}, {15,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {11,18}, {8,11}, {4,17}, {4,15}, {2,9}, {3,5}, {9,15}, {8,19}, {11,14}, {11,13}, {4,11}, {6,19}, {14,17}, {1,7}, {15,18}, {7,18}, {8,9}, {2,12}, {5,20}, {3,12}, {7,16}, {6,20}, {6,16}, {1,14}, {9,18}, {10,17}, {7,9}, {2,8}, {1,20}, {5,11}, {3,16}, {4,18}, {5,10}, {3,8}, {15,17}, {3,20}, {11,20}, {5,12}, {9,14}, {3,6}, {3,17}, {10,20}, {4,9}, {2,7}, {5,18}, {9,16}, {13,19}, {7,17}, {1,8}, {7,12}, {5,16}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {12,13}, {9,20} }; // ET20.32 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 122880 EdgePairs[20][32]:={ {1,15}, {10,19}, {7,19}, {6,12}, {11,17}, {6,10}, {6,18}, {4,14}, {12,19}, {4,8}, {6,17}, {3,7}, {13,18}, {2,3}, {14,19}, {17,19}, {14,18}, {9,12}, {12,17}, {16,18}, {1,9}, {4,5}, {9,19}, {1,5}, {12,18}, {16,20}, {4,6}, {14,20}, {2,15}, {6,9}, {8,14}, {8,13}, {7,11}, {5,9}, {13,20}, {4,12}, {3,18}, {13,16}, {7,10}, {2,14}, {3,11}, {1,3}, {2,10}, {6,11}, {1,10}, {4,7}, {14,16}, {3,13}, {10,12}, {2,16}, {1,16}, {16,17}, {8,10}, {3,14}, {2,13}, {10,15}, {10,16}, {16,19}, {5,15}, {7,20}, {15,20}, {7,13}, {7,14}, {6,15}, {11,18}, {8,11}, {15,19}, {4,17}, {2,9}, {3,5}, {9,15}, {1,4}, {18,19}, {8,19}, {2,4}, {4,11}, {14,17}, {1,7}, {15,18}, {11,19}, {8,9}, {5,17}, {3,12}, {8,20}, {2,6}, {6,16}, {18,20}, {1,14}, {7,9}, {2,8}, {14,15}, {9,11}, {5,11}, {1,13}, {4,18}, {5,10}, {3,8}, {13,17}, {15,17}, {11,20}, {13,15}, {5,12}, {3,6}, {3,17}, {10,20}, {2,7}, {5,18}, {17,20}, {9,16}, {13,19}, {1,8}, {7,12}, {5,16}, {4,13}, {10,11}, {1,6}, {12,20}, {2,5}, {9,20}, {8,12} }; // ET20.33 // Bipartite(7,13) Valencies [13,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31384184832000 EdgePairs[20][33]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {7,11}, {7,16}, {3,12}, {7,9}, {2,10}, {7,12}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {7,8}, {6,12}, {7,13}, {5,11}, {6,10}, {1,20}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,15}, {3,20}, {5,8}, {5,9}, {5,16}, {6,16}, {4,12}, {5,20}, {2,16}, {4,18}, {1,15}, {7,10}, {3,11}, {3,16}, {2,20}, {1,16}, {3,15}, {7,18}, {6,20}, {3,17}, {5,19}, {2,18}, {4,20}, {3,19}, {5,17}, {7,15}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {7,20}, {1,17}, {7,19}, {6,18}, {6,19}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {7,17}, {6,11}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {7,14}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET20.34 // Bipartite(6,14) Valencies [14,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 62768369664000 EdgePairs[20][34]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {6,12}, {5,11}, {6,10}, {4,7}, {1,20}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {3,20}, {5,8}, {5,9}, {5,16}, {6,16}, {4,12}, {5,20}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {3,16}, {3,7}, {2,20}, {1,16}, {3,15}, {6,20}, {3,17}, {5,19}, {2,18}, {4,20}, {3,19}, {5,17}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {6,18}, {6,19}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {6,11}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET20.35 // Bipartite(5,15) Valencies [15,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 156920924160000 EdgePairs[20][35]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {5,10}, {1,6}, {2,6}, {5,11}, {4,7}, {1,20}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {3,20}, {5,8}, {4,6}, {5,9}, {5,16}, {4,12}, {5,20}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,16}, {3,15}, {3,17}, {5,19}, {2,18}, {4,20}, {3,19}, {5,17}, {5,6}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {3,6}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {3,10} }; // ET20.36 // Non-bipartite Valency 15 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 4976640000 EdgePairs[20][36]:={ {11,17}, {1,11}, {5,17}, {1,20}, {11,20}, {6,16}, {7,15}, {8,12}, {14,19}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {3,9}, {3,6}, {3,13}, {3,15}, {2,15}, {4,19}, {2,19}, {1,19}, {5,20}, {2,9}, {2,14}, {8,15}, {6,11}, {9,11}, {13,16}, {10,15}, {15,16}, {3,18}, {3,17}, {3,7}, {8,16}, {7,12}, {4,10}, {1,17}, {1,7}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {12,17}, {4,8}, {12,20}, {5,11}, {2,10}, {9,19}, {8,14}, {3,12}, {7,13}, {9,14}, {6,12}, {12,16}, {3,20}, {15,19}, {2,13}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {7,16}, {1,12}, {5,18}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {1,9}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {10,12}, {3,10}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {3,19}, {4,9}, {14,18}, {12,19}, {2,7}, {9,12}, {6,19}, {1,15}, {6,14}, {2,11}, {10,11}, {14,20}, {3,16}, {15,18}, {11,16}, {13,19}, {9,18}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {10,18}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {5,6}, {2,12}, {1,14}, {2,8}, {10,20}, {1,6}, {5,15}, {10,14}, {5,19}, {6,20}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,16}, {12,18}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET20.37 // Bipartite(4,16) Valencies [16,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 502146957312000 EdgePairs[20][37]:={ {2,11}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {1,6}, {3,5}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {4,16}, {3,9}, {2,12}, {3,20}, {4,6}, {4,12}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,16}, {3,15}, {3,17}, {2,18}, {4,20}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {1,5}, {4,15}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {3,10} }; // ET20.38 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 955514880 EdgePairs[20][38]:={ {11,17}, {5,17}, {1,20}, {11,20}, {7,15}, {8,12}, {14,19}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {8,9}, {3,9}, {3,6}, {3,15}, {17,20}, {2,15}, {4,19}, {16,19}, {2,19}, {1,19}, {2,4}, {5,20}, {16,18}, {2,9}, {11,14}, {8,10}, {6,7}, {2,14}, {8,15}, {6,11}, {3,5}, {9,11}, {13,16}, {10,15}, {3,18}, {3,17}, {3,7}, {8,16}, {7,12}, {4,10}, {1,17}, {1,7}, {8,19}, {1,18}, {7,11}, {7,20}, {12,17}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {8,14}, {6,8}, {11,15}, {11,13}, {3,12}, {7,13}, {9,14}, {6,12}, {12,13}, {12,16}, {3,20}, {15,19}, {2,13}, {2,20}, {14,16}, {6,18}, {13,18}, {2,16}, {7,16}, {5,18}, {14,15}, {2,6}, {8,11}, {5,7}, {8,13}, {1,9}, {15,20}, {5,14}, {4,15}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {3,19}, {4,9}, {14,18}, {12,19}, {18,19}, {12,14}, {17,19}, {2,7}, {9,12}, {6,19}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {10,11}, {4,5}, {14,20}, {16,17}, {3,16}, {15,18}, {11,16}, {13,19}, {9,18}, {10,17}, {1,16}, {5,8}, {9,17}, {10,18}, {16,20}, {7,9}, {6,10}, {5,10}, {4,18}, {5,9}, {11,19}, {1,4}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {1,14}, {2,8}, {1,6}, {10,14}, {5,19}, {6,20}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,16}, {12,18}, {11,18}, {10,16} }; // ET20.39 // Bipartite(3,17) Valencies [17,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2134124568576000 EdgePairs[20][39]:={ {2,11}, {2,14}, {1,14}, {3,12}, {2,10}, {1,10}, {1,6}, {3,5}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,9}, {2,12}, {2,4}, {3,20}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,16}, {3,15}, {3,17}, {2,18}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {1,5}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {2,13}, {2,8}, {1,11}, {3,10} }; // ET20.40 // Bipartite(2,18) Valencies [18,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12804747411456000 EdgePairs[20][40]:={ {1,4}, {1,20}, {1,3}, {1,14}, {2,17}, {1,7}, {2,11}, {2,19}, {1,5}, {1,15}, {1,16}, {1,10}, {2,7}, {1,12}, {2,13}, {1,13}, {1,17}, {2,3}, {2,20}, {2,18}, {2,4}, {1,11}, {1,19}, {1,18}, {2,6}, {2,8}, {2,16}, {2,15}, {1,9}, {2,5}, {2,10}, {2,12}, {2,9}, {2,14}, {1,8}, {1,6} }; // ET20.41 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 3715891200 EdgePairs[20][41]:={ {11,17}, {1,11}, {5,17}, {1,20}, {11,20}, {6,16}, {7,15}, {8,12}, {14,19}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {8,9}, {3,9}, {3,6}, {3,13}, {3,15}, {17,20}, {2,15}, {4,19}, {16,19}, {2,19}, {1,19}, {2,4}, {5,20}, {16,18}, {2,9}, {11,14}, {8,10}, {6,7}, {2,14}, {8,15}, {6,11}, {3,5}, {9,11}, {13,16}, {10,15}, {3,18}, {3,17}, {3,7}, {8,16}, {7,12}, {4,10}, {1,17}, {1,7}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {12,17}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {6,8}, {11,13}, {11,15}, {3,12}, {7,13}, {9,14}, {6,12}, {12,13}, {12,16}, {3,20}, {15,19}, {2,13}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {7,16}, {1,12}, {5,18}, {14,15}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {1,9}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {3,19}, {4,9}, {14,18}, {12,19}, {18,19}, {12,14}, {17,19}, {2,7}, {9,12}, {6,19}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {2,11}, {10,11}, {4,5}, {14,20}, {16,17}, {3,16}, {15,18}, {11,16}, {13,19}, {9,18}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {10,18}, {16,20}, {7,9}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {1,4}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {2,12}, {1,14}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,16}, {12,18}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET20.42 // Bipartite(1,19) Valencies [19,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 121645100408832000 EdgePairs[20][42]:={ {1,3}, {1,8}, {1,5}, {1,11}, {1,19}, {1,14}, {1,15}, {1,7}, {1,9}, {1,6}, {1,4}, {1,10}, {1,2}, {1,16}, {1,13}, {1,17}, {1,20}, {1,18}, {1,12} }; // ET20.43 // Non-bipartite Valency 19 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 2432902008176640000 EdgePairs[20][43]:={ {11,17}, {19,20}, {1,11}, {5,17}, {1,20}, {11,20}, {6,16}, {7,15}, {8,12}, {14,19}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {8,9}, {3,9}, {3,6}, {3,13}, {3,15}, {17,20}, {2,15}, {4,19}, {16,19}, {2,19}, {7,8}, {1,19}, {2,4}, {5,20}, {16,18}, {2,9}, {11,14}, {8,10}, {6,7}, {11,12}, {2,14}, {8,15}, {6,11}, {3,5}, {9,11}, {13,16}, {10,15}, {15,16}, {3,18}, {3,17}, {3,7}, {8,16}, {7,12}, {4,10}, {1,17}, {1,7}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {12,17}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {6,8}, {11,13}, {11,15}, {3,12}, {7,13}, {9,14}, {6,12}, {12,13}, {12,16}, {3,20}, {1,2}, {15,19}, {2,13}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {7,16}, {1,12}, {3,4}, {5,18}, {14,15}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {1,9}, {9,10}, {15,20}, {17,18}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {3,19}, {4,9}, {14,18}, {12,19}, {18,19}, {12,14}, {17,19}, {2,7}, {9,12}, {6,19}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {2,11}, {10,11}, {4,5}, {14,20}, {16,17}, {3,16}, {15,18}, {11,16}, {13,19}, {9,18}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {10,18}, {16,20}, {7,9}, {13,14}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {1,4}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {5,6}, {2,12}, {1,14}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,16}, {12,18}, {11,18}, {7,18}, {10,16}, {5,16} }; // Total number of connected ET graphs of order 20 is 43 // ******************************************************************************************** // Order 21 // ET21.1 // Non-bipartite Valency 2 // Diameter 10 Girth 21 // Twin-free VT AT // Automorphism group of order 42 EdgePairs[21][1]:={ {9,13}, {8,15}, {11,17}, {6,20}, {3,17}, {12,18}, {4,21}, {3,7}, {13,21}, {5,19}, {4,12}, {10,16}, {1,18}, {6,11}, {5,10}, {15,20}, {2,16}, {1,8}, {14,19}, {2,9}, {7,14} }; // ET21.2 // Bipartite(7,14) Valencies [4,2] // Diameter 7 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1792 EdgePairs[21][2]:={ {1,13}, {4,14}, {1,20}, {6,11}, {6,13}, {6,18}, {7,12}, {2,14}, {5,16}, {4,19}, {5,9}, {3,17}, {1,8}, {3,15}, {2,21}, {4,21}, {1,15}, {4,12}, {5,18}, {7,19}, {7,10}, {6,20}, {5,11}, {2,16}, {3,8}, {7,17}, {2,9}, {3,10} }; // ET21.3 // Bipartite(9,12) Valencies [4,3] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 432 EdgePairs[21][3]:={ {4,20}, {7,10}, {8,21}, {6,21}, {3,20}, {4,17}, {3,19}, {2,19}, {7,21}, {7,17}, {8,11}, {5,20}, {8,15}, {6,12}, {9,13}, {1,16}, {6,16}, {4,14}, {5,15}, {3,11}, {1,17}, {6,14}, {2,18}, {1,11}, {5,16}, {1,18}, {8,13}, {9,10}, {3,12}, {2,15}, {4,13}, {9,18}, {7,19}, {2,14}, {5,10}, {9,12} }; // ET21.4 // Bipartite(9,12) Valencies [4,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4608 EdgePairs[21][4]:={ {3,16}, {7,14}, {6,21}, {6,15}, {3,10}, {5,13}, {5,14}, {7,20}, {7,21}, {2,21}, {8,11}, {8,12}, {9,11}, {7,15}, {5,20}, {6,18}, {6,12}, {4,18}, {1,16}, {1,10}, {8,18}, {4,19}, {3,17}, {3,11}, {1,13}, {8,17}, {1,19}, {9,14}, {2,16}, {2,15}, {9,20}, {4,13}, {2,10}, {5,19}, {9,17}, {4,12} }; // ET21.5 // Non-bipartite Valency 4 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 84 EdgePairs[21][5]:={ {4,20}, {13,19}, {11,17}, {11,18}, {7,14}, {6,21}, {12,16}, {5,21}, {2,17}, {15,21}, {10,16}, {14,20}, {1,7}, {9,15}, {12,18}, {3,18}, {5,20}, {8,15}, {15,20}, {6,12}, {6,10}, {9,13}, {1,16}, {8,14}, {5,12}, {3,17}, {4,19}, {4,11}, {3,9}, {5,11}, {1,18}, {7,13}, {2,8}, {2,16}, {6,19}, {13,21}, {14,19}, {10,17}, {4,10}, {2,9}, {3,7}, {1,8} }; // ET21.6 // Non-bipartite Valency 4 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[21][6]:={ {6,20}, {14,18}, {1,20}, {11,17}, {3,16}, {8,21}, {6,15}, {4,17}, {15,16}, {9,19}, {4,7}, {5,21}, {2,17}, {10,16}, {2,19}, {1,5}, {3,15}, {8,11}, {6,18}, {1,10}, {5,8}, {1,13}, {10,19}, {13,20}, {6,11}, {16,19}, {12,21}, {2,4}, {8,17}, {18,20}, {9,14}, {7,13}, {14,21}, {3,12}, {7,12}, {11,15}, {4,13}, {9,18}, {2,9}, {3,7}, {12,14}, {5,10} }; // ET21.7 // Bipartite(6,15) Valencies [5,2] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[21][7]:={ {6,21}, {3,10}, {1,14}, {5,21}, {1,7}, {3,8}, {3,15}, {5,20}, {6,18}, {6,12}, {1,16}, {6,16}, {4,14}, {4,19}, {5,15}, {3,11}, {2,7}, {1,17}, {1,13}, {4,9}, {2,20}, {2,18}, {6,11}, {5,17}, {2,8}, {3,13}, {4,10}, {5,19}, {2,9}, {4,12} }; // ET21.8 // Bipartite(7,14) Valencies [6,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 42 EdgePairs[21][8]:={ {6,20}, {3,16}, {6,13}, {7,14}, {3,10}, {5,14}, {3,19}, {5,18}, {7,16}, {7,20}, {4,15}, {7,21}, {7,17}, {4,8}, {3,21}, {6,18}, {6,12}, {6,10}, {4,14}, {4,19}, {5,15}, {3,11}, {1,12}, {1,17}, {2,20}, {6,11}, {4,11}, {3,9}, {1,19}, {1,18}, {5,17}, {7,13}, {2,8}, {2,16}, {2,15}, {1,21}, {4,13}, {2,12}, {5,9}, {2,9}, {5,10}, {1,8} }; // ET21.9 // Bipartite(7,14) Valencies [6,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 21504 EdgePairs[21][9]:={ {5,12}, {7,16}, {7,9}, {2,10}, {6,14}, {4,11}, {7,13}, {6,10}, {5,15}, {2,12}, {6,15}, {3,20}, {5,8}, {5,20}, {4,12}, {4,18}, {2,16}, {1,15}, {3,11}, {1,16}, {3,17}, {5,19}, {4,21}, {6,21}, {3,18}, {1,18}, {7,21}, {7,20}, {2,19}, {2,17}, {3,13}, {6,17}, {1,8}, {5,13}, {2,9}, {1,9}, {4,14}, {4,19}, {7,14}, {1,11}, {6,8}, {3,10} }; // ET21.10 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 126 EdgePairs[21][10]:={ {5,12}, {4,13}, {10,15}, {8,20}, {12,18}, {11,17}, {9,21}, {2,10}, {7,12}, {8,16}, {4,11}, {3,21}, {11,20}, {7,13}, {2,6}, {6,10}, {9,15}, {4,7}, {1,12}, {9,11}, {4,16}, {3,9}, {6,15}, {5,8}, {13,18}, {8,10}, {5,20}, {1,7}, {3,4}, {10,16}, {1,15}, {3,11}, {3,16}, {2,20}, {15,19}, {17,20}, {7,18}, {2,18}, {5,17}, {3,14}, {12,14}, {6,21}, {13,20}, {15,17}, {1,5}, {11,13}, {16,19}, {1,17}, {7,19}, {18,21}, {6,18}, {14,21}, {10,19}, {5,14}, {8,14}, {1,19}, {2,13}, {2,8}, {4,19}, {14,16}, {9,17}, {12,21}, {6,9} }; // ET21.11 // Non-bipartite Valency 6 // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 3919104 EdgePairs[21][11]:={ {5,12}, {11,16}, {13,19}, {14,19}, {12,18}, {11,17}, {15,20}, {4,11}, {12,16}, {4,10}, {5,10}, {8,15}, {6,12}, {7,13}, {6,10}, {5,11}, {9,15}, {3,8}, {3,9}, {5,21}, {5,20}, {4,12}, {15,21}, {2,16}, {10,16}, {1,7}, {2,7}, {3,16}, {3,7}, {1,16}, {15,19}, {6,20}, {3,17}, {5,19}, {2,18}, {4,21}, {4,20}, {7,15}, {8,13}, {6,21}, {3,18}, {13,20}, {1,18}, {9,13}, {13,21}, {1,17}, {6,19}, {14,21}, {10,17}, {2,17}, {9,14}, {1,8}, {14,20}, {8,14}, {2,9}, {6,11}, {1,9}, {2,8}, {7,14}, {4,19}, {11,18}, {12,17}, {10,18} }; // ET21.12 // Bipartite(7,14) Valencies [8,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 21504 EdgePairs[21][12]:={ {2,11}, {5,12}, {4,8}, {4,13}, {7,16}, {3,12}, {7,9}, {1,10}, {6,14}, {4,11}, {3,21}, {7,8}, {7,13}, {6,10}, {5,15}, {1,12}, {2,12}, {3,20}, {5,8}, {5,9}, {5,16}, {6,16}, {5,21}, {4,18}, {2,16}, {1,15}, {7,10}, {2,20}, {3,17}, {5,19}, {2,18}, {4,21}, {4,20}, {3,19}, {7,15}, {3,14}, {6,21}, {1,18}, {4,15}, {7,20}, {1,17}, {6,18}, {2,19}, {5,14}, {3,13}, {6,17}, {1,8}, {1,19}, {2,9}, {7,17}, {6,11}, {2,13}, {4,14}, {1,11}, {3,10}, {6,9} }; // ET21.13 // Bipartite(9,12) Valencies [8,6] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 432 EdgePairs[21][13]:={ {2,11}, {5,12}, {8,19}, {9,19}, {1,14}, {7,11}, {7,16}, {8,20}, {9,20}, {9,21}, {2,10}, {9,16}, {7,12}, {8,16}, {1,10}, {4,11}, {4,10}, {3,21}, {7,13}, {6,10}, {5,11}, {9,15}, {1,20}, {1,12}, {9,11}, {4,16}, {2,12}, {6,15}, {2,21}, {5,21}, {8,10}, {4,12}, {4,18}, {2,16}, {1,15}, {3,16}, {2,20}, {3,15}, {7,18}, {6,20}, {3,17}, {5,19}, {1,21}, {4,21}, {5,17}, {7,15}, {3,14}, {8,12}, {3,18}, {4,15}, {7,20}, {6,18}, {6,19}, {5,14}, {2,17}, {5,18}, {9,14}, {3,13}, {6,17}, {1,13}, {8,14}, {8,18}, {5,13}, {1,19}, {6,11}, {2,13}, {4,19}, {7,14}, {8,17}, {6,13}, {9,17}, {3,10} }; // ET21.14 // Bipartite(9,12) Valencies [8,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 17915904 EdgePairs[21][14]:={ {2,11}, {5,12}, {2,14}, {4,13}, {9,19}, {1,14}, {7,11}, {7,16}, {8,20}, {3,12}, {9,21}, {9,16}, {1,10}, {8,11}, {4,11}, {4,10}, {8,21}, {3,21}, {8,15}, {6,12}, {7,13}, {6,10}, {5,11}, {9,15}, {1,20}, {5,15}, {4,16}, {2,12}, {6,15}, {2,21}, {6,16}, {5,21}, {5,20}, {7,10}, {3,16}, {2,20}, {1,16}, {3,15}, {9,10}, {2,18}, {9,12}, {4,20}, {3,19}, {5,17}, {2,15}, {8,12}, {6,21}, {3,18}, {4,17}, {7,20}, {9,13}, {1,17}, {7,19}, {6,18}, {6,19}, {9,18}, {5,14}, {2,17}, {5,18}, {3,13}, {1,13}, {8,14}, {8,18}, {1,19}, {7,17}, {4,14}, {7,14}, {4,19}, {1,11}, {8,17}, {6,13}, {3,10} }; // ET21.15 // Bipartite(9,12) Valencies [8,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4608 EdgePairs[21][15]:={ {5,12}, {2,14}, {4,13}, {1,14}, {9,20}, {9,21}, {2,10}, {7,12}, {8,16}, {1,10}, {8,11}, {4,11}, {4,10}, {8,21}, {3,21}, {8,15}, {6,12}, {7,13}, {6,10}, {5,11}, {9,15}, {1,20}, {9,11}, {4,16}, {6,15}, {3,20}, {2,21}, {6,16}, {8,10}, {5,20}, {4,12}, {4,18}, {2,16}, {3,11}, {3,16}, {2,20}, {1,16}, {3,15}, {7,18}, {3,17}, {5,19}, {9,12}, {5,17}, {7,15}, {2,15}, {3,14}, {8,12}, {6,21}, {4,17}, {7,21}, {7,20}, {1,17}, {7,19}, {6,18}, {6,19}, {2,19}, {9,18}, {5,14}, {5,18}, {9,14}, {1,13}, {8,18}, {5,13}, {1,19}, {2,13}, {4,19}, {7,14}, {1,11}, {8,17}, {6,13}, {9,17}, {3,10} }; // ET21.16 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[21][16]:={ {4,8}, {12,20}, {8,19}, {10,15}, {11,16}, {9,19}, {7,11}, {11,15}, {12,18}, {11,17}, {2,10}, {9,16}, {15,20}, {8,11}, {6,14}, {4,11}, {5,10}, {1,6}, {8,15}, {6,10}, {5,15}, {1,12}, {2,4}, {11,21}, {13,18}, {2,21}, {5,9}, {6,16}, {5,20}, {4,12}, {5,7}, {2,16}, {1,7}, {3,4}, {1,16}, {3,7}, {2,20}, {15,19}, {3,15}, {9,10}, {7,18}, {17,19}, {3,17}, {9,12}, {4,20}, {3,19}, {5,17}, {8,13}, {3,14}, {12,14}, {6,21}, {3,18}, {15,16}, {17,21}, {12,13}, {12,19}, {4,17}, {1,5}, {7,21}, {7,20}, {13,21}, {16,20}, {6,18}, {6,19}, {14,21}, {9,14}, {1,13}, {8,18}, {5,13}, {2,9}, {1,19}, {10,21}, {18,20}, {2,13}, {4,14}, {2,8}, {7,14}, {1,11}, {14,16}, {13,17}, {9,17}, {10,18}, {6,8}, {3,10} }; // ET21.17 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[21][17]:={ {2,11}, {5,12}, {2,14}, {4,13}, {4,9}, {13,19}, {1,14}, {14,19}, {7,16}, {8,20}, {3,12}, {14,18}, {9,20}, {9,21}, {7,12}, {8,16}, {12,16}, {8,21}, {3,21}, {11,20}, {6,12}, {3,5}, {7,13}, {2,6}, {5,11}, {9,15}, {4,7}, {1,20}, {3,8}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {3,20}, {5,16}, {5,21}, {8,10}, {10,13}, {4,18}, {10,16}, {1,15}, {7,10}, {3,11}, {5,19}, {2,18}, {1,21}, {4,21}, {7,15}, {10,14}, {2,15}, {8,12}, {18,19}, {2,5}, {13,20}, {15,17}, {16,21}, {1,18}, {4,15}, {9,13}, {11,13}, {16,19}, {1,17}, {18,21}, {3,6}, {10,19}, {10,17}, {2,17}, {5,18}, {1,8}, {14,20}, {7,17}, {6,11}, {1,9}, {4,19}, {11,19}, {10,20}, {12,17}, {11,14}, {14,17}, {8,17}, {15,18}, {6,13}, {6,9} }; // ET21.18 // Bipartite(6,15) Valencies [10,4] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[21][18]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {3,21}, {6,12}, {5,11}, {6,10}, {4,7}, {5,15}, {4,16}, {3,9}, {6,7}, {6,15}, {5,9}, {6,16}, {5,21}, {5,20}, {4,12}, {2,16}, {1,7}, {1,15}, {3,11}, {3,16}, {3,7}, {2,20}, {6,20}, {3,17}, {5,19}, {2,18}, {1,21}, {4,20}, {3,19}, {5,17}, {6,21}, {1,18}, {4,15}, {6,18}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,8}, {1,13}, {1,19}, {2,9}, {2,13}, {4,14}, {2,8}, {4,19}, {1,11}, {6,8}, {3,10} }; // ET21.19 // Bipartite(6,15) Valencies [10,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 82944000 EdgePairs[21][19]:={ {2,11}, {5,12}, {4,8}, {2,14}, {4,13}, {1,14}, {3,12}, {1,10}, {4,11}, {4,10}, {3,21}, {6,12}, {5,11}, {6,10}, {4,7}, {1,20}, {5,15}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {5,8}, {2,21}, {5,9}, {6,16}, {5,21}, {5,20}, {1,7}, {3,16}, {3,7}, {2,20}, {1,16}, {3,15}, {2,18}, {4,20}, {3,19}, {5,17}, {2,15}, {3,18}, {6,21}, {4,17}, {1,17}, {6,18}, {6,19}, {5,14}, {2,17}, {5,18}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {4,14}, {2,8}, {4,19}, {1,11}, {6,13}, {3,10}, {6,9} }; // ET21.20 // Non-bipartite Valency 10 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 5040 EdgePairs[21][20]:={ {1,15}, {7,19}, {6,12}, {3,15}, {11,17}, {6,10}, {4,14}, {12,19}, {6,14}, {4,8}, {6,17}, {3,7}, {13,18}, {2,11}, {2,20}, {14,18}, {9,12}, {6,13}, {9,21}, {6,7}, {11,16}, {5,7}, {5,13}, {3,10}, {14,20}, {2,19}, {2,18}, {6,9}, {8,14}, {8,13}, {9,17}, {10,18}, {5,9}, {3,19}, {4,12}, {8,15}, {12,21}, {16,21}, {3,11}, {2,10}, {4,7}, {14,16}, {1,17}, {3,13}, {10,12}, {2,16}, {1,16}, {10,13}, {8,21}, {2,17}, {3,14}, {10,15}, {1,12}, {10,16}, {3,9}, {5,15}, {6,8}, {7,20}, {1,19}, {15,19}, {4,21}, {4,17}, {4,15}, {2,9}, {9,15}, {18,19}, {8,19}, {11,14}, {11,13}, {4,11}, {6,19}, {2,21}, {11,12}, {5,8}, {11,19}, {7,18}, {5,20}, {8,20}, {15,16}, {7,16}, {6,16}, {3,21}, {1,14}, {9,18}, {13,21}, {2,8}, {1,20}, {5,11}, {1,13}, {4,18}, {13,17}, {15,17}, {3,20}, {7,21}, {5,12}, {9,14}, {10,20}, {5,18}, {17,20}, {7,17}, {5,16}, {1,21}, {1,18}, {12,20}, {4,10} }; // ET21.21 // Non-bipartite Valency 10 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 5040 EdgePairs[21][21]:={ {13,14}, {10,19}, {9,13}, {14,21}, {11,15}, {5,14}, {10,21}, {19,20}, {6,18}, {1,11}, {12,16}, {2,3}, {14,19}, {17,19}, {4,16}, {12,17}, {12,15}, {12,14}, {20,21}, {16,18}, {1,9}, {4,5}, {9,19}, {1,5}, {12,18}, {16,20}, {7,15}, {18,21}, {4,6}, {9,10}, {17,18}, {2,15}, {7,11}, {1,2}, {13,20}, {5,21}, {5,6}, {3,18}, {13,16}, {7,10}, {2,14}, {1,3}, {4,20}, {6,11}, {1,10}, {6,21}, {16,17}, {8,10}, {8,18}, {2,13}, {16,19}, {5,19}, {15,20}, {7,13}, {8,17}, {7,14}, {6,15}, {11,18}, {8,11}, {3,5}, {1,4}, {2,4}, {7,8}, {3,4}, {14,17}, {15,21}, {1,7}, {15,18}, {8,9}, {2,12}, {10,14}, {8,16}, {5,17}, {3,12}, {2,6}, {6,20}, {11,21}, {18,20}, {10,17}, {17,21}, {7,9}, {14,15}, {9,11}, {3,16}, {5,10}, {3,8}, {11,20}, {13,15}, {3,6}, {3,17}, {4,9}, {2,7}, {9,16}, {13,19}, {19,21}, {1,8}, {7,12}, {4,13}, {10,11}, {1,6}, {4,19}, {2,5}, {12,13}, {9,20}, {8,12} }; // ET21.22 // Bipartite(10,11) Valencies [11,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 144850083840000 EdgePairs[21][22]:={ {1,15}, {9,13}, {10,19}, {7,19}, {6,12}, {5,14}, {10,21}, {3,15}, {6,18}, {4,14}, {1,11}, {6,14}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {9,21}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {8,15}, {2,14}, {3,11}, {4,20}, {6,11}, {1,17}, {3,13}, {2,16}, {10,12}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {5,19}, {5,15}, {7,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {9,15}, {8,19}, {4,11}, {6,19}, {2,21}, {7,18}, {2,12}, {5,20}, {10,14}, {8,16}, {5,17}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {9,11}, {5,11}, {3,16}, {1,13}, {4,18}, {3,20}, {7,21}, {5,12}, {9,14}, {3,17}, {10,20}, {5,18}, {9,16}, {7,17}, {7,12}, {5,16}, {4,13}, {10,11}, {1,21}, {1,18}, {4,19}, {9,20}, {8,12} }; // ET21.23 // Bipartite(3,18) Valencies [12,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2239488000 EdgePairs[21][23]:={ {1,4}, {1,20}, {3,16}, {3,10}, {1,14}, {3,19}, {2,17}, {1,7}, {2,11}, {1,5}, {3,6}, {3,18}, {3,15}, {3,4}, {2,21}, {3,21}, {1,16}, {1,10}, {1,17}, {1,13}, {2,20}, {2,18}, {3,9}, {1,11}, {1,19}, {2,6}, {2,8}, {3,12}, {2,15}, {3,13}, {2,5}, {2,12}, {2,9}, {3,7}, {2,14}, {1,8} }; // ET21.24 // Bipartite(7,14) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 645120 EdgePairs[21][24]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {7,11}, {7,16}, {3,12}, {7,9}, {2,10}, {1,10}, {6,14}, {4,11}, {5,10}, {3,21}, {7,8}, {6,12}, {7,13}, {5,11}, {6,10}, {1,20}, {1,12}, {5,15}, {3,8}, {4,16}, {2,12}, {6,15}, {3,20}, {5,8}, {2,21}, {5,9}, {5,16}, {6,16}, {5,21}, {4,12}, {2,16}, {4,18}, {1,15}, {7,10}, {3,11}, {1,16}, {2,20}, {3,15}, {7,18}, {6,20}, {3,17}, {5,19}, {2,18}, {4,21}, {4,20}, {3,19}, {5,17}, {7,15}, {3,14}, {3,18}, {6,21}, {1,18}, {7,21}, {4,15}, {7,20}, {1,17}, {6,19}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,8}, {1,13}, {1,19}, {2,9}, {7,17}, {1,9}, {2,13}, {4,14}, {4,19}, {7,14}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET21.25 // Bipartite(9,12) Valencies [12,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 173820100608000 EdgePairs[21][25]:={ {1,15}, {9,13}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {6,14}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {9,21}, {7,15}, {5,13}, {3,10}, {2,19}, {9,10}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {8,15}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {1,10}, {1,17}, {3,13}, {2,16}, {1,16}, {6,21}, {8,10}, {8,18}, {2,17}, {8,21}, {3,14}, {2,13}, {1,12}, {5,19}, {5,15}, {7,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {9,15}, {8,19}, {4,11}, {6,19}, {2,21}, {7,18}, {2,12}, {5,20}, {8,16}, {5,17}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {9,18}, {1,20}, {9,11}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {7,21}, {5,12}, {9,14}, {3,17}, {5,18}, {9,16}, {7,17}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {8,12}, {9,20} }; // ET21.26 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 30240 EdgePairs[21][26]:={ {1,15}, {9,13}, {7,19}, {6,12}, {11,15}, {10,21}, {3,15}, {11,17}, {4,14}, {1,11}, {12,19}, {6,14}, {4,8}, {6,17}, {12,16}, {13,18}, {2,11}, {2,20}, {14,19}, {17,19}, {14,18}, {9,12}, {6,13}, {12,15}, {1,9}, {9,21}, {6,7}, {12,18}, {5,7}, {7,15}, {18,21}, {5,13}, {3,10}, {14,20}, {8,13}, {9,17}, {5,9}, {3,19}, {4,12}, {3,18}, {8,15}, {7,10}, {2,14}, {16,21}, {6,11}, {1,10}, {14,16}, {2,16}, {1,16}, {6,21}, {10,13}, {8,10}, {8,18}, {2,17}, {3,14}, {2,13}, {3,9}, {10,16}, {16,19}, {5,19}, {5,15}, {6,8}, {15,20}, {7,14}, {1,19}, {11,18}, {8,11}, {4,21}, {4,17}, {4,15}, {3,5}, {1,4}, {8,19}, {11,14}, {2,4}, {15,21}, {2,21}, {1,7}, {11,19}, {7,18}, {2,12}, {5,20}, {10,14}, {8,16}, {3,12}, {8,20}, {15,16}, {6,16}, {6,20}, {11,21}, {18,20}, {3,21}, {10,17}, {13,21}, {2,8}, {1,20}, {9,11}, {5,11}, {1,13}, {4,18}, {5,10}, {3,8}, {13,17}, {15,17}, {7,21}, {3,6}, {9,14}, {3,17}, {10,20}, {4,9}, {2,7}, {5,18}, {17,20}, {9,16}, {13,19}, {7,17}, {7,12}, {5,16}, {1,6}, {1,18}, {12,20}, {4,19}, {4,10}, {2,5}, {12,13}, {9,20} }; // ET21.27 // Bipartite(8,13) Valencies [13,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 251073478656000 EdgePairs[21][27]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {6,14}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {1,9}, {7,15}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {8,14}, {8,13}, {7,11}, {5,9}, {5,21}, {3,19}, {4,12}, {3,18}, {8,15}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {1,10}, {1,17}, {3,13}, {2,16}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {3,9}, {5,19}, {5,15}, {7,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {2,9}, {8,19}, {4,11}, {6,19}, {2,21}, {7,18}, {8,9}, {2,12}, {5,20}, {5,17}, {8,16}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {7,9}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {7,21}, {5,12}, {3,17}, {4,9}, {5,18}, {7,17}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {8,12} }; // ET21.28 // Bipartite(7,14) Valencies [14,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 439378587648000 EdgePairs[21][28]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {6,14}, {4,8}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {1,9}, {7,15}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {7,11}, {5,9}, {5,21}, {3,19}, {4,12}, {3,18}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {1,10}, {1,17}, {3,13}, {2,16}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {5,19}, {5,15}, {6,8}, {7,20}, {7,13}, {7,14}, {6,15}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,11}, {7,8}, {6,19}, {2,21}, {5,8}, {7,18}, {2,12}, {5,20}, {5,17}, {3,12}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {7,9}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,8}, {3,20}, {7,21}, {5,12}, {3,17}, {4,9}, {5,18}, {7,17}, {1,8}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10} }; // ET21.29 // Non-bipartite Valency 14 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 768144384000 EdgePairs[21][29]:={ {11,17}, {1,11}, {5,17}, {1,20}, {11,20}, {6,16}, {13,21}, {7,15}, {14,19}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {3,9}, {3,13}, {3,15}, {2,15}, {4,19}, {2,19}, {7,8}, {1,19}, {5,20}, {1,21}, {2,9}, {2,14}, {8,15}, {6,11}, {13,16}, {10,15}, {3,18}, {3,17}, {8,16}, {6,21}, {7,12}, {4,10}, {1,17}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {4,8}, {12,20}, {5,11}, {2,10}, {9,19}, {6,8}, {11,15}, {3,12}, {7,13}, {6,12}, {12,16}, {4,21}, {3,20}, {10,21}, {2,13}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {5,18}, {14,15}, {7,17}, {1,9}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {3,10}, {6,15}, {2,17}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {14,18}, {12,19}, {3,21}, {6,19}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {2,11}, {14,20}, {3,16}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {10,18}, {7,9}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {2,12}, {1,14}, {2,8}, {10,20}, {5,15}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET21.30 // Bipartite(6,15) Valencies [15,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 941525544960000 EdgePairs[21][30]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {3,21}, {6,12}, {5,11}, {6,10}, {4,7}, {1,20}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {3,20}, {5,8}, {2,21}, {5,9}, {5,16}, {6,16}, {5,21}, {4,12}, {5,20}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {3,16}, {3,7}, {2,20}, {1,16}, {3,15}, {6,20}, {3,17}, {5,19}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {5,17}, {2,15}, {3,14}, {3,18}, {6,21}, {4,17}, {1,18}, {4,15}, {1,17}, {6,18}, {6,19}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {6,11}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET21.31 // Bipartite(5,16) Valencies [16,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2510734786560000 EdgePairs[21][31]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {5,10}, {3,21}, {1,6}, {2,6}, {5,11}, {4,7}, {1,20}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {3,20}, {5,8}, {2,21}, {4,6}, {5,9}, {5,16}, {5,21}, {4,12}, {5,20}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,16}, {3,15}, {3,17}, {5,19}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {5,17}, {5,6}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {3,6}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {3,10} }; // ET21.32 // Bipartite(4,17) Valencies [17,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8536498274304000 EdgePairs[21][32]:={ {2,11}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {3,21}, {1,6}, {3,5}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {4,16}, {3,9}, {2,12}, {3,20}, {2,21}, {4,6}, {4,12}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {1,5}, {4,15}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {3,10} }; // ET21.33 // Bipartite(3,18) Valencies [18,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 38414242234368000 EdgePairs[21][33]:={ {2,11}, {2,14}, {1,14}, {3,12}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,9}, {2,12}, {2,4}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {1,5}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {2,13}, {2,8}, {1,11}, {3,10} }; // ET21.34 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1410877440 EdgePairs[21][34]:={ {11,17}, {1,11}, {5,17}, {1,20}, {11,20}, {6,16}, {13,21}, {7,15}, {8,12}, {14,19}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {3,9}, {3,6}, {3,13}, {3,15}, {17,20}, {2,15}, {4,19}, {16,19}, {2,19}, {1,19}, {2,4}, {5,20}, {1,21}, {2,9}, {11,14}, {17,21}, {18,21}, {8,10}, {6,7}, {2,14}, {8,15}, {6,11}, {3,5}, {9,11}, {13,16}, {10,15}, {15,16}, {3,18}, {3,17}, {3,7}, {8,16}, {6,21}, {7,12}, {4,10}, {1,17}, {1,7}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {6,8}, {11,13}, {11,15}, {3,12}, {7,13}, {9,14}, {6,12}, {12,13}, {12,16}, {4,21}, {3,20}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {3,4}, {5,18}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {1,9}, {9,10}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {3,10}, {6,15}, {2,17}, {9,13}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {14,18}, {12,19}, {18,19}, {12,14}, {3,21}, {17,19}, {2,7}, {9,12}, {6,19}, {6,9}, {1,15}, {12,15}, {6,14}, {2,11}, {14,20}, {15,21}, {16,21}, {3,16}, {15,18}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {10,18}, {16,20}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {1,4}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {2,12}, {1,14}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET21.35 // Bipartite(2,19) Valencies [19,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 243290200817664000 EdgePairs[21][35]:={ {1,4}, {1,20}, {1,3}, {1,14}, {2,17}, {1,7}, {2,11}, {2,19}, {1,5}, {1,15}, {2,21}, {1,16}, {1,10}, {2,7}, {1,12}, {2,13}, {1,13}, {1,17}, {2,3}, {2,20}, {2,18}, {2,4}, {1,11}, {1,19}, {1,18}, {2,6}, {2,8}, {2,16}, {2,15}, {1,21}, {1,9}, {2,5}, {2,10}, {2,12}, {2,9}, {2,14}, {1,8}, {1,6} }; // ET21.36 // Bipartite(1,20) Valencies [20,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 2432902008176640000 EdgePairs[21][36]:={ {1,13}, {1,16}, {1,14}, {1,17}, {1,20}, {1,3}, {1,19}, {1,4}, {1,9}, {1,2}, {1,8}, {1,15}, {1,5}, {1,10}, {1,6}, {1,11}, {1,21}, {1,12}, {1,7}, {1,18} }; // ET21.37 // Non-bipartite Valency 20 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 51090942171709440000 EdgePairs[21][37]:={ {11,17}, {19,20}, {1,11}, {5,17}, {1,20}, {11,20}, {6,16}, {13,21}, {7,15}, {8,12}, {14,19}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {8,9}, {3,9}, {3,6}, {3,13}, {3,15}, {17,20}, {2,15}, {4,19}, {16,19}, {2,19}, {7,8}, {1,19}, {2,4}, {5,20}, {20,21}, {1,21}, {16,18}, {2,9}, {11,14}, {17,21}, {18,21}, {8,10}, {6,7}, {11,12}, {2,14}, {8,15}, {6,11}, {3,5}, {9,11}, {13,16}, {10,15}, {19,21}, {15,16}, {3,18}, {3,17}, {3,7}, {8,16}, {6,21}, {7,12}, {4,10}, {1,17}, {1,7}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {6,8}, {11,13}, {11,15}, {3,12}, {7,13}, {9,14}, {6,12}, {12,13}, {12,16}, {4,21}, {3,20}, {1,2}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {3,4}, {5,18}, {14,15}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {1,9}, {9,10}, {15,20}, {17,18}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {14,18}, {12,19}, {18,19}, {12,14}, {3,21}, {17,19}, {2,7}, {9,12}, {6,19}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {2,11}, {10,11}, {4,5}, {14,20}, {15,21}, {16,17}, {16,21}, {3,16}, {15,18}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {1,16}, {4,14}, {5,8}, {9,17}, {10,18}, {16,20}, {7,9}, {13,14}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {1,4}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {5,6}, {2,12}, {1,14}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // Total number of connected ET graphs of order 21 is 37 // ******************************************************************************************** // Order 22 // ET22.1 // Bipartite(11,11) Valencies [2,2] // Diameter 11 Girth 22 // Twin-free VT AT // Automorphism group of order 44 EdgePairs[22][1]:={ {1,12}, {9,15}, {6,20}, {5,18}, {5,22}, {8,21}, {2,13}, {7,19}, {6,21}, {3,14}, {11,15}, {1,14}, {7,22}, {8,17}, {11,13}, {9,19}, {2,16}, {4,16}, {4,20}, {10,12}, {10,17}, {3,18} }; // ET22.2 // Non-bipartite Valency 4 // Diameter 5 Girth 4 // Has twins VT AT // Automorphism group of order 45056 EdgePairs[22][2]:={ {14,18}, {1,20}, {18,22}, {11,16}, {14,17}, {12,16}, {4,7}, {10,13}, {2,19}, {3,8}, {1,5}, {4,8}, {8,12}, {10,14}, {8,11}, {4,21}, {3,21}, {15,20}, {18,21}, {6,10}, {9,13}, {15,19}, {16,20}, {17,21}, {6,9}, {2,20}, {13,18}, {16,19}, {3,22}, {4,22}, {7,11}, {1,19}, {2,6}, {9,14}, {7,12}, {12,15}, {11,15}, {17,22}, {2,5}, {5,9}, {3,7}, {13,17}, {1,6}, {5,10} }; // ET22.3 // Bipartite(11,11) Valencies [5,5] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1320 EdgePairs[22][3]:={ {5,12}, {4,13}, {8,19}, {11,16}, {8,20}, {7,16}, {3,12}, {9,20}, {9,16}, {6,14}, {8,21}, {3,21}, {8,15}, {1,12}, {4,16}, {6,15}, {3,20}, {11,21}, {2,21}, {4,12}, {10,13}, {10,16}, {1,15}, {7,18}, {6,20}, {5,19}, {2,18}, {9,12}, {4,21}, {11,22}, {7,15}, {5,17}, {3,14}, {3,18}, {1,18}, {4,15}, {9,22}, {10,19}, {6,22}, {5,14}, {2,17}, {5,13}, {1,19}, {7,17}, {1,22}, {2,13}, {7,14}, {11,19}, {10,20}, {11,14}, {8,17}, {2,22}, {6,13}, {9,17}, {10,18} }; // ET22.4 // Bipartite(10,12) Valencies [6,5] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[22][4]:={ {5,12}, {3,22}, {2,14}, {4,13}, {8,19}, {10,15}, {8,20}, {3,12}, {9,21}, {9,16}, {8,11}, {4,11}, {6,12}, {7,13}, {5,15}, {1,12}, {9,11}, {4,16}, {10,12}, {6,15}, {2,21}, {6,16}, {10,16}, {3,11}, {1,16}, {2,20}, {7,18}, {6,20}, {1,21}, {4,20}, {3,19}, {5,17}, {7,15}, {8,13}, {2,15}, {3,14}, {6,21}, {3,18}, {4,17}, {1,18}, {7,21}, {8,22}, {9,13}, {4,22}, {6,19}, {2,19}, {9,18}, {10,17}, {5,14}, {5,18}, {8,14}, {7,17}, {1,19}, {10,22}, {2,13}, {7,14}, {10,20}, {1,11}, {5,22}, {9,17} }; // ET22.5 // Bipartite(10,12) Valencies [6,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3840 EdgePairs[22][5]:={ {5,12}, {3,22}, {2,14}, {8,19}, {10,15}, {1,14}, {9,20}, {9,21}, {9,16}, {7,12}, {8,16}, {6,14}, {4,11}, {7,13}, {5,11}, {9,15}, {1,20}, {2,12}, {6,15}, {5,20}, {4,12}, {4,18}, {2,16}, {10,16}, {3,11}, {3,16}, {2,20}, {7,18}, {6,20}, {3,17}, {2,18}, {4,21}, {10,11}, {3,19}, {5,17}, {7,15}, {8,13}, {8,12}, {6,21}, {4,17}, {7,21}, {8,22}, {4,15}, {1,17}, {7,19}, {6,19}, {9,22}, {10,17}, {5,14}, {5,18}, {9,14}, {3,13}, {1,13}, {8,18}, {1,19}, {10,22}, {10,21}, {1,11}, {2,22}, {6,13} }; // ET22.6 // Bipartite(11,11) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1320 EdgePairs[22][6]:={ {5,12}, {3,22}, {2,14}, {8,19}, {10,15}, {1,14}, {11,15}, {9,20}, {11,17}, {9,21}, {7,12}, {8,21}, {8,15}, {11,20}, {1,12}, {4,16}, {10,12}, {2,21}, {5,16}, {6,16}, {5,21}, {2,16}, {10,16}, {1,16}, {3,15}, {11,12}, {7,18}, {6,20}, {3,17}, {2,18}, {4,21}, {4,20}, {3,19}, {5,17}, {8,13}, {10,14}, {2,15}, {3,14}, {8,12}, {3,18}, {4,17}, {7,21}, {8,22}, {4,15}, {7,20}, {9,13}, {11,13}, {1,17}, {7,19}, {6,18}, {6,19}, {9,22}, {6,22}, {5,18}, {9,14}, {1,13}, {1,19}, {10,22}, {2,13}, {7,14}, {4,19}, {10,20}, {11,18}, {5,22}, {6,13}, {9,17} }; // ET22.7 // Bipartite(8,14) Valencies [7,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1344 EdgePairs[22][7]:={ {2,11}, {3,22}, {5,12}, {2,14}, {4,13}, {7,11}, {7,16}, {8,20}, {8,16}, {4,10}, {5,15}, {1,12}, {2,21}, {5,9}, {6,16}, {8,10}, {4,12}, {7,10}, {3,11}, {1,16}, {2,20}, {3,15}, {6,20}, {5,19}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {5,17}, {2,15}, {8,12}, {3,18}, {4,17}, {1,18}, {7,21}, {8,22}, {4,15}, {7,19}, {6,22}, {5,14}, {3,13}, {6,17}, {1,13}, {8,14}, {8,18}, {7,17}, {2,9}, {1,19}, {6,11}, {1,9}, {7,14}, {5,22}, {6,13}, {3,10}, {6,9} }; // ET22.8 // Bipartite(6,16) Valencies [8,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7962624 EdgePairs[22][8]:={ {4,20}, {1,20}, {6,7}, {6,15}, {5,13}, {5,14}, {3,19}, {5,18}, {5,21}, {2,17}, {1,7}, {1,15}, {3,15}, {4,8}, {2,21}, {4,16}, {3,21}, {6,18}, {5,22}, {4,18}, {6,10}, {1,16}, {4,14}, {3,17}, {3,11}, {1,12}, {2,13}, {2,20}, {6,14}, {6,11}, {3,9}, {4,22}, {1,11}, {6,22}, {1,19}, {5,17}, {2,8}, {2,16}, {3,13}, {6,19}, {2,12}, {4,10}, {5,9}, {2,9}, {3,7}, {4,12}, {1,8}, {5,10} }; // ET22.9 // Bipartite(6,16) Valencies [8,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12288 EdgePairs[22][9]:={ {4,20}, {6,13}, {6,21}, {3,20}, {5,13}, {3,19}, {5,21}, {2,17}, {1,7}, {1,15}, {6,8}, {3,15}, {4,21}, {6,18}, {6,10}, {1,16}, {2,22}, {1,10}, {6,16}, {4,14}, {3,17}, {4,19}, {5,8}, {5,15}, {3,11}, {1,17}, {2,20}, {6,14}, {2,18}, {4,11}, {3,9}, {4,22}, {6,22}, {5,7}, {5,11}, {5,16}, {1,18}, {3,12}, {1,9}, {2,10}, {2,12}, {4,13}, {2,9}, {5,19}, {3,7}, {4,12}, {2,14}, {1,8} }; // ET22.10 // Bipartite(4,18) Valencies [9,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1119744 EdgePairs[22][10]:={ {4,20}, {3,19}, {2,17}, {1,7}, {2,11}, {1,5}, {4,15}, {3,6}, {3,18}, {3,15}, {4,8}, {1,22}, {4,16}, {4,21}, {3,21}, {1,16}, {1,10}, {4,14}, {1,17}, {1,13}, {4,9}, {2,20}, {2,18}, {3,9}, {4,22}, {1,11}, {1,19}, {2,6}, {2,8}, {3,12}, {3,13}, {2,5}, {2,12}, {4,10}, {3,7}, {2,14} }; // ET22.11 // Bipartite(11,11) Valencies [10,10] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 79833600 EdgePairs[22][11]:={ {1,15}, {9,13}, {10,19}, {7,19}, {6,12}, {11,15}, {5,14}, {11,17}, {10,22}, {6,18}, {4,14}, {2,22}, {6,14}, {2,20}, {9,12}, {6,13}, {9,19}, {9,21}, {11,16}, {11,22}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {4,20}, {1,17}, {3,13}, {10,12}, {2,16}, {1,22}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {3,22}, {5,19}, {5,15}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {11,18}, {4,21}, {4,17}, {4,15}, {9,15}, {11,14}, {11,13}, {5,22}, {6,19}, {2,21}, {11,19}, {7,18}, {2,12}, {4,22}, {5,20}, {10,14}, {8,16}, {5,17}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {11,21}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {7,22}, {3,16}, {4,18}, {3,20}, {7,21}, {11,20}, {5,12}, {9,14}, {3,17}, {10,20}, {9,16}, {7,17}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {9,20}, {8,12} }; // ET22.12 // Bipartite(11,11) Valencies [11,11] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 3186701844480000 EdgePairs[22][12]:={ {1,15}, {9,13}, {10,19}, {7,19}, {6,12}, {11,15}, {5,14}, {10,21}, {3,15}, {11,17}, {10,22}, {6,18}, {4,14}, {2,22}, {6,14}, {6,17}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {9,21}, {11,16}, {11,22}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {2,14}, {4,20}, {1,17}, {3,13}, {2,16}, {10,12}, {1,22}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {3,22}, {5,19}, {5,15}, {7,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {11,18}, {4,21}, {4,17}, {4,15}, {9,15}, {8,19}, {11,14}, {11,13}, {5,22}, {6,19}, {2,21}, {11,12}, {11,19}, {7,18}, {2,12}, {4,22}, {5,20}, {10,14}, {8,16}, {5,17}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {11,21}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {7,22}, {3,16}, {1,13}, {4,18}, {3,20}, {7,21}, {11,20}, {5,12}, {9,14}, {3,17}, {10,20}, {5,18}, {9,16}, {7,17}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {9,20}, {8,12}, {9,22} }; // ET22.13 // Bipartite(10,12) Valencies [12,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1738201006080000 EdgePairs[22][13]:={ {1,15}, {9,13}, {10,19}, {7,19}, {6,12}, {5,14}, {10,21}, {3,15}, {10,22}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {9,21}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {7,11}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {2,14}, {3,11}, {4,20}, {6,11}, {1,17}, {3,13}, {2,16}, {10,12}, {1,22}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {3,22}, {5,19}, {5,15}, {7,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {9,15}, {8,19}, {4,11}, {5,22}, {6,19}, {2,21}, {7,18}, {2,12}, {4,22}, {5,20}, {10,14}, {8,16}, {5,17}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {3,20}, {7,21}, {5,12}, {9,14}, {3,17}, {10,20}, {5,18}, {9,16}, {7,17}, {7,12}, {5,16}, {4,13}, {1,21}, {10,11}, {1,18}, {4,19}, {8,12}, {9,20}, {9,22} }; // ET22.14 // Bipartite(9,13) Valencies [13,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2259661307904000 EdgePairs[22][14]:={ {1,15}, {9,13}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {9,21}, {7,15}, {5,13}, {3,10}, {2,19}, {9,10}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {7,11}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {3,22}, {5,19}, {5,15}, {7,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {9,15}, {8,19}, {4,11}, {5,22}, {6,19}, {2,21}, {7,18}, {2,12}, {4,22}, {5,20}, {5,17}, {8,16}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {9,18}, {1,20}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {7,21}, {5,12}, {9,14}, {3,17}, {5,18}, {9,16}, {7,17}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {8,12}, {9,20}, {9,22} }; // ET22.15 // Bipartite(8,14) Valencies [14,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3515028701184000 EdgePairs[22][15]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {1,9}, {7,15}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {8,14}, {8,13}, {7,11}, {6,22}, {5,9}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {7,20}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {2,9}, {8,19}, {4,11}, {5,22}, {6,19}, {2,21}, {7,18}, {8,9}, {2,12}, {4,22}, {5,20}, {5,17}, {8,16}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {7,9}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {7,21}, {5,12}, {3,17}, {4,9}, {5,18}, {7,17}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {8,12} }; // ET22.16 // Bipartite(7,15) Valencies [15,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6590678814720000 EdgePairs[22][16]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {6,17}, {2,11}, {2,20}, {4,16}, {6,13}, {1,9}, {7,15}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {7,11}, {6,22}, {5,9}, {5,21}, {3,19}, {4,12}, {3,18}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {6,8}, {7,20}, {7,13}, {7,14}, {6,15}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,11}, {7,8}, {5,22}, {6,19}, {2,21}, {5,8}, {7,18}, {2,12}, {4,22}, {5,20}, {5,17}, {3,12}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {7,9}, {2,8}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,8}, {3,20}, {7,21}, {5,12}, {3,17}, {4,9}, {5,18}, {7,17}, {1,8}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10} }; // ET22.17 // Bipartite(6,16) Valencies [16,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 15064408719360000 EdgePairs[22][17]:={ {2,11}, {3,22}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {3,21}, {6,12}, {5,11}, {6,10}, {4,7}, {1,20}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {3,20}, {5,8}, {2,21}, {5,9}, {5,16}, {6,16}, {5,21}, {4,12}, {5,20}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,16}, {3,15}, {6,20}, {3,17}, {5,19}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {5,17}, {2,15}, {3,14}, {3,18}, {6,21}, {4,17}, {1,18}, {4,15}, {1,17}, {4,22}, {6,18}, {6,19}, {6,22}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {6,17}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {6,11}, {1,9}, {1,22}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {5,22}, {2,22}, {6,13}, {6,8}, {3,10}, {6,9} }; // ET22.18 // Bipartite(5,17) Valencies [17,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 42682491371520000 EdgePairs[22][18]:={ {2,11}, {3,22}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {5,10}, {3,21}, {1,6}, {2,6}, {5,11}, {4,7}, {1,20}, {1,12}, {5,15}, {3,8}, {4,16}, {3,9}, {2,12}, {3,20}, {5,8}, {2,21}, {4,6}, {5,9}, {5,16}, {5,21}, {4,12}, {5,20}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,16}, {3,15}, {3,17}, {5,19}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {5,17}, {5,6}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {4,22}, {3,6}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {1,9}, {1,22}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {5,22}, {2,22}, {3,10} }; // ET22.19 // Bipartite(4,18) Valencies [18,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 153656968937472000 EdgePairs[22][19]:={ {2,11}, {3,22}, {2,14}, {4,8}, {4,13}, {4,9}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {3,21}, {1,6}, {3,5}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {4,16}, {3,9}, {2,12}, {3,20}, {2,21}, {4,6}, {4,12}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {1,5}, {4,15}, {1,17}, {4,22}, {3,6}, {2,19}, {2,17}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {4,14}, {4,19}, {1,11}, {2,22}, {3,10} }; // ET22.20 // Bipartite(3,19) Valencies [19,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 729870602452992000 EdgePairs[22][20]:={ {2,11}, {3,22}, {2,14}, {1,14}, {3,12}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,9}, {2,12}, {2,4}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {1,5}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {1,11}, {2,22}, {3,10} }; // ET22.21 // Bipartite(2,20) Valencies [20,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4865804016353280000 EdgePairs[22][21]:={ {1,4}, {1,20}, {1,3}, {1,14}, {2,17}, {1,7}, {2,11}, {2,19}, {1,5}, {1,15}, {2,21}, {1,22}, {1,16}, {1,10}, {2,22}, {2,7}, {1,12}, {2,13}, {1,13}, {1,17}, {2,3}, {2,20}, {2,18}, {2,4}, {1,11}, {1,19}, {1,18}, {2,6}, {2,8}, {2,16}, {2,15}, {1,21}, {1,9}, {2,5}, {2,10}, {2,12}, {2,9}, {2,14}, {1,8}, {1,6} }; // ET22.22 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 81749606400 EdgePairs[22][22]:={ {11,17}, {1,11}, {5,17}, {1,20}, {11,20}, {6,16}, {13,21}, {7,15}, {8,12}, {14,19}, {3,22}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {8,9}, {12,22}, {3,9}, {3,6}, {3,13}, {3,15}, {17,20}, {2,15}, {4,19}, {16,19}, {7,22}, {2,19}, {1,19}, {2,4}, {5,20}, {20,21}, {1,21}, {16,18}, {2,9}, {11,14}, {17,21}, {18,21}, {8,10}, {6,7}, {2,14}, {8,15}, {6,11}, {3,5}, {9,11}, {13,16}, {10,15}, {10,22}, {19,21}, {6,22}, {3,18}, {3,17}, {3,7}, {8,16}, {6,21}, {7,12}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {19,22}, {6,8}, {11,13}, {11,15}, {3,12}, {11,22}, {7,13}, {9,14}, {1,22}, {6,12}, {12,13}, {12,16}, {4,21}, {3,20}, {13,22}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {5,18}, {14,15}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {8,22}, {1,9}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {16,22}, {9,22}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {14,18}, {14,22}, {12,19}, {18,19}, {12,14}, {3,21}, {17,19}, {2,7}, {9,12}, {6,19}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {2,11}, {10,11}, {4,5}, {14,20}, {15,21}, {16,17}, {16,21}, {3,16}, {15,18}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {2,22}, {1,16}, {4,14}, {15,22}, {5,8}, {18,22}, {9,17}, {10,18}, {16,20}, {7,9}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {1,4}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {2,12}, {1,14}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {17,22}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET22.23 // Bipartite(1,21) Valencies [21,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 51090942171709440000 EdgePairs[22][23]:={ {1,13}, {1,22}, {1,16}, {1,14}, {1,17}, {1,20}, {1,3}, {1,19}, {1,4}, {1,9}, {1,2}, {1,8}, {1,15}, {1,5}, {1,10}, {1,6}, {1,11}, {1,21}, {1,12}, {1,7}, {1,18} }; // ET22.24 // Non-bipartite Valency 21 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 1124000727777607680000 EdgePairs[22][24]:={ {11,17}, {19,20}, {1,11}, {5,17}, {1,20}, {11,20}, {6,16}, {13,21}, {7,15}, {8,12}, {14,19}, {3,22}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {8,9}, {12,22}, {3,9}, {3,6}, {3,13}, {3,15}, {17,20}, {2,15}, {4,19}, {16,19}, {7,22}, {2,19}, {7,8}, {1,19}, {2,4}, {5,20}, {20,21}, {1,21}, {16,18}, {2,9}, {11,14}, {21,22}, {17,21}, {18,21}, {8,10}, {6,7}, {11,12}, {2,14}, {8,15}, {6,11}, {3,5}, {9,11}, {13,16}, {10,15}, {10,22}, {19,21}, {15,16}, {6,22}, {3,18}, {3,17}, {3,7}, {8,16}, {6,21}, {7,12}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {19,22}, {6,8}, {11,13}, {11,15}, {3,12}, {11,22}, {7,13}, {9,14}, {1,22}, {6,12}, {12,13}, {12,16}, {4,21}, {3,20}, {1,2}, {13,22}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {3,4}, {5,18}, {14,15}, {2,6}, {7,17}, {8,11}, {5,7}, {8,13}, {8,22}, {1,9}, {9,10}, {15,20}, {17,18}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {16,22}, {9,22}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {14,18}, {14,22}, {12,19}, {18,19}, {12,14}, {3,21}, {17,19}, {2,7}, {6,19}, {9,12}, {6,9}, {13,15}, {1,15}, {12,15}, {6,14}, {2,11}, {10,11}, {4,5}, {14,20}, {15,21}, {16,17}, {16,21}, {3,16}, {15,18}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {2,22}, {1,16}, {4,14}, {15,22}, {5,8}, {18,22}, {9,17}, {10,18}, {16,20}, {7,9}, {13,14}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {1,4}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {5,6}, {2,12}, {1,14}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {17,22}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // Total number of connected ET graphs of order 22 is 24 // ******************************************************************************************** // Order 23 // ET23.1 // Non-bipartite Valency 2 // Diameter 11 Girth 23 // Twin-free VT AT // Automorphism group of order 46 EdgePairs[23][1]:={ {8,13}, {4,9}, {4,22}, {9,14}, {10,15}, {11,16}, {3,21}, {12,17}, {1,6}, {5,23}, {16,21}, {6,11}, {5,10}, {15,20}, {1,19}, {2,7}, {13,18}, {18,23}, {14,19}, {7,12}, {3,8}, {17,22}, {2,20} }; // ET23.2 // Bipartite(11,12) Valencies [12,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 19120211066880000 EdgePairs[23][2]:={ {1,15}, {9,13}, {10,19}, {7,19}, {6,12}, {11,15}, {5,14}, {10,21}, {3,15}, {11,17}, {10,22}, {6,18}, {11,23}, {4,14}, {2,22}, {6,14}, {6,17}, {6,23}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {9,21}, {11,16}, {11,22}, {7,23}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {6,22}, {5,21}, {10,23}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {2,14}, {5,23}, {4,20}, {2,23}, {1,17}, {3,13}, {2,16}, {10,12}, {1,22}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {3,22}, {5,19}, {9,23}, {5,15}, {7,20}, {7,13}, {8,17}, {3,23}, {7,14}, {6,15}, {1,19}, {11,18}, {4,21}, {4,17}, {4,15}, {9,15}, {8,19}, {11,14}, {11,13}, {5,22}, {6,19}, {1,23}, {2,21}, {11,12}, {11,19}, {7,18}, {2,12}, {4,22}, {5,20}, {10,14}, {8,16}, {5,17}, {3,12}, {8,20}, {8,23}, {7,16}, {6,20}, {6,16}, {11,21}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {7,22}, {3,16}, {1,13}, {4,18}, {3,20}, {7,21}, {11,20}, {5,12}, {9,14}, {3,17}, {10,20}, {5,18}, {9,16}, {7,17}, {4,23}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {8,12}, {9,20}, {9,22} }; // ET23.3 // Bipartite(10,13) Valencies [13,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 22596613079040000 EdgePairs[23][3]:={ {1,15}, {9,13}, {10,19}, {7,19}, {6,12}, {5,14}, {10,21}, {3,15}, {10,22}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {6,23}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {9,21}, {7,23}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {7,11}, {6,22}, {5,21}, {10,23}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {2,14}, {5,23}, {3,11}, {4,20}, {6,11}, {2,23}, {1,17}, {3,13}, {2,16}, {10,12}, {1,22}, {1,16}, {6,21}, {10,13}, {2,17}, {8,18}, {8,21}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {3,22}, {5,19}, {9,23}, {5,15}, {7,20}, {7,13}, {8,17}, {3,23}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {9,15}, {8,19}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {7,18}, {2,12}, {4,22}, {5,20}, {10,14}, {8,16}, {5,17}, {3,12}, {8,20}, {8,23}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {3,20}, {7,21}, {5,12}, {9,14}, {3,17}, {10,20}, {5,18}, {9,16}, {7,17}, {4,23}, {7,12}, {5,16}, {4,13}, {1,21}, {10,11}, {1,18}, {4,19}, {8,12}, {9,20}, {9,22} }; // ET23.4 // Bipartite(9,14) Valencies [14,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31635258310656000 EdgePairs[23][4]:={ {1,15}, {9,13}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {6,23}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {9,21}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {9,10}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {7,11}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {7,10}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {3,22}, {5,19}, {9,23}, {5,15}, {7,20}, {7,13}, {3,23}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {9,15}, {8,19}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {7,18}, {2,12}, {4,22}, {5,20}, {5,17}, {8,16}, {3,12}, {8,20}, {8,23}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {9,18}, {1,20}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {7,21}, {5,12}, {9,14}, {3,17}, {5,18}, {9,16}, {7,17}, {4,23}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {8,12}, {9,20}, {9,22} }; // ET23.5 // Bipartite(8,15) Valencies [15,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 52725430517760000 EdgePairs[23][5]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {6,23}, {2,20}, {4,16}, {6,13}, {1,9}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {8,14}, {8,13}, {7,11}, {6,22}, {5,9}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {7,10}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {7,20}, {7,13}, {3,23}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {2,9}, {8,19}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {7,18}, {8,9}, {2,12}, {4,22}, {5,20}, {5,17}, {8,16}, {3,12}, {8,20}, {8,23}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {7,9}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {7,21}, {5,12}, {3,17}, {4,9}, {5,18}, {7,17}, {4,23}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {8,12} }; // ET23.6 // Bipartite(7,16) Valencies [16,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 105450861035520000 EdgePairs[23][6]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {6,17}, {2,11}, {6,23}, {2,20}, {4,16}, {6,13}, {1,9}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {7,10}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {6,8}, {7,20}, {3,23}, {7,13}, {7,14}, {6,15}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,11}, {5,22}, {7,8}, {6,19}, {1,23}, {2,21}, {5,8}, {7,18}, {2,12}, {4,22}, {5,20}, {5,17}, {3,12}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {7,9}, {2,8}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,8}, {3,20}, {7,21}, {5,12}, {3,17}, {4,9}, {5,18}, {7,17}, {4,23}, {1,8}, {5,16}, {7,12}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10} }; // ET23.7 // Bipartite(6,17) Valencies [17,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 256094948229120000 EdgePairs[23][7]:={ {1,15}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {6,17}, {3,7}, {2,11}, {6,23}, {2,20}, {4,16}, {6,13}, {1,9}, {6,7}, {5,7}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {5,9}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {6,8}, {3,23}, {6,15}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {5,17}, {3,12}, {6,16}, {6,20}, {3,21}, {1,14}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,8}, {3,20}, {5,12}, {3,17}, {4,9}, {2,7}, {5,18}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10} }; // ET23.8 // Bipartite(5,18) Valencies [18,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 768284844687360000 EdgePairs[23][8]:={ {2,11}, {3,22}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {4,23}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {5,10}, {3,21}, {1,6}, {2,6}, {5,11}, {4,7}, {1,20}, {1,12}, {5,15}, {3,8}, {3,23}, {4,16}, {3,9}, {2,12}, {3,20}, {5,8}, {2,21}, {4,6}, {5,9}, {5,16}, {5,23}, {5,21}, {4,12}, {5,20}, {5,7}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,16}, {3,15}, {3,17}, {5,19}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {5,17}, {5,6}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {4,22}, {3,6}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {1,9}, {1,22}, {2,13}, {2,8}, {4,14}, {1,23}, {4,19}, {1,11}, {5,22}, {2,22}, {3,10} }; // ET23.9 // Bipartite(4,19) Valencies [19,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2919482409811968000 EdgePairs[23][9]:={ {2,11}, {3,22}, {2,14}, {4,8}, {4,13}, {4,9}, {4,23}, {1,14}, {3,12}, {2,10}, {1,10}, {4,11}, {4,10}, {3,21}, {1,6}, {3,5}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {3,23}, {4,16}, {3,9}, {2,12}, {3,20}, {2,21}, {4,6}, {4,12}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {1,5}, {4,15}, {1,17}, {4,22}, {3,6}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {4,14}, {1,23}, {4,19}, {1,11}, {2,22}, {3,10} }; // ET23.10 // Bipartite(3,20) Valencies [20,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14597412049059840000 EdgePairs[23][10]:={ {2,11}, {3,22}, {2,14}, {1,14}, {3,12}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,23}, {3,9}, {2,12}, {2,4}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {1,5}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {1,23}, {1,11}, {2,22}, {3,10} }; // ET23.11 // Bipartite(2,21) Valencies [21,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 102181884343418880000 EdgePairs[23][11]:={ {1,4}, {1,20}, {1,3}, {1,14}, {1,23}, {2,17}, {1,7}, {2,11}, {2,19}, {1,5}, {1,15}, {2,21}, {1,22}, {1,16}, {1,10}, {2,22}, {2,7}, {1,12}, {2,13}, {1,13}, {1,17}, {2,3}, {2,20}, {2,18}, {2,4}, {1,11}, {2,23}, {1,19}, {1,18}, {2,6}, {2,8}, {2,16}, {2,15}, {1,21}, {1,9}, {2,5}, {2,10}, {2,12}, {2,9}, {2,14}, {1,8}, {1,6} }; // ET23.12 // Bipartite(1,22) Valencies [22,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 1124000727777607680000 EdgePairs[23][12]:={ {1,13}, {1,22}, {1,16}, {1,14}, {1,17}, {1,20}, {1,3}, {1,19}, {1,4}, {1,9}, {1,2}, {1,8}, {1,15}, {1,5}, {1,10}, {1,6}, {1,23}, {1,11}, {1,21}, {1,12}, {1,7}, {1,18} }; // ET23.13 // Non-bipartite Valency 22 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 25852016738884976640000 EdgePairs[23][13]:={ {11,17}, {19,20}, {21,23}, {1,11}, {5,17}, {1,20}, {11,20}, {6,16}, {13,21}, {7,15}, {8,12}, {14,19}, {3,22}, {3,8}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,9}, {12,22}, {3,9}, {3,6}, {3,13}, {3,15}, {10,23}, {17,20}, {2,15}, {4,19}, {16,19}, {7,22}, {2,19}, {7,8}, {1,19}, {2,4}, {5,20}, {20,21}, {1,21}, {16,18}, {2,9}, {11,14}, {21,22}, {17,21}, {18,21}, {8,10}, {6,7}, {11,12}, {2,14}, {8,15}, {6,11}, {16,23}, {4,23}, {3,5}, {9,11}, {13,16}, {10,15}, {10,22}, {19,21}, {15,16}, {6,22}, {3,18}, {3,17}, {3,7}, {8,16}, {6,21}, {7,12}, {14,23}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {19,22}, {6,8}, {11,13}, {11,15}, {17,23}, {3,12}, {11,22}, {7,13}, {9,14}, {1,22}, {6,12}, {12,13}, {12,16}, {5,23}, {4,21}, {3,20}, {1,2}, {13,22}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {3,4}, {5,18}, {14,15}, {1,23}, {11,23}, {2,6}, {7,17}, {8,11}, {5,7}, {13,23}, {8,13}, {8,22}, {1,9}, {9,10}, {15,20}, {17,18}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {10,12}, {6,23}, {3,10}, {2,3}, {1,3}, {16,22}, {9,22}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {14,18}, {12,23}, {22,23}, {14,22}, {12,19}, {20,23}, {3,23}, {8,23}, {18,19}, {12,14}, {3,21}, {17,19}, {2,7}, {6,19}, {9,12}, {6,9}, {13,15}, {1,15}, {12,15}, {18,23}, {6,14}, {2,11}, {10,11}, {4,5}, {14,20}, {15,21}, {16,17}, {16,21}, {3,16}, {15,18}, {7,23}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {2,22}, {1,16}, {4,14}, {15,22}, {5,8}, {18,22}, {9,17}, {10,18}, {16,20}, {7,9}, {13,14}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {1,4}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {15,23}, {5,6}, {2,12}, {1,14}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {17,22}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {19,23}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // Total number of connected ET graphs of order 23 is 13 // ******************************************************************************************** // Order 24 // ET24.1 // Bipartite(12,12) Valencies [2,2] // Diameter 12 Girth 24 // Twin-free VT AT // Automorphism group of order 48 EdgePairs[24][1]:={ {1,13}, {1,22}, {12,23}, {6,14}, {5,14}, {8,18}, {3,24}, {9,17}, {10,16}, {2,21}, {12,22}, {8,20}, {11,23}, {4,24}, {7,19}, {5,15}, {9,18}, {10,17}, {2,13}, {3,21}, {6,19}, {4,15}, {7,20}, {11,16} }; // ET24.2 // Bipartite(12,12) Valencies [3,3] // Diameter 4 Girth 6 // Twin-free VT AT // Automorphism group of order 144 EdgePairs[24][2]:={ {8,13}, {10,21}, {11,14}, {4,22}, {7,15}, {9,22}, {4,24}, {6,24}, {1,17}, {8,15}, {4,19}, {12,14}, {3,19}, {11,20}, {1,13}, {9,15}, {3,17}, {12,18}, {3,21}, {2,18}, {8,21}, {11,24}, {7,23}, {5,16}, {5,19}, {2,22}, {5,23}, {10,16}, {10,20}, {6,23}, {1,14}, {9,20}, {2,17}, {7,18}, {6,13}, {12,16} }; // ET24.3 // Bipartite(8,16) Valencies [4,2] // Diameter 4 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 1152 EdgePairs[24][3]:={ {8,24}, {5,11}, {6,17}, {3,15}, {5,14}, {4,9}, {7,16}, {3,22}, {6,14}, {8,22}, {4,19}, {8,23}, {3,19}, {1,13}, {6,18}, {6,12}, {2,13}, {8,21}, {7,23}, {2,10}, {2,15}, {4,11}, {7,17}, {1,18}, {5,10}, {5,21}, {4,16}, {1,24}, {7,20}, {1,9}, {3,12}, {2,20} }; // ET24.4 // Bipartite(8,16) Valencies [4,2] // Diameter 8 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4096 EdgePairs[24][4]:={ {5,12}, {8,24}, {7,16}, {7,15}, {3,22}, {8,9}, {6,14}, {1,17}, {4,19}, {5,20}, {1,10}, {2,19}, {3,21}, {2,18}, {7,23}, {2,11}, {2,10}, {4,11}, {4,12}, {3,14}, {6,15}, {6,23}, {6,22}, {8,17}, {5,13}, {1,18}, {8,16}, {5,21}, {4,20}, {1,9}, {7,24}, {3,13} }; // ET24.5 // Bipartite(12,12) Valencies [4,4] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 768 EdgePairs[24][5]:={ {3,22}, {4,13}, {4,24}, {10,15}, {8,19}, {9,23}, {8,20}, {5,24}, {9,21}, {9,16}, {11,24}, {12,16}, {8,21}, {8,15}, {11,20}, {9,15}, {1,20}, {3,23}, {11,23}, {3,20}, {2,21}, {5,16}, {6,16}, {5,19}, {2,18}, {4,21}, {7,15}, {3,14}, {12,14}, {12,19}, {1,17}, {10,17}, {12,22}, {5,18}, {6,17}, {1,13}, {7,17}, {1,19}, {10,22}, {2,13}, {4,14}, {7,14}, {11,18}, {6,23}, {2,22}, {6,13}, {10,18}, {7,24} }; // ET24.6 // Bipartite(12,12) Valencies [4,4] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 96 EdgePairs[24][6]:={ {6,20}, {4,20}, {3,24}, {3,16}, {11,22}, {4,24}, {7,23}, {12,16}, {4,17}, {1,14}, {9,19}, {5,18}, {12,19}, {2,17}, {10,13}, {1,24}, {2,19}, {11,13}, {7,20}, {12,23}, {9,22}, {9,23}, {3,18}, {7,17}, {7,15}, {8,15}, {3,21}, {6,18}, {10,23}, {8,18}, {4,14}, {5,15}, {1,13}, {6,24}, {12,21}, {6,22}, {10,21}, {5,16}, {8,13}, {5,17}, {8,22}, {10,15}, {2,16}, {1,21}, {9,20}, {11,19}, {11,14}, {2,14} }; // ET24.7 // Bipartite(12,12) Valencies [4,4] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 96 EdgePairs[24][7]:={ {6,20}, {3,24}, {1,20}, {11,17}, {8,21}, {4,24}, {7,23}, {9,16}, {5,13}, {5,14}, {4,17}, {1,14}, {3,19}, {5,18}, {10,13}, {2,19}, {3,23}, {12,22}, {9,22}, {12,18}, {7,17}, {6,23}, {7,15}, {1,22}, {3,21}, {10,23}, {8,18}, {6,16}, {4,14}, {12,24}, {10,20}, {8,14}, {1,13}, {2,13}, {11,21}, {12,21}, {4,22}, {8,17}, {5,16}, {10,15}, {2,16}, {2,15}, {6,19}, {7,24}, {11,15}, {9,20}, {9,18}, {11,19} }; // ET24.8 // Bipartite(12,12) Valencies [4,4] // Diameter 6 Girth 4 // Has twins VT AT // Automorphism group of order 98304 EdgePairs[24][8]:={ {2,14}, {11,16}, {10,15}, {8,19}, {8,20}, {1,24}, {12,18}, {11,17}, {9,20}, {9,21}, {3,21}, {7,13}, {9,15}, {11,23}, {4,16}, {3,20}, {5,16}, {5,23}, {10,16}, {2,20}, {3,15}, {7,18}, {4,21}, {11,22}, {5,17}, {8,13}, {12,23}, {3,14}, {12,24}, {1,18}, {4,15}, {7,19}, {6,18}, {4,22}, {2,19}, {9,14}, {6,17}, {1,13}, {8,14}, {1,19}, {10,22}, {10,21}, {2,13}, {12,17}, {5,22}, {6,23}, {7,24}, {6,24} }; // ET24.9 // Bipartite(12,12) Valencies [4,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3072 EdgePairs[24][9]:={ {6,20}, {8,20}, {11,18}, {6,21}, {4,24}, {7,23}, {12,16}, {5,13}, {4,17}, {5,24}, {1,23}, {5,18}, {5,21}, {12,19}, {10,16}, {9,15}, {11,13}, {9,22}, {8,23}, {3,18}, {1,15}, {3,15}, {10,14}, {7,15}, {4,16}, {2,22}, {6,16}, {4,14}, {8,14}, {3,17}, {1,13}, {11,21}, {2,20}, {12,20}, {3,22}, {11,24}, {12,21}, {2,23}, {10,24}, {1,19}, {8,22}, {7,13}, {6,19}, {9,18}, {10,17}, {9,17}, {7,19}, {2,14} }; // ET24.10 // Non-bipartite Valency 4 // Diameter 3 Girth 5 // Twin-free VT AT // Automorphism group of order 96 EdgePairs[24][10]:={ {19,23}, {9,23}, {7,11}, {14,18}, {7,9}, {21,23}, {15,20}, {1,6}, {3,5}, {20,21}, {19,22}, {4,7}, {5,15}, {3,8}, {2,12}, {20,24}, {11,21}, {4,6}, {2,21}, {6,16}, {8,10}, {22,24}, {5,7}, {2,16}, {1,15}, {16,18}, {17,19}, {9,12}, {10,11}, {10,14}, {8,12}, {3,18}, {2,5}, {15,17}, {4,17}, {10,24}, {9,13}, {16,19}, {12,22}, {14,23}, {13,24}, {3,13}, {18,20}, {1,22}, {4,14}, {1,11}, {13,17}, {6,8} }; // ET24.11 // Non-bipartite Valency 4 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 96 EdgePairs[24][11]:={ {2,11}, {4,8}, {4,13}, {19,24}, {20,22}, {8,9}, {20,23}, {7,12}, {8,11}, {2,6}, {1,12}, {9,11}, {10,12}, {6,7}, {6,15}, {5,8}, {13,18}, {5,16}, {10,13}, {4,18}, {7,10}, {9,24}, {21,24}, {10,23}, {3,7}, {15,19}, {1,16}, {17,20}, {19,21}, {3,17}, {1,21}, {11,22}, {2,15}, {3,14}, {18,19}, {4,5}, {1,5}, {13,23}, {22,23}, {16,20}, {3,6}, {9,14}, {14,24}, {16,17}, {14,17}, {15,18}, {2,22}, {12,21} }; // ET24.12 // Bipartite(12,12) Valencies [5,5] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 480 EdgePairs[24][12]:={ {12,20}, {4,24}, {8,19}, {11,16}, {4,23}, {1,14}, {9,23}, {11,15}, {9,20}, {11,17}, {2,24}, {12,16}, {8,21}, {3,21}, {8,15}, {5,15}, {8,24}, {3,23}, {5,16}, {6,16}, {5,20}, {3,16}, {2,20}, {10,23}, {7,18}, {5,19}, {7,15}, {2,15}, {3,14}, {3,18}, {12,24}, {4,17}, {1,18}, {7,22}, {7,21}, {9,13}, {11,13}, {4,22}, {6,19}, {10,19}, {9,18}, {5,18}, {1,13}, {8,14}, {7,17}, {1,19}, {10,22}, {10,21}, {1,22}, {2,13}, {4,14}, {10,20}, {12,17}, {11,14}, {6,23}, {2,22}, {6,13}, {9,17}, {6,24}, {12,21} }; // ET24.13 // Bipartite(6,18) Valencies [6,2] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 559872 EdgePairs[24][13]:={ {6,7}, {1,20}, {3,16}, {6,13}, {3,10}, {4,17}, {5,24}, {1,14}, {5,18}, {4,23}, {1,7}, {3,15}, {2,21}, {4,16}, {3,21}, {6,18}, {6,12}, {5,12}, {1,13}, {5,23}, {2,20}, {6,24}, {3,22}, {4,22}, {3,9}, {4,11}, {5,11}, {1,19}, {5,17}, {2,8}, {2,15}, {6,19}, {4,10}, {2,9}, {2,14}, {1,8} }; // ET24.14 // Bipartite(6,18) Valencies [6,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 36864 EdgePairs[24][14]:={ {4,20}, {6,13}, {6,21}, {3,10}, {5,13}, {5,24}, {3,19}, {4,7}, {2,24}, {1,7}, {3,23}, {3,14}, {6,8}, {5,20}, {4,16}, {3,21}, {5,22}, {6,12}, {1,16}, {4,19}, {5,15}, {1,17}, {6,17}, {2,18}, {4,11}, {6,22}, {5,11}, {2,23}, {1,18}, {3,12}, {2,15}, {1,9}, {4,10}, {2,9}, {2,14}, {1,8} }; // ET24.15 // Bipartite(8,16) Valencies [6,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12288 EdgePairs[24][15]:={ {2,11}, {4,24}, {4,23}, {7,11}, {1,24}, {3,12}, {2,10}, {7,12}, {8,16}, {8,21}, {4,10}, {3,21}, {6,12}, {6,10}, {5,15}, {8,24}, {3,23}, {4,16}, {3,20}, {2,21}, {5,9}, {5,23}, {4,18}, {1,16}, {3,15}, {6,20}, {2,18}, {5,17}, {8,13}, {7,22}, {8,22}, {4,15}, {7,20}, {1,17}, {7,19}, {6,18}, {2,19}, {5,14}, {3,13}, {6,17}, {8,14}, {1,19}, {1,9}, {2,13}, {7,14}, {1,11}, {5,22}, {6,9} }; // ET24.16 // Bipartite(12,12) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 288 EdgePairs[24][16]:={ {3,22}, {4,13}, {4,24}, {11,16}, {9,19}, {1,14}, {9,23}, {7,16}, {12,18}, {9,20}, {11,17}, {7,23}, {8,21}, {3,21}, {8,15}, {11,20}, {9,15}, {5,15}, {3,23}, {3,24}, {6,15}, {3,20}, {11,21}, {2,21}, {5,16}, {5,20}, {10,13}, {2,16}, {10,16}, {1,16}, {2,20}, {10,23}, {6,20}, {8,13}, {2,15}, {6,21}, {3,18}, {12,19}, {12,24}, {4,17}, {7,22}, {10,24}, {4,22}, {6,19}, {9,22}, {10,19}, {9,18}, {10,17}, {12,22}, {5,14}, {2,17}, {5,18}, {1,13}, {8,14}, {8,18}, {5,13}, {1,19}, {7,17}, {1,22}, {2,13}, {4,14}, {1,23}, {12,15}, {7,14}, {4,19}, {11,18}, {11,14}, {8,17}, {6,23}, {7,24}, {6,24}, {12,21} }; // ET24.17 // Bipartite(12,12) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1152 EdgePairs[24][17]:={ {3,22}, {2,14}, {8,19}, {10,15}, {11,16}, {4,23}, {9,19}, {1,14}, {8,20}, {12,18}, {6,14}, {11,24}, {8,15}, {7,13}, {9,15}, {5,15}, {8,24}, {3,23}, {11,23}, {6,15}, {3,20}, {2,21}, {5,16}, {6,16}, {5,21}, {10,13}, {4,18}, {10,16}, {3,16}, {2,20}, {1,16}, {10,23}, {7,18}, {6,20}, {1,21}, {4,21}, {4,20}, {3,19}, {12,23}, {6,21}, {12,24}, {7,22}, {8,22}, {10,24}, {4,15}, {7,20}, {9,13}, {1,17}, {9,18}, {10,17}, {12,22}, {2,17}, {5,18}, {9,14}, {3,13}, {2,23}, {5,13}, {1,19}, {1,22}, {2,13}, {7,14}, {4,19}, {11,19}, {11,18}, {12,17}, {11,14}, {5,22}, {8,17}, {7,24}, {9,17}, {6,24}, {12,21} }; // ET24.18 // Bipartite(12,12) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1152 EdgePairs[24][18]:={ {3,22}, {2,14}, {4,13}, {12,20}, {4,24}, {8,19}, {4,23}, {9,19}, {1,14}, {7,16}, {5,24}, {12,18}, {9,20}, {11,17}, {2,24}, {9,21}, {8,16}, {3,21}, {8,15}, {11,20}, {9,15}, {5,15}, {3,23}, {11,23}, {11,21}, {5,16}, {6,16}, {5,21}, {10,13}, {4,18}, {10,16}, {1,15}, {9,24}, {3,16}, {2,20}, {7,18}, {4,21}, {5,17}, {8,13}, {3,14}, {3,18}, {12,13}, {4,15}, {7,20}, {1,17}, {6,19}, {10,19}, {12,22}, {9,14}, {6,17}, {2,23}, {8,14}, {8,18}, {7,17}, {1,19}, {10,22}, {10,21}, {1,22}, {2,13}, {1,23}, {12,15}, {7,14}, {11,19}, {10,20}, {11,18}, {12,17}, {5,22}, {6,23}, {2,22}, {6,13}, {7,24}, {6,24} }; // ET24.19 // Bipartite(12,12) Valencies [6,6] // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 26873856 EdgePairs[24][19]:={ {2,14}, {4,13}, {8,19}, {11,16}, {4,23}, {1,14}, {11,15}, {7,16}, {2,24}, {7,23}, {9,21}, {8,23}, {6,14}, {11,24}, {8,21}, {8,15}, {11,20}, {3,23}, {11,23}, {3,24}, {3,20}, {6,16}, {5,21}, {2,16}, {10,16}, {3,16}, {2,20}, {3,15}, {6,20}, {2,18}, {1,21}, {4,21}, {3,19}, {5,17}, {7,15}, {8,13}, {10,14}, {12,23}, {12,13}, {12,19}, {4,17}, {1,18}, {10,24}, {4,15}, {7,20}, {9,13}, {1,17}, {7,19}, {6,18}, {9,22}, {6,22}, {9,18}, {5,14}, {5,18}, {9,14}, {1,13}, {5,13}, {10,22}, {1,22}, {12,15}, {4,19}, {11,19}, {10,20}, {12,17}, {5,22}, {8,17}, {2,22}, {7,24}, {9,17}, {10,18}, {6,24}, {12,21} }; // ET24.20 // Bipartite(12,12) Valencies [6,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1990656 EdgePairs[24][20]:={ {2,14}, {4,24}, {4,23}, {9,19}, {11,15}, {1,24}, {5,24}, {12,18}, {11,17}, {7,23}, {9,21}, {8,16}, {8,23}, {6,14}, {12,16}, {3,21}, {11,20}, {9,15}, {5,15}, {8,24}, {3,23}, {11,23}, {4,16}, {3,20}, {11,21}, {6,16}, {5,21}, {10,13}, {4,18}, {2,16}, {10,16}, {1,15}, {9,24}, {2,20}, {3,15}, {6,20}, {3,17}, {5,19}, {1,21}, {7,15}, {10,14}, {12,23}, {3,14}, {12,24}, {4,17}, {1,18}, {7,21}, {8,22}, {7,20}, {9,13}, {4,22}, {6,19}, {10,19}, {6,22}, {2,19}, {9,18}, {12,22}, {5,18}, {1,13}, {8,18}, {5,13}, {1,19}, {7,17}, {10,22}, {2,13}, {7,14}, {10,20}, {12,17}, {11,14}, {8,17}, {2,22}, {6,13} }; // ET24.21 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 144 EdgePairs[24][21]:={ {4,8}, {4,13}, {19,23}, {9,19}, {4,23}, {9,23}, {11,15}, {1,24}, {14,18}, {20,22}, {8,9}, {7,12}, {13,16}, {15,20}, {8,11}, {12,16}, {1,6}, {3,5}, {1,4}, {6,10}, {5,15}, {17,22}, {3,24}, {2,12}, {6,7}, {20,24}, {5,8}, {4,6}, {5,9}, {6,16}, {5,20}, {10,13}, {4,18}, {2,16}, {7,10}, {1,15}, {21,24}, {3,7}, {17,20}, {19,21}, {3,17}, {1,21}, {9,12}, {2,3}, {10,11}, {11,22}, {3,14}, {12,14}, {18,19}, {2,5}, {7,21}, {8,22}, {10,24}, {13,23}, {22,23}, {11,13}, {16,19}, {18,21}, {6,19}, {9,14}, {2,23}, {8,18}, {14,24}, {7,17}, {16,17}, {14,15}, {10,20}, {1,11}, {15,18}, {2,22}, {13,17}, {12,21} }; // ET24.22 // Non-bipartite Valency 7 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[24][22]:={ {3,22}, {2,14}, {10,15}, {13,19}, {4,23}, {7,16}, {1,24}, {9,20}, {21,23}, {7,12}, {8,23}, {15,20}, {8,11}, {1,10}, {11,24}, {8,21}, {1,6}, {11,20}, {6,10}, {5,11}, {9,15}, {19,22}, {4,7}, {15,23}, {3,8}, {4,16}, {2,12}, {20,24}, {3,20}, {2,21}, {5,9}, {4,12}, {1,7}, {3,4}, {10,16}, {1,15}, {3,11}, {3,16}, {9,10}, {17,20}, {5,19}, {4,20}, {8,13}, {12,23}, {18,19}, {6,21}, {2,5}, {12,13}, {12,19}, {16,21}, {1,18}, {13,22}, {4,15}, {16,22}, {7,19}, {9,22}, {14,21}, {5,14}, {2,17}, {18,23}, {5,18}, {3,13}, {6,17}, {2,23}, {8,18}, {14,24}, {1,19}, {2,9}, {10,22}, {10,21}, {7,14}, {11,18}, {12,17}, {11,14}, {5,22}, {14,16}, {15,18}, {13,17}, {6,13}, {7,24}, {9,17}, {17,24}, {6,8}, {6,24} }; // ET24.23 // Bipartite(8,16) Valencies [8,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 384 EdgePairs[24][23]:={ {5,12}, {3,22}, {2,14}, {4,24}, {4,23}, {1,24}, {7,23}, {2,10}, {8,9}, {7,12}, {8,16}, {1,10}, {4,11}, {4,10}, {3,21}, {8,15}, {6,12}, {5,11}, {1,20}, {3,9}, {3,20}, {2,21}, {5,16}, {6,16}, {5,23}, {5,21}, {4,12}, {7,10}, {1,15}, {3,11}, {3,16}, {2,20}, {7,18}, {4,21}, {4,20}, {3,19}, {5,17}, {7,15}, {8,13}, {2,15}, {1,18}, {8,22}, {6,18}, {6,19}, {5,14}, {3,13}, {6,17}, {2,23}, {8,14}, {8,18}, {5,13}, {1,19}, {7,17}, {6,11}, {1,9}, {1,22}, {2,13}, {7,14}, {4,19}, {8,17}, {2,22}, {7,24}, {6,24}, {6,9} }; // ET24.24 // Bipartite(8,16) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 42467328 EdgePairs[24][24]:={ {5,12}, {2,14}, {8,19}, {4,23}, {7,11}, {7,16}, {1,24}, {3,12}, {5,24}, {7,23}, {2,10}, {7,12}, {8,23}, {6,14}, {8,11}, {4,11}, {4,10}, {8,15}, {6,10}, {1,20}, {1,12}, {3,23}, {3,24}, {3,20}, {2,21}, {5,9}, {5,16}, {5,21}, {8,10}, {5,20}, {4,18}, {3,11}, {3,16}, {1,16}, {3,15}, {2,18}, {1,21}, {3,19}, {5,17}, {7,15}, {6,21}, {8,22}, {4,15}, {7,20}, {1,17}, {7,19}, {6,18}, {4,22}, {6,22}, {2,17}, {6,17}, {1,13}, {8,14}, {8,18}, {5,13}, {2,9}, {1,9}, {2,13}, {4,14}, {4,19}, {2,22}, {6,13}, {7,24}, {6,9} }; // ET24.25 // Bipartite(8,16) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 49152 EdgePairs[24][25]:={ {5,12}, {3,22}, {2,14}, {4,13}, {4,24}, {7,11}, {7,16}, {1,24}, {2,24}, {7,23}, {8,9}, {8,23}, {4,11}, {5,10}, {3,21}, {8,15}, {6,12}, {5,11}, {6,10}, {1,20}, {1,12}, {5,15}, {4,16}, {2,21}, {5,23}, {8,10}, {5,20}, {4,12}, {2,16}, {1,15}, {3,11}, {1,16}, {6,20}, {5,19}, {4,21}, {4,20}, {3,19}, {7,15}, {3,14}, {3,18}, {6,21}, {7,22}, {8,22}, {1,17}, {7,19}, {6,18}, {2,17}, {5,18}, {3,13}, {6,17}, {8,14}, {8,18}, {2,9}, {1,9}, {2,13}, {1,23}, {4,19}, {7,14}, {8,17}, {2,22}, {6,13}, {7,24}, {3,10}, {6,9} }; // ET24.26 // Bipartite(12,12) Valencies [8,8] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 2293235712 EdgePairs[24][26]:={ {2,14}, {4,13}, {12,20}, {4,24}, {8,19}, {10,15}, {11,16}, {9,23}, {7,16}, {8,20}, {1,24}, {12,18}, {9,20}, {11,17}, {9,21}, {8,16}, {8,23}, {6,14}, {3,21}, {11,20}, {7,13}, {9,15}, {3,23}, {11,23}, {4,16}, {3,24}, {6,15}, {3,20}, {5,16}, {5,23}, {5,20}, {10,13}, {4,18}, {2,16}, {10,16}, {1,15}, {9,24}, {1,16}, {2,20}, {3,15}, {7,18}, {6,20}, {3,17}, {5,19}, {1,21}, {4,21}, {11,22}, {5,17}, {7,15}, {8,13}, {12,23}, {3,14}, {12,14}, {3,18}, {6,21}, {12,24}, {1,18}, {7,22}, {7,21}, {8,22}, {10,24}, {4,15}, {11,13}, {7,19}, {6,18}, {4,22}, {10,19}, {2,19}, {9,18}, {5,14}, {2,17}, {9,14}, {6,17}, {2,23}, {1,13}, {8,14}, {5,13}, {1,19}, {10,22}, {10,21}, {1,22}, {2,13}, {12,15}, {4,19}, {11,19}, {12,17}, {11,14}, {5,22}, {8,17}, {2,22}, {6,23}, {7,24}, {9,17}, {10,18}, {6,24}, {12,21} }; // ET24.27 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 196608 EdgePairs[24][27]:={ {2,11}, {3,22}, {4,13}, {4,24}, {8,19}, {13,19}, {4,23}, {9,19}, {7,11}, {9,23}, {14,19}, {8,20}, {1,24}, {12,18}, {9,20}, {11,17}, {7,9}, {2,24}, {2,10}, {8,9}, {7,12}, {1,10}, {6,14}, {8,11}, {3,21}, {5,15}, {1,12}, {3,23}, {4,16}, {3,24}, {2,12}, {6,15}, {11,21}, {2,21}, {5,16}, {6,16}, {8,10}, {5,20}, {15,21}, {7,10}, {9,24}, {3,16}, {10,23}, {3,15}, {16,18}, {7,18}, {6,20}, {5,19}, {1,21}, {4,21}, {11,22}, {5,17}, {3,14}, {8,12}, {13,20}, {15,17}, {16,21}, {10,24}, {4,15}, {16,22}, {7,20}, {13,23}, {7,19}, {6,18}, {4,22}, {6,19}, {10,19}, {12,22}, {14,23}, {5,14}, {5,18}, {13,24}, {3,13}, {6,17}, {2,23}, {14,20}, {8,18}, {14,24}, {5,13}, {2,9}, {7,17}, {16,17}, {1,9}, {1,22}, {4,14}, {1,23}, {10,20}, {11,18}, {12,17}, {1,11}, {8,17}, {15,18}, {2,22}, {6,13}, {12,21}, {15,22} }; // ET24.28 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1152 EdgePairs[24][28]:={ {1,15}, {9,13}, {14,21}, {11,15}, {8,24}, {6,10}, {4,14}, {1,11}, {12,19}, {6,14}, {12,16}, {2,3}, {13,24}, {17,19}, {14,18}, {9,12}, {12,22}, {20,21}, {16,18}, {16,23}, {9,19}, {19,23}, {7,23}, {7,15}, {5,7}, {18,21}, {4,6}, {5,13}, {2,18}, {22,24}, {9,17}, {10,18}, {7,11}, {6,22}, {5,9}, {5,21}, {3,18}, {8,22}, {2,23}, {1,10}, {4,7}, {14,16}, {1,17}, {3,13}, {2,16}, {1,22}, {8,10}, {8,18}, {16,19}, {9,23}, {10,24}, {5,15}, {6,8}, {20,24}, {15,20}, {4,17}, {2,9}, {3,5}, {1,4}, {13,22}, {11,14}, {4,11}, {6,19}, {17,22}, {2,21}, {14,23}, {2,12}, {5,20}, {10,14}, {8,16}, {3,24}, {3,12}, {21,23}, {11,21}, {18,20}, {6,16}, {19,22}, {7,9}, {3,8}, {13,17}, {15,17}, {11,20}, {13,15}, {7,21}, {3,20}, {10,20}, {7,17}, {4,23}, {10,11}, {1,6}, {15,24}, {4,19}, {2,5}, {12,13}, {8,12}, {1,24} }; // ET24.29 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1152 EdgePairs[24][29]:={ {10,19}, {5,14}, {15,23}, {2,22}, {4,8}, {3,7}, {13,18}, {2,11}, {7,24}, {12,15}, {6,13}, {12,14}, {20,23}, {1,9}, {4,5}, {1,5}, {19,24}, {11,16}, {6,7}, {11,22}, {16,20}, {2,15}, {6,9}, {10,23}, {3,19}, {4,12}, {8,15}, {12,21}, {13,16}, {7,10}, {3,11}, {1,3}, {2,10}, {4,20}, {10,12}, {1,16}, {16,17}, {6,21}, {10,13}, {8,21}, {2,17}, {3,14}, {1,12}, {5,19}, {3,23}, {8,17}, {22,23}, {6,15}, {8,11}, {15,19}, {18,19}, {2,4}, {2,24}, {11,13}, {5,22}, {14,17}, {1,23}, {14,22}, {15,18}, {5,8}, {11,19}, {7,18}, {8,9}, {9,24}, {8,23}, {7,16}, {6,20}, {2,6}, {17,21}, {10,17}, {9,18}, {13,21}, {14,15}, {9,11}, {7,22}, {4,18}, {5,10}, {13,23}, {3,6}, {9,14}, {3,17}, {18,22}, {17,20}, {20,22}, {19,21}, {7,12}, {5,16}, {4,13}, {1,21}, {12,20}, {1,18}, {14,24}, {21,24}, {4,24}, {9,20}, {16,24} }; // ET24.30 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 384 EdgePairs[24][30]:={ {3,22}, {2,14}, {12,20}, {4,9}, {8,19}, {10,15}, {11,16}, {13,19}, {19,24}, {1,14}, {9,23}, {14,19}, {7,16}, {3,12}, {12,18}, {9,20}, {21,23}, {7,23}, {2,10}, {8,16}, {1,10}, {11,24}, {12,16}, {5,10}, {8,21}, {3,21}, {11,20}, {15,24}, {6,10}, {5,11}, {9,15}, {4,7}, {5,15}, {1,12}, {11,23}, {3,9}, {2,12}, {20,24}, {5,8}, {5,16}, {5,21}, {4,12}, {4,18}, {2,16}, {9,24}, {3,16}, {3,7}, {2,20}, {3,15}, {7,18}, {6,20}, {1,21}, {4,20}, {11,22}, {2,15}, {3,14}, {4,17}, {1,18}, {7,21}, {13,23}, {22,23}, {13,21}, {1,17}, {7,19}, {6,18}, {13,15}, {6,19}, {9,22}, {14,21}, {2,19}, {10,17}, {12,22}, {18,23}, {13,24}, {6,17}, {1,8}, {8,18}, {5,13}, {6,11}, {10,22}, {1,22}, {4,14}, {2,8}, {4,19}, {14,15}, {16,24}, {10,20}, {11,18}, {14,17}, {5,22}, {13,17}, {6,13}, {7,24}, {9,17}, {6,8}, {17,23} }; // ET24.31 // Bipartite(12,12) Valencies [9,9] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 80621568 EdgePairs[24][31]:={ {9,13}, {10,19}, {7,19}, {11,15}, {5,14}, {10,21}, {3,15}, {8,24}, {10,22}, {6,18}, {11,23}, {12,19}, {2,22}, {6,14}, {6,17}, {12,16}, {7,24}, {6,23}, {4,16}, {6,13}, {12,15}, {12,17}, {5,24}, {9,21}, {11,16}, {11,22}, {7,23}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,13}, {9,17}, {10,18}, {6,22}, {5,21}, {10,23}, {3,19}, {3,18}, {8,15}, {12,21}, {2,14}, {4,20}, {2,23}, {1,17}, {1,22}, {1,16}, {6,21}, {10,13}, {8,21}, {2,17}, {3,14}, {2,13}, {10,15}, {3,22}, {7,20}, {3,23}, {8,17}, {7,14}, {6,15}, {11,18}, {4,21}, {4,17}, {4,15}, {8,19}, {11,14}, {12,24}, {12,23}, {5,22}, {6,19}, {2,21}, {11,19}, {7,18}, {5,20}, {10,14}, {8,16}, {5,17}, {3,24}, {9,24}, {8,20}, {8,23}, {7,16}, {1,14}, {9,18}, {10,17}, {1,20}, {7,22}, {3,16}, {1,13}, {3,20}, {11,20}, {9,14}, {5,18}, {9,16}, {4,23}, {11,24}, {5,16}, {4,13}, {1,21}, {1,18}, {12,20}, {4,19}, {4,24}, {12,13}, {9,20}, {1,24}, {9,22} }; // ET24.32 // Bipartite(4,20) Valencies [10,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1658880000 EdgePairs[24][32]:={ {3,24}, {1,20}, {3,16}, {4,6}, {3,20}, {3,19}, {4,7}, {2,17}, {4,23}, {1,24}, {3,23}, {3,8}, {1,5}, {4,15}, {3,15}, {2,21}, {4,18}, {1,16}, {2,22}, {4,14}, {4,19}, {3,11}, {1,12}, {2,13}, {1,13}, {1,17}, {2,18}, {4,11}, {4,22}, {2,6}, {3,12}, {1,21}, {1,9}, {2,5}, {2,10}, {4,10}, {2,9}, {3,7}, {2,14}, {1,8} }; // ET24.33 // Bipartite(9,15) Valencies [10,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2239488000 EdgePairs[24][33]:={ {2,11}, {3,22}, {5,12}, {2,14}, {4,13}, {4,23}, {9,19}, {1,14}, {7,11}, {7,16}, {8,20}, {3,12}, {5,24}, {2,24}, {7,23}, {9,21}, {9,16}, {8,23}, {1,10}, {8,11}, {4,11}, {4,10}, {8,21}, {3,21}, {8,15}, {6,12}, {7,13}, {6,10}, {5,11}, {9,15}, {1,20}, {5,15}, {8,24}, {4,16}, {3,24}, {2,12}, {6,15}, {2,21}, {6,16}, {5,23}, {5,21}, {5,20}, {7,10}, {9,24}, {3,16}, {2,20}, {1,16}, {3,15}, {9,10}, {2,18}, {9,12}, {4,20}, {3,19}, {5,17}, {2,15}, {8,12}, {3,18}, {6,21}, {4,17}, {7,22}, {7,20}, {9,13}, {1,17}, {7,19}, {4,22}, {6,18}, {6,19}, {9,22}, {6,22}, {9,18}, {5,14}, {2,17}, {5,18}, {3,13}, {2,23}, {1,13}, {8,14}, {8,18}, {1,19}, {7,17}, {1,22}, {4,14}, {1,23}, {4,19}, {7,14}, {1,11}, {8,17}, {6,13}, {6,24}, {3,10} }; // ET24.34 // Bipartite(12,12) Valencies [10,10] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 5898240 EdgePairs[24][34]:={ {1,15}, {10,19}, {9,13}, {7,19}, {11,15}, {5,14}, {3,15}, {11,17}, {8,24}, {10,22}, {6,18}, {11,23}, {4,14}, {12,19}, {2,22}, {6,14}, {6,17}, {7,24}, {6,23}, {2,20}, {4,16}, {6,13}, {12,15}, {12,17}, {12,14}, {9,19}, {9,21}, {11,16}, {12,18}, {11,22}, {7,15}, {5,13}, {2,18}, {2,15}, {8,14}, {9,17}, {10,18}, {5,21}, {10,23}, {3,19}, {3,18}, {8,22}, {8,15}, {12,21}, {2,14}, {5,23}, {4,20}, {2,23}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {10,16}, {3,22}, {9,23}, {5,19}, {10,24}, {5,15}, {7,20}, {7,13}, {8,17}, {3,23}, {7,14}, {6,15}, {1,19}, {4,17}, {9,15}, {11,14}, {12,24}, {12,23}, {2,24}, {11,13}, {5,22}, {6,19}, {2,21}, {11,19}, {7,18}, {5,20}, {4,22}, {10,14}, {8,16}, {5,17}, {3,24}, {9,24}, {8,20}, {8,23}, {7,16}, {6,20}, {11,21}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {7,22}, {3,16}, {1,13}, {4,18}, {7,21}, {11,20}, {3,17}, {10,20}, {6,24}, {9,16}, {4,23}, {5,16}, {4,13}, {1,21}, {1,18}, {12,20}, {4,19}, {4,24}, {12,13}, {1,24}, {9,22} }; // ET24.35 // Non-bipartite Valency 10 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 491520 EdgePairs[24][35]:={ {9,13}, {10,19}, {11,15}, {6,12}, {15,23}, {6,10}, {4,14}, {1,11}, {4,8}, {3,7}, {13,18}, {12,16}, {2,11}, {2,20}, {13,24}, {14,19}, {17,19}, {14,18}, {12,15}, {12,22}, {16,23}, {9,19}, {1,5}, {11,16}, {11,22}, {14,20}, {2,19}, {2,18}, {6,9}, {22,24}, {7,11}, {5,9}, {13,20}, {10,23}, {3,18}, {8,22}, {12,21}, {16,21}, {6,11}, {15,22}, {4,7}, {1,17}, {3,13}, {10,13}, {8,21}, {8,18}, {2,17}, {3,14}, {10,15}, {1,12}, {10,16}, {3,22}, {9,23}, {10,24}, {5,19}, {5,15}, {3,23}, {8,17}, {22,23}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {9,15}, {18,19}, {6,19}, {14,17}, {15,21}, {1,7}, {7,18}, {14,23}, {2,12}, {4,22}, {5,20}, {10,14}, {3,24}, {9,24}, {21,23}, {16,22}, {2,6}, {6,20}, {6,16}, {11,21}, {18,20}, {3,21}, {2,8}, {1,20}, {5,11}, {7,22}, {4,18}, {5,10}, {13,23}, {3,8}, {13,17}, {7,21}, {5,12}, {9,14}, {3,17}, {10,20}, {2,7}, {17,20}, {9,16}, {13,19}, {7,17}, {4,23}, {1,8}, {7,12}, {5,16}, {4,13}, {1,6}, {1,18}, {15,24}, {14,24}, {21,24}, {4,24}, {2,5}, {9,20}, {8,12}, {16,24} }; // ET24.36 // Bipartite(12,12) Valencies [11,11] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 958003200 EdgePairs[24][36]:={ {1,15}, {9,13}, {10,19}, {7,19}, {11,15}, {5,14}, {10,21}, {11,17}, {8,24}, {10,22}, {6,18}, {11,23}, {4,14}, {12,19}, {2,22}, {6,14}, {6,17}, {12,16}, {7,24}, {6,23}, {2,20}, {4,16}, {6,13}, {12,15}, {12,17}, {12,14}, {12,22}, {5,24}, {9,19}, {9,21}, {11,16}, {12,18}, {11,22}, {7,23}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,13}, {9,17}, {6,22}, {5,21}, {10,23}, {3,19}, {3,18}, {8,22}, {8,15}, {2,14}, {5,23}, {4,20}, {1,17}, {3,13}, {2,16}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {3,14}, {2,13}, {10,15}, {10,16}, {3,22}, {5,19}, {9,23}, {10,24}, {5,15}, {7,20}, {3,23}, {8,17}, {7,14}, {6,15}, {1,19}, {11,18}, {4,21}, {4,15}, {9,15}, {8,19}, {11,14}, {12,24}, {12,23}, {2,24}, {11,13}, {5,22}, {1,23}, {2,21}, {11,19}, {7,18}, {4,22}, {10,14}, {8,16}, {5,17}, {3,24}, {9,24}, {8,20}, {8,23}, {7,16}, {6,20}, {6,16}, {11,21}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {7,22}, {3,16}, {1,13}, {4,18}, {3,20}, {7,21}, {11,20}, {9,14}, {3,17}, {10,20}, {6,24}, {5,18}, {7,17}, {4,23}, {5,16}, {4,13}, {1,21}, {1,18}, {12,20}, {4,19}, {4,24}, {12,13}, {9,20}, {1,24}, {9,22} }; // ET24.37 // Bipartite(6,18) Valencies [12,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 17915904000 EdgePairs[24][37]:={ {2,11}, {3,22}, {5,12}, {4,8}, {2,14}, {4,13}, {4,23}, {1,14}, {3,12}, {5,24}, {2,24}, {1,10}, {4,11}, {4,10}, {3,21}, {6,12}, {5,11}, {6,10}, {4,7}, {1,20}, {5,15}, {4,16}, {3,24}, {3,9}, {2,12}, {6,7}, {6,15}, {5,8}, {2,21}, {5,9}, {5,23}, {6,16}, {5,21}, {5,20}, {1,7}, {3,16}, {3,7}, {2,20}, {1,16}, {3,15}, {2,18}, {4,20}, {3,19}, {5,17}, {2,15}, {3,18}, {6,21}, {4,17}, {1,17}, {4,22}, {6,18}, {6,19}, {6,22}, {5,14}, {2,17}, {5,18}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,22}, {4,14}, {2,8}, {1,23}, {4,19}, {1,11}, {6,13}, {6,24}, {3,10}, {6,9} }; // ET24.38 // Bipartite(6,18) Valencies [12,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 36864 EdgePairs[24][38]:={ {2,11}, {3,22}, {4,8}, {2,14}, {4,13}, {1,14}, {3,12}, {5,24}, {2,24}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {3,21}, {6,12}, {5,11}, {4,7}, {1,12}, {5,15}, {3,23}, {4,16}, {3,24}, {6,15}, {3,20}, {5,8}, {5,9}, {5,16}, {4,12}, {5,20}, {5,7}, {2,16}, {1,7}, {2,7}, {3,11}, {1,16}, {2,20}, {3,15}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {5,17}, {2,15}, {3,14}, {6,21}, {4,17}, {1,18}, {1,17}, {4,22}, {6,18}, {6,22}, {2,19}, {5,18}, {3,13}, {6,17}, {2,23}, {1,8}, {1,19}, {2,9}, {5,13}, {1,9}, {1,23}, {4,19}, {5,22}, {6,23}, {6,13}, {6,8}, {6,24}, {3,10}, {6,9} }; // ET24.39 // Bipartite(8,16) Valencies [12,6] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1152 EdgePairs[24][39]:={ {5,12}, {4,13}, {4,24}, {8,19}, {4,23}, {1,14}, {7,11}, {7,16}, {8,20}, {3,12}, {5,24}, {7,9}, {2,24}, {7,23}, {2,10}, {7,12}, {8,16}, {8,23}, {6,14}, {8,11}, {4,11}, {4,10}, {3,21}, {8,15}, {5,11}, {6,10}, {1,12}, {5,15}, {8,24}, {3,23}, {4,16}, {3,24}, {3,9}, {2,12}, {6,15}, {3,20}, {2,21}, {5,9}, {6,16}, {5,21}, {8,10}, {4,12}, {5,20}, {4,18}, {2,16}, {7,10}, {3,11}, {1,16}, {2,20}, {3,15}, {7,18}, {6,20}, {3,17}, {5,19}, {2,18}, {1,21}, {4,21}, {3,19}, {8,13}, {2,15}, {3,14}, {6,21}, {4,17}, {1,18}, {7,22}, {8,22}, {4,15}, {7,20}, {1,17}, {6,19}, {6,22}, {5,14}, {2,17}, {5,18}, {6,17}, {1,13}, {8,14}, {8,18}, {1,19}, {2,9}, {5,13}, {7,17}, {1,9}, {1,22}, {2,13}, {1,23}, {4,19}, {7,14}, {1,11}, {5,22}, {2,22}, {6,23}, {6,13}, {7,24}, {3,10}, {6,9} }; // ET24.40 // Bipartite(8,16) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 127401984 EdgePairs[24][40]:={ {7,19}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {2,22}, {6,14}, {6,17}, {2,11}, {7,24}, {6,23}, {4,16}, {6,13}, {5,24}, {1,9}, {7,23}, {7,15}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {8,13}, {7,11}, {6,22}, {5,9}, {5,21}, {3,19}, {4,12}, {3,18}, {8,15}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {1,22}, {1,16}, {6,21}, {2,17}, {8,21}, {3,14}, {2,13}, {1,12}, {3,22}, {7,20}, {3,23}, {8,17}, {7,14}, {6,15}, {8,11}, {4,21}, {4,17}, {4,15}, {2,9}, {8,19}, {4,11}, {5,22}, {6,19}, {2,21}, {7,18}, {8,9}, {5,20}, {8,16}, {5,17}, {3,24}, {3,12}, {8,20}, {8,23}, {7,16}, {1,14}, {1,20}, {7,22}, {3,16}, {1,13}, {5,10}, {3,20}, {5,12}, {4,9}, {5,18}, {4,23}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,24}, {8,12}, {1,24} }; // ET24.41 // Bipartite(12,12) Valencies [12,12] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 458885065605120000 EdgePairs[24][41]:={ {11,17}, {10,24}, {1,20}, {5,17}, {2,24}, {11,20}, {6,16}, {7,15}, {4,24}, {3,22}, {4,16}, {6,17}, {2,23}, {1,13}, {12,22}, {3,13}, {3,15}, {10,23}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {1,21}, {11,14}, {2,14}, {8,15}, {4,23}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {12,17}, {12,20}, {9,19}, {8,14}, {11,15}, {11,13}, {11,22}, {7,13}, {9,14}, {1,22}, {12,13}, {12,16}, {5,23}, {4,21}, {3,20}, {10,21}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {11,21}, {7,16}, {5,18}, {11,23}, {1,23}, {6,24}, {7,17}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {10,13}, {6,23}, {9,22}, {6,15}, {2,17}, {9,13}, {8,21}, {3,19}, {1,24}, {12,23}, {11,24}, {12,19}, {3,23}, {8,23}, {12,14}, {3,21}, {6,19}, {1,15}, {12,15}, {6,14}, {3,16}, {11,16}, {7,23}, {2,21}, {9,18}, {10,17}, {3,24}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {8,18}, {4,18}, {11,19}, {10,19}, {4,20}, {5,13}, {8,20}, {12,24}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET24.42 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 589824 EdgePairs[24][42]:={ {1,15}, {10,19}, {7,19}, {14,21}, {6,12}, {5,14}, {10,21}, {15,23}, {8,24}, {10,22}, {6,18}, {11,23}, {4,14}, {1,11}, {12,19}, {2,22}, {6,14}, {6,17}, {13,18}, {2,11}, {7,24}, {13,24}, {14,18}, {6,13}, {12,22}, {16,18}, {1,9}, {16,23}, {9,19}, {9,21}, {11,22}, {16,20}, {7,23}, {7,15}, {5,13}, {3,10}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {12,21}, {7,10}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {16,17}, {8,21}, {2,17}, {8,10}, {3,14}, {1,12}, {3,9}, {16,19}, {5,19}, {5,15}, {7,20}, {15,20}, {7,13}, {3,23}, {7,14}, {6,15}, {15,19}, {4,17}, {2,9}, {8,19}, {13,22}, {12,24}, {12,23}, {2,24}, {4,11}, {5,22}, {6,19}, {14,17}, {1,23}, {2,21}, {14,22}, {15,18}, {11,19}, {8,9}, {14,23}, {2,12}, {5,20}, {8,16}, {5,17}, {3,24}, {3,12}, {8,20}, {8,23}, {7,16}, {6,20}, {6,16}, {11,21}, {9,18}, {10,17}, {7,9}, {13,21}, {5,11}, {7,22}, {4,18}, {13,23}, {13,17}, {15,17}, {3,20}, {7,21}, {11,20}, {5,12}, {3,17}, {10,20}, {4,9}, {5,18}, {4,23}, {11,24}, {5,16}, {4,13}, {1,21}, {1,18}, {12,20}, {15,24}, {4,19}, {14,24}, {4,10}, {4,24}, {9,20}, {1,24}, {9,22}, {16,24} }; // ET24.43 // Bipartite(11,13) Valencies [13,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 248562743869440000 EdgePairs[24][43]:={ {11,17}, {10,24}, {1,20}, {5,17}, {2,24}, {11,20}, {6,16}, {7,15}, {4,24}, {8,12}, {3,22}, {4,16}, {6,17}, {2,23}, {1,13}, {3,13}, {3,15}, {10,23}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {1,21}, {11,14}, {11,12}, {2,14}, {8,15}, {4,23}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {9,19}, {8,14}, {11,15}, {11,13}, {3,12}, {11,22}, {7,13}, {9,14}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {10,21}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {10,13}, {10,12}, {6,23}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {11,24}, {3,23}, {8,23}, {3,21}, {9,12}, {6,19}, {1,15}, {6,14}, {3,16}, {11,16}, {7,23}, {2,21}, {9,18}, {10,17}, {3,24}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {8,18}, {4,18}, {11,19}, {10,19}, {4,12}, {4,20}, {5,13}, {8,20}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET24.44 // Bipartite(3,21) Valencies [14,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 768144384000 EdgePairs[24][44]:={ {1,4}, {1,20}, {3,24}, {3,16}, {3,10}, {1,14}, {1,23}, {3,19}, {2,17}, {2,24}, {1,7}, {2,11}, {1,5}, {3,6}, {3,18}, {3,15}, {3,4}, {2,21}, {1,22}, {3,21}, {1,16}, {1,10}, {1,17}, {1,13}, {2,20}, {2,18}, {3,22}, {3,9}, {1,11}, {2,23}, {1,19}, {2,6}, {2,8}, {3,12}, {2,15}, {3,13}, {2,5}, {2,12}, {2,9}, {3,7}, {2,14}, {1,8} }; // ET24.45 // Bipartite(8,16) Valencies [14,7] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10321920 EdgePairs[24][45]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {4,16}, {5,24}, {1,9}, {7,23}, {7,15}, {5,13}, {2,19}, {2,18}, {6,9}, {2,15}, {8,14}, {8,13}, {7,11}, {6,22}, {5,9}, {5,21}, {3,19}, {8,22}, {7,10}, {2,14}, {5,23}, {3,11}, {2,10}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,15}, {7,20}, {7,13}, {3,23}, {8,17}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {8,19}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {7,18}, {8,9}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {8,16}, {3,12}, {8,20}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {7,9}, {1,20}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {7,21}, {5,12}, {3,17}, {4,9}, {6,24}, {5,18}, {7,17}, {4,23}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {4,24}, {8,12} }; // ET24.46 // Bipartite(10,14) Valencies [14,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 316352583106560000 EdgePairs[24][46]:={ {1,15}, {9,13}, {10,19}, {7,19}, {6,12}, {5,14}, {10,21}, {3,15}, {8,24}, {10,22}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {4,16}, {6,13}, {9,12}, {5,24}, {9,19}, {9,21}, {7,23}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {7,11}, {6,22}, {5,21}, {10,23}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {2,14}, {5,23}, {3,11}, {4,20}, {6,11}, {2,23}, {1,17}, {3,13}, {2,16}, {10,12}, {1,22}, {1,16}, {6,21}, {10,13}, {2,17}, {8,18}, {8,21}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {3,22}, {5,19}, {9,23}, {10,24}, {5,15}, {7,20}, {7,13}, {3,23}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {9,15}, {8,19}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {7,18}, {2,12}, {4,22}, {5,20}, {10,14}, {3,24}, {5,17}, {8,16}, {9,24}, {3,12}, {8,20}, {8,23}, {7,16}, {6,20}, {6,16}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {3,20}, {7,21}, {5,12}, {9,14}, {3,17}, {10,20}, {6,24}, {5,18}, {9,16}, {7,17}, {4,23}, {7,12}, {5,16}, {4,13}, {1,21}, {10,11}, {1,18}, {4,19}, {4,24}, {8,12}, {9,20}, {1,24}, {9,22} }; // ET24.47 // Non-bipartite Valency 14 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 241920 EdgePairs[24][47]:={ {21,23}, {1,11}, {10,24}, {1,20}, {5,17}, {2,24}, {11,20}, {13,21}, {7,15}, {14,19}, {8,12}, {15,24}, {3,22}, {4,16}, {1,10}, {6,17}, {1,13}, {3,9}, {3,6}, {3,13}, {3,15}, {19,24}, {17,20}, {2,15}, {4,19}, {16,19}, {7,22}, {2,19}, {2,4}, {5,20}, {1,21}, {2,9}, {21,22}, {18,21}, {8,10}, {2,14}, {8,15}, {6,11}, {4,23}, {3,5}, {9,11}, {10,15}, {10,22}, {15,16}, {6,22}, {3,18}, {3,7}, {8,16}, {6,21}, {14,23}, {7,12}, {4,10}, {1,17}, {1,7}, {4,22}, {8,19}, {7,11}, {12,17}, {16,24}, {18,20}, {12,20}, {5,11}, {2,5}, {6,8}, {11,15}, {11,13}, {17,23}, {3,12}, {11,22}, {9,14}, {6,12}, {12,13}, {12,16}, {5,23}, {3,20}, {13,22}, {10,21}, {14,16}, {6,18}, {13,18}, {11,23}, {1,23}, {6,24}, {7,17}, {5,24}, {5,7}, {8,13}, {8,22}, {18,24}, {9,10}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {20,22}, {4,7}, {15,17}, {3,10}, {16,22}, {6,15}, {2,17}, {9,13}, {3,19}, {4,9}, {14,18}, {1,24}, {12,23}, {14,22}, {13,24}, {3,23}, {8,23}, {12,14}, {17,19}, {6,19}, {6,9}, {18,23}, {6,14}, {2,11}, {14,20}, {15,21}, {16,21}, {3,16}, {11,16}, {13,19}, {2,21}, {10,17}, {2,22}, {1,16}, {5,8}, {9,17}, {10,18}, {20,24}, {5,10}, {8,18}, {4,18}, {11,19}, {10,19}, {1,4}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {12,24}, {15,23}, {7,24}, {2,12}, {1,14}, {9,24}, {2,8}, {1,6}, {10,14}, {17,22}, {5,21}, {13,17}, {2,18}, {19,23}, {7,19}, {9,21}, {9,16}, {9,23}, {7,21}, {11,18}, {12,21}, {7,18}, {5,16} }; // ET24.48 // Bipartite(4,20) Valencies [15,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4976640000 EdgePairs[24][48]:={ {2,11}, {3,22}, {2,14}, {4,8}, {4,13}, {4,9}, {4,24}, {4,23}, {1,14}, {1,24}, {3,12}, {2,10}, {1,10}, {4,11}, {1,6}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {3,23}, {4,16}, {3,24}, {3,20}, {2,21}, {4,12}, {2,7}, {3,11}, {3,16}, {3,7}, {1,16}, {3,15}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {2,15}, {3,14}, {3,18}, {2,5}, {4,5}, {4,17}, {1,18}, {1,5}, {4,15}, {1,17}, {3,6}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {2,9}, {1,9}, {1,22}, {2,13}, {4,19}, {2,22}, {3,10} }; // ET24.49 // Bipartite(6,18) Valencies [15,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 33592320 EdgePairs[24][49]:={ {2,11}, {5,12}, {2,14}, {4,8}, {4,13}, {4,9}, {4,23}, {1,24}, {3,12}, {5,24}, {2,24}, {2,10}, {1,10}, {6,14}, {4,11}, {4,10}, {5,10}, {3,21}, {6,12}, {5,11}, {6,10}, {4,7}, {1,12}, {5,15}, {3,8}, {3,23}, {4,16}, {3,9}, {3,24}, {2,12}, {6,7}, {6,15}, {3,20}, {5,8}, {5,9}, {5,16}, {5,23}, {6,16}, {5,21}, {5,20}, {2,16}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {3,7}, {2,20}, {3,15}, {6,20}, {3,17}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {5,17}, {3,14}, {3,18}, {6,21}, {4,17}, {1,18}, {4,15}, {1,17}, {4,22}, {6,18}, {6,19}, {6,22}, {2,19}, {5,14}, {2,17}, {5,18}, {3,13}, {2,23}, {1,13}, {1,19}, {1,9}, {1,22}, {2,13}, {2,8}, {4,14}, {1,23}, {4,19}, {1,11}, {5,22}, {2,22}, {6,13}, {6,8}, {6,24}, {6,9} }; // ET24.50 // Bipartite(9,15) Valencies [15,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 474528874659840000 EdgePairs[24][50]:={ {1,15}, {9,13}, {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {4,16}, {6,13}, {9,12}, {5,24}, {9,19}, {9,21}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {9,10}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {7,11}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {7,10}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {3,22}, {5,19}, {9,23}, {5,15}, {7,20}, {7,13}, {3,23}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {9,15}, {8,19}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {7,18}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {8,16}, {9,24}, {3,12}, {8,20}, {8,23}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {9,18}, {1,20}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {7,21}, {5,12}, {9,14}, {3,17}, {6,24}, {5,18}, {9,16}, {7,17}, {4,23}, {7,12}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {4,24}, {8,12}, {9,20}, {1,24}, {9,22} }; // ET24.51 // Non-bipartite Valency 15 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 17280 EdgePairs[24][51]:={ {11,17}, {1,11}, {10,24}, {1,20}, {2,24}, {11,20}, {6,16}, {14,19}, {15,24}, {3,22}, {3,8}, {1,10}, {6,17}, {2,23}, {8,9}, {12,22}, {3,9}, {3,6}, {3,13}, {10,23}, {19,24}, {2,15}, {4,19}, {16,19}, {7,22}, {2,19}, {1,19}, {5,20}, {20,21}, {17,24}, {16,18}, {2,9}, {11,14}, {18,21}, {8,10}, {8,15}, {6,11}, {16,23}, {4,23}, {3,5}, {10,15}, {19,21}, {3,18}, {3,17}, {6,21}, {7,12}, {14,23}, {4,10}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {14,21}, {12,17}, {5,11}, {2,5}, {9,19}, {8,14}, {19,22}, {11,13}, {17,23}, {3,12}, {11,22}, {7,13}, {9,14}, {14,24}, {1,22}, {6,12}, {12,13}, {5,23}, {4,21}, {3,20}, {13,22}, {10,21}, {2,13}, {2,20}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {13,23}, {8,13}, {8,22}, {18,24}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {6,23}, {3,10}, {16,22}, {9,22}, {6,15}, {2,17}, {4,6}, {5,12}, {14,17}, {8,21}, {4,9}, {1,24}, {12,23}, {11,24}, {13,24}, {12,19}, {20,23}, {8,23}, {12,14}, {3,21}, {2,7}, {6,19}, {6,9}, {1,15}, {12,15}, {18,23}, {2,11}, {4,5}, {14,20}, {15,21}, {16,17}, {16,21}, {3,16}, {15,18}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {1,16}, {4,14}, {15,22}, {7,9}, {5,10}, {8,18}, {4,18}, {10,19}, {4,11}, {1,8}, {7,10}, {7,24}, {2,12}, {1,14}, {9,24}, {2,8}, {10,20}, {1,6}, {5,15}, {5,19}, {6,20}, {17,22}, {9,15}, {6,13}, {13,20}, {4,17}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET24.52 // Bipartite(8,16) Valencies [16,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 843606888284160000 EdgePairs[24][52]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {4,16}, {6,13}, {5,24}, {1,9}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {8,14}, {8,13}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {7,10}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {7,20}, {3,23}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {2,9}, {8,19}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {7,18}, {8,9}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {8,16}, {3,12}, {8,20}, {8,23}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {7,9}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,20}, {7,21}, {5,12}, {3,17}, {4,9}, {6,24}, {5,18}, {7,17}, {4,23}, {5,16}, {7,12}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {4,24}, {8,12}, {1,24} }; // ET24.53 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 393289924608000 EdgePairs[24][53]:={ {11,17}, {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {11,20}, {6,16}, {13,21}, {7,15}, {4,24}, {8,12}, {14,19}, {15,24}, {3,22}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,9}, {12,22}, {3,9}, {3,13}, {3,15}, {10,23}, {2,15}, {4,19}, {16,19}, {7,22}, {2,19}, {1,19}, {5,20}, {1,21}, {16,18}, {2,9}, {8,10}, {2,14}, {8,15}, {6,11}, {16,23}, {4,23}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {7,12}, {14,23}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {16,24}, {12,20}, {5,11}, {2,10}, {9,19}, {8,14}, {3,12}, {11,22}, {7,13}, {14,24}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {13,22}, {15,19}, {10,21}, {2,13}, {2,20}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {8,11}, {5,24}, {13,23}, {8,13}, {8,22}, {1,9}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {15,17}, {6,23}, {3,10}, {16,22}, {9,22}, {6,15}, {2,17}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {1,24}, {14,18}, {12,23}, {14,22}, {11,24}, {13,24}, {12,19}, {3,23}, {8,23}, {3,21}, {6,19}, {6,9}, {1,15}, {6,14}, {2,11}, {14,20}, {15,21}, {16,17}, {16,21}, {3,16}, {15,18}, {7,23}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {2,22}, {1,16}, {4,14}, {15,22}, {9,17}, {10,18}, {16,20}, {8,24}, {7,9}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {12,24}, {7,10}, {15,23}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {5,19}, {6,20}, {5,21}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {5,16} }; // ET24.54 // Bipartite(7,17) Valencies [17,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1792664637603840000 EdgePairs[24][54]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {4,16}, {6,13}, {5,24}, {1,9}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {7,10}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {6,8}, {7,20}, {3,23}, {7,13}, {7,14}, {6,15}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {2,24}, {4,11}, {5,22}, {7,8}, {6,19}, {1,23}, {2,21}, {5,8}, {7,18}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {7,9}, {2,8}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,8}, {3,20}, {7,21}, {5,12}, {3,17}, {4,9}, {6,24}, {5,18}, {7,17}, {4,23}, {1,8}, {5,16}, {7,12}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {4,24}, {1,24} }; // ET24.55 // Bipartite(6,18) Valencies [18,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4609709068124160000 EdgePairs[24][55]:={ {1,15}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {3,7}, {6,17}, {2,11}, {6,23}, {2,20}, {4,16}, {6,13}, {5,24}, {1,9}, {6,7}, {5,7}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {5,9}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {6,8}, {3,23}, {6,15}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {3,21}, {1,14}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,8}, {3,20}, {5,12}, {3,17}, {4,9}, {6,24}, {2,7}, {5,18}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {4,24}, {1,24} }; // ET24.56 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 6449725440000 EdgePairs[24][56]:={ {11,17}, {21,23}, {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {6,16}, {4,24}, {8,12}, {14,19}, {3,22}, {3,8}, {4,16}, {6,17}, {2,23}, {1,13}, {8,9}, {12,22}, {3,9}, {3,6}, {3,13}, {3,15}, {10,23}, {19,24}, {17,20}, {2,15}, {16,19}, {7,22}, {2,19}, {1,19}, {2,4}, {5,20}, {20,21}, {1,21}, {17,24}, {16,18}, {11,14}, {17,21}, {18,21}, {8,10}, {6,7}, {2,14}, {6,11}, {4,23}, {3,5}, {9,11}, {13,16}, {10,15}, {10,22}, {19,21}, {3,18}, {3,17}, {3,7}, {7,12}, {14,23}, {4,10}, {1,7}, {4,22}, {8,19}, {7,11}, {7,20}, {3,14}, {12,17}, {4,8}, {18,20}, {1,5}, {5,11}, {2,5}, {9,19}, {8,14}, {19,22}, {6,8}, {11,13}, {11,15}, {17,23}, {11,22}, {7,13}, {9,14}, {14,24}, {1,22}, {6,12}, {12,13}, {12,16}, {5,23}, {4,21}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {1,12}, {5,18}, {14,15}, {1,23}, {11,23}, {6,24}, {2,6}, {7,17}, {8,11}, {5,24}, {5,7}, {13,23}, {8,13}, {8,22}, {18,24}, {15,20}, {9,20}, {4,15}, {4,13}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {10,12}, {6,23}, {3,10}, {2,3}, {1,3}, {16,22}, {9,22}, {6,15}, {4,6}, {9,13}, {5,12}, {14,17}, {8,21}, {4,9}, {1,24}, {14,18}, {12,23}, {22,23}, {11,24}, {13,24}, {20,23}, {3,23}, {18,19}, {12,14}, {3,21}, {17,19}, {2,7}, {9,12}, {6,19}, {6,9}, {13,15}, {1,15}, {12,15}, {18,23}, {2,11}, {10,11}, {4,5}, {14,20}, {15,21}, {16,17}, {16,21}, {22,24}, {3,16}, {15,18}, {11,16}, {13,19}, {2,21}, {3,24}, {2,22}, {1,16}, {4,14}, {15,22}, {5,8}, {18,22}, {16,20}, {7,9}, {20,24}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {1,4}, {10,19}, {1,8}, {8,20}, {12,24}, {7,10}, {2,12}, {1,14}, {9,24}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {17,22}, {21,24}, {9,15}, {13,17}, {13,20}, {19,23}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET24.57 // Bipartite(5,19) Valencies [19,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14597412049059840000 EdgePairs[24][57]:={ {1,15}, {5,14}, {3,15}, {4,14}, {1,11}, {2,22}, {4,8}, {3,7}, {2,11}, {2,20}, {4,16}, {5,24}, {1,9}, {5,7}, {4,6}, {5,13}, {3,10}, {2,19}, {2,18}, {2,15}, {5,9}, {5,21}, {3,19}, {4,12}, {5,6}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {3,23}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {2,24}, {4,11}, {5,22}, {1,23}, {2,21}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,8}, {3,20}, {5,12}, {3,6}, {3,17}, {4,9}, {2,7}, {5,18}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,6}, {1,18}, {4,19}, {4,10}, {4,24}, {1,24} }; // ET24.58 // Bipartite(4,20) Valencies [20,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 58389648196239360000 EdgePairs[24][58]:={ {2,11}, {3,22}, {2,14}, {4,8}, {4,13}, {4,9}, {4,24}, {4,23}, {1,14}, {1,24}, {3,12}, {2,24}, {2,10}, {1,10}, {4,11}, {4,10}, {3,21}, {1,6}, {3,5}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {3,23}, {4,16}, {3,9}, {3,24}, {2,12}, {3,20}, {2,21}, {4,6}, {4,12}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {4,21}, {4,20}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {1,5}, {4,15}, {1,17}, {4,22}, {3,6}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {4,14}, {1,23}, {4,19}, {1,11}, {2,22}, {3,10} }; // ET24.59 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 137594142720 EdgePairs[24][59]:={ {11,17}, {21,23}, {1,11}, {5,17}, {1,20}, {10,24}, {11,20}, {6,16}, {13,21}, {7,15}, {4,24}, {8,12}, {14,19}, {15,24}, {3,22}, {3,8}, {4,16}, {1,10}, {6,17}, {1,13}, {12,22}, {3,9}, {3,13}, {3,15}, {10,23}, {19,24}, {17,20}, {2,15}, {4,19}, {16,19}, {7,22}, {2,19}, {1,19}, {2,4}, {5,20}, {1,21}, {17,24}, {2,9}, {17,21}, {18,21}, {6,7}, {2,14}, {8,15}, {6,11}, {16,23}, {4,23}, {9,11}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {3,7}, {8,16}, {6,21}, {7,12}, {14,23}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {16,24}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {6,8}, {11,15}, {17,23}, {3,12}, {11,22}, {7,13}, {9,14}, {14,24}, {1,22}, {6,12}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {5,18}, {14,15}, {11,23}, {6,24}, {2,6}, {7,17}, {8,11}, {5,24}, {5,7}, {13,23}, {8,13}, {8,22}, {1,9}, {18,24}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {10,13}, {10,12}, {6,23}, {3,10}, {2,3}, {1,3}, {16,22}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {14,18}, {12,23}, {22,23}, {14,22}, {11,24}, {13,24}, {12,19}, {20,23}, {3,23}, {8,23}, {18,19}, {3,21}, {17,19}, {2,7}, {6,19}, {9,12}, {6,9}, {13,15}, {1,15}, {12,15}, {18,23}, {6,14}, {2,11}, {10,11}, {14,20}, {15,21}, {16,21}, {22,24}, {3,16}, {7,23}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {2,22}, {1,16}, {4,14}, {15,22}, {5,8}, {18,22}, {9,17}, {10,18}, {16,20}, {8,24}, {20,24}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {1,4}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {12,24}, {15,23}, {7,24}, {2,12}, {1,14}, {9,24}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {17,22}, {21,24}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {19,23}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET24.60 // Bipartite(3,21) Valencies [21,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 306545653030256640000 EdgePairs[24][60]:={ {2,11}, {3,22}, {2,14}, {1,14}, {1,24}, {3,12}, {2,24}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,23}, {3,9}, {3,24}, {2,12}, {2,4}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {1,5}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {1,23}, {1,11}, {2,22}, {3,10} }; // ET24.61 // Non-bipartite Valency 21 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 67722117120 EdgePairs[24][61]:={ {11,17}, {21,23}, {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {11,20}, {6,16}, {13,21}, {7,15}, {4,24}, {8,12}, {14,19}, {15,24}, {3,22}, {3,8}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {12,22}, {3,9}, {3,6}, {3,13}, {3,15}, {10,23}, {19,24}, {17,20}, {2,15}, {4,19}, {16,19}, {7,22}, {2,19}, {1,19}, {2,4}, {5,20}, {1,21}, {17,24}, {2,9}, {11,14}, {21,22}, {17,21}, {18,21}, {8,10}, {6,7}, {2,14}, {8,15}, {6,11}, {16,23}, {4,23}, {3,5}, {9,11}, {13,16}, {10,15}, {10,22}, {15,16}, {6,22}, {3,18}, {3,17}, {3,7}, {8,16}, {6,21}, {7,12}, {14,23}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {16,24}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {19,22}, {6,8}, {11,13}, {11,15}, {17,23}, {3,12}, {11,22}, {7,13}, {9,14}, {14,24}, {1,22}, {6,12}, {12,13}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {3,4}, {5,18}, {1,23}, {11,23}, {6,24}, {2,6}, {7,17}, {8,11}, {5,24}, {5,7}, {13,23}, {8,13}, {8,22}, {1,9}, {18,24}, {9,10}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {6,23}, {3,10}, {16,22}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {1,24}, {14,18}, {12,23}, {14,22}, {11,24}, {13,24}, {12,19}, {20,23}, {3,23}, {8,23}, {18,19}, {12,14}, {3,21}, {17,19}, {2,7}, {6,19}, {9,12}, {6,9}, {1,15}, {12,15}, {18,23}, {6,14}, {2,11}, {14,20}, {15,21}, {16,21}, {3,16}, {15,18}, {7,23}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {2,22}, {1,16}, {4,14}, {15,22}, {5,8}, {18,22}, {9,17}, {10,18}, {16,20}, {8,24}, {20,24}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {1,4}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {12,24}, {7,10}, {15,23}, {7,24}, {2,12}, {1,14}, {9,24}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {17,22}, {21,24}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {19,23}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET24.62 // Bipartite(2,22) Valencies [22,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2248001455555215360000 EdgePairs[24][62]:={ {1,4}, {1,20}, {1,3}, {1,14}, {1,23}, {2,17}, {1,24}, {2,24}, {1,7}, {2,11}, {2,19}, {1,5}, {1,15}, {2,21}, {1,22}, {1,16}, {1,10}, {2,22}, {2,7}, {1,12}, {1,13}, {1,17}, {2,13}, {2,3}, {2,20}, {2,18}, {2,4}, {1,11}, {2,23}, {1,19}, {1,18}, {2,6}, {2,8}, {2,16}, {2,15}, {1,21}, {1,9}, {2,5}, {2,10}, {2,12}, {2,9}, {1,6}, {1,8}, {2,14} }; // ET24.63 // Non-bipartite Valency 22 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1961990553600 EdgePairs[24][63]:={ {11,17}, {21,23}, {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {11,20}, {6,16}, {13,21}, {7,15}, {4,24}, {8,12}, {14,19}, {15,24}, {3,22}, {3,8}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,9}, {12,22}, {3,9}, {3,6}, {3,13}, {3,15}, {10,23}, {19,24}, {17,20}, {2,15}, {4,19}, {16,19}, {7,22}, {2,19}, {1,19}, {2,4}, {5,20}, {20,21}, {1,21}, {17,24}, {16,18}, {2,9}, {11,14}, {17,21}, {18,21}, {8,10}, {6,7}, {2,14}, {8,15}, {6,11}, {16,23}, {4,23}, {3,5}, {9,11}, {13,16}, {10,15}, {10,22}, {19,21}, {6,22}, {3,18}, {3,17}, {3,7}, {8,16}, {6,21}, {7,12}, {14,23}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {16,24}, {4,8}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {19,22}, {6,8}, {11,13}, {11,15}, {17,23}, {3,12}, {11,22}, {7,13}, {9,14}, {14,24}, {1,22}, {6,12}, {12,13}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {7,16}, {1,12}, {5,18}, {14,15}, {1,23}, {11,23}, {6,24}, {2,6}, {7,17}, {8,11}, {5,24}, {5,7}, {13,23}, {8,13}, {8,22}, {1,9}, {18,24}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {10,12}, {6,23}, {3,10}, {2,3}, {1,3}, {16,22}, {9,22}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {1,24}, {14,18}, {12,23}, {22,23}, {14,22}, {11,24}, {13,24}, {12,19}, {20,23}, {3,23}, {8,23}, {18,19}, {12,14}, {3,21}, {17,19}, {2,7}, {6,19}, {9,12}, {6,9}, {13,15}, {1,15}, {12,15}, {18,23}, {6,14}, {2,11}, {10,11}, {4,5}, {14,20}, {15,21}, {16,17}, {16,21}, {22,24}, {3,16}, {15,18}, {7,23}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {2,22}, {1,16}, {4,14}, {15,22}, {5,8}, {18,22}, {9,17}, {10,18}, {16,20}, {8,24}, {7,9}, {20,24}, {6,10}, {5,10}, {8,18}, {4,18}, {5,9}, {11,19}, {1,4}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {12,24}, {7,10}, {15,23}, {7,24}, {2,12}, {1,14}, {9,24}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {17,22}, {21,24}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {19,23}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET24.64 // Bipartite(1,23) Valencies [23,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 25852016738884976640000 EdgePairs[24][64]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,12}, {1,2}, {1,3}, {1,17}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,6}, {1,14}, {1,18}, {1,21}, {1,19}, {1,20}, {1,8}, {1,24}, {1,9}, {1,23} }; // ET24.65 // Non-bipartite Valency 23 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 620448401733239439360000 EdgePairs[24][65]:={ {13,21}, {5,7}, {5,22}, {10,18}, {9,17}, {3,8}, {9,10}, {17,18}, {12,22}, {5,11}, {16,22}, {1,3}, {6,15}, {11,15}, {8,21}, {5,6}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {2,7}, {6,9}, {21,22}, {6,14}, {16,21}, {19,20}, {10,11}, {19,21}, {11,17}, {1,12}, {9,11}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {4,24}, {2,6}, {8,13}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {3,10}, {2,5}, {8,9}, {2,10}, {19,22}, {3,9}, {17,20}, {2,17}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {12,13}, {13,20}, {15,19}, {6,18}, {4,23}, {11,18}, {6,24}, {13,16}, {13,19}, {3,17}, {7,15}, {8,22}, {9,20}, {4,22}, {8,19}, {1,18}, {7,14}, {6,17}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {3,13}, {11,22}, {9,13}, {5,12}, {2,8}, {4,9}, {6,12}, {19,23}, {4,21}, {13,17}, {18,19}, {7,19}, {16,18}, {1,2}, {2,13}, {13,18}, {12,15}, {8,10}, {8,15}, {11,21}, {8,17}, {10,16}, {16,17}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {7,12}, {8,24}, {4,10}, {18,20}, {14,21}, {5,14}, {12,17}, {2,23}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {19,24}, {6,8}, {11,13}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {7,8}, {13,22}, {6,13}, {6,19}, {2,20}, {9,16}, {4,17}, {17,19}, {9,12}, {12,18}, {2,16}, {6,11}, {4,5}, {10,22}, {7,23}, {6,22}, {15,24}, {3,7}, {1,16}, {3,22}, {4,14}, {5,8}, {4,15}, {6,23}, {15,17}, {13,14}, {1,5}, {2,3}, {7,24}, {9,24}, {17,22}, {2,19}, {6,20}, {5,23}, {5,20}, {12,14}, {18,21}, {10,21}, {9,21}, {9,23}, {7,21}, {14,16}, {2,11}, {10,15}, {3,5}, {2,21}, {1,11}, {5,24}, {2,22}, {16,20}, {8,11}, {18,24}, {14,19}, {1,7}, {3,14}, {3,11}, {4,8}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {8,14}, {7,10}, {3,6}, {14,24}, {3,15}, {7,22}, {1,14}, {14,18}, {22,23}, {5,21}, {9,15}, {17,24}, {20,23}, {2,4}, {17,21}, {16,23}, {18,23}, {13,15}, {15,21}, {14,20}, {1,15}, {11,12}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {15,18}, {5,17}, {3,4}, {15,16}, {7,17}, {13,23}, {6,21}, {15,22}, {15,20}, {16,24}, {7,20}, {7,9}, {5,10}, {4,20}, {8,20}, {5,13}, {17,23}, {10,23}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {16,19}, {10,14}, {21,24}, {12,19}, {20,21}, {23,24}, {2,9}, {12,21}, {6,7}, {2,14}, {21,23} }; // Total number of connected ET graphs of order 24 is 65 // ******************************************************************************************** // Order 25 // ET25.1 // Non-bipartite Valency 2 // Diameter 12 Girth 25 // Twin-free VT AT // Automorphism group of order 50 EdgePairs[25][1]:={ {6,19}, {1,16}, {9,24}, {15,23}, {4,19}, {8,23}, {5,20}, {4,14}, {11,24}, {13,21}, {1,11}, {6,21}, {14,22}, {7,22}, {5,15}, {2,17}, {8,16}, {12,25}, {9,17}, {10,18}, {7,20}, {10,25}, {3,18}, {3,13}, {2,12} }; // ET25.2 // Bipartite(10,15) Valencies [3,2] // Diameter 6 Girth 10 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[25][2]:={ {1,16}, {5,14}, {9,13}, {3,24}, {8,22}, {8,15}, {3,19}, {6,18}, {7,13}, {7,23}, {8,12}, {4,15}, {1,11}, {2,22}, {5,23}, {7,17}, {6,21}, {9,16}, {9,20}, {2,21}, {5,24}, {2,17}, {6,11}, {1,19}, {10,18}, {10,14}, {4,20}, {4,25}, {10,25}, {3,12} }; // ET25.3 // Non-bipartite Valency 4 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 200 EdgePairs[25][3]:={ {5,12}, {2,14}, {9,23}, {8,20}, {11,25}, {9,16}, {8,16}, {11,24}, {4,11}, {8,21}, {15,24}, {5,11}, {1,12}, {15,23}, {4,16}, {3,20}, {5,16}, {10,23}, {3,15}, {14,22}, {2,18}, {4,20}, {3,19}, {5,17}, {3,14}, {7,25}, {1,18}, {7,21}, {13,22}, {8,22}, {10,24}, {4,15}, {7,20}, {13,21}, {1,17}, {7,19}, {12,25}, {6,18}, {9,22}, {6,19}, {2,19}, {10,17}, {14,23}, {6,25}, {1,13}, {2,13}, {9,17}, {10,18}, {6,24}, {12,21} }; // ET25.4 // Non-bipartite Valency 4 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 100 EdgePairs[25][4]:={ {4,20}, {4,6}, {6,21}, {11,16}, {3,10}, {12,25}, {5,24}, {9,19}, {3,19}, {18,24}, {4,23}, {10,13}, {8,23}, {7,17}, {3,15}, {8,11}, {2,21}, {7,15}, {7,22}, {15,20}, {8,18}, {6,16}, {10,25}, {10,20}, {15,23}, {5,12}, {1,17}, {1,13}, {17,23}, {6,14}, {2,18}, {13,18}, {3,22}, {11,24}, {4,11}, {19,25}, {5,7}, {5,16}, {1,25}, {16,22}, {20,21}, {13,21}, {14,19}, {9,24}, {2,9}, {14,22}, {12,17}, {9,12}, {1,8}, {2,14} }; // ET25.5 // Bipartite(10,15) Valencies [6,4] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[25][5]:={ {3,22}, {4,24}, {9,19}, {4,23}, {1,14}, {7,11}, {9,23}, {7,16}, {1,24}, {3,12}, {9,21}, {7,12}, {8,21}, {8,15}, {8,25}, {5,11}, {5,15}, {3,24}, {2,21}, {2,16}, {3,16}, {2,20}, {1,16}, {7,18}, {5,19}, {1,21}, {9,12}, {4,20}, {3,19}, {5,17}, {7,15}, {10,14}, {8,12}, {8,22}, {10,24}, {4,15}, {7,20}, {6,18}, {4,25}, {6,22}, {9,18}, {10,17}, {5,14}, {2,17}, {9,14}, {6,25}, {3,13}, {2,23}, {5,13}, {6,11}, {10,22}, {2,13}, {4,19}, {10,20}, {1,11}, {8,17}, {1,25}, {6,23}, {6,13}, {10,18} }; // ET25.6 // Bipartite(10,15) Valencies [6,4] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2488320 EdgePairs[25][6]:={ {5,12}, {4,13}, {4,23}, {1,14}, {9,23}, {1,24}, {5,24}, {9,25}, {9,20}, {7,12}, {8,16}, {8,23}, {8,11}, {6,14}, {8,21}, {3,21}, {9,15}, {3,23}, {10,12}, {2,12}, {6,16}, {4,18}, {3,11}, {3,16}, {2,20}, {1,16}, {5,19}, {1,21}, {4,20}, {7,15}, {5,17}, {8,13}, {10,14}, {2,15}, {6,21}, {3,18}, {7,25}, {7,22}, {10,24}, {4,15}, {7,20}, {9,13}, {4,25}, {6,19}, {10,19}, {9,18}, {10,17}, {5,14}, {2,17}, {3,13}, {8,18}, {7,17}, {1,19}, {6,11}, {10,22}, {2,25}, {1,11}, {5,22}, {2,22}, {6,24} }; // ET25.7 // Bipartite(10,15) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 933120 EdgePairs[25][7]:={ {3,22}, {4,13}, {10,15}, {4,23}, {1,14}, {1,24}, {3,12}, {5,24}, {9,25}, {9,20}, {9,21}, {9,16}, {7,12}, {8,16}, {6,14}, {8,11}, {4,11}, {8,21}, {9,15}, {5,15}, {3,23}, {9,11}, {4,16}, {2,12}, {5,20}, {10,13}, {4,18}, {5,25}, {1,16}, {2,20}, {10,23}, {3,17}, {5,19}, {1,21}, {4,21}, {2,15}, {8,12}, {3,18}, {7,22}, {8,22}, {7,19}, {6,18}, {6,19}, {5,14}, {2,17}, {3,13}, {7,17}, {1,19}, {2,25}, {10,25}, {7,14}, {10,20}, {1,11}, {8,17}, {6,23}, {2,22}, {6,13}, {7,24}, {10,18}, {6,24} }; // ET25.8 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 300 EdgePairs[25][8]:={ {2,11}, {4,13}, {12,20}, {1,14}, {7,16}, {3,12}, {9,25}, {11,25}, {2,24}, {7,23}, {9,21}, {2,10}, {20,23}, {13,16}, {8,16}, {8,11}, {6,14}, {11,24}, {8,25}, {15,24}, {19,22}, {4,7}, {15,23}, {8,24}, {17,25}, {4,16}, {3,20}, {5,8}, {5,16}, {4,12}, {10,13}, {1,15}, {3,11}, {6,20}, {14,22}, {2,18}, {9,12}, {3,25}, {4,21}, {4,20}, {3,19}, {5,17}, {7,15}, {2,15}, {1,18}, {13,22}, {7,20}, {13,21}, {1,17}, {18,21}, {12,25}, {3,6}, {6,19}, {10,19}, {6,22}, {2,19}, {9,18}, {14,23}, {5,14}, {5,13}, {10,22}, {1,9}, {10,21}, {1,23}, {11,19}, {16,24}, {14,17}, {5,22}, {8,17}, {15,18}, {6,23}, {7,24}, {9,17}, {10,18}, {12,21} }; // ET25.9 // Bipartite(5,20) Valencies [8,2] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 79626240 EdgePairs[25][9]:={ {2,25}, {5,12}, {4,10}, {1,16}, {5,14}, {5,17}, {4,23}, {3,21}, {3,16}, {5,22}, {3,11}, {4,13}, {5,9}, {2,10}, {4,15}, {1,11}, {2,15}, {5,19}, {1,6}, {2,22}, {4,18}, {1,14}, {5,7}, {2,17}, {3,23}, {5,24}, {1,21}, {3,6}, {1,19}, {2,7}, {1,24}, {4,20}, {4,25}, {1,9}, {3,18}, {3,13}, {3,8}, {2,12}, {4,8}, {2,20} }; // ET25.10 // Bipartite(5,20) Valencies [8,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 122880 EdgePairs[25][10]:={ {4,20}, {4,6}, {5,14}, {5,24}, {1,14}, {1,23}, {3,19}, {2,17}, {1,24}, {3,8}, {3,18}, {3,15}, {4,16}, {4,21}, {5,20}, {3,21}, {1,16}, {2,22}, {5,15}, {3,11}, {2,7}, {1,13}, {2,13}, {5,25}, {2,18}, {4,11}, {3,9}, {4,22}, {5,7}, {2,23}, {1,19}, {5,17}, {2,8}, {1,9}, {2,12}, {3,25}, {4,10}, {4,12}, {1,6}, {5,10} }; // ET25.11 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1200 EdgePairs[25][11]:={ {1,15}, {5,14}, {15,23}, {14,25}, {3,15}, {10,22}, {12,19}, {13,18}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {14,19}, {13,24}, {1,25}, {12,17}, {6,13}, {5,24}, {1,9}, {16,23}, {6,25}, {9,21}, {19,24}, {11,16}, {11,22}, {18,23}, {12,25}, {8,13}, {9,17}, {10,18}, {13,20}, {5,21}, {5,6}, {3,18}, {8,22}, {20,25}, {8,15}, {2,14}, {16,21}, {2,10}, {6,11}, {2,23}, {17,24}, {4,7}, {14,16}, {10,12}, {1,22}, {1,16}, {2,17}, {10,15}, {3,9}, {10,16}, {3,22}, {9,23}, {10,24}, {7,20}, {18,25}, {15,20}, {7,14}, {1,19}, {11,18}, {4,17}, {4,25}, {8,19}, {12,23}, {4,11}, {6,19}, {17,22}, {15,21}, {2,21}, {14,22}, {1,7}, {5,8}, {7,18}, {5,20}, {8,16}, {3,24}, {3,12}, {13,21}, {2,8}, {9,11}, {3,16}, {1,13}, {8,25}, {15,17}, {7,21}, {5,12}, {9,14}, {3,6}, {5,18}, {20,22}, {19,21}, {4,23}, {11,24}, {7,12}, {4,13}, {4,19}, {4,10}, {9,20} }; // ET25.12 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 28800 EdgePairs[25][12]:={ {9,13}, {16,25}, {7,19}, {13,25}, {14,21}, {6,12}, {15,23}, {11,17}, {3,15}, {10,22}, {11,23}, {6,18}, {4,8}, {3,7}, {12,16}, {7,24}, {6,23}, {2,20}, {14,18}, {1,25}, {4,16}, {20,21}, {5,24}, {9,21}, {12,18}, {19,23}, {5,13}, {14,20}, {12,25}, {2,19}, {2,15}, {8,14}, {9,17}, {10,18}, {7,11}, {5,9}, {5,21}, {10,23}, {4,12}, {5,6}, {18,24}, {2,14}, {17,23}, {3,11}, {15,22}, {2,23}, {1,10}, {1,22}, {8,21}, {3,9}, {7,25}, {3,22}, {7,20}, {20,24}, {7,13}, {6,15}, {1,19}, {15,19}, {4,17}, {4,25}, {9,15}, {12,24}, {4,11}, {6,19}, {2,21}, {14,22}, {1,7}, {10,14}, {8,16}, {5,17}, {3,24}, {8,20}, {15,16}, {16,22}, {2,6}, {1,14}, {17,21}, {10,17}, {13,21}, {2,8}, {3,16}, {1,13}, {8,25}, {13,17}, {11,20}, {3,20}, {5,12}, {6,24}, {18,22}, {5,18}, {19,25}, {9,16}, {13,19}, {4,23}, {11,24}, {10,11}, {1,18}, {4,10}, {8,12}, {9,22} }; // ET25.13 // Bipartite(10,15) Valencies [9,6] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[25][13]:={ {5,12}, {2,14}, {4,13}, {10,15}, {9,19}, {7,11}, {9,23}, {7,16}, {8,20}, {1,24}, {5,24}, {9,25}, {7,23}, {9,21}, {7,12}, {8,16}, {6,14}, {4,11}, {8,21}, {3,21}, {8,15}, {8,25}, {1,20}, {1,12}, {5,15}, {3,23}, {4,16}, {2,12}, {6,15}, {5,16}, {5,23}, {6,16}, {5,21}, {4,12}, {10,13}, {4,18}, {3,11}, {9,24}, {3,16}, {2,20}, {10,23}, {3,15}, {7,18}, {6,20}, {3,17}, {5,19}, {1,21}, {3,25}, {10,11}, {2,15}, {3,14}, {8,12}, {6,21}, {8,22}, {10,24}, {7,20}, {1,17}, {4,22}, {4,25}, {6,19}, {9,22}, {6,22}, {2,19}, {9,18}, {2,17}, {5,18}, {9,14}, {3,13}, {2,23}, {1,13}, {8,18}, {5,13}, {1,19}, {7,17}, {6,11}, {10,22}, {2,13}, {4,14}, {10,25}, {4,19}, {7,14}, {10,20}, {1,11}, {1,25}, {8,17}, {2,22}, {7,24}, {9,17}, {10,18}, {6,24} }; // ET25.14 // Bipartite(10,15) Valencies [9,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 933120 EdgePairs[25][14]:={ {2,11}, {2,14}, {4,24}, {8,19}, {1,14}, {9,23}, {1,24}, {5,24}, {2,24}, {7,23}, {9,21}, {9,16}, {7,12}, {8,16}, {8,11}, {8,21}, {3,21}, {6,12}, {7,13}, {5,11}, {1,20}, {8,24}, {3,23}, {9,11}, {10,12}, {6,15}, {3,20}, {2,21}, {5,16}, {6,16}, {5,23}, {5,21}, {4,12}, {10,13}, {2,16}, {1,15}, {3,11}, {3,16}, {2,20}, {10,23}, {3,15}, {7,18}, {6,20}, {5,19}, {3,25}, {9,12}, {4,20}, {7,15}, {10,14}, {2,15}, {8,12}, {6,21}, {3,18}, {4,17}, {7,25}, {1,18}, {7,22}, {8,22}, {10,24}, {4,15}, {7,20}, {9,13}, {4,22}, {4,25}, {9,22}, {10,19}, {6,22}, {2,19}, {9,18}, {10,17}, {5,14}, {5,18}, {6,25}, {3,13}, {6,17}, {1,13}, {8,14}, {5,13}, {1,19}, {7,17}, {6,11}, {10,22}, {2,25}, {4,14}, {1,23}, {4,19}, {1,25}, {8,17}, {9,17}, {10,18} }; // ET25.15 // Non-bipartite Valency 10 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 248832000000 EdgePairs[25][15]:={ {1,15}, {10,19}, {7,19}, {13,25}, {14,21}, {5,14}, {10,21}, {14,25}, {15,23}, {3,15}, {8,24}, {10,22}, {6,18}, {11,23}, {4,14}, {1,11}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {13,24}, {4,16}, {12,22}, {6,25}, {9,19}, {9,21}, {11,22}, {7,23}, {5,13}, {12,25}, {2,19}, {2,18}, {2,15}, {9,17}, {10,18}, {6,22}, {10,23}, {3,19}, {4,12}, {3,18}, {8,22}, {12,21}, {2,14}, {3,11}, {4,20}, {15,22}, {1,17}, {3,13}, {10,25}, {2,16}, {15,25}, {1,16}, {6,21}, {8,21}, {8,18}, {2,17}, {3,14}, {2,13}, {1,12}, {10,16}, {7,25}, {9,23}, {5,19}, {10,24}, {5,15}, {7,20}, {8,17}, {1,19}, {4,17}, {9,25}, {4,15}, {8,19}, {13,22}, {12,24}, {12,23}, {4,11}, {6,19}, {15,21}, {14,22}, {7,18}, {14,23}, {2,12}, {5,20}, {8,16}, {5,17}, {9,24}, {3,12}, {11,25}, {8,20}, {8,23}, {7,16}, {6,20}, {6,16}, {11,21}, {1,14}, {9,18}, {10,17}, {13,21}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {8,25}, {13,23}, {3,20}, {7,21}, {5,12}, {3,17}, {10,20}, {6,24}, {5,18}, {9,16}, {7,17}, {11,24}, {5,16}, {4,13}, {1,18}, {15,24}, {4,19}, {14,24}, {9,20}, {9,22} }; // ET25.16 // Bipartite(5,20) Valencies [12,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 122880 EdgePairs[25][16]:={ {2,11}, {3,22}, {5,12}, {2,14}, {4,13}, {4,9}, {4,23}, {1,14}, {1,24}, {3,12}, {2,24}, {1,10}, {4,10}, {5,11}, {4,7}, {1,20}, {3,8}, {4,16}, {3,24}, {2,12}, {3,20}, {5,8}, {4,6}, {5,9}, {2,21}, {5,16}, {5,21}, {5,7}, {1,7}, {3,16}, {3,15}, {5,19}, {1,21}, {3,25}, {4,20}, {5,17}, {5,6}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {3,6}, {4,25}, {2,19}, {5,18}, {2,23}, {1,8}, {1,13}, {2,9}, {2,13}, {2,25}, {1,23}, {4,19}, {1,11}, {5,22}, {2,22}, {3,10} }; // ET25.17 // Bipartite(10,15) Valencies [12,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 29859840 EdgePairs[25][17]:={ {7,19}, {6,12}, {10,21}, {3,15}, {8,24}, {10,22}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {7,24}, {6,23}, {2,20}, {4,16}, {6,13}, {9,12}, {9,19}, {9,21}, {7,23}, {7,15}, {5,13}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {10,18}, {6,22}, {5,21}, {10,23}, {3,19}, {4,12}, {3,18}, {8,15}, {2,14}, {5,23}, {3,11}, {4,20}, {6,11}, {2,23}, {1,17}, {3,13}, {10,25}, {10,12}, {1,22}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {3,14}, {2,13}, {10,15}, {1,12}, {10,16}, {7,25}, {5,15}, {7,20}, {7,13}, {3,23}, {7,14}, {1,19}, {8,11}, {4,21}, {4,17}, {9,25}, {4,15}, {4,25}, {9,15}, {8,19}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {7,18}, {2,12}, {4,22}, {5,20}, {8,16}, {5,17}, {3,24}, {9,24}, {8,20}, {8,23}, {6,16}, {3,21}, {1,14}, {10,17}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {8,25}, {3,25}, {3,20}, {5,12}, {2,25}, {9,14}, {10,20}, {6,24}, {5,18}, {9,16}, {7,17}, {7,12}, {5,16}, {1,21}, {10,11}, {1,18}, {5,25}, {4,19}, {4,24}, {9,20}, {1,24}, {9,22} }; // ET25.18 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 600 EdgePairs[25][18]:={ {10,24}, {1,20}, {5,17}, {2,24}, {11,20}, {13,21}, {7,15}, {8,12}, {15,24}, {4,16}, {1,10}, {11,25}, {6,17}, {2,23}, {3,6}, {3,25}, {2,15}, {2,19}, {17,24}, {16,25}, {2,9}, {17,21}, {18,21}, {8,25}, {8,15}, {16,23}, {13,16}, {9,11}, {10,22}, {19,21}, {6,22}, {3,17}, {3,7}, {8,16}, {14,23}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {16,24}, {4,8}, {12,20}, {5,11}, {2,10}, {19,22}, {3,12}, {11,22}, {1,22}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {15,19}, {10,21}, {2,13}, {14,16}, {8,17}, {2,16}, {9,25}, {7,16}, {1,12}, {1,23}, {2,6}, {8,11}, {5,7}, {12,25}, {8,22}, {1,9}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {10,12}, {6,23}, {3,10}, {6,15}, {4,6}, {9,13}, {14,17}, {3,19}, {14,18}, {1,24}, {12,23}, {14,22}, {13,24}, {11,24}, {17,25}, {12,19}, {20,23}, {18,25}, {3,21}, {9,12}, {6,19}, {1,15}, {6,14}, {2,11}, {15,21}, {14,25}, {15,18}, {7,23}, {9,18}, {3,24}, {5,8}, {18,22}, {9,17}, {10,18}, {8,24}, {6,25}, {20,24}, {4,18}, {5,9}, {11,19}, {10,19}, {4,25}, {1,8}, {4,12}, {4,20}, {5,13}, {15,23}, {7,24}, {1,14}, {10,14}, {5,19}, {6,20}, {5,21}, {13,17}, {6,13}, {13,20}, {2,18}, {19,23}, {9,21}, {9,23}, {7,21}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET25.19 // Bipartite(12,13) Valencies [13,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2982752926433280000 EdgePairs[25][19]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {6,16}, {7,15}, {4,24}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {1,13}, {12,22}, {3,13}, {3,25}, {3,15}, {10,23}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {1,21}, {11,14}, {8,25}, {2,14}, {8,15}, {4,23}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {12,17}, {12,20}, {9,19}, {8,14}, {5,25}, {11,15}, {11,13}, {11,22}, {7,13}, {9,14}, {7,25}, {1,22}, {12,13}, {12,16}, {5,23}, {4,21}, {3,20}, {10,21}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {5,18}, {11,23}, {1,23}, {6,24}, {7,17}, {5,24}, {12,25}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {10,13}, {6,23}, {9,22}, {6,15}, {2,17}, {9,13}, {8,21}, {3,19}, {1,24}, {12,23}, {11,24}, {12,19}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {1,15}, {12,15}, {6,14}, {3,16}, {11,16}, {7,23}, {2,21}, {9,18}, {10,17}, {3,24}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {5,13}, {8,20}, {12,24}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET25.20 // Bipartite(11,14) Valencies [14,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3479878414172160000 EdgePairs[25][20]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {6,16}, {7,15}, {4,24}, {8,12}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {1,13}, {3,13}, {3,25}, {3,15}, {10,23}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {1,21}, {11,14}, {8,25}, {11,12}, {2,14}, {8,15}, {4,23}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {10,21}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {10,13}, {10,12}, {6,23}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {11,24}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,14}, {3,16}, {7,23}, {11,16}, {2,21}, {9,18}, {10,17}, {3,24}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,12}, {4,20}, {5,13}, {8,20}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET25.21 // Bipartite(10,15) Valencies [15,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4745288746598400000 EdgePairs[25][21]:={ {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {6,16}, {7,15}, {4,24}, {8,12}, {3,22}, {4,16}, {6,17}, {2,23}, {1,13}, {3,13}, {3,25}, {3,15}, {10,23}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {1,21}, {8,25}, {2,14}, {8,15}, {6,11}, {4,23}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {5,11}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {8,17}, {2,16}, {9,25}, {7,16}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {10,13}, {10,12}, {6,23}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,14}, {2,11}, {10,11}, {3,16}, {7,23}, {2,21}, {9,18}, {10,17}, {3,24}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {8,18}, {4,18}, {10,19}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {7,18}, {10,16}, {5,16} }; // ET25.22 // Bipartite(5,20) Valencies [16,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 955514880 EdgePairs[25][22]:={ {5,12}, {2,14}, {4,9}, {4,24}, {1,14}, {1,24}, {2,24}, {2,10}, {4,11}, {4,10}, {5,10}, {3,21}, {1,6}, {5,11}, {4,7}, {1,12}, {5,15}, {3,8}, {3,23}, {4,16}, {3,9}, {3,24}, {2,12}, {3,20}, {5,8}, {4,6}, {5,16}, {5,23}, {5,21}, {4,12}, {5,20}, {5,7}, {1,7}, {5,25}, {2,7}, {3,11}, {1,16}, {2,20}, {3,16}, {3,15}, {2,18}, {1,21}, {3,25}, {4,21}, {4,20}, {3,19}, {5,17}, {5,6}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {4,15}, {1,17}, {4,22}, {3,6}, {4,25}, {2,19}, {2,17}, {5,18}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {5,13}, {1,9}, {1,22}, {2,13}, {2,25}, {2,8}, {4,14}, {1,23}, {4,19}, {1,11}, {5,22}, {2,22}, {3,10} }; // ET25.23 // Bipartite(9,16) Valencies [16,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7592461994557440000 EdgePairs[25][23]:={ {1,15}, {9,13}, {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {9,12}, {5,24}, {6,25}, {9,19}, {9,21}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {9,10}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {7,10}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {7,25}, {3,22}, {5,19}, {9,23}, {5,15}, {7,20}, {3,23}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {9,25}, {4,15}, {4,25}, {9,15}, {8,19}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {7,18}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {8,16}, {9,24}, {3,12}, {8,20}, {8,23}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {9,18}, {1,20}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {8,25}, {3,20}, {7,21}, {5,12}, {2,25}, {9,14}, {3,17}, {6,24}, {5,18}, {9,16}, {7,17}, {4,23}, {5,16}, {7,12}, {4,13}, {1,21}, {1,18}, {5,25}, {4,19}, {4,10}, {4,24}, {8,12}, {9,20}, {1,24}, {9,22} }; // ET25.24 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 28800 EdgePairs[25][24]:={ {19,20}, {21,23}, {1,11}, {10,25}, {1,20}, {2,24}, {10,24}, {6,16}, {7,15}, {4,24}, {14,19}, {15,24}, {3,8}, {11,25}, {6,17}, {8,9}, {12,22}, {3,6}, {3,13}, {3,25}, {19,24}, {17,20}, {4,19}, {16,19}, {7,22}, {7,8}, {2,4}, {5,20}, {1,21}, {17,24}, {16,18}, {2,9}, {11,14}, {21,22}, {18,21}, {8,10}, {6,7}, {11,12}, {8,15}, {6,11}, {16,23}, {3,5}, {9,11}, {13,16}, {10,15}, {19,21}, {6,22}, {15,25}, {3,18}, {3,17}, {6,21}, {2,25}, {7,12}, {14,23}, {1,17}, {5,22}, {4,22}, {8,19}, {3,14}, {12,17}, {16,24}, {18,20}, {12,20}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {19,22}, {6,8}, {5,25}, {11,15}, {11,13}, {3,12}, {11,22}, {9,14}, {14,24}, {24,25}, {12,13}, {5,23}, {4,21}, {1,2}, {13,22}, {10,21}, {2,13}, {14,16}, {13,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {1,12}, {3,4}, {14,15}, {1,23}, {7,17}, {8,11}, {21,25}, {5,7}, {13,23}, {23,25}, {8,13}, {8,22}, {1,9}, {9,10}, {15,20}, {17,18}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {10,12}, {2,3}, {3,10}, {1,3}, {2,17}, {4,6}, {22,25}, {14,17}, {3,19}, {4,9}, {1,24}, {12,23}, {22,23}, {13,24}, {17,25}, {12,19}, {20,23}, {3,23}, {8,23}, {18,19}, {18,25}, {12,14}, {20,25}, {3,21}, {17,19}, {2,7}, {9,12}, {6,9}, {13,15}, {1,15}, {12,15}, {18,23}, {6,14}, {2,11}, {4,5}, {15,21}, {14,25}, {16,17}, {16,21}, {22,24}, {15,18}, {11,16}, {7,23}, {9,18}, {2,22}, {1,16}, {4,14}, {5,8}, {16,20}, {8,24}, {6,25}, {7,9}, {13,14}, {6,10}, {5,10}, {8,18}, {4,18}, {11,19}, {10,19}, {1,4}, {1,8}, {4,20}, {7,10}, {2,12}, {9,24}, {10,20}, {1,6}, {5,15}, {5,19}, {6,20}, {17,22}, {21,24}, {6,13}, {13,20}, {2,18}, {23,24}, {9,23}, {7,21}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET25.25 // Bipartite(8,17) Valencies [17,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14341317100830720000 EdgePairs[25][25]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {8,14}, {8,13}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {7,10}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {3,9}, {7,25}, {3,22}, {5,19}, {5,15}, {7,20}, {3,23}, {7,13}, {8,17}, {7,14}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {8,19}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {7,18}, {8,9}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {8,16}, {3,12}, {8,20}, {8,23}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {7,9}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {8,25}, {3,20}, {7,21}, {5,12}, {2,25}, {3,17}, {4,9}, {6,24}, {5,18}, {7,17}, {4,23}, {5,16}, {7,12}, {4,13}, {1,21}, {1,18}, {5,25}, {4,19}, {4,10}, {4,24}, {8,12}, {1,24} }; // ET25.26 // Bipartite(7,18) Valencies [18,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 32267963476869120000 EdgePairs[25][26]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {2,18}, {2,15}, {6,9}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {7,10}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {7,25}, {3,22}, {5,19}, {5,15}, {6,8}, {7,20}, {3,23}, {7,13}, {7,14}, {6,15}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {2,24}, {4,11}, {5,22}, {7,8}, {6,19}, {1,23}, {2,21}, {5,8}, {7,18}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {7,9}, {2,8}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {3,8}, {3,20}, {7,21}, {5,12}, {2,25}, {3,17}, {4,9}, {6,24}, {5,18}, {7,17}, {4,23}, {1,8}, {5,16}, {7,12}, {4,13}, {1,21}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET25.27 // Bipartite(6,19) Valencies [19,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 87584472294359040000 EdgePairs[25][27]:={ {1,15}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {3,7}, {6,17}, {2,11}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {6,7}, {5,7}, {5,13}, {3,10}, {2,19}, {2,18}, {2,15}, {6,9}, {5,9}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {6,8}, {3,23}, {6,15}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {3,21}, {1,14}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {3,8}, {3,20}, {5,12}, {2,25}, {3,17}, {4,9}, {6,24}, {2,7}, {5,18}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET25.28 // Bipartite(5,20) Valencies [20,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 291948240981196800000 EdgePairs[25][28]:={ {1,15}, {5,14}, {3,15}, {4,14}, {1,11}, {2,22}, {4,8}, {3,7}, {2,11}, {2,20}, {1,25}, {4,16}, {5,24}, {1,9}, {5,7}, {4,6}, {5,13}, {3,10}, {2,19}, {2,18}, {2,15}, {5,9}, {5,21}, {3,19}, {4,12}, {5,6}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {3,23}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {2,24}, {4,11}, {5,22}, {1,23}, {2,21}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {3,8}, {3,20}, {5,12}, {2,25}, {3,6}, {3,17}, {4,9}, {2,7}, {5,18}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET25.29 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 2985984000000 EdgePairs[25][29]:={ {11,17}, {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {6,16}, {13,21}, {7,15}, {4,24}, {8,12}, {14,19}, {15,24}, {3,22}, {3,8}, {4,16}, {1,10}, {11,25}, {6,17}, {2,23}, {1,13}, {12,22}, {3,9}, {3,6}, {3,13}, {3,25}, {3,15}, {10,23}, {19,24}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {20,21}, {1,21}, {17,24}, {16,25}, {2,9}, {17,21}, {18,21}, {8,25}, {2,14}, {8,15}, {6,11}, {16,23}, {4,23}, {9,11}, {13,16}, {10,15}, {10,22}, {19,21}, {15,16}, {6,22}, {15,25}, {3,18}, {3,17}, {3,7}, {8,16}, {6,21}, {2,25}, {7,12}, {14,23}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {12,17}, {16,24}, {4,8}, {12,20}, {5,11}, {2,10}, {9,19}, {8,14}, {19,22}, {5,25}, {17,23}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {14,24}, {1,22}, {6,12}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {2,6}, {7,17}, {8,11}, {5,24}, {5,7}, {13,23}, {12,25}, {8,13}, {8,22}, {1,9}, {13,25}, {18,24}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {10,12}, {6,23}, {3,10}, {16,22}, {9,22}, {6,15}, {2,17}, {4,6}, {9,13}, {5,12}, {14,17}, {8,21}, {3,19}, {4,9}, {1,24}, {14,18}, {12,23}, {14,22}, {11,24}, {13,24}, {17,25}, {12,19}, {20,23}, {3,23}, {8,23}, {18,25}, {20,25}, {3,21}, {2,7}, {1,25}, {6,19}, {9,12}, {1,15}, {18,23}, {6,14}, {2,11}, {10,11}, {14,20}, {15,21}, {14,25}, {16,21}, {3,16}, {15,18}, {7,23}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {2,22}, {1,16}, {4,14}, {15,22}, {5,8}, {18,22}, {9,17}, {10,18}, {8,24}, {6,25}, {20,24}, {5,10}, {19,25}, {8,18}, {4,18}, {5,9}, {11,19}, {4,25}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {12,24}, {15,23}, {5,6}, {7,24}, {2,12}, {1,14}, {9,24}, {2,8}, {1,6}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {17,22}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {2,18}, {19,23}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET25.30 // Bipartite(4,21) Valencies [21,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1226182612121026560000 EdgePairs[25][30]:={ {2,11}, {3,22}, {2,14}, {4,8}, {4,13}, {4,9}, {4,24}, {4,23}, {1,14}, {1,24}, {3,12}, {2,24}, {2,10}, {1,10}, {4,11}, {4,10}, {3,21}, {1,6}, {3,5}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {3,23}, {4,16}, {3,9}, {3,24}, {2,12}, {3,20}, {2,21}, {4,6}, {4,12}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {3,25}, {4,21}, {4,20}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {1,5}, {4,15}, {1,17}, {4,22}, {3,6}, {4,25}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {4,14}, {1,23}, {4,19}, {1,11}, {1,25}, {2,22}, {3,10} }; // ET25.31 // Bipartite(3,22) Valencies [22,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6744004366665646080000 EdgePairs[25][31]:={ {2,11}, {3,22}, {2,14}, {1,14}, {1,24}, {3,12}, {2,24}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,23}, {3,9}, {3,24}, {2,12}, {2,4}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {3,25}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {1,5}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22}, {3,10} }; // ET25.32 // Bipartite(2,23) Valencies [23,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 51704033477769953280000 EdgePairs[25][32]:={ {2,11}, {2,14}, {1,14}, {1,24}, {2,24}, {2,10}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {2,12}, {2,4}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {1,16}, {2,20}, {2,18}, {1,21}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,17}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET25.33 // Bipartite(1,24) Valencies [24,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 620448401733239439360000 EdgePairs[25][33]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,12}, {1,2}, {1,3}, {1,17}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,6}, {1,14}, {1,18}, {1,21}, {1,19}, {1,20}, {1,8}, {1,24}, {1,9}, {1,23}, {1,25} }; // ET25.34 // Non-bipartite Valency 24 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 15511210043330985984000000 EdgePairs[25][34]:={ {13,21}, {5,7}, {6,25}, {5,22}, {10,18}, {9,17}, {3,8}, {11,25}, {9,10}, {17,18}, {12,22}, {5,11}, {16,22}, {1,3}, {6,15}, {11,15}, {8,21}, {5,6}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {2,7}, {6,9}, {21,22}, {6,14}, {16,21}, {19,20}, {10,11}, {19,21}, {11,17}, {1,12}, {9,11}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,25}, {4,24}, {2,6}, {8,13}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {3,10}, {2,5}, {8,9}, {2,10}, {19,22}, {3,9}, {2,17}, {17,20}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {15,19}, {6,18}, {4,23}, {11,18}, {6,24}, {13,16}, {13,19}, {3,17}, {7,15}, {8,22}, {9,20}, {4,22}, {8,19}, {1,18}, {7,14}, {6,17}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {3,13}, {11,22}, {9,13}, {5,12}, {2,8}, {4,9}, {6,12}, {19,23}, {4,21}, {13,17}, {18,19}, {20,25}, {7,19}, {16,18}, {1,2}, {2,13}, {13,18}, {12,15}, {8,10}, {8,15}, {11,21}, {8,17}, {10,16}, {16,17}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {7,12}, {8,24}, {4,10}, {14,21}, {18,20}, {5,14}, {12,17}, {2,23}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {6,8}, {11,13}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {7,8}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {17,19}, {9,12}, {12,18}, {2,16}, {6,11}, {9,25}, {4,5}, {10,22}, {7,23}, {6,22}, {10,25}, {15,24}, {3,7}, {12,25}, {1,16}, {3,22}, {4,14}, {5,8}, {4,15}, {6,23}, {15,17}, {13,14}, {1,5}, {2,3}, {7,24}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {12,14}, {18,21}, {10,21}, {9,21}, {9,23}, {7,21}, {14,16}, {2,11}, {10,15}, {3,5}, {2,21}, {1,11}, {5,24}, {2,22}, {16,20}, {8,11}, {18,24}, {14,19}, {1,7}, {3,14}, {19,25}, {3,11}, {4,8}, {4,25}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {8,14}, {7,10}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {14,18}, {22,23}, {5,21}, {9,15}, {17,24}, {20,23}, {2,4}, {17,21}, {16,23}, {18,23}, {13,15}, {14,25}, {15,21}, {14,20}, {1,15}, {11,12}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {15,18}, {5,17}, {3,4}, {15,16}, {7,17}, {13,23}, {6,21}, {15,22}, {15,20}, {23,25}, {16,24}, {7,20}, {7,9}, {5,10}, {4,20}, {8,20}, {5,13}, {5,25}, {17,23}, {10,23}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {16,19}, {10,14}, {21,24}, {12,19}, {20,21}, {8,25}, {23,24}, {2,9}, {12,21}, {6,7}, {2,14}, {15,25}, {21,23} }; // Total number of connected ET graphs of order 25 is 34 // ******************************************************************************************** // Order 26 // ET26.1 // Bipartite(13,13) Valencies [2,2] // Diameter 13 Girth 26 // Twin-free VT AT // Automorphism group of order 52 EdgePairs[26][1]:={ {11,17}, {3,16}, {3,20}, {5,24}, {1,14}, {9,21}, {12,19}, {8,23}, {5,20}, {13,15}, {4,18}, {10,23}, {1,16}, {7,25}, {11,21}, {10,19}, {2,18}, {4,22}, {6,22}, {8,26}, {9,25}, {6,26}, {2,15}, {7,24}, {12,14}, {13,17} }; // ET26.2 // Bipartite(13,13) Valencies [3,3] // Diameter 5 Girth 6 // Twin-free VT AT // Automorphism group of order 78 EdgePairs[26][2]:={ {13,19}, {7,26}, {3,16}, {8,21}, {11,16}, {4,17}, {1,14}, {11,25}, {13,24}, {13,23}, {3,14}, {4,15}, {8,23}, {5,20}, {1,22}, {3,21}, {10,20}, {6,17}, {6,24}, {12,20}, {2,18}, {7,18}, {11,24}, {6,22}, {10,21}, {2,23}, {5,16}, {4,25}, {9,14}, {8,22}, {10,15}, {9,25}, {2,15}, {9,18}, {1,26}, {5,19}, {12,26}, {12,17}, {7,19} }; // ET26.3 // Bipartite(13,13) Valencies [4,4] // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 104 EdgePairs[26][3]:={ {1,20}, {3,16}, {11,18}, {6,15}, {5,14}, {4,17}, {1,14}, {9,19}, {10,16}, {7,16}, {2,24}, {9,15}, {3,23}, {2,19}, {8,24}, {7,20}, {12,23}, {12,22}, {9,22}, {7,21}, {6,23}, {5,20}, {4,21}, {13,15}, {5,22}, {4,18}, {10,23}, {1,16}, {8,18}, {12,24}, {8,14}, {7,25}, {11,21}, {6,17}, {6,24}, {10,26}, {2,18}, {3,22}, {11,20}, {8,26}, {9,25}, {2,15}, {4,26}, {13,21}, {13,25}, {11,19}, {3,25}, {10,17}, {1,26}, {5,19}, {12,14}, {13,17} }; // ET26.4 // Bipartite(13,13) Valencies [4,4] // Diameter 3 Girth 6 // Twin-free VT AT // Automorphism group of order 11232 EdgePairs[26][4]:={ {12,20}, {11,16}, {8,19}, {4,23}, {9,23}, {1,24}, {12,18}, {11,25}, {9,20}, {13,16}, {8,23}, {6,26}, {8,21}, {8,15}, {5,15}, {11,23}, {3,24}, {13,14}, {6,15}, {2,21}, {6,16}, {5,20}, {10,16}, {5,25}, {1,15}, {9,24}, {7,18}, {3,25}, {3,19}, {1,18}, {3,26}, {12,26}, {13,21}, {7,19}, {4,22}, {10,19}, {5,14}, {2,17}, {13,24}, {6,17}, {7,17}, {10,22}, {4,26}, {1,22}, {2,25}, {4,14}, {7,14}, {11,18}, {10,20}, {2,22}, {9,17}, {12,21} }; // ET26.5 // Non-bipartite Valency 4 // Diameter 6 Girth 4 // Has twins VT AT // Automorphism group of order 212992 EdgePairs[26][5]:={ {3,22}, {12,20}, {7,16}, {3,12}, {5,24}, {18,26}, {2,10}, {8,16}, {1,10}, {6,14}, {4,11}, {16,23}, {3,21}, {8,15}, {11,20}, {8,25}, {15,24}, {1,20}, {15,23}, {17,25}, {5,23}, {4,12}, {3,11}, {2,20}, {14,22}, {18,25}, {4,21}, {7,15}, {12,19}, {7,25}, {13,22}, {13,21}, {4,22}, {14,21}, {2,19}, {10,17}, {9,18}, {8,26}, {5,14}, {5,13}, {2,9}, {1,19}, {1,9}, {11,19}, {16,24}, {17,26}, {6,23}, {6,13}, {10,18}, {9,17}, {6,24}, {7,26} }; // ET26.6 // Bipartite(13,13) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 156 EdgePairs[26][6]:={ {1,26}, {4,24}, {10,15}, {11,16}, {9,19}, {1,14}, {9,23}, {11,15}, {8,20}, {2,26}, {12,18}, {9,25}, {9,20}, {11,25}, {7,23}, {9,21}, {11,24}, {12,16}, {8,21}, {3,21}, {13,25}, {1,20}, {5,15}, {8,24}, {3,23}, {3,24}, {11,21}, {13,18}, {2,21}, {5,16}, {6,16}, {5,23}, {4,18}, {3,16}, {2,20}, {1,16}, {10,23}, {10,26}, {7,18}, {6,20}, {3,17}, {5,19}, {2,18}, {4,20}, {5,17}, {10,14}, {2,15}, {3,14}, {12,14}, {12,19}, {7,25}, {8,22}, {10,24}, {12,26}, {13,22}, {4,15}, {13,21}, {1,17}, {7,19}, {6,18}, {13,15}, {6,22}, {8,26}, {12,22}, {9,14}, {6,25}, {2,23}, {7,17}, {10,22}, {4,14}, {4,19}, {11,19}, {5,22}, {1,25}, {8,17}, {13,17}, {6,24}, {7,26} }; // ET26.7 // Bipartite(10,16) Valencies [8,5] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1920 EdgePairs[26][7]:={ {4,13}, {9,19}, {1,14}, {7,11}, {9,23}, {8,20}, {1,24}, {3,12}, {5,24}, {2,24}, {7,23}, {9,16}, {8,23}, {6,26}, {8,21}, {8,25}, {5,11}, {1,20}, {1,12}, {5,15}, {8,24}, {9,11}, {10,12}, {2,12}, {6,15}, {2,21}, {5,16}, {6,16}, {5,21}, {5,20}, {2,16}, {3,11}, {9,24}, {3,16}, {10,23}, {3,15}, {10,26}, {7,18}, {3,17}, {9,12}, {4,21}, {4,20}, {3,19}, {7,15}, {10,14}, {3,14}, {6,21}, {4,17}, {8,22}, {4,15}, {7,20}, {7,19}, {6,18}, {4,25}, {6,19}, {9,22}, {10,19}, {6,22}, {8,26}, {9,18}, {10,17}, {2,17}, {5,18}, {3,13}, {6,17}, {1,13}, {8,18}, {5,13}, {10,22}, {4,26}, {2,13}, {2,25}, {4,14}, {10,25}, {1,23}, {7,14}, {1,11}, {1,25}, {2,22}, {7,26} }; // ET26.8 // Non-bipartite Valency 8 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 425984 EdgePairs[26][8]:={ {1,15}, {7,19}, {13,25}, {14,21}, {5,14}, {10,21}, {14,25}, {15,23}, {3,15}, {12,26}, {10,22}, {11,23}, {6,18}, {12,19}, {6,14}, {6,17}, {6,23}, {2,20}, {4,16}, {6,13}, {5,24}, {1,9}, {16,23}, {9,21}, {7,15}, {5,13}, {12,25}, {2,19}, {2,15}, {9,17}, {10,18}, {10,23}, {4,12}, {3,18}, {8,22}, {8,15}, {2,14}, {5,23}, {3,11}, {2,10}, {1,10}, {7,26}, {13,26}, {2,16}, {1,16}, {8,21}, {2,13}, {7,25}, {3,22}, {9,23}, {10,24}, {5,19}, {7,20}, {18,25}, {8,26}, {14,26}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {8,19}, {11,26}, {13,22}, {12,24}, {12,23}, {4,11}, {6,19}, {14,22}, {11,19}, {5,20}, {4,22}, {8,16}, {5,17}, {9,24}, {3,12}, {11,25}, {8,20}, {7,16}, {6,20}, {3,21}, {1,14}, {9,18}, {10,17}, {13,21}, {1,20}, {7,22}, {3,16}, {1,13}, {4,18}, {8,25}, {11,20}, {7,21}, {3,17}, {17,26}, {6,24}, {5,18}, {11,24}, {12,20}, {15,24}, {17,25}, {18,26}, {9,22}, {16,24} }; // ET26.9 // Bipartite(8,18) Valencies [9,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 17915904 EdgePairs[26][9]:={ {3,22}, {1,26}, {4,13}, {4,24}, {8,19}, {1,14}, {7,11}, {7,16}, {8,20}, {2,24}, {7,23}, {2,10}, {6,12}, {7,13}, {8,25}, {5,11}, {6,10}, {1,20}, {5,15}, {8,24}, {3,23}, {2,12}, {6,15}, {2,21}, {5,9}, {5,23}, {6,16}, {5,21}, {5,20}, {4,12}, {4,18}, {2,16}, {1,15}, {7,10}, {3,11}, {3,16}, {3,17}, {2,18}, {3,25}, {1,21}, {4,20}, {3,19}, {5,17}, {8,13}, {2,15}, {8,12}, {6,21}, {7,25}, {7,22}, {1,17}, {7,19}, {6,18}, {4,25}, {6,22}, {8,26}, {5,14}, {3,13}, {5,26}, {8,14}, {8,18}, {2,9}, {7,17}, {1,9}, {4,26}, {4,14}, {1,23}, {4,19}, {1,11}, {2,22}, {6,24}, {3,10}, {6,9} }; // ET26.10 // Bipartite(8,18) Valencies [9,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2239488 EdgePairs[26][10]:={ {5,12}, {3,22}, {2,14}, {4,9}, {8,20}, {2,26}, {5,24}, {7,12}, {8,16}, {4,10}, {3,21}, {6,12}, {7,13}, {6,10}, {5,11}, {8,24}, {3,23}, {4,16}, {3,9}, {2,21}, {6,16}, {5,23}, {8,10}, {5,25}, {1,15}, {3,11}, {3,16}, {2,20}, {3,15}, {7,18}, {3,17}, {5,19}, {1,21}, {4,21}, {4,20}, {5,17}, {2,15}, {8,12}, {7,25}, {8,22}, {4,15}, {7,20}, {1,17}, {7,19}, {6,18}, {4,22}, {6,22}, {2,19}, {8,26}, {5,18}, {6,17}, {1,13}, {8,14}, {8,18}, {5,13}, {2,9}, {1,19}, {6,11}, {1,9}, {4,26}, {2,13}, {2,25}, {4,14}, {1,23}, {7,14}, {1,11}, {1,25}, {6,23}, {7,24}, {6,24}, {3,10}, {7,26} }; // ET26.11 // Bipartite(13,13) Valencies [9,9] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 11232 EdgePairs[26][11]:={ {13,25}, {11,15}, {10,21}, {11,17}, {3,15}, {8,24}, {6,18}, {12,19}, {6,14}, {12,16}, {13,18}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {12,15}, {12,17}, {12,14}, {12,22}, {5,24}, {6,25}, {9,19}, {9,21}, {11,22}, {7,23}, {7,15}, {12,25}, {2,19}, {2,18}, {2,15}, {5,26}, {8,14}, {10,18}, {6,22}, {13,20}, {5,21}, {10,23}, {3,18}, {8,22}, {2,14}, {5,23}, {4,20}, {2,23}, {7,26}, {1,17}, {10,25}, {13,26}, {2,16}, {1,16}, {6,21}, {8,18}, {3,14}, {10,15}, {7,25}, {3,22}, {5,19}, {10,24}, {7,20}, {8,26}, {3,23}, {8,17}, {1,19}, {4,21}, {4,17}, {9,25}, {4,15}, {4,25}, {9,15}, {1,26}, {11,26}, {13,22}, {11,14}, {12,24}, {12,23}, {2,24}, {5,22}, {6,19}, {1,23}, {11,19}, {10,14}, {8,16}, {5,17}, {8,20}, {7,16}, {9,26}, {6,20}, {11,21}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {7,22}, {3,16}, {4,18}, {8,25}, {13,23}, {2,26}, {13,17}, {11,20}, {7,21}, {3,20}, {13,15}, {9,14}, {3,17}, {6,24}, {5,18}, {10,26}, {9,16}, {13,19}, {11,24}, {5,16}, {1,21}, {4,19}, {4,24}, {9,22} }; // ET26.12 // Bipartite(6,20) Valencies [10,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[26][12]:={ {2,11}, {5,12}, {4,8}, {4,13}, {4,9}, {4,23}, {1,14}, {1,24}, {3,12}, {2,26}, {5,24}, {2,24}, {2,10}, {3,21}, {6,12}, {6,10}, {1,20}, {3,23}, {4,16}, {6,7}, {5,9}, {5,16}, {6,16}, {5,23}, {5,21}, {5,20}, {1,7}, {3,11}, {3,7}, {3,15}, {6,20}, {2,18}, {1,21}, {3,19}, {2,15}, {4,17}, {3,26}, {4,15}, {4,22}, {6,18}, {6,19}, {6,22}, {5,14}, {2,17}, {5,18}, {3,13}, {6,25}, {6,17}, {5,26}, {1,8}, {1,13}, {2,9}, {1,22}, {2,25}, {2,8}, {4,14}, {4,19}, {1,11}, {1,25}, {3,10} }; // ET26.13 // Bipartite(6,20) Valencies [10,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4976640000 EdgePairs[26][13]:={ {4,8}, {4,24}, {1,24}, {2,24}, {6,14}, {6,26}, {4,10}, {5,10}, {3,21}, {6,10}, {1,20}, {1,12}, {3,23}, {4,16}, {3,9}, {2,12}, {6,7}, {6,15}, {2,21}, {5,9}, {5,21}, {4,12}, {4,18}, {2,16}, {1,7}, {5,25}, {1,15}, {3,11}, {1,16}, {3,7}, {2,20}, {3,15}, {3,17}, {3,25}, {4,20}, {3,19}, {5,17}, {4,22}, {6,18}, {6,19}, {6,22}, {5,14}, {2,17}, {5,18}, {3,13}, {5,26}, {1,8}, {5,13}, {2,9}, {1,19}, {6,11}, {4,26}, {2,13}, {2,25}, {2,8}, {4,14}, {1,23}, {1,11}, {5,22}, {6,23} }; // ET26.14 // Bipartite(6,20) Valencies [10,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 61440 EdgePairs[26][14]:={ {2,11}, {3,22}, {5,12}, {1,26}, {4,8}, {2,14}, {3,12}, {2,24}, {2,10}, {1,10}, {6,14}, {6,26}, {4,11}, {5,10}, {4,7}, {1,20}, {5,15}, {3,23}, {3,24}, {3,9}, {6,15}, {2,21}, {5,16}, {5,23}, {6,16}, {4,12}, {5,20}, {4,18}, {1,7}, {5,25}, {1,16}, {3,7}, {2,20}, {3,17}, {2,18}, {1,21}, {4,21}, {3,19}, {3,14}, {4,17}, {4,15}, {1,17}, {4,22}, {6,18}, {4,25}, {6,19}, {3,13}, {6,25}, {2,23}, {5,26}, {5,13}, {1,19}, {1,9}, {2,13}, {2,8}, {1,11}, {5,22}, {6,8}, {6,24}, {6,9} }; // ET26.15 // Bipartite(13,13) Valencies [12,12] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 12454041600 EdgePairs[26][15]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {11,20}, {6,16}, {13,21}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {12,22}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {2,19}, {1,19}, {2,26}, {1,21}, {11,14}, {8,25}, {2,14}, {8,15}, {4,23}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {12,20}, {9,19}, {8,14}, {5,25}, {11,15}, {11,22}, {9,14}, {7,25}, {1,22}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {10,21}, {2,20}, {6,18}, {13,18}, {8,17}, {11,21}, {7,16}, {7,26}, {5,18}, {11,23}, {1,23}, {6,24}, {7,17}, {5,24}, {13,23}, {12,25}, {8,22}, {13,25}, {5,14}, {9,20}, {4,15}, {7,14}, {6,23}, {3,26}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {3,19}, {1,24}, {11,24}, {13,24}, {12,19}, {6,26}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {13,15}, {12,15}, {6,14}, {3,16}, {13,26}, {11,16}, {7,23}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,26}, {8,18}, {11,19}, {10,19}, {4,25}, {4,20}, {12,24}, {8,20}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET26.16 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 638976 EdgePairs[26][16]:={ {14,21}, {6,12}, {5,14}, {15,23}, {11,17}, {12,19}, {2,22}, {6,14}, {24,26}, {23,25}, {6,23}, {2,20}, {2,3}, {14,19}, {17,19}, {1,25}, {9,12}, {6,13}, {12,17}, {12,14}, {20,21}, {5,24}, {16,18}, {1,9}, {6,25}, {16,23}, {4,5}, {6,7}, {12,18}, {18,23}, {5,7}, {7,15}, {4,6}, {5,13}, {3,10}, {14,20}, {2,19}, {5,26}, {8,14}, {22,24}, {8,13}, {9,17}, {10,18}, {13,20}, {4,12}, {18,24}, {20,25}, {8,15}, {13,16}, {7,10}, {16,21}, {17,23}, {5,23}, {1,3}, {3,11}, {2,10}, {6,11}, {15,22}, {17,24}, {1,10}, {7,26}, {19,26}, {14,16}, {10,12}, {1,22}, {16,17}, {8,10}, {10,15}, {3,9}, {10,16}, {7,25}, {3,22}, {6,8}, {18,25}, {8,26}, {7,13}, {3,23}, {7,14}, {22,23}, {6,26}, {1,19}, {11,18}, {4,21}, {2,9}, {3,5}, {9,15}, {1,4}, {18,19}, {1,26}, {13,22}, {11,14}, {2,4}, {11,13}, {4,11}, {15,21}, {2,21}, {14,22}, {1,7}, {15,18}, {5,8}, {11,19}, {8,9}, {4,22}, {8,16}, {3,24}, {3,12}, {21,23}, {16,22}, {7,16}, {18,20}, {3,21}, {19,22}, {9,18}, {10,17}, {20,26}, {7,9}, {13,21}, {24,25}, {2,8}, {14,15}, {1,20}, {9,11}, {5,11}, {8,25}, {2,26}, {15,17}, {11,20}, {13,15}, {5,12}, {2,25}, {3,6}, {17,26}, {4,9}, {6,24}, {2,7}, {17,20}, {19,25}, {20,22}, {9,16}, {23,26}, {13,19}, {19,21}, {4,23}, {1,8}, {1,21}, {10,11}, {12,20}, {15,24}, {5,25}, {21,24}, {4,10}, {4,24}, {12,13}, {17,25}, {18,26}, {16,24} }; // ET26.17 // Bipartite(13,13) Valencies [13,13] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 77551576087265280000 EdgePairs[26][17]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {6,16}, {13,21}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {12,22}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,14}, {8,15}, {4,23}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {12,20}, {9,19}, {8,14}, {5,25}, {11,15}, {11,22}, {9,14}, {7,25}, {1,22}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {10,21}, {2,20}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {11,23}, {1,23}, {6,24}, {7,17}, {5,24}, {13,23}, {12,25}, {8,22}, {13,25}, {5,14}, {9,20}, {4,15}, {7,14}, {6,23}, {3,26}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {8,21}, {3,19}, {1,24}, {12,23}, {11,24}, {13,24}, {6,26}, {12,19}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {13,15}, {1,15}, {12,15}, {6,14}, {3,16}, {11,26}, {13,26}, {11,16}, {7,23}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {13,14}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {8,20}, {12,24}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET26.18 // Bipartite(12,14) Valencies [14,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 41758540970065920000 EdgePairs[26][18]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {6,16}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {1,13}, {12,22}, {3,13}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,14}, {8,15}, {4,23}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {12,20}, {9,19}, {8,14}, {5,25}, {11,15}, {11,13}, {11,22}, {7,13}, {9,14}, {7,25}, {1,22}, {12,13}, {12,16}, {5,23}, {4,21}, {3,20}, {10,21}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {5,24}, {12,25}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {10,13}, {6,23}, {3,26}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {9,13}, {8,21}, {3,19}, {1,24}, {12,23}, {11,24}, {6,26}, {12,19}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {1,15}, {12,15}, {6,14}, {3,16}, {11,26}, {11,16}, {7,23}, {2,21}, {9,18}, {10,17}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {5,13}, {8,20}, {12,24}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET26.19 // Bipartite(11,15) Valencies [15,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 52198176212582400000 EdgePairs[26][19]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {6,16}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {1,13}, {3,13}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {11,12}, {2,14}, {8,15}, {4,23}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {9,26}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {10,13}, {10,12}, {6,23}, {3,26}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {11,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,14}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {9,18}, {10,17}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,12}, {4,20}, {5,13}, {8,20}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET26.20 // Bipartite(10,16) Valencies [16,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 75924619945574400000 EdgePairs[26][20]:={ {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {6,16}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {6,17}, {2,23}, {1,13}, {3,13}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {2,26}, {1,21}, {8,25}, {2,14}, {8,15}, {6,11}, {4,23}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {5,11}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {10,13}, {10,12}, {6,23}, {3,26}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,14}, {2,11}, {10,11}, {3,16}, {7,23}, {2,21}, {9,18}, {10,17}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,26}, {8,18}, {4,18}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {7,18}, {10,16}, {5,16} }; // ET26.21 // Bipartite(9,17) Valencies [17,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 129071853907476480000 EdgePairs[26][21]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {3,13}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {2,26}, {1,21}, {8,10}, {8,25}, {2,14}, {8,15}, {6,11}, {4,23}, {9,11}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {5,11}, {2,10}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {6,23}, {3,10}, {3,26}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,14}, {2,11}, {3,16}, {7,23}, {2,21}, {9,18}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {6,10}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {7,18}, {5,16} }; // ET26.22 // Bipartite(8,18) Valencies [18,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 258143707814952960000 EdgePairs[26][22]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {3,13}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {2,26}, {1,21}, {2,9}, {8,10}, {8,25}, {2,14}, {8,15}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {5,11}, {2,10}, {8,14}, {5,25}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {5,14}, {4,15}, {4,13}, {3,11}, {7,14}, {6,23}, {3,10}, {3,26}, {8,26}, {6,15}, {2,17}, {5,12}, {8,21}, {3,19}, {4,9}, {1,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {1,15}, {6,14}, {2,11}, {3,16}, {7,23}, {2,21}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {6,10}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {7,24}, {2,12}, {1,14}, {5,15}, {5,19}, {6,20}, {5,21}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {7,18}, {5,16} }; // ET26.23 // Bipartite(7,19) Valencies [19,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 613091306060513280000 EdgePairs[26][23]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {7,10}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {7,26}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {7,25}, {3,22}, {5,19}, {5,15}, {6,8}, {7,20}, {3,23}, {7,13}, {7,14}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {7,8}, {6,19}, {1,23}, {2,21}, {5,8}, {7,18}, {2,12}, {4,22}, {5,20}, {3,26}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {7,9}, {2,8}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {7,21}, {5,12}, {2,25}, {3,17}, {4,9}, {6,24}, {5,18}, {7,17}, {4,23}, {1,8}, {5,16}, {7,12}, {4,13}, {1,21}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET26.24 // Bipartite(6,20) Valencies [20,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1751689445887180800000 EdgePairs[26][24]:={ {1,15}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {3,7}, {6,17}, {2,11}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {6,7}, {5,7}, {5,13}, {3,10}, {2,19}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {6,8}, {3,23}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {2,21}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,26}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {3,21}, {1,14}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {5,12}, {2,25}, {3,17}, {4,9}, {6,24}, {2,7}, {5,18}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET26.25 // Bipartite(5,21) Valencies [21,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6130913060605132800000 EdgePairs[26][25]:={ {1,15}, {5,14}, {3,15}, {4,14}, {1,11}, {2,22}, {4,8}, {3,7}, {2,11}, {2,20}, {1,25}, {4,16}, {5,24}, {1,9}, {5,7}, {4,6}, {5,13}, {3,10}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {3,19}, {4,12}, {5,6}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {3,23}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {1,23}, {2,21}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,26}, {3,24}, {5,17}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {5,12}, {2,25}, {3,6}, {3,17}, {4,9}, {2,7}, {5,18}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET26.26 // Bipartite(4,22) Valencies [22,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 26976017466662584320000 EdgePairs[26][26]:={ {2,11}, {3,22}, {1,26}, {2,14}, {4,8}, {4,13}, {4,9}, {4,24}, {4,23}, {1,14}, {1,24}, {2,26}, {3,12}, {2,24}, {2,10}, {1,10}, {4,11}, {4,10}, {3,21}, {1,6}, {3,5}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {3,23}, {4,16}, {3,9}, {3,24}, {2,12}, {3,20}, {2,21}, {4,6}, {4,12}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {3,25}, {4,21}, {4,20}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {3,26}, {1,5}, {4,15}, {1,17}, {4,22}, {3,6}, {4,25}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {4,26}, {1,22}, {2,13}, {2,8}, {2,25}, {4,14}, {1,23}, {4,19}, {1,11}, {1,25}, {2,22}, {3,10} }; // ET26.27 // Bipartite(3,23) Valencies [23,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 155112100433309859840000 EdgePairs[26][27]:={ {2,11}, {3,22}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {3,12}, {2,24}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,23}, {3,9}, {3,24}, {2,12}, {2,4}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {3,25}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {3,26}, {1,5}, {1,17}, {3,6}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22}, {3,10} }; // ET26.28 // Bipartite(2,24) Valencies [24,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1240896803466478878720000 EdgePairs[26][28]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {2,24}, {2,10}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {2,12}, {2,4}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {1,16}, {2,20}, {2,18}, {1,21}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,17}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET26.29 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 51011754393600 EdgePairs[26][29]:={ {13,21}, {5,7}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {11,25}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {1,3}, {6,15}, {11,15}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {2,7}, {6,9}, {6,14}, {16,21}, {10,11}, {19,21}, {11,17}, {1,12}, {9,11}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {2,25}, {4,24}, {2,6}, {8,13}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {12,26}, {3,10}, {2,5}, {8,9}, {2,10}, {19,22}, {3,9}, {10,26}, {2,17}, {17,20}, {10,20}, {17,26}, {1,24}, {13,24}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {15,19}, {6,18}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {7,14}, {6,17}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {3,13}, {11,22}, {9,13}, {5,12}, {2,8}, {4,9}, {6,12}, {19,23}, {4,21}, {13,17}, {18,19}, {20,25}, {7,19}, {16,18}, {2,13}, {13,18}, {12,15}, {8,10}, {8,15}, {11,21}, {8,17}, {10,16}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {12,17}, {2,23}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {6,8}, {11,13}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {17,19}, {9,12}, {12,18}, {2,16}, {6,11}, {9,25}, {4,5}, {10,22}, {7,23}, {6,22}, {10,25}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {4,15}, {6,23}, {15,17}, {1,5}, {2,3}, {7,24}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {9,23}, {7,21}, {14,16}, {2,11}, {14,26}, {10,15}, {3,5}, {2,21}, {1,11}, {5,24}, {2,22}, {16,20}, {8,11}, {18,24}, {14,19}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {4,25}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {8,14}, {7,10}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {14,18}, {22,23}, {5,21}, {9,15}, {17,24}, {20,23}, {2,4}, {17,21}, {16,23}, {18,23}, {13,15}, {14,25}, {15,21}, {14,20}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {15,18}, {5,17}, {7,17}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {23,25}, {16,24}, {7,20}, {7,9}, {5,10}, {4,20}, {8,20}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {20,21}, {8,25}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {21,23} }; // ET26.30 // Bipartite(1,25) Valencies [25,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 15511210043330985984000000 EdgePairs[26][30]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,12}, {1,2}, {1,3}, {1,17}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,6}, {1,14}, {1,26}, {1,18}, {1,21}, {1,19}, {1,20}, {1,8}, {1,24}, {1,9}, {1,23}, {1,25} }; // ET26.31 // Non-bipartite Valency 25 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 403291461126605635584000000 EdgePairs[26][31]:={ {13,21}, {5,7}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {11,25}, {9,10}, {17,18}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {1,3}, {6,15}, {11,15}, {8,21}, {5,6}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {2,7}, {6,9}, {21,22}, {6,14}, {16,21}, {19,20}, {10,11}, {19,21}, {11,17}, {1,12}, {9,11}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {2,25}, {4,24}, {2,6}, {8,13}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {12,26}, {3,10}, {2,5}, {8,9}, {2,10}, {19,22}, {3,9}, {10,26}, {2,17}, {17,20}, {10,20}, {17,26}, {1,24}, {13,24}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {15,19}, {6,18}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {7,14}, {6,17}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {25,26}, {3,13}, {11,22}, {9,13}, {5,12}, {2,8}, {4,9}, {6,12}, {19,23}, {4,21}, {13,17}, {18,19}, {20,25}, {7,19}, {16,18}, {1,2}, {2,13}, {13,18}, {12,15}, {8,10}, {8,15}, {11,21}, {8,17}, {10,16}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {12,17}, {2,23}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {6,8}, {11,13}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {7,8}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {17,19}, {9,12}, {12,18}, {2,16}, {6,11}, {9,25}, {4,5}, {10,22}, {7,23}, {6,22}, {10,25}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {4,15}, {6,23}, {15,17}, {13,14}, {1,5}, {2,3}, {7,24}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {9,23}, {7,21}, {14,16}, {2,11}, {14,26}, {10,15}, {3,5}, {2,21}, {1,11}, {5,24}, {2,22}, {16,20}, {8,11}, {18,24}, {14,19}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {4,25}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {8,14}, {7,10}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {14,18}, {22,23}, {5,21}, {9,15}, {17,24}, {20,23}, {2,4}, {17,21}, {16,23}, {18,23}, {13,15}, {14,25}, {15,21}, {14,20}, {1,15}, {11,12}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {15,18}, {5,17}, {3,4}, {15,16}, {7,17}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {23,25}, {16,24}, {7,20}, {7,9}, {5,10}, {4,20}, {8,20}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {20,21}, {8,25}, {23,24}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {21,23} }; // Total number of connected ET graphs of order 26 is 31 // ******************************************************************************************** // Order 27 // ET27.1 // Non-bipartite Valency 2 // Diameter 13 Girth 27 // Twin-free VT AT // Automorphism group of order 54 EdgePairs[27][1]:={ {8,13}, {4,10}, {6,26}, {5,11}, {5,25}, {9,14}, {20,25}, {7,15}, {3,24}, {1,22}, {6,12}, {11,18}, {4,27}, {13,21}, {18,22}, {16,23}, {15,20}, {2,7}, {14,19}, {1,9}, {10,17}, {19,27}, {2,23}, {17,24}, {3,8}, {12,16}, {21,26} }; // ET27.2 // Bipartite(9,18) Valencies [4,2] // Diameter 6 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 72 EdgePairs[27][2]:={ {3,24}, {8,21}, {5,14}, {1,14}, {9,19}, {4,23}, {2,11}, {7,27}, {9,15}, {7,20}, {8,24}, {3,18}, {9,23}, {5,20}, {4,21}, {1,22}, {7,15}, {1,16}, {1,10}, {6,16}, {8,10}, {3,27}, {2,13}, {5,25}, {2,18}, {6,11}, {3,22}, {5,17}, {8,19}, {6,26}, {6,25}, {4,26}, {7,12}, {4,13}, {2,12}, {9,17} }; // ET27.3 // Bipartite(9,18) Valencies [4,2] // Diameter 9 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 9216 EdgePairs[27][3]:={ {2,27}, {7,14}, {6,15}, {3,10}, {7,23}, {5,13}, {3,19}, {2,11}, {9,15}, {7,21}, {9,22}, {8,23}, {5,20}, {4,16}, {8,16}, {3,21}, {5,22}, {4,18}, {9,13}, {1,10}, {8,14}, {1,17}, {4,27}, {6,17}, {6,24}, {2,20}, {2,18}, {5,11}, {1,19}, {4,25}, {8,25}, {6,26}, {3,12}, {7,12}, {1,26}, {9,24} }; // ET27.4 // Non-bipartite Valency 4 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 108 EdgePairs[27][4]:={ {5,12}, {3,22}, {11,16}, {13,19}, {18,22}, {14,19}, {1,24}, {19,26}, {2,24}, {15,20}, {6,26}, {12,16}, {4,11}, {16,23}, {4,10}, {8,15}, {6,12}, {19,25}, {6,10}, {5,11}, {3,23}, {3,8}, {15,21}, {21,27}, {20,27}, {5,25}, {2,7}, {3,7}, {4,27}, {7,15}, {8,13}, {6,27}, {21,25}, {16,22}, {9,13}, {13,21}, {4,25}, {10,17}, {20,26}, {9,14}, {5,26}, {14,20}, {1,8}, {2,9}, {18,24}, {1,9}, {1,23}, {7,14}, {11,18}, {12,17}, {2,22}, {17,24}, {10,18}, {17,23} }; // ET27.5 // Non-bipartite Valency 4 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 216 EdgePairs[27][5]:={ {5,12}, {3,22}, {8,19}, {1,24}, {9,25}, {14,26}, {2,10}, {6,14}, {11,24}, {4,10}, {4,7}, {5,15}, {17,25}, {3,9}, {11,21}, {13,18}, {2,21}, {5,16}, {5,23}, {7,27}, {2,16}, {20,27}, {10,16}, {9,24}, {3,15}, {6,20}, {12,23}, {15,16}, {3,18}, {4,17}, {8,22}, {7,20}, {13,21}, {12,25}, {10,19}, {6,22}, {14,23}, {9,18}, {18,27}, {21,26}, {14,20}, {1,8}, {7,17}, {1,19}, {11,26}, {13,27}, {23,26}, {2,13}, {4,19}, {12,17}, {1,11}, {24,25}, {6,8}, {15,22} }; // ET27.6 // Non-bipartite Valency 4 // Diameter 3 Girth 5 // Twin-free VT Non-AT // Automorphism group of order 54 EdgePairs[27][6]:={ {1,26}, {12,27}, {4,9}, {19,24}, {9,23}, {11,15}, {11,17}, {9,20}, {22,25}, {21,22}, {4,10}, {13,26}, {15,27}, {3,8}, {9,11}, {3,24}, {2,4}, {5,8}, {6,16}, {5,20}, {21,27}, {1,7}, {3,16}, {3,15}, {10,26}, {4,27}, {5,17}, {12,23}, {8,13}, {8,12}, {12,14}, {18,19}, {16,21}, {7,22}, {1,5}, {13,21}, {7,19}, {20,25}, {6,19}, {24,26}, {2,17}, {18,23}, {6,25}, {14,20}, {10,22}, {6,11}, {2,13}, {2,25}, {1,23}, {7,14}, {15,18}, {14,16}, {17,24}, {10,18} }; // ET27.7 // Bipartite(12,15) Valencies [5,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[27][7]:={ {12,27}, {11,16}, {10,15}, {8,19}, {1,14}, {11,15}, {9,23}, {9,25}, {11,25}, {7,23}, {5,27}, {8,21}, {11,20}, {3,27}, {7,13}, {8,24}, {3,24}, {6,16}, {5,21}, {5,20}, {4,18}, {10,16}, {10,23}, {1,16}, {6,20}, {2,18}, {4,20}, {3,19}, {5,17}, {7,15}, {12,23}, {6,27}, {2,15}, {3,18}, {3,26}, {7,21}, {12,26}, {4,22}, {12,25}, {2,19}, {10,17}, {9,18}, {9,14}, {1,13}, {8,14}, {1,19}, {10,22}, {11,26}, {4,26}, {1,22}, {2,13}, {2,25}, {4,14}, {5,22}, {8,17}, {6,13}, {9,17}, {7,24}, {6,24}, {12,21} }; // ET27.8 // Bipartite(12,15) Valencies [5,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 46080 EdgePairs[27][8]:={ {2,14}, {12,27}, {10,15}, {9,19}, {2,26}, {12,18}, {11,25}, {2,24}, {7,23}, {9,21}, {9,16}, {5,27}, {3,21}, {8,15}, {7,13}, {11,27}, {1,20}, {8,24}, {11,23}, {4,16}, {11,21}, {5,23}, {5,21}, {4,18}, {10,16}, {5,25}, {3,16}, {3,17}, {4,20}, {3,19}, {8,13}, {6,27}, {2,15}, {3,14}, {12,24}, {7,22}, {4,15}, {7,20}, {7,19}, {6,18}, {4,25}, {6,22}, {8,26}, {12,22}, {9,14}, {6,17}, {5,26}, {1,13}, {8,14}, {1,19}, {11,26}, {1,22}, {2,13}, {10,25}, {1,23}, {10,20}, {12,17}, {9,17}, {10,18}, {6,24} }; // ET27.9 // Bipartite(9,18) Valencies [6,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 108 EdgePairs[27][9]:={ {2,11}, {1,26}, {2,14}, {4,23}, {9,19}, {7,11}, {9,23}, {8,20}, {5,24}, {9,20}, {2,24}, {7,12}, {1,10}, {8,21}, {4,10}, {8,15}, {3,27}, {6,10}, {5,11}, {9,15}, {2,21}, {6,16}, {5,20}, {4,12}, {7,27}, {2,16}, {3,16}, {3,15}, {7,18}, {5,19}, {3,25}, {9,12}, {4,21}, {9,27}, {5,17}, {8,13}, {3,14}, {3,18}, {1,18}, {7,22}, {1,17}, {4,22}, {6,19}, {8,26}, {6,25}, {1,13}, {8,14}, {5,13}, {7,17}, {4,26}, {1,25}, {6,23}, {2,22}, {6,24} }; // ET27.10 // Bipartite(9,18) Valencies [6,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3359232 EdgePairs[27][10]:={ {3,22}, {4,13}, {4,24}, {9,23}, {9,20}, {2,10}, {8,23}, {8,11}, {1,10}, {6,12}, {8,24}, {3,23}, {9,11}, {6,15}, {2,21}, {5,20}, {4,12}, {7,27}, {4,18}, {2,16}, {5,25}, {3,11}, {3,16}, {1,16}, {3,17}, {5,19}, {7,15}, {6,27}, {2,15}, {8,12}, {6,21}, {7,21}, {7,20}, {2,27}, {6,18}, {4,25}, {5,14}, {9,14}, {5,26}, {1,13}, {8,18}, {5,13}, {1,19}, {9,26}, {1,22}, {7,14}, {4,19}, {1,25}, {8,17}, {2,22}, {9,17}, {6,24}, {3,10}, {7,26} }; // ET27.11 // Bipartite(9,18) Valencies [6,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 55296 EdgePairs[27][11]:={ {2,11}, {5,12}, {2,14}, {4,24}, {9,23}, {8,20}, {2,26}, {9,25}, {9,16}, {7,12}, {8,11}, {6,26}, {1,10}, {8,15}, {5,11}, {8,24}, {3,23}, {3,24}, {5,16}, {5,21}, {5,20}, {4,12}, {4,18}, {5,25}, {7,10}, {1,16}, {2,20}, {3,15}, {4,27}, {4,21}, {9,27}, {3,19}, {8,13}, {6,27}, {3,14}, {7,21}, {8,22}, {4,15}, {7,19}, {6,18}, {6,22}, {9,18}, {2,17}, {9,14}, {6,17}, {2,23}, {1,13}, {7,17}, {1,19}, {1,22}, {1,25}, {6,13}, {3,10}, {7,26} }; // ET27.12 // Non-bipartite Valency 6 // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 181398528 EdgePairs[27][12]:={ {12,27}, {4,9}, {10,15}, {18,22}, {1,14}, {14,19}, {8,20}, {14,18}, {14,26}, {7,23}, {9,21}, {20,23}, {7,12}, {5,27}, {15,20}, {11,24}, {12,16}, {16,23}, {5,10}, {13,25}, {1,4}, {15,27}, {19,22}, {8,24}, {9,11}, {3,24}, {3,9}, {5,16}, {8,10}, {5,20}, {4,12}, {5,7}, {4,18}, {1,7}, {21,24}, {10,23}, {1,16}, {17,20}, {22,26}, {19,27}, {23,27}, {7,15}, {8,13}, {2,15}, {12,14}, {6,21}, {2,5}, {3,18}, {15,16}, {3,26}, {1,27}, {11,13}, {13,21}, {16,19}, {7,19}, {18,21}, {20,25}, {3,6}, {9,22}, {10,17}, {12,22}, {2,17}, {21,26}, {9,14}, {6,25}, {3,13}, {6,17}, {2,23}, {6,11}, {11,26}, {4,26}, {1,22}, {2,25}, {2,8}, {10,25}, {4,19}, {11,18}, {24,25}, {13,17}, {17,24}, {6,8} }; // ET27.13 // Non-bipartite Valency 6 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 324 EdgePairs[27][13]:={ {3,22}, {4,13}, {12,20}, {12,27}, {4,24}, {4,9}, {9,19}, {1,14}, {14,19}, {7,16}, {12,18}, {23,25}, {11,17}, {2,24}, {7,23}, {2,10}, {15,20}, {4,10}, {8,21}, {6,12}, {8,25}, {5,11}, {1,12}, {8,24}, {3,8}, {11,23}, {6,15}, {3,20}, {13,18}, {6,16}, {5,21}, {5,7}, {7,27}, {10,16}, {2,7}, {3,11}, {3,16}, {19,27}, {18,25}, {2,18}, {1,21}, {4,20}, {17,27}, {2,15}, {12,24}, {15,17}, {4,17}, {7,20}, {13,23}, {13,21}, {1,17}, {20,25}, {6,19}, {9,22}, {2,19}, {9,18}, {24,26}, {5,14}, {5,18}, {21,26}, {3,13}, {22,27}, {14,24}, {10,22}, {11,26}, {1,9}, {9,26}, {10,21}, {13,27}, {15,26}, {10,25}, {1,23}, {11,19}, {14,25}, {5,22}, {8,17}, {14,16}, {6,23}, {6,8}, {15,22}, {16,26} }; // ET27.14 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1296 EdgePairs[27][14]:={ {4,8}, {2,14}, {12,20}, {9,19}, {14,19}, {7,16}, {1,24}, {12,18}, {19,26}, {11,17}, {14,26}, {7,23}, {15,20}, {6,14}, {8,21}, {5,10}, {3,21}, {13,25}, {11,27}, {15,27}, {8,24}, {3,23}, {11,23}, {2,12}, {6,7}, {13,18}, {5,9}, {5,16}, {5,23}, {4,12}, {4,18}, {2,16}, {20,27}, {10,16}, {2,20}, {3,7}, {3,15}, {10,26}, {22,26}, {6,20}, {23,27}, {3,17}, {5,19}, {9,27}, {4,21}, {21,25}, {12,24}, {15,17}, {7,25}, {1,18}, {16,25}, {4,15}, {7,20}, {13,23}, {13,21}, {4,22}, {12,25}, {9,22}, {8,26}, {9,18}, {18,27}, {6,17}, {1,8}, {1,13}, {14,24}, {5,13}, {2,9}, {1,19}, {6,11}, {10,22}, {10,21}, {11,19}, {17,26}, {1,11}, {8,17}, {14,16}, {24,25}, {2,22}, {6,24}, {3,10}, {15,22} }; // ET27.15 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 324 EdgePairs[27][15]:={ {2,11}, {5,12}, {12,20}, {4,23}, {9,19}, {10,27}, {14,19}, {7,16}, {3,12}, {5,24}, {12,18}, {24,27}, {9,25}, {11,17}, {11,25}, {18,26}, {22,25}, {7,23}, {15,20}, {1,10}, {4,11}, {8,21}, {19,25}, {6,10}, {13,26}, {4,7}, {1,20}, {5,15}, {8,24}, {11,23}, {17,25}, {4,16}, {3,24}, {3,9}, {5,8}, {13,18}, {2,21}, {8,27}, {16,27}, {5,20}, {21,27}, {1,7}, {10,16}, {1,15}, {1,16}, {3,19}, {5,17}, {3,14}, {6,21}, {3,18}, {12,24}, {15,17}, {15,25}, {12,26}, {7,20}, {13,23}, {13,21}, {6,18}, {9,22}, {6,22}, {9,18}, {14,27}, {20,26}, {2,17}, {2,23}, {14,24}, {10,22}, {10,21}, {23,26}, {1,22}, {2,13}, {4,14}, {2,8}, {4,19}, {11,19}, {8,17}, {14,16}, {6,13}, {15,22}, {7,26}, {6,9} }; // ET27.16 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1296 EdgePairs[27][16]:={ {3,22}, {4,8}, {12,20}, {12,27}, {8,19}, {9,19}, {7,16}, {14,18}, {19,26}, {24,27}, {9,25}, {11,17}, {9,16}, {2,10}, {8,16}, {1,10}, {6,14}, {4,11}, {11,20}, {15,24}, {5,11}, {15,27}, {3,23}, {11,23}, {17,25}, {4,16}, {3,24}, {5,8}, {13,18}, {2,21}, {5,21}, {5,20}, {15,21}, {4,18}, {1,7}, {2,7}, {1,16}, {3,7}, {2,20}, {10,23}, {23,27}, {5,19}, {18,25}, {9,27}, {12,23}, {4,17}, {1,18}, {15,25}, {7,22}, {16,25}, {8,22}, {12,26}, {13,21}, {1,17}, {7,19}, {12,25}, {9,22}, {14,21}, {6,22}, {2,19}, {10,17}, {20,26}, {5,14}, {21,26}, {13,24}, {3,13}, {22,27}, {1,13}, {14,24}, {6,11}, {9,26}, {15,26}, {2,13}, {4,14}, {10,20}, {12,17}, {15,18}, {6,23}, {6,8}, {6,24}, {3,10} }; // ET27.17 // Bipartite(9,18) Valencies [8,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[27][17]:={ {2,11}, {5,12}, {4,13}, {4,24}, {8,19}, {4,23}, {1,14}, {7,11}, {8,20}, {1,24}, {2,26}, {5,24}, {2,24}, {2,10}, {9,16}, {5,27}, {8,23}, {1,10}, {4,11}, {8,21}, {3,21}, {6,12}, {7,13}, {6,10}, {1,20}, {5,15}, {9,11}, {4,16}, {2,21}, {4,12}, {7,27}, {1,15}, {3,16}, {2,20}, {1,16}, {3,15}, {7,18}, {3,17}, {5,19}, {3,25}, {9,12}, {4,21}, {3,19}, {7,15}, {8,13}, {6,27}, {7,25}, {1,18}, {3,26}, {8,22}, {7,20}, {2,27}, {6,18}, {4,25}, {6,19}, {9,22}, {6,22}, {9,18}, {5,14}, {9,14}, {6,25}, {5,26}, {8,14}, {5,13}, {7,17}, {9,26}, {1,23}, {8,17}, {2,22}, {6,23}, {9,17}, {3,10} }; // ET27.18 // Bipartite(9,18) Valencies [8,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 36864 EdgePairs[27][18]:={ {2,11}, {3,22}, {5,12}, {1,26}, {4,24}, {2,26}, {9,25}, {2,24}, {9,21}, {9,16}, {7,12}, {5,27}, {8,23}, {1,10}, {6,14}, {6,26}, {4,10}, {8,21}, {8,15}, {7,13}, {5,11}, {9,15}, {1,20}, {8,24}, {3,23}, {4,16}, {3,20}, {6,16}, {5,23}, {5,21}, {5,20}, {7,27}, {4,18}, {7,10}, {3,11}, {9,24}, {1,16}, {2,20}, {7,18}, {4,27}, {2,18}, {9,12}, {3,19}, {2,15}, {3,14}, {8,12}, {7,22}, {7,21}, {4,15}, {9,13}, {2,27}, {1,17}, {7,19}, {4,25}, {9,22}, {6,22}, {8,26}, {5,14}, {2,17}, {5,18}, {3,13}, {6,25}, {6,17}, {8,14}, {1,19}, {4,19}, {1,11}, {1,25}, {8,17}, {6,23}, {6,13}, {3,10} }; // ET27.19 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 216 EdgePairs[27][19]:={ {1,15}, {16,25}, {13,25}, {6,12}, {14,25}, {11,17}, {6,10}, {4,14}, {12,19}, {2,22}, {3,7}, {6,17}, {7,24}, {2,20}, {23,27}, {14,19}, {14,18}, {6,13}, {12,22}, {5,24}, {19,27}, {9,19}, {11,16}, {12,18}, {21,25}, {11,22}, {12,27}, {5,7}, {5,13}, {3,10}, {6,9}, {10,18}, {10,23}, {3,19}, {20,25}, {12,21}, {22,25}, {2,14}, {3,11}, {7,26}, {19,26}, {14,16}, {10,25}, {1,16}, {6,21}, {8,21}, {8,18}, {2,17}, {3,14}, {1,12}, {9,23}, {10,24}, {5,19}, {15,20}, {3,23}, {8,17}, {4,21}, {4,15}, {2,9}, {13,22}, {15,26}, {2,24}, {4,11}, {15,21}, {1,23}, {16,27}, {8,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {8,23}, {7,16}, {9,26}, {6,16}, {3,21}, {11,27}, {2,8}, {1,20}, {5,11}, {7,22}, {15,27}, {1,13}, {4,18}, {22,26}, {8,25}, {13,23}, {15,17}, {13,17}, {11,20}, {7,21}, {24,27}, {3,17}, {10,20}, {17,26}, {4,9}, {6,24}, {5,18}, {10,26}, {9,16}, {13,19}, {4,23}, {1,18}, {15,24}, {14,24}, {9,20}, {18,26} }; // ET27.20 // Non-bipartite Valency 8 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1296 EdgePairs[27][20]:={ {1,15}, {9,13}, {7,19}, {11,15}, {3,15}, {12,26}, {10,22}, {11,23}, {4,8}, {4,27}, {13,18}, {10,27}, {23,27}, {14,18}, {1,25}, {9,12}, {12,15}, {16,23}, {9,19}, {9,21}, {19,24}, {6,7}, {11,22}, {16,20}, {19,23}, {5,7}, {7,15}, {18,21}, {12,25}, {5,26}, {8,13}, {5,9}, {5,21}, {18,24}, {3,18}, {8,15}, {22,25}, {7,10}, {2,14}, {17,23}, {4,20}, {17,24}, {14,16}, {2,16}, {1,16}, {6,21}, {10,13}, {8,21}, {2,17}, {8,10}, {3,14}, {2,13}, {16,19}, {10,24}, {7,20}, {6,8}, {20,24}, {7,14}, {3,27}, {6,26}, {8,11}, {4,25}, {3,5}, {1,4}, {18,19}, {1,26}, {11,14}, {2,4}, {12,24}, {12,23}, {2,27}, {6,19}, {5,20}, {10,14}, {21,22}, {11,25}, {8,20}, {21,23}, {15,16}, {16,22}, {17,21}, {11,27}, {24,25}, {9,11}, {1,13}, {22,26}, {3,25}, {2,26}, {15,17}, {13,17}, {24,27}, {3,6}, {9,14}, {3,17}, {4,9}, {18,22}, {10,26}, {17,20}, {6,27}, {20,22}, {23,26}, {7,12}, {1,6}, {1,18}, {5,25}, {4,19}, {2,5}, {12,13} }; // ET27.21 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1296 EdgePairs[27][21]:={ {10,19}, {5,14}, {15,23}, {14,25}, {11,17}, {8,24}, {10,22}, {6,10}, {11,23}, {13,18}, {6,23}, {23,27}, {14,19}, {13,24}, {9,12}, {12,15}, {6,25}, {9,19}, {13,27}, {12,18}, {16,20}, {19,23}, {18,23}, {7,23}, {5,7}, {12,25}, {2,19}, {2,15}, {8,14}, {4,26}, {3,18}, {12,21}, {7,10}, {3,11}, {2,10}, {9,27}, {14,16}, {3,13}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {1,12}, {10,16}, {3,9}, {7,25}, {3,22}, {7,20}, {6,8}, {20,24}, {15,20}, {8,26}, {7,13}, {6,15}, {8,11}, {4,17}, {1,4}, {9,15}, {18,19}, {1,26}, {11,14}, {12,24}, {15,26}, {2,24}, {4,11}, {5,22}, {2,27}, {17,22}, {1,23}, {16,27}, {14,22}, {5,27}, {1,7}, {5,20}, {21,22}, {6,16}, {1,14}, {17,21}, {20,26}, {11,27}, {13,21}, {24,25}, {2,8}, {22,26}, {3,25}, {15,17}, {11,20}, {3,20}, {5,12}, {3,6}, {4,9}, {5,18}, {10,26}, {19,25}, {9,16}, {7,17}, {4,13}, {1,21}, {4,19}, {4,24}, {2,5}, {17,25}, {18,26}, {9,22}, {16,24}, {21,27} }; // ET27.22 // Bipartite(12,15) Valencies [10,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 143327232000 EdgePairs[27][22]:={ {9,13}, {10,19}, {7,19}, {11,15}, {5,14}, {3,15}, {11,17}, {8,24}, {10,22}, {6,18}, {11,23}, {4,14}, {12,19}, {12,16}, {2,20}, {1,25}, {4,16}, {6,13}, {12,15}, {12,22}, {5,24}, {6,25}, {9,19}, {9,21}, {12,18}, {12,27}, {7,23}, {12,25}, {2,18}, {2,15}, {5,26}, {4,26}, {8,14}, {6,22}, {5,21}, {10,23}, {3,19}, {3,18}, {8,15}, {12,21}, {2,14}, {5,23}, {4,20}, {9,27}, {2,23}, {7,26}, {1,17}, {3,13}, {10,25}, {1,22}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {10,16}, {7,25}, {3,22}, {5,15}, {7,20}, {8,26}, {7,13}, {8,17}, {7,14}, {3,27}, {6,15}, {1,19}, {11,18}, {4,17}, {9,25}, {4,25}, {9,15}, {1,26}, {11,26}, {11,14}, {12,24}, {2,24}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {8,27}, {5,20}, {4,22}, {10,14}, {3,24}, {5,17}, {9,24}, {8,20}, {8,23}, {7,16}, {6,16}, {11,21}, {3,21}, {1,14}, {9,18}, {10,17}, {11,27}, {1,20}, {7,22}, {3,16}, {1,13}, {3,25}, {2,26}, {11,20}, {10,20}, {6,24}, {5,18}, {10,26}, {6,27}, {9,16}, {7,17}, {4,23}, {11,24}, {4,13}, {4,19}, {12,13}, {9,22} }; // ET27.23 // Bipartite(12,15) Valencies [10,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 46080 EdgePairs[27][23]:={ {9,13}, {10,19}, {7,19}, {11,15}, {10,21}, {3,15}, {11,17}, {8,24}, {12,26}, {10,22}, {6,18}, {11,23}, {4,14}, {2,22}, {6,14}, {12,16}, {7,24}, {6,23}, {2,20}, {1,25}, {6,13}, {12,14}, {12,22}, {5,24}, {7,27}, {9,19}, {12,18}, {12,27}, {2,19}, {2,15}, {5,26}, {4,26}, {8,14}, {9,17}, {10,18}, {6,22}, {5,21}, {3,19}, {3,18}, {8,22}, {8,15}, {12,21}, {2,14}, {5,23}, {4,20}, {9,27}, {2,23}, {1,17}, {3,13}, {10,25}, {2,16}, {1,16}, {6,21}, {10,13}, {2,17}, {10,15}, {7,25}, {3,22}, {9,23}, {5,15}, {7,20}, {8,26}, {7,13}, {8,17}, {3,23}, {7,14}, {3,27}, {6,26}, {1,19}, {11,18}, {4,21}, {9,25}, {4,15}, {4,25}, {9,15}, {8,19}, {11,26}, {12,24}, {12,23}, {2,24}, {5,27}, {5,20}, {4,22}, {10,14}, {8,16}, {5,17}, {11,25}, {8,20}, {8,23}, {7,16}, {6,16}, {11,21}, {1,14}, {9,18}, {11,27}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {7,21}, {11,20}, {3,17}, {10,20}, {6,24}, {5,18}, {10,26}, {6,27}, {9,16}, {7,17}, {11,24}, {4,13}, {1,21}, {5,25}, {4,19}, {12,13}, {1,24}, {9,22} }; // ET27.24 // Non-bipartite Valency 10 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 51840 EdgePairs[27][24]:={ {14,21}, {20,27}, {11,15}, {14,25}, {3,15}, {8,24}, {4,14}, {24,26}, {12,16}, {6,17}, {2,11}, {23,25}, {6,23}, {2,20}, {2,3}, {23,27}, {14,19}, {17,19}, {1,25}, {12,15}, {6,13}, {12,17}, {12,14}, {12,22}, {19,27}, {6,25}, {16,23}, {4,5}, {21,26}, {7,27}, {13,27}, {11,16}, {21,25}, {11,22}, {16,20}, {18,23}, {7,23}, {7,15}, {18,21}, {4,6}, {9,10}, {6,9}, {4,26}, {8,13}, {10,18}, {7,11}, {1,2}, {13,20}, {5,21}, {10,23}, {14,27}, {4,12}, {5,6}, {3,18}, {20,25}, {22,25}, {2,14}, {16,21}, {1,3}, {4,20}, {6,11}, {2,23}, {17,24}, {1,10}, {4,7}, {19,26}, {13,26}, {15,25}, {1,22}, {1,16}, {10,13}, {2,17}, {8,18}, {10,15}, {3,9}, {16,19}, {10,24}, {5,15}, {15,20}, {3,27}, {1,19}, {11,18}, {15,19}, {1,4}, {18,19}, {8,19}, {11,14}, {22,27}, {15,26}, {12,23}, {11,13}, {7,8}, {5,22}, {6,19}, {17,22}, {5,27}, {1,7}, {5,8}, {8,9}, {10,14}, {3,24}, {3,12}, {9,26}, {18,20}, {3,21}, {10,17}, {17,21}, {7,9}, {13,21}, {24,25}, {2,8}, {1,13}, {4,18}, {5,10}, {22,26}, {8,25}, {2,26}, {7,21}, {24,27}, {3,6}, {9,14}, {18,22}, {17,20}, {9,16}, {23,26}, {7,17}, {11,24}, {5,16}, {4,24}, {12,13}, {2,5}, {9,20}, {8,12}, {9,22}, {16,24} }; // ET27.25 // Bipartite(9,18) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 483729408000 EdgePairs[27][25]:={ {9,13}, {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {4,14}, {1,11}, {2,11}, {2,20}, {1,25}, {4,16}, {6,13}, {9,12}, {5,24}, {6,25}, {9,19}, {9,21}, {7,23}, {3,10}, {9,10}, {2,18}, {2,15}, {5,26}, {4,26}, {8,14}, {7,11}, {6,22}, {5,21}, {3,19}, {3,18}, {8,15}, {7,10}, {2,14}, {5,23}, {4,20}, {9,27}, {2,23}, {1,10}, {7,26}, {1,17}, {3,13}, {1,22}, {1,16}, {6,21}, {2,17}, {8,18}, {8,21}, {7,25}, {3,22}, {5,15}, {7,20}, {8,26}, {7,13}, {8,17}, {7,14}, {3,27}, {6,15}, {1,19}, {8,11}, {4,17}, {9,25}, {4,25}, {9,15}, {1,26}, {2,24}, {4,11}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {8,27}, {2,12}, {4,22}, {5,20}, {3,24}, {5,17}, {9,24}, {3,12}, {8,20}, {8,23}, {7,16}, {6,16}, {3,21}, {1,14}, {9,18}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {3,25}, {2,26}, {5,12}, {6,24}, {5,18}, {6,27}, {9,16}, {7,17}, {4,23}, {4,13}, {4,19}, {4,10}, {8,12}, {9,22} }; // ET27.26 // Bipartite(9,18) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3359232 EdgePairs[27][26]:={ {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {1,11}, {2,22}, {7,24}, {2,20}, {1,25}, {4,16}, {6,13}, {9,12}, {5,24}, {6,25}, {7,27}, {9,21}, {7,15}, {5,13}, {3,10}, {2,19}, {2,15}, {5,26}, {9,17}, {6,22}, {4,12}, {8,22}, {8,15}, {2,14}, {5,23}, {3,11}, {2,10}, {9,27}, {1,10}, {7,26}, {1,17}, {2,16}, {1,22}, {1,16}, {6,21}, {8,21}, {8,18}, {8,10}, {3,14}, {2,13}, {7,25}, {3,22}, {5,19}, {9,23}, {7,20}, {7,13}, {8,17}, {3,23}, {7,14}, {3,27}, {6,15}, {1,19}, {8,11}, {4,17}, {4,25}, {9,15}, {1,26}, {4,11}, {2,27}, {6,19}, {1,23}, {2,21}, {8,27}, {7,18}, {5,20}, {4,22}, {3,26}, {8,16}, {5,17}, {9,24}, {8,23}, {6,16}, {9,26}, {3,21}, {1,14}, {9,18}, {1,20}, {9,11}, {5,11}, {3,16}, {1,13}, {4,18}, {2,26}, {3,20}, {7,21}, {5,12}, {2,25}, {9,14}, {3,17}, {6,24}, {5,18}, {6,27}, {4,23}, {7,12}, {4,13}, {5,25}, {4,19}, {4,10}, {4,24}, {8,12}, {9,20} }; // ET27.27 // Bipartite(9,18) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 55296 EdgePairs[27][27]:={ {1,15}, {9,13}, {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {1,11}, {2,22}, {6,14}, {6,17}, {2,11}, {6,23}, {2,20}, {1,25}, {9,12}, {5,24}, {6,25}, {9,19}, {9,21}, {7,23}, {5,13}, {3,10}, {9,10}, {2,18}, {8,14}, {4,26}, {7,11}, {3,19}, {4,12}, {3,18}, {8,15}, {7,10}, {5,23}, {4,20}, {9,27}, {1,10}, {7,26}, {3,13}, {2,16}, {1,16}, {6,21}, {2,17}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {7,25}, {3,22}, {5,15}, {7,20}, {8,26}, {7,13}, {3,23}, {8,17}, {7,14}, {3,27}, {6,26}, {1,19}, {8,11}, {4,21}, {4,17}, {9,25}, {4,15}, {9,15}, {4,11}, {5,22}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {8,27}, {2,12}, {4,22}, {5,20}, {3,26}, {3,24}, {9,24}, {8,20}, {8,23}, {7,16}, {6,16}, {1,14}, {9,18}, {1,20}, {5,11}, {7,22}, {2,26}, {2,25}, {3,17}, {5,18}, {6,27}, {9,16}, {7,17}, {5,16}, {4,13}, {1,21}, {5,25}, {4,19}, {4,10}, {4,24}, {8,12}, {1,24}, {9,22} }; // ET27.28 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 725594112 EdgePairs[27][28]:={ {1,11}, {10,25}, {1,20}, {5,17}, {10,24}, {11,20}, {13,21}, {14,19}, {15,24}, {3,8}, {23,27}, {4,16}, {16,27}, {11,25}, {6,17}, {2,23}, {1,13}, {3,9}, {20,27}, {3,13}, {3,15}, {2,15}, {1,19}, {16,25}, {8,25}, {6,7}, {2,14}, {6,11}, {4,23}, {8,27}, {13,16}, {10,22}, {6,22}, {15,25}, {3,17}, {14,23}, {4,10}, {1,17}, {1,7}, {4,22}, {8,19}, {1,18}, {14,21}, {19,26}, {12,17}, {4,8}, {9,26}, {5,11}, {2,10}, {11,22}, {14,24}, {22,27}, {24,25}, {1,22}, {15,27}, {21,27}, {6,12}, {12,16}, {5,23}, {4,21}, {13,22}, {15,19}, {2,20}, {14,16}, {6,18}, {13,18}, {24,26}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {11,23}, {6,24}, {7,17}, {21,25}, {5,24}, {13,23}, {23,25}, {8,22}, {1,9}, {13,25}, {15,20}, {9,20}, {18,26}, {4,15}, {18,27}, {3,11}, {4,7}, {15,17}, {3,10}, {12,26}, {9,22}, {12,27}, {14,17}, {3,19}, {1,24}, {12,23}, {17,25}, {12,19}, {3,23}, {3,21}, {2,7}, {6,19}, {6,9}, {6,14}, {3,16}, {13,26}, {11,26}, {15,18}, {22,26}, {11,16}, {7,23}, {2,21}, {9,18}, {10,17}, {20,26}, {3,24}, {10,27}, {2,22}, {4,14}, {15,22}, {5,8}, {10,18}, {8,24}, {5,10}, {19,25}, {8,18}, {4,18}, {5,9}, {10,19}, {4,12}, {4,20}, {5,13}, {8,20}, {12,24}, {7,27}, {7,24}, {2,12}, {1,14}, {2,8}, {10,20}, {17,26}, {5,15}, {5,19}, {6,20}, {5,21}, {6,13}, {13,20}, {2,18}, {7,19}, {9,21}, {9,16}, {9,23}, {14,27}, {7,21}, {11,18}, {12,21}, {14,26}, {5,16} }; // ET27.29 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1296 EdgePairs[27][29]:={ {11,17}, {1,11}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {6,16}, {13,21}, {16,26}, {15,24}, {3,22}, {3,8}, {4,16}, {6,17}, {2,23}, {1,13}, {12,22}, {3,9}, {20,27}, {3,13}, {24,27}, {10,23}, {2,15}, {7,22}, {2,19}, {1,19}, {5,20}, {16,25}, {2,9}, {8,25}, {6,7}, {2,14}, {6,11}, {4,23}, {15,16}, {3,18}, {8,16}, {6,21}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {14,21}, {12,17}, {9,27}, {12,20}, {2,10}, {9,19}, {6,8}, {15,26}, {3,12}, {11,22}, {14,24}, {22,27}, {24,25}, {1,22}, {15,27}, {6,12}, {23,26}, {12,16}, {4,21}, {21,26}, {3,20}, {13,22}, {15,19}, {14,16}, {13,18}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {11,23}, {6,24}, {7,17}, {21,25}, {5,24}, {17,27}, {13,23}, {12,25}, {23,25}, {13,25}, {15,20}, {5,14}, {18,26}, {4,15}, {18,27}, {4,7}, {6,23}, {3,10}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {5,12}, {14,17}, {4,9}, {1,24}, {14,22}, {17,25}, {3,23}, {8,23}, {3,21}, {2,7}, {6,19}, {1,15}, {2,11}, {14,20}, {14,25}, {3,16}, {13,26}, {11,26}, {15,18}, {22,26}, {13,19}, {2,21}, {9,18}, {20,26}, {11,27}, {10,27}, {4,14}, {5,8}, {9,17}, {10,18}, {8,24}, {5,10}, {19,25}, {8,18}, {4,18}, {5,9}, {11,19}, {10,19}, {4,11}, {1,8}, {4,20}, {5,13}, {8,20}, {12,24}, {7,27}, {15,23}, {7,24}, {10,20}, {5,19}, {13,17}, {6,13}, {9,21}, {9,23}, {14,27}, {7,21}, {19,27}, {11,18}, {12,21}, {10,16} }; // ET27.30 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1296 EdgePairs[27][30]:={ {21,23}, {1,11}, {10,25}, {1,20}, {5,17}, {4,24}, {16,26}, {3,8}, {23,27}, {4,16}, {16,27}, {2,23}, {1,13}, {20,27}, {3,15}, {19,24}, {17,20}, {16,19}, {4,19}, {7,22}, {2,19}, {2,4}, {5,20}, {2,26}, {1,21}, {2,9}, {21,22}, {18,21}, {8,25}, {6,7}, {2,14}, {4,23}, {8,27}, {3,5}, {10,15}, {10,22}, {15,16}, {6,22}, {3,18}, {3,7}, {8,16}, {6,21}, {4,10}, {5,22}, {19,26}, {12,17}, {4,8}, {9,26}, {12,20}, {1,5}, {5,11}, {2,10}, {8,14}, {6,8}, {11,15}, {11,13}, {17,23}, {7,13}, {14,24}, {22,27}, {24,25}, {1,22}, {15,27}, {6,12}, {12,13}, {12,16}, {21,26}, {3,20}, {10,21}, {14,16}, {6,18}, {13,18}, {24,26}, {11,21}, {9,25}, {7,26}, {3,4}, {1,12}, {11,23}, {2,6}, {7,17}, {8,11}, {21,25}, {5,24}, {17,27}, {5,7}, {13,23}, {23,25}, {1,9}, {13,25}, {18,24}, {18,26}, {4,15}, {3,11}, {3,27}, {20,22}, {15,17}, {6,23}, {3,10}, {16,22}, {2,17}, {12,27}, {3,19}, {4,9}, {14,18}, {14,22}, {13,24}, {17,25}, {6,27}, {12,19}, {8,23}, {18,25}, {12,14}, {20,25}, {2,7}, {1,25}, {9,12}, {6,14}, {14,20}, {15,21}, {11,26}, {22,26}, {11,16}, {13,19}, {2,21}, {10,17}, {3,24}, {1,16}, {4,14}, {15,22}, {9,17}, {10,18}, {20,24}, {5,26}, {8,18}, {5,9}, {11,19}, {4,25}, {1,8}, {5,13}, {8,20}, {12,24}, {7,27}, {7,10}, {15,23}, {2,12}, {9,24}, {10,20}, {1,6}, {5,15}, {10,14}, {9,15}, {13,17}, {6,13}, {19,23}, {7,19}, {9,21}, {9,16}, {19,27}, {11,18}, {14,26}, {7,18} }; // ET27.31 // Bipartite(6,21) Valencies [14,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6145155072000 EdgePairs[27][31]:={ {2,11}, {3,22}, {5,12}, {1,26}, {4,8}, {2,14}, {4,13}, {4,23}, {1,14}, {2,26}, {3,12}, {5,24}, {2,24}, {5,27}, {1,10}, {4,11}, {4,10}, {3,21}, {3,27}, {6,12}, {5,11}, {6,10}, {4,7}, {1,20}, {5,15}, {4,16}, {3,24}, {3,9}, {2,12}, {6,7}, {6,15}, {5,8}, {2,21}, {5,9}, {5,23}, {6,16}, {5,21}, {5,20}, {1,7}, {3,16}, {3,7}, {2,20}, {1,16}, {3,15}, {2,18}, {3,25}, {4,20}, {3,19}, {5,17}, {6,27}, {2,15}, {3,18}, {6,21}, {4,17}, {2,27}, {1,17}, {4,22}, {6,18}, {4,25}, {6,19}, {6,22}, {5,14}, {2,17}, {5,18}, {3,13}, {6,25}, {2,23}, {5,26}, {1,8}, {1,13}, {1,19}, {2,9}, {4,26}, {1,22}, {4,14}, {2,8}, {1,23}, {4,19}, {1,11}, {1,25}, {6,13}, {6,24}, {3,10}, {6,9} }; // ET27.32 // Bipartite(13,14) Valencies [14,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 542861032610856960000 EdgePairs[27][32]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {6,16}, {4,27}, {13,21}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {12,22}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,14}, {8,15}, {4,23}, {8,27}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {12,20}, {9,19}, {8,14}, {5,25}, {11,15}, {11,22}, {9,14}, {7,25}, {1,22}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {10,21}, {2,20}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {11,23}, {1,23}, {6,24}, {7,17}, {5,24}, {13,23}, {12,25}, {8,22}, {13,25}, {5,14}, {9,20}, {4,15}, {7,14}, {3,27}, {6,23}, {3,26}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {13,15}, {1,15}, {12,15}, {6,14}, {13,27}, {3,16}, {11,26}, {13,26}, {11,16}, {7,23}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {13,14}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {8,20}, {12,24}, {7,27}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET27.33 // Bipartite(12,15) Valencies [15,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 626378114550988800000 EdgePairs[27][33]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {6,16}, {4,27}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {1,13}, {12,22}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,14}, {8,15}, {4,23}, {8,27}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {12,20}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {11,22}, {7,13}, {9,14}, {7,25}, {1,22}, {12,13}, {12,16}, {5,23}, {4,21}, {3,20}, {10,21}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {5,24}, {12,25}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {3,27}, {10,13}, {6,23}, {3,26}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {9,13}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {6,26}, {12,19}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {1,15}, {12,15}, {6,14}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {5,13}, {8,20}, {12,24}, {7,27}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET27.34 // Bipartite(3,24) Valencies [16,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 393289924608000 EdgePairs[27][34]:={ {1,4}, {2,27}, {1,20}, {3,24}, {3,16}, {3,10}, {1,14}, {1,23}, {3,19}, {2,17}, {2,24}, {1,7}, {2,11}, {1,5}, {2,26}, {3,6}, {3,18}, {3,15}, {2,21}, {3,4}, {1,22}, {3,21}, {1,16}, {1,10}, {3,27}, {1,17}, {1,13}, {2,20}, {2,18}, {3,22}, {3,9}, {1,11}, {2,23}, {1,19}, {1,25}, {2,6}, {2,8}, {3,12}, {2,15}, {3,13}, {2,5}, {2,12}, {3,25}, {1,26}, {2,9}, {3,7}, {2,14}, {1,8} }; // ET27.35 // Bipartite(9,18) Valencies [16,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 185794560 EdgePairs[27][35]:={ {1,15}, {9,13}, {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,27}, {2,11}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {9,12}, {5,24}, {6,25}, {7,27}, {9,19}, {9,21}, {7,23}, {3,10}, {9,10}, {2,18}, {2,15}, {5,26}, {4,26}, {8,13}, {9,17}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {7,10}, {2,14}, {5,23}, {3,11}, {6,11}, {9,27}, {2,23}, {1,10}, {7,26}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {8,21}, {3,14}, {2,13}, {1,12}, {7,25}, {3,22}, {5,19}, {9,23}, {5,15}, {7,20}, {8,26}, {3,23}, {7,13}, {8,17}, {7,14}, {3,27}, {6,15}, {1,19}, {8,11}, {4,21}, {4,17}, {4,15}, {4,25}, {9,15}, {1,26}, {8,19}, {2,24}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {8,27}, {7,18}, {2,12}, {4,22}, {5,20}, {3,26}, {3,24}, {5,17}, {8,16}, {9,24}, {8,20}, {6,16}, {6,20}, {7,16}, {9,26}, {1,14}, {9,18}, {1,20}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {8,25}, {2,26}, {3,20}, {7,21}, {5,12}, {2,25}, {9,14}, {3,17}, {6,24}, {5,18}, {6,27}, {7,17}, {4,23}, {5,16}, {7,12}, {4,13}, {1,21}, {5,25}, {4,19}, {4,10}, {4,24}, {8,12}, {9,20}, {1,24}, {9,22} }; // ET27.36 // Bipartite(11,16) Valencies [16,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 835170819401318400000 EdgePairs[27][36]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {1,13}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {11,12}, {2,14}, {8,15}, {4,23}, {8,27}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {9,26}, {9,27}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {7,14}, {3,27}, {10,13}, {10,12}, {6,23}, {3,26}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {11,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,14}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,12}, {4,20}, {5,13}, {8,20}, {7,27}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET27.37 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 51840 EdgePairs[27][37]:={ {21,23}, {1,11}, {10,25}, {1,20}, {5,17}, {10,24}, {4,27}, {7,15}, {8,12}, {15,24}, {16,26}, {3,8}, {4,16}, {1,10}, {11,25}, {6,17}, {2,23}, {1,13}, {12,22}, {20,27}, {24,27}, {1,27}, {3,15}, {10,23}, {19,24}, {17,20}, {16,19}, {7,22}, {1,19}, {2,4}, {2,26}, {17,24}, {16,25}, {2,9}, {18,21}, {8,10}, {8,25}, {6,7}, {2,14}, {8,15}, {6,11}, {16,23}, {4,23}, {8,27}, {3,5}, {9,11}, {13,16}, {10,15}, {15,16}, {6,22}, {15,25}, {3,17}, {3,7}, {8,16}, {2,25}, {7,12}, {14,23}, {4,10}, {1,17}, {4,22}, {8,19}, {1,18}, {7,11}, {3,14}, {14,21}, {19,26}, {12,17}, {4,8}, {9,26}, {18,20}, {12,20}, {1,5}, {5,11}, {19,22}, {5,25}, {11,15}, {11,13}, {17,23}, {3,12}, {11,22}, {9,14}, {14,24}, {22,27}, {1,22}, {15,27}, {6,12}, {12,13}, {23,26}, {12,16}, {5,23}, {4,21}, {21,26}, {13,22}, {15,19}, {10,21}, {2,13}, {2,20}, {6,18}, {24,26}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {3,4}, {6,24}, {2,6}, {21,25}, {5,24}, {17,27}, {13,23}, {23,25}, {8,13}, {8,22}, {1,9}, {13,25}, {18,24}, {9,10}, {9,20}, {4,15}, {18,27}, {7,14}, {3,27}, {20,22}, {4,7}, {3,10}, {3,26}, {12,26}, {16,22}, {9,13}, {12,27}, {22,25}, {14,17}, {3,19}, {1,24}, {14,18}, {12,23}, {6,27}, {11,24}, {6,26}, {12,19}, {20,23}, {3,23}, {8,23}, {18,25}, {12,14}, {20,25}, {3,21}, {17,19}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,14}, {2,11}, {14,20}, {15,21}, {16,21}, {3,16}, {11,26}, {13,26}, {15,18}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {10,27}, {2,22}, {4,14}, {15,22}, {5,8}, {18,22}, {9,17}, {10,18}, {5,10}, {5,26}, {4,18}, {5,9}, {11,19}, {4,25}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,27}, {7,24}, {2,12}, {9,24}, {10,20}, {1,6}, {17,26}, {5,15}, {10,14}, {5,19}, {6,20}, {21,24}, {5,21}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {9,21}, {9,23}, {7,21}, {14,27}, {19,27}, {11,18}, {14,26}, {7,18}, {5,16} }; // ET27.38 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 2177280 EdgePairs[27][38]:={ {1,11}, {10,24}, {2,24}, {11,20}, {6,16}, {4,27}, {13,21}, {7,15}, {4,24}, {8,12}, {14,19}, {15,24}, {16,26}, {4,26}, {3,22}, {3,8}, {23,27}, {11,25}, {16,27}, {6,17}, {1,13}, {12,22}, {3,9}, {20,27}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {17,20}, {4,19}, {16,19}, {7,22}, {2,19}, {1,19}, {2,27}, {2,4}, {5,20}, {1,21}, {17,24}, {11,14}, {21,22}, {18,21}, {2,14}, {8,15}, {6,11}, {16,23}, {4,23}, {8,27}, {3,5}, {13,16}, {10,15}, {15,16}, {6,22}, {15,25}, {3,17}, {6,21}, {2,25}, {14,23}, {1,17}, {1,7}, {5,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {14,21}, {19,26}, {12,17}, {16,24}, {18,20}, {9,27}, {12,20}, {1,5}, {2,10}, {9,19}, {19,22}, {6,8}, {5,25}, {11,13}, {11,22}, {9,14}, {7,25}, {14,24}, {22,27}, {24,25}, {15,27}, {21,27}, {12,16}, {4,21}, {3,20}, {13,22}, {15,19}, {10,21}, {2,13}, {2,20}, {24,26}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {3,4}, {1,12}, {5,18}, {1,23}, {2,6}, {7,17}, {8,11}, {21,25}, {5,24}, {17,27}, {5,7}, {13,23}, {12,25}, {23,25}, {8,13}, {1,9}, {13,25}, {9,10}, {15,20}, {5,14}, {9,20}, {18,26}, {4,15}, {4,13}, {3,11}, {7,14}, {4,7}, {10,13}, {6,23}, {3,10}, {3,26}, {8,26}, {12,26}, {9,22}, {6,15}, {9,13}, {5,12}, {14,17}, {8,21}, {4,9}, {1,24}, {14,18}, {12,23}, {11,24}, {17,25}, {6,26}, {20,23}, {3,23}, {8,23}, {18,25}, {12,14}, {3,21}, {17,19}, {2,7}, {9,12}, {6,9}, {1,15}, {12,15}, {18,23}, {6,14}, {16,21}, {3,16}, {13,26}, {15,18}, {22,26}, {11,16}, {7,23}, {9,18}, {10,17}, {20,26}, {11,27}, {10,27}, {1,26}, {2,22}, {15,22}, {5,8}, {18,22}, {10,18}, {8,24}, {6,25}, {20,24}, {6,10}, {5,27}, {5,10}, {19,25}, {8,18}, {4,18}, {11,19}, {10,19}, {4,11}, {4,12}, {5,13}, {7,10}, {2,12}, {9,24}, {2,8}, {1,6}, {5,19}, {6,20}, {17,22}, {21,24}, {13,17}, {13,20}, {2,18}, {19,23}, {4,17}, {9,16}, {7,21}, {14,27}, {11,18}, {12,21}, {14,26}, {5,16} }; // ET27.39 // Bipartite(10,17) Valencies [17,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1290718539074764800000 EdgePairs[27][39]:={ {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {6,17}, {2,23}, {1,13}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,14}, {8,15}, {6,11}, {4,23}, {8,27}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {3,27}, {10,13}, {10,12}, {6,23}, {3,26}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,14}, {2,11}, {10,11}, {3,16}, {7,23}, {2,21}, {9,18}, {10,17}, {3,24}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {7,27}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {7,18}, {10,16}, {5,16} }; // ET27.40 // Bipartite(9,18) Valencies [18,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2323293370334576640000 EdgePairs[27][40]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,10}, {8,25}, {2,14}, {8,15}, {6,11}, {4,23}, {8,27}, {9,11}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {2,10}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {3,11}, {7,14}, {3,27}, {6,23}, {3,10}, {3,26}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,14}, {2,11}, {3,16}, {7,23}, {2,21}, {9,18}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {7,27}, {7,10}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {7,18}, {5,16} }; // ET27.41 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 286708355039232000 EdgePairs[27][41]:={ {11,17}, {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {6,16}, {13,21}, {4,24}, {14,19}, {15,24}, {16,26}, {3,22}, {3,8}, {23,27}, {4,16}, {1,10}, {11,25}, {16,27}, {6,17}, {2,23}, {1,13}, {12,22}, {3,9}, {20,27}, {3,13}, {24,27}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {1,21}, {16,25}, {2,9}, {8,25}, {6,7}, {2,14}, {6,11}, {4,23}, {8,27}, {13,16}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {3,17}, {3,7}, {8,16}, {6,21}, {14,23}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {14,21}, {19,26}, {12,17}, {4,8}, {9,26}, {9,27}, {12,20}, {5,11}, {2,10}, {9,19}, {6,8}, {15,26}, {3,12}, {11,22}, {7,25}, {14,24}, {22,27}, {24,25}, {1,22}, {15,27}, {21,27}, {6,12}, {23,26}, {12,16}, {5,23}, {4,21}, {21,26}, {3,20}, {13,22}, {15,19}, {2,13}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {24,26}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {21,25}, {5,24}, {17,27}, {5,7}, {13,23}, {12,25}, {23,25}, {8,22}, {1,9}, {13,25}, {15,20}, {5,14}, {9,20}, {18,26}, {4,15}, {4,13}, {18,27}, {3,11}, {4,7}, {15,17}, {6,23}, {3,10}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {12,27}, {5,12}, {22,25}, {14,17}, {8,21}, {3,19}, {4,9}, {1,24}, {14,18}, {12,23}, {14,22}, {11,24}, {13,24}, {17,25}, {12,19}, {3,23}, {8,23}, {18,25}, {20,25}, {3,21}, {2,7}, {6,19}, {6,9}, {1,15}, {6,14}, {2,11}, {13,27}, {14,20}, {15,21}, {14,25}, {3,16}, {11,26}, {13,26}, {15,18}, {22,26}, {7,23}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {20,26}, {3,24}, {11,27}, {10,27}, {2,22}, {1,16}, {4,14}, {15,22}, {5,8}, {9,17}, {10,18}, {8,24}, {6,10}, {5,10}, {19,25}, {8,18}, {4,18}, {5,9}, {11,19}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {12,24}, {7,27}, {15,23}, {7,24}, {2,12}, {1,14}, {9,24}, {2,8}, {10,20}, {17,26}, {5,15}, {5,19}, {6,20}, {5,21}, {13,17}, {6,13}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {12,18}, {19,27}, {11,18}, {12,21}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET27.42 // Bipartite(8,19) Valencies [19,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4904730448484106240000 EdgePairs[27][42]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {8,10}, {8,25}, {2,14}, {8,15}, {6,11}, {4,23}, {8,27}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {5,11}, {2,10}, {8,14}, {5,25}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {5,14}, {4,15}, {4,13}, {3,11}, {7,14}, {3,27}, {6,23}, {3,10}, {3,26}, {8,26}, {6,15}, {2,17}, {5,12}, {8,21}, {3,19}, {4,9}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {1,15}, {6,14}, {2,11}, {3,16}, {7,23}, {2,21}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {7,27}, {7,10}, {7,24}, {2,12}, {1,14}, {5,15}, {5,19}, {6,20}, {5,21}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {7,18}, {5,16} }; // ET27.43 // Bipartite(7,20) Valencies [20,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12261826121210265600000 EdgePairs[27][43]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {4,27}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {7,27}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {7,10}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {7,26}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {7,25}, {3,22}, {5,19}, {5,15}, {6,8}, {7,20}, {3,23}, {7,13}, {7,14}, {3,27}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {7,8}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {5,8}, {7,18}, {2,12}, {4,22}, {5,20}, {3,26}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {7,9}, {2,8}, {1,20}, {1,27}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {7,21}, {5,12}, {2,25}, {3,17}, {4,9}, {6,24}, {5,18}, {6,27}, {7,17}, {4,23}, {1,8}, {5,16}, {7,12}, {4,13}, {1,21}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET27.44 // Bipartite(6,21) Valencies [21,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 36785478363630796800000 EdgePairs[27][44]:={ {1,15}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {4,27}, {3,7}, {6,17}, {2,11}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {6,7}, {5,7}, {5,13}, {3,10}, {2,19}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {6,8}, {3,23}, {3,27}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,26}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {2,25}, {5,12}, {3,17}, {4,9}, {6,24}, {2,7}, {5,18}, {6,27}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET27.45 // Bipartite(5,22) Valencies [22,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 134880087333312921600000 EdgePairs[27][45]:={ {1,15}, {5,14}, {3,15}, {4,14}, {1,11}, {2,22}, {4,8}, {4,27}, {3,7}, {2,11}, {2,20}, {1,25}, {4,16}, {5,24}, {1,9}, {5,7}, {4,6}, {5,13}, {3,10}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {3,19}, {4,12}, {5,6}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {3,23}, {3,27}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,26}, {3,24}, {5,17}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {5,12}, {3,17}, {4,9}, {2,7}, {5,18}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET27.46 // Bipartite(4,23) Valencies [23,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 620448401733239439360000 EdgePairs[27][46]:={ {2,11}, {3,22}, {1,26}, {2,14}, {4,8}, {4,13}, {4,9}, {4,24}, {4,23}, {1,14}, {1,24}, {2,26}, {3,12}, {2,24}, {2,10}, {1,10}, {4,11}, {4,10}, {3,21}, {1,6}, {3,5}, {3,27}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {3,23}, {4,16}, {3,9}, {3,24}, {2,12}, {3,20}, {2,21}, {4,6}, {4,12}, {2,16}, {4,18}, {1,7}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {3,25}, {4,27}, {4,21}, {4,20}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {3,26}, {1,5}, {4,15}, {1,27}, {1,17}, {2,27}, {4,22}, {3,6}, {4,25}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {4,26}, {1,22}, {2,13}, {2,8}, {2,25}, {4,14}, {1,23}, {4,19}, {1,11}, {1,25}, {2,22}, {3,10} }; // ET27.47 // Bipartite(3,24) Valencies [24,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3722690410399436636160000 EdgePairs[27][47]:={ {2,11}, {3,22}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {3,12}, {2,24}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {3,27}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,23}, {3,9}, {3,24}, {2,12}, {2,4}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,15}, {3,17}, {2,18}, {1,21}, {3,25}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {3,26}, {1,5}, {1,27}, {1,17}, {2,27}, {3,6}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22}, {3,10} }; // ET27.48 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 3656994324480 EdgePairs[27][48]:={ {13,21}, {5,7}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {11,25}, {9,10}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {6,15}, {11,15}, {8,21}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {2,7}, {6,9}, {21,22}, {13,27}, {6,14}, {16,21}, {11,17}, {1,12}, {9,11}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {2,25}, {4,24}, {2,6}, {8,13}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {12,26}, {3,10}, {2,5}, {7,27}, {2,10}, {19,22}, {3,9}, {10,26}, {2,17}, {17,20}, {10,20}, {17,26}, {1,24}, {13,24}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {15,19}, {6,18}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {6,10}, {4,7}, {8,18}, {4,18}, {12,24}, {12,27}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,8}, {4,9}, {6,12}, {19,23}, {4,21}, {13,17}, {18,19}, {20,25}, {7,19}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {11,21}, {8,17}, {10,16}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {12,17}, {2,23}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {6,8}, {11,13}, {2,27}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {17,19}, {9,12}, {14,27}, {12,18}, {2,16}, {6,11}, {9,25}, {10,22}, {7,23}, {6,22}, {10,25}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {4,15}, {6,23}, {15,17}, {1,5}, {24,27}, {7,24}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {9,23}, {7,21}, {14,16}, {8,27}, {2,11}, {14,26}, {10,15}, {3,5}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {16,20}, {8,11}, {18,24}, {14,19}, {18,27}, {16,27}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {4,25}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {20,27}, {8,14}, {7,10}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {5,21}, {21,27}, {9,15}, {17,24}, {20,23}, {2,4}, {17,21}, {16,23}, {18,23}, {1,15}, {14,25}, {15,21}, {14,20}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {15,18}, {10,27}, {5,17}, {3,4}, {15,16}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {5,10}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {8,25}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {21,23} }; // ET27.49 // Bipartite(2,25) Valencies [25,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31022420086661971968000000 EdgePairs[27][49]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {2,24}, {2,10}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {2,12}, {2,4}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {1,16}, {2,20}, {2,18}, {1,21}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET27.50 // Bipartite(1,26) Valencies [26,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 403291461126605635584000000 EdgePairs[27][50]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,12}, {1,2}, {1,3}, {1,17}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,6}, {1,14}, {1,26}, {1,18}, {1,27}, {1,21}, {1,19}, {1,20}, {1,8}, {1,24}, {1,9}, {1,23}, {1,25} }; // ET27.51 // Non-bipartite Valency 26 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 10888869450418352160768000000 EdgePairs[27][51]:={ {13,21}, {5,7}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {11,25}, {9,10}, {17,18}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {1,3}, {6,15}, {11,15}, {8,21}, {5,6}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {2,7}, {6,9}, {21,22}, {13,27}, {6,14}, {16,21}, {19,20}, {10,11}, {19,21}, {11,17}, {1,12}, {9,11}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {2,25}, {4,24}, {2,6}, {8,13}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {12,26}, {3,10}, {2,5}, {7,27}, {8,9}, {2,10}, {19,22}, {3,9}, {10,26}, {2,17}, {17,20}, {10,20}, {17,26}, {1,24}, {13,24}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {6,18}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {12,27}, {25,26}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,8}, {4,9}, {6,12}, {19,23}, {4,21}, {13,17}, {18,19}, {20,25}, {7,19}, {16,18}, {1,2}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {11,21}, {8,17}, {10,16}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {12,17}, {2,23}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {6,8}, {11,13}, {2,27}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {7,8}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {17,19}, {9,12}, {14,27}, {12,18}, {2,16}, {6,11}, {9,25}, {4,5}, {10,22}, {7,23}, {6,22}, {10,25}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {4,15}, {6,23}, {15,17}, {13,14}, {1,5}, {2,3}, {26,27}, {24,27}, {7,24}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {9,23}, {7,21}, {14,16}, {8,27}, {2,11}, {14,26}, {10,15}, {3,5}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {16,20}, {8,11}, {18,24}, {14,19}, {18,27}, {16,27}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {4,25}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {20,27}, {8,14}, {7,10}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {22,23}, {5,21}, {21,27}, {9,15}, {17,24}, {20,23}, {2,4}, {17,21}, {16,23}, {18,23}, {13,15}, {1,15}, {14,20}, {14,25}, {15,21}, {11,12}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {3,4}, {15,16}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {5,10}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {25,27}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {20,21}, {8,25}, {23,24}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {21,23} }; // Total number of connected ET graphs of order 27 is 51 // ******************************************************************************************** // Order 28 // ET28.1 // Bipartite(14,14) Valencies [2,2] // Diameter 14 Girth 28 // Twin-free VT AT // Automorphism group of order 56 EdgePairs[28][1]:={ {13,19}, {4,20}, {7,26}, {14,17}, {3,20}, {5,24}, {8,28}, {9,27}, {12,19}, {1,15}, {3,18}, {5,22}, {10,23}, {1,16}, {10,25}, {8,27}, {11,21}, {6,24}, {2,18}, {12,21}, {4,22}, {11,23}, {9,25}, {6,26}, {2,16}, {7,28}, {14,15}, {13,17} }; // ET28.2 // Non-bipartite Valency 3 // Diameter 4 Girth 7 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[28][2]:={ {15,24}, {7,27}, {10,22}, {10,13}, {4,10}, {9,23}, {22,28}, {5,14}, {11,19}, {8,25}, {14,26}, {3,19}, {6,18}, {13,27}, {21,25}, {5,22}, {18,21}, {12,20}, {1,15}, {9,26}, {2,14}, {1,28}, {5,19}, {1,6}, {6,9}, {11,15}, {17,26}, {16,23}, {11,25}, {2,21}, {3,23}, {8,16}, {20,28}, {13,18}, {4,17}, {7,24}, {3,27}, {16,20}, {17,24}, {7,12}, {2,12}, {4,8} }; // ET28.3 // Bipartite(12,16) Valencies [4,3] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 576 EdgePairs[28][3]:={ {3,16}, {7,14}, {8,21}, {6,15}, {11,22}, {4,24}, {7,23}, {5,13}, {5,24}, {9,19}, {2,17}, {3,14}, {1,27}, {12,23}, {9,22}, {12,18}, {7,15}, {4,16}, {4,21}, {8,15}, {11,26}, {9,13}, {10,25}, {2,28}, {3,27}, {10,20}, {9,28}, {1,13}, {8,27}, {5,23}, {5,25}, {6,17}, {6,24}, {10,19}, {12,20}, {2,18}, {12,21}, {4,22}, {11,20}, {1,18}, {8,19}, {6,26}, {2,16}, {3,25}, {10,17}, {1,26}, {7,28}, {11,14} }; // ET28.4 // Bipartite(12,16) Valencies [4,3] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 192 EdgePairs[28][4]:={ {10,27}, {8,20}, {2,24}, {9,21}, {9,16}, {8,21}, {8,25}, {11,27}, {1,20}, {5,15}, {3,23}, {11,23}, {4,16}, {3,24}, {2,16}, {3,15}, {7,18}, {6,20}, {11,22}, {7,15}, {5,17}, {10,14}, {6,27}, {12,14}, {12,19}, {4,17}, {7,25}, {3,26}, {10,24}, {9,13}, {4,22}, {12,25}, {2,28}, {2,19}, {9,18}, {8,26}, {12,22}, {5,14}, {7,28}, {6,17}, {1,13}, {5,13}, {1,19}, {10,21}, {4,26}, {6,28}, {1,23}, {11,18} }; // ET28.5 // Bipartite(12,16) Valencies [4,3] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12288 EdgePairs[28][5]:={ {4,24}, {9,23}, {2,24}, {8,23}, {6,26}, {12,16}, {8,15}, {3,27}, {7,13}, {8,25}, {11,27}, {9,15}, {3,23}, {4,16}, {7,27}, {2,16}, {2,20}, {3,15}, {6,20}, {1,21}, {11,22}, {3,19}, {12,13}, {12,24}, {7,21}, {1,17}, {7,19}, {6,18}, {4,22}, {2,28}, {9,18}, {10,17}, {5,14}, {5,18}, {5,26}, {1,13}, {10,28}, {9,26}, {6,28}, {4,14}, {10,25}, {11,19}, {10,20}, {11,14}, {5,22}, {1,25}, {8,17}, {12,21} }; // ET28.6 // Bipartite(14,14) Valencies [4,4] // Diameter 4 Girth 6 // Twin-free VT AT // Automorphism group of order 672 EdgePairs[28][6]:={ {3,22}, {4,24}, {8,28}, {11,15}, {2,26}, {11,25}, {7,23}, {9,21}, {13,16}, {11,20}, {13,25}, {8,25}, {13,26}, {3,24}, {11,21}, {5,16}, {5,21}, {4,18}, {1,15}, {9,24}, {3,16}, {2,20}, {10,23}, {3,15}, {5,19}, {4,27}, {12,23}, {6,27}, {6,21}, {7,25}, {8,22}, {12,26}, {1,27}, {1,17}, {7,19}, {6,22}, {2,19}, {10,17}, {14,27}, {5,18}, {14,20}, {8,18}, {1,19}, {4,26}, {12,28}, {9,28}, {12,15}, {14,28}, {10,20}, {14,16}, {6,23}, {2,22}, {13,17}, {7,24}, {10,18}, {9,17} }; // ET28.7 // Bipartite(14,14) Valencies [4,4] // Diameter 7 Girth 4 // Has twins VT AT // Automorphism group of order 458752 EdgePairs[28][7]:={ {9,19}, {9,23}, {7,16}, {1,24}, {2,26}, {12,18}, {14,18}, {7,23}, {9,16}, {3,21}, {8,15}, {11,20}, {11,27}, {8,24}, {3,24}, {6,15}, {5,21}, {2,16}, {5,25}, {1,15}, {3,28}, {7,18}, {6,20}, {3,17}, {5,28}, {4,27}, {4,20}, {6,27}, {13,20}, {7,25}, {10,24}, {8,22}, {13,22}, {1,17}, {12,25}, {13,15}, {6,22}, {2,19}, {10,17}, {14,23}, {5,18}, {2,23}, {10,28}, {11,26}, {10,21}, {9,26}, {13,27}, {4,26}, {12,28}, {1,22}, {4,19}, {11,19}, {14,25}, {8,17}, {14,16}, {12,21} }; // ET28.8 // Non-bipartite Valency 4 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 1792 EdgePairs[28][8]:={ {2,11}, {4,8}, {4,13}, {11,16}, {19,23}, {9,19}, {7,11}, {2,26}, {5,24}, {24,27}, {22,25}, {5,10}, {3,21}, {1,6}, {3,27}, {1,20}, {1,12}, {5,15}, {17,22}, {20,24}, {13,18}, {6,16}, {18,28}, {15,19}, {3,7}, {7,18}, {9,27}, {11,22}, {10,14}, {17,27}, {3,14}, {8,12}, {2,5}, {7,25}, {15,25}, {9,13}, {4,28}, {16,20}, {18,21}, {4,22}, {2,19}, {8,26}, {14,23}, {21,26}, {13,24}, {10,28}, {12,15}, {10,20}, {23,28}, {14,17}, {8,17}, {1,25}, {6,23}, {12,21}, {16,26}, {6,9} }; // ET28.9 // Bipartite(7,21) Valencies [6,2] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 5040 EdgePairs[28][9]:={ {1,20}, {3,16}, {7,26}, {6,28}, {6,21}, {3,10}, {5,13}, {5,14}, {1,24}, {2,24}, {1,27}, {4,15}, {6,8}, {7,17}, {6,23}, {5,20}, {3,21}, {5,22}, {6,12}, {4,18}, {3,11}, {1,17}, {4,27}, {7,25}, {4,28}, {3,22}, {5,26}, {7,18}, {1,11}, {2,23}, {2,16}, {2,15}, {7,12}, {6,19}, {7,9}, {4,13}, {3,25}, {4,10}, {5,19}, {2,9}, {2,14}, {1,8} }; // ET28.10 // Bipartite(7,21) Valencies [6,2] // Diameter 7 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3919104 EdgePairs[28][10]:={ {6,20}, {3,24}, {1,20}, {7,10}, {7,26}, {6,13}, {3,10}, {5,18}, {1,27}, {3,8}, {1,15}, {7,17}, {3,15}, {2,21}, {1,22}, {4,21}, {6,18}, {6,27}, {2,28}, {4,14}, {4,19}, {3,17}, {1,13}, {5,23}, {5,25}, {4,28}, {6,11}, {3,22}, {5,11}, {2,23}, {5,16}, {2,16}, {6,25}, {4,26}, {7,12}, {7,24}, {5,9}, {2,9}, {4,12}, {7,19}, {2,14}, {1,8} }; // ET28.11 // Bipartite(14,14) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 168 EdgePairs[28][11]:={ {3,22}, {10,15}, {11,16}, {8,28}, {4,23}, {9,23}, {10,27}, {11,15}, {14,19}, {2,26}, {14,18}, {9,25}, {13,16}, {5,27}, {8,16}, {11,28}, {12,16}, {3,21}, {13,25}, {8,25}, {11,27}, {13,26}, {9,15}, {1,20}, {8,24}, {3,24}, {6,15}, {13,18}, {2,21}, {8,27}, {5,20}, {1,15}, {9,24}, {3,16}, {10,26}, {6,20}, {14,22}, {3,17}, {5,28}, {1,21}, {2,18}, {4,21}, {9,27}, {4,20}, {3,19}, {5,17}, {12,23}, {12,24}, {4,17}, {7,25}, {1,18}, {7,21}, {12,26}, {7,20}, {13,23}, {4,22}, {4,25}, {6,19}, {9,22}, {2,28}, {6,22}, {2,19}, {14,23}, {14,27}, {2,17}, {7,28}, {5,18}, {1,19}, {11,26}, {6,28}, {10,25}, {1,23}, {12,15}, {11,19}, {10,20}, {5,22}, {8,17}, {14,16}, {13,17}, {7,24}, {10,18}, {6,24}, {12,21}, {7,26} }; // ET28.12 // Bipartite(14,14) Valencies [6,6] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 5505024 EdgePairs[28][12]:={ {1,26}, {4,24}, {8,19}, {13,19}, {13,28}, {9,23}, {10,27}, {11,15}, {8,20}, {12,18}, {14,18}, {11,17}, {11,25}, {9,21}, {9,16}, {6,26}, {11,24}, {12,16}, {8,15}, {3,27}, {13,26}, {9,15}, {1,20}, {3,23}, {3,24}, {3,20}, {2,21}, {8,27}, {5,16}, {5,23}, {7,27}, {4,18}, {2,16}, {5,25}, {10,16}, {1,15}, {3,16}, {10,23}, {7,18}, {3,17}, {5,19}, {11,22}, {12,23}, {2,15}, {6,21}, {12,19}, {4,17}, {7,25}, {7,21}, {8,22}, {10,24}, {12,26}, {4,15}, {1,27}, {7,20}, {13,21}, {4,22}, {12,25}, {4,25}, {6,19}, {9,22}, {2,28}, {14,21}, {8,26}, {10,17}, {14,27}, {7,28}, {5,18}, {13,24}, {6,17}, {5,26}, {2,23}, {14,20}, {1,19}, {1,22}, {6,28}, {9,28}, {14,28}, {10,20}, {11,18}, {14,25}, {2,22}, {13,17}, {6,24} }; // ET28.13 // Bipartite(14,14) Valencies [6,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5376 EdgePairs[28][13]:={ {1,26}, {8,19}, {8,28}, {13,19}, {9,19}, {9,23}, {11,15}, {1,24}, {5,24}, {7,23}, {9,16}, {12,16}, {8,15}, {11,20}, {13,25}, {8,25}, {9,15}, {8,24}, {3,23}, {11,21}, {13,18}, {5,16}, {5,21}, {7,27}, {4,18}, {2,16}, {5,25}, {10,16}, {1,15}, {3,16}, {3,28}, {10,23}, {10,26}, {6,20}, {3,17}, {4,21}, {9,27}, {4,20}, {11,22}, {5,17}, {6,27}, {2,15}, {3,18}, {12,24}, {13,20}, {3,26}, {7,21}, {4,15}, {7,20}, {2,27}, {6,18}, {4,22}, {12,25}, {6,19}, {9,22}, {14,21}, {2,19}, {1,28}, {8,26}, {10,17}, {12,22}, {14,23}, {14,27}, {7,28}, {6,25}, {6,17}, {2,23}, {14,20}, {14,24}, {1,19}, {10,28}, {11,26}, {13,27}, {4,26}, {14,28}, {11,18}, {12,17}, {5,22}, {1,25}, {2,22}, {13,17}, {7,24}, {10,18}, {12,21} }; // ET28.14 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 168 EdgePairs[28][14]:={ {2,14}, {4,24}, {24,28}, {9,19}, {7,11}, {10,27}, {11,15}, {5,24}, {12,18}, {11,17}, {18,26}, {2,10}, {15,20}, {11,24}, {12,16}, {16,23}, {8,21}, {8,25}, {15,24}, {20,21}, {6,10}, {13,26}, {19,22}, {1,20}, {3,23}, {17,25}, {4,16}, {6,15}, {13,18}, {5,9}, {5,16}, {16,27}, {4,12}, {2,7}, {3,11}, {3,15}, {22,26}, {19,27}, {6,20}, {23,27}, {5,19}, {5,28}, {1,21}, {20,28}, {8,13}, {10,14}, {12,23}, {6,27}, {21,25}, {8,12}, {3,18}, {4,5}, {4,17}, {3,26}, {7,22}, {15,28}, {13,22}, {9,13}, {16,19}, {2,27}, {12,25}, {3,6}, {4,25}, {9,22}, {14,21}, {2,19}, {1,28}, {18,23}, {1,8}, {1,13}, {8,18}, {7,17}, {11,26}, {1,9}, {10,21}, {9,28}, {7,14}, {10,20}, {14,17}, {14,25}, {6,23}, {2,22}, {17,24}, {7,26} }; // ET28.15 // Non-bipartite Valency 6 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[28][15]:={ {5,12}, {1,26}, {11,16}, {10,15}, {13,19}, {19,24}, {14,19}, {23,25}, {24,27}, {20,22}, {7,9}, {22,25}, {9,16}, {8,9}, {20,23}, {7,12}, {15,20}, {8,11}, {5,10}, {1,6}, {6,12}, {3,5}, {20,21}, {5,11}, {9,15}, {19,22}, {4,7}, {17,22}, {3,8}, {13,18}, {22,28}, {4,6}, {8,10}, {10,13}, {21,27}, {10,16}, {1,7}, {7,10}, {2,7}, {3,28}, {16,18}, {19,21}, {4,27}, {3,25}, {21,28}, {12,14}, {2,5}, {12,13}, {4,5}, {13,20}, {15,17}, {3,26}, {1,27}, {11,13}, {16,19}, {2,27}, {18,21}, {3,6}, {4,25}, {2,28}, {1,28}, {24,26}, {18,23}, {21,26}, {9,14}, {22,27}, {1,8}, {14,20}, {6,11}, {18,24}, {16,17}, {23,26}, {4,26}, {2,25}, {2,8}, {12,15}, {23,28}, {11,14}, {14,17}, {15,18}, {24,25}, {17,24}, {17,23}, {6,9} }; // ET28.16 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[28][16]:={ {16,25}, {14,21}, {1,11}, {24,26}, {12,16}, {3,7}, {10,27}, {6,23}, {2,20}, {23,27}, {14,19}, {4,16}, {6,13}, {12,14}, {20,23}, {19,27}, {1,9}, {19,23}, {12,27}, {7,15}, {2,18}, {5,26}, {4,26}, {9,17}, {10,18}, {15,28}, {12,21}, {3,11}, {3,13}, {15,25}, {1,22}, {6,21}, {8,21}, {8,10}, {3,9}, {18,25}, {7,20}, {7,13}, {8,17}, {6,26}, {6,15}, {8,11}, {12,28}, {15,19}, {5,28}, {4,25}, {3,5}, {13,22}, {18,27}, {12,24}, {14,17}, {14,22}, {10,28}, {4,22}, {8,20}, {8,23}, {11,21}, {19,22}, {9,18}, {10,17}, {13,21}, {1,20}, {5,11}, {3,16}, {5,10}, {16,28}, {2,26}, {15,17}, {24,27}, {9,14}, {2,25}, {2,7}, {19,25}, {20,22}, {9,16}, {23,26}, {7,17}, {11,24}, {4,13}, {1,18}, {4,24}, {2,5}, {1,24}, {6,28} }; // ET28.17 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[28][17]:={ {5,12}, {1,26}, {12,27}, {4,9}, {9,19}, {4,23}, {13,28}, {19,24}, {1,14}, {7,11}, {14,19}, {8,20}, {7,16}, {1,24}, {3,12}, {17,28}, {21,23}, {15,20}, {6,14}, {11,24}, {4,11}, {12,16}, {16,23}, {3,27}, {8,25}, {6,10}, {13,26}, {15,27}, {1,20}, {3,8}, {11,23}, {17,25}, {11,21}, {2,21}, {5,16}, {5,23}, {10,16}, {7,10}, {1,15}, {2,20}, {3,15}, {22,26}, {7,18}, {19,27}, {14,22}, {3,17}, {4,27}, {3,25}, {2,18}, {9,27}, {4,21}, {21,28}, {10,14}, {12,23}, {7,25}, {16,25}, {13,22}, {13,21}, {2,28}, {6,22}, {20,26}, {6,17}, {5,26}, {8,18}, {14,24}, {5,13}, {1,19}, {10,22}, {18,24}, {18,20}, {15,26}, {2,13}, {6,28}, {2,8}, {10,25}, {9,28}, {12,15}, {4,19}, {11,18}, {5,22}, {8,17}, {7,24}, {9,17}, {6,9} }; // ET28.18 // Bipartite(12,16) Valencies [8,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 768 EdgePairs[28][18]:={ {1,15}, {10,19}, {11,15}, {3,15}, {8,24}, {12,26}, {11,23}, {12,19}, {2,22}, {6,14}, {4,27}, {7,24}, {6,23}, {1,25}, {4,16}, {12,17}, {12,14}, {5,24}, {7,27}, {9,21}, {11,16}, {12,18}, {11,22}, {12,27}, {7,23}, {5,13}, {2,28}, {12,25}, {2,19}, {2,15}, {4,26}, {8,13}, {9,17}, {6,22}, {10,23}, {12,21}, {5,23}, {4,20}, {8,28}, {10,25}, {6,21}, {2,17}, {8,18}, {3,14}, {2,13}, {10,15}, {7,25}, {9,23}, {10,24}, {5,19}, {7,20}, {8,26}, {8,17}, {7,14}, {11,28}, {6,15}, {1,19}, {4,21}, {1,26}, {11,13}, {5,22}, {6,19}, {2,21}, {5,27}, {10,28}, {7,18}, {4,22}, {9,28}, {10,14}, {3,28}, {3,26}, {8,16}, {5,17}, {7,16}, {6,20}, {3,21}, {9,18}, {10,17}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {8,25}, {3,25}, {2,26}, {11,20}, {3,20}, {9,14}, {5,18}, {6,27}, {9,16}, {11,24}, {4,13}, {1,24}, {9,22} }; // ET28.19 // Bipartite(12,16) Valencies [8,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1152 EdgePairs[28][19]:={ {1,26}, {12,20}, {4,24}, {11,16}, {8,28}, {9,19}, {10,27}, {11,15}, {7,16}, {2,26}, {9,20}, {11,17}, {7,23}, {8,16}, {8,23}, {6,26}, {8,21}, {8,15}, {11,20}, {7,13}, {8,25}, {5,15}, {4,16}, {3,24}, {11,21}, {2,21}, {8,27}, {5,23}, {5,21}, {7,27}, {5,25}, {9,24}, {3,16}, {3,28}, {2,20}, {1,16}, {10,23}, {3,15}, {7,18}, {6,20}, {5,19}, {4,27}, {3,25}, {2,18}, {4,20}, {3,19}, {5,17}, {7,15}, {12,23}, {3,14}, {12,14}, {6,21}, {12,24}, {1,18}, {7,22}, {10,24}, {1,27}, {4,28}, {9,13}, {11,13}, {2,27}, {1,17}, {4,22}, {12,25}, {6,19}, {9,22}, {10,19}, {1,28}, {8,26}, {9,18}, {12,22}, {2,17}, {5,18}, {9,14}, {6,25}, {3,13}, {6,17}, {2,23}, {1,13}, {5,13}, {1,19}, {10,28}, {10,22}, {11,26}, {4,26}, {6,28}, {4,14}, {10,25}, {12,15}, {7,14}, {11,14}, {2,22}, {9,17}, {10,18}, {6,24}, {12,21} }; // ET28.20 // Bipartite(12,16) Valencies [8,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 192 EdgePairs[28][20]:={ {2,14}, {4,24}, {8,28}, {9,19}, {9,23}, {10,27}, {11,15}, {7,16}, {1,24}, {9,20}, {11,17}, {7,23}, {9,21}, {5,27}, {8,16}, {6,14}, {6,26}, {11,24}, {11,28}, {8,15}, {7,13}, {8,25}, {1,20}, {5,15}, {3,23}, {4,16}, {3,24}, {6,15}, {11,21}, {2,21}, {8,27}, {5,23}, {2,16}, {10,16}, {1,15}, {9,24}, {1,16}, {2,20}, {10,23}, {3,15}, {7,18}, {6,20}, {1,21}, {3,25}, {4,21}, {4,20}, {3,19}, {5,17}, {12,23}, {6,27}, {12,14}, {3,18}, {12,19}, {7,25}, {1,18}, {3,26}, {7,21}, {12,26}, {1,27}, {4,28}, {9,13}, {11,13}, {2,27}, {12,25}, {4,25}, {6,19}, {9,22}, {2,28}, {10,19}, {6,22}, {8,26}, {12,22}, {5,14}, {2,17}, {7,28}, {5,18}, {3,13}, {1,13}, {8,14}, {8,18}, {5,13}, {7,17}, {10,22}, {11,26}, {4,26}, {12,28}, {10,25}, {4,19}, {10,20}, {12,17}, {11,14}, {5,22}, {2,22}, {9,17}, {10,18}, {6,24} }; // ET28.21 // Bipartite(12,16) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3439853568 EdgePairs[28][21]:={ {9,13}, {7,19}, {11,15}, {10,21}, {3,15}, {12,26}, {10,22}, {6,18}, {11,23}, {4,14}, {12,19}, {2,22}, {6,14}, {4,27}, {6,17}, {7,24}, {1,25}, {6,13}, {12,15}, {12,14}, {12,22}, {5,24}, {6,25}, {7,27}, {9,21}, {11,16}, {12,18}, {12,27}, {7,23}, {7,15}, {5,13}, {2,18}, {8,14}, {4,26}, {9,17}, {10,18}, {6,22}, {5,21}, {3,19}, {8,22}, {8,15}, {7,28}, {2,14}, {1,17}, {10,25}, {1,16}, {6,21}, {10,13}, {2,17}, {8,18}, {2,13}, {7,20}, {8,26}, {3,23}, {11,28}, {3,27}, {6,26}, {5,28}, {9,25}, {4,15}, {8,19}, {12,23}, {2,21}, {8,27}, {11,19}, {5,20}, {9,28}, {4,22}, {10,14}, {3,28}, {3,24}, {5,17}, {9,24}, {8,23}, {7,16}, {10,17}, {11,27}, {1,20}, {3,16}, {1,13}, {4,18}, {2,26}, {11,20}, {3,20}, {2,25}, {1,28}, {10,26}, {9,16}, {4,23}, {11,24}, {5,16}, {1,21}, {5,25}, {4,19}, {9,20}, {1,24} }; // ET28.22 // Bipartite(12,16) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 509607936 EdgePairs[28][22]:={ {9,13}, {11,15}, {3,15}, {10,22}, {11,23}, {4,14}, {2,22}, {6,17}, {12,16}, {1,25}, {4,16}, {6,13}, {12,17}, {5,24}, {6,25}, {9,19}, {9,21}, {11,16}, {12,25}, {2,19}, {2,18}, {2,15}, {8,14}, {4,26}, {9,17}, {10,18}, {3,19}, {8,22}, {8,15}, {12,21}, {2,14}, {5,23}, {4,20}, {9,27}, {2,23}, {7,26}, {1,17}, {3,13}, {1,22}, {6,21}, {8,18}, {4,28}, {10,16}, {7,25}, {9,23}, {10,24}, {5,19}, {5,15}, {8,26}, {7,13}, {3,23}, {7,14}, {11,28}, {3,27}, {12,28}, {5,28}, {9,25}, {9,15}, {1,26}, {8,19}, {12,24}, {2,27}, {5,27}, {8,27}, {10,28}, {11,19}, {7,18}, {5,20}, {4,22}, {10,14}, {8,23}, {6,16}, {6,20}, {3,21}, {1,14}, {11,27}, {7,22}, {1,13}, {4,18}, {3,25}, {2,26}, {11,20}, {7,21}, {3,17}, {10,20}, {6,24}, {10,26}, {7,17}, {11,24}, {5,16}, {1,21}, {1,18}, {12,20}, {4,24}, {12,13}, {6,28} }; // ET28.23 // Bipartite(12,16) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 786432 EdgePairs[28][23]:={ {1,15}, {10,19}, {9,13}, {5,14}, {11,17}, {3,15}, {8,24}, {12,19}, {6,14}, {12,16}, {4,27}, {10,27}, {7,24}, {2,20}, {12,14}, {12,22}, {9,21}, {11,22}, {12,27}, {7,23}, {7,15}, {5,13}, {2,28}, {2,18}, {2,15}, {4,26}, {9,17}, {10,18}, {6,22}, {5,21}, {3,18}, {8,15}, {4,20}, {2,23}, {8,28}, {3,13}, {10,25}, {2,16}, {1,22}, {1,16}, {8,18}, {4,28}, {9,23}, {5,19}, {8,26}, {7,13}, {3,23}, {7,14}, {12,28}, {4,17}, {9,25}, {4,25}, {9,15}, {11,14}, {12,24}, {2,24}, {11,13}, {5,22}, {6,19}, {1,23}, {5,27}, {10,28}, {11,19}, {3,26}, {8,16}, {5,17}, {11,25}, {8,20}, {8,23}, {7,16}, {9,26}, {6,20}, {6,16}, {11,21}, {3,21}, {1,14}, {9,18}, {10,17}, {11,27}, {7,22}, {1,13}, {4,18}, {3,25}, {2,26}, {7,21}, {3,17}, {10,20}, {6,24}, {10,26}, {6,27}, {1,21}, {12,20}, {5,25}, {4,19}, {1,24}, {6,28} }; // ET28.24 // Bipartite(12,16) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 49152 EdgePairs[28][24]:={ {11,15}, {10,21}, {11,17}, {3,15}, {12,26}, {11,23}, {6,18}, {4,14}, {12,16}, {6,17}, {4,27}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {12,14}, {12,22}, {6,25}, {9,19}, {12,18}, {7,23}, {7,15}, {5,13}, {2,28}, {2,19}, {2,15}, {5,26}, {8,14}, {9,17}, {5,21}, {8,22}, {8,15}, {9,27}, {2,23}, {7,26}, {1,17}, {10,25}, {2,16}, {1,22}, {10,13}, {8,18}, {3,14}, {10,16}, {3,22}, {5,19}, {10,24}, {8,26}, {7,13}, {3,23}, {6,26}, {6,15}, {12,28}, {4,21}, {5,28}, {9,25}, {1,26}, {8,19}, {12,24}, {2,24}, {11,13}, {2,27}, {5,27}, {8,27}, {10,28}, {11,19}, {7,18}, {5,20}, {9,28}, {4,22}, {3,24}, {11,25}, {8,23}, {7,16}, {6,20}, {11,21}, {1,14}, {10,17}, {11,27}, {3,16}, {1,13}, {3,25}, {7,21}, {9,14}, {3,17}, {10,20}, {5,18}, {4,13}, {1,21}, {12,20}, {1,18}, {4,19}, {4,24}, {9,20}, {9,22}, {6,28} }; // ET28.25 // Bipartite(14,14) Valencies [8,8] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 5505024 EdgePairs[28][25]:={ {1,15}, {7,19}, {13,25}, {11,15}, {10,21}, {14,25}, {3,15}, {12,26}, {10,22}, {11,23}, {6,18}, {12,19}, {12,16}, {6,17}, {4,27}, {13,18}, {10,27}, {7,24}, {6,23}, {2,20}, {13,24}, {14,19}, {1,25}, {14,18}, {4,16}, {12,17}, {12,15}, {12,22}, {5,24}, {6,25}, {7,27}, {9,19}, {9,21}, {11,16}, {11,22}, {2,28}, {14,20}, {2,19}, {5,26}, {14,27}, {8,22}, {8,15}, {13,16}, {5,23}, {4,20}, {9,27}, {2,23}, {7,26}, {8,28}, {2,16}, {1,22}, {6,21}, {8,21}, {8,18}, {10,15}, {7,25}, {3,22}, {9,23}, {10,24}, {5,19}, {5,15}, {7,20}, {8,26}, {3,27}, {14,26}, {1,19}, {11,18}, {4,15}, {4,25}, {1,26}, {8,19}, {12,24}, {12,23}, {5,22}, {2,27}, {14,17}, {2,21}, {10,28}, {7,18}, {4,22}, {9,28}, {3,28}, {3,24}, {5,17}, {11,25}, {13,28}, {6,16}, {9,26}, {3,21}, {10,17}, {11,27}, {13,21}, {4,18}, {8,25}, {13,23}, {2,26}, {13,17}, {11,20}, {3,20}, {1,28}, {3,17}, {10,20}, {6,24}, {9,16}, {7,17}, {4,23}, {5,16}, {1,21}, {1,18}, {14,24}, {9,20}, {6,28} }; // ET28.26 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 64210599936 EdgePairs[28][26]:={ {9,13}, {10,19}, {16,25}, {11,15}, {6,10}, {4,14}, {1,11}, {17,27}, {4,8}, {4,27}, {3,7}, {13,18}, {12,16}, {10,27}, {2,11}, {6,23}, {2,20}, {23,27}, {13,24}, {14,18}, {1,25}, {12,15}, {12,22}, {5,24}, {20,23}, {21,26}, {9,19}, {1,5}, {19,24}, {11,16}, {21,25}, {11,22}, {16,20}, {19,23}, {18,21}, {2,19}, {6,9}, {7,11}, {5,9}, {12,21}, {22,25}, {5,23}, {9,27}, {7,26}, {4,7}, {3,13}, {15,25}, {10,13}, {8,18}, {4,28}, {3,14}, {1,12}, {16,26}, {7,25}, {16,19}, {3,22}, {5,15}, {20,24}, {15,20}, {8,26}, {8,17}, {3,27}, {6,15}, {1,19}, {8,11}, {15,19}, {4,21}, {1,26}, {18,27}, {15,26}, {17,22}, {14,17}, {10,28}, {18,28}, {7,18}, {14,23}, {2,12}, {9,28}, {4,22}, {10,14}, {3,28}, {2,6}, {6,16}, {11,21}, {3,21}, {17,21}, {1,20}, {5,10}, {22,26}, {8,25}, {13,23}, {2,26}, {3,8}, {13,17}, {24,27}, {9,14}, {2,25}, {23,28}, {10,20}, {6,24}, {18,22}, {17,28}, {7,17}, {7,12}, {5,16}, {4,13}, {1,6}, {14,24}, {2,5}, {9,20}, {8,12}, {24,28} }; // ET28.27 // Bipartite(7,21) Valencies [9,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 47029248 EdgePairs[28][27]:={ {5,12}, {7,16}, {2,26}, {7,9}, {2,24}, {7,23}, {2,10}, {5,27}, {6,14}, {4,11}, {3,27}, {7,13}, {6,10}, {5,15}, {3,24}, {2,12}, {6,15}, {3,20}, {5,8}, {4,12}, {5,20}, {7,27}, {4,18}, {2,16}, {1,15}, {3,11}, {1,16}, {3,17}, {5,19}, {3,25}, {4,21}, {3,18}, {6,21}, {1,18}, {7,21}, {7,20}, {4,28}, {4,25}, {6,22}, {2,19}, {2,17}, {7,28}, {3,13}, {6,17}, {2,23}, {5,26}, {1,8}, {5,13}, {2,9}, {1,9}, {4,26}, {1,22}, {4,14}, {6,28}, {1,23}, {4,19}, {7,14}, {1,11}, {1,25}, {5,22}, {6,8}, {6,24}, {3,10} }; // ET28.28 // Bipartite(10,18) Valencies [9,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2799360 EdgePairs[28][28]:={ {5,12}, {3,22}, {1,26}, {2,14}, {4,24}, {8,19}, {10,15}, {8,28}, {4,23}, {1,14}, {10,27}, {2,26}, {5,24}, {9,20}, {2,24}, {9,21}, {9,16}, {7,12}, {8,16}, {6,14}, {6,26}, {4,11}, {7,13}, {8,25}, {5,11}, {9,15}, {1,20}, {8,24}, {3,23}, {2,12}, {6,15}, {5,23}, {5,20}, {4,12}, {7,27}, {4,18}, {2,16}, {10,16}, {3,11}, {3,16}, {3,28}, {2,20}, {10,23}, {7,18}, {6,20}, {3,17}, {4,27}, {3,25}, {2,18}, {4,21}, {9,27}, {10,11}, {3,19}, {5,17}, {7,15}, {8,13}, {6,27}, {8,12}, {6,21}, {4,17}, {7,25}, {7,21}, {8,22}, {4,15}, {1,17}, {7,19}, {6,19}, {9,22}, {2,28}, {10,17}, {5,14}, {5,18}, {9,14}, {6,25}, {3,13}, {5,26}, {1,13}, {8,18}, {1,19}, {10,28}, {10,22}, {9,26}, {10,21}, {9,28}, {1,23}, {1,11}, {1,25}, {2,22}, {6,13}, {7,24} }; // ET28.29 // Non-bipartite Valency 9 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 504 EdgePairs[28][29]:={ {16,25}, {11,15}, {6,12}, {10,21}, {10,22}, {6,10}, {3,7}, {6,17}, {4,27}, {13,18}, {2,11}, {2,20}, {13,24}, {17,19}, {1,25}, {9,12}, {6,13}, {12,17}, {5,24}, {16,18}, {1,9}, {16,23}, {7,27}, {1,5}, {13,27}, {11,22}, {26,27}, {19,23}, {12,27}, {7,23}, {7,15}, {18,21}, {14,20}, {23,24}, {2,18}, {8,14}, {10,18}, {7,11}, {5,9}, {21,28}, {15,28}, {3,19}, {20,25}, {12,21}, {22,25}, {2,14}, {4,20}, {9,27}, {17,24}, {1,10}, {4,7}, {19,26}, {3,13}, {10,13}, {8,21}, {16,26}, {3,22}, {5,19}, {18,25}, {15,20}, {8,17}, {25,28}, {6,26}, {1,19}, {8,11}, {15,19}, {4,21}, {4,15}, {4,25}, {1,4}, {9,15}, {18,27}, {12,23}, {11,13}, {2,27}, {14,17}, {1,23}, {14,22}, {18,28}, {14,23}, {9,28}, {10,14}, {3,28}, {8,16}, {5,17}, {11,25}, {21,23}, {7,16}, {9,26}, {6,20}, {2,6}, {3,21}, {1,14}, {19,22}, {2,8}, {5,11}, {7,22}, {3,16}, {22,26}, {8,25}, {2,26}, {3,8}, {15,17}, {13,15}, {24,27}, {3,6}, {1,28}, {5,18}, {17,28}, {10,26}, {20,22}, {9,16}, {23,26}, {13,19}, {11,24}, {7,12}, {5,16}, {12,20}, {14,24}, {21,24}, {4,10}, {4,24}, {2,5}, {9,20}, {8,12}, {6,28} }; // ET28.30 // Bipartite(8,20) Valencies [10,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 26542080000 EdgePairs[28][30]:={ {5,12}, {2,14}, {8,19}, {4,23}, {7,11}, {7,16}, {1,24}, {3,12}, {2,26}, {5,24}, {7,23}, {2,10}, {7,12}, {8,23}, {6,14}, {6,26}, {8,11}, {4,11}, {4,10}, {8,15}, {3,27}, {6,10}, {1,20}, {1,12}, {3,23}, {3,24}, {3,20}, {2,21}, {5,9}, {5,16}, {8,27}, {5,21}, {8,10}, {5,20}, {7,27}, {4,18}, {5,25}, {3,11}, {3,16}, {3,28}, {1,16}, {3,15}, {5,28}, {1,21}, {2,18}, {4,27}, {3,19}, {5,17}, {7,15}, {6,21}, {8,22}, {4,15}, {7,20}, {1,17}, {7,19}, {4,22}, {6,18}, {6,22}, {1,28}, {8,26}, {2,17}, {7,28}, {6,25}, {6,17}, {1,13}, {8,14}, {8,18}, {5,13}, {2,9}, {1,9}, {4,26}, {2,13}, {2,25}, {4,14}, {4,19}, {1,25}, {2,22}, {6,13}, {7,24}, {6,9} }; // ET28.31 // Bipartite(4,24) Valencies [12,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2149908480000 EdgePairs[28][31]:={ {2,14}, {4,23}, {1,24}, {3,12}, {2,26}, {2,10}, {4,11}, {4,10}, {3,27}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {3,23}, {3,24}, {3,20}, {4,6}, {2,21}, {4,18}, {3,11}, {3,16}, {3,7}, {3,28}, {1,16}, {3,15}, {2,18}, {1,21}, {4,27}, {3,19}, {2,5}, {1,5}, {4,15}, {1,17}, {4,22}, {1,28}, {2,17}, {1,8}, {1,13}, {2,9}, {1,9}, {4,26}, {2,13}, {2,25}, {4,14}, {4,19}, {1,25}, {2,22} }; // ET28.32 // Bipartite(4,24) Valencies [12,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4586471424 EdgePairs[28][32]:={ {2,11}, {4,8}, {2,14}, {4,9}, {2,26}, {3,12}, {2,24}, {1,10}, {4,10}, {3,21}, {3,27}, {2,6}, {4,16}, {3,24}, {3,9}, {2,12}, {1,7}, {1,16}, {3,7}, {2,20}, {3,15}, {4,27}, {3,25}, {2,18}, {4,21}, {4,20}, {3,19}, {3,18}, {2,5}, {1,5}, {4,15}, {4,28}, {1,17}, {4,22}, {3,6}, {1,28}, {2,17}, {3,13}, {2,23}, {1,13}, {1,19}, {4,26}, {1,22}, {4,14}, {2,8}, {1,23}, {1,11}, {1,25} }; // ET28.33 // Bipartite(7,21) Valencies [12,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 47029248 EdgePairs[28][33]:={ {1,15}, {5,14}, {6,10}, {6,18}, {4,14}, {1,11}, {6,14}, {4,8}, {6,17}, {4,27}, {2,11}, {7,24}, {6,23}, {2,20}, {1,25}, {6,25}, {7,27}, {7,15}, {7,23}, {3,10}, {2,19}, {2,18}, {6,9}, {5,26}, {5,9}, {5,21}, {3,19}, {7,10}, {5,23}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {6,21}, {4,28}, {3,14}, {2,13}, {1,12}, {5,19}, {5,15}, {7,20}, {7,13}, {3,27}, {1,19}, {4,21}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {4,11}, {7,8}, {5,22}, {2,27}, {5,8}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {7,16}, {6,16}, {3,21}, {7,9}, {7,22}, {4,18}, {2,26}, {3,20}, {5,12}, {2,25}, {3,17}, {6,24}, {7,17}, {1,8}, {5,16}, {4,13}, {1,18}, {1,24}, {6,28} }; // ET28.34 // Bipartite(12,16) Valencies [12,9] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 576 EdgePairs[28][34]:={ {1,15}, {9,13}, {10,19}, {7,19}, {11,15}, {5,14}, {10,21}, {3,15}, {11,17}, {8,24}, {12,26}, {10,22}, {6,18}, {11,23}, {4,14}, {12,19}, {6,14}, {4,27}, {6,17}, {10,27}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {12,15}, {12,17}, {12,14}, {12,22}, {7,27}, {9,19}, {9,21}, {11,22}, {12,27}, {7,23}, {7,15}, {5,13}, {2,28}, {12,25}, {2,19}, {2,15}, {5,26}, {4,26}, {5,21}, {3,18}, {8,22}, {7,28}, {12,21}, {2,14}, {4,20}, {9,27}, {2,23}, {8,28}, {3,13}, {10,25}, {2,16}, {1,22}, {1,16}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {4,28}, {2,13}, {10,16}, {3,22}, {5,19}, {9,23}, {10,24}, {5,15}, {7,20}, {8,26}, {7,13}, {3,27}, {6,26}, {1,19}, {11,18}, {12,28}, {4,21}, {4,17}, {5,28}, {9,25}, {4,15}, {4,25}, {9,15}, {1,26}, {8,19}, {11,26}, {11,14}, {12,24}, {12,23}, {2,24}, {11,13}, {5,22}, {2,27}, {6,19}, {1,23}, {5,27}, {8,27}, {7,18}, {10,14}, {3,28}, {3,26}, {8,16}, {5,17}, {3,24}, {11,25}, {8,20}, {8,23}, {6,16}, {6,20}, {11,21}, {1,14}, {9,18}, {10,17}, {7,22}, {3,16}, {1,13}, {4,18}, {3,25}, {8,25}, {3,20}, {7,21}, {11,20}, {2,25}, {9,14}, {1,28}, {3,17}, {10,20}, {6,24}, {5,18}, {10,26}, {9,16}, {7,17}, {4,23}, {11,24}, {5,16}, {1,18}, {9,20}, {1,24}, {6,28}, {9,22} }; // ET28.35 // Bipartite(12,16) Valencies [12,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10319560704 EdgePairs[28][35]:={ {9,13}, {10,19}, {7,19}, {11,15}, {5,14}, {10,21}, {3,15}, {8,24}, {10,22}, {6,18}, {11,23}, {12,19}, {2,22}, {6,14}, {4,27}, {6,17}, {12,16}, {10,27}, {7,24}, {6,23}, {1,25}, {4,16}, {6,13}, {12,15}, {12,17}, {5,24}, {6,25}, {7,27}, {9,21}, {11,16}, {11,22}, {12,27}, {7,23}, {7,15}, {5,13}, {12,25}, {2,19}, {2,18}, {2,15}, {5,26}, {8,13}, {9,17}, {10,18}, {6,22}, {5,21}, {10,23}, {3,19}, {3,18}, {8,15}, {7,28}, {12,21}, {2,14}, {4,20}, {2,23}, {7,26}, {8,28}, {1,17}, {10,25}, {1,22}, {1,16}, {6,21}, {10,13}, {8,21}, {2,17}, {4,28}, {3,14}, {2,13}, {10,15}, {3,22}, {7,20}, {3,23}, {8,17}, {7,14}, {11,28}, {3,27}, {6,26}, {6,15}, {11,18}, {12,28}, {4,21}, {4,17}, {5,28}, {9,25}, {4,15}, {4,25}, {1,26}, {8,19}, {11,26}, {11,14}, {12,24}, {12,23}, {5,22}, {2,27}, {6,19}, {2,21}, {8,27}, {11,19}, {7,18}, {5,20}, {9,28}, {10,14}, {3,28}, {3,26}, {8,16}, {5,17}, {3,24}, {9,24}, {8,20}, {8,23}, {7,16}, {9,26}, {1,14}, {9,18}, {10,17}, {11,27}, {1,20}, {7,22}, {3,16}, {1,13}, {8,25}, {2,26}, {3,20}, {11,20}, {2,25}, {9,14}, {1,28}, {5,18}, {10,26}, {6,27}, {9,16}, {4,23}, {11,24}, {5,16}, {4,13}, {1,21}, {1,18}, {12,20}, {5,25}, {4,19}, {4,24}, {12,13}, {9,20}, {1,24}, {9,22} }; // ET28.36 // Bipartite(14,14) Valencies [12,12] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 165150720 EdgePairs[28][36]:={ {11,17}, {10,24}, {1,20}, {5,17}, {9,28}, {6,16}, {13,21}, {14,19}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {12,22}, {8,28}, {1,27}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {8,15}, {14,28}, {4,23}, {8,27}, {13,16}, {10,15}, {10,22}, {6,22}, {11,28}, {3,17}, {6,21}, {14,23}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,20}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {9,19}, {5,25}, {11,15}, {11,22}, {7,25}, {14,24}, {10,28}, {1,22}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {11,23}, {6,24}, {7,17}, {5,24}, {13,23}, {12,25}, {8,22}, {13,25}, {13,28}, {9,20}, {4,15}, {1,28}, {3,27}, {4,28}, {6,23}, {3,26}, {8,26}, {12,26}, {9,22}, {6,15}, {12,27}, {14,17}, {8,21}, {3,19}, {14,18}, {1,24}, {12,23}, {13,24}, {11,24}, {6,27}, {12,19}, {3,23}, {3,21}, {1,25}, {13,15}, {1,15}, {6,28}, {12,15}, {13,27}, {14,20}, {14,25}, {7,28}, {3,16}, {11,26}, {11,16}, {7,23}, {2,21}, {9,18}, {10,17}, {3,24}, {10,27}, {1,26}, {2,22}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {12,24}, {8,20}, {3,28}, {7,27}, {7,24}, {10,20}, {5,15}, {5,19}, {6,20}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {12,18}, {11,18}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET28.37 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 40320 EdgePairs[28][37]:={ {1,11}, {10,24}, {9,28}, {4,27}, {4,24}, {8,12}, {15,24}, {3,22}, {23,27}, {4,16}, {11,25}, {6,17}, {1,13}, {12,22}, {3,9}, {8,28}, {3,6}, {3,13}, {24,27}, {1,27}, {23,28}, {3,25}, {19,24}, {10,26}, {2,15}, {4,19}, {16,19}, {2,19}, {5,20}, {2,26}, {16,25}, {18,21}, {16,23}, {8,15}, {4,23}, {3,5}, {10,15}, {19,21}, {6,22}, {3,18}, {11,28}, {3,17}, {14,23}, {7,12}, {2,25}, {4,10}, {1,17}, {1,7}, {1,18}, {7,11}, {3,14}, {14,21}, {12,17}, {12,20}, {11,13}, {17,23}, {15,26}, {7,25}, {15,27}, {5,23}, {21,26}, {13,22}, {15,19}, {10,21}, {2,20}, {13,18}, {2,16}, {11,21}, {9,25}, {7,16}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {21,25}, {8,11}, {17,27}, {8,13}, {8,22}, {13,25}, {18,24}, {20,28}, {15,20}, {13,28}, {5,14}, {18,26}, {9,20}, {4,15}, {1,28}, {7,14}, {20,22}, {4,28}, {3,10}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {4,6}, {9,13}, {12,27}, {22,25}, {14,17}, {4,9}, {14,18}, {1,24}, {12,23}, {13,24}, {17,25}, {11,24}, {6,27}, {20,23}, {12,14}, {3,21}, {2,7}, {6,19}, {6,9}, {12,15}, {2,11}, {4,5}, {16,21}, {22,26}, {11,16}, {7,23}, {2,21}, {20,26}, {18,28}, {10,27}, {2,22}, {15,22}, {16,20}, {10,18}, {9,17}, {8,24}, {6,25}, {6,10}, {5,10}, {19,25}, {5,26}, {8,18}, {5,9}, {11,19}, {10,19}, {1,8}, {4,20}, {8,20}, {7,27}, {2,12}, {1,14}, {2,8}, {10,14}, {17,22}, {5,21}, {13,17}, {6,13}, {7,19}, {9,16}, {16,28}, {9,23}, {14,27}, {7,21}, {19,27}, {24,28}, {11,18}, {14,26}, {5,16} }; // ET28.38 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1344 EdgePairs[28][38]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {11,20}, {6,16}, {13,21}, {7,15}, {14,19}, {16,26}, {4,26}, {3,8}, {1,10}, {16,27}, {2,23}, {8,9}, {20,27}, {3,15}, {10,23}, {7,22}, {1,19}, {2,27}, {20,21}, {1,21}, {17,24}, {16,18}, {2,9}, {11,14}, {17,21}, {8,10}, {8,25}, {2,28}, {2,14}, {6,11}, {14,28}, {8,27}, {10,22}, {15,25}, {3,7}, {8,16}, {19,28}, {6,21}, {5,22}, {4,22}, {8,19}, {7,20}, {19,26}, {16,24}, {4,8}, {9,26}, {9,27}, {1,5}, {5,11}, {2,5}, {2,10}, {9,19}, {8,14}, {19,22}, {5,25}, {11,15}, {3,12}, {11,22}, {7,13}, {9,14}, {10,28}, {14,24}, {22,27}, {24,25}, {1,22}, {21,27}, {6,12}, {12,13}, {23,26}, {12,16}, {4,21}, {3,20}, {2,13}, {6,18}, {24,26}, {8,17}, {7,26}, {11,23}, {2,6}, {5,24}, {13,23}, {12,28}, {12,25}, {23,25}, {1,9}, {4,13}, {18,27}, {3,11}, {3,27}, {4,7}, {15,17}, {10,13}, {6,23}, {16,22}, {2,17}, {17,28}, {5,12}, {8,21}, {3,19}, {14,22}, {12,19}, {6,26}, {3,23}, {8,23}, {18,25}, {20,25}, {1,25}, {22,28}, {1,15}, {6,28}, {18,23}, {6,14}, {13,27}, {14,20}, {15,21}, {14,25}, {16,17}, {7,28}, {3,16}, {13,26}, {11,26}, {15,18}, {13,19}, {9,18}, {10,17}, {3,24}, {11,27}, {1,26}, {1,16}, {4,14}, {18,22}, {7,9}, {20,24}, {5,27}, {15,28}, {4,18}, {4,25}, {4,11}, {4,12}, {5,13}, {3,28}, {12,24}, {7,10}, {15,23}, {7,24}, {9,24}, {10,20}, {1,6}, {17,26}, {5,15}, {5,19}, {6,20}, {9,15}, {13,20}, {2,18}, {19,23}, {21,28}, {4,17}, {9,21}, {12,18}, {12,21}, {7,18}, {10,16} }; // ET28.39 // Bipartite(14,14) Valencies [13,13] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 174356582400 EdgePairs[28][39]:={ {11,17}, {10,25}, {1,20}, {10,24}, {11,20}, {9,28}, {6,16}, {13,21}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {12,22}, {8,28}, {1,27}, {3,25}, {3,15}, {10,23}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {8,25}, {2,28}, {8,15}, {14,28}, {4,23}, {8,27}, {13,16}, {10,15}, {10,22}, {3,18}, {11,28}, {3,17}, {8,16}, {6,21}, {2,25}, {14,23}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,20}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {9,19}, {5,25}, {11,22}, {7,25}, {10,28}, {14,24}, {1,22}, {5,23}, {4,21}, {3,20}, {13,22}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {14,15}, {11,23}, {1,23}, {6,24}, {7,17}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,28}, {4,15}, {1,28}, {3,27}, {4,28}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {12,27}, {14,17}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {3,23}, {3,21}, {1,25}, {6,19}, {13,15}, {1,15}, {6,28}, {12,15}, {13,27}, {14,20}, {14,25}, {7,28}, {3,16}, {11,26}, {13,26}, {11,16}, {7,23}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {8,20}, {12,24}, {7,27}, {7,24}, {9,24}, {10,20}, {5,15}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {12,18}, {11,18}, {12,21}, {14,26}, {10,16}, {5,16} }; // ET28.40 // Non-bipartite Valency 13 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 2184 EdgePairs[28][40]:={ {11,17}, {1,11}, {9,28}, {4,24}, {4,26}, {23,27}, {16,27}, {11,25}, {6,17}, {2,23}, {1,13}, {3,9}, {8,28}, {3,6}, {3,25}, {10,23}, {10,26}, {17,20}, {1,19}, {2,27}, {2,4}, {2,26}, {1,21}, {17,24}, {16,25}, {17,21}, {8,10}, {8,25}, {2,14}, {8,15}, {14,28}, {10,15}, {19,21}, {6,22}, {3,17}, {3,7}, {14,23}, {7,12}, {4,10}, {1,17}, {4,22}, {3,14}, {14,21}, {16,24}, {4,8}, {12,20}, {5,11}, {2,5}, {2,10}, {26,27}, {8,14}, {6,8}, {5,25}, {11,13}, {15,26}, {3,12}, {11,22}, {7,13}, {25,28}, {22,27}, {6,12}, {21,26}, {13,22}, {15,19}, {10,21}, {2,20}, {14,16}, {13,18}, {24,26}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {5,18}, {8,11}, {5,24}, {17,27}, {5,7}, {12,28}, {23,25}, {8,22}, {1,9}, {20,28}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,27}, {20,22}, {4,28}, {6,23}, {1,3}, {5,28}, {12,26}, {16,22}, {9,22}, {6,15}, {9,13}, {22,25}, {14,17}, {3,19}, {1,24}, {12,23}, {22,23}, {13,24}, {11,24}, {6,27}, {6,26}, {3,23}, {8,23}, {18,19}, {18,25}, {12,14}, {3,21}, {2,7}, {1,25}, {9,12}, {6,9}, {13,15}, {1,15}, {12,15}, {18,23}, {13,27}, {10,11}, {4,5}, {14,20}, {15,21}, {14,25}, {16,17}, {3,16}, {13,26}, {15,18}, {11,16}, {13,19}, {9,18}, {10,17}, {20,26}, {11,27}, {18,28}, {10,27}, {2,22}, {18,22}, {16,20}, {7,9}, {20,24}, {5,10}, {19,25}, {15,28}, {4,18}, {11,19}, {10,19}, {4,11}, {1,8}, {4,20}, {8,20}, {7,27}, {15,23}, {7,24}, {2,12}, {9,24}, {1,6}, {17,26}, {10,14}, {5,19}, {6,20}, {21,24}, {5,21}, {6,13}, {2,18}, {19,23}, {7,19}, {21,28}, {9,16}, {7,21}, {12,18}, {19,27}, {24,28}, {12,21}, {7,18}, {5,16} }; // ET28.41 // Bipartite(14,14) Valencies [14,14] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 15200108913103994880000 EdgePairs[28][41]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {9,28}, {6,16}, {4,27}, {13,21}, {7,15}, {4,24}, {14,19}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {12,22}, {8,28}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {8,15}, {14,28}, {4,23}, {8,27}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {3,17}, {8,16}, {6,21}, {2,25}, {14,23}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,20}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {9,19}, {5,25}, {11,15}, {11,22}, {7,25}, {10,28}, {14,24}, {1,22}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {14,15}, {11,23}, {1,23}, {6,24}, {7,17}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {9,20}, {4,15}, {1,28}, {3,27}, {4,28}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {12,27}, {14,17}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {13,15}, {1,15}, {6,28}, {12,15}, {13,27}, {14,20}, {14,25}, {7,28}, {3,16}, {11,26}, {13,26}, {11,16}, {7,23}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {9,24}, {10,20}, {5,15}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {12,18}, {11,18}, {12,21}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET28.42 // Bipartite(7,21) Valencies [15,5] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 5040 EdgePairs[28][42]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,18}, {4,14}, {1,11}, {4,8}, {6,17}, {4,27}, {7,24}, {6,23}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {7,15}, {7,23}, {5,13}, {2,28}, {2,19}, {2,18}, {6,9}, {4,26}, {7,11}, {6,22}, {5,9}, {5,21}, {4,12}, {3,18}, {7,10}, {2,14}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {7,26}, {1,17}, {3,13}, {2,16}, {6,21}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {7,25}, {3,22}, {5,15}, {7,20}, {3,23}, {7,14}, {3,27}, {6,15}, {1,19}, {5,28}, {4,25}, {1,26}, {2,24}, {4,11}, {7,8}, {5,22}, {2,27}, {6,19}, {1,23}, {2,21}, {5,8}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {5,17}, {6,16}, {6,20}, {7,16}, {3,21}, {1,20}, {1,27}, {5,11}, {7,22}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {7,21}, {5,12}, {2,25}, {1,28}, {4,9}, {5,18}, {6,27}, {7,17}, {1,8}, {5,16}, {4,19}, {4,10}, {1,24} }; // ET28.43 // Bipartite(8,20) Valencies [15,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 79626240000 EdgePairs[28][43]:={ {7,19}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {2,22}, {6,14}, {4,27}, {6,17}, {2,11}, {7,24}, {6,23}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {7,27}, {7,15}, {7,23}, {5,13}, {3,10}, {2,19}, {2,18}, {6,9}, {2,15}, {5,26}, {8,13}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {7,28}, {8,15}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {7,26}, {8,28}, {1,17}, {1,22}, {1,16}, {6,21}, {2,17}, {8,21}, {4,28}, {3,14}, {2,13}, {1,12}, {3,22}, {7,20}, {3,23}, {8,17}, {7,14}, {3,27}, {6,15}, {6,26}, {8,11}, {4,21}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {8,19}, {4,11}, {5,22}, {2,27}, {6,19}, {2,21}, {8,27}, {7,18}, {8,9}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {8,16}, {3,12}, {8,20}, {8,23}, {7,16}, {1,14}, {1,20}, {7,22}, {3,16}, {1,13}, {5,10}, {8,25}, {2,26}, {3,20}, {5,12}, {2,25}, {1,28}, {4,9}, {5,18}, {6,27}, {4,23}, {5,16}, {7,12}, {4,13}, {1,21}, {1,18}, {5,25}, {4,19}, {4,24}, {8,12}, {1,24} }; // ET28.44 // Bipartite(13,15) Valencies [15,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8142915489162854400000 EdgePairs[28][44]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {9,28}, {6,16}, {4,27}, {13,21}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {12,22}, {8,28}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {8,15}, {4,23}, {8,27}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {12,20}, {9,19}, {8,14}, {5,25}, {11,15}, {11,22}, {9,14}, {7,25}, {10,28}, {1,22}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {10,21}, {2,20}, {6,18}, {13,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {5,14}, {9,20}, {4,15}, {1,28}, {7,14}, {3,27}, {4,28}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {13,15}, {1,15}, {6,28}, {12,15}, {6,14}, {13,27}, {7,28}, {3,16}, {11,26}, {13,26}, {11,16}, {7,23}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {13,14}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET28.45 // Non-bipartite Valency 15 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 40320 EdgePairs[28][45]:={ {11,17}, {21,23}, {2,24}, {1,20}, {5,17}, {9,28}, {6,16}, {4,27}, {13,21}, {7,15}, {4,26}, {3,8}, {4,16}, {11,25}, {2,23}, {12,22}, {8,28}, {3,13}, {24,27}, {1,27}, {23,28}, {3,25}, {3,15}, {10,26}, {17,20}, {16,19}, {2,19}, {7,8}, {1,19}, {2,27}, {2,26}, {1,21}, {16,25}, {2,9}, {11,14}, {18,21}, {8,25}, {2,28}, {6,11}, {14,28}, {8,27}, {13,16}, {10,22}, {6,22}, {3,18}, {11,28}, {3,17}, {19,28}, {14,23}, {7,12}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {19,26}, {16,24}, {4,8}, {9,26}, {18,20}, {9,27}, {12,20}, {2,10}, {6,8}, {5,25}, {11,15}, {15,26}, {17,23}, {3,12}, {11,22}, {10,28}, {14,24}, {1,22}, {15,27}, {21,27}, {12,16}, {4,21}, {10,21}, {2,13}, {2,20}, {6,18}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {7,17}, {21,25}, {5,24}, {17,27}, {13,23}, {12,25}, {8,22}, {18,24}, {20,28}, {15,20}, {5,14}, {18,26}, {1,28}, {4,13}, {3,11}, {7,14}, {3,27}, {4,28}, {6,23}, {3,10}, {3,26}, {5,28}, {8,26}, {16,22}, {6,15}, {12,27}, {5,12}, {8,21}, {4,9}, {1,24}, {12,23}, {22,23}, {13,24}, {11,24}, {6,27}, {17,25}, {12,19}, {3,23}, {8,23}, {18,19}, {12,14}, {20,25}, {17,19}, {1,25}, {6,19}, {6,9}, {13,15}, {1,15}, {12,15}, {18,23}, {6,14}, {2,11}, {15,21}, {14,25}, {16,21}, {22,24}, {3,16}, {13,26}, {22,26}, {7,23}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {15,22}, {5,8}, {9,17}, {10,18}, {8,24}, {6,25}, {7,9}, {20,24}, {13,14}, {6,10}, {5,10}, {4,18}, {15,28}, {5,9}, {11,19}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,10}, {25,26}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {17,22}, {5,21}, {9,15}, {13,17}, {6,13}, {13,20}, {7,19}, {4,17}, {9,16}, {16,28}, {9,23}, {7,21}, {14,27}, {12,18}, {19,27}, {11,18}, {14,26}, {10,16} }; // ET28.46 // Bipartite(12,16) Valencies [16,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10022049832815820800000 EdgePairs[28][46]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {1,13}, {12,22}, {8,28}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {8,15}, {4,23}, {8,27}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {12,20}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {12,13}, {12,16}, {5,23}, {4,21}, {3,20}, {10,21}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {5,24}, {12,28}, {12,25}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {9,13}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {6,26}, {12,19}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {1,15}, {6,28}, {12,15}, {6,14}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {5,13}, {8,20}, {3,28}, {12,24}, {7,27}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET28.47 // Bipartite(11,17) Valencies [17,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14197903929822412800000 EdgePairs[28][47]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {1,13}, {8,28}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {11,12}, {2,28}, {2,14}, {8,15}, {4,23}, {8,27}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {9,26}, {9,27}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {7,17}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {11,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,28}, {6,14}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,27}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET28.48 // Bipartite(4,24) Valencies [18,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6449725440000 EdgePairs[28][48]:={ {2,11}, {3,22}, {1,26}, {2,14}, {4,8}, {4,13}, {4,9}, {4,24}, {4,23}, {1,14}, {1,24}, {3,12}, {2,26}, {2,10}, {1,10}, {4,11}, {1,6}, {3,27}, {2,6}, {4,7}, {1,20}, {1,12}, {3,8}, {3,23}, {4,16}, {3,24}, {3,20}, {2,21}, {4,12}, {2,7}, {3,11}, {1,16}, {3,7}, {3,16}, {3,28}, {3,15}, {2,18}, {1,21}, {4,27}, {4,21}, {4,20}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {4,5}, {4,17}, {1,18}, {3,26}, {1,5}, {4,15}, {4,28}, {2,27}, {1,17}, {3,6}, {4,25}, {2,19}, {1,28}, {2,17}, {2,23}, {1,8}, {1,13}, {2,9}, {1,9}, {1,22}, {2,13}, {2,25}, {4,19}, {1,25}, {2,22}, {3,10} }; // ET28.49 // Bipartite(7,21) Valencies [18,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1410877440 EdgePairs[28][49]:={ {1,15}, {6,12}, {5,14}, {3,15}, {6,10}, {4,14}, {1,11}, {6,14}, {4,8}, {4,27}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {7,27}, {7,15}, {7,23}, {3,10}, {2,28}, {2,19}, {2,18}, {6,9}, {5,26}, {4,26}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {7,28}, {7,10}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {7,25}, {3,22}, {5,19}, {5,15}, {6,8}, {7,20}, {7,13}, {7,14}, {3,27}, {6,15}, {6,26}, {1,19}, {4,21}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {7,8}, {2,27}, {6,19}, {1,23}, {2,21}, {5,8}, {7,18}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {7,16}, {3,21}, {7,9}, {1,20}, {1,27}, {5,11}, {7,22}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {7,21}, {5,12}, {2,25}, {3,17}, {4,9}, {6,24}, {5,18}, {6,27}, {7,17}, {4,23}, {1,8}, {5,16}, {4,13}, {1,18}, {5,25}, {4,19}, {1,24}, {6,28} }; // ET28.50 // Bipartite(10,18) Valencies [18,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23232933703345766400000 EdgePairs[28][50]:={ {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {6,17}, {2,23}, {1,13}, {8,28}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {2,14}, {8,15}, {6,11}, {4,23}, {8,27}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,28}, {6,14}, {2,11}, {10,11}, {7,28}, {3,16}, {7,23}, {2,21}, {9,18}, {10,17}, {3,24}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,27}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {7,18}, {10,16}, {5,16} }; // ET28.51 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 120960 EdgePairs[28][51]:={ {11,17}, {1,11}, {2,24}, {1,20}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {14,19}, {15,24}, {16,26}, {4,26}, {3,22}, {3,8}, {1,10}, {11,25}, {16,27}, {6,17}, {2,23}, {8,9}, {12,22}, {3,9}, {3,6}, {20,27}, {3,13}, {24,27}, {1,27}, {23,28}, {3,25}, {10,23}, {19,24}, {2,15}, {4,19}, {16,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {20,21}, {17,24}, {16,18}, {16,25}, {2,9}, {11,14}, {18,21}, {8,10}, {8,25}, {2,28}, {8,15}, {6,11}, {16,23}, {14,28}, {4,23}, {8,27}, {3,5}, {10,15}, {19,21}, {15,25}, {3,18}, {11,28}, {3,17}, {19,28}, {6,21}, {2,25}, {7,12}, {14,23}, {4,10}, {1,7}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,20}, {14,21}, {19,26}, {12,17}, {9,26}, {9,27}, {5,11}, {2,5}, {9,19}, {8,14}, {19,22}, {11,13}, {15,26}, {17,23}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {14,24}, {22,27}, {24,25}, {1,22}, {21,27}, {6,12}, {12,13}, {23,26}, {5,23}, {4,21}, {21,26}, {3,20}, {13,22}, {2,13}, {10,21}, {2,20}, {13,18}, {24,26}, {8,17}, {2,16}, {11,21}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {17,27}, {13,23}, {12,25}, {23,25}, {8,13}, {8,22}, {18,24}, {13,28}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {18,27}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {6,23}, {3,10}, {3,26}, {5,28}, {8,26}, {12,26}, {16,22}, {9,22}, {6,15}, {2,17}, {4,6}, {17,28}, {12,27}, {5,12}, {22,25}, {14,17}, {8,21}, {4,9}, {1,24}, {12,23}, {6,27}, {11,24}, {13,24}, {12,19}, {20,23}, {8,23}, {18,25}, {12,14}, {20,25}, {3,21}, {2,7}, {6,19}, {22,28}, {6,9}, {1,15}, {6,28}, {12,15}, {18,23}, {2,11}, {13,27}, {4,5}, {14,20}, {15,21}, {14,25}, {16,17}, {16,21}, {7,28}, {3,16}, {11,26}, {13,26}, {15,18}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {20,26}, {3,24}, {18,28}, {10,27}, {1,26}, {1,16}, {4,14}, {15,22}, {6,25}, {7,9}, {5,27}, {5,10}, {19,25}, {5,26}, {8,18}, {4,18}, {15,28}, {4,25}, {10,19}, {4,11}, {1,8}, {3,28}, {7,10}, {7,24}, {2,12}, {1,14}, {9,24}, {2,8}, {1,6}, {10,20}, {17,26}, {5,15}, {5,19}, {6,20}, {17,22}, {9,15}, {6,13}, {13,20}, {21,28}, {4,17}, {9,16}, {9,23}, {7,21}, {14,27}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET28.52 // Bipartite(9,19) Valencies [19,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 44142574036356956160000 EdgePairs[28][52]:={ {1,11}, {2,24}, {1,20}, {5,17}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,28}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,10}, {8,25}, {2,28}, {2,14}, {8,15}, {6,11}, {4,23}, {8,27}, {9,11}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {2,10}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {6,23}, {3,10}, {3,26}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {9,18}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,27}, {7,10}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {7,18}, {5,16} }; // ET28.53 // Bipartite(8,20) Valencies [20,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 98094608969682124800000 EdgePairs[28][53]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {8,10}, {8,25}, {2,28}, {2,14}, {8,15}, {6,11}, {4,23}, {8,27}, {6,22}, {3,18}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {5,11}, {2,10}, {8,14}, {5,25}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {8,17}, {2,16}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {6,23}, {3,10}, {3,26}, {5,28}, {8,26}, {6,15}, {2,17}, {5,12}, {8,21}, {3,19}, {4,9}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,24}, {1,26}, {2,22}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,27}, {7,10}, {7,24}, {2,12}, {1,14}, {5,15}, {5,19}, {6,20}, {5,21}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {7,18}, {5,16} }; // ET28.54 // Bipartite(7,21) Valencies [21,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 257498348545415577600000 EdgePairs[28][54]:={ {1,15}, {7,19}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {4,27}, {6,17}, {2,11}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {7,27}, {7,15}, {7,23}, {5,13}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {4,12}, {3,18}, {7,28}, {7,10}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {7,26}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {7,25}, {3,22}, {5,19}, {5,15}, {6,8}, {7,20}, {3,23}, {7,13}, {7,14}, {3,27}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {7,8}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {5,8}, {7,18}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {7,16}, {3,21}, {1,14}, {7,9}, {2,8}, {1,20}, {1,27}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {7,21}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {6,24}, {5,18}, {6,27}, {7,17}, {4,23}, {1,8}, {5,16}, {7,12}, {4,13}, {1,21}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24}, {6,28} }; // ET28.55 // Non-bipartite Valency 21 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 15485790781440000 EdgePairs[28][55]:={ {13,21}, {19,28}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {6,15}, {11,15}, {8,21}, {3,19}, {15,27}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {6,9}, {21,22}, {13,27}, {6,14}, {11,17}, {1,12}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {12,26}, {3,10}, {7,27}, {2,10}, {19,22}, {3,9}, {10,26}, {2,17}, {10,20}, {17,26}, {1,24}, {13,24}, {2,15}, {12,23}, {13,20}, {16,25}, {6,18}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {8,18}, {4,18}, {12,24}, {12,27}, {3,13}, {11,22}, {5,12}, {6,27}, {2,8}, {4,9}, {6,12}, {19,23}, {4,21}, {13,17}, {20,25}, {7,19}, {2,13}, {13,18}, {19,27}, {12,15}, {8,15}, {14,28}, {11,21}, {8,17}, {10,16}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {5,14}, {12,17}, {2,23}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {17,28}, {6,8}, {2,27}, {2,12}, {1,22}, {11,24}, {5,19}, {7,8}, {18,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {9,25}, {10,22}, {7,23}, {6,22}, {10,25}, {15,24}, {16,26}, {12,25}, {1,16}, {3,22}, {4,14}, {5,8}, {4,15}, {6,23}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {2,28}, {9,23}, {7,21}, {14,16}, {8,27}, {2,11}, {14,26}, {10,15}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {18,24}, {14,19}, {18,27}, {20,28}, {16,27}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {4,25}, {3,28}, {5,9}, {11,19}, {1,8}, {4,12}, {20,27}, {7,10}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {14,18}, {5,21}, {21,27}, {9,15}, {17,24}, {20,23}, {6,28}, {16,23}, {18,23}, {13,15}, {14,25}, {14,20}, {1,15}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {5,17}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {3,12}, {7,13}, {14,17}, {21,24}, {12,19}, {21,26}, {8,25}, {2,9}, {12,21}, {2,14}, {11,26}, {15,25}, {21,23} }; // ET28.56 // Bipartite(6,22) Valencies [22,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 809280523999877529600000 EdgePairs[28][56]:={ {1,15}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {2,22}, {6,14}, {4,8}, {4,27}, {3,7}, {6,17}, {2,11}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {6,7}, {5,7}, {5,13}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {5,21}, {3,19}, {4,12}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {6,8}, {3,23}, {3,27}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {6,24}, {2,7}, {5,18}, {6,27}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24}, {6,28} }; // ET28.57 // Bipartite(5,23) Valencies [23,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3102242008666197196800000 EdgePairs[28][57]:={ {1,15}, {5,14}, {3,15}, {4,14}, {1,11}, {2,22}, {4,8}, {4,27}, {3,7}, {2,11}, {2,20}, {1,25}, {4,16}, {5,24}, {1,9}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {3,19}, {4,12}, {5,6}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {5,19}, {5,15}, {3,23}, {3,27}, {1,19}, {4,21}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {2,7}, {5,18}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET28.58 // Bipartite(4,24) Valencies [24,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14890761641597746544640000 EdgePairs[28][58]:={ {1,15}, {3,15}, {4,14}, {1,11}, {2,22}, {4,8}, {3,7}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {1,9}, {4,5}, {1,5}, {4,6}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {4,26}, {3,19}, {4,12}, {3,18}, {2,14}, {3,11}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {3,27}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {3,5}, {1,26}, {2,24}, {4,11}, {2,27}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {1,28}, {3,17}, {4,9}, {2,7}, {4,23}, {1,8}, {4,13}, {1,21}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET28.59 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 23115815976960 EdgePairs[28][59]:={ {13,21}, {19,28}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {6,15}, {11,15}, {8,21}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {2,7}, {6,9}, {13,27}, {6,14}, {16,21}, {24,28}, {19,21}, {11,17}, {1,12}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {2,6}, {8,13}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {12,26}, {3,10}, {2,5}, {7,27}, {8,9}, {2,10}, {19,22}, {3,9}, {10,26}, {2,17}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {15,19}, {6,18}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {4,18}, {12,24}, {12,27}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,8}, {4,9}, {6,12}, {19,23}, {4,21}, {13,17}, {20,25}, {7,19}, {16,18}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {14,28}, {8,15}, {11,21}, {8,17}, {10,16}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {5,14}, {12,17}, {2,23}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {17,28}, {11,13}, {2,27}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {9,25}, {4,5}, {10,22}, {7,23}, {6,22}, {10,25}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {23,27}, {4,15}, {6,23}, {15,17}, {1,5}, {24,27}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {2,28}, {9,23}, {7,21}, {8,27}, {2,11}, {14,26}, {10,15}, {3,5}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {16,20}, {8,11}, {18,24}, {14,19}, {18,27}, {20,28}, {16,27}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {4,25}, {3,28}, {5,9}, {11,19}, {1,8}, {4,12}, {20,27}, {8,14}, {7,10}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {5,21}, {21,27}, {9,15}, {17,24}, {20,23}, {17,21}, {6,28}, {16,23}, {18,23}, {1,15}, {14,25}, {14,20}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {15,18}, {10,27}, {5,17}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {16,19}, {10,14}, {12,19}, {23,26}, {21,26}, {20,21}, {22,28}, {8,25}, {2,9}, {12,21}, {2,14}, {11,26}, {15,25} }; // ET28.60 // Bipartite(3,25) Valencies [25,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 93067260259985915904000000 EdgePairs[28][60]:={ {2,11}, {3,22}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {3,12}, {2,24}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {3,27}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,23}, {3,9}, {3,24}, {2,12}, {2,4}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,28}, {3,15}, {3,17}, {2,18}, {1,21}, {3,25}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {3,26}, {1,5}, {1,27}, {1,17}, {2,27}, {3,6}, {2,28}, {2,19}, {1,28}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22}, {3,10} }; // ET28.61 // Bipartite(2,26) Valencies [26,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 806582922253211271168000000 EdgePairs[28][61]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {2,24}, {2,10}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {2,12}, {2,4}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {1,16}, {2,20}, {2,18}, {1,21}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {2,19}, {1,28}, {2,17}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET28.62 // Non-bipartite Valency 26 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1428329123020800 EdgePairs[28][62]:={ {13,21}, {19,28}, {5,7}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {1,3}, {6,15}, {11,15}, {8,21}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {2,7}, {6,9}, {13,27}, {6,14}, {16,21}, {24,28}, {10,11}, {19,21}, {11,17}, {1,12}, {9,11}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {2,6}, {8,13}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {12,26}, {3,10}, {2,5}, {7,27}, {8,9}, {2,10}, {19,22}, {3,9}, {10,26}, {2,17}, {17,20}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {6,18}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {12,27}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,8}, {4,9}, {6,12}, {19,23}, {4,21}, {13,17}, {18,19}, {20,25}, {7,19}, {16,18}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {14,28}, {11,21}, {8,17}, {10,16}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {12,17}, {2,23}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {17,28}, {6,8}, {11,13}, {2,27}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {17,19}, {9,12}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {9,25}, {4,5}, {10,22}, {7,23}, {6,22}, {10,25}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {4,15}, {6,23}, {15,17}, {1,5}, {2,3}, {26,27}, {24,27}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {2,28}, {9,23}, {7,21}, {14,16}, {8,27}, {2,11}, {14,26}, {10,15}, {3,5}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {16,20}, {8,11}, {18,24}, {14,19}, {18,27}, {20,28}, {16,27}, {1,7}, {26,28}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {4,25}, {3,28}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {20,27}, {8,14}, {7,10}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {22,23}, {5,21}, {21,27}, {9,15}, {17,24}, {20,23}, {2,4}, {17,21}, {6,28}, {16,23}, {18,23}, {13,15}, {1,15}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {25,27}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {25,28}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {20,21}, {22,28}, {8,25}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {21,23} }; // ET28.63 // Bipartite(1,27) Valencies [27,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 10888869450418352160768000000 EdgePairs[28][63]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,12}, {1,2}, {1,3}, {1,17}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,28}, {1,6}, {1,14}, {1,26}, {1,18}, {1,27}, {1,21}, {1,19}, {1,20}, {1,8}, {1,24}, {1,9}, {1,23}, {1,25} }; // ET28.64 // Non-bipartite Valency 27 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 304888344611713860501504000000 EdgePairs[28][64]:={ {13,21}, {19,28}, {5,7}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {9,10}, {17,18}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {1,3}, {6,15}, {11,15}, {8,21}, {5,6}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {2,7}, {6,9}, {21,22}, {13,27}, {6,14}, {16,21}, {24,28}, {19,20}, {10,11}, {19,21}, {11,17}, {1,12}, {9,11}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {2,6}, {8,13}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {27,28}, {7,11}, {12,20}, {1,13}, {12,26}, {3,10}, {2,5}, {7,27}, {8,9}, {2,10}, {19,22}, {3,9}, {10,26}, {2,17}, {17,20}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {6,18}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {12,27}, {25,26}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,8}, {4,9}, {6,12}, {19,23}, {4,21}, {13,17}, {18,19}, {20,25}, {7,19}, {16,18}, {1,2}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {14,28}, {11,21}, {8,17}, {10,16}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {12,17}, {2,23}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {17,28}, {6,8}, {11,13}, {2,27}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {7,8}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {17,19}, {9,12}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {9,25}, {4,5}, {10,22}, {7,23}, {6,22}, {10,25}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {4,15}, {6,23}, {15,17}, {13,14}, {1,5}, {2,3}, {26,27}, {24,27}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {2,28}, {9,23}, {7,21}, {14,16}, {8,27}, {2,11}, {14,26}, {10,15}, {3,5}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {16,20}, {8,11}, {18,24}, {14,19}, {18,27}, {20,28}, {16,27}, {1,7}, {26,28}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {4,25}, {3,28}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {20,27}, {8,14}, {7,10}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {22,23}, {5,21}, {21,27}, {9,15}, {17,24}, {20,23}, {2,4}, {17,21}, {6,28}, {16,23}, {18,23}, {13,15}, {1,15}, {14,20}, {14,25}, {15,21}, {11,12}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {3,4}, {15,16}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {25,27}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {25,28}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {20,21}, {22,28}, {8,25}, {23,24}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {21,23} }; // Total number of connected ET graphs of order 28 is 64 // ******************************************************************************************** // Order 29 // ET29.1 // Non-bipartite Valency 2 // Diameter 14 Girth 29 // Twin-free VT AT // Automorphism group of order 58 EdgePairs[29][1]:={ {11,21}, {23,25}, {28,29}, {9,24}, {3,10}, {15,19}, {13,27}, {16,19}, {6,12}, {4,21}, {14,15}, {4,27}, {1,28}, {2,22}, {8,20}, {17,26}, {1,14}, {6,22}, {5,29}, {2,5}, {8,16}, {13,18}, {9,11}, {3,12}, {10,23}, {20,26}, {7,18}, {17,24}, {7,25} }; // ET29.2 // Non-bipartite Valency 4 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 116 EdgePairs[29][2]:={ {28,29}, {13,19}, {1,14}, {8,20}, {3,12}, {5,24}, {23,25}, {5,29}, {21,22}, {5,27}, {8,16}, {11,28}, {7,8}, {6,12}, {15,27}, {15,23}, {9,11}, {3,24}, {2,4}, {11,21}, {13,18}, {18,28}, {9,29}, {1,7}, {9,24}, {3,16}, {15,19}, {10,23}, {16,18}, {22,26}, {7,18}, {6,20}, {4,27}, {9,12}, {1,21}, {4,21}, {8,12}, {2,5}, {7,25}, {16,19}, {20,25}, {10,19}, {6,22}, {1,28}, {10,17}, {20,26}, {2,17}, {13,29}, {6,11}, {13,27}, {23,26}, {4,14}, {14,15}, {17,26}, {14,25}, {2,22}, {17,24}, {3,10} }; // ET29.3 // Non-bipartite Valency 14 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 406 EdgePairs[29][3]:={ {21,23}, {2,24}, {1,20}, {11,20}, {4,27}, {12,29}, {4,24}, {15,24}, {4,26}, {3,8}, {23,27}, {4,16}, {1,10}, {11,25}, {2,23}, {8,9}, {8,28}, {3,13}, {24,27}, {23,28}, {10,23}, {19,24}, {10,26}, {2,15}, {16,19}, {7,22}, {2,19}, {25,29}, {5,20}, {20,21}, {17,24}, {17,21}, {18,21}, {8,25}, {6,7}, {2,14}, {4,23}, {8,27}, {3,5}, {9,11}, {16,29}, {10,22}, {19,21}, {6,22}, {15,25}, {3,18}, {6,29}, {3,17}, {3,7}, {8,16}, {19,28}, {15,29}, {2,25}, {7,12}, {4,10}, {1,18}, {7,11}, {3,14}, {19,26}, {16,24}, {9,27}, {12,20}, {2,5}, {2,10}, {5,29}, {26,27}, {9,19}, {27,29}, {26,29}, {8,14}, {19,29}, {11,15}, {11,13}, {15,26}, {3,12}, {11,22}, {9,14}, {7,25}, {24,25}, {1,22}, {6,12}, {12,13}, {5,23}, {10,29}, {4,21}, {21,26}, {1,2}, {13,22}, {15,19}, {6,18}, {13,18}, {28,29}, {11,21}, {7,16}, {1,12}, {14,15}, {11,29}, {7,17}, {8,11}, {21,25}, {17,27}, {5,7}, {13,23}, {12,28}, {12,25}, {23,25}, {18,24}, {20,28}, {15,20}, {13,28}, {5,14}, {9,20}, {18,26}, {1,28}, {7,14}, {3,27}, {4,7}, {15,17}, {10,13}, {3,29}, {3,10}, {2,3}, {6,23}, {16,22}, {17,28}, {9,13}, {5,12}, {22,25}, {14,17}, {8,21}, {1,24}, {22,23}, {14,22}, {13,24}, {6,27}, {6,26}, {20,23}, {18,19}, {3,21}, {17,19}, {6,19}, {22,28}, {6,9}, {13,15}, {12,15}, {6,28}, {6,14}, {13,27}, {10,11}, {4,5}, {14,20}, {16,17}, {11,26}, {11,16}, {2,21}, {9,18}, {20,26}, {10,27}, {1,26}, {2,22}, {1,16}, {15,22}, {10,18}, {8,24}, {6,25}, {7,9}, {5,10}, {5,9}, {4,25}, {1,4}, {1,8}, {4,12}, {4,20}, {12,24}, {8,20}, {3,28}, {25,27}, {9,24}, {1,14}, {2,8}, {1,6}, {17,26}, {5,15}, {5,19}, {17,22}, {13,17}, {13,20}, {2,18}, {19,23}, {21,28}, {4,17}, {9,16}, {16,28}, {9,23}, {14,27}, {7,21}, {8,29}, {12,18}, {11,18}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET29.4 // Bipartite(14,15) Valencies [15,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 114000816848279961600000 EdgePairs[29][4]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {7,15}, {4,24}, {14,19}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {12,22}, {8,28}, {4,29}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {8,15}, {14,28}, {4,23}, {8,27}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {14,23}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {5,25}, {11,15}, {11,22}, {7,25}, {10,28}, {14,24}, {1,22}, {12,16}, {5,23}, {10,29}, {4,21}, {3,20}, {13,22}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {14,15}, {1,23}, {11,23}, {6,24}, {11,29}, {7,17}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {9,20}, {4,15}, {1,28}, {3,27}, {4,28}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {12,27}, {14,17}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {12,15}, {13,27}, {14,20}, {14,25}, {7,28}, {3,16}, {11,26}, {13,26}, {11,16}, {7,23}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {9,24}, {10,20}, {5,15}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {8,29}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET29.5 // Bipartite(13,16) Valencies [16,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 130286647826605670400000 EdgePairs[29][5]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {12,22}, {8,28}, {4,29}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {8,15}, {4,23}, {8,27}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {5,25}, {11,15}, {11,22}, {9,14}, {7,25}, {10,28}, {1,22}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {13,22}, {10,21}, {2,20}, {6,18}, {13,18}, {1,29}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {7,17}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {5,14}, {9,20}, {4,15}, {1,28}, {7,14}, {3,27}, {4,28}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {13,27}, {7,28}, {3,16}, {11,26}, {13,26}, {7,23}, {11,16}, {13,19}, {2,21}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {13,14}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {8,29}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET29.6 // Bipartite(12,17) Valencies [17,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 170374847157868953600000 EdgePairs[29][6]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {1,13}, {12,22}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {8,15}, {4,23}, {8,27}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {12,13}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {7,17}, {5,24}, {12,28}, {12,25}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {9,13}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {6,26}, {12,19}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {5,13}, {8,20}, {3,28}, {12,24}, {7,27}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {8,29}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET29.7 // Bipartite(11,18) Valencies [18,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 255562270736803430400000 EdgePairs[29][7]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {11,25}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {11,12}, {2,28}, {2,14}, {8,15}, {4,23}, {8,27}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,26}, {9,27}, {5,29}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {5,23}, {4,21}, {10,29}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {7,17}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {11,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,27}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET29.8 // Bipartite(10,19) Valencies [19,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 441425740363569561600000 EdgePairs[29][8]:={ {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {2,14}, {8,15}, {6,11}, {4,23}, {8,27}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {5,29}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {5,23}, {4,21}, {10,29}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {10,11}, {7,28}, {3,16}, {7,23}, {2,21}, {9,18}, {10,17}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,27}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {7,18}, {10,16}, {5,16} }; // ET29.9 // Bipartite(9,20) Valencies [20,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 882851480727139123200000 EdgePairs[29][9]:={ {1,11}, {2,24}, {1,20}, {5,17}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,10}, {8,25}, {2,28}, {2,14}, {8,15}, {6,11}, {4,23}, {8,27}, {9,11}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,10}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {5,19}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {7,18}, {5,16} }; // ET29.10 // Bipartite(8,21) Valencies [21,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2059986788363324620800000 EdgePairs[29][10]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {8,10}, {8,25}, {2,28}, {2,14}, {6,11}, {8,15}, {4,23}, {8,27}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {5,11}, {2,10}, {5,29}, {8,14}, {5,25}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {8,17}, {2,16}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {6,15}, {2,17}, {5,12}, {8,21}, {3,19}, {4,9}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,10}, {7,24}, {2,12}, {1,14}, {5,15}, {5,19}, {6,20}, {5,21}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {8,29}, {7,18}, {5,16} }; // ET29.11 // Bipartite(7,22) Valencies [22,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5664963667999142707200000 EdgePairs[29][11]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {4,27}, {7,15}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {7,8}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {2,28}, {2,14}, {6,11}, {4,23}, {6,22}, {3,18}, {6,29}, {3,17}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {1,18}, {7,11}, {7,20}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {7,16}, {1,12}, {7,26}, {5,18}, {1,23}, {6,24}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {6,27}, {6,26}, {3,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {5,19}, {6,20}, {5,21}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {7,18}, {5,16} }; // ET29.12 // Bipartite(6,23) Valencies [23,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 18613452051997183180800000 EdgePairs[29][12]:={ {1,15}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {3,29}, {2,22}, {6,14}, {4,8}, {4,27}, {3,7}, {6,17}, {2,11}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {6,7}, {5,7}, {5,13}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {4,29}, {3,9}, {3,22}, {5,19}, {5,15}, {6,8}, {3,23}, {5,29}, {3,27}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {6,29}, {2,24}, {4,11}, {5,22}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {6,24}, {2,7}, {5,18}, {6,27}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24}, {6,28} }; // ET29.13 // Bipartite(5,24) Valencies [24,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 74453808207988732723200000 EdgePairs[29][13]:={ {1,15}, {5,14}, {3,15}, {4,14}, {1,11}, {3,29}, {2,22}, {4,8}, {4,27}, {3,7}, {2,11}, {2,20}, {1,25}, {4,16}, {5,24}, {1,9}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {2,29}, {3,19}, {1,29}, {5,6}, {4,12}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {4,29}, {3,9}, {3,22}, {5,19}, {5,15}, {3,23}, {5,29}, {3,27}, {1,19}, {4,21}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {2,7}, {5,18}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET29.14 // Bipartite(4,25) Valencies [25,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 372269041039943663616000000 EdgePairs[29][14]:={ {1,15}, {3,15}, {4,14}, {1,11}, {3,29}, {2,22}, {4,8}, {3,7}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {1,9}, {4,5}, {1,5}, {4,6}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {2,14}, {3,11}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {3,27}, {1,19}, {4,21}, {4,17}, {4,15}, {2,9}, {4,25}, {3,5}, {1,26}, {2,24}, {4,11}, {2,27}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {1,28}, {3,17}, {4,9}, {2,7}, {4,23}, {1,8}, {4,13}, {1,21}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET29.15 // Bipartite(3,26) Valencies [26,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2419748766759633813504000000 EdgePairs[29][15]:={ {2,11}, {3,22}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {3,12}, {1,29}, {2,29}, {2,24}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {3,27}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,23}, {3,9}, {3,24}, {2,12}, {2,4}, {3,29}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,28}, {3,15}, {3,17}, {2,18}, {1,21}, {3,25}, {3,19}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {3,26}, {1,5}, {1,27}, {1,17}, {2,27}, {3,6}, {2,28}, {2,19}, {1,28}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22}, {3,10} }; // ET29.16 // Bipartite(2,27) Valencies [27,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 21777738900836704321536000000 EdgePairs[29][16]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {1,29}, {2,29}, {2,24}, {2,10}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {2,12}, {2,4}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {1,16}, {2,20}, {2,18}, {1,21}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {2,19}, {1,28}, {2,17}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET29.17 // Bipartite(1,28) Valencies [28,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 304888344611713860501504000000 EdgePairs[29][17]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,12}, {1,2}, {1,3}, {1,17}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,28}, {1,6}, {1,14}, {1,26}, {1,18}, {1,27}, {1,21}, {1,19}, {1,29}, {1,20}, {1,8}, {1,24}, {1,9}, {1,23}, {1,25} }; // ET29.18 // Non-bipartite Valency 28 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 8841761993739701954543616000000 EdgePairs[29][18]:={ {13,21}, {19,28}, {5,7}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {9,10}, {17,18}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {1,3}, {6,15}, {11,15}, {8,21}, {5,6}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {2,7}, {6,9}, {21,22}, {13,27}, {14,29}, {6,14}, {16,21}, {24,28}, {19,20}, {10,11}, {19,21}, {11,29}, {11,17}, {1,12}, {9,11}, {11,27}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {2,6}, {8,13}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {27,28}, {7,11}, {12,20}, {1,13}, {12,26}, {3,10}, {2,5}, {7,27}, {8,9}, {2,10}, {19,22}, {3,9}, {26,29}, {10,26}, {2,17}, {17,20}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {6,18}, {1,29}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,16}, {1,26}, {13,19}, {3,17}, {7,15}, {8,22}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {12,27}, {25,26}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,8}, {4,9}, {6,12}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {18,19}, {20,25}, {7,19}, {16,18}, {1,2}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {20,22}, {22,29}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {17,28}, {6,8}, {11,13}, {2,27}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {7,8}, {10,29}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {17,19}, {9,12}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {13,29}, {9,25}, {4,5}, {10,22}, {7,23}, {6,22}, {10,25}, {12,29}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {4,15}, {6,23}, {15,17}, {13,14}, {4,29}, {1,5}, {2,3}, {24,29}, {26,27}, {19,29}, {24,27}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {28,29}, {2,11}, {14,26}, {10,15}, {3,5}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {8,11}, {18,24}, {14,19}, {18,27}, {20,28}, {16,27}, {1,7}, {26,28}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {5,29}, {4,25}, {3,28}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {20,27}, {8,14}, {7,10}, {27,29}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {22,23}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {20,23}, {2,4}, {17,21}, {6,28}, {16,23}, {18,23}, {1,15}, {13,15}, {14,20}, {14,25}, {15,21}, {11,12}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {3,4}, {15,16}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {25,27}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {25,28}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {20,21}, {22,28}, {8,25}, {23,24}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {21,23} }; // Total number of connected ET graphs of order 29 is 18 // ******************************************************************************************** // Order 30 // ET30.1 // Bipartite(15,15) Valencies [2,2] // Diameter 15 Girth 30 // Twin-free VT AT // Automorphism group of order 60 EdgePairs[30][1]:={ {13,19}, {4,20}, {7,26}, {6,28}, {7,30}, {4,24}, {12,25}, {8,28}, {9,27}, {2,17}, {8,29}, {13,23}, {3,18}, {10,29}, {5,22}, {1,16}, {10,25}, {15,19}, {15,17}, {6,24}, {2,20}, {3,22}, {12,21}, {5,26}, {11,27}, {1,18}, {9,30}, {11,23}, {14,21}, {14,16} }; // ET30.2 // Bipartite(15,15) Valencies [3,3] // Diameter 4 Girth 8 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[30][2]:={ {3,22}, {11,30}, {1,26}, {4,24}, {8,28}, {9,23}, {10,27}, {7,16}, {5,29}, {2,24}, {5,27}, {8,23}, {12,16}, {8,21}, {13,25}, {10,30}, {15,27}, {1,20}, {4,16}, {3,29}, {3,20}, {13,18}, {15,21}, {9,29}, {9,24}, {10,26}, {2,18}, {11,22}, {5,17}, {13,20}, {7,22}, {7,21}, {12,25}, {6,19}, {2,19}, {14,23}, {1,28}, {6,17}, {4,26}, {6,28}, {11,19}, {12,17}, {14,25}, {15,18}, {14,30} }; // ET30.3 // Bipartite(10,20) Valencies [4,2] // Diameter 6 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 240 EdgePairs[30][3]:={ {8,20}, {6,13}, {3,29}, {6,28}, {6,21}, {7,30}, {4,30}, {4,17}, {1,23}, {9,21}, {9,27}, {7,16}, {3,14}, {4,15}, {3,15}, {8,11}, {10,14}, {8,16}, {5,22}, {10,27}, {2,22}, {4,19}, {1,17}, {5,25}, {5,26}, {1,11}, {2,23}, {10,24}, {3,28}, {1,18}, {8,26}, {7,13}, {2,29}, {6,25}, {7,24}, {9,20}, {2,12}, {5,19}, {10,18}, {9,12} }; // ET30.4 // Bipartite(10,20) Valencies [4,2] // Diameter 5 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 320 EdgePairs[30][4]:={ {1,20}, {6,28}, {7,23}, {8,30}, {9,16}, {5,14}, {4,30}, {5,24}, {6,29}, {5,18}, {9,21}, {9,27}, {10,16}, {10,12}, {7,17}, {3,15}, {6,23}, {2,25}, {3,21}, {10,29}, {4,18}, {2,28}, {1,12}, {1,17}, {8,27}, {10,22}, {6,24}, {2,20}, {4,22}, {1,11}, {5,11}, {3,26}, {8,19}, {9,14}, {7,13}, {8,25}, {2,15}, {4,26}, {3,13}, {7,19} }; // ET30.5 // Bipartite(10,20) Valencies [4,2] // Diameter 10 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 20480 EdgePairs[30][5]:={ {7,14}, {6,28}, {4,24}, {9,19}, {6,29}, {5,27}, {4,23}, {3,18}, {7,15}, {1,22}, {8,16}, {6,18}, {8,15}, {2,22}, {4,14}, {3,27}, {10,20}, {10,30}, {3,17}, {1,12}, {2,13}, {7,25}, {9,29}, {5,26}, {1,11}, {2,23}, {10,21}, {10,11}, {5,16}, {3,28}, {5,17}, {8,26}, {9,30}, {8,25}, {6,19}, {1,21}, {7,24}, {9,20}, {4,13}, {2,12} }; // ET30.6 // Bipartite(15,15) Valencies [4,4] // Diameter 4 Girth 6 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[30][6]:={ {11,30}, {12,27}, {12,20}, {11,16}, {8,19}, {4,24}, {9,19}, {8,20}, {2,26}, {5,24}, {2,29}, {5,29}, {15,20}, {8,21}, {3,21}, {3,27}, {11,29}, {13,26}, {6,30}, {15,23}, {3,23}, {4,16}, {13,18}, {5,21}, {4,18}, {1,16}, {15,30}, {9,27}, {4,20}, {5,17}, {6,27}, {3,18}, {7,22}, {12,29}, {15,28}, {1,17}, {14,21}, {10,19}, {12,22}, {8,26}, {7,28}, {6,25}, {2,23}, {10,22}, {1,22}, {2,25}, {10,25}, {9,28}, {1,23}, {13,30}, {14,28}, {11,19}, {14,25}, {14,16}, {13,17}, {7,24}, {10,18}, {9,17}, {6,24}, {7,26} }; // ET30.7 // Bipartite(15,15) Valencies [4,4] // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 120 EdgePairs[30][7]:={ {11,30}, {1,26}, {12,20}, {11,16}, {8,19}, {4,24}, {10,27}, {1,24}, {2,29}, {5,29}, {5,27}, {8,23}, {15,20}, {13,25}, {13,26}, {6,30}, {3,23}, {11,23}, {4,16}, {13,18}, {2,21}, {8,27}, {9,24}, {1,16}, {15,19}, {5,19}, {3,25}, {4,21}, {3,19}, {5,17}, {3,18}, {15,17}, {1,18}, {15,25}, {7,22}, {10,29}, {7,21}, {7,20}, {6,18}, {4,22}, {9,22}, {2,28}, {14,21}, {8,26}, {12,22}, {2,17}, {9,30}, {11,26}, {13,27}, {12,28}, {10,25}, {9,28}, {14,28}, {10,20}, {12,17}, {14,16}, {6,23}, {6,24}, {14,30}, {7,29} }; // ET30.8 // Non-bipartite Valency 4 // Diameter 3 Girth 5 // Twin-free VT AT // Automorphism group of order 240 EdgePairs[30][8]:={ {3,22}, {11,16}, {8,28}, {18,22}, {19,24}, {2,26}, {1,29}, {2,30}, {5,29}, {14,26}, {7,23}, {8,9}, {2,10}, {20,23}, {15,20}, {11,20}, {13,25}, {11,27}, {6,30}, {8,24}, {22,28}, {5,23}, {7,27}, {21,27}, {4,18}, {7,10}, {1,16}, {6,20}, {3,17}, {5,19}, {9,27}, {4,21}, {11,22}, {5,17}, {8,13}, {2,15}, {17,21}, {12,19}, {3,26}, {15,25}, {10,29}, {13,23}, {16,19}, {6,18}, {4,25}, {3,13}, {17,30}, {18,29}, {14,24}, {10,28}, {9,30}, {1,9}, {12,28}, {4,14}, {12,15}, {7,14}, {1,25}, {6,24}, {12,21}, {16,26} }; // ET30.9 // Non-bipartite Valency 4 // Diameter 5 Girth 3 // Twin-free VT AT // Automorphism group of order 120 EdgePairs[30][9]:={ {28,29}, {2,14}, {4,24}, {8,19}, {24,28}, {7,11}, {19,29}, {14,18}, {9,25}, {9,21}, {6,14}, {3,5}, {8,25}, {2,6}, {3,23}, {11,23}, {6,15}, {4,6}, {5,16}, {20,30}, {15,21}, {4,12}, {18,28}, {20,27}, {2,7}, {3,11}, {22,29}, {19,28}, {3,16}, {2,20}, {21,30}, {10,26}, {22,26}, {23,27}, {15,30}, {10,14}, {17,27}, {21,25}, {8,12}, {12,24}, {1,5}, {4,15}, {16,22}, {7,20}, {9,13}, {12,25}, {27,30}, {1,8}, {1,13}, {5,13}, {1,19}, {10,22}, {18,24}, {11,26}, {16,29}, {13,17}, {9,17}, {10,18}, {17,23}, {7,26} }; // ET30.10 // Non-bipartite Valency 4 // Diameter 7 Girth 4 // Has twins VT AT // Automorphism group of order 983040 EdgePairs[30][10]:={ {2,11}, {3,22}, {4,13}, {9,19}, {10,27}, {5,24}, {1,29}, {2,30}, {1,30}, {2,29}, {9,20}, {20,22}, {14,26}, {11,24}, {3,21}, {13,25}, {8,25}, {20,21}, {13,26}, {15,27}, {19,22}, {5,15}, {1,12}, {11,23}, {2,12}, {6,15}, {5,16}, {6,16}, {5,23}, {16,27}, {7,18}, {19,21}, {9,27}, {4,21}, {12,23}, {18,30}, {3,14}, {12,24}, {7,25}, {15,28}, {4,22}, {10,19}, {8,26}, {16,28}, {3,13}, {17,30}, {18,29}, {8,18}, {7,17}, {10,28}, {4,14}, {9,28}, {10,20}, {17,29}, {1,11}, {14,25}, {8,17}, {6,23}, {6,24}, {7,26} }; // ET30.11 // Non-bipartite Valency 4 // Diameter 5 Girth 3 // Twin-free VT AT // Automorphism group of order 240 EdgePairs[30][11]:={ {28,29}, {12,20}, {8,19}, {24,29}, {13,16}, {7,12}, {8,11}, {1,10}, {3,5}, {2,6}, {13,26}, {11,23}, {6,7}, {5,8}, {22,28}, {4,6}, {16,27}, {21,27}, {20,27}, {2,7}, {22,29}, {19,28}, {3,16}, {15,19}, {21,30}, {1,21}, {10,14}, {3,18}, {12,24}, {4,17}, {1,5}, {15,28}, {4,15}, {7,20}, {9,13}, {16,20}, {12,25}, {9,22}, {27,30}, {5,18}, {3,13}, {6,17}, {17,30}, {18,29}, {1,8}, {2,9}, {23,30}, {18,24}, {11,26}, {10,21}, {9,26}, {23,26}, {4,14}, {10,25}, {11,19}, {14,15}, {14,25}, {24,25}, {2,22}, {17,23} }; // ET30.12 // Non-bipartite Valency 4 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 120 EdgePairs[30][12]:={ {5,12}, {11,30}, {2,14}, {12,27}, {4,24}, {10,15}, {19,23}, {24,28}, {2,26}, {2,29}, {7,9}, {8,23}, {8,16}, {12,16}, {3,27}, {8,25}, {20,21}, {19,25}, {1,4}, {4,7}, {6,30}, {1,12}, {6,15}, {3,20}, {4,30}, {5,9}, {20,29}, {8,27}, {18,28}, {9,29}, {21,24}, {10,23}, {22,26}, {14,22}, {5,19}, {18,25}, {10,11}, {13,20}, {15,17}, {16,21}, {3,26}, {7,22}, {1,17}, {18,21}, {2,28}, {14,23}, {7,17}, {1,19}, {13,27}, {15,26}, {9,28}, {25,30}, {11,18}, {11,14}, {5,22}, {16,29}, {13,17}, {6,13}, {6,24}, {3,10} }; // ET30.13 // Non-bipartite Valency 4 // Diameter 3 Girth 5 // Twin-free VT AT // Automorphism group of order 120 EdgePairs[30][13]:={ {3,22}, {8,19}, {2,26}, {3,12}, {7,23}, {6,26}, {4,11}, {1,6}, {20,21}, {6,10}, {15,29}, {19,22}, {8,24}, {9,11}, {11,23}, {10,12}, {3,29}, {4,30}, {5,9}, {16,27}, {18,28}, {16,30}, {20,27}, {1,7}, {5,25}, {9,24}, {19,28}, {10,23}, {2,20}, {16,18}, {3,25}, {4,21}, {11,22}, {21,28}, {8,13}, {17,27}, {2,5}, {15,17}, {12,24}, {15,28}, {7,20}, {13,23}, {13,15}, {26,29}, {5,18}, {6,17}, {22,27}, {14,24}, {1,19}, {14,29}, {4,26}, {2,8}, {13,30}, {7,14}, {25,30}, {1,25}, {14,16}, {9,17}, {10,18}, {12,21} }; // ET30.14 // Bipartite(10,20) Valencies [6,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[30][14]:={ {3,22}, {2,14}, {8,28}, {1,14}, {1,24}, {2,30}, {2,29}, {9,25}, {9,20}, {7,23}, {7,12}, {8,23}, {8,11}, {6,26}, {3,21}, {8,25}, {5,11}, {5,15}, {4,16}, {10,12}, {3,29}, {4,30}, {8,27}, {6,16}, {5,20}, {10,13}, {4,18}, {5,25}, {1,15}, {3,16}, {7,18}, {6,20}, {3,17}, {5,19}, {9,27}, {6,27}, {2,15}, {8,12}, {6,21}, {3,18}, {5,30}, {10,29}, {7,21}, {10,24}, {9,13}, {9,22}, {1,28}, {2,17}, {1,19}, {10,28}, {6,11}, {10,22}, {4,26}, {2,13}, {4,14}, {1,23}, {4,19}, {7,24}, {9,17}, {7,26} }; // ET30.15 // Bipartite(10,20) Valencies [6,3] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 122880 EdgePairs[30][15]:={ {5,12}, {1,26}, {1,14}, {7,11}, {9,23}, {1,24}, {2,26}, {5,29}, {8,11}, {8,21}, {6,12}, {3,27}, {6,30}, {5,15}, {8,24}, {3,23}, {3,20}, {4,30}, {8,27}, {10,13}, {4,18}, {2,16}, {5,25}, {10,16}, {1,15}, {9,24}, {1,16}, {10,23}, {10,26}, {7,18}, {6,20}, {3,17}, {5,19}, {2,18}, {9,12}, {4,20}, {7,15}, {3,30}, {6,21}, {7,25}, {10,29}, {7,21}, {9,13}, {4,28}, {2,27}, {9,22}, {2,28}, {10,19}, {6,22}, {2,17}, {7,28}, {9,14}, {3,13}, {8,14}, {6,11}, {4,19}, {5,22}, {1,25}, {8,17}, {4,29} }; // ET30.16 // Bipartite(12,18) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[30][16]:={ {3,22}, {4,24}, {8,19}, {10,15}, {4,23}, {1,14}, {10,27}, {1,24}, {12,18}, {2,30}, {1,30}, {9,25}, {5,29}, {11,17}, {7,23}, {9,21}, {5,27}, {6,26}, {12,16}, {11,20}, {11,29}, {9,15}, {1,20}, {3,24}, {7,30}, {2,21}, {5,16}, {8,27}, {7,27}, {10,16}, {3,16}, {3,28}, {2,20}, {10,23}, {7,18}, {5,19}, {2,18}, {3,25}, {4,21}, {4,20}, {7,15}, {8,13}, {10,14}, {3,14}, {12,29}, {7,21}, {8,22}, {11,13}, {4,25}, {6,22}, {2,19}, {2,17}, {5,18}, {1,13}, {8,14}, {11,26}, {9,26}, {4,26}, {12,28}, {6,28}, {10,25}, {9,28}, {1,23}, {12,15}, {8,30}, {11,19}, {12,17}, {6,29}, {5,22}, {6,13}, {9,17}, {6,24} }; // ET30.17 // Bipartite(12,18) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[30][17]:={ {2,14}, {4,13}, {12,27}, {8,28}, {4,23}, {1,14}, {1,29}, {2,24}, {9,21}, {8,16}, {11,24}, {8,21}, {11,20}, {6,30}, {5,15}, {3,23}, {3,29}, {11,21}, {7,30}, {4,30}, {5,16}, {6,16}, {5,20}, {7,27}, {5,25}, {9,24}, {3,16}, {3,28}, {10,26}, {5,19}, {3,25}, {4,20}, {7,15}, {5,17}, {6,27}, {2,15}, {6,21}, {12,19}, {12,24}, {1,18}, {3,26}, {7,22}, {10,29}, {12,29}, {4,15}, {1,27}, {11,13}, {12,25}, {6,19}, {9,22}, {2,28}, {10,17}, {12,22}, {1,13}, {8,18}, {8,14}, {7,17}, {9,30}, {10,22}, {9,26}, {4,26}, {2,13}, {2,25}, {9,28}, {1,23}, {7,14}, {11,19}, {10,20}, {11,18}, {8,17}, {6,23}, {10,18} }; // ET30.18 // Bipartite(12,18) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[30][18]:={ {4,13}, {12,27}, {9,19}, {1,14}, {9,23}, {11,15}, {8,20}, {2,26}, {9,25}, {2,24}, {9,16}, {8,16}, {6,26}, {11,24}, {12,16}, {8,21}, {3,21}, {8,15}, {3,27}, {10,30}, {12,30}, {6,30}, {3,24}, {3,29}, {11,21}, {4,30}, {5,16}, {5,23}, {7,27}, {2,20}, {7,18}, {5,19}, {4,27}, {3,25}, {2,18}, {4,20}, {3,19}, {5,17}, {7,15}, {8,13}, {7,25}, {10,29}, {12,26}, {4,15}, {1,17}, {4,22}, {9,22}, {1,28}, {8,26}, {10,17}, {12,22}, {5,14}, {2,17}, {2,23}, {1,13}, {5,13}, {10,28}, {1,22}, {6,28}, {9,28}, {7,14}, {11,19}, {10,20}, {11,18}, {11,14}, {6,29}, {1,25}, {6,23}, {10,18}, {6,24}, {12,21}, {7,29} }; // ET30.19 // Bipartite(12,18) Valencies [6,4] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 35831808 EdgePairs[30][19]:={ {3,22}, {11,30}, {1,26}, {2,14}, {4,23}, {1,14}, {8,20}, {2,26}, {5,24}, {12,18}, {5,29}, {11,17}, {9,21}, {9,16}, {11,24}, {8,21}, {3,21}, {8,15}, {3,27}, {7,13}, {11,29}, {12,30}, {9,15}, {6,30}, {1,20}, {11,23}, {4,16}, {2,21}, {8,27}, {5,23}, {10,16}, {3,16}, {3,28}, {2,20}, {10,23}, {3,15}, {9,27}, {5,17}, {2,15}, {12,13}, {12,19}, {12,24}, {4,17}, {7,25}, {5,30}, {10,29}, {7,20}, {4,28}, {2,27}, {7,19}, {6,18}, {4,22}, {12,25}, {6,19}, {9,22}, {8,26}, {10,17}, {5,18}, {6,25}, {1,13}, {8,14}, {1,19}, {10,28}, {10,22}, {9,28}, {7,14}, {11,18}, {1,25}, {6,13}, {6,24}, {7,26}, {4,29} }; // ET30.20 // Bipartite(12,18) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2359296 EdgePairs[30][20]:={ {11,30}, {4,13}, {12,27}, {1,14}, {8,20}, {1,24}, {12,18}, {2,30}, {2,29}, {9,25}, {9,20}, {11,17}, {2,24}, {7,23}, {9,16}, {6,14}, {11,28}, {8,21}, {8,15}, {3,27}, {7,13}, {8,24}, {4,16}, {8,29}, {3,29}, {3,20}, {11,21}, {2,21}, {5,21}, {9,29}, {10,13}, {10,16}, {1,15}, {3,16}, {2,20}, {10,26}, {5,19}, {5,28}, {3,25}, {9,27}, {7,15}, {5,17}, {12,23}, {6,27}, {2,15}, {12,14}, {3,18}, {12,19}, {4,17}, {5,30}, {7,22}, {6,18}, {4,22}, {4,25}, {6,19}, {9,18}, {10,17}, {5,26}, {1,13}, {10,22}, {11,26}, {4,26}, {12,28}, {1,22}, {6,28}, {10,25}, {1,23}, {7,14}, {8,30}, {11,19}, {6,23}, {7,24} }; // ET30.21 // Bipartite(12,18) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2239488 EdgePairs[30][21]:={ {2,14}, {4,24}, {10,15}, {9,23}, {10,27}, {8,20}, {2,26}, {1,29}, {11,25}, {5,27}, {12,16}, {3,21}, {11,20}, {3,27}, {7,13}, {5,15}, {8,24}, {4,16}, {6,15}, {7,30}, {4,30}, {5,16}, {5,21}, {9,29}, {4,18}, {2,16}, {9,24}, {2,20}, {3,15}, {10,26}, {7,18}, {5,28}, {3,25}, {3,19}, {10,14}, {12,23}, {6,27}, {6,21}, {7,25}, {12,29}, {4,28}, {11,13}, {1,17}, {7,19}, {4,22}, {2,28}, {8,26}, {9,18}, {12,22}, {3,13}, {6,17}, {1,13}, {8,18}, {8,14}, {1,19}, {9,30}, {11,26}, {10,21}, {12,28}, {1,23}, {8,30}, {11,19}, {10,20}, {12,17}, {11,14}, {6,29}, {1,25}, {5,22}, {6,23}, {2,22}, {7,24}, {9,17} }; // ET30.22 // Bipartite(12,18) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 221184 EdgePairs[30][22]:={ {1,26}, {12,20}, {12,27}, {8,19}, {10,15}, {11,16}, {8,28}, {9,23}, {11,15}, {12,18}, {1,30}, {2,29}, {11,17}, {11,25}, {2,24}, {9,21}, {5,27}, {8,16}, {6,14}, {6,26}, {11,24}, {3,21}, {3,27}, {7,13}, {8,25}, {4,16}, {3,24}, {4,30}, {5,16}, {5,23}, {7,27}, {5,25}, {2,20}, {10,23}, {3,15}, {7,18}, {6,20}, {1,21}, {4,21}, {4,20}, {3,30}, {8,13}, {10,14}, {2,15}, {3,18}, {12,19}, {7,22}, {12,29}, {8,22}, {10,24}, {9,13}, {1,17}, {4,25}, {9,22}, {10,19}, {1,28}, {5,14}, {5,18}, {9,14}, {6,17}, {7,17}, {1,19}, {9,30}, {10,28}, {11,26}, {12,28}, {2,13}, {6,29}, {6,23}, {2,22}, {7,26}, {4,29} }; // ET30.23 // Bipartite(15,15) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[30][23]:={ {14,21}, {15,23}, {11,17}, {8,24}, {10,22}, {11,23}, {2,22}, {4,27}, {10,27}, {11,29}, {13,24}, {14,18}, {1,25}, {4,16}, {12,17}, {9,19}, {13,27}, {9,21}, {12,18}, {3,30}, {15,29}, {12,25}, {2,18}, {5,26}, {4,26}, {13,20}, {15,28}, {10,30}, {1,29}, {3,18}, {8,22}, {13,16}, {14,16}, {1,17}, {10,25}, {14,30}, {6,21}, {2,17}, {4,29}, {7,25}, {10,24}, {7,20}, {8,26}, {3,23}, {8,17}, {5,29}, {3,27}, {14,26}, {15,19}, {12,28}, {7,30}, {9,25}, {13,22}, {12,24}, {12,23}, {5,22}, {6,19}, {15,21}, {6,30}, {15,18}, {10,28}, {8,27}, {11,19}, {5,20}, {9,28}, {3,28}, {3,26}, {5,17}, {9,24}, {8,23}, {7,16}, {6,16}, {1,20}, {7,22}, {2,26}, {11,20}, {7,21}, {14,29}, {2,25}, {6,27}, {13,19}, {4,23}, {11,24}, {5,16}, {2,30}, {1,21}, {1,18}, {4,19}, {9,20}, {6,28} }; // ET30.24 // Bipartite(15,15) Valencies [6,6] // Diameter 5 Girth 4 // Has twins VT AT // Automorphism group of order 1209323520 EdgePairs[30][24]:={ {1,26}, {12,20}, {12,27}, {8,19}, {11,16}, {8,28}, {13,19}, {13,28}, {10,27}, {5,24}, {2,30}, {9,25}, {5,29}, {9,20}, {14,26}, {9,21}, {9,16}, {5,27}, {8,23}, {6,26}, {11,28}, {15,24}, {12,30}, {15,29}, {15,27}, {8,24}, {3,23}, {11,23}, {4,16}, {3,24}, {8,29}, {3,29}, {11,21}, {13,18}, {7,30}, {4,30}, {6,16}, {7,27}, {1,16}, {3,28}, {2,20}, {15,19}, {5,19}, {1,21}, {4,21}, {4,20}, {3,19}, {5,17}, {6,21}, {3,18}, {15,17}, {7,25}, {1,18}, {7,22}, {10,29}, {10,24}, {7,20}, {13,23}, {2,27}, {6,18}, {12,25}, {4,25}, {14,21}, {10,19}, {1,28}, {10,17}, {12,22}, {2,17}, {13,24}, {13,29}, {14,20}, {8,18}, {7,17}, {9,30}, {10,22}, {11,26}, {9,26}, {4,26}, {6,28}, {2,25}, {1,23}, {11,18}, {12,17}, {14,25}, {5,22}, {14,16}, {6,23}, {2,22}, {14,30}, {15,22} }; // ET30.25 // Non-bipartite Valency 6 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[30][25]:={ {9,13}, {14,21}, {20,27}, {12,26}, {10,22}, {11,23}, {6,17}, {10,27}, {7,24}, {11,29}, {14,19}, {1,25}, {5,24}, {19,27}, {1,9}, {21,26}, {21,25}, {11,22}, {7,15}, {15,29}, {12,25}, {2,18}, {8,13}, {6,22}, {13,20}, {10,30}, {8,22}, {20,25}, {8,15}, {12,30}, {5,23}, {17,30}, {19,26}, {1,17}, {2,16}, {6,21}, {3,9}, {14,28}, {9,23}, {10,24}, {5,19}, {15,20}, {7,14}, {16,29}, {11,28}, {3,27}, {15,19}, {4,21}, {4,17}, {12,29}, {13,30}, {12,24}, {12,23}, {1,7}, {10,28}, {18,28}, {5,20}, {4,22}, {3,26}, {9,24}, {11,25}, {13,28}, {8,23}, {6,16}, {6,20}, {11,27}, {13,21}, {2,8}, {1,27}, {7,22}, {3,16}, {4,18}, {18,30}, {16,28}, {17,29}, {2,26}, {3,8}, {14,29}, {9,14}, {2,25}, {3,17}, {6,24}, {2,7}, {5,18}, {10,26}, {15,30}, {4,23}, {5,16}, {1,18}, {4,19} }; // ET30.26 // Bipartite(15,15) Valencies [7,7] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 40320 EdgePairs[30][26]:={ {10,21}, {14,25}, {11,17}, {8,24}, {12,26}, {10,22}, {11,23}, {6,18}, {12,19}, {2,22}, {5,30}, {12,16}, {6,17}, {4,27}, {10,27}, {11,29}, {14,19}, {14,18}, {5,24}, {13,27}, {9,21}, {15,29}, {2,28}, {2,19}, {4,26}, {13,20}, {10,23}, {15,28}, {3,19}, {1,29}, {8,22}, {12,21}, {12,30}, {15,22}, {7,26}, {14,30}, {2,17}, {8,18}, {4,28}, {10,16}, {4,29}, {9,23}, {7,20}, {8,26}, {5,29}, {11,28}, {3,27}, {4,30}, {1,19}, {15,19}, {7,30}, {4,21}, {13,30}, {9,25}, {4,25}, {10,29}, {11,26}, {13,22}, {12,24}, {15,26}, {12,23}, {2,24}, {5,22}, {14,17}, {2,21}, {6,30}, {8,27}, {15,18}, {7,18}, {14,23}, {5,20}, {9,28}, {3,26}, {13,28}, {8,23}, {15,16}, {6,16}, {9,18}, {10,17}, {1,20}, {1,27}, {7,22}, {3,16}, {8,25}, {3,25}, {13,23}, {11,20}, {7,21}, {3,20}, {14,29}, {2,25}, {3,17}, {6,24}, {6,27}, {9,16}, {13,19}, {7,17}, {11,24}, {5,16}, {1,21}, {1,18}, {5,25}, {9,20}, {1,24}, {6,28} }; // ET30.27 // Bipartite(6,24) Valencies [8,2] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2293235712 EdgePairs[30][27]:={ {2,27}, {1,20}, {6,7}, {3,16}, {6,13}, {3,10}, {4,17}, {5,24}, {1,14}, {5,18}, {5,29}, {5,30}, {4,23}, {6,30}, {1,7}, {2,26}, {3,15}, {2,21}, {4,16}, {3,21}, {6,18}, {6,12}, {3,27}, {5,12}, {1,13}, {5,23}, {4,28}, {2,20}, {6,24}, {3,22}, {4,22}, {3,9}, {4,11}, {5,11}, {1,19}, {3,28}, {1,25}, {5,17}, {2,8}, {2,15}, {6,25}, {4,29}, {6,19}, {4,10}, {1,26}, {2,9}, {2,14}, {1,8} }; // ET30.28 // Bipartite(6,24) Valencies [8,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 196608 EdgePairs[30][28]:={ {5,12}, {4,8}, {2,14}, {4,23}, {2,26}, {3,12}, {5,24}, {1,29}, {2,29}, {5,27}, {6,14}, {6,26}, {4,11}, {4,10}, {3,21}, {6,10}, {5,15}, {3,23}, {3,24}, {3,9}, {6,15}, {4,30}, {5,7}, {4,18}, {2,16}, {1,7}, {3,11}, {3,16}, {3,28}, {2,20}, {5,19}, {1,21}, {4,20}, {6,27}, {5,30}, {1,17}, {4,22}, {2,28}, {6,22}, {2,17}, {5,18}, {6,25}, {1,13}, {1,19}, {1,9}, {2,8}, {1,25}, {6,13} }; // ET30.29 // Bipartite(10,20) Valencies [8,4] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2548039680 EdgePairs[30][29]:={ {5,12}, {1,26}, {4,13}, {8,28}, {4,23}, {1,14}, {9,23}, {10,27}, {1,24}, {5,24}, {1,29}, {2,30}, {9,25}, {5,29}, {9,20}, {7,12}, {5,27}, {8,16}, {8,23}, {6,14}, {6,26}, {8,11}, {8,21}, {3,21}, {9,15}, {3,23}, {10,12}, {2,12}, {4,30}, {7,30}, {6,16}, {7,27}, {4,18}, {3,11}, {3,16}, {3,28}, {2,20}, {1,16}, {5,19}, {1,21}, {4,20}, {5,17}, {7,15}, {8,13}, {10,14}, {2,15}, {6,21}, {3,18}, {7,25}, {3,26}, {7,22}, {10,29}, {10,24}, {4,15}, {7,20}, {4,28}, {9,13}, {2,27}, {4,25}, {6,19}, {10,19}, {8,26}, {9,18}, {10,17}, {5,14}, {2,17}, {3,13}, {8,18}, {1,19}, {7,17}, {9,30}, {6,11}, {10,22}, {2,25}, {9,28}, {1,11}, {5,22}, {6,29}, {2,22}, {6,24} }; // ET30.30 // Bipartite(10,20) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 955514880 EdgePairs[30][30]:={ {3,22}, {1,26}, {4,13}, {10,15}, {4,23}, {1,14}, {1,24}, {3,12}, {5,24}, {1,29}, {2,30}, {9,25}, {5,29}, {9,20}, {9,21}, {9,16}, {7,12}, {8,16}, {6,14}, {8,11}, {4,11}, {8,21}, {3,27}, {10,30}, {9,15}, {5,15}, {3,23}, {9,11}, {4,16}, {2,12}, {8,27}, {5,20}, {7,27}, {10,13}, {4,18}, {5,25}, {1,16}, {3,28}, {2,20}, {10,23}, {3,17}, {5,19}, {1,21}, {4,21}, {2,15}, {8,12}, {3,18}, {5,30}, {7,22}, {8,22}, {4,28}, {2,27}, {7,19}, {6,18}, {6,19}, {8,26}, {5,14}, {2,17}, {3,13}, {1,19}, {7,17}, {9,30}, {10,28}, {9,26}, {4,26}, {6,28}, {2,25}, {10,25}, {7,14}, {10,20}, {1,11}, {6,29}, {8,17}, {6,23}, {2,22}, {6,13}, {7,24}, {10,18}, {6,24}, {7,29} }; // ET30.31 // Bipartite(10,20) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3932160 EdgePairs[30][31]:={ {5,12}, {10,15}, {1,14}, {8,20}, {1,24}, {1,29}, {9,25}, {5,29}, {7,23}, {9,21}, {9,16}, {7,12}, {8,16}, {8,23}, {6,14}, {4,11}, {7,13}, {10,30}, {9,15}, {5,15}, {8,24}, {3,23}, {9,11}, {4,16}, {10,12}, {3,24}, {2,12}, {3,20}, {5,20}, {7,27}, {5,25}, {3,16}, {7,18}, {5,19}, {4,27}, {1,21}, {2,18}, {4,21}, {9,27}, {3,30}, {8,13}, {3,14}, {6,21}, {4,17}, {5,30}, {3,26}, {1,18}, {7,22}, {10,29}, {4,15}, {2,27}, {6,18}, {4,25}, {6,19}, {2,28}, {10,19}, {1,28}, {8,26}, {2,17}, {7,28}, {3,13}, {2,23}, {8,14}, {1,19}, {7,17}, {6,11}, {10,22}, {9,26}, {4,26}, {2,13}, {6,28}, {10,25}, {8,30}, {10,20}, {1,11}, {6,29}, {5,22}, {2,22}, {9,17}, {6,24} }; // ET30.32 // Bipartite(10,20) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 40960 EdgePairs[30][32]:={ {2,11}, {4,13}, {10,15}, {4,23}, {9,19}, {5,24}, {1,30}, {2,29}, {9,25}, {9,16}, {5,27}, {6,14}, {8,11}, {8,21}, {8,15}, {3,27}, {8,25}, {9,15}, {6,30}, {1,20}, {8,24}, {10,12}, {2,12}, {3,29}, {3,20}, {4,30}, {2,21}, {5,16}, {5,23}, {4,12}, {7,27}, {9,29}, {10,13}, {10,16}, {3,16}, {10,23}, {10,26}, {7,18}, {6,20}, {3,17}, {2,18}, {1,21}, {4,20}, {3,19}, {3,30}, {5,17}, {7,15}, {8,12}, {6,21}, {7,25}, {1,18}, {3,26}, {8,22}, {1,27}, {1,17}, {4,22}, {2,28}, {2,19}, {1,28}, {9,18}, {5,14}, {7,28}, {5,26}, {8,14}, {5,13}, {7,17}, {6,11}, {10,22}, {9,26}, {10,25}, {9,28}, {7,14}, {4,19}, {1,11}, {6,23}, {2,22}, {6,13}, {7,24}, {6,24}, {4,29} }; // ET30.33 // Bipartite(14,16) Valencies [8,7] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 2688 EdgePairs[30][33]:={ {1,15}, {7,19}, {11,15}, {13,29}, {14,25}, {3,15}, {10,22}, {11,23}, {6,18}, {12,19}, {3,29}, {5,30}, {4,27}, {6,17}, {11,29}, {4,16}, {6,25}, {9,19}, {13,27}, {3,30}, {11,22}, {12,27}, {7,23}, {7,15}, {2,28}, {2,18}, {5,26}, {4,26}, {9,17}, {10,18}, {13,20}, {10,23}, {2,29}, {3,19}, {14,27}, {8,22}, {12,21}, {13,16}, {4,20}, {9,27}, {2,23}, {8,28}, {1,17}, {13,26}, {2,16}, {14,30}, {6,21}, {8,18}, {4,28}, {14,28}, {10,24}, {5,15}, {7,20}, {3,27}, {14,26}, {11,18}, {12,28}, {4,21}, {4,17}, {12,29}, {9,25}, {4,25}, {9,15}, {1,26}, {8,19}, {13,22}, {12,24}, {12,23}, {5,22}, {6,19}, {1,23}, {2,21}, {14,22}, {6,30}, {10,28}, {11,19}, {7,18}, {8,16}, {5,17}, {9,24}, {8,20}, {7,16}, {3,21}, {11,30}, {10,17}, {1,27}, {3,16}, {8,25}, {3,25}, {13,23}, {2,26}, {7,21}, {13,15}, {14,29}, {10,20}, {6,24}, {5,18}, {10,26}, {7,17}, {11,24}, {1,30}, {5,16}, {2,30}, {1,21}, {12,20}, {5,25}, {14,24}, {9,20}, {1,24}, {8,29}, {9,22}, {6,28} }; // ET30.34 // Bipartite(14,16) Valencies [8,7] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 344064 EdgePairs[30][34]:={ {1,15}, {7,19}, {11,15}, {13,29}, {14,25}, {11,17}, {12,26}, {10,22}, {11,23}, {3,29}, {2,22}, {12,16}, {4,27}, {13,18}, {7,24}, {11,29}, {13,24}, {14,19}, {12,22}, {7,27}, {9,19}, {9,21}, {12,18}, {14,20}, {2,18}, {5,26}, {4,26}, {6,22}, {10,23}, {2,29}, {10,30}, {14,27}, {8,22}, {8,15}, {12,30}, {13,16}, {5,23}, {9,27}, {7,26}, {8,28}, {10,25}, {13,26}, {14,30}, {1,16}, {6,21}, {8,21}, {2,17}, {10,15}, {10,16}, {7,25}, {14,28}, {10,24}, {5,15}, {4,30}, {1,19}, {12,28}, {5,28}, {4,15}, {6,29}, {12,24}, {6,19}, {14,17}, {1,23}, {2,21}, {14,22}, {6,30}, {11,19}, {7,18}, {5,20}, {9,28}, {4,22}, {3,28}, {3,24}, {5,17}, {11,25}, {8,20}, {8,23}, {7,16}, {9,26}, {6,16}, {11,21}, {3,21}, {9,18}, {10,17}, {11,27}, {13,21}, {1,20}, {1,27}, {3,16}, {4,18}, {9,29}, {3,25}, {13,23}, {2,26}, {3,20}, {13,15}, {2,25}, {1,28}, {3,17}, {6,24}, {5,18}, {8,30}, {6,27}, {7,17}, {4,23}, {2,30}, {12,20}, {5,25}, {4,19}, {9,20}, {1,24}, {8,29} }; // ET30.35 // Bipartite(15,15) Valencies [8,8] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 40320 EdgePairs[30][35]:={ {10,19}, {13,25}, {14,21}, {13,29}, {14,25}, {15,23}, {8,24}, {12,26}, {10,22}, {6,18}, {9,30}, {12,19}, {2,22}, {5,30}, {4,27}, {6,17}, {12,16}, {7,24}, {2,20}, {13,24}, {14,18}, {12,17}, {6,25}, {7,27}, {9,21}, {11,16}, {12,18}, {7,23}, {15,29}, {2,28}, {14,20}, {2,19}, {5,26}, {9,17}, {6,22}, {5,21}, {10,23}, {15,28}, {10,30}, {3,19}, {1,29}, {3,18}, {12,21}, {13,16}, {4,20}, {7,26}, {8,28}, {15,25}, {1,22}, {1,16}, {2,17}, {10,16}, {4,29}, {9,23}, {5,19}, {8,26}, {15,20}, {3,23}, {8,17}, {5,29}, {11,28}, {3,27}, {4,30}, {14,26}, {11,18}, {7,30}, {12,29}, {1,26}, {13,22}, {2,24}, {5,22}, {2,27}, {15,21}, {2,21}, {14,22}, {5,27}, {6,30}, {10,28}, {11,19}, {14,23}, {9,28}, {3,28}, {3,26}, {11,25}, {8,20}, {15,16}, {7,16}, {6,20}, {6,16}, {11,21}, {11,30}, {9,18}, {1,27}, {15,27}, {4,18}, {8,25}, {3,25}, {9,29}, {13,23}, {13,17}, {7,21}, {1,28}, {3,17}, {10,20}, {8,30}, {10,26}, {6,27}, {13,19}, {7,17}, {4,23}, {11,24}, {1,18}, {12,20}, {5,25}, {4,19}, {14,24}, {4,24}, {1,24}, {8,29}, {9,22} }; // ET30.36 // Bipartite(15,15) Valencies [8,8] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[30][36]:={ {13,25}, {14,21}, {10,21}, {13,29}, {14,25}, {15,23}, {8,24}, {10,22}, {6,18}, {9,30}, {3,29}, {13,18}, {10,27}, {6,23}, {14,19}, {1,25}, {4,16}, {12,17}, {12,22}, {5,24}, {7,27}, {9,19}, {13,27}, {11,16}, {3,30}, {7,23}, {2,28}, {5,26}, {4,26}, {9,17}, {10,18}, {6,22}, {13,20}, {5,21}, {10,23}, {15,28}, {3,19}, {1,29}, {3,18}, {12,30}, {13,16}, {4,20}, {15,22}, {7,26}, {14,16}, {10,25}, {13,26}, {2,16}, {1,22}, {14,30}, {1,16}, {2,17}, {7,29}, {4,29}, {3,22}, {14,28}, {9,23}, {5,19}, {7,20}, {8,26}, {15,20}, {8,17}, {11,28}, {14,26}, {12,28}, {15,19}, {4,21}, {5,28}, {12,29}, {4,25}, {8,19}, {13,22}, {6,29}, {12,24}, {12,23}, {2,24}, {2,27}, {6,19}, {14,17}, {1,23}, {2,21}, {5,27}, {6,30}, {8,27}, {15,18}, {11,19}, {9,28}, {8,16}, {5,17}, {3,24}, {11,25}, {7,16}, {11,21}, {11,30}, {9,18}, {11,27}, {1,27}, {7,22}, {4,18}, {8,25}, {9,29}, {2,26}, {15,17}, {3,20}, {7,21}, {3,17}, {10,20}, {6,24}, {8,30}, {10,26}, {4,23}, {11,24}, {2,30}, {1,21}, {12,20}, {1,18}, {15,24}, {5,25}, {9,20}, {6,28} }; // ET30.37 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 1966080 EdgePairs[30][37]:={ {1,15}, {10,19}, {9,13}, {13,25}, {13,29}, {14,25}, {11,23}, {4,14}, {1,11}, {5,30}, {4,27}, {10,27}, {2,11}, {6,23}, {1,25}, {20,21}, {5,24}, {9,19}, {12,27}, {18,23}, {2,15}, {7,11}, {10,23}, {15,28}, {2,29}, {1,29}, {18,24}, {3,18}, {8,22}, {20,25}, {16,21}, {17,23}, {5,23}, {17,30}, {15,22}, {9,27}, {17,24}, {7,26}, {19,26}, {13,26}, {3,13}, {2,16}, {14,30}, {1,16}, {10,13}, {8,21}, {8,18}, {4,28}, {3,14}, {1,12}, {7,25}, {3,22}, {9,23}, {10,24}, {5,19}, {5,15}, {8,26}, {8,17}, {5,29}, {11,28}, {3,27}, {14,26}, {6,15}, {8,11}, {12,28}, {4,21}, {4,17}, {13,30}, {1,26}, {6,29}, {12,24}, {12,23}, {6,19}, {15,21}, {16,27}, {6,30}, {10,28}, {7,18}, {2,12}, {9,28}, {4,22}, {5,20}, {10,14}, {3,28}, {9,24}, {16,22}, {6,16}, {6,20}, {3,21}, {18,29}, {19,22}, {20,26}, {11,27}, {7,22}, {15,27}, {4,18}, {18,30}, {16,28}, {8,25}, {17,29}, {2,26}, {7,21}, {14,29}, {9,14}, {2,25}, {3,17}, {10,20}, {6,24}, {19,25}, {20,22}, {7,17}, {19,21}, {11,24}, {1,30}, {5,16}, {7,12}, {4,13}, {2,30}, {9,20}, {8,12} }; // ET30.38 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[30][38]:={ {14,21}, {11,15}, {6,12}, {11,17}, {1,11}, {3,29}, {6,14}, {17,27}, {12,16}, {13,18}, {16,30}, {10,27}, {7,24}, {6,23}, {2,20}, {23,27}, {14,19}, {1,25}, {12,14}, {20,21}, {5,24}, {16,18}, {7,27}, {13,27}, {12,18}, {21,25}, {19,23}, {12,27}, {5,13}, {15,29}, {2,28}, {6,9}, {22,24}, {6,22}, {13,20}, {5,21}, {2,29}, {10,30}, {20,25}, {8,15}, {16,21}, {1,3}, {15,22}, {4,7}, {8,28}, {19,26}, {10,12}, {15,25}, {8,21}, {8,18}, {2,17}, {8,10}, {4,28}, {2,13}, {10,15}, {3,9}, {16,26}, {7,25}, {14,28}, {9,23}, {10,24}, {5,19}, {18,25}, {20,24}, {8,26}, {25,29}, {5,29}, {11,28}, {19,29}, {26,30}, {3,27}, {4,30}, {6,15}, {1,19}, {12,29}, {4,25}, {13,22}, {2,4}, {11,13}, {14,17}, {6,30}, {18,28}, {2,12}, {9,28}, {3,26}, {3,24}, {8,23}, {21,23}, {20,30}, {7,16}, {6,20}, {1,14}, {11,30}, {19,22}, {17,21}, {7,9}, {9,11}, {1,27}, {5,11}, {7,22}, {5,10}, {22,26}, {9,29}, {13,23}, {2,26}, {3,8}, {15,17}, {3,20}, {17,26}, {18,22}, {9,16}, {7,17}, {4,23}, {1,30}, {5,16}, {1,18}, {4,19}, {14,24}, {4,10}, {24,28} }; // ET30.39 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[30][39]:={ {9,13}, {13,25}, {10,21}, {15,23}, {4,27}, {14,19}, {14,18}, {12,17}, {22,30}, {24,29}, {4,5}, {13,27}, {21,25}, {16,20}, {19,23}, {5,7}, {18,21}, {3,10}, {12,25}, {2,18}, {23,30}, {13,20}, {2,29}, {18,24}, {20,25}, {8,15}, {7,28}, {17,23}, {5,23}, {1,3}, {17,30}, {6,11}, {9,27}, {1,10}, {7,26}, {19,26}, {1,17}, {10,25}, {15,25}, {1,22}, {28,29}, {8,21}, {8,10}, {7,29}, {3,14}, {2,13}, {10,15}, {16,26}, {14,28}, {5,19}, {5,15}, {6,8}, {20,24}, {5,29}, {22,23}, {14,26}, {11,18}, {8,11}, {12,28}, {15,19}, {5,28}, {12,29}, {4,15}, {2,9}, {18,19}, {11,26}, {11,14}, {2,4}, {2,24}, {2,27}, {17,22}, {15,21}, {1,23}, {2,21}, {21,29}, {6,30}, {10,28}, {8,27}, {11,19}, {10,14}, {3,28}, {3,24}, {27,30}, {16,22}, {7,16}, {9,26}, {6,20}, {6,16}, {1,14}, {18,29}, {11,30}, {7,9}, {11,27}, {7,22}, {3,16}, {22,26}, {8,25}, {13,17}, {3,20}, {5,12}, {3,6}, {1,28}, {4,9}, {6,24}, {8,30}, {17,20}, {6,27}, {9,16}, {4,23}, {1,30}, {7,12}, {4,13}, {12,20}, {4,19}, {21,24}, {12,13}, {17,25}, {18,26}, {9,22}, {16,24} }; // ET30.40 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 3932160 EdgePairs[30][40]:={ {6,12}, {10,21}, {13,29}, {3,15}, {10,22}, {6,10}, {6,18}, {1,11}, {24,26}, {4,27}, {6,17}, {16,30}, {10,27}, {2,11}, {23,25}, {23,27}, {17,19}, {1,25}, {4,16}, {9,12}, {22,30}, {12,14}, {9,21}, {16,20}, {22,28}, {15,29}, {6,9}, {5,9}, {21,28}, {3,19}, {8,22}, {13,16}, {2,14}, {4,20}, {6,11}, {9,27}, {2,23}, {7,26}, {14,16}, {10,12}, {14,30}, {8,21}, {8,18}, {4,28}, {7,29}, {2,13}, {22,29}, {1,12}, {7,25}, {16,19}, {5,19}, {18,25}, {8,26}, {15,20}, {3,23}, {8,17}, {16,29}, {3,27}, {15,19}, {7,30}, {13,30}, {4,15}, {18,19}, {1,26}, {11,14}, {22,27}, {2,24}, {11,13}, {21,30}, {6,19}, {1,23}, {21,29}, {10,28}, {7,18}, {2,12}, {9,28}, {5,20}, {3,28}, {3,24}, {5,17}, {6,20}, {18,20}, {1,14}, {24,25}, {14,15}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {5,10}, {8,25}, {2,26}, {3,20}, {13,15}, {7,21}, {24,27}, {14,29}, {5,12}, {2,25}, {23,28}, {17,26}, {5,18}, {8,30}, {17,20}, {23,26}, {15,30}, {7,17}, {4,23}, {10,11}, {4,19}, {4,24}, {12,13}, {17,25}, {18,26}, {1,24}, {8,29}, {24,28}, {9,22}, {21,27} }; // ET30.41 // Bipartite(12,18) Valencies [9,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1451188224 EdgePairs[30][41]:={ {1,15}, {10,19}, {9,13}, {11,15}, {11,17}, {3,15}, {8,24}, {10,22}, {11,23}, {9,30}, {3,29}, {2,22}, {6,14}, {5,30}, {12,16}, {11,29}, {2,20}, {1,25}, {4,16}, {6,13}, {12,17}, {12,22}, {5,24}, {6,25}, {7,27}, {9,19}, {9,21}, {12,18}, {7,23}, {7,15}, {5,13}, {2,28}, {2,19}, {6,22}, {5,21}, {8,22}, {12,30}, {2,14}, {9,27}, {7,26}, {8,28}, {10,25}, {2,16}, {10,13}, {8,18}, {4,28}, {7,29}, {3,14}, {2,13}, {10,16}, {4,29}, {5,19}, {5,15}, {7,20}, {3,23}, {8,17}, {7,14}, {3,27}, {4,30}, {6,26}, {1,19}, {12,28}, {4,17}, {12,29}, {9,25}, {9,15}, {11,26}, {11,14}, {12,24}, {12,23}, {6,19}, {5,27}, {10,28}, {4,22}, {10,14}, {3,26}, {8,16}, {9,24}, {8,23}, {11,21}, {6,20}, {6,16}, {3,21}, {9,18}, {11,27}, {1,27}, {1,13}, {4,18}, {2,26}, {11,20}, {7,21}, {3,20}, {2,25}, {3,17}, {10,20}, {5,18}, {8,30}, {10,26}, {7,17}, {4,23}, {1,30}, {1,21}, {1,18}, {5,25}, {4,24}, {1,24}, {8,29}, {6,28} }; // ET30.42 // Non-bipartite Valency 9 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 7255941120 EdgePairs[30][42]:={ {7,19}, {13,25}, {14,21}, {13,29}, {14,25}, {11,17}, {8,24}, {12,26}, {6,18}, {1,11}, {3,29}, {5,30}, {24,26}, {12,16}, {6,17}, {3,7}, {10,27}, {2,11}, {23,25}, {7,24}, {6,23}, {23,27}, {14,19}, {17,19}, {4,16}, {12,17}, {5,24}, {1,9}, {9,19}, {13,27}, {9,21}, {11,16}, {12,18}, {3,30}, {16,20}, {12,27}, {7,23}, {18,21}, {3,10}, {15,29}, {2,28}, {14,20}, {12,25}, {10,18}, {6,22}, {13,20}, {15,28}, {2,29}, {14,27}, {1,29}, {8,22}, {22,25}, {16,21}, {5,23}, {3,11}, {2,10}, {1,10}, {13,26}, {10,25}, {15,25}, {14,30}, {8,21}, {4,28}, {1,12}, {4,29}, {10,16}, {3,9}, {16,19}, {14,28}, {9,23}, {7,20}, {15,20}, {5,29}, {4,30}, {14,26}, {11,18}, {15,19}, {4,17}, {5,28}, {13,30}, {2,9}, {18,19}, {8,19}, {11,26}, {6,29}, {22,27}, {15,26}, {5,22}, {15,21}, {6,30}, {1,7}, {2,12}, {4,22}, {3,28}, {5,17}, {9,24}, {3,12}, {11,25}, {13,28}, {8,20}, {8,23}, {6,16}, {18,20}, {10,17}, {17,21}, {11,27}, {13,21}, {24,25}, {2,8}, {7,22}, {15,27}, {4,18}, {22,26}, {3,8}, {7,21}, {24,27}, {14,29}, {1,28}, {6,24}, {2,7}, {5,18}, {10,26}, {17,20}, {23,26}, {13,19}, {15,30}, {4,23}, {1,8}, {1,30}, {5,16}, {2,30}, {4,24}, {9,20}, {9,22}, {6,28} }; // ET30.43 // Bipartite(5,25) Valencies [10,2] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 248832000000 EdgePairs[30][43]:={ {5,12}, {1,26}, {4,8}, {4,13}, {4,23}, {1,14}, {1,24}, {5,24}, {1,29}, {2,30}, {5,29}, {2,10}, {5,27}, {4,10}, {3,21}, {1,6}, {3,23}, {3,8}, {2,12}, {4,30}, {5,9}, {5,7}, {4,18}, {2,7}, {3,11}, {3,16}, {3,28}, {2,20}, {1,16}, {5,19}, {1,21}, {4,20}, {5,17}, {2,15}, {3,18}, {3,26}, {4,15}, {4,28}, {2,27}, {3,6}, {4,25}, {5,14}, {2,17}, {3,13}, {1,19}, {1,9}, {2,25}, {1,11}, {5,22}, {2,22} }; // ET30.44 // Bipartite(15,15) Valencies [10,10] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 35831808000000 EdgePairs[30][44]:={ {11,17}, {10,25}, {5,17}, {10,24}, {11,20}, {4,27}, {12,29}, {13,21}, {14,19}, {4,24}, {15,24}, {4,16}, {4,30}, {11,25}, {6,17}, {2,23}, {8,28}, {1,27}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {1,30}, {14,28}, {13,16}, {10,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {15,29}, {6,21}, {14,23}, {2,25}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {5,25}, {15,26}, {11,22}, {7,25}, {10,28}, {1,22}, {15,27}, {6,30}, {5,23}, {4,21}, {3,20}, {13,22}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {7,30}, {8,17}, {2,16}, {7,16}, {11,23}, {11,29}, {6,24}, {8,22}, {13,25}, {15,20}, {13,28}, {9,20}, {1,28}, {3,27}, {4,28}, {15,17}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {13,30}, {2,17}, {12,27}, {14,17}, {1,24}, {12,23}, {14,22}, {13,24}, {6,27}, {6,26}, {12,30}, {3,23}, {8,23}, {3,21}, {1,25}, {9,30}, {13,27}, {14,20}, {15,21}, {14,25}, {7,28}, {11,26}, {15,18}, {11,16}, {13,19}, {3,30}, {9,18}, {3,24}, {2,29}, {10,27}, {2,22}, {1,16}, {9,17}, {10,18}, {5,26}, {4,18}, {11,19}, {10,19}, {4,25}, {12,24}, {8,20}, {7,27}, {15,23}, {7,24}, {9,24}, {5,19}, {6,20}, {15,30}, {7,19}, {9,21}, {9,23}, {7,21}, {8,29}, {12,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET30.45 // Non-bipartite Valency 10 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 7200 EdgePairs[30][45]:={ {9,13}, {10,19}, {16,25}, {6,12}, {10,21}, {13,29}, {14,25}, {11,17}, {8,24}, {12,26}, {9,30}, {3,29}, {12,16}, {6,17}, {4,27}, {16,30}, {2,20}, {23,27}, {13,24}, {14,18}, {20,21}, {1,9}, {6,25}, {13,27}, {12,18}, {11,22}, {19,23}, {22,28}, {7,23}, {5,13}, {25,26}, {15,29}, {2,28}, {14,20}, {2,18}, {2,15}, {5,26}, {8,14}, {7,11}, {6,22}, {5,21}, {3,19}, {1,29}, {5,6}, {4,12}, {18,24}, {8,22}, {7,28}, {12,21}, {17,23}, {5,23}, {3,11}, {2,10}, {4,20}, {2,23}, {7,26}, {19,30}, {4,7}, {1,17}, {1,22}, {14,30}, {3,14}, {2,13}, {1,12}, {10,16}, {3,9}, {14,28}, {9,23}, {10,24}, {20,24}, {25,29}, {7,13}, {8,17}, {4,30}, {6,15}, {1,19}, {12,28}, {15,19}, {4,17}, {5,28}, {9,25}, {4,15}, {4,25}, {9,15}, {10,29}, {8,19}, {23,29}, {13,22}, {18,27}, {15,26}, {12,23}, {21,30}, {15,21}, {16,27}, {6,30}, {1,7}, {8,27}, {5,8}, {7,18}, {14,23}, {4,22}, {9,28}, {10,14}, {3,26}, {24,30}, {3,24}, {11,25}, {15,16}, {16,22}, {7,16}, {6,20}, {3,21}, {1,14}, {18,29}, {11,30}, {9,18}, {17,21}, {20,26}, {11,27}, {2,8}, {1,27}, {5,11}, {3,16}, {22,26}, {20,29}, {13,17}, {11,20}, {7,21}, {3,6}, {2,25}, {17,26}, {18,22}, {5,18}, {17,28}, {10,26}, {6,27}, {19,25}, {13,19}, {5,16}, {19,28}, {2,30}, {10,11}, {15,24}, {4,10}, {9,20}, {8,12}, {1,24}, {8,29}, {24,28}, {21,27} }; // ET30.46 // Bipartite(6,24) Valencies [12,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6449725440000 EdgePairs[30][46]:={ {4,8}, {4,24}, {1,24}, {2,29}, {5,29}, {2,24}, {6,14}, {6,26}, {4,10}, {5,10}, {3,21}, {3,27}, {6,10}, {6,30}, {1,20}, {1,12}, {3,23}, {4,16}, {3,9}, {2,12}, {6,7}, {3,29}, {6,15}, {4,30}, {5,9}, {2,21}, {5,21}, {4,12}, {4,18}, {2,16}, {1,7}, {5,25}, {1,15}, {3,11}, {1,16}, {3,7}, {2,20}, {3,15}, {3,17}, {3,25}, {4,20}, {3,19}, {5,17}, {6,27}, {5,30}, {1,27}, {4,28}, {4,22}, {6,18}, {6,19}, {2,28}, {6,22}, {1,28}, {5,14}, {2,17}, {5,18}, {3,13}, {5,26}, {1,8}, {5,13}, {2,9}, {1,19}, {6,11}, {4,26}, {2,13}, {2,25}, {2,8}, {4,14}, {1,23}, {1,11}, {5,22}, {6,23} }; // ET30.47 // Bipartite(6,24) Valencies [12,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 80621568 EdgePairs[30][47]:={ {1,26}, {2,14}, {4,13}, {1,24}, {3,12}, {2,26}, {5,24}, {2,30}, {5,29}, {2,10}, {5,27}, {1,10}, {6,14}, {6,26}, {4,11}, {3,27}, {5,11}, {6,10}, {6,30}, {5,15}, {3,23}, {3,9}, {2,12}, {3,20}, {5,8}, {4,30}, {5,16}, {5,23}, {6,16}, {5,21}, {4,12}, {5,7}, {1,7}, {1,15}, {3,11}, {1,16}, {3,7}, {3,28}, {2,20}, {3,15}, {3,17}, {5,19}, {2,18}, {3,25}, {4,27}, {4,21}, {4,20}, {3,19}, {6,21}, {1,18}, {4,28}, {1,17}, {4,22}, {6,18}, {2,28}, {6,22}, {2,17}, {1,8}, {2,9}, {5,13}, {1,9}, {2,25}, {4,14}, {1,23}, {4,19}, {1,25}, {6,29}, {2,22}, {6,13}, {6,8}, {6,24}, {4,29} }; // ET30.48 // Bipartite(10,20) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 955514880 EdgePairs[30][48]:={ {1,15}, {9,13}, {10,19}, {6,12}, {5,14}, {3,15}, {8,24}, {10,22}, {4,14}, {4,27}, {6,17}, {10,27}, {2,11}, {2,20}, {1,25}, {9,12}, {5,24}, {6,25}, {7,27}, {9,21}, {3,30}, {7,23}, {7,15}, {5,13}, {2,19}, {2,15}, {5,26}, {8,14}, {9,17}, {10,18}, {6,22}, {5,21}, {10,23}, {2,29}, {1,29}, {4,12}, {3,18}, {8,22}, {7,28}, {2,14}, {5,23}, {3,11}, {4,20}, {6,11}, {9,27}, {3,13}, {2,16}, {10,12}, {6,21}, {10,13}, {8,21}, {4,29}, {7,25}, {5,19}, {9,23}, {10,24}, {7,20}, {8,26}, {7,13}, {8,17}, {3,23}, {5,29}, {4,30}, {6,26}, {6,15}, {1,19}, {8,11}, {7,30}, {4,17}, {5,28}, {4,15}, {4,25}, {10,29}, {8,19}, {2,24}, {1,23}, {2,21}, {6,30}, {8,27}, {10,28}, {7,18}, {4,22}, {9,28}, {10,14}, {3,28}, {3,26}, {8,16}, {6,16}, {6,20}, {9,26}, {3,21}, {1,14}, {9,18}, {10,17}, {1,20}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {3,25}, {2,26}, {3,20}, {2,25}, {1,28}, {5,18}, {6,27}, {9,16}, {7,17}, {1,30}, {5,16}, {7,12}, {2,30}, {1,18}, {4,19}, {4,24}, {8,12}, {1,24}, {8,29}, {9,22} }; // ET30.49 // Bipartite(10,20) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3932160 EdgePairs[30][49]:={ {1,15}, {7,19}, {6,12}, {5,14}, {10,21}, {3,15}, {10,22}, {6,18}, {4,14}, {9,30}, {3,29}, {10,27}, {7,24}, {6,23}, {2,20}, {1,25}, {6,13}, {9,12}, {5,24}, {6,25}, {7,27}, {9,21}, {3,30}, {5,13}, {2,28}, {2,19}, {2,18}, {5,26}, {8,13}, {6,22}, {5,21}, {10,23}, {2,29}, {3,19}, {1,29}, {4,12}, {8,15}, {7,28}, {2,14}, {5,23}, {3,11}, {4,20}, {7,26}, {3,13}, {2,16}, {10,12}, {1,22}, {1,16}, {10,13}, {2,17}, {8,21}, {4,28}, {7,29}, {1,12}, {10,16}, {10,24}, {7,20}, {3,23}, {8,17}, {7,14}, {3,27}, {4,30}, {6,26}, {6,15}, {1,19}, {8,11}, {7,30}, {4,21}, {9,25}, {4,15}, {4,25}, {9,15}, {1,26}, {8,19}, {6,29}, {2,24}, {4,11}, {5,22}, {2,27}, {6,19}, {1,23}, {5,27}, {8,27}, {7,18}, {4,22}, {9,28}, {10,14}, {5,17}, {9,24}, {8,20}, {8,23}, {7,16}, {6,16}, {3,21}, {9,18}, {10,17}, {9,11}, {5,11}, {1,13}, {4,18}, {3,25}, {8,25}, {2,26}, {3,20}, {5,12}, {9,14}, {1,28}, {3,17}, {8,30}, {10,26}, {7,17}, {5,16}, {2,30}, {10,11}, {1,18}, {4,24}, {9,20}, {8,29}, {6,28}, {9,22} }; // ET30.50 // Bipartite(10,20) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 122880 EdgePairs[30][50]:={ {7,19}, {5,14}, {10,22}, {6,18}, {1,11}, {9,30}, {3,29}, {6,14}, {5,30}, {4,27}, {6,17}, {10,27}, {2,11}, {7,24}, {6,23}, {2,20}, {4,16}, {6,13}, {5,24}, {6,25}, {7,27}, {9,19}, {9,21}, {5,13}, {2,19}, {2,15}, {5,26}, {4,26}, {8,13}, {9,17}, {10,18}, {5,21}, {2,29}, {3,19}, {10,30}, {1,29}, {4,12}, {3,18}, {8,22}, {8,15}, {2,14}, {5,23}, {3,11}, {9,27}, {2,23}, {7,26}, {8,28}, {1,17}, {10,25}, {10,12}, {1,22}, {8,18}, {7,29}, {3,14}, {2,13}, {10,15}, {1,12}, {3,22}, {10,24}, {7,20}, {8,26}, {7,14}, {6,15}, {1,19}, {7,30}, {4,21}, {4,17}, {5,28}, {9,25}, {4,15}, {4,25}, {9,15}, {6,29}, {2,24}, {4,11}, {6,19}, {1,23}, {2,21}, {10,28}, {5,20}, {4,22}, {10,14}, {3,28}, {3,26}, {8,16}, {3,24}, {3,12}, {8,20}, {8,23}, {7,16}, {9,26}, {3,21}, {10,17}, {1,27}, {9,11}, {5,11}, {7,22}, {3,16}, {1,13}, {8,25}, {9,29}, {2,25}, {1,28}, {10,20}, {6,24}, {5,18}, {8,30}, {6,27}, {9,16}, {7,17}, {4,23}, {7,12}, {5,16}, {4,13}, {1,21}, {2,30}, {1,18}, {8,12}, {9,20}, {6,28} }; // ET30.51 // Bipartite(12,18) Valencies [12,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 30958682112000 EdgePairs[30][51]:={ {9,13}, {10,19}, {7,19}, {11,15}, {5,14}, {3,15}, {11,17}, {8,24}, {10,22}, {6,18}, {11,23}, {4,14}, {9,30}, {12,19}, {5,30}, {12,16}, {11,29}, {2,20}, {1,25}, {4,16}, {6,13}, {12,15}, {12,22}, {5,24}, {6,25}, {9,19}, {9,21}, {12,18}, {3,30}, {12,27}, {7,23}, {12,25}, {2,18}, {2,15}, {5,26}, {4,26}, {8,14}, {6,22}, {5,21}, {10,23}, {2,29}, {3,19}, {1,29}, {3,18}, {8,15}, {7,28}, {12,21}, {12,30}, {2,14}, {5,23}, {4,20}, {9,27}, {2,23}, {7,26}, {1,17}, {3,13}, {10,25}, {1,22}, {1,16}, {6,21}, {10,13}, {2,17}, {8,18}, {8,21}, {4,28}, {7,29}, {4,29}, {10,16}, {7,25}, {3,22}, {5,15}, {7,20}, {8,26}, {7,13}, {8,17}, {5,29}, {7,14}, {3,27}, {6,15}, {1,19}, {11,18}, {12,28}, {4,17}, {9,25}, {4,25}, {9,15}, {10,29}, {1,26}, {11,26}, {11,14}, {12,24}, {2,24}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {6,30}, {8,27}, {10,28}, {5,20}, {4,22}, {9,28}, {10,14}, {3,28}, {3,24}, {5,17}, {9,24}, {8,20}, {8,23}, {7,16}, {6,16}, {11,21}, {3,21}, {1,14}, {11,30}, {9,18}, {10,17}, {11,27}, {1,20}, {7,22}, {3,16}, {1,13}, {3,25}, {2,26}, {11,20}, {1,28}, {10,20}, {6,24}, {5,18}, {8,30}, {10,26}, {6,27}, {9,16}, {7,17}, {4,23}, {11,24}, {4,13}, {2,30}, {4,19}, {12,13}, {8,29}, {6,28}, {9,22} }; // ET30.52 // Bipartite(12,18) Valencies [12,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2359296 EdgePairs[30][52]:={ {1,15}, {10,19}, {11,15}, {5,14}, {11,17}, {8,24}, {10,22}, {6,18}, {11,23}, {4,14}, {9,30}, {12,19}, {3,29}, {2,22}, {6,14}, {5,30}, {4,27}, {10,27}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {12,15}, {12,14}, {5,24}, {7,27}, {9,19}, {9,21}, {12,18}, {3,30}, {11,22}, {12,27}, {7,15}, {7,23}, {5,13}, {2,15}, {5,26}, {4,26}, {8,13}, {9,17}, {10,18}, {5,21}, {10,23}, {2,29}, {3,19}, {1,29}, {3,18}, {8,22}, {8,15}, {12,21}, {12,30}, {5,23}, {9,27}, {10,25}, {2,16}, {1,22}, {1,16}, {6,21}, {10,13}, {2,17}, {8,21}, {4,28}, {7,29}, {2,13}, {10,16}, {7,25}, {5,19}, {5,15}, {7,20}, {8,26}, {7,13}, {8,17}, {7,14}, {11,28}, {3,27}, {6,15}, {12,28}, {4,17}, {5,28}, {12,29}, {9,25}, {4,25}, {11,26}, {6,29}, {11,14}, {12,24}, {12,23}, {2,24}, {11,13}, {5,22}, {6,19}, {1,23}, {2,21}, {6,30}, {10,28}, {11,19}, {7,18}, {4,22}, {9,28}, {10,14}, {3,28}, {3,26}, {5,17}, {8,16}, {8,20}, {6,20}, {7,16}, {9,26}, {11,21}, {3,21}, {1,14}, {11,30}, {9,18}, {10,17}, {1,20}, {1,27}, {7,22}, {3,16}, {1,13}, {4,18}, {3,25}, {8,25}, {9,29}, {2,26}, {3,20}, {2,25}, {3,17}, {6,24}, {8,30}, {10,26}, {6,27}, {9,16}, {4,23}, {11,24}, {4,13}, {2,30}, {1,18}, {12,20}, {4,19}, {9,20}, {1,24}, {8,29}, {6,28} }; // ET30.53 // Bipartite(12,18) Valencies [12,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 221184 EdgePairs[30][53]:={ {1,15}, {7,19}, {10,21}, {8,24}, {12,26}, {10,22}, {6,18}, {11,23}, {4,14}, {3,29}, {5,30}, {4,27}, {12,16}, {10,27}, {7,24}, {11,29}, {1,25}, {6,13}, {12,15}, {12,17}, {12,14}, {12,22}, {5,24}, {6,25}, {9,19}, {11,22}, {7,23}, {7,15}, {5,13}, {2,28}, {12,25}, {2,19}, {2,18}, {5,26}, {4,26}, {8,14}, {9,17}, {10,18}, {6,22}, {5,21}, {3,19}, {10,30}, {1,29}, {7,28}, {8,15}, {12,21}, {12,30}, {2,14}, {9,27}, {2,23}, {3,13}, {10,25}, {2,16}, {1,22}, {1,16}, {6,21}, {10,13}, {2,17}, {8,18}, {8,21}, {4,28}, {7,29}, {3,14}, {10,16}, {7,25}, {3,22}, {5,19}, {5,15}, {7,20}, {8,26}, {3,23}, {8,17}, {5,29}, {7,14}, {11,28}, {6,15}, {11,18}, {7,30}, {4,17}, {5,28}, {9,25}, {4,15}, {9,15}, {10,29}, {11,14}, {12,24}, {12,23}, {11,13}, {5,22}, {2,27}, {6,19}, {1,23}, {2,21}, {6,30}, {8,27}, {11,19}, {5,20}, {4,22}, {9,28}, {3,28}, {3,26}, {5,17}, {9,24}, {8,20}, {8,23}, {7,16}, {6,16}, {9,26}, {11,21}, {1,14}, {11,30}, {9,18}, {10,17}, {11,27}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {9,29}, {2,26}, {3,20}, {7,21}, {11,20}, {2,25}, {3,17}, {10,20}, {6,24}, {8,30}, {10,26}, {6,27}, {9,16}, {4,23}, {4,13}, {2,30}, {1,18}, {4,19}, {4,24}, {12,13}, {9,20}, {1,24}, {8,29}, {6,28} }; // ET30.54 // Bipartite(15,15) Valencies [12,12] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[30][54]:={ {11,17}, {10,25}, {10,24}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {14,19}, {15,24}, {4,30}, {11,25}, {8,30}, {2,23}, {12,22}, {4,29}, {1,27}, {3,25}, {10,23}, {4,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {1,30}, {14,28}, {4,23}, {8,27}, {13,29}, {13,16}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {11,28}, {6,29}, {3,17}, {8,16}, {15,29}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,20}, {14,21}, {9,26}, {9,27}, {12,20}, {9,19}, {5,25}, {15,26}, {7,25}, {10,28}, {14,24}, {1,22}, {6,30}, {5,23}, {10,29}, {4,21}, {13,22}, {15,19}, {10,21}, {2,20}, {14,16}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {9,25}, {7,26}, {5,18}, {11,23}, {1,23}, {11,29}, {6,24}, {5,30}, {7,17}, {5,24}, {13,23}, {12,28}, {8,22}, {13,28}, {15,20}, {9,20}, {3,27}, {4,28}, {15,17}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {13,30}, {2,17}, {12,27}, {14,17}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {13,24}, {11,24}, {6,27}, {12,19}, {6,26}, {12,30}, {3,23}, {3,21}, {1,25}, {7,29}, {9,30}, {13,27}, {14,20}, {7,28}, {3,16}, {13,26}, {11,26}, {11,16}, {13,19}, {7,23}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {2,22}, {1,16}, {15,22}, {9,17}, {10,18}, {8,24}, {6,25}, {5,26}, {8,18}, {4,18}, {15,28}, {10,19}, {4,25}, {4,20}, {12,24}, {8,20}, {3,28}, {7,27}, {15,23}, {7,24}, {10,20}, {5,19}, {6,20}, {5,21}, {2,30}, {13,17}, {15,30}, {7,19}, {4,17}, {9,21}, {9,16}, {14,27}, {8,29}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET30.55 // Bipartite(15,15) Valencies [12,12] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 14511882240 EdgePairs[30][55]:={ {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {4,24}, {14,19}, {15,24}, {4,26}, {3,22}, {4,16}, {11,25}, {8,30}, {12,22}, {8,28}, {4,29}, {3,25}, {10,23}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {1,30}, {14,28}, {4,23}, {8,27}, {13,16}, {10,22}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {15,29}, {6,21}, {2,25}, {14,23}, {5,22}, {4,22}, {9,29}, {1,18}, {7,20}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {5,25}, {7,25}, {10,28}, {14,24}, {15,27}, {6,30}, {12,16}, {5,23}, {10,29}, {4,21}, {3,20}, {13,22}, {15,19}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {7,16}, {7,26}, {5,18}, {11,23}, {1,23}, {11,29}, {6,24}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,25}, {8,22}, {13,25}, {13,28}, {15,20}, {1,28}, {3,27}, {4,28}, {15,17}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {13,30}, {2,17}, {12,27}, {14,17}, {8,21}, {1,24}, {14,18}, {14,22}, {11,24}, {12,19}, {6,26}, {12,30}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {13,27}, {3,16}, {11,26}, {13,26}, {15,18}, {11,16}, {2,21}, {3,30}, {9,18}, {10,17}, {2,29}, {10,27}, {1,26}, {2,22}, {1,16}, {15,22}, {9,17}, {10,18}, {6,25}, {5,27}, {8,18}, {4,18}, {15,28}, {11,19}, {10,19}, {12,24}, {8,20}, {3,28}, {7,27}, {15,23}, {7,24}, {9,24}, {10,20}, {5,19}, {6,20}, {2,30}, {13,17}, {15,30}, {13,20}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {11,18}, {12,21}, {14,29}, {14,26} }; // ET30.56 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[30][56]:={ {11,17}, {21,23}, {2,24}, {4,27}, {8,12}, {15,24}, {3,22}, {23,27}, {1,10}, {16,27}, {2,23}, {1,13}, {8,28}, {4,29}, {24,27}, {23,28}, {3,15}, {19,24}, {17,20}, {16,19}, {2,19}, {1,19}, {2,4}, {25,30}, {17,24}, {1,21}, {16,25}, {18,21}, {8,10}, {8,25}, {2,14}, {16,23}, {6,11}, {8,27}, {3,5}, {13,16}, {9,11}, {10,15}, {15,16}, {15,25}, {19,28}, {14,23}, {7,12}, {4,10}, {26,28}, {8,19}, {9,29}, {7,11}, {7,20}, {3,14}, {9,26}, {18,20}, {19,30}, {12,20}, {27,30}, {1,5}, {5,11}, {2,10}, {5,29}, {9,19}, {27,29}, {26,29}, {19,22}, {6,8}, {5,25}, {11,15}, {11,13}, {17,23}, {15,26}, {3,12}, {25,28}, {24,25}, {1,22}, {6,12}, {12,13}, {6,30}, {23,26}, {12,16}, {3,20}, {13,22}, {10,21}, {2,13}, {2,20}, {1,29}, {7,30}, {8,17}, {11,21}, {9,25}, {7,16}, {7,26}, {3,4}, {1,12}, {1,23}, {5,30}, {2,6}, {7,17}, {5,7}, {18,24}, {20,28}, {9,10}, {5,14}, {9,20}, {18,26}, {4,15}, {4,13}, {1,28}, {18,27}, {3,11}, {20,22}, {4,7}, {4,28}, {22,29}, {16,22}, {6,15}, {20,29}, {22,25}, {14,17}, {8,21}, {4,9}, {14,18}, {14,22}, {13,24}, {17,25}, {6,27}, {12,19}, {6,26}, {20,23}, {21,29}, {21,30}, {12,14}, {17,19}, {3,21}, {6,9}, {1,15}, {6,28}, {6,14}, {9,30}, {13,27}, {2,11}, {14,25}, {16,21}, {7,28}, {13,26}, {15,18}, {22,26}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {5,8}, {18,22}, {5,10}, {5,26}, {8,18}, {11,19}, {4,25}, {24,29}, {4,12}, {5,13}, {3,28}, {7,27}, {15,23}, {10,20}, {1,6}, {17,26}, {10,14}, {21,24}, {2,30}, {13,17}, {22,30}, {9,16}, {14,27}, {7,21}, {8,29}, {12,18}, {24,28}, {11,18}, {23,30}, {10,16} }; // ET30.57 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 23592960 EdgePairs[30][57]:={ {11,17}, {21,23}, {1,11}, {10,25}, {5,17}, {2,24}, {9,28}, {12,29}, {13,21}, {4,24}, {3,22}, {4,16}, {1,10}, {4,30}, {16,27}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,15}, {10,26}, {2,15}, {4,19}, {16,19}, {25,29}, {5,20}, {25,30}, {17,24}, {16,18}, {2,9}, {6,7}, {2,14}, {6,11}, {4,23}, {8,27}, {13,29}, {13,16}, {9,11}, {10,22}, {6,22}, {6,21}, {1,7}, {5,22}, {4,22}, {8,19}, {7,20}, {14,21}, {19,26}, {12,17}, {9,26}, {9,27}, {27,30}, {5,11}, {2,10}, {9,19}, {27,29}, {26,29}, {14,30}, {6,8}, {17,23}, {3,12}, {10,28}, {22,27}, {24,25}, {15,27}, {21,27}, {6,12}, {23,26}, {4,21}, {3,20}, {13,22}, {15,19}, {10,21}, {2,13}, {14,16}, {6,18}, {28,29}, {7,30}, {24,26}, {2,16}, {9,25}, {1,12}, {14,15}, {5,18}, {1,23}, {11,29}, {11,30}, {17,27}, {5,7}, {23,25}, {1,9}, {13,25}, {18,24}, {15,20}, {5,14}, {9,20}, {18,26}, {4,15}, {18,27}, {3,11}, {15,17}, {10,12}, {3,29}, {9,22}, {13,30}, {17,28}, {5,12}, {3,19}, {1,24}, {22,23}, {14,22}, {17,25}, {12,30}, {3,23}, {8,23}, {18,25}, {20,25}, {3,21}, {2,7}, {9,12}, {6,19}, {22,28}, {13,15}, {7,29}, {1,15}, {18,23}, {6,14}, {2,11}, {10,11}, {14,25}, {16,17}, {7,28}, {28,30}, {22,24}, {3,16}, {13,26}, {15,18}, {7,23}, {3,30}, {20,26}, {3,24}, {18,28}, {10,27}, {1,16}, {5,8}, {16,20}, {8,24}, {19,25}, {15,28}, {10,19}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {8,20}, {7,27}, {7,24}, {2,12}, {1,14}, {2,8}, {10,20}, {17,26}, {5,19}, {6,20}, {21,24}, {5,21}, {6,13}, {7,19}, {21,28}, {9,21}, {16,28}, {8,29}, {12,18}, {11,18}, {14,29}, {14,26}, {26,30} }; // ET30.58 // Non-bipartite Valency 12 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 1934917632000000 EdgePairs[30][58]:={ {11,17}, {10,24}, {1,20}, {2,24}, {11,20}, {4,27}, {7,15}, {4,24}, {16,26}, {18,29}, {4,26}, {3,22}, {4,30}, {16,27}, {2,23}, {12,22}, {4,29}, {1,27}, {3,25}, {10,23}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {16,25}, {11,14}, {2,28}, {1,30}, {8,15}, {14,28}, {4,23}, {13,29}, {16,29}, {10,15}, {10,22}, {6,22}, {15,25}, {6,29}, {8,16}, {16,30}, {15,29}, {6,21}, {2,25}, {5,22}, {4,22}, {8,19}, {7,20}, {12,17}, {12,20}, {5,29}, {9,19}, {8,14}, {14,30}, {5,25}, {11,15}, {11,13}, {15,26}, {11,22}, {7,13}, {9,14}, {1,22}, {15,27}, {12,13}, {6,30}, {12,16}, {5,23}, {4,21}, {3,20}, {10,21}, {2,20}, {1,29}, {8,17}, {18,30}, {11,21}, {7,16}, {11,23}, {1,23}, {6,24}, {5,30}, {7,17}, {17,30}, {5,24}, {17,27}, {8,13}, {8,22}, {13,25}, {13,28}, {9,20}, {18,26}, {1,28}, {18,27}, {7,14}, {3,27}, {4,28}, {10,13}, {3,29}, {6,23}, {3,26}, {5,28}, {9,22}, {13,30}, {17,28}, {9,13}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {17,25}, {12,19}, {6,26}, {3,23}, {8,23}, {18,25}, {12,14}, {17,29}, {3,21}, {1,25}, {6,19}, {12,15}, {6,28}, {13,27}, {14,25}, {13,26}, {11,16}, {7,23}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {18,28}, {1,26}, {2,22}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {15,28}, {11,19}, {10,19}, {4,25}, {4,20}, {12,24}, {8,20}, {3,28}, {7,24}, {9,24}, {10,20}, {17,26}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {15,30}, {7,19}, {9,21}, {9,16}, {16,28}, {9,23}, {7,21}, {14,27}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16} }; // ET30.59 // Bipartite(9,21) Valencies [14,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 165919186944000 EdgePairs[30][59]:={ {9,13}, {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {4,14}, {1,11}, {9,30}, {5,30}, {2,11}, {2,20}, {1,25}, {4,16}, {6,13}, {9,12}, {5,24}, {6,25}, {9,19}, {9,21}, {3,30}, {7,23}, {3,10}, {9,10}, {2,18}, {2,15}, {5,26}, {4,26}, {8,14}, {7,11}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {3,18}, {7,28}, {8,15}, {7,10}, {2,14}, {5,23}, {4,20}, {9,27}, {2,23}, {1,10}, {7,26}, {1,17}, {3,13}, {1,22}, {1,16}, {6,21}, {2,17}, {8,18}, {8,21}, {4,28}, {7,29}, {4,29}, {7,25}, {3,22}, {5,15}, {7,20}, {8,26}, {7,13}, {8,17}, {5,29}, {7,14}, {3,27}, {6,15}, {1,19}, {8,11}, {4,17}, {9,25}, {4,25}, {9,15}, {1,26}, {2,24}, {4,11}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {6,30}, {8,27}, {2,12}, {4,22}, {5,20}, {9,28}, {3,28}, {3,24}, {5,17}, {9,24}, {3,12}, {8,20}, {8,23}, {7,16}, {6,16}, {3,21}, {1,14}, {9,18}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {3,25}, {2,26}, {5,12}, {1,28}, {6,24}, {5,18}, {8,30}, {6,27}, {9,16}, {7,17}, {4,23}, {4,13}, {2,30}, {4,19}, {4,10}, {8,12}, {8,29}, {6,28}, {9,22} }; // ET30.60 // Bipartite(15,15) Valencies [14,14] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 2615348736000 EdgePairs[30][60]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {4,24}, {14,19}, {15,24}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {8,28}, {4,29}, {1,27}, {3,25}, {10,23}, {10,26}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {1,30}, {14,28}, {4,23}, {8,27}, {13,29}, {13,16}, {10,22}, {15,16}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {15,29}, {6,21}, {2,25}, {14,23}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {7,20}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {9,19}, {14,30}, {5,25}, {15,26}, {11,22}, {7,25}, {10,28}, {14,24}, {1,22}, {15,27}, {6,30}, {12,16}, {5,23}, {10,29}, {4,21}, {3,20}, {13,22}, {15,19}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {5,24}, {13,23}, {12,28}, {12,25}, {13,25}, {13,28}, {15,20}, {1,28}, {3,27}, {4,28}, {15,17}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {13,30}, {2,17}, {12,27}, {8,21}, {3,19}, {1,24}, {14,18}, {14,22}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {13,27}, {14,20}, {15,21}, {14,25}, {11,26}, {13,26}, {15,18}, {11,16}, {7,23}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {15,22}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {15,28}, {11,19}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {15,23}, {7,24}, {9,24}, {10,20}, {5,19}, {6,20}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {8,29}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET30.61 // Bipartite(12,18) Valencies [15,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2149908480 EdgePairs[30][61]:={ {11,17}, {10,25}, {5,17}, {2,24}, {11,20}, {6,16}, {4,27}, {7,15}, {4,26}, {4,16}, {8,30}, {2,23}, {1,13}, {12,22}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {1,30}, {4,23}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {11,15}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {12,13}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,21}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {12,28}, {12,25}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,27}, {4,28}, {10,13}, {3,29}, {3,26}, {5,28}, {8,26}, {12,26}, {6,15}, {2,17}, {9,13}, {12,27}, {3,19}, {1,24}, {6,27}, {11,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {7,28}, {11,26}, {7,23}, {11,16}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {2,22}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {10,19}, {4,25}, {4,20}, {8,20}, {12,24}, {7,27}, {7,24}, {9,24}, {10,20}, {5,15}, {10,14}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,23}, {7,21}, {8,29}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET30.62 // Bipartite(15,15) Valencies [15,15] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 3420024505448398848000000 EdgePairs[30][62]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {4,24}, {14,19}, {15,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {8,28}, {4,29}, {1,27}, {3,25}, {10,23}, {10,26}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {1,30}, {14,28}, {4,23}, {8,27}, {13,29}, {13,16}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {15,29}, {6,21}, {2,25}, {14,23}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {14,30}, {5,25}, {15,26}, {11,22}, {7,25}, {10,28}, {14,24}, {1,22}, {15,27}, {6,30}, {12,16}, {5,23}, {10,29}, {4,21}, {3,20}, {13,22}, {15,19}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {15,20}, {9,20}, {1,28}, {3,27}, {4,28}, {15,17}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {13,30}, {2,17}, {12,27}, {14,17}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {13,27}, {14,20}, {15,21}, {14,25}, {7,28}, {3,16}, {11,26}, {13,26}, {15,18}, {11,16}, {7,23}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {15,22}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {15,28}, {11,19}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {15,23}, {7,24}, {9,24}, {10,20}, {5,19}, {6,20}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {8,29}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET30.63 // Bipartite(6,24) Valencies [16,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3146319396864000 EdgePairs[30][63]:={ {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {5,30}, {4,8}, {3,7}, {2,11}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {6,25}, {6,7}, {3,30}, {3,10}, {2,18}, {6,9}, {2,15}, {5,26}, {4,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {3,18}, {2,14}, {5,23}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {1,22}, {1,16}, {6,21}, {2,17}, {4,28}, {3,9}, {4,29}, {3,22}, {5,15}, {5,29}, {3,27}, {6,15}, {1,19}, {4,17}, {4,25}, {2,9}, {1,26}, {2,24}, {4,11}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {1,7}, {6,30}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,24}, {5,17}, {3,12}, {6,16}, {3,21}, {1,14}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {3,25}, {2,26}, {5,12}, {1,28}, {6,24}, {5,18}, {6,27}, {4,23}, {1,8}, {4,13}, {2,30}, {4,19}, {4,10}, {6,28} }; // ET30.64 // Bipartite(10,20) Valencies [16,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 30576476160 EdgePairs[30][64]:={ {1,11}, {2,24}, {5,17}, {10,25}, {6,16}, {4,27}, {7,15}, {4,24}, {4,26}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {1,21}, {8,25}, {2,28}, {2,14}, {8,15}, {6,11}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,26}, {9,27}, {5,11}, {9,19}, {8,14}, {5,25}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {9,25}, {1,12}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {8,13}, {9,20}, {4,15}, {1,28}, {3,11}, {7,14}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {2,17}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {9,12}, {6,19}, {7,29}, {6,28}, {6,14}, {9,30}, {10,11}, {7,28}, {3,16}, {7,23}, {3,30}, {10,17}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {5,27}, {5,26}, {8,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,27}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {8,29}, {7,18}, {10,16}, {5,16} }; // ET30.65 // Bipartite(14,16) Valencies [16,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1824013069572479385600000 EdgePairs[30][65]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {7,15}, {4,24}, {14,19}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {8,28}, {4,29}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {1,30}, {8,15}, {14,28}, {4,23}, {8,27}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {14,23}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {14,30}, {5,25}, {11,15}, {11,22}, {7,25}, {10,28}, {14,24}, {1,22}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {13,22}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {14,15}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {9,20}, {4,15}, {1,28}, {3,27}, {4,28}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {13,30}, {2,17}, {12,27}, {14,17}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {12,15}, {9,30}, {13,27}, {14,20}, {14,25}, {7,28}, {3,16}, {11,26}, {13,26}, {7,23}, {11,16}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {9,24}, {10,20}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {8,29}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET30.66 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 23592960 EdgePairs[30][66]:={ {1,11}, {2,24}, {1,20}, {10,24}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {7,15}, {4,24}, {8,12}, {15,24}, {16,26}, {18,29}, {4,26}, {3,22}, {16,27}, {8,30}, {2,23}, {12,22}, {8,28}, {20,27}, {3,13}, {3,25}, {10,23}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {5,20}, {20,21}, {2,26}, {1,21}, {17,24}, {16,25}, {8,25}, {1,30}, {8,15}, {6,11}, {16,23}, {20,30}, {4,23}, {8,27}, {13,29}, {10,15}, {10,22}, {19,21}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {19,28}, {2,25}, {7,12}, {14,23}, {1,17}, {4,22}, {9,29}, {1,18}, {7,11}, {3,14}, {14,21}, {19,26}, {16,24}, {19,30}, {9,27}, {5,11}, {5,29}, {9,19}, {8,14}, {19,29}, {14,30}, {19,22}, {5,25}, {15,26}, {17,23}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {14,24}, {1,22}, {15,27}, {6,12}, {6,30}, {5,23}, {4,21}, {10,29}, {3,20}, {13,22}, {10,21}, {2,20}, {1,29}, {7,30}, {8,17}, {2,16}, {18,30}, {11,21}, {7,16}, {7,26}, {1,12}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {17,30}, {8,11}, {11,30}, {5,24}, {17,27}, {13,23}, {12,28}, {8,13}, {8,22}, {13,25}, {18,24}, {20,28}, {5,14}, {9,20}, {18,26}, {4,13}, {18,27}, {3,11}, {7,14}, {3,27}, {20,22}, {4,28}, {10,13}, {6,23}, {3,26}, {5,28}, {8,26}, {16,22}, {9,22}, {6,15}, {13,30}, {2,17}, {17,28}, {20,29}, {9,13}, {12,27}, {5,12}, {8,21}, {3,19}, {1,24}, {12,23}, {14,22}, {6,27}, {11,24}, {13,24}, {17,25}, {6,26}, {12,30}, {3,23}, {18,25}, {17,29}, {20,25}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {18,23}, {6,14}, {9,30}, {2,11}, {15,21}, {14,25}, {16,21}, {7,28}, {13,26}, {2,21}, {9,18}, {10,17}, {20,26}, {3,24}, {2,29}, {11,27}, {18,28}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {15,22}, {9,17}, {10,18}, {6,25}, {5,27}, {19,25}, {5,26}, {8,18}, {4,18}, {15,28}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {12,24}, {7,27}, {15,23}, {2,12}, {9,24}, {10,20}, {17,26}, {5,15}, {10,14}, {5,19}, {6,20}, {9,15}, {2,30}, {6,13}, {2,18}, {4,17}, {9,21}, {9,16}, {16,28}, {9,23}, {7,21}, {8,29}, {19,27}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET30.67 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 23592960 EdgePairs[30][67]:={ {1,11}, {10,25}, {2,24}, {10,24}, {6,16}, {4,27}, {12,29}, {14,19}, {15,24}, {16,26}, {18,29}, {3,22}, {23,29}, {4,16}, {4,30}, {16,27}, {2,23}, {1,13}, {12,22}, {3,9}, {8,28}, {4,29}, {20,27}, {3,15}, {10,23}, {10,26}, {17,20}, {4,19}, {7,22}, {5,20}, {2,26}, {24,30}, {1,21}, {16,25}, {11,14}, {17,21}, {18,21}, {8,25}, {6,7}, {2,14}, {1,30}, {16,23}, {14,28}, {20,30}, {8,27}, {13,29}, {10,15}, {15,25}, {3,18}, {11,28}, {10,30}, {3,17}, {19,28}, {2,25}, {14,23}, {4,10}, {1,17}, {1,7}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {16,24}, {9,26}, {18,20}, {19,30}, {9,19}, {8,14}, {19,29}, {14,30}, {6,8}, {5,25}, {11,15}, {11,13}, {15,26}, {3,12}, {11,22}, {7,13}, {7,25}, {14,24}, {22,27}, {24,25}, {1,22}, {15,27}, {21,27}, {12,13}, {23,26}, {12,16}, {5,23}, {10,29}, {4,21}, {21,26}, {3,20}, {2,13}, {1,29}, {24,26}, {8,17}, {18,30}, {11,21}, {9,25}, {7,26}, {1,12}, {1,23}, {11,23}, {6,24}, {11,29}, {7,17}, {17,30}, {11,30}, {21,25}, {5,24}, {5,7}, {13,23}, {12,28}, {23,25}, {8,13}, {8,22}, {20,28}, {13,28}, {5,14}, {9,20}, {18,26}, {4,15}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {5,28}, {8,26}, {16,22}, {6,15}, {13,30}, {2,17}, {20,29}, {12,27}, {22,25}, {8,21}, {3,19}, {4,9}, {1,24}, {12,23}, {6,27}, {11,24}, {13,24}, {17,25}, {6,26}, {12,30}, {18,19}, {18,25}, {12,14}, {17,29}, {3,21}, {17,19}, {2,7}, {1,25}, {6,19}, {22,28}, {6,9}, {6,28}, {12,15}, {6,14}, {9,30}, {2,11}, {13,27}, {14,20}, {15,21}, {16,21}, {7,28}, {3,16}, {22,26}, {11,16}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {2,29}, {11,27}, {1,26}, {2,22}, {15,22}, {5,8}, {18,22}, {9,17}, {10,18}, {6,25}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {15,28}, {5,9}, {10,19}, {4,11}, {1,8}, {24,29}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {12,24}, {7,27}, {15,23}, {2,12}, {1,14}, {9,24}, {2,8}, {10,20}, {17,26}, {5,15}, {5,19}, {6,20}, {17,22}, {9,15}, {2,30}, {6,13}, {13,20}, {2,18}, {7,19}, {21,28}, {4,17}, {9,16}, {16,28}, {9,23}, {7,21}, {14,27}, {19,27}, {12,21}, {14,29}, {23,30}, {7,18}, {10,16}, {5,16} }; // ET30.68 // Bipartite(13,17) Valencies [17,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2214873013052296396800000 EdgePairs[30][68]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {8,28}, {4,29}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {1,30}, {8,15}, {4,23}, {8,27}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {5,25}, {11,15}, {11,22}, {9,14}, {7,25}, {10,28}, {1,22}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {13,22}, {10,21}, {2,20}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {5,14}, {9,20}, {4,15}, {1,28}, {7,14}, {3,27}, {4,28}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {13,30}, {2,17}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {13,27}, {7,28}, {3,16}, {11,26}, {13,26}, {7,23}, {11,16}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {13,14}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {9,24}, {1,14}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {13,17}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {8,29}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET30.69 // Bipartite(3,27) Valencies [18,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 286708355039232000 EdgePairs[30][69]:={ {2,11}, {3,22}, {1,26}, {2,14}, {1,14}, {2,26}, {3,12}, {1,29}, {2,30}, {2,29}, {2,24}, {1,10}, {3,21}, {3,27}, {2,6}, {1,4}, {1,20}, {3,24}, {3,9}, {2,12}, {2,21}, {1,7}, {3,4}, {3,16}, {3,7}, {3,28}, {2,20}, {1,16}, {3,15}, {2,18}, {3,25}, {3,19}, {3,30}, {2,15}, {3,18}, {2,5}, {1,5}, {2,27}, {1,17}, {3,6}, {1,28}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,22}, {2,8}, {1,23}, {1,11}, {1,25}, {3,10} }; // ET30.70 // Bipartite(10,20) Valencies [18,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3715891200 EdgePairs[30][70]:={ {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {8,30}, {2,23}, {1,13}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {2,14}, {1,30}, {8,15}, {6,11}, {4,23}, {8,27}, {9,11}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {9,19}, {8,14}, {5,25}, {3,12}, {7,25}, {10,28}, {6,12}, {6,30}, {5,23}, {10,29}, {3,20}, {2,13}, {10,21}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {3,29}, {6,23}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {10,11}, {7,28}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {4,18}, {4,25}, {10,19}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,27}, {7,24}, {2,12}, {1,14}, {10,20}, {5,15}, {10,14}, {6,20}, {5,21}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {7,18}, {10,16}, {5,16} }; // ET30.71 // Bipartite(12,18) Valencies [18,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3066747248841641164800000 EdgePairs[30][71]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {12,22}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {1,30}, {8,15}, {4,23}, {8,27}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {12,13}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {12,28}, {12,25}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {6,15}, {2,17}, {9,13}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {5,13}, {8,20}, {3,28}, {12,24}, {7,27}, {7,24}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET30.72 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 21772800 EdgePairs[30][72]:={ {13,21}, {5,7}, {6,25}, {23,29}, {5,22}, {10,18}, {19,26}, {3,8}, {4,28}, {11,25}, {3,26}, {8,26}, {5,11}, {6,15}, {11,15}, {5,15}, {1,19}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {21,28}, {16,28}, {7,30}, {2,7}, {6,9}, {13,27}, {24,28}, {11,17}, {1,12}, {9,11}, {11,27}, {3,18}, {9,18}, {12,28}, {2,25}, {4,24}, {2,6}, {8,13}, {1,17}, {1,9}, {1,10}, {4,13}, {27,28}, {12,20}, {1,13}, {13,30}, {12,26}, {2,5}, {7,27}, {2,10}, {19,22}, {10,26}, {2,17}, {17,20}, {10,20}, {17,26}, {13,24}, {24,30}, {22,25}, {12,23}, {12,13}, {13,20}, {16,25}, {15,19}, {4,23}, {13,26}, {13,16}, {2,29}, {7,15}, {9,29}, {9,20}, {8,19}, {5,27}, {15,28}, {6,17}, {6,10}, {4,7}, {8,18}, {4,18}, {12,24}, {11,22}, {5,12}, {6,27}, {4,9}, {6,12}, {25,29}, {17,29}, {18,19}, {20,25}, {7,19}, {1,30}, {2,13}, {13,18}, {19,27}, {8,10}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,23}, {6,16}, {18,22}, {21,25}, {19,30}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {5,14}, {3,29}, {12,17}, {2,23}, {20,22}, {22,29}, {15,23}, {9,22}, {4,11}, {19,24}, {6,8}, {11,13}, {25,30}, {6,30}, {1,22}, {10,29}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {20,30}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {14,27}, {7,28}, {12,18}, {13,29}, {17,30}, {10,22}, {10,30}, {7,23}, {6,22}, {12,29}, {15,24}, {3,7}, {16,26}, {12,25}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {6,23}, {15,17}, {4,29}, {1,5}, {19,29}, {24,27}, {9,24}, {17,22}, {2,19}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {26,30}, {18,30}, {2,28}, {8,29}, {7,21}, {14,16}, {2,11}, {10,15}, {11,30}, {18,28}, {5,24}, {15,29}, {16,20}, {8,11}, {14,19}, {20,28}, {18,27}, {26,28}, {3,14}, {5,26}, {3,11}, {5,29}, {4,25}, {14,30}, {11,19}, {1,4}, {1,8}, {20,27}, {8,14}, {7,10}, {27,29}, {3,6}, {3,15}, {7,25}, {7,22}, {5,21}, {9,15}, {21,29}, {17,24}, {20,23}, {17,21}, {23,30}, {6,28}, {16,23}, {18,23}, {1,15}, {14,25}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {15,18}, {10,27}, {3,4}, {7,17}, {17,27}, {6,21}, {4,26}, {15,20}, {1,28}, {16,24}, {3,27}, {9,27}, {8,28}, {4,20}, {8,20}, {1,27}, {15,26}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {22,28}, {8,25}, {2,9}, {2,14}, {15,25}, {5,30}, {21,23} }; // ET30.73 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 7255941120 EdgePairs[30][73]:={ {19,28}, {5,7}, {6,25}, {23,29}, {9,17}, {19,26}, {9,10}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {6,15}, {11,15}, {21,30}, {3,19}, {5,15}, {1,19}, {3,23}, {3,20}, {2,18}, {1,21}, {3,21}, {21,28}, {16,28}, {11,14}, {7,30}, {6,9}, {21,22}, {6,14}, {24,28}, {11,29}, {9,11}, {1,20}, {3,18}, {8,16}, {20,26}, {9,18}, {12,28}, {2,25}, {2,6}, {8,30}, {8,13}, {8,12}, {1,17}, {4,13}, {20,24}, {27,28}, {7,11}, {12,20}, {1,13}, {2,5}, {7,27}, {19,22}, {26,29}, {2,17}, {23,28}, {20,29}, {10,20}, {17,26}, {1,24}, {13,24}, {24,30}, {2,15}, {12,23}, {12,13}, {16,25}, {13,16}, {1,26}, {3,17}, {7,15}, {27,30}, {18,29}, {9,29}, {18,26}, {1,18}, {5,27}, {7,14}, {6,10}, {4,7}, {8,18}, {12,24}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {4,9}, {6,12}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {20,25}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {11,21}, {8,17}, {16,29}, {3,16}, {2,24}, {11,23}, {3,24}, {14,23}, {18,22}, {21,25}, {19,30}, {7,12}, {4,10}, {9,26}, {5,14}, {2,23}, {10,13}, {20,22}, {22,29}, {10,19}, {15,23}, {4,11}, {3,25}, {19,24}, {17,28}, {6,8}, {11,13}, {25,30}, {22,30}, {2,27}, {12,30}, {1,22}, {11,24}, {1,6}, {5,19}, {10,29}, {18,25}, {13,22}, {6,13}, {1,25}, {20,30}, {6,19}, {2,20}, {9,16}, {9,30}, {9,12}, {7,28}, {2,16}, {6,11}, {9,25}, {17,30}, {10,22}, {10,30}, {16,30}, {12,29}, {15,24}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {4,15}, {15,17}, {1,5}, {24,29}, {19,29}, {10,28}, {17,22}, {17,25}, {2,19}, {6,20}, {5,20}, {2,26}, {12,14}, {10,21}, {26,30}, {7,29}, {18,30}, {8,29}, {14,16}, {8,27}, {10,15}, {11,30}, {3,5}, {9,28}, {2,21}, {4,27}, {18,28}, {2,22}, {8,11}, {18,24}, {20,28}, {18,27}, {16,27}, {26,28}, {3,14}, {5,26}, {19,25}, {4,8}, {4,25}, {5,9}, {11,19}, {1,4}, {4,12}, {20,27}, {8,14}, {7,10}, {27,29}, {3,6}, {14,24}, {3,15}, {7,25}, {1,14}, {6,26}, {14,18}, {21,27}, {5,21}, {9,15}, {21,29}, {17,24}, {20,23}, {2,4}, {23,30}, {16,23}, {18,23}, {1,15}, {7,26}, {7,18}, {11,28}, {7,16}, {1,23}, {10,24}, {11,20}, {15,18}, {3,4}, {15,16}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {16,24}, {3,27}, {9,27}, {5,10}, {8,28}, {4,20}, {1,27}, {5,13}, {5,25}, {17,23}, {10,23}, {4,19}, {14,22}, {7,13}, {9,14}, {14,17}, {25,28}, {10,14}, {21,24}, {12,19}, {21,26}, {22,28}, {8,25}, {12,21}, {6,7}, {2,14}, {21,23} }; // ET30.74 // Bipartite(11,19) Valencies [19,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4855683143999265177600000 EdgePairs[30][74]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {11,12}, {2,28}, {2,14}, {1,30}, {8,15}, {4,23}, {8,27}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,26}, {9,27}, {5,29}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {10,29}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {11,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,27}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET30.75 // Bipartite(5,25) Valencies [20,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2985984000000 EdgePairs[30][75]:={ {3,15}, {4,14}, {1,11}, {3,29}, {2,22}, {5,30}, {4,27}, {2,20}, {4,16}, {1,9}, {3,30}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,21}, {2,29}, {3,19}, {1,29}, {5,6}, {4,12}, {3,18}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {2,23}, {4,7}, {1,17}, {3,13}, {1,22}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {4,29}, {3,9}, {5,15}, {3,23}, {4,30}, {1,19}, {4,21}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {1,23}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {3,21}, {1,14}, {2,8}, {1,27}, {5,11}, {3,16}, {1,13}, {5,10}, {3,25}, {3,8}, {3,20}, {5,12}, {2,25}, {3,6}, {1,28}, {4,9}, {2,7}, {5,18}, {1,8}, {5,16}, {2,30}, {1,21}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET30.76 // Bipartite(6,24) Valencies [20,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 137594142720 EdgePairs[30][76]:={ {1,15}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {3,29}, {2,22}, {6,14}, {5,30}, {4,8}, {4,27}, {3,7}, {2,11}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {6,7}, {3,30}, {2,28}, {2,19}, {2,18}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {3,18}, {2,14}, {5,23}, {3,11}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {4,29}, {3,9}, {5,15}, {6,8}, {3,23}, {5,29}, {3,27}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {5,28}, {4,15}, {4,25}, {2,24}, {4,11}, {5,22}, {6,19}, {1,23}, {5,27}, {1,7}, {6,30}, {5,8}, {2,12}, {4,22}, {5,20}, {3,26}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {3,21}, {2,8}, {1,27}, {5,11}, {1,13}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {5,12}, {2,25}, {1,28}, {3,17}, {4,9}, {6,24}, {2,7}, {5,18}, {6,27}, {4,23}, {1,30}, {5,16}, {4,13}, {1,21}, {2,30}, {1,18}, {4,19}, {4,10}, {1,24}, {6,28} }; // ET30.77 // Bipartite(10,20) Valencies [20,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8828514807271391232000000 EdgePairs[30][77]:={ {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {2,14}, {1,30}, {8,15}, {6,11}, {4,23}, {8,27}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {5,29}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {10,29}, {3,20}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {10,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {7,18}, {10,16}, {5,16} }; // ET30.78 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 286708355039232000000 EdgePairs[30][78]:={ {13,21}, {19,28}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {6,15}, {8,21}, {3,19}, {15,27}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {7,30}, {13,27}, {14,29}, {6,14}, {16,21}, {10,11}, {19,21}, {11,29}, {1,12}, {9,11}, {11,27}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {4,16}, {4,13}, {20,24}, {7,11}, {1,13}, {13,30}, {12,26}, {7,27}, {19,22}, {10,26}, {2,17}, {20,29}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {2,15}, {12,23}, {16,25}, {6,18}, {1,29}, {4,23}, {13,26}, {6,24}, {2,29}, {1,26}, {3,17}, {7,15}, {8,22}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {10,12}, {12,24}, {12,27}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {6,12}, {19,23}, {4,21}, {17,29}, {20,25}, {7,19}, {1,30}, {2,13}, {19,27}, {8,15}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {14,23}, {6,16}, {18,22}, {13,25}, {19,30}, {7,12}, {8,24}, {14,21}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {17,28}, {2,27}, {12,30}, {6,30}, {2,12}, {1,22}, {11,24}, {5,19}, {10,29}, {18,25}, {13,22}, {6,13}, {1,25}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {14,27}, {7,28}, {2,16}, {6,11}, {13,29}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {10,25}, {12,29}, {15,24}, {16,26}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,29}, {19,29}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {2,11}, {14,26}, {10,15}, {11,30}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {15,29}, {2,22}, {8,11}, {18,24}, {18,27}, {20,28}, {16,27}, {3,14}, {5,26}, {19,25}, {3,11}, {5,29}, {4,25}, {14,30}, {3,28}, {4,12}, {20,27}, {8,14}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {5,21}, {9,15}, {17,24}, {20,23}, {17,21}, {6,28}, {16,23}, {18,23}, {1,15}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {5,17}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {10,14}, {20,21}, {8,25}, {12,21}, {2,14}, {11,26}, {15,25}, {5,30} }; // ET30.79 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 86400 EdgePairs[30][79]:={ {13,21}, {19,28}, {5,7}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {11,25}, {4,28}, {3,26}, {8,26}, {5,11}, {16,22}, {6,15}, {8,21}, {21,30}, {5,6}, {3,19}, {15,27}, {1,19}, {12,16}, {3,20}, {2,18}, {3,21}, {16,28}, {21,28}, {7,30}, {13,27}, {6,14}, {24,28}, {19,21}, {10,11}, {11,29}, {11,17}, {1,12}, {9,11}, {11,27}, {6,29}, {1,20}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {2,6}, {4,30}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {13,30}, {12,26}, {3,10}, {2,10}, {19,22}, {3,9}, {10,26}, {20,29}, {17,26}, {1,24}, {13,24}, {24,30}, {2,15}, {12,23}, {13,20}, {16,25}, {15,19}, {1,29}, {6,18}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {13,19}, {3,17}, {7,15}, {8,22}, {18,29}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {4,7}, {4,18}, {10,12}, {12,24}, {25,26}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {2,8}, {6,12}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {7,19}, {1,30}, {2,13}, {19,27}, {8,15}, {14,28}, {8,17}, {16,29}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {3,24}, {14,23}, {18,22}, {13,25}, {19,30}, {8,24}, {4,10}, {9,26}, {14,21}, {5,14}, {3,29}, {2,23}, {10,13}, {20,22}, {22,29}, {10,19}, {15,23}, {9,22}, {4,11}, {3,25}, {17,28}, {22,30}, {12,30}, {6,30}, {1,22}, {11,24}, {5,19}, {10,29}, {18,25}, {13,22}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {14,27}, {7,28}, {12,18}, {2,16}, {13,29}, {9,25}, {17,30}, {10,22}, {16,30}, {7,23}, {6,22}, {12,29}, {15,24}, {3,7}, {12,25}, {3,22}, {5,8}, {23,27}, {4,15}, {6,23}, {15,17}, {24,27}, {7,24}, {10,28}, {17,25}, {2,19}, {6,20}, {5,23}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {2,11}, {14,26}, {11,30}, {9,28}, {2,21}, {4,27}, {5,24}, {15,29}, {8,11}, {18,24}, {18,27}, {20,28}, {16,27}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {5,29}, {4,25}, {14,30}, {5,9}, {11,19}, {1,8}, {4,12}, {20,27}, {8,14}, {3,6}, {3,15}, {7,25}, {1,14}, {14,18}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {20,23}, {17,21}, {23,30}, {6,28}, {16,23}, {1,15}, {14,25}, {15,21}, {14,20}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {15,18}, {10,27}, {5,17}, {15,16}, {15,22}, {4,26}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {4,20}, {8,20}, {1,27}, {5,13}, {25,27}, {17,23}, {10,23}, {15,26}, {4,6}, {14,22}, {3,12}, {7,13}, {14,17}, {25,28}, {10,14}, {12,19}, {23,26}, {20,21}, {22,28}, {8,25}, {2,9}, {12,21}, {2,14} }; // ET30.80 // Bipartite(9,21) Valencies [21,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 18539881095269921587200000 EdgePairs[30][80]:={ {1,11}, {2,24}, {1,20}, {5,17}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {6,11}, {8,15}, {4,23}, {8,27}, {9,11}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,10}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {7,18}, {5,16} }; // ET30.81 // Bipartite(8,22) Valencies [22,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 45319709343993141657600000 EdgePairs[30][81]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {6,11}, {8,15}, {4,23}, {8,27}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {5,11}, {2,10}, {5,29}, {8,14}, {5,25}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {7,16}, {1,12}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {6,15}, {2,17}, {5,12}, {8,21}, {3,19}, {4,9}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {7,24}, {2,12}, {1,14}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {8,29}, {7,18}, {5,16} }; // ET30.82 // Bipartite(7,23) Valencies [23,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 130294164363980282265600000 EdgePairs[30][82]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {4,27}, {7,15}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {7,8}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {6,11}, {4,23}, {6,22}, {3,18}, {6,29}, {3,17}, {6,21}, {2,25}, {7,12}, {4,10}, {1,17}, {5,22}, {4,22}, {1,18}, {7,11}, {3,14}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {7,16}, {1,12}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {6,27}, {6,26}, {3,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {7,18}, {5,16} }; // ET30.83 // Bipartite(6,24) Valencies [24,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 446722849247932396339200000 EdgePairs[30][83]:={ {1,15}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {3,29}, {2,22}, {6,14}, {5,30}, {4,8}, {3,7}, {4,27}, {6,17}, {2,11}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,9}, {6,25}, {6,7}, {3,30}, {5,7}, {5,13}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {6,11}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {5,19}, {5,15}, {6,8}, {3,23}, {5,29}, {3,27}, {4,30}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {6,29}, {2,24}, {4,11}, {5,22}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {1,7}, {6,30}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {6,24}, {2,7}, {5,18}, {6,27}, {4,23}, {1,8}, {1,30}, {5,16}, {4,13}, {1,21}, {2,30}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24}, {6,28} }; // ET30.84 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 23219011584000000 EdgePairs[30][84]:={ {13,21}, {19,28}, {5,7}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {6,15}, {11,15}, {8,21}, {21,30}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {7,30}, {2,7}, {6,9}, {13,27}, {14,29}, {6,14}, {16,21}, {24,28}, {11,29}, {11,17}, {1,12}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {12,20}, {1,13}, {13,30}, {12,26}, {3,10}, {7,27}, {2,10}, {3,9}, {10,26}, {2,17}, {17,20}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {24,30}, {15,30}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {6,18}, {1,29}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {4,18}, {12,24}, {12,27}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {2,8}, {4,9}, {6,12}, {4,21}, {17,29}, {18,19}, {20,25}, {7,19}, {1,30}, {2,13}, {19,27}, {12,15}, {8,15}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {19,30}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {22,29}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {17,28}, {6,8}, {11,13}, {22,30}, {2,27}, {12,30}, {6,30}, {2,12}, {1,22}, {11,24}, {5,19}, {10,29}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {9,30}, {17,19}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {13,29}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {10,25}, {12,29}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {4,15}, {6,23}, {4,29}, {24,29}, {19,29}, {24,27}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {2,11}, {14,26}, {10,15}, {11,30}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {14,19}, {18,27}, {20,28}, {16,27}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {5,29}, {4,25}, {3,28}, {14,30}, {5,9}, {11,19}, {1,8}, {4,12}, {20,27}, {8,14}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {17,21}, {23,30}, {6,28}, {16,23}, {18,23}, {1,15}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {5,17}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {16,19}, {10,14}, {12,19}, {23,26}, {21,26}, {22,28}, {8,25}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {5,30} }; // ET30.85 // Bipartite(5,25) Valencies [25,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1861345205199718318080000000 EdgePairs[30][85]:={ {1,15}, {5,14}, {3,15}, {4,14}, {1,11}, {3,29}, {2,22}, {5,30}, {4,8}, {3,7}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {5,24}, {1,9}, {3,30}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {5,6}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {5,19}, {5,15}, {3,23}, {5,29}, {3,27}, {4,30}, {1,19}, {4,21}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {2,7}, {5,18}, {1,8}, {4,23}, {1,30}, {5,16}, {4,13}, {1,21}, {2,30}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET30.86 // Non-bipartite Valency 25 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 2149908480000000 EdgePairs[30][86]:={ {13,21}, {19,28}, {5,7}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {6,15}, {8,21}, {21,30}, {5,6}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {7,30}, {2,7}, {13,27}, {14,29}, {6,14}, {16,21}, {24,28}, {10,11}, {19,21}, {11,29}, {11,17}, {1,12}, {9,11}, {11,27}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {2,6}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {12,26}, {13,30}, {3,10}, {7,27}, {2,10}, {19,22}, {3,9}, {10,26}, {2,17}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {24,30}, {15,30}, {2,15}, {12,23}, {13,20}, {16,25}, {6,18}, {1,29}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {12,27}, {25,26}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {2,8}, {4,9}, {6,12}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {20,25}, {7,19}, {1,30}, {2,13}, {13,18}, {19,27}, {8,15}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,23}, {6,16}, {18,22}, {13,25}, {19,30}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {20,22}, {22,29}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {17,28}, {25,30}, {22,30}, {2,27}, {12,30}, {6,30}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {10,29}, {18,25}, {13,22}, {6,13}, {1,25}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {13,29}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {10,25}, {12,29}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {4,15}, {6,23}, {15,17}, {4,29}, {24,29}, {19,29}, {24,27}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {2,11}, {14,26}, {10,15}, {11,30}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {8,11}, {18,24}, {14,19}, {18,27}, {20,28}, {16,27}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {5,29}, {4,25}, {3,28}, {14,30}, {5,9}, {11,19}, {1,8}, {4,12}, {20,27}, {8,14}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {20,23}, {17,21}, {23,30}, {6,28}, {16,23}, {18,23}, {1,15}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {15,16}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {25,27}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {25,28}, {10,14}, {12,19}, {23,26}, {21,26}, {20,21}, {22,28}, {8,25}, {2,9}, {12,21}, {2,14}, {11,26}, {15,25}, {5,30} }; // ET30.87 // Bipartite(4,26) Valencies [26,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 9678995067038535254016000000 EdgePairs[30][87]:={ {1,15}, {3,15}, {1,11}, {4,14}, {3,29}, {2,22}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {1,9}, {4,5}, {1,5}, {3,30}, {4,6}, {3,10}, {2,28}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {2,14}, {3,11}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {3,27}, {4,30}, {1,19}, {4,21}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,26}, {2,24}, {4,11}, {2,27}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {1,28}, {3,17}, {4,9}, {2,7}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET30.88 // Bipartite(3,27) Valencies [27,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 65333216702510112964608000000 EdgePairs[30][88]:={ {2,11}, {3,22}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {3,12}, {1,29}, {2,30}, {1,30}, {2,29}, {2,24}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {3,27}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,23}, {3,9}, {3,24}, {2,12}, {2,4}, {3,29}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {1,16}, {2,20}, {3,7}, {3,16}, {3,28}, {3,15}, {3,17}, {2,18}, {1,21}, {3,25}, {3,19}, {3,30}, {2,15}, {3,14}, {2,5}, {3,18}, {1,18}, {3,26}, {1,5}, {1,27}, {1,17}, {2,27}, {3,6}, {2,28}, {2,19}, {1,28}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22}, {3,10} }; // ET30.89 // Non-bipartite Valency 27 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 219419659468800 EdgePairs[30][89]:={ {13,21}, {19,28}, {5,7}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {9,10}, {3,26}, {12,22}, {8,26}, {5,11}, {16,22}, {6,15}, {11,15}, {8,21}, {21,30}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {7,30}, {2,7}, {6,9}, {21,22}, {13,27}, {14,29}, {6,14}, {16,21}, {24,28}, {11,29}, {11,17}, {1,12}, {9,11}, {11,27}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {2,6}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {27,28}, {7,11}, {12,20}, {1,13}, {12,26}, {13,30}, {3,10}, {2,5}, {7,27}, {2,10}, {19,22}, {3,9}, {26,29}, {10,26}, {2,17}, {17,20}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {24,30}, {15,30}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {6,18}, {1,29}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,16}, {1,26}, {13,19}, {3,17}, {7,15}, {8,22}, {27,30}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {4,18}, {12,24}, {12,27}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {2,8}, {4,9}, {6,12}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {18,19}, {20,25}, {7,19}, {1,30}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {19,30}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {20,22}, {22,29}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {17,28}, {6,8}, {11,13}, {25,30}, {22,30}, {2,27}, {12,30}, {6,30}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {10,29}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {9,30}, {17,19}, {9,12}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {13,29}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {10,25}, {12,29}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {4,15}, {6,23}, {15,17}, {4,29}, {1,5}, {24,29}, {19,29}, {24,27}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {26,30}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {2,11}, {14,26}, {10,15}, {11,30}, {3,5}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {8,11}, {18,24}, {14,19}, {18,27}, {20,28}, {16,27}, {1,7}, {26,28}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {5,29}, {4,25}, {3,28}, {14,30}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {20,27}, {8,14}, {7,10}, {27,29}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {20,23}, {2,4}, {17,21}, {23,30}, {6,28}, {16,23}, {18,23}, {1,15}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {3,4}, {15,16}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {25,28}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {22,28}, {8,25}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {5,30}, {21,23} }; // ET30.90 // Bipartite(2,28) Valencies [28,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 609776689223427721003008000000 EdgePairs[30][90]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {1,29}, {2,30}, {1,30}, {2,29}, {2,24}, {2,10}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {2,12}, {2,4}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {1,16}, {2,20}, {2,18}, {1,21}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {2,19}, {1,28}, {2,17}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET30.91 // Non-bipartite Valency 28 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 42849873690624000 EdgePairs[30][91]:={ {13,21}, {19,28}, {5,7}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {5,11}, {16,22}, {1,3}, {6,15}, {11,15}, {8,21}, {21,30}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {7,30}, {2,7}, {6,9}, {13,27}, {14,29}, {6,14}, {16,21}, {24,28}, {10,11}, {19,21}, {11,29}, {11,17}, {1,12}, {9,11}, {11,27}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {2,6}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {1,13}, {12,26}, {13,30}, {3,10}, {2,5}, {7,27}, {8,9}, {2,10}, {19,22}, {3,9}, {26,29}, {10,26}, {2,17}, {17,20}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {24,30}, {15,30}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {28,30}, {6,18}, {1,29}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,16}, {1,26}, {13,19}, {3,17}, {7,15}, {8,22}, {27,30}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {12,27}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {2,8}, {4,9}, {6,12}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {18,19}, {20,25}, {7,19}, {1,30}, {16,18}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,30}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {19,30}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {20,22}, {22,29}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {17,28}, {6,8}, {11,13}, {25,30}, {22,30}, {2,27}, {12,30}, {6,30}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {10,29}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {9,30}, {17,19}, {9,12}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {13,29}, {9,25}, {4,5}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {10,25}, {12,29}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {4,15}, {6,23}, {15,17}, {4,29}, {1,5}, {2,3}, {24,29}, {26,27}, {19,29}, {24,27}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {26,30}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {28,29}, {2,11}, {14,26}, {10,15}, {11,30}, {3,5}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {8,11}, {18,24}, {14,19}, {18,27}, {20,28}, {16,27}, {1,7}, {26,28}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {5,29}, {4,25}, {3,28}, {14,30}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {20,27}, {8,14}, {7,10}, {27,29}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {22,23}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {20,23}, {2,4}, {17,21}, {23,30}, {6,28}, {16,23}, {18,23}, {1,15}, {13,15}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {25,27}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {25,28}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {20,21}, {22,28}, {8,25}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {5,30}, {21,23} }; // ET30.92 // Bipartite(1,29) Valencies [29,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 8841761993739701954543616000000 EdgePairs[30][92]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,12}, {1,2}, {1,3}, {1,17}, {1,30}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,28}, {1,6}, {1,14}, {1,26}, {1,18}, {1,27}, {1,21}, {1,19}, {1,29}, {1,20}, {1,8}, {1,24}, {1,9}, {1,23}, {1,25} }; // ET30.93 // Non-bipartite Valency 29 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 265252859812191058636308480000000 EdgePairs[30][93]:={ {13,21}, {19,28}, {5,7}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {9,10}, {17,18}, {3,26}, {12,22}, {8,26}, {5,11}, {16,22}, {1,3}, {6,15}, {11,15}, {8,21}, {21,30}, {5,6}, {3,19}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {7,30}, {2,7}, {6,9}, {21,22}, {13,27}, {14,29}, {6,14}, {16,21}, {24,28}, {19,20}, {10,11}, {19,21}, {11,29}, {11,17}, {1,12}, {9,11}, {11,27}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {2,25}, {4,24}, {2,6}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {20,24}, {27,28}, {7,11}, {12,20}, {1,13}, {12,26}, {13,30}, {3,10}, {2,5}, {7,27}, {8,9}, {2,10}, {19,22}, {3,9}, {26,29}, {10,26}, {2,17}, {17,20}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {24,30}, {15,30}, {2,15}, {12,23}, {22,25}, {12,13}, {13,20}, {16,25}, {28,30}, {6,18}, {1,29}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,16}, {1,26}, {13,19}, {3,17}, {7,15}, {8,22}, {27,30}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {12,24}, {12,27}, {25,26}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {2,8}, {4,9}, {6,12}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {18,19}, {20,25}, {7,19}, {1,30}, {16,18}, {1,2}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,30}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {19,30}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {20,22}, {22,29}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {3,25}, {19,24}, {17,28}, {6,8}, {11,13}, {25,30}, {22,30}, {2,27}, {12,30}, {6,30}, {2,12}, {1,22}, {11,24}, {1,6}, {5,19}, {7,8}, {10,29}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {9,30}, {17,19}, {9,12}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {13,29}, {9,25}, {4,5}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {10,25}, {12,29}, {15,24}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {5,8}, {23,27}, {4,15}, {6,23}, {15,17}, {13,14}, {4,29}, {1,5}, {2,3}, {24,29}, {26,27}, {19,29}, {24,27}, {7,24}, {10,28}, {9,24}, {29,30}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {26,30}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {28,29}, {2,11}, {14,26}, {10,15}, {11,30}, {3,5}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {8,11}, {18,24}, {14,19}, {18,27}, {20,28}, {16,27}, {1,7}, {26,28}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {5,29}, {4,25}, {3,28}, {14,30}, {5,9}, {11,19}, {1,4}, {4,12}, {1,8}, {20,27}, {8,14}, {7,10}, {27,29}, {3,6}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {22,23}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {20,23}, {2,4}, {17,21}, {23,30}, {6,28}, {16,23}, {18,23}, {1,15}, {13,15}, {14,20}, {14,25}, {15,21}, {11,12}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {3,4}, {15,16}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {25,27}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {3,12}, {9,14}, {7,13}, {14,17}, {25,28}, {16,19}, {10,14}, {21,24}, {12,19}, {23,26}, {21,26}, {20,21}, {22,28}, {8,25}, {23,24}, {2,9}, {12,21}, {6,7}, {2,14}, {11,26}, {15,25}, {5,30}, {21,23} }; // Total number of connected ET graphs of order 30 is 93 // ******************************************************************************************** // Order 31 // ET31.1 // Non-bipartite Valency 2 // Diameter 15 Girth 31 // Twin-free VT AT // Automorphism group of order 62 EdgePairs[31][1]:={ {21,26}, {3,29}, {11,16}, {4,30}, {18,23}, {1,27}, {3,8}, {26,31}, {15,20}, {2,28}, {16,21}, {2,7}, {4,9}, {5,31}, {6,11}, {13,18}, {20,25}, {22,27}, {8,13}, {23,28}, {9,14}, {10,15}, {24,29}, {25,30}, {7,12}, {17,22}, {14,19}, {19,24}, {12,17}, {1,6}, {5,10} }; // ET31.2 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 186 EdgePairs[31][2]:={ {28,29}, {1,26}, {26,31}, {11,16}, {10,15}, {4,9}, {13,19}, {19,24}, {14,19}, {24,29}, {25,26}, {12,18}, {11,17}, {8,9}, {7,12}, {21,22}, {15,20}, {24,30}, {1,2}, {4,10}, {5,10}, {7,8}, {1,6}, {6,31}, {29,30}, {6,12}, {7,13}, {20,21}, {19,25}, {5,11}, {9,15}, {17,22}, {3,8}, {1,31}, {3,9}, {13,14}, {6,7}, {3,29}, {30,31}, {13,18}, {22,28}, {4,30}, {15,21}, {21,27}, {23,29}, {10,16}, {5,31}, {3,4}, {1,7}, {23,24}, {2,7}, {3,28}, {11,12}, {9,10}, {17,18}, {2,3}, {10,11}, {8,13}, {5,6}, {18,19}, {15,16}, {4,5}, {12,13}, {16,21}, {19,20}, {5,30}, {27,28}, {16,22}, {1,27}, {26,27}, {22,23}, {2,27}, {20,25}, {2,28}, {25,31}, {20,26}, {18,23}, {21,26}, {9,14}, {22,27}, {14,20}, {8,14}, {6,11}, {18,24}, {16,17}, {2,8}, {14,15}, {25,30}, {23,28}, {12,17}, {24,25}, {17,23}, {4,29} }; // ET31.3 // Non-bipartite Valency 10 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 310 EdgePairs[31][3]:={ {1,11}, {2,24}, {11,20}, {6,16}, {14,19}, {4,24}, {16,26}, {15,24}, {18,29}, {4,26}, {3,8}, {1,10}, {4,30}, {16,27}, {8,30}, {26,31}, {6,17}, {2,23}, {12,22}, {8,28}, {3,13}, {1,27}, {23,28}, {3,25}, {19,24}, {10,23}, {2,15}, {1,19}, {25,30}, {1,21}, {16,25}, {2,28}, {6,11}, {20,30}, {16,29}, {10,15}, {15,25}, {10,30}, {19,28}, {14,23}, {7,12}, {4,22}, {8,19}, {9,29}, {3,14}, {7,20}, {12,17}, {19,30}, {9,27}, {9,19}, {19,29}, {5,25}, {15,26}, {3,12}, {11,22}, {9,14}, {7,25}, {14,24}, {20,31}, {11,31}, {10,28}, {22,27}, {1,22}, {5,23}, {21,26}, {10,31}, {13,22}, {10,21}, {2,13}, {2,20}, {13,18}, {8,17}, {13,31}, {11,21}, {7,16}, {1,12}, {5,18}, {1,23}, {11,29}, {6,24}, {17,30}, {7,17}, {17,27}, {13,23}, {12,25}, {8,13}, {15,20}, {5,14}, {9,20}, {4,15}, {4,13}, {18,27}, {21,31}, {3,29}, {8,26}, {18,31}, {9,22}, {6,15}, {20,29}, {17,28}, {8,21}, {4,9}, {12,23}, {13,24}, {11,24}, {6,27}, {5,31}, {6,26}, {12,30}, {3,23}, {21,30}, {20,25}, {3,21}, {2,7}, {6,19}, {7,29}, {18,23}, {6,28}, {22,31}, {9,30}, {2,11}, {14,25}, {16,21}, {7,28}, {3,16}, {13,26}, {11,16}, {9,18}, {3,24}, {18,28}, {2,22}, {4,14}, {5,27}, {5,10}, {5,26}, {8,18}, {15,28}, {10,19}, {4,25}, {24,29}, {7,27}, {2,12}, {1,14}, {10,20}, {1,6}, {17,26}, {5,15}, {17,22}, {9,31}, {4,17}, {14,27}, {8,29}, {12,21}, {7,18}, {5,16} }; // ET31.4 // Bipartite(15,16) Valencies [16,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 27360196043587190784000000 EdgePairs[31][4]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {4,24}, {14,19}, {15,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {8,28}, {15,31}, {4,29}, {1,27}, {3,25}, {10,23}, {10,26}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {14,31}, {1,21}, {8,25}, {2,28}, {1,30}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {13,16}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {15,29}, {6,21}, {2,25}, {14,23}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {14,30}, {5,25}, {15,26}, {1,31}, {11,22}, {7,25}, {10,28}, {11,31}, {14,24}, {1,22}, {15,27}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {13,22}, {15,19}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {15,20}, {9,20}, {1,28}, {3,27}, {4,28}, {15,17}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {13,30}, {2,17}, {12,27}, {14,17}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {13,27}, {14,20}, {15,21}, {14,25}, {7,28}, {3,16}, {11,26}, {13,26}, {15,18}, {7,23}, {11,16}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {15,22}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {15,28}, {11,19}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {15,23}, {7,24}, {3,31}, {9,24}, {10,20}, {12,31}, {5,19}, {6,20}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {8,29}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET31.5 // Bipartite(14,17) Valencies [17,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31008222182732149555200000 EdgePairs[31][5]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {7,15}, {4,24}, {14,19}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {8,28}, {4,29}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {14,31}, {1,21}, {8,25}, {2,28}, {1,30}, {8,15}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {14,23}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {14,30}, {5,25}, {11,15}, {1,31}, {11,22}, {7,25}, {10,28}, {11,31}, {14,24}, {1,22}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {13,22}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {14,15}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {9,20}, {4,15}, {1,28}, {3,27}, {4,28}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {6,15}, {13,30}, {2,17}, {12,27}, {14,17}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {12,15}, {9,30}, {13,27}, {14,20}, {14,25}, {7,28}, {3,16}, {11,26}, {13,26}, {7,23}, {11,16}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {3,31}, {9,24}, {10,20}, {5,15}, {12,31}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {13,17}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {8,29}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET31.6 // Bipartite(13,18) Valencies [18,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 39867714234941335142400000 EdgePairs[31][6]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {13,21}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {8,28}, {4,29}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {1,30}, {8,15}, {4,23}, {8,31}, {8,27}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {5,25}, {11,15}, {1,31}, {11,22}, {9,14}, {7,25}, {10,28}, {11,31}, {1,22}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {13,22}, {10,21}, {2,20}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {5,14}, {9,20}, {4,15}, {1,28}, {7,14}, {3,27}, {4,28}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {6,15}, {13,30}, {2,17}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {13,27}, {7,28}, {3,16}, {11,26}, {13,26}, {7,23}, {11,16}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {13,14}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {3,31}, {1,14}, {9,24}, {10,20}, {5,15}, {12,31}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {13,17}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET31.7 // Bipartite(12,19) Valencies [19,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 58268197727991182131200000 EdgePairs[31][7]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {12,29}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {12,22}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {1,30}, {8,15}, {4,23}, {8,27}, {8,31}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {1,31}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {11,31}, {1,22}, {12,13}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {12,28}, {12,25}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {5,31}, {6,27}, {11,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {12,14}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {5,13}, {8,20}, {3,28}, {12,24}, {7,27}, {7,24}, {3,31}, {1,14}, {9,24}, {10,20}, {5,15}, {12,31}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET31.8 // Bipartite(11,20) Valencies [20,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 97113662879985303552000000 EdgePairs[31][8]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {11,12}, {2,28}, {2,14}, {1,30}, {8,15}, {4,23}, {8,27}, {8,31}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,26}, {9,27}, {5,29}, {9,19}, {8,14}, {5,25}, {11,13}, {11,15}, {1,31}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {11,31}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {11,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,24}, {3,31}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET31.9 // Bipartite(10,21) Valencies [21,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 185398810952699215872000000 EdgePairs[31][9]:={ {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {2,14}, {1,30}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {5,29}, {9,19}, {8,14}, {5,25}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {10,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,24}, {3,31}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {7,18}, {10,16}, {5,16} }; // ET31.10 // Bipartite(9,22) Valencies [22,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 407877384095938274918400000 EdgePairs[31][10]:={ {1,11}, {2,24}, {1,20}, {5,17}, {9,28}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {9,11}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {9,19}, {8,14}, {5,25}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {9,25}, {7,16}, {7,26}, {1,12}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,10}, {7,24}, {3,31}, {2,12}, {1,14}, {9,24}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {7,18}, {5,16} }; // ET31.11 // Bipartite(8,23) Valencies [23,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1042353314911842258124800000 EdgePairs[31][11]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {3,14}, {7,20}, {5,11}, {2,10}, {5,29}, {8,14}, {5,25}, {1,31}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {7,16}, {1,12}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {5,12}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {8,29}, {7,18}, {5,16} }; // ET31.12 // Bipartite(7,24) Valencies [24,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3127059944735526774374400000 EdgePairs[31][12]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {4,27}, {7,15}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {6,11}, {4,23}, {6,22}, {3,18}, {6,29}, {3,17}, {6,21}, {2,25}, {7,12}, {6,31}, {4,10}, {1,17}, {5,22}, {4,22}, {1,18}, {7,11}, {3,14}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {1,31}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {7,16}, {1,12}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {7,18}, {5,16} }; // ET31.13 // Bipartite(6,25) Valencies [25,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 11168071231198309908480000000 EdgePairs[31][13]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {4,27}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {6,7}, {2,28}, {2,14}, {1,30}, {6,11}, {4,23}, {6,22}, {3,18}, {6,29}, {3,17}, {3,7}, {6,21}, {2,25}, {6,31}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {1,31}, {3,12}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {1,12}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {3,16}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {5,8}, {6,25}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {4,17}, {5,16} }; // ET31.14 // Bipartite(5,26) Valencies [26,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 48394975335192676270080000000 EdgePairs[31][14]:={ {1,15}, {5,14}, {3,15}, {4,14}, {1,11}, {3,29}, {2,22}, {5,30}, {4,8}, {3,7}, {1,31}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {5,24}, {1,9}, {3,30}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {5,6}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {5,19}, {5,15}, {3,23}, {5,29}, {4,31}, {3,27}, {4,30}, {1,19}, {4,21}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {5,31}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {2,7}, {5,18}, {1,8}, {4,23}, {1,30}, {5,16}, {4,13}, {1,21}, {2,30}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET31.15 // Bipartite(4,27) Valencies [27,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 261332866810040451858432000000 EdgePairs[31][15]:={ {1,15}, {3,15}, {1,11}, {4,14}, {3,29}, {2,22}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {1,9}, {4,5}, {1,5}, {3,30}, {4,6}, {3,10}, {2,28}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {2,14}, {3,11}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {3,27}, {4,30}, {1,19}, {4,21}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,26}, {2,24}, {4,11}, {2,27}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {1,28}, {3,17}, {4,9}, {2,7}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET31.16 // Bipartite(3,28) Valencies [28,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1829330067670283163009024000000 EdgePairs[31][16]:={ {2,11}, {3,22}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {3,12}, {1,29}, {2,30}, {1,30}, {2,29}, {2,24}, {2,10}, {1,10}, {3,21}, {1,6}, {3,5}, {3,27}, {2,6}, {1,4}, {1,20}, {1,12}, {3,8}, {3,23}, {1,31}, {3,9}, {3,24}, {2,12}, {2,4}, {3,29}, {3,20}, {2,21}, {2,16}, {1,7}, {3,4}, {1,15}, {2,7}, {3,11}, {2,31}, {1,16}, {2,20}, {3,7}, {3,16}, {3,28}, {3,15}, {3,17}, {2,18}, {1,21}, {3,25}, {3,19}, {3,30}, {2,15}, {3,14}, {2,5}, {3,18}, {3,31}, {1,18}, {3,26}, {1,5}, {1,27}, {1,17}, {2,27}, {3,6}, {2,28}, {1,28}, {2,19}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22}, {3,10} }; // ET31.17 // Bipartite(2,29) Valencies [29,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 17683523987479403909087232000000 EdgePairs[31][17]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {1,29}, {2,30}, {1,30}, {2,29}, {2,24}, {2,10}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {1,31}, {2,12}, {2,4}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {2,18}, {1,21}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET31.18 // Bipartite(1,30) Valencies [30,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 265252859812191058636308480000000 EdgePairs[31][18]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,31}, {1,12}, {1,2}, {1,3}, {1,17}, {1,30}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,28}, {1,6}, {1,14}, {1,26}, {1,18}, {1,27}, {1,21}, {1,19}, {1,29}, {1,20}, {1,8}, {1,24}, {1,9}, {1,23}, {1,25} }; // ET31.19 // Non-bipartite Valency 30 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 8222838654177922817725562880000000 EdgePairs[31][19]:={ {13,25}, {15,28}, {15,17}, {10,17}, {3,29}, {20,26}, {9,18}, {16,28}, {5,13}, {4,26}, {20,25}, {14,29}, {2,4}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {11,12}, {4,24}, {8,31}, {1,5}, {7,24}, {15,16}, {26,27}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {23,29}, {14,15}, {8,26}, {10,29}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {8,24}, {8,11}, {12,27}, {17,22}, {21,31}, {3,13}, {2,21}, {7,26}, {11,27}, {18,28}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {20,29}, {12,22}, {4,5}, {15,20}, {9,10}, {17,18}, {17,25}, {3,27}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {21,30}, {16,23}, {3,14}, {25,26}, {9,22}, {5,20}, {1,20}, {18,27}, {7,14}, {23,24}, {15,24}, {10,23}, {22,27}, {1,26}, {18,31}, {9,27}, {1,25}, {19,21}, {10,16}, {6,14}, {24,30}, {16,30}, {5,27}, {9,31}, {3,6}, {7,23}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {10,14}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {9,26}, {18,20}, {6,12}, {7,31}, {13,18}, {1,29}, {21,22}, {10,19}, {12,19}, {15,27}, {9,11}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {5,28}, {12,18}, {8,30}, {4,21}, {2,5}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {13,19}, {9,29}, {2,22}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {6,10}, {1,28}, {14,18}, {1,17}, {20,23}, {9,14}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {17,28}, {5,21}, {22,24}, {13,26}, {11,24}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {10,11}, {1,13}, {10,24}, {2,25}, {17,23}, {23,28}, {21,29}, {3,28}, {2,14}, {12,24}, {18,19}, {3,4}, {14,28}, {2,3}, {12,20}, {16,29}, {1,11}, {15,30}, {3,19}, {2,16}, {18,25}, {14,19}, {21,27}, {7,8}, {9,13}, {21,23}, {15,29}, {4,15}, {4,29}, {8,25}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {19,23}, {11,16}, {1,4}, {7,25}, {8,27}, {24,31}, {5,30}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,30}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {5,6}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {15,31}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {2,27}, {1,19}, {2,10}, {6,17}, {19,29}, {11,14}, {7,12}, {13,20}, {13,21}, {3,11}, {4,10}, {11,23}, {3,5}, {15,19}, {8,16}, {20,21}, {8,9}, {14,30}, {17,24}, {12,23}, {13,31}, {8,18}, {22,23}, {5,31}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {8,15}, {24,28}, {4,14}, {11,28}, {6,25}, {11,17}, {15,18}, {24,29}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {4,9}, {5,10}, {24,26}, {11,26}, {13,24}, {11,13}, {6,16}, {4,31}, {2,15}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {20,30}, {2,29}, {14,21}, {3,21}, {19,27}, {26,30}, {2,6}, {13,30}, {9,24}, {1,2}, {4,6}, {6,20}, {11,15}, {6,26}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {19,20}, {2,23}, {15,21}, {12,30}, {1,8}, {19,26}, {12,14}, {4,23}, {27,30}, {8,13}, {16,21}, {6,27}, {29,30}, {6,30}, {11,25}, {17,27}, {2,17}, {25,31}, {16,18}, {5,14}, {11,22}, {9,16}, {27,28}, {23,30}, {21,26}, {22,31}, {30,31}, {26,29}, {1,21}, {13,14}, {6,21}, {9,15}, {8,12}, {7,20}, {23,27}, {16,19}, {27,31}, {7,18}, {10,21}, {28,30}, {5,17}, {1,24}, {19,25}, {6,8}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {26,28}, {4,8}, {29,31}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {12,31}, {1,15}, {27,29}, {12,29}, {7,19}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {6,29}, {2,31} }; // Total number of connected ET graphs of order 31 is 19 // ******************************************************************************************** // Order 32 // ET32.1 // Bipartite(16,16) Valencies [2,2] // Diameter 16 Girth 32 // Twin-free VT AT // Automorphism group of order 64 EdgePairs[32][1]:={ {14,18}, {2,32}, {9,19}, {13,24}, {9,21}, {6,29}, {14,20}, {7,27}, {5,22}, {10,27}, {10,23}, {13,28}, {4,31}, {15,17}, {12,24}, {16,30}, {15,18}, {1,17}, {5,25}, {2,30}, {16,28}, {12,21}, {11,20}, {6,31}, {3,26}, {8,19}, {11,23}, {8,22}, {4,32}, {3,25}, {1,26}, {7,29} }; // ET32.2 // Bipartite(16,16) Valencies [3,3] // Diameter 5 Girth 6 // Twin-free VT AT // Automorphism group of order 192 EdgePairs[32][2]:={ {8,20}, {13,19}, {2,32}, {3,29}, {6,21}, {12,25}, {14,27}, {5,27}, {4,23}, {2,19}, {8,24}, {9,32}, {16,18}, {8,23}, {7,17}, {14,28}, {1,22}, {5,22}, {1,28}, {12,29}, {4,31}, {16,20}, {15,17}, {15,24}, {16,30}, {9,28}, {14,31}, {1,17}, {10,22}, {10,19}, {2,20}, {5,26}, {7,18}, {12,21}, {11,27}, {6,31}, {10,24}, {3,26}, {4,25}, {11,23}, {6,32}, {13,26}, {13,21}, {3,30}, {9,18}, {7,29}, {11,30}, {15,25} }; // ET32.3 // Bipartite(16,16) Valencies [4,4] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 4096 EdgePairs[32][3]:={ {3,32}, {15,32}, {4,23}, {13,28}, {8,20}, {2,26}, {12,18}, {2,30}, {11,17}, {11,25}, {2,24}, {9,31}, {16,23}, {15,27}, {1,20}, {12,31}, {3,29}, {6,32}, {11,21}, {7,30}, {8,27}, {5,23}, {13,32}, {4,18}, {5,25}, {5,31}, {5,28}, {3,25}, {15,30}, {4,21}, {6,21}, {3,31}, {12,19}, {13,20}, {15,28}, {8,22}, {1,27}, {4,28}, {1,17}, {7,19}, {16,20}, {6,18}, {10,19}, {8,26}, {9,18}, {12,22}, {14,23}, {14,27}, {13,24}, {7,17}, {1,19}, {10,22}, {11,26}, {10,21}, {9,26}, {14,29}, {10,25}, {16,24}, {6,29}, {16,29}, {2,22}, {7,24}, {9,17}, {14,30} }; // ET32.4 // Bipartite(16,16) Valencies [4,4] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 128 EdgePairs[32][4]:={ {11,30}, {15,32}, {8,28}, {9,23}, {14,19}, {1,29}, {9,25}, {9,31}, {11,20}, {3,27}, {13,25}, {11,27}, {12,32}, {15,23}, {4,31}, {3,23}, {7,30}, {4,30}, {8,27}, {4,32}, {16,27}, {9,29}, {4,18}, {7,32}, {16,30}, {5,25}, {15,31}, {2,31}, {16,18}, {6,20}, {3,17}, {5,19}, {5,28}, {1,21}, {2,18}, {11,22}, {6,21}, {12,24}, {13,20}, {3,26}, {8,22}, {12,26}, {13,22}, {7,20}, {1,17}, {14,21}, {10,19}, {2,19}, {10,17}, {8,26}, {13,29}, {14,24}, {16,17}, {10,21}, {12,28}, {15,26}, {2,25}, {1,23}, {14,28}, {6,29}, {5,22}, {7,24}, {10,18}, {6,24} }; // ET32.5 // Bipartite(16,16) Valencies [4,4] // Diameter 4 Girth 6 // Twin-free VT AT // Automorphism group of order 2304 EdgePairs[32][5]:={ {12,20}, {1,30}, {2,29}, {11,25}, {1,32}, {14,26}, {9,31}, {5,27}, {8,23}, {10,32}, {11,27}, {15,23}, {4,31}, {3,23}, {8,29}, {6,32}, {3,20}, {13,18}, {7,30}, {8,27}, {5,21}, {16,27}, {15,21}, {4,18}, {15,31}, {9,24}, {3,28}, {15,19}, {2,18}, {3,25}, {11,32}, {12,19}, {4,17}, {7,25}, {5,30}, {13,23}, {1,17}, {7,19}, {16,20}, {9,22}, {6,19}, {14,21}, {12,22}, {1,28}, {13,24}, {10,21}, {14,29}, {4,26}, {2,25}, {9,28}, {14,28}, {13,30}, {16,24}, {10,20}, {12,17}, {11,31}, {6,29}, {8,17}, {5,22}, {2,22}, {10,18}, {6,24}, {16,26}, {7,26} }; // ET32.6 // Bipartite(16,16) Valencies [4,4] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 256 EdgePairs[32][6]:={ {1,26}, {15,32}, {4,24}, {8,31}, {1,29}, {2,30}, {9,21}, {15,20}, {6,26}, {11,20}, {6,31}, {11,27}, {8,24}, {11,23}, {8,29}, {6,32}, {3,20}, {9,32}, {13,18}, {4,30}, {8,27}, {5,23}, {15,31}, {10,23}, {3,17}, {5,19}, {5,28}, {3,25}, {4,27}, {4,21}, {14,32}, {3,18}, {12,19}, {16,21}, {7,25}, {1,18}, {15,25}, {12,26}, {13,22}, {16,22}, {16,19}, {2,27}, {7,19}, {1,17}, {2,28}, {7,28}, {13,24}, {2,23}, {13,29}, {7,17}, {9,30}, {10,22}, {9,26}, {14,28}, {16,24}, {10,20}, {12,17}, {11,31}, {14,25}, {6,29}, {5,22}, {10,18}, {12,21}, {14,30} }; // ET32.7 // Bipartite(16,16) Valencies [4,4] // Diameter 8 Girth 4 // Has twins VT AT // Automorphism group of order 2097152 EdgePairs[32][7]:={ {12,20}, {13,19}, {14,19}, {1,24}, {2,26}, {8,31}, {9,25}, {5,29}, {1,32}, {7,23}, {7,31}, {5,27}, {8,23}, {11,28}, {16,23}, {11,20}, {16,31}, {6,30}, {15,23}, {8,24}, {3,20}, {9,32}, {7,30}, {8,32}, {16,32}, {5,21}, {15,31}, {9,24}, {3,28}, {10,26}, {14,22}, {5,19}, {2,18}, {15,30}, {4,21}, {4,20}, {6,27}, {3,18}, {3,26}, {7,22}, {12,29}, {4,28}, {13,21}, {1,17}, {6,19}, {6,22}, {10,17}, {14,27}, {2,17}, {13,29}, {11,26}, {13,27}, {12,28}, {2,25}, {10,25}, {16,24}, {11,18}, {1,25}, {9,17}, {10,18}, {12,21}, {14,30}, {15,22}, {4,29} }; // ET32.8 // Bipartite(16,16) Valencies [4,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 294912 EdgePairs[32][8]:={ {11,30}, {1,26}, {12,27}, {4,24}, {13,19}, {8,31}, {5,29}, {1,32}, {14,26}, {9,21}, {7,31}, {6,26}, {11,20}, {3,27}, {16,31}, {15,24}, {11,27}, {3,23}, {11,23}, {8,29}, {3,20}, {9,32}, {13,18}, {2,21}, {8,32}, {16,32}, {16,30}, {15,31}, {10,23}, {6,20}, {14,22}, {5,19}, {4,27}, {1,21}, {2,18}, {3,30}, {12,19}, {12,24}, {4,17}, {7,25}, {15,25}, {15,28}, {13,22}, {1,17}, {2,28}, {6,22}, {7,28}, {5,18}, {6,25}, {2,23}, {13,29}, {14,20}, {10,28}, {10,21}, {9,26}, {8,30}, {4,19}, {12,17}, {14,25}, {5,22}, {16,29}, {7,24}, {10,18}, {9,17} }; // ET32.9 // Bipartite(12,20) Valencies [5,3] // Diameter 6 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[32][9]:={ {1,26}, {12,20}, {4,24}, {9,19}, {11,15}, {7,16}, {2,32}, {11,17}, {2,24}, {9,31}, {6,26}, {11,24}, {12,16}, {3,21}, {8,15}, {11,20}, {11,27}, {12,30}, {12,32}, {4,31}, {3,23}, {8,29}, {3,29}, {6,15}, {5,16}, {5,21}, {7,32}, {5,25}, {2,31}, {10,23}, {2,20}, {7,18}, {4,27}, {2,18}, {6,27}, {3,14}, {7,25}, {5,30}, {4,22}, {9,22}, {10,19}, {9,18}, {5,14}, {7,28}, {3,13}, {1,13}, {8,14}, {1,19}, {10,28}, {10,21}, {4,26}, {1,22}, {10,25}, {9,28}, {1,23}, {8,30}, {12,17}, {6,29}, {8,17}, {6,13} }; // ET32.10 // Bipartite(16,16) Valencies [5,5] // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 3840 EdgePairs[32][10]:={ {1,26}, {4,24}, {8,19}, {13,28}, {9,23}, {14,19}, {8,20}, {2,30}, {14,18}, {1,30}, {9,25}, {5,29}, {11,25}, {7,23}, {9,21}, {5,27}, {6,31}, {11,20}, {10,32}, {13,25}, {15,24}, {11,27}, {10,30}, {12,30}, {12,32}, {15,27}, {4,31}, {3,23}, {12,31}, {8,29}, {11,21}, {13,18}, {2,21}, {4,32}, {15,21}, {4,18}, {7,32}, {15,31}, {9,24}, {2,31}, {2,20}, {3,28}, {10,23}, {16,18}, {6,20}, {5,28}, {3,25}, {1,21}, {3,19}, {5,17}, {6,27}, {14,32}, {15,17}, {3,26}, {12,29}, {16,25}, {16,22}, {16,19}, {1,17}, {16,20}, {6,18}, {4,22}, {9,22}, {10,19}, {8,26}, {7,28}, {13,24}, {5,26}, {7,17}, {10,22}, {11,26}, {13,27}, {14,29}, {1,23}, {14,28}, {8,30}, {12,17}, {6,29}, {2,22}, {7,24} }; // ET32.11 // Non-bipartite Valency 5 // Diameter 4 Girth 5 // Twin-free VT AT // Automorphism group of order 1920 EdgePairs[32][11]:={ {4,8}, {5,32}, {19,24}, {1,14}, {24,29}, {3,12}, {8,31}, {11,25}, {18,26}, {22,25}, {14,26}, {20,23}, {1,10}, {4,11}, {6,31}, {7,13}, {13,25}, {6,10}, {15,27}, {15,23}, {11,23}, {17,25}, {4,16}, {12,31}, {8,29}, {2,4}, {6,15}, {7,30}, {5,9}, {2,21}, {8,27}, {5,16}, {15,21}, {4,18}, {7,32}, {21,29}, {25,27}, {2,20}, {3,7}, {3,15}, {17,20}, {19,27}, {3,17}, {9,12}, {11,32}, {20,28}, {9,27}, {10,11}, {5,17}, {18,30}, {20,31}, {18,19}, {1,3}, {12,24}, {10,29}, {22,31}, {12,26}, {16,22}, {6,18}, {14,23}, {19,32}, {5,14}, {7,28}, {21,26}, {13,24}, {16,28}, {8,14}, {10,28}, {2,9}, {9,30}, {1,19}, {23,30}, {1,22}, {2,13}, {21,32}, {16,24}, {17,29}, {22,30}, {6,13}, {26,28} }; // ET32.12 // Bipartite(8,24) Valencies [6,2] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 384 EdgePairs[32][12]:={ {4,20}, {3,24}, {6,28}, {8,21}, {7,30}, {7,23}, {4,30}, {5,18}, {5,21}, {5,27}, {3,14}, {7,27}, {1,29}, {4,15}, {8,23}, {3,15}, {2,25}, {5,20}, {8,16}, {1,28}, {1,10}, {8,14}, {4,19}, {3,17}, {3,11}, {2,13}, {7,25}, {6,24}, {2,18}, {5,26}, {4,22}, {8,9}, {1,11}, {6,22}, {6,31}, {1,19}, {5,17}, {6,32}, {2,16}, {3,12}, {6,26}, {7,32}, {1,9}, {4,13}, {2,12}, {2,10}, {8,31}, {7,29} }; // ET32.13 // Bipartite(8,24) Valencies [6,2] // Diameter 8 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 26873856 EdgePairs[32][13]:={ {2,11}, {3,22}, {5,12}, {1,26}, {7,16}, {2,26}, {5,29}, {7,23}, {7,31}, {2,10}, {8,9}, {8,16}, {1,10}, {6,14}, {4,11}, {3,21}, {6,31}, {8,25}, {6,30}, {8,24}, {3,29}, {6,15}, {8,32}, {5,21}, {5,20}, {4,12}, {7,32}, {5,28}, {2,18}, {4,27}, {4,20}, {7,15}, {3,30}, {3,14}, {1,18}, {4,28}, {2,27}, {1,17}, {6,22}, {2,19}, {3,13}, {5,13}, {1,9}, {4,19}, {1,25}, {8,17}, {6,23}, {7,24} }; // ET32.14 // Bipartite(8,24) Valencies [6,2] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 196608 EdgePairs[32][14]:={ {4,24}, {7,11}, {1,32}, {2,24}, {7,23}, {7,31}, {6,14}, {6,26}, {4,10}, {1,20}, {3,23}, {2,12}, {3,29}, {5,9}, {5,16}, {4,32}, {5,21}, {8,10}, {4,12}, {7,27}, {1,15}, {3,11}, {2,31}, {3,16}, {3,28}, {3,17}, {5,28}, {1,21}, {4,20}, {7,15}, {5,30}, {8,22}, {1,27}, {7,19}, {4,22}, {2,19}, {8,26}, {5,18}, {6,25}, {6,17}, {8,14}, {8,18}, {1,9}, {2,13}, {2,25}, {8,30}, {6,29}, {6,13} }; // ET32.15 // Bipartite(16,16) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 384 EdgePairs[32][15]:={ {13,25}, {14,21}, {10,21}, {8,31}, {11,23}, {6,18}, {3,29}, {2,22}, {5,30}, {1,31}, {13,24}, {14,18}, {12,17}, {5,24}, {3,32}, {6,25}, {16,23}, {7,27}, {9,19}, {12,18}, {16,20}, {12,27}, {15,29}, {2,18}, {5,26}, {10,18}, {6,22}, {10,30}, {14,27}, {3,18}, {12,30}, {13,26}, {1,17}, {2,32}, {6,21}, {4,28}, {7,29}, {10,31}, {16,26}, {16,19}, {14,28}, {5,19}, {7,20}, {8,26}, {8,17}, {3,27}, {4,30}, {12,28}, {4,17}, {5,28}, {12,29}, {9,25}, {10,29}, {1,26}, {8,19}, {13,22}, {6,29}, {2,27}, {15,21}, {14,17}, {15,31}, {1,23}, {2,21}, {10,28}, {11,19}, {14,31}, {13,32}, {5,31}, {9,24}, {11,25}, {8,23}, {16,22}, {6,20}, {9,26}, {15,27}, {7,22}, {11,32}, {7,32}, {3,25}, {13,23}, {15,17}, {11,20}, {7,21}, {3,20}, {2,25}, {1,28}, {8,30}, {15,30}, {16,32}, {4,23}, {11,24}, {4,19}, {4,24}, {9,20}, {1,24}, {9,22} }; // ET32.16 // Bipartite(16,16) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 384 EdgePairs[32][16]:={ {10,19}, {5,32}, {10,21}, {15,23}, {14,25}, {13,29}, {12,26}, {6,18}, {12,19}, {3,29}, {6,17}, {10,27}, {7,24}, {11,29}, {2,20}, {14,19}, {12,22}, {16,18}, {7,31}, {13,27}, {12,18}, {3,30}, {1,32}, {16,20}, {14,20}, {9,17}, {5,21}, {15,28}, {2,29}, {8,22}, {12,30}, {16,21}, {4,20}, {2,23}, {8,28}, {1,17}, {15,25}, {10,31}, {7,25}, {3,22}, {5,19}, {8,17}, {11,28}, {4,31}, {14,26}, {6,26}, {1,19}, {7,30}, {5,28}, {13,30}, {9,25}, {6,29}, {12,23}, {6,31}, {5,22}, {14,17}, {15,31}, {2,21}, {16,27}, {8,27}, {10,28}, {7,18}, {13,32}, {3,28}, {11,31}, {3,26}, {3,24}, {8,20}, {8,23}, {16,22}, {9,18}, {4,32}, {13,21}, {1,27}, {11,32}, {4,18}, {9,29}, {13,23}, {2,26}, {15,17}, {11,20}, {7,21}, {2,25}, {9,32}, {10,26}, {6,27}, {15,30}, {4,23}, {11,24}, {1,30}, {5,25}, {4,19}, {14,24}, {1,24}, {9,22}, {16,24} }; // ET32.17 // Bipartite(16,16) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 23040 EdgePairs[32][17]:={ {13,25}, {13,29}, {11,17}, {8,31}, {12,26}, {11,23}, {9,30}, {4,27}, {10,27}, {14,19}, {16,18}, {7,27}, {11,22}, {16,20}, {7,23}, {9,31}, {3,31}, {2,18}, {5,26}, {13,20}, {15,28}, {2,29}, {3,19}, {8,22}, {7,28}, {12,21}, {12,30}, {5,23}, {15,22}, {9,27}, {2,31}, {2,23}, {1,17}, {10,25}, {15,25}, {6,21}, {16,17}, {8,21}, {8,18}, {2,17}, {7,29}, {10,31}, {4,29}, {5,19}, {3,23}, {6,26}, {14,26}, {1,19}, {4,21}, {13,30}, {4,25}, {8,19}, {6,29}, {12,24}, {15,26}, {12,23}, {6,31}, {14,17}, {14,22}, {5,27}, {15,18}, {13,32}, {8,32}, {5,20}, {3,28}, {3,24}, {9,24}, {11,25}, {11,21}, {6,20}, {10,17}, {1,27}, {7,22}, {4,18}, {16,28}, {7,32}, {3,25}, {10,32}, {11,20}, {14,29}, {12,32}, {1,28}, {5,18}, {10,26}, {13,19}, {15,30}, {16,32}, {1,30}, {2,30}, {1,21}, {14,24}, {4,24}, {9,20}, {9,22}, {6,28}, {16,24} }; // ET32.18 // Bipartite(16,16) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1536 EdgePairs[32][18]:={ {14,21}, {5,32}, {10,22}, {13,18}, {4,27}, {11,29}, {14,19}, {13,24}, {14,18}, {1,25}, {12,17}, {12,22}, {5,24}, {6,32}, {7,31}, {16,23}, {9,19}, {13,27}, {7,23}, {2,28}, {3,31}, {2,19}, {2,18}, {5,26}, {4,26}, {15,32}, {2,29}, {10,30}, {3,18}, {9,27}, {2,31}, {8,28}, {1,17}, {10,25}, {14,30}, {6,21}, {2,17}, {8,18}, {4,28}, {7,29}, {4,29}, {16,26}, {7,25}, {16,19}, {3,22}, {9,23}, {10,24}, {8,26}, {5,29}, {3,27}, {1,19}, {7,30}, {4,21}, {12,29}, {9,25}, {1,26}, {15,26}, {12,23}, {14,32}, {6,31}, {15,31}, {14,22}, {10,28}, {11,19}, {4,22}, {9,28}, {8,20}, {8,23}, {16,22}, {6,20}, {11,30}, {10,17}, {11,27}, {13,21}, {1,20}, {15,27}, {3,25}, {13,23}, {15,17}, {13,17}, {11,20}, {7,21}, {3,20}, {12,32}, {9,32}, {6,24}, {5,18}, {8,30}, {15,30}, {11,24}, {16,31}, {1,21}, {12,20}, {5,25}, {6,28}, {16,24} }; // ET32.19 // Bipartite(16,16) Valencies [6,6] // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 6291456 EdgePairs[32][19]:={ {7,19}, {16,25}, {14,21}, {5,32}, {11,17}, {8,24}, {10,22}, {11,23}, {9,30}, {12,19}, {2,22}, {13,18}, {4,27}, {6,23}, {2,20}, {13,24}, {1,25}, {12,31}, {12,22}, {5,24}, {6,32}, {7,27}, {13,27}, {9,21}, {16,20}, {12,27}, {15,29}, {2,28}, {3,31}, {2,18}, {5,26}, {9,17}, {10,18}, {15,28}, {10,30}, {1,29}, {3,18}, {7,28}, {12,30}, {8,28}, {13,26}, {1,17}, {1,22}, {6,21}, {16,17}, {7,29}, {5,19}, {7,20}, {15,20}, {3,23}, {8,17}, {4,31}, {4,30}, {11,18}, {15,19}, {9,25}, {11,26}, {6,29}, {12,23}, {14,32}, {6,31}, {15,21}, {5,27}, {10,28}, {14,31}, {13,32}, {14,23}, {8,32}, {4,22}, {11,31}, {3,26}, {11,25}, {8,20}, {15,27}, {16,28}, {8,25}, {3,25}, {9,29}, {2,26}, {7,21}, {14,29}, {3,17}, {10,20}, {6,24}, {5,18}, {10,26}, {13,19}, {16,32}, {4,23}, {1,30}, {2,30}, {1,21}, {14,24}, {4,19}, {9,22}, {16,24} }; // ET32.20 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 192 EdgePairs[32][20]:={ {13,25}, {6,12}, {8,31}, {6,18}, {9,30}, {4,14}, {12,19}, {2,22}, {20,28}, {1,31}, {4,27}, {2,11}, {11,29}, {23,27}, {22,30}, {16,18}, {19,27}, {16,23}, {21,25}, {3,30}, {11,22}, {3,10}, {14,20}, {2,15}, {8,13}, {9,17}, {10,18}, {10,23}, {15,28}, {14,27}, {12,21}, {12,30}, {17,30}, {23,32}, {2,23}, {3,13}, {15,25}, {2,32}, {1,16}, {8,10}, {10,31}, {1,12}, {4,29}, {16,26}, {7,25}, {3,22}, {5,19}, {5,15}, {7,20}, {18,25}, {8,26}, {3,23}, {8,17}, {5,29}, {7,14}, {24,31}, {14,26}, {4,21}, {10,29}, {1,26}, {8,19}, {16,27}, {21,29}, {14,22}, {5,27}, {6,30}, {7,18}, {3,28}, {11,31}, {5,17}, {9,24}, {13,28}, {6,16}, {6,20}, {18,29}, {7,9}, {13,21}, {5,11}, {22,26}, {7,32}, {15,17}, {11,20}, {12,32}, {2,25}, {17,26}, {20,31}, {4,9}, {9,32}, {19,32}, {13,19}, {1,21}, {15,24}, {4,24}, {1,24}, {24,28}, {6,28} }; // ET32.21 // Non-bipartite Valency 6 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 384 EdgePairs[32][21]:={ {7,19}, {13,25}, {14,21}, {20,27}, {15,23}, {22,32}, {8,24}, {21,31}, {6,18}, {1,11}, {12,19}, {3,29}, {2,22}, {6,14}, {17,27}, {5,30}, {1,31}, {4,27}, {1,25}, {22,30}, {12,22}, {16,18}, {7,31}, {7,23}, {7,15}, {5,13}, {14,20}, {8,14}, {9,17}, {10,18}, {10,30}, {3,19}, {4,20}, {1,10}, {10,25}, {2,32}, {6,21}, {2,17}, {3,9}, {7,25}, {9,23}, {10,24}, {5,15}, {18,25}, {8,26}, {7,13}, {3,23}, {4,30}, {14,26}, {12,28}, {13,30}, {2,9}, {23,29}, {13,22}, {6,29}, {4,11}, {5,22}, {15,31}, {21,29}, {5,27}, {18,28}, {2,12}, {8,32}, {3,28}, {11,31}, {24,30}, {23,31}, {5,17}, {8,16}, {3,12}, {24,32}, {8,20}, {11,21}, {9,26}, {6,16}, {20,26}, {11,27}, {15,27}, {16,28}, {9,29}, {2,26}, {15,17}, {11,20}, {14,29}, {12,32}, {17,26}, {19,25}, {13,19}, {16,32}, {19,28}, {1,21}, {1,18}, {4,10}, {4,24}, {6,28}, {16,24} }; // ET32.22 // Non-bipartite Valency 6 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 384 EdgePairs[32][22]:={ {2,11}, {1,26}, {15,32}, {12,20}, {12,27}, {4,9}, {8,19}, {4,23}, {14,19}, {24,29}, {7,16}, {8,31}, {17,28}, {19,26}, {9,25}, {5,29}, {18,26}, {1,32}, {2,10}, {8,23}, {11,28}, {16,23}, {8,15}, {3,27}, {16,31}, {8,25}, {15,24}, {13,26}, {6,30}, {1,12}, {17,25}, {3,24}, {12,31}, {6,15}, {3,20}, {2,21}, {5,16}, {5,21}, {16,27}, {4,12}, {23,32}, {7,32}, {3,11}, {9,24}, {22,29}, {2,31}, {10,23}, {21,30}, {10,26}, {19,27}, {14,22}, {5,28}, {2,18}, {11,32}, {20,28}, {11,22}, {3,30}, {8,13}, {6,27}, {13,20}, {10,29}, {22,31}, {15,28}, {7,20}, {4,28}, {13,21}, {1,17}, {20,25}, {6,22}, {9,18}, {10,17}, {5,14}, {18,27}, {5,18}, {6,17}, {13,29}, {9,30}, {23,30}, {16,17}, {1,9}, {24,31}, {1,22}, {2,25}, {21,32}, {7,14}, {4,19}, {11,19}, {14,25}, {15,18}, {6,13}, {7,24}, {3,10}, {12,21}, {14,30}, {7,26}, {4,29} }; // ET32.23 // Bipartite(16,16) Valencies [7,7] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 1344 EdgePairs[32][23]:={ {10,19}, {7,19}, {16,25}, {5,32}, {10,21}, {14,25}, {8,31}, {8,24}, {10,22}, {9,30}, {12,19}, {3,29}, {2,22}, {1,31}, {13,18}, {16,30}, {10,27}, {11,29}, {6,23}, {1,25}, {12,17}, {5,24}, {16,23}, {3,30}, {16,20}, {12,27}, {7,23}, {2,28}, {9,31}, {2,19}, {5,26}, {4,26}, {9,17}, {6,22}, {15,32}, {13,20}, {5,21}, {15,28}, {2,29}, {14,27}, {3,19}, {3,18}, {8,22}, {7,28}, {12,21}, {12,30}, {16,21}, {15,22}, {2,23}, {13,26}, {1,17}, {8,21}, {8,18}, {16,26}, {7,25}, {5,19}, {7,20}, {16,29}, {11,28}, {4,31}, {3,27}, {11,18}, {4,21}, {4,17}, {13,30}, {9,25}, {10,29}, {11,26}, {13,22}, {12,24}, {12,23}, {14,32}, {2,24}, {6,31}, {6,30}, {15,18}, {14,31}, {14,23}, {4,22}, {9,28}, {3,28}, {11,31}, {9,24}, {6,20}, {9,26}, {4,32}, {1,20}, {1,27}, {11,32}, {15,27}, {7,32}, {3,25}, {2,26}, {10,32}, {13,17}, {15,17}, {11,20}, {14,29}, {10,20}, {5,18}, {8,30}, {6,27}, {13,19}, {7,17}, {4,23}, {1,21}, {1,18}, {15,24}, {5,25}, {14,24}, {8,29}, {6,28} }; // ET32.24 // Bipartite(16,16) Valencies [8,8] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 43008 EdgePairs[32][24]:={ {13,25}, {10,21}, {15,23}, {12,26}, {10,22}, {9,30}, {12,19}, {3,29}, {5,30}, {13,18}, {10,27}, {7,24}, {1,25}, {12,17}, {12,31}, {16,18}, {3,32}, {6,32}, {7,31}, {6,25}, {7,27}, {9,19}, {11,22}, {16,20}, {2,28}, {9,31}, {14,20}, {3,31}, {5,26}, {4,26}, {9,17}, {10,18}, {6,22}, {15,32}, {10,23}, {14,27}, {1,29}, {8,22}, {12,21}, {5,23}, {15,22}, {2,31}, {8,28}, {1,17}, {15,25}, {1,22}, {2,32}, {6,21}, {7,29}, {16,26}, {7,25}, {16,19}, {8,26}, {3,23}, {16,29}, {11,28}, {3,27}, {4,30}, {14,26}, {1,19}, {11,18}, {4,21}, {4,17}, {12,29}, {13,30}, {9,25}, {10,29}, {8,19}, {6,29}, {12,23}, {14,32}, {2,24}, {2,27}, {6,19}, {14,17}, {15,21}, {1,23}, {2,21}, {14,22}, {5,27}, {10,28}, {7,18}, {8,32}, {4,22}, {5,20}, {3,28}, {5,31}, {5,17}, {9,24}, {11,25}, {13,28}, {8,20}, {8,23}, {11,30}, {11,27}, {13,21}, {1,20}, {15,27}, {4,18}, {16,28}, {3,25}, {13,23}, {2,26}, {15,17}, {11,20}, {7,21}, {3,20}, {14,29}, {12,32}, {9,32}, {6,24}, {5,18}, {8,30}, {10,26}, {13,31}, {13,19}, {15,30}, {7,17}, {11,24}, {16,31}, {2,30}, {1,18}, {4,19}, {14,24}, {4,24}, {9,20}, {6,28}, {16,24} }; // ET32.25 // Bipartite(16,16) Valencies [8,8] // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 1761205026816 EdgePairs[32][25]:={ {7,19}, {16,25}, {13,25}, {13,29}, {15,23}, {8,31}, {10,22}, {11,23}, {6,18}, {9,30}, {12,19}, {2,22}, {5,30}, {4,27}, {13,18}, {7,24}, {2,20}, {1,25}, {14,18}, {12,17}, {12,31}, {3,32}, {6,32}, {7,31}, {16,23}, {7,27}, {9,21}, {12,27}, {7,23}, {2,28}, {14,20}, {12,25}, {3,31}, {2,18}, {5,26}, {9,17}, {10,18}, {6,22}, {15,32}, {5,21}, {15,28}, {10,30}, {3,19}, {1,29}, {7,28}, {12,21}, {16,21}, {1,17}, {13,26}, {1,22}, {14,30}, {2,32}, {16,17}, {8,21}, {4,29}, {16,19}, {14,28}, {10,24}, {7,20}, {15,20}, {3,23}, {8,17}, {5,29}, {16,29}, {11,28}, {4,31}, {3,27}, {6,26}, {14,26}, {15,19}, {4,21}, {4,17}, {12,29}, {13,30}, {9,25}, {4,25}, {1,26}, {8,19}, {13,22}, {12,23}, {14,32}, {2,24}, {5,22}, {15,31}, {16,27}, {14,22}, {6,30}, {10,28}, {8,27}, {11,19}, {3,28}, {11,31}, {3,24}, {5,17}, {8,23}, {6,20}, {9,26}, {9,18}, {11,27}, {13,21}, {11,32}, {15,27}, {8,25}, {7,32}, {9,29}, {2,26}, {10,32}, {13,17}, {11,20}, {3,20}, {10,20}, {6,24}, {5,18}, {10,26}, {4,23}, {11,24}, {1,30}, {16,31}, {2,30}, {1,21}, {1,18}, {15,24}, {5,25}, {4,19}, {14,24}, {8,29}, {9,22}, {6,28} }; // ET32.26 // Bipartite(16,16) Valencies [8,8] // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 25165824 EdgePairs[32][26]:={ {10,19}, {16,25}, {10,21}, {15,23}, {8,31}, {10,22}, {11,23}, {6,18}, {9,30}, {3,29}, {2,22}, {5,30}, {13,18}, {10,27}, {7,24}, {6,23}, {11,29}, {14,19}, {1,25}, {14,18}, {12,17}, {12,22}, {16,18}, {6,32}, {7,31}, {16,23}, {13,27}, {1,32}, {16,20}, {7,23}, {15,29}, {12,25}, {3,31}, {2,19}, {5,26}, {9,17}, {15,32}, {13,20}, {2,29}, {3,19}, {10,30}, {14,27}, {12,21}, {12,30}, {4,20}, {8,28}, {1,17}, {13,26}, {15,25}, {1,22}, {2,32}, {16,17}, {8,18}, {4,28}, {7,29}, {4,29}, {16,26}, {7,25}, {5,19}, {10,24}, {8,26}, {3,23}, {8,17}, {11,28}, {3,27}, {4,30}, {6,26}, {14,26}, {12,28}, {4,21}, {4,17}, {5,28}, {12,29}, {13,30}, {9,25}, {4,25}, {10,29}, {1,26}, {13,22}, {14,32}, {2,24}, {6,31}, {5,22}, {2,27}, {6,19}, {15,21}, {15,31}, {2,21}, {5,27}, {11,19}, {14,31}, {14,23}, {5,20}, {4,22}, {3,28}, {11,31}, {9,24}, {13,28}, {8,20}, {8,23}, {11,21}, {9,26}, {3,21}, {9,18}, {11,27}, {16,28}, {8,25}, {7,32}, {10,32}, {15,17}, {11,20}, {7,21}, {3,20}, {9,32}, {6,24}, {5,18}, {6,27}, {13,19}, {7,17}, {1,30}, {16,31}, {2,30}, {1,18}, {12,20}, {15,24}, {14,24}, {1,24}, {9,22} }; // ET32.27 // Bipartite(16,16) Valencies [8,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 98304 EdgePairs[32][27]:={ {16,25}, {13,25}, {10,21}, {13,29}, {14,25}, {15,23}, {11,17}, {8,24}, {10,22}, {9,30}, {12,19}, {3,29}, {2,22}, {4,27}, {6,17}, {16,30}, {11,29}, {13,24}, {14,19}, {12,31}, {5,24}, {6,32}, {7,31}, {6,25}, {16,23}, {12,18}, {3,30}, {1,32}, {12,27}, {7,23}, {2,28}, {14,20}, {2,18}, {9,17}, {10,18}, {15,32}, {13,20}, {5,21}, {10,23}, {2,29}, {3,19}, {10,30}, {14,27}, {8,22}, {16,21}, {4,20}, {15,22}, {9,27}, {2,31}, {2,23}, {7,26}, {1,17}, {15,25}, {16,17}, {8,21}, {4,28}, {10,31}, {4,29}, {16,26}, {7,25}, {9,23}, {5,19}, {7,20}, {8,26}, {15,20}, {8,17}, {5,29}, {11,28}, {4,31}, {3,27}, {6,26}, {14,26}, {12,28}, {12,29}, {10,29}, {1,26}, {13,22}, {15,26}, {14,32}, {5,22}, {6,19}, {14,17}, {15,31}, {1,23}, {2,21}, {10,28}, {15,18}, {11,19}, {7,18}, {5,20}, {9,28}, {3,28}, {3,24}, {5,31}, {8,23}, {16,22}, {11,21}, {9,26}, {6,20}, {3,21}, {11,30}, {9,18}, {11,27}, {4,32}, {13,21}, {1,27}, {7,22}, {4,18}, {8,25}, {7,32}, {12,32}, {1,28}, {3,17}, {9,32}, {6,24}, {8,30}, {13,31}, {6,27}, {13,19}, {11,24}, {1,30}, {2,30}, {1,18}, {12,20}, {5,25}, {4,19}, {14,24}, {16,24} }; // ET32.28 // Bipartite(8,24) Valencies [9,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 80621568 EdgePairs[32][28]:={ {2,11}, {4,24}, {4,23}, {7,11}, {1,24}, {3,12}, {2,26}, {2,29}, {1,32}, {2,10}, {7,12}, {8,16}, {6,26}, {4,10}, {8,21}, {3,21}, {6,12}, {6,10}, {5,15}, {4,31}, {8,24}, {3,23}, {4,16}, {8,29}, {3,29}, {3,20}, {2,21}, {5,9}, {7,30}, {8,32}, {5,23}, {4,32}, {7,27}, {4,18}, {5,25}, {5,31}, {1,16}, {3,28}, {3,15}, {6,20}, {2,18}, {5,17}, {8,13}, {3,31}, {5,30}, {7,22}, {8,22}, {4,15}, {1,27}, {7,20}, {2,27}, {1,17}, {7,19}, {6,18}, {2,19}, {5,14}, {7,28}, {3,13}, {6,25}, {6,17}, {8,14}, {1,19}, {1,9}, {4,26}, {2,13}, {6,28}, {7,14}, {8,30}, {1,11}, {5,22}, {1,25}, {6,9} }; // ET32.29 // Bipartite(16,16) Valencies [9,9] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 2304 EdgePairs[32][29]:={ {10,19}, {16,25}, {13,25}, {14,21}, {5,32}, {10,21}, {8,31}, {8,24}, {12,26}, {10,22}, {11,23}, {9,30}, {12,19}, {3,29}, {2,22}, {5,30}, {1,31}, {6,17}, {13,18}, {10,27}, {7,24}, {11,29}, {2,20}, {14,19}, {1,25}, {12,22}, {16,18}, {7,27}, {9,19}, {9,21}, {12,18}, {16,20}, {7,23}, {15,29}, {2,28}, {14,20}, {4,26}, {6,22}, {15,32}, {2,29}, {10,30}, {3,18}, {8,22}, {7,28}, {5,23}, {4,20}, {9,27}, {2,31}, {8,28}, {1,17}, {13,26}, {15,25}, {1,22}, {14,30}, {2,17}, {4,28}, {4,29}, {16,26}, {7,25}, {16,19}, {9,23}, {10,24}, {5,19}, {7,20}, {15,20}, {3,23}, {16,29}, {11,28}, {4,31}, {3,27}, {14,26}, {11,18}, {12,28}, {7,30}, {12,29}, {13,30}, {4,25}, {10,29}, {1,26}, {8,19}, {12,24}, {12,23}, {6,31}, {5,22}, {2,27}, {6,19}, {14,17}, {15,21}, {1,23}, {2,21}, {5,27}, {6,30}, {10,28}, {15,18}, {14,31}, {13,32}, {8,32}, {4,22}, {3,28}, {5,31}, {5,17}, {8,20}, {8,23}, {11,21}, {9,26}, {6,20}, {3,21}, {11,30}, {9,18}, {11,27}, {13,21}, {1,27}, {11,32}, {4,18}, {8,25}, {3,25}, {7,32}, {2,26}, {13,17}, {15,17}, {3,20}, {14,29}, {12,32}, {3,17}, {9,32}, {6,24}, {10,26}, {13,31}, {6,27}, {13,19}, {15,30}, {16,32}, {7,17}, {4,23}, {11,24}, {16,31}, {1,21}, {1,18}, {15,24}, {5,25}, {14,24}, {9,22}, {6,28}, {16,24} }; // ET32.30 // Non-bipartite Valency 9 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1152 EdgePairs[32][30]:={ {7,19}, {13,25}, {5,32}, {10,21}, {3,15}, {12,26}, {6,10}, {9,30}, {3,29}, {1,31}, {6,17}, {13,18}, {10,27}, {2,11}, {11,29}, {2,20}, {4,16}, {12,17}, {12,31}, {12,22}, {3,32}, {6,25}, {21,26}, {7,27}, {9,19}, {22,28}, {3,10}, {2,28}, {14,20}, {2,15}, {5,26}, {4,26}, {8,14}, {5,9}, {10,23}, {14,27}, {1,29}, {8,22}, {12,30}, {22,25}, {7,10}, {16,21}, {5,23}, {17,30}, {6,11}, {15,22}, {2,23}, {8,28}, {15,25}, {1,22}, {2,32}, {1,16}, {16,17}, {8,18}, {3,14}, {2,13}, {10,31}, {1,12}, {16,26}, {7,25}, {16,19}, {3,22}, {5,19}, {5,15}, {8,26}, {15,20}, {7,13}, {3,23}, {16,29}, {4,31}, {19,29}, {4,30}, {14,26}, {1,19}, {11,18}, {8,11}, {7,30}, {4,21}, {10,29}, {23,29}, {18,27}, {12,23}, {14,32}, {6,31}, {14,17}, {2,21}, {5,27}, {15,18}, {8,9}, {9,28}, {24,30}, {9,24}, {11,25}, {13,28}, {8,20}, {20,30}, {11,21}, {6,20}, {6,16}, {21,32}, {1,14}, {18,29}, {20,26}, {24,25}, {1,27}, {11,32}, {15,27}, {4,18}, {16,28}, {3,25}, {13,23}, {7,21}, {24,27}, {5,12}, {18,31}, {23,28}, {3,17}, {10,20}, {20,31}, {4,9}, {6,24}, {9,32}, {17,32}, {5,18}, {17,28}, {13,31}, {19,32}, {19,25}, {22,31}, {23,26}, {13,19}, {15,30}, {7,17}, {11,24}, {7,12}, {4,13}, {2,30}, {14,24}, {4,24}, {1,24}, {8,29}, {9,22}, {6,28}, {21,27} }; // ET32.31 // Bipartite(12,20) Valencies [10,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1440 EdgePairs[32][31]:={ {10,19}, {7,19}, {5,32}, {11,15}, {5,14}, {10,21}, {8,31}, {8,24}, {12,19}, {2,22}, {6,14}, {5,30}, {1,31}, {4,27}, {6,23}, {11,29}, {1,25}, {12,15}, {12,17}, {12,14}, {5,24}, {7,27}, {9,19}, {9,21}, {3,30}, {11,22}, {12,27}, {3,31}, {2,18}, {2,15}, {4,26}, {8,13}, {6,22}, {5,21}, {10,23}, {2,29}, {3,19}, {12,21}, {12,30}, {5,23}, {4,20}, {2,23}, {3,13}, {10,25}, {2,16}, {1,22}, {2,32}, {1,16}, {10,13}, {8,18}, {4,28}, {7,29}, {3,14}, {10,31}, {4,29}, {10,16}, {7,25}, {9,23}, {5,15}, {8,26}, {7,13}, {8,17}, {3,27}, {6,26}, {6,15}, {11,18}, {12,29}, {9,25}, {4,25}, {9,15}, {1,26}, {11,26}, {2,24}, {6,31}, {1,23}, {2,21}, {6,30}, {8,27}, {10,28}, {7,18}, {8,32}, {9,28}, {4,22}, {10,14}, {3,28}, {3,26}, {8,16}, {5,17}, {5,31}, {7,16}, {6,20}, {11,30}, {10,17}, {11,27}, {11,32}, {1,13}, {4,18}, {9,29}, {7,32}, {3,20}, {7,21}, {11,20}, {9,14}, {2,25}, {12,32}, {1,28}, {3,17}, {6,24}, {8,30}, {7,17}, {11,24}, {5,16}, {4,13}, {1,18}, {12,20}, {4,19}, {9,20}, {1,24}, {9,22}, {6,28} }; // ET32.32 // Bipartite(12,20) Valencies [10,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[32][32]:={ {1,15}, {9,13}, {5,32}, {10,21}, {12,26}, {10,22}, {6,18}, {11,23}, {4,14}, {9,30}, {12,19}, {3,29}, {2,22}, {6,14}, {6,17}, {12,16}, {10,27}, {6,23}, {6,13}, {12,17}, {12,31}, {12,22}, {3,32}, {7,31}, {9,19}, {11,16}, {3,30}, {1,32}, {12,27}, {7,23}, {7,15}, {5,13}, {3,31}, {8,14}, {8,13}, {10,18}, {8,15}, {7,28}, {5,23}, {2,23}, {7,26}, {10,25}, {2,16}, {2,32}, {6,21}, {8,18}, {4,28}, {3,14}, {2,13}, {10,15}, {10,31}, {4,29}, {5,19}, {10,24}, {5,15}, {8,26}, {8,17}, {5,29}, {4,31}, {4,30}, {11,18}, {12,28}, {7,30}, {4,15}, {10,29}, {1,26}, {8,19}, {11,26}, {6,29}, {11,14}, {2,24}, {5,22}, {2,21}, {5,27}, {11,19}, {7,18}, {9,28}, {11,31}, {5,17}, {9,24}, {11,25}, {8,20}, {6,16}, {3,21}, {1,14}, {9,18}, {11,27}, {4,32}, {1,20}, {1,27}, {7,22}, {3,16}, {1,13}, {8,25}, {3,25}, {9,29}, {2,26}, {3,20}, {7,21}, {2,25}, {12,32}, {1,28}, {3,17}, {10,20}, {8,30}, {6,27}, {9,16}, {7,17}, {4,23}, {11,24}, {2,30}, {1,21}, {12,20}, {5,25}, {4,19}, {4,24}, {9,20}, {1,24}, {6,28}, {9,22} }; // ET32.33 // Bipartite(12,20) Valencies [10,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2149908480000 EdgePairs[32][33]:={ {9,13}, {7,19}, {5,32}, {11,15}, {10,21}, {3,15}, {8,31}, {12,26}, {10,22}, {6,18}, {11,23}, {4,14}, {12,19}, {2,22}, {6,14}, {4,27}, {6,17}, {7,24}, {1,25}, {6,13}, {12,15}, {12,31}, {12,14}, {12,22}, {5,24}, {3,32}, {7,31}, {6,25}, {7,27}, {9,21}, {11,16}, {12,18}, {1,32}, {12,27}, {7,23}, {7,15}, {5,13}, {3,31}, {2,18}, {8,14}, {4,26}, {9,17}, {10,18}, {6,22}, {5,21}, {2,29}, {3,19}, {10,30}, {1,29}, {8,22}, {8,15}, {7,28}, {12,30}, {2,14}, {1,17}, {10,25}, {1,16}, {6,21}, {10,13}, {2,17}, {8,18}, {2,13}, {7,20}, {8,26}, {3,23}, {5,29}, {4,31}, {11,28}, {3,27}, {4,30}, {6,26}, {5,28}, {9,25}, {4,15}, {10,29}, {8,19}, {6,29}, {12,23}, {2,21}, {6,30}, {8,27}, {11,19}, {5,20}, {4,22}, {9,28}, {10,14}, {3,28}, {11,31}, {3,24}, {5,17}, {9,24}, {8,23}, {7,16}, {10,17}, {11,27}, {1,20}, {11,32}, {3,16}, {1,13}, {4,18}, {7,32}, {9,29}, {2,26}, {3,20}, {11,20}, {2,25}, {1,28}, {9,32}, {8,30}, {10,26}, {9,16}, {4,23}, {11,24}, {5,16}, {2,30}, {1,21}, {5,25}, {4,19}, {9,20}, {1,24} }; // ET32.34 // Bipartite(12,20) Valencies [10,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 318504960000 EdgePairs[32][34]:={ {9,13}, {5,32}, {11,15}, {3,15}, {8,31}, {10,22}, {11,23}, {4,14}, {3,29}, {2,22}, {6,17}, {12,16}, {1,25}, {4,16}, {6,13}, {12,17}, {5,24}, {6,32}, {6,25}, {9,19}, {9,21}, {11,16}, {9,31}, {12,25}, {3,31}, {2,19}, {2,18}, {2,15}, {8,14}, {4,26}, {9,17}, {10,18}, {3,19}, {10,30}, {1,29}, {8,22}, {8,15}, {12,21}, {2,14}, {5,23}, {4,20}, {9,27}, {2,31}, {2,23}, {7,26}, {1,17}, {3,13}, {1,22}, {6,21}, {8,18}, {4,28}, {7,29}, {10,16}, {7,25}, {5,19}, {9,23}, {10,24}, {5,15}, {8,26}, {7,13}, {3,23}, {7,14}, {11,28}, {3,27}, {4,30}, {12,28}, {7,30}, {5,28}, {12,29}, {9,25}, {9,15}, {1,26}, {8,19}, {6,29}, {12,24}, {2,27}, {5,27}, {8,27}, {10,28}, {11,19}, {7,18}, {5,20}, {4,22}, {10,14}, {11,31}, {5,31}, {8,23}, {6,16}, {6,20}, {3,21}, {1,14}, {11,27}, {4,32}, {7,22}, {11,32}, {1,13}, {4,18}, {3,25}, {9,29}, {2,26}, {10,32}, {7,21}, {11,20}, {12,32}, {3,17}, {10,20}, {6,24}, {8,30}, {10,26}, {7,17}, {11,24}, {1,30}, {5,16}, {2,30}, {1,21}, {1,18}, {12,20}, {4,24}, {12,13}, {6,28} }; // ET32.35 // Bipartite(12,20) Valencies [10,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3932160 EdgePairs[32][35]:={ {1,15}, {9,13}, {5,32}, {10,21}, {3,15}, {8,24}, {4,14}, {9,30}, {3,29}, {6,14}, {4,27}, {10,27}, {11,29}, {2,20}, {1,25}, {12,15}, {12,31}, {12,14}, {12,22}, {6,32}, {6,25}, {7,27}, {9,19}, {11,16}, {3,30}, {1,32}, {11,22}, {7,23}, {7,15}, {12,25}, {2,19}, {5,26}, {8,14}, {10,18}, {6,22}, {5,21}, {10,23}, {2,29}, {3,19}, {3,18}, {12,21}, {12,30}, {2,14}, {7,26}, {1,17}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {10,13}, {2,17}, {4,28}, {10,31}, {7,25}, {9,23}, {5,19}, {10,24}, {8,26}, {7,13}, {8,17}, {3,23}, {5,29}, {4,31}, {11,28}, {6,15}, {11,18}, {4,21}, {4,17}, {5,28}, {9,25}, {9,15}, {1,26}, {8,19}, {11,26}, {12,24}, {2,24}, {6,31}, {5,22}, {2,27}, {1,23}, {6,30}, {8,27}, {10,28}, {11,19}, {9,28}, {10,14}, {3,28}, {11,31}, {8,16}, {5,31}, {8,20}, {7,16}, {6,20}, {11,21}, {9,18}, {10,17}, {1,27}, {7,22}, {11,32}, {1,13}, {4,18}, {7,32}, {3,25}, {9,29}, {2,26}, {3,20}, {12,32}, {6,24}, {5,18}, {8,30}, {7,17}, {4,23}, {5,16}, {4,13}, {2,30}, {12,20}, {4,24}, {9,20}, {8,29} }; // ET32.36 // Bipartite(12,20) Valencies [10,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 46080 EdgePairs[32][36]:={ {9,13}, {10,19}, {7,19}, {5,32}, {11,15}, {10,21}, {8,31}, {8,24}, {12,26}, {10,22}, {6,18}, {4,14}, {3,29}, {5,30}, {1,31}, {12,16}, {6,23}, {11,29}, {6,13}, {12,31}, {12,22}, {5,24}, {3,32}, {7,31}, {6,25}, {7,27}, {9,19}, {9,21}, {12,18}, {11,22}, {12,25}, {2,15}, {5,26}, {8,14}, {9,17}, {6,22}, {10,23}, {3,19}, {3,18}, {8,15}, {7,28}, {2,14}, {4,20}, {9,27}, {2,31}, {2,23}, {7,26}, {1,17}, {3,13}, {10,25}, {2,16}, {2,32}, {8,21}, {2,17}, {4,28}, {10,15}, {4,29}, {5,15}, {7,20}, {7,13}, {8,17}, {5,29}, {7,14}, {3,27}, {6,26}, {1,19}, {11,18}, {12,28}, {7,30}, {4,21}, {9,25}, {4,15}, {4,25}, {10,29}, {1,26}, {11,26}, {12,24}, {12,23}, {2,24}, {6,31}, {5,22}, {2,21}, {5,27}, {10,28}, {8,32}, {4,22}, {5,20}, {10,14}, {8,16}, {8,23}, {6,16}, {3,21}, {1,14}, {11,30}, {9,18}, {11,27}, {1,20}, {1,27}, {11,32}, {3,16}, {1,13}, {3,25}, {9,29}, {11,20}, {1,28}, {3,17}, {10,20}, {6,24}, {9,32}, {5,18}, {8,30}, {9,16}, {7,17}, {4,23}, {11,24}, {1,30}, {2,30}, {4,19}, {12,13}, {6,28} }; // ET32.37 // Bipartite(12,20) Valencies [10,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 122880 EdgePairs[32][37]:={ {1,15}, {9,13}, {7,19}, {5,32}, {5,14}, {8,31}, {12,26}, {10,22}, {6,18}, {11,23}, {9,30}, {4,14}, {3,29}, {2,22}, {1,31}, {4,27}, {12,16}, {6,23}, {11,29}, {1,25}, {6,13}, {12,15}, {12,17}, {12,22}, {5,24}, {6,32}, {7,31}, {7,27}, {3,30}, {12,27}, {2,28}, {12,25}, {3,31}, {2,18}, {2,15}, {8,13}, {10,18}, {6,22}, {10,30}, {3,19}, {8,15}, {12,30}, {4,20}, {2,23}, {7,26}, {2,32}, {1,16}, {6,21}, {8,21}, {2,17}, {7,29}, {3,14}, {2,13}, {10,16}, {4,29}, {9,23}, {10,24}, {5,19}, {8,17}, {5,29}, {11,28}, {4,30}, {6,26}, {11,18}, {4,17}, {5,28}, {9,25}, {4,15}, {4,25}, {9,15}, {1,26}, {8,19}, {11,14}, {6,31}, {11,13}, {5,22}, {2,27}, {1,23}, {5,27}, {8,27}, {10,28}, {11,19}, {9,28}, {10,14}, {11,31}, {3,26}, {3,24}, {5,17}, {9,24}, {8,23}, {7,16}, {6,16}, {11,21}, {3,21}, {9,18}, {1,20}, {7,22}, {3,16}, {1,13}, {8,25}, {7,32}, {10,32}, {3,20}, {7,21}, {9,14}, {2,25}, {12,32}, {10,20}, {5,18}, {10,26}, {7,17}, {11,24}, {1,30}, {1,21}, {12,20}, {4,19}, {4,24}, {9,20}, {8,29}, {6,28} }; // ET32.38 // Bipartite(16,16) Valencies [10,10] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 23040 EdgePairs[32][38]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {13,32}, {9,28}, {4,27}, {13,21}, {14,19}, {15,24}, {16,26}, {11,25}, {16,27}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {16,31}, {4,29}, {1,27}, {3,25}, {10,23}, {10,26}, {4,19}, {7,22}, {4,31}, {1,19}, {5,20}, {1,21}, {16,18}, {16,25}, {2,28}, {5,32}, {14,28}, {8,31}, {8,27}, {16,29}, {6,22}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {16,30}, {15,29}, {6,21}, {2,25}, {6,31}, {1,17}, {5,22}, {4,22}, {9,29}, {1,18}, {7,20}, {14,21}, {12,17}, {15,32}, {16,24}, {9,26}, {9,27}, {5,29}, {9,19}, {14,30}, {11,22}, {7,25}, {10,28}, {1,22}, {15,27}, {6,30}, {5,23}, {10,31}, {13,22}, {15,19}, {2,20}, {7,30}, {13,31}, {11,21}, {7,26}, {2,32}, {16,32}, {11,23}, {11,29}, {6,24}, {5,24}, {13,25}, {15,20}, {13,28}, {4,28}, {3,29}, {8,26}, {9,22}, {7,31}, {13,30}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {14,18}, {1,24}, {12,23}, {13,24}, {6,27}, {5,31}, {12,19}, {12,30}, {3,23}, {8,23}, {3,21}, {1,25}, {7,29}, {6,28}, {9,30}, {14,20}, {15,21}, {16,17}, {13,26}, {11,26}, {7,23}, {13,19}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {11,32}, {14,32}, {8,24}, {5,26}, {8,18}, {4,18}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {15,23}, {3,31}, {9,24}, {10,20}, {12,31}, {5,19}, {6,20}, {2,30}, {15,30}, {2,18}, {9,23}, {7,21}, {4,32}, {12,18}, {12,21}, {14,29}, {14,26}, {7,18} }; // ET32.39 // Non-bipartite Valency 10 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 125829120 EdgePairs[32][39]:={ {11,17}, {21,23}, {1,11}, {11,20}, {13,32}, {4,27}, {13,21}, {7,15}, {16,26}, {4,26}, {8,9}, {3,9}, {3,6}, {1,32}, {3,13}, {1,27}, {3,25}, {7,22}, {2,27}, {20,21}, {14,31}, {2,26}, {17,24}, {16,18}, {16,25}, {11,14}, {8,10}, {6,7}, {2,28}, {8,15}, {6,11}, {20,30}, {3,5}, {13,16}, {16,29}, {19,21}, {15,25}, {6,29}, {8,16}, {16,30}, {23,32}, {15,29}, {2,25}, {4,10}, {1,7}, {3,14}, {14,21}, {9,32}, {19,26}, {12,17}, {19,30}, {12,20}, {27,30}, {5,11}, {5,29}, {9,19}, {27,29}, {19,29}, {19,22}, {6,8}, {11,13}, {17,23}, {15,26}, {1,31}, {22,27}, {24,25}, {21,27}, {6,12}, {12,13}, {6,30}, {23,26}, {5,23}, {10,31}, {13,22}, {24,32}, {14,16}, {28,29}, {24,26}, {13,31}, {7,16}, {2,32}, {1,12}, {14,15}, {6,24}, {5,30}, {5,24}, {17,27}, {5,7}, {23,25}, {8,22}, {18,24}, {9,20}, {18,27}, {4,13}, {1,28}, {3,27}, {20,22}, {4,28}, {15,17}, {6,23}, {3,10}, {3,26}, {30,32}, {29,32}, {4,6}, {20,29}, {17,28}, {5,12}, {8,21}, {4,9}, {22,23}, {14,22}, {12,19}, {10,32}, {12,14}, {20,25}, {2,7}, {1,25}, {22,28}, {13,15}, {18,23}, {2,11}, {4,5}, {16,17}, {28,30}, {22,24}, {15,18}, {9,18}, {20,26}, {10,17}, {18,28}, {1,26}, {4,14}, {5,8}, {29,31}, {9,17}, {14,32}, {10,18}, {7,9}, {2,31}, {19,25}, {11,19}, {10,19}, {4,25}, {1,8}, {3,28}, {7,10}, {23,31}, {2,12}, {2,8}, {10,20}, {30,31}, {21,24}, {15,30}, {9,31}, {21,28}, {7,21}, {12,18}, {24,31}, {11,18} }; // ET32.40 // Bipartite(8,24) Valencies [12,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 192 EdgePairs[32][40]:={ {3,22}, {5,12}, {2,14}, {4,24}, {8,19}, {8,28}, {4,23}, {5,32}, {7,16}, {1,24}, {3,12}, {2,32}, {2,29}, {5,29}, {1,32}, {7,9}, {2,24}, {7,23}, {8,16}, {6,26}, {8,11}, {4,11}, {3,21}, {6,31}, {6,12}, {7,13}, {8,25}, {5,11}, {6,10}, {1,20}, {5,15}, {3,23}, {1,31}, {2,12}, {8,29}, {3,20}, {2,21}, {7,30}, {5,16}, {8,27}, {8,10}, {5,20}, {7,27}, {4,18}, {7,32}, {5,31}, {1,15}, {7,10}, {3,11}, {1,16}, {5,19}, {5,28}, {4,21}, {4,20}, {3,30}, {6,27}, {2,15}, {3,14}, {6,21}, {3,31}, {4,17}, {7,25}, {1,18}, {3,26}, {5,30}, {7,22}, {4,15}, {4,28}, {2,27}, {1,17}, {6,18}, {4,25}, {6,19}, {2,28}, {6,22}, {8,26}, {3,13}, {8,18}, {1,19}, {2,9}, {5,13}, {7,17}, {1,9}, {4,26}, {1,22}, {2,13}, {2,25}, {4,14}, {1,23}, {7,14}, {8,30}, {6,29}, {8,17}, {6,24}, {3,10}, {6,9} }; // ET32.41 // Bipartite(8,24) Valencies [12,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 34398535680000 EdgePairs[32][41]:={ {7,19}, {5,32}, {3,15}, {8,31}, {6,10}, {6,18}, {4,14}, {2,22}, {6,14}, {4,27}, {6,17}, {7,24}, {1,25}, {6,13}, {5,24}, {3,32}, {1,9}, {7,31}, {6,25}, {7,27}, {1,32}, {7,23}, {7,15}, {5,13}, {3,31}, {2,18}, {6,9}, {4,26}, {8,14}, {7,11}, {6,22}, {5,9}, {5,21}, {2,29}, {3,19}, {1,29}, {8,22}, {7,28}, {8,15}, {2,14}, {3,11}, {2,10}, {1,17}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {2,13}, {1,12}, {7,20}, {8,26}, {3,23}, {5,29}, {4,31}, {3,27}, {4,30}, {6,26}, {8,11}, {5,28}, {4,15}, {2,9}, {8,19}, {6,29}, {4,11}, {2,21}, {6,30}, {8,27}, {5,20}, {4,22}, {3,28}, {3,24}, {5,17}, {3,12}, {8,23}, {7,16}, {1,20}, {3,16}, {1,13}, {4,18}, {7,32}, {2,26}, {3,20}, {5,12}, {2,25}, {1,28}, {8,30}, {4,23}, {7,12}, {5,16}, {2,30}, {1,21}, {5,25}, {4,19}, {4,10}, {1,24} }; // ET32.42 // Bipartite(8,24) Valencies [12,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 73383542784 EdgePairs[32][42]:={ {1,15}, {7,19}, {5,32}, {6,12}, {5,14}, {8,24}, {8,31}, {6,10}, {6,18}, {4,14}, {1,11}, {3,29}, {2,22}, {1,9}, {7,31}, {1,32}, {7,23}, {3,10}, {2,28}, {3,31}, {2,18}, {6,9}, {2,15}, {5,26}, {4,26}, {8,14}, {8,13}, {7,11}, {6,22}, {5,9}, {5,21}, {3,19}, {1,29}, {4,12}, {7,28}, {7,10}, {5,23}, {3,11}, {2,10}, {4,20}, {1,17}, {3,13}, {2,16}, {6,21}, {8,18}, {7,29}, {7,25}, {3,22}, {5,15}, {8,26}, {7,13}, {3,23}, {5,29}, {4,31}, {4,30}, {6,15}, {4,25}, {2,9}, {1,26}, {8,19}, {2,24}, {2,27}, {1,23}, {2,21}, {5,27}, {6,30}, {2,12}, {5,20}, {8,32}, {3,28}, {5,17}, {8,20}, {7,16}, {6,16}, {1,14}, {4,32}, {1,20}, {1,27}, {5,11}, {7,22}, {3,16}, {4,18}, {3,25}, {8,25}, {3,17}, {6,24}, {8,30}, {6,27}, {7,17}, {4,13}, {1,21}, {2,30}, {4,19}, {4,24}, {8,12}, {6,28} }; // ET32.43 // Bipartite(8,24) Valencies [12,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 9172942848 EdgePairs[32][43]:={ {3,22}, {5,12}, {2,14}, {4,9}, {8,28}, {8,20}, {2,26}, {5,24}, {2,32}, {1,29}, {5,29}, {7,31}, {7,12}, {8,16}, {4,10}, {3,21}, {3,27}, {6,12}, {7,13}, {5,11}, {6,10}, {6,30}, {8,24}, {3,23}, {4,16}, {1,31}, {3,9}, {3,29}, {2,21}, {7,30}, {8,32}, {4,32}, {5,23}, {6,16}, {8,10}, {7,32}, {5,25}, {5,31}, {1,15}, {3,11}, {2,31}, {3,16}, {3,28}, {2,20}, {3,15}, {7,18}, {3,17}, {5,19}, {1,21}, {4,27}, {4,21}, {4,20}, {5,17}, {2,15}, {8,12}, {7,25}, {5,30}, {8,22}, {4,15}, {1,27}, {7,20}, {4,28}, {2,27}, {1,17}, {7,19}, {4,22}, {6,18}, {6,22}, {2,19}, {8,26}, {5,18}, {6,17}, {1,13}, {8,14}, {8,18}, {1,19}, {2,9}, {5,13}, {6,11}, {1,9}, {4,26}, {2,13}, {2,25}, {4,14}, {6,28}, {1,23}, {7,14}, {8,30}, {1,11}, {1,25}, {6,29}, {6,23}, {7,24}, {6,24}, {3,10}, {7,26} }; // ET32.44 // Bipartite(8,24) Valencies [12,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 322486272 EdgePairs[32][44]:={ {1,15}, {7,19}, {6,12}, {8,31}, {6,10}, {6,18}, {3,29}, {2,22}, {1,31}, {6,17}, {4,27}, {7,24}, {1,25}, {4,16}, {6,13}, {1,9}, {7,31}, {6,25}, {7,27}, {3,30}, {1,32}, {7,23}, {7,15}, {3,10}, {6,9}, {5,26}, {8,14}, {7,11}, {2,29}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {2,14}, {5,23}, {3,11}, {4,20}, {1,17}, {3,13}, {2,16}, {2,32}, {1,16}, {6,21}, {8,10}, {8,18}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {4,29}, {3,22}, {5,19}, {5,15}, {8,26}, {8,17}, {7,14}, {3,27}, {6,26}, {7,30}, {4,21}, {5,28}, {2,9}, {6,29}, {2,24}, {4,11}, {1,23}, {2,21}, {5,27}, {8,9}, {5,20}, {3,26}, {5,31}, {8,23}, {7,16}, {6,20}, {3,21}, {4,32}, {1,20}, {5,11}, {7,22}, {5,10}, {7,32}, {8,25}, {5,12}, {2,25}, {1,28}, {5,18}, {8,30}, {4,13}, {2,30}, {4,19}, {4,24}, {1,24}, {6,28} }; // ET32.45 // Bipartite(8,24) Valencies [12,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 786432 EdgePairs[32][45]:={ {1,15}, {7,19}, {5,14}, {3,15}, {6,14}, {5,30}, {1,31}, {4,27}, {2,11}, {7,24}, {2,20}, {1,25}, {6,13}, {1,9}, {6,32}, {7,31}, {6,25}, {3,10}, {2,28}, {3,31}, {6,9}, {5,26}, {8,14}, {8,13}, {5,9}, {5,21}, {2,29}, {3,19}, {4,12}, {8,22}, {7,28}, {7,10}, {5,23}, {3,11}, {4,20}, {2,23}, {2,16}, {2,32}, {6,21}, {8,10}, {2,17}, {8,18}, {7,29}, {3,14}, {1,12}, {7,25}, {3,22}, {5,19}, {8,26}, {7,13}, {8,17}, {3,23}, {5,29}, {3,27}, {4,30}, {6,26}, {6,15}, {1,19}, {4,15}, {2,9}, {2,24}, {4,11}, {2,21}, {2,12}, {4,22}, {8,32}, {3,28}, {3,26}, {5,31}, {5,17}, {8,20}, {7,16}, {6,20}, {6,16}, {4,32}, {1,27}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {8,25}, {5,18}, {8,30}, {6,27}, {7,17}, {4,23}, {1,30}, {7,12}, {1,21}, {1,18}, {4,10}, {4,24}, {1,24}, {8,29}, {6,28} }; // ET32.46 // Bipartite(16,16) Valencies [12,12] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 2304 EdgePairs[32][46]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {13,32}, {9,28}, {6,32}, {4,27}, {4,24}, {4,26}, {4,30}, {11,25}, {16,27}, {8,30}, {6,17}, {2,23}, {12,32}, {8,28}, {15,31}, {1,32}, {3,25}, {10,23}, {10,26}, {4,19}, {16,19}, {7,22}, {4,31}, {1,19}, {2,27}, {14,31}, {1,21}, {16,18}, {16,25}, {2,28}, {5,32}, {14,28}, {4,23}, {8,27}, {13,29}, {16,29}, {10,22}, {3,18}, {11,28}, {6,29}, {16,30}, {15,29}, {2,25}, {14,23}, {6,31}, {1,17}, {5,22}, {4,22}, {9,29}, {1,18}, {7,20}, {14,21}, {12,17}, {15,32}, {16,24}, {12,20}, {9,19}, {5,25}, {15,26}, {11,22}, {7,25}, {11,31}, {14,24}, {1,22}, {15,27}, {10,29}, {10,31}, {3,20}, {13,22}, {15,19}, {10,21}, {6,18}, {1,29}, {7,30}, {13,31}, {7,26}, {2,32}, {5,18}, {16,32}, {1,23}, {11,29}, {6,24}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {9,20}, {1,28}, {3,27}, {15,17}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {16,22}, {9,22}, {7,31}, {13,30}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {14,18}, {12,23}, {14,22}, {13,24}, {6,27}, {5,31}, {12,19}, {12,30}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {14,20}, {15,21}, {14,25}, {16,17}, {16,21}, {13,26}, {11,26}, {15,18}, {7,23}, {13,19}, {2,21}, {3,30}, {9,18}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {11,32}, {9,17}, {10,18}, {16,20}, {8,24}, {6,25}, {2,31}, {5,26}, {8,18}, {4,18}, {15,28}, {10,19}, {4,20}, {12,24}, {8,20}, {3,28}, {7,27}, {15,23}, {3,31}, {9,24}, {5,19}, {6,20}, {5,21}, {2,30}, {15,30}, {13,20}, {9,31}, {7,19}, {4,17}, {9,21}, {9,23}, {7,21}, {14,27}, {8,29}, {4,32}, {11,18}, {12,21}, {14,26} }; // ET32.47 // Bipartite(16,16) Valencies [12,12] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 5283615080448 EdgePairs[32][47]:={ {10,25}, {1,20}, {5,17}, {11,20}, {13,32}, {9,28}, {4,27}, {12,29}, {13,21}, {14,19}, {4,24}, {15,24}, {3,22}, {16,27}, {6,17}, {2,23}, {12,32}, {8,28}, {16,31}, {15,31}, {4,29}, {1,32}, {10,23}, {10,26}, {4,19}, {16,19}, {7,22}, {4,31}, {2,19}, {2,27}, {5,20}, {2,26}, {14,31}, {1,21}, {16,25}, {8,25}, {1,30}, {5,32}, {16,23}, {4,23}, {8,31}, {8,27}, {13,29}, {16,29}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {6,21}, {2,25}, {14,23}, {6,31}, {1,17}, {5,22}, {8,19}, {9,29}, {1,18}, {7,20}, {9,32}, {14,21}, {12,17}, {15,32}, {16,24}, {9,26}, {12,20}, {5,29}, {14,30}, {5,25}, {7,32}, {15,26}, {11,22}, {11,31}, {1,22}, {15,27}, {6,30}, {4,21}, {10,29}, {10,31}, {3,20}, {13,22}, {15,19}, {10,21}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {3,32}, {9,25}, {7,26}, {5,18}, {16,32}, {11,23}, {5,30}, {11,30}, {5,24}, {12,28}, {12,25}, {13,25}, {13,28}, {15,20}, {9,20}, {1,28}, {3,27}, {4,28}, {6,23}, {3,26}, {5,28}, {9,22}, {7,31}, {13,30}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {14,18}, {1,24}, {12,23}, {14,22}, {13,24}, {11,24}, {6,27}, {12,19}, {6,26}, {3,23}, {8,23}, {1,25}, {6,19}, {9,30}, {14,25}, {16,17}, {16,21}, {7,28}, {13,26}, {11,26}, {15,18}, {7,23}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {15,22}, {11,32}, {9,17}, {10,18}, {16,20}, {8,24}, {6,25}, {2,31}, {5,26}, {15,28}, {11,19}, {10,19}, {4,25}, {4,20}, {12,24}, {8,20}, {3,28}, {7,27}, {15,23}, {7,24}, {3,31}, {9,24}, {12,31}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {2,18}, {7,19}, {4,17}, {9,21}, {16,28}, {14,27}, {8,29}, {4,32}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18} }; // ET32.48 // Bipartite(16,16) Valencies [12,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 294912 EdgePairs[32][48]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {13,32}, {4,27}, {12,29}, {13,21}, {4,24}, {15,24}, {16,26}, {4,26}, {3,22}, {11,25}, {16,27}, {8,30}, {6,17}, {2,23}, {12,32}, {8,28}, {16,31}, {15,31}, {4,29}, {1,27}, {3,25}, {10,23}, {10,26}, {4,19}, {16,19}, {7,22}, {4,31}, {1,19}, {5,20}, {2,26}, {14,31}, {1,21}, {16,18}, {2,28}, {1,30}, {5,32}, {16,23}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {6,22}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {16,30}, {6,21}, {14,23}, {2,25}, {6,31}, {1,17}, {5,22}, {8,19}, {9,29}, {7,20}, {14,21}, {15,32}, {16,24}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {14,30}, {7,32}, {15,26}, {1,31}, {11,22}, {7,25}, {11,31}, {10,28}, {14,24}, {1,22}, {6,30}, {5,23}, {10,29}, {4,21}, {3,20}, {13,22}, {15,19}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {3,32}, {9,25}, {7,26}, {2,32}, {16,32}, {11,23}, {11,29}, {6,24}, {5,30}, {7,17}, {13,23}, {12,25}, {8,22}, {13,28}, {15,20}, {9,20}, {3,27}, {15,17}, {3,29}, {6,23}, {5,28}, {8,26}, {12,26}, {16,22}, {9,22}, {7,31}, {13,30}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {14,18}, {1,24}, {12,23}, {14,22}, {6,27}, {12,19}, {3,23}, {8,23}, {10,32}, {1,25}, {6,28}, {9,30}, {13,27}, {14,25}, {16,21}, {7,28}, {13,26}, {15,18}, {13,19}, {2,21}, {10,17}, {2,29}, {11,27}, {1,26}, {15,22}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,26}, {8,18}, {4,18}, {15,28}, {11,19}, {4,25}, {4,20}, {12,24}, {3,28}, {7,24}, {3,31}, {9,24}, {10,20}, {12,31}, {5,19}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {2,18}, {9,31}, {7,19}, {9,21}, {16,28}, {14,27}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {7,18} }; // ET32.49 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 75497472 EdgePairs[32][49]:={ {1,11}, {10,25}, {5,17}, {10,24}, {11,20}, {6,16}, {4,27}, {13,21}, {7,15}, {14,19}, {4,24}, {15,24}, {23,29}, {1,10}, {4,30}, {16,27}, {21,32}, {6,17}, {12,22}, {12,32}, {3,9}, {16,31}, {15,31}, {4,29}, {20,27}, {1,32}, {10,23}, {10,26}, {4,19}, {2,26}, {24,30}, {22,32}, {1,21}, {16,18}, {2,9}, {8,25}, {8,15}, {16,23}, {4,23}, {8,31}, {13,29}, {6,22}, {11,28}, {10,30}, {6,29}, {8,16}, {19,28}, {23,32}, {6,21}, {2,25}, {4,10}, {1,17}, {5,22}, {8,19}, {9,29}, {1,18}, {7,20}, {14,21}, {19,26}, {15,32}, {16,24}, {9,26}, {12,20}, {2,10}, {5,29}, {8,14}, {14,30}, {7,32}, {1,31}, {3,12}, {11,22}, {7,13}, {7,25}, {11,31}, {1,22}, {15,27}, {6,30}, {10,29}, {3,20}, {13,22}, {24,32}, {6,18}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {2,32}, {5,18}, {16,32}, {5,30}, {17,27}, {12,28}, {8,13}, {1,9}, {13,25}, {20,28}, {5,14}, {18,26}, {18,27}, {3,11}, {7,14}, {3,27}, {4,28}, {15,17}, {21,31}, {3,29}, {3,10}, {22,29}, {5,28}, {8,26}, {7,31}, {6,15}, {13,30}, {2,17}, {17,28}, {12,27}, {8,32}, {3,19}, {4,9}, {14,22}, {6,27}, {17,25}, {12,19}, {21,29}, {3,23}, {8,23}, {18,25}, {21,30}, {20,25}, {1,25}, {6,28}, {6,14}, {22,31}, {9,30}, {2,11}, {14,20}, {14,25}, {16,17}, {13,26}, {15,18}, {7,23}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {20,26}, {3,24}, {11,27}, {18,28}, {1,26}, {2,22}, {11,32}, {9,17}, {10,18}, {8,24}, {2,31}, {5,27}, {19,25}, {15,28}, {11,19}, {4,11}, {24,29}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {15,23}, {23,31}, {7,24}, {2,12}, {9,24}, {17,26}, {5,15}, {12,31}, {5,21}, {6,13}, {13,20}, {2,18}, {22,30}, {7,19}, {16,28}, {9,23}, {19,27}, {24,31}, {12,21}, {14,29}, {14,26}, {23,30}, {5,16} }; // ET32.50 // Non-bipartite Valency 12 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1536 EdgePairs[32][50]:={ {1,11}, {10,24}, {1,20}, {5,17}, {13,32}, {9,28}, {6,16}, {12,29}, {13,21}, {7,15}, {4,24}, {18,29}, {3,22}, {23,29}, {4,30}, {2,23}, {12,22}, {8,9}, {12,32}, {3,9}, {15,31}, {24,27}, {23,28}, {10,26}, {2,15}, {16,19}, {7,22}, {4,31}, {2,19}, {2,27}, {5,20}, {14,31}, {2,26}, {24,30}, {22,32}, {1,21}, {16,18}, {16,25}, {1,30}, {5,32}, {6,11}, {8,27}, {13,29}, {16,29}, {6,22}, {3,18}, {10,30}, {8,16}, {14,23}, {7,12}, {6,31}, {4,10}, {1,17}, {9,29}, {3,14}, {9,32}, {12,17}, {16,24}, {19,30}, {12,20}, {2,10}, {5,29}, {8,14}, {14,30}, {15,26}, {1,31}, {7,13}, {7,25}, {11,31}, {20,31}, {22,27}, {24,25}, {15,27}, {6,30}, {23,26}, {4,21}, {21,26}, {10,31}, {24,32}, {10,21}, {2,13}, {6,18}, {13,18}, {7,30}, {8,17}, {3,32}, {11,21}, {9,25}, {2,32}, {16,32}, {17,30}, {8,11}, {11,30}, {5,24}, {17,27}, {12,28}, {12,25}, {1,9}, {13,25}, {20,28}, {15,20}, {13,28}, {9,20}, {18,26}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,28}, {15,17}, {21,31}, {3,29}, {6,23}, {3,26}, {8,26}, {18,31}, {9,22}, {7,31}, {20,29}, {5,12}, {22,25}, {14,17}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {14,22}, {13,24}, {11,24}, {17,25}, {21,29}, {3,23}, {1,25}, {6,19}, {6,9}, {6,28}, {6,14}, {14,20}, {16,21}, {7,28}, {19,32}, {3,16}, {11,26}, {7,23}, {13,19}, {20,26}, {2,29}, {11,27}, {18,28}, {10,27}, {2,22}, {1,16}, {15,22}, {9,17}, {10,18}, {8,24}, {6,25}, {5,27}, {5,10}, {19,25}, {5,26}, {11,19}, {10,19}, {4,25}, {4,12}, {4,20}, {5,13}, {8,20}, {7,10}, {15,23}, {23,31}, {2,12}, {1,14}, {5,15}, {5,21}, {15,30}, {2,18}, {22,30}, {7,19}, {21,28}, {4,17}, {17,32}, {16,28}, {9,23}, {14,27}, {8,29}, {19,27}, {11,18}, {14,26}, {7,18} }; // ET32.51 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 12582912 EdgePairs[32][51]:={ {11,17}, {10,25}, {1,20}, {2,24}, {4,27}, {8,12}, {3,22}, {23,29}, {4,16}, {4,30}, {16,27}, {21,32}, {2,23}, {1,13}, {8,9}, {12,32}, {16,31}, {15,31}, {4,29}, {20,27}, {1,32}, {3,13}, {3,15}, {10,26}, {2,15}, {16,19}, {7,22}, {2,19}, {1,19}, {5,20}, {2,26}, {24,30}, {22,32}, {8,10}, {8,25}, {2,14}, {6,11}, {8,31}, {13,29}, {10,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {19,28}, {23,32}, {14,23}, {7,12}, {2,25}, {4,22}, {9,29}, {7,11}, {3,14}, {19,26}, {12,17}, {15,32}, {9,26}, {5,11}, {5,29}, {9,19}, {14,30}, {7,32}, {1,31}, {7,25}, {14,24}, {11,31}, {15,27}, {6,12}, {6,30}, {5,23}, {10,29}, {4,21}, {15,19}, {24,32}, {10,21}, {2,13}, {2,20}, {13,18}, {8,17}, {2,16}, {9,25}, {7,26}, {2,32}, {16,32}, {11,23}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {17,27}, {13,23}, {12,28}, {8,22}, {13,25}, {20,28}, {15,20}, {9,20}, {18,26}, {4,15}, {4,13}, {18,27}, {3,27}, {4,28}, {21,31}, {3,29}, {6,23}, {22,29}, {5,28}, {8,26}, {16,22}, {9,22}, {7,31}, {13,30}, {17,28}, {12,27}, {5,12}, {14,17}, {8,32}, {8,21}, {14,18}, {1,24}, {12,23}, {13,24}, {11,24}, {6,27}, {17,25}, {21,29}, {18,25}, {21,30}, {20,25}, {3,21}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {22,31}, {9,30}, {15,21}, {14,25}, {16,21}, {3,16}, {13,26}, {3,30}, {20,26}, {11,27}, {18,28}, {1,26}, {1,16}, {4,14}, {15,22}, {11,32}, {16,20}, {7,9}, {2,31}, {6,10}, {5,27}, {5,10}, {19,25}, {8,18}, {15,28}, {4,18}, {5,9}, {10,19}, {24,29}, {12,24}, {3,28}, {7,10}, {23,31}, {1,14}, {10,20}, {17,26}, {12,31}, {5,19}, {6,20}, {13,17}, {22,30}, {4,17}, {9,21}, {16,28}, {7,21}, {12,18}, {19,27}, {24,31}, {11,18}, {14,29}, {14,26}, {23,30}, {7,18} }; // ET32.52 // Bipartite(4,28) Valencies [14,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5161930260480000 EdgePairs[32][52]:={ {3,32}, {2,14}, {4,23}, {1,24}, {3,12}, {2,26}, {1,29}, {2,30}, {2,29}, {1,32}, {2,10}, {4,11}, {4,10}, {3,27}, {2,6}, {4,7}, {1,20}, {1,12}, {4,31}, {3,8}, {3,23}, {3,24}, {3,20}, {2,21}, {4,6}, {4,30}, {4,18}, {3,11}, {3,16}, {3,7}, {3,28}, {1,16}, {3,15}, {2,18}, {1,21}, {4,27}, {3,19}, {2,5}, {3,31}, {1,5}, {4,15}, {1,17}, {4,22}, {1,28}, {2,17}, {1,8}, {1,13}, {2,9}, {1,9}, {4,26}, {2,13}, {2,25}, {4,14}, {4,19}, {1,25}, {2,22} }; // ET32.53 // Bipartite(16,16) Valencies [14,14] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 5284823040 EdgePairs[32][53]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {9,28}, {13,32}, {6,32}, {4,27}, {12,29}, {13,21}, {4,24}, {14,19}, {16,26}, {4,26}, {3,22}, {4,30}, {11,25}, {16,27}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {16,31}, {15,31}, {4,29}, {1,32}, {1,27}, {3,25}, {10,23}, {10,26}, {4,19}, {16,19}, {7,22}, {4,31}, {1,19}, {5,20}, {2,26}, {1,21}, {16,18}, {2,28}, {1,30}, {5,32}, {16,23}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {16,29}, {10,22}, {6,22}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {16,30}, {15,29}, {6,21}, {2,25}, {1,17}, {4,22}, {8,19}, {9,29}, {7,20}, {9,32}, {14,21}, {12,17}, {16,24}, {9,27}, {5,29}, {9,19}, {14,30}, {5,25}, {15,26}, {1,31}, {11,22}, {7,25}, {10,28}, {11,31}, {14,24}, {1,22}, {15,27}, {6,30}, {5,23}, {10,29}, {4,21}, {10,31}, {3,20}, {15,19}, {10,21}, {2,20}, {6,18}, {13,18}, {1,29}, {7,30}, {13,31}, {3,32}, {9,25}, {7,26}, {2,32}, {5,18}, {16,32}, {11,23}, {1,23}, {6,24}, {7,17}, {11,30}, {5,24}, {13,23}, {12,25}, {8,22}, {13,25}, {13,28}, {15,20}, {9,20}, {1,28}, {3,27}, {15,17}, {3,26}, {5,28}, {8,26}, {12,26}, {16,22}, {9,22}, {7,31}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {5,31}, {11,24}, {6,27}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {10,32}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {13,27}, {14,20}, {15,21}, {14,25}, {16,21}, {7,28}, {11,26}, {13,26}, {15,18}, {7,23}, {13,19}, {2,21}, {3,30}, {10,17}, {3,24}, {2,29}, {11,27}, {2,22}, {15,22}, {11,32}, {9,17}, {10,18}, {14,32}, {16,20}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {15,28}, {11,19}, {4,25}, {3,28}, {8,20}, {12,24}, {7,27}, {15,23}, {3,31}, {9,24}, {10,20}, {12,31}, {5,19}, {6,20}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {9,21}, {16,28}, {9,23}, {7,21}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18} }; // ET32.54 // Bipartite(12,20) Valencies [15,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6449725440000 EdgePairs[32][54]:={ {10,25}, {1,20}, {5,17}, {11,20}, {9,28}, {4,27}, {12,29}, {7,15}, {4,24}, {3,22}, {4,16}, {6,17}, {2,23}, {1,13}, {12,32}, {8,28}, {4,29}, {1,32}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,31}, {8,27}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {8,16}, {6,21}, {2,25}, {6,31}, {1,17}, {5,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,32}, {12,17}, {9,26}, {12,20}, {5,29}, {5,25}, {7,32}, {11,15}, {11,22}, {9,14}, {11,31}, {1,22}, {12,13}, {6,30}, {12,16}, {4,21}, {10,29}, {10,31}, {3,20}, {10,21}, {2,13}, {6,18}, {1,29}, {7,30}, {8,17}, {3,32}, {9,25}, {7,16}, {7,26}, {5,18}, {11,23}, {5,30}, {11,30}, {5,24}, {12,28}, {12,25}, {8,13}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {6,23}, {3,26}, {5,28}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {6,26}, {12,19}, {3,23}, {8,23}, {1,25}, {6,19}, {12,15}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {5,26}, {11,19}, {10,19}, {4,25}, {4,20}, {5,13}, {8,20}, {3,28}, {12,24}, {7,27}, {7,24}, {3,31}, {9,24}, {1,14}, {12,31}, {10,14}, {5,21}, {2,30}, {6,13}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {8,29}, {4,32}, {11,18}, {12,21}, {7,18}, {5,16} }; // ET32.55 // Bipartite(16,16) Valencies [15,15] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 41845579776000 EdgePairs[32][55]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,20}, {9,28}, {13,32}, {6,32}, {4,27}, {12,29}, {13,21}, {4,24}, {14,19}, {15,24}, {16,26}, {4,26}, {3,22}, {4,30}, {11,25}, {16,27}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {16,31}, {15,31}, {4,29}, {1,32}, {1,27}, {3,25}, {10,23}, {10,26}, {4,19}, {16,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {16,18}, {16,25}, {8,25}, {2,28}, {1,30}, {5,32}, {16,23}, {14,28}, {4,23}, {8,31}, {13,29}, {16,29}, {10,22}, {6,22}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {16,30}, {15,29}, {6,21}, {2,25}, {14,23}, {6,31}, {1,17}, {4,22}, {8,19}, {9,29}, {7,20}, {9,32}, {14,21}, {12,17}, {16,24}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {14,30}, {5,25}, {7,32}, {15,26}, {1,31}, {11,22}, {7,25}, {11,31}, {14,24}, {1,22}, {15,27}, {6,30}, {5,23}, {10,29}, {4,21}, {10,31}, {3,20}, {13,22}, {15,19}, {10,21}, {2,20}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {13,31}, {3,32}, {11,21}, {9,25}, {7,26}, {2,32}, {5,18}, {16,32}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {15,20}, {9,20}, {1,28}, {3,27}, {4,28}, {15,17}, {3,29}, {6,23}, {5,28}, {8,26}, {12,26}, {16,22}, {9,22}, {7,31}, {13,30}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {1,24}, {14,18}, {14,22}, {5,31}, {6,27}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {7,29}, {6,28}, {13,27}, {14,20}, {15,21}, {14,25}, {16,21}, {7,28}, {11,26}, {13,26}, {15,18}, {7,23}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {15,22}, {11,32}, {9,17}, {10,18}, {14,32}, {16,20}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {15,28}, {11,19}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {15,23}, {7,24}, {3,31}, {9,24}, {10,20}, {12,31}, {5,19}, {6,20}, {5,21}, {2,30}, {13,17}, {15,30}, {2,18}, {9,31}, {7,19}, {4,17}, {9,21}, {16,28}, {9,23}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18} }; // ET32.56 // Non-bipartite Valency 15 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 23040 EdgePairs[32][56]:={ {1,11}, {5,17}, {9,28}, {6,32}, {6,16}, {4,27}, {13,21}, {7,15}, {4,24}, {16,26}, {4,26}, {23,29}, {3,8}, {23,27}, {4,16}, {18,32}, {4,30}, {26,31}, {2,23}, {1,13}, {12,22}, {8,9}, {12,32}, {3,9}, {3,6}, {15,31}, {20,27}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {19,24}, {10,26}, {17,20}, {2,15}, {4,19}, {16,19}, {1,19}, {28,32}, {5,20}, {24,30}, {25,30}, {22,32}, {17,24}, {17,21}, {2,28}, {2,14}, {1,30}, {6,11}, {20,30}, {8,31}, {8,27}, {16,29}, {10,15}, {19,21}, {6,22}, {15,25}, {6,29}, {3,17}, {8,16}, {19,28}, {23,32}, {2,25}, {7,12}, {14,23}, {4,10}, {4,22}, {1,18}, {19,26}, {12,17}, {16,24}, {12,20}, {27,30}, {2,5}, {2,10}, {26,27}, {26,29}, {8,14}, {19,29}, {6,8}, {11,15}, {7,32}, {11,13}, {1,31}, {7,13}, {7,25}, {11,31}, {20,31}, {25,28}, {22,27}, {1,22}, {15,27}, {12,16}, {10,29}, {21,26}, {3,20}, {27,31}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {28,29}, {7,30}, {24,26}, {8,17}, {13,31}, {18,30}, {11,21}, {9,25}, {2,32}, {16,32}, {11,23}, {11,29}, {5,30}, {8,11}, {5,24}, {5,7}, {12,28}, {12,25}, {23,25}, {8,22}, {1,9}, {13,25}, {13,28}, {15,20}, {5,14}, {9,20}, {18,27}, {3,11}, {20,22}, {4,7}, {21,31}, {3,29}, {2,3}, {6,23}, {8,26}, {17,31}, {29,32}, {16,22}, {9,22}, {13,30}, {2,17}, {17,28}, {9,13}, {5,12}, {22,25}, {25,32}, {14,17}, {1,24}, {22,23}, {14,22}, {5,31}, {13,24}, {20,23}, {12,30}, {21,29}, {3,23}, {8,23}, {18,19}, {10,32}, {18,25}, {12,14}, {17,29}, {20,25}, {3,21}, {2,7}, {9,12}, {6,19}, {6,9}, {13,15}, {6,28}, {18,23}, {9,30}, {10,11}, {4,5}, {14,20}, {15,21}, {16,17}, {7,28}, {19,32}, {11,26}, {15,18}, {13,19}, {2,21}, {2,29}, {11,27}, {10,27}, {1,26}, {1,16}, {4,14}, {18,22}, {9,17}, {10,18}, {14,32}, {6,25}, {5,27}, {5,10}, {5,26}, {4,18}, {11,19}, {10,19}, {1,4}, {1,8}, {4,12}, {12,24}, {8,20}, {3,28}, {7,10}, {15,23}, {7,24}, {3,31}, {2,12}, {9,24}, {1,6}, {17,26}, {30,31}, {5,15}, {10,14}, {21,24}, {5,21}, {15,30}, {6,13}, {22,30}, {9,31}, {7,19}, {21,28}, {9,16}, {16,28}, {7,21}, {14,27}, {8,29}, {4,32}, {24,28}, {24,31}, {11,18}, {14,29}, {14,26}, {7,18} }; // ET32.57 // Non-bipartite Valency 15 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 23040 EdgePairs[32][57]:={ {11,17}, {21,23}, {10,25}, {1,20}, {2,24}, {10,24}, {11,20}, {13,32}, {25,31}, {12,29}, {8,12}, {14,19}, {15,24}, {18,29}, {3,22}, {1,10}, {11,25}, {16,27}, {8,30}, {21,32}, {6,17}, {8,28}, {16,31}, {4,29}, {1,32}, {24,27}, {23,28}, {7,22}, {4,31}, {2,19}, {2,27}, {2,4}, {25,29}, {20,21}, {2,26}, {14,31}, {1,21}, {16,18}, {16,25}, {2,9}, {11,14}, {18,21}, {8,10}, {8,25}, {6,7}, {5,32}, {8,15}, {16,23}, {14,28}, {4,23}, {3,5}, {13,29}, {9,11}, {13,16}, {10,22}, {3,18}, {11,28}, {10,30}, {3,7}, {16,30}, {15,29}, {6,21}, {6,31}, {1,17}, {1,7}, {5,22}, {26,28}, {8,19}, {9,29}, {7,11}, {7,20}, {3,14}, {9,32}, {14,21}, {15,32}, {4,8}, {9,26}, {18,20}, {19,30}, {9,27}, {1,5}, {5,11}, {5,29}, {9,19}, {27,29}, {14,30}, {19,22}, {5,25}, {15,26}, {17,23}, {3,12}, {11,22}, {9,14}, {10,28}, {14,24}, {24,25}, {21,27}, {6,12}, {12,13}, {6,30}, {23,26}, {5,23}, {4,21}, {10,31}, {13,22}, {15,19}, {24,32}, {2,13}, {1,29}, {2,16}, {3,32}, {7,16}, {7,26}, {1,12}, {5,18}, {14,15}, {1,23}, {6,24}, {2,6}, {7,17}, {17,30}, {11,30}, {21,25}, {17,27}, {13,23}, {8,13}, {18,24}, {20,28}, {18,26}, {19,31}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {15,17}, {10,13}, {10,12}, {3,10}, {22,29}, {3,26}, {1,3}, {30,32}, {5,28}, {18,31}, {12,26}, {7,31}, {6,15}, {4,6}, {20,29}, {12,27}, {8,32}, {8,21}, {3,19}, {4,9}, {14,18}, {12,23}, {6,27}, {11,24}, {17,25}, {6,26}, {12,19}, {21,30}, {17,19}, {1,25}, {22,28}, {26,32}, {7,29}, {27,32}, {1,15}, {12,15}, {6,14}, {22,31}, {2,11}, {13,27}, {14,25}, {16,21}, {28,30}, {22,24}, {3,16}, {13,26}, {22,26}, {11,16}, {7,23}, {3,30}, {9,18}, {10,17}, {20,26}, {3,24}, {18,28}, {2,22}, {15,22}, {5,8}, {29,31}, {11,32}, {16,20}, {8,24}, {7,9}, {20,24}, {2,31}, {6,10}, {19,25}, {8,18}, {15,28}, {5,9}, {4,25}, {4,11}, {24,29}, {4,20}, {5,13}, {7,27}, {28,31}, {25,27}, {23,31}, {1,14}, {2,8}, {10,20}, {12,31}, {5,19}, {6,20}, {17,22}, {9,15}, {2,30}, {13,17}, {13,20}, {2,18}, {19,23}, {4,17}, {17,32}, {9,21}, {9,23}, {20,32}, {12,18}, {19,27}, {12,21}, {23,30}, {26,30}, {10,16}, {5,16} }; // ET32.58 // Bipartite(16,16) Valencies [16,16] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 875526273394790105088000000 EdgePairs[32][58]:={ {11,17}, {10,24}, {1,20}, {5,17}, {2,24}, {10,25}, {11,20}, {9,28}, {13,32}, {6,32}, {4,27}, {12,29}, {13,21}, {4,24}, {14,19}, {15,24}, {16,26}, {4,26}, {3,22}, {4,30}, {11,25}, {16,27}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {16,31}, {15,31}, {4,29}, {1,32}, {1,27}, {3,25}, {10,23}, {10,26}, {4,19}, {16,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {14,31}, {1,21}, {16,18}, {16,25}, {8,25}, {2,28}, {1,30}, {5,32}, {16,23}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {16,29}, {10,22}, {6,22}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {16,30}, {15,29}, {6,21}, {2,25}, {14,23}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {9,32}, {14,21}, {12,17}, {15,32}, {16,24}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {14,30}, {5,25}, {7,32}, {15,26}, {1,31}, {11,22}, {7,25}, {10,28}, {11,31}, {14,24}, {1,22}, {15,27}, {6,30}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {13,22}, {15,19}, {10,21}, {2,20}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {13,31}, {3,32}, {11,21}, {9,25}, {7,26}, {2,32}, {5,18}, {16,32}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {15,20}, {9,20}, {1,28}, {3,27}, {4,28}, {15,17}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {16,22}, {9,22}, {7,31}, {13,30}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {13,27}, {14,20}, {15,21}, {14,25}, {16,17}, {16,21}, {7,28}, {11,26}, {13,26}, {15,18}, {7,23}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {15,22}, {11,32}, {9,17}, {10,18}, {14,32}, {16,20}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {15,28}, {11,19}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {15,23}, {7,24}, {3,31}, {9,24}, {10,20}, {12,31}, {5,19}, {6,20}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {9,21}, {16,28}, {9,23}, {7,21}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18} }; // ET32.59 // Bipartite(15,17) Valencies [17,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 465123332740982243328000000 EdgePairs[32][59]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {13,32}, {6,32}, {6,16}, {4,27}, {12,29}, {13,21}, {4,24}, {14,19}, {15,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {15,31}, {4,29}, {1,32}, {1,27}, {3,25}, {10,23}, {10,26}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {14,31}, {1,21}, {8,25}, {2,28}, {1,30}, {5,32}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {13,16}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {15,29}, {6,21}, {2,25}, {14,23}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {9,32}, {14,21}, {12,17}, {15,32}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {14,30}, {5,25}, {7,32}, {15,26}, {1,31}, {11,22}, {7,25}, {10,28}, {11,31}, {14,24}, {1,22}, {15,27}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {13,22}, {15,19}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {3,32}, {11,21}, {9,25}, {7,16}, {7,26}, {2,32}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {15,20}, {9,20}, {1,28}, {3,27}, {4,28}, {15,17}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {13,30}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {13,27}, {14,20}, {15,21}, {14,25}, {7,28}, {3,16}, {11,26}, {13,26}, {15,18}, {7,23}, {11,16}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {15,22}, {11,32}, {9,17}, {10,18}, {14,32}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {15,28}, {11,19}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {15,23}, {7,24}, {3,31}, {9,24}, {10,20}, {12,31}, {5,19}, {6,20}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET32.60 // Bipartite(8,24) Valencies [18,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 103195607040000 EdgePairs[32][60]:={ {7,19}, {5,32}, {5,14}, {3,15}, {8,24}, {8,31}, {6,10}, {6,18}, {2,22}, {6,14}, {5,30}, {4,27}, {6,17}, {2,11}, {7,24}, {6,23}, {1,25}, {4,16}, {6,13}, {5,24}, {3,32}, {1,9}, {6,25}, {7,31}, {7,27}, {3,30}, {1,32}, {7,15}, {7,23}, {5,13}, {3,10}, {3,31}, {2,19}, {2,18}, {2,15}, {6,9}, {5,26}, {8,13}, {5,9}, {6,22}, {7,11}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {7,28}, {8,15}, {7,10}, {2,14}, {3,11}, {2,10}, {4,20}, {6,11}, {2,31}, {2,23}, {1,10}, {7,26}, {8,28}, {1,17}, {1,22}, {1,16}, {6,21}, {2,17}, {8,21}, {4,28}, {3,14}, {2,13}, {1,12}, {4,29}, {3,22}, {7,20}, {3,23}, {8,17}, {5,29}, {7,14}, {4,31}, {3,27}, {6,15}, {6,26}, {8,11}, {4,21}, {7,30}, {4,17}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {8,19}, {6,29}, {6,31}, {4,11}, {5,22}, {2,27}, {6,19}, {2,21}, {6,30}, {8,27}, {7,18}, {8,9}, {5,20}, {8,32}, {3,28}, {3,26}, {3,24}, {5,17}, {8,16}, {3,12}, {8,20}, {8,23}, {7,16}, {1,14}, {4,32}, {1,20}, {7,22}, {3,16}, {1,13}, {5,10}, {7,32}, {8,25}, {2,26}, {3,20}, {5,12}, {2,25}, {1,28}, {4,9}, {5,18}, {6,27}, {4,23}, {1,30}, {5,16}, {7,12}, {4,13}, {1,21}, {2,30}, {1,18}, {5,25}, {4,19}, {4,24}, {8,12}, {1,24}, {8,29} }; // ET32.61 // Bipartite(14,18) Valencies [18,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 558147999289178691993600000 EdgePairs[32][61]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {13,32}, {6,32}, {6,16}, {4,27}, {12,29}, {13,21}, {7,15}, {4,24}, {14,19}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {4,29}, {1,32}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {14,31}, {1,21}, {8,25}, {2,28}, {1,30}, {5,32}, {8,15}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {14,23}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {9,32}, {14,21}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {14,30}, {5,25}, {7,32}, {11,15}, {1,31}, {11,22}, {7,25}, {10,28}, {11,31}, {14,24}, {1,22}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {13,22}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {3,32}, {11,21}, {9,25}, {7,16}, {7,26}, {2,32}, {5,18}, {14,15}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {9,20}, {4,15}, {1,28}, {3,27}, {4,28}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {6,15}, {13,30}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {12,15}, {9,30}, {13,27}, {14,20}, {14,25}, {7,28}, {3,16}, {11,26}, {13,26}, {7,23}, {11,16}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {11,32}, {9,17}, {10,18}, {14,32}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {3,31}, {9,24}, {10,20}, {5,15}, {12,31}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {13,17}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {9,21}, {9,16}, {9,23}, {7,21}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET32.62 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 75497472 EdgePairs[32][62]:={ {9,32}, {6,25}, {23,29}, {19,26}, {11,25}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {4,31}, {6,15}, {8,21}, {14,31}, {15,27}, {5,15}, {1,19}, {3,23}, {1,21}, {3,21}, {16,28}, {21,28}, {5,32}, {7,30}, {6,9}, {13,27}, {16,21}, {24,28}, {6,32}, {11,29}, {11,17}, {1,12}, {1,20}, {3,18}, {20,26}, {19,31}, {4,24}, {18,32}, {4,30}, {8,13}, {8,30}, {8,12}, {4,16}, {4,13}, {7,11}, {1,13}, {12,26}, {3,10}, {7,27}, {8,9}, {3,9}, {12,31}, {20,29}, {23,28}, {10,20}, {1,24}, {13,24}, {24,30}, {15,30}, {2,15}, {12,23}, {22,25}, {13,20}, {16,25}, {15,19}, {1,29}, {6,18}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,19}, {14,32}, {3,17}, {8,22}, {18,29}, {9,29}, {9,20}, {4,22}, {8,19}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {8,18}, {4,18}, {12,24}, {1,31}, {3,31}, {3,13}, {11,22}, {5,12}, {6,27}, {2,30}, {4,9}, {6,12}, {4,21}, {17,29}, {13,17}, {20,25}, {7,19}, {4,32}, {16,18}, {1,30}, {2,13}, {13,18}, {8,10}, {14,28}, {11,21}, {8,17}, {16,29}, {16,17}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {3,24}, {14,23}, {6,16}, {13,25}, {21,25}, {21,31}, {19,30}, {7,12}, {4,10}, {3,29}, {17,31}, {12,17}, {2,23}, {10,19}, {9,22}, {9,19}, {20,31}, {3,25}, {17,28}, {2,27}, {12,30}, {2,12}, {1,22}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {24,25}, {22,31}, {6,19}, {20,30}, {2,20}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {17,30}, {10,22}, {10,30}, {16,30}, {12,29}, {6,31}, {11,32}, {21,32}, {16,26}, {12,25}, {1,16}, {3,22}, {4,14}, {23,27}, {4,15}, {18,31}, {6,23}, {15,17}, {4,29}, {1,32}, {24,29}, {19,29}, {24,27}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {20,32}, {5,20}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {2,11}, {13,32}, {14,26}, {11,30}, {9,28}, {2,21}, {1,11}, {18,28}, {5,24}, {15,29}, {2,22}, {16,20}, {8,11}, {2,31}, {14,19}, {18,27}, {16,27}, {3,14}, {5,26}, {19,25}, {4,25}, {5,9}, {8,14}, {7,10}, {11,31}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {21,27}, {23,30}, {6,28}, {19,32}, {1,15}, {14,25}, {15,21}, {14,20}, {7,26}, {7,18}, {5,18}, {5,16}, {1,23}, {10,24}, {15,18}, {10,27}, {5,17}, {7,17}, {13,23}, {17,27}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {23,25}, {7,20}, {9,27}, {7,9}, {12,32}, {5,10}, {8,28}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {22,32}, {7,13}, {14,17}, {16,19}, {10,32}, {17,32}, {23,26}, {21,26}, {22,28}, {8,25}, {2,32}, {12,21}, {2,14}, {11,26}, {15,25} }; // ET32.63 // Bipartite(13,19) Valencies [19,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 757486570463885367705600000 EdgePairs[32][63]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {13,32}, {6,32}, {6,16}, {4,27}, {12,29}, {13,21}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {4,29}, {1,32}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,27}, {8,31}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,32}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {11,15}, {1,31}, {11,22}, {9,14}, {7,25}, {10,28}, {11,31}, {1,22}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {13,22}, {10,21}, {2,20}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {3,32}, {11,21}, {9,25}, {7,16}, {7,26}, {2,32}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {5,14}, {9,20}, {4,15}, {1,28}, {7,14}, {3,27}, {4,28}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {6,15}, {13,30}, {2,17}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {10,32}, {12,14}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {13,27}, {7,28}, {3,16}, {11,26}, {13,26}, {7,23}, {11,16}, {13,19}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {13,14}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {3,31}, {1,14}, {9,24}, {10,20}, {5,15}, {12,31}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {13,17}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET32.64 // Bipartite(12,20) Valencies [20,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1165363954559823642624000000 EdgePairs[32][64]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,32}, {6,16}, {4,27}, {12,29}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {12,22}, {12,32}, {8,28}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,27}, {8,31}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,32}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {11,13}, {11,15}, {1,31}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {11,31}, {1,22}, {12,13}, {6,30}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {11,21}, {9,25}, {7,16}, {7,26}, {2,32}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {12,28}, {12,25}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {5,31}, {6,27}, {11,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {10,32}, {12,14}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {5,13}, {8,20}, {3,28}, {12,24}, {7,27}, {7,24}, {3,31}, {1,14}, {9,24}, {10,20}, {5,15}, {12,31}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET32.65 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 125829120 EdgePairs[32][65]:={ {19,28}, {6,25}, {23,29}, {5,22}, {3,8}, {11,25}, {12,22}, {8,26}, {16,22}, {1,3}, {4,31}, {6,15}, {11,15}, {21,30}, {3,19}, {15,27}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {5,32}, {7,30}, {6,9}, {8,31}, {13,27}, {14,29}, {6,14}, {16,21}, {24,28}, {10,11}, {6,32}, {11,29}, {9,11}, {11,27}, {1,20}, {3,18}, {12,28}, {19,31}, {4,24}, {2,6}, {18,32}, {15,32}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {28,31}, {1,10}, {20,24}, {7,11}, {1,13}, {13,30}, {12,26}, {2,5}, {7,27}, {2,10}, {26,29}, {10,26}, {2,17}, {17,20}, {12,31}, {23,28}, {17,26}, {1,24}, {13,24}, {24,30}, {2,15}, {12,23}, {22,25}, {27,32}, {13,20}, {15,19}, {1,29}, {6,18}, {4,23}, {13,26}, {2,29}, {13,19}, {3,17}, {18,29}, {9,29}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {4,18}, {10,12}, {7,32}, {12,24}, {3,31}, {12,27}, {11,22}, {9,13}, {6,27}, {2,30}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {18,19}, {7,19}, {4,32}, {1,30}, {2,13}, {13,18}, {19,27}, {12,15}, {14,28}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {21,31}, {7,12}, {8,24}, {9,26}, {18,20}, {5,14}, {3,29}, {17,31}, {2,23}, {10,13}, {22,29}, {25,32}, {15,23}, {9,22}, {4,11}, {20,31}, {19,24}, {25,30}, {22,30}, {12,30}, {1,22}, {11,24}, {1,6}, {5,19}, {10,29}, {18,25}, {6,13}, {22,31}, {6,19}, {2,20}, {9,16}, {4,17}, {17,19}, {9,30}, {9,12}, {3,32}, {14,27}, {7,28}, {25,31}, {2,16}, {13,29}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {6,22}, {10,25}, {12,29}, {26,31}, {6,31}, {11,32}, {15,24}, {21,32}, {3,7}, {12,25}, {1,16}, {3,22}, {23,27}, {4,15}, {18,31}, {16,31}, {4,29}, {1,5}, {2,3}, {24,29}, {26,27}, {28,32}, {8,32}, {24,27}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {20,32}, {5,20}, {18,21}, {10,21}, {9,21}, {26,30}, {7,29}, {18,30}, {8,29}, {9,23}, {8,27}, {14,26}, {10,15}, {11,30}, {9,28}, {2,21}, {2,22}, {16,20}, {8,11}, {14,19}, {20,28}, {16,27}, {26,28}, {5,26}, {3,11}, {4,8}, {14,30}, {7,31}, {5,9}, {1,4}, {4,12}, {20,27}, {8,14}, {11,31}, {14,24}, {3,15}, {7,25}, {1,14}, {6,26}, {26,32}, {14,18}, {5,21}, {9,15}, {21,29}, {20,23}, {2,4}, {17,21}, {23,30}, {6,28}, {16,23}, {19,32}, {1,15}, {14,25}, {15,21}, {14,20}, {7,26}, {7,18}, {11,28}, {5,18}, {5,16}, {1,23}, {10,24}, {10,27}, {5,17}, {7,17}, {13,23}, {6,21}, {15,22}, {15,20}, {13,28}, {16,24}, {7,20}, {9,27}, {12,32}, {15,31}, {5,10}, {8,28}, {4,20}, {8,20}, {5,13}, {5,25}, {25,27}, {10,23}, {27,31}, {4,19}, {22,32}, {3,12}, {9,14}, {7,13}, {14,17}, {25,28}, {16,19}, {10,14}, {17,32}, {21,26}, {8,25}, {2,9}, {16,32}, {12,21}, {2,14}, {11,26} }; // ET32.66 // Bipartite(4,28) Valencies [21,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 15485790781440000 EdgePairs[32][66]:={ {2,11}, {3,22}, {3,32}, {1,26}, {2,14}, {4,8}, {4,13}, {4,9}, {4,24}, {4,23}, {1,14}, {1,24}, {2,26}, {3,12}, {1,29}, {2,30}, {1,30}, {2,29}, {1,32}, {2,10}, {1,10}, {4,11}, {1,6}, {3,27}, {2,6}, {4,7}, {1,20}, {1,12}, {4,31}, {3,8}, {3,23}, {4,16}, {3,24}, {3,20}, {2,21}, {4,32}, {4,12}, {2,7}, {3,11}, {2,31}, {1,16}, {3,7}, {3,16}, {3,28}, {3,15}, {2,18}, {1,21}, {4,27}, {4,21}, {4,20}, {3,19}, {3,30}, {2,15}, {3,14}, {2,5}, {3,18}, {3,31}, {4,5}, {4,17}, {1,18}, {3,26}, {1,5}, {4,15}, {4,28}, {2,27}, {1,17}, {3,6}, {4,25}, {2,19}, {1,28}, {2,17}, {2,23}, {1,8}, {1,13}, {2,9}, {1,9}, {1,22}, {2,13}, {2,25}, {4,19}, {1,25}, {2,22}, {3,10}, {4,29} }; // ET32.67 // Bipartite(8,24) Valencies [21,7] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 67722117120 EdgePairs[32][67]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,32}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {8,27}, {6,22}, {3,17}, {8,16}, {7,12}, {6,31}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {2,10}, {5,29}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {8,17}, {2,16}, {3,32}, {7,16}, {7,26}, {1,12}, {2,32}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {3,29}, {6,23}, {5,28}, {8,26}, {7,31}, {6,15}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {4,14}, {8,24}, {6,25}, {7,9}, {2,31}, {6,10}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {5,13}, {3,28}, {8,20}, {7,27}, {7,10}, {7,24}, {3,31}, {2,12}, {1,14}, {5,15}, {6,20}, {5,21}, {2,30}, {2,18}, {7,19}, {4,17}, {7,21}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET32.68 // Bipartite(11,21) Valencies [21,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2039386920479691374592000000 EdgePairs[32][68]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {6,32}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {11,12}, {2,28}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,27}, {8,31}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {11,13}, {11,15}, {1,31}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {11,31}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {2,32}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {11,24}, {6,26}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,24}, {3,31}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET32.69 // Non-bipartite Valency 21 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 967680 EdgePairs[32][69]:={ {13,21}, {19,28}, {9,32}, {23,29}, {5,22}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {4,31}, {11,15}, {8,21}, {21,30}, {3,19}, {14,31}, {15,27}, {5,15}, {3,23}, {12,16}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {5,32}, {7,30}, {2,7}, {6,9}, {13,27}, {6,14}, {16,21}, {19,21}, {6,32}, {11,29}, {11,17}, {1,12}, {6,29}, {11,27}, {1,20}, {3,18}, {9,18}, {10,17}, {20,26}, {12,28}, {4,24}, {18,32}, {15,32}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {4,16}, {28,31}, {1,10}, {4,13}, {12,20}, {1,13}, {13,30}, {3,10}, {2,5}, {7,27}, {19,22}, {3,9}, {10,26}, {2,17}, {12,31}, {20,29}, {23,28}, {10,20}, {1,24}, {24,30}, {12,23}, {27,32}, {12,13}, {16,25}, {24,31}, {28,30}, {15,19}, {1,29}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,19}, {14,32}, {1,26}, {3,17}, {7,15}, {8,22}, {27,30}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {4,7}, {8,18}, {4,18}, {12,24}, {3,31}, {12,27}, {11,22}, {9,13}, {6,27}, {2,8}, {4,9}, {6,12}, {25,29}, {13,17}, {20,25}, {7,19}, {4,32}, {16,18}, {1,30}, {2,13}, {13,18}, {12,15}, {8,10}, {14,28}, {8,15}, {11,21}, {8,17}, {16,29}, {10,16}, {16,17}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {14,23}, {6,16}, {13,25}, {21,25}, {21,31}, {19,30}, {7,12}, {8,24}, {4,10}, {9,26}, {3,29}, {17,31}, {2,23}, {10,13}, {20,22}, {22,29}, {25,32}, {10,19}, {15,23}, {9,22}, {4,11}, {20,31}, {3,25}, {19,24}, {17,28}, {2,27}, {12,30}, {2,12}, {1,22}, {10,31}, {5,19}, {1,6}, {10,29}, {24,25}, {13,22}, {6,13}, {1,25}, {22,31}, {6,19}, {20,30}, {2,20}, {13,31}, {9,30}, {14,27}, {12,18}, {25,31}, {2,16}, {6,11}, {13,29}, {9,25}, {17,30}, {16,30}, {7,23}, {26,31}, {6,31}, {15,24}, {21,32}, {16,26}, {12,25}, {3,22}, {4,15}, {18,31}, {6,23}, {15,17}, {1,32}, {1,5}, {24,29}, {19,29}, {8,32}, {24,27}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {26,30}, {7,29}, {2,28}, {8,29}, {7,21}, {28,29}, {2,11}, {23,32}, {11,30}, {3,5}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {15,29}, {16,20}, {8,11}, {18,24}, {2,31}, {14,19}, {18,27}, {1,7}, {3,14}, {19,25}, {4,8}, {4,25}, {14,30}, {7,31}, {5,9}, {11,19}, {20,27}, {8,14}, {7,10}, {27,29}, {3,6}, {11,31}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {26,32}, {22,27}, {14,18}, {21,27}, {9,15}, {17,24}, {20,23}, {23,30}, {6,28}, {18,23}, {19,32}, {1,15}, {14,25}, {15,21}, {14,20}, {7,26}, {7,18}, {7,16}, {5,16}, {5,18}, {10,24}, {10,27}, {7,17}, {13,23}, {17,27}, {6,21}, {15,20}, {1,28}, {23,25}, {16,24}, {3,27}, {7,9}, {12,32}, {15,31}, {5,10}, {8,28}, {4,20}, {8,20}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,6}, {4,19}, {14,22}, {22,32}, {3,12}, {9,14}, {10,14}, {10,32}, {17,32}, {12,19}, {23,26}, {20,21}, {22,28}, {8,25}, {2,9}, {16,32}, {2,32}, {2,14}, {11,26}, {5,30} }; // ET32.70 // Bipartite(10,22) Valencies [22,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4078773840959382749184000000 EdgePairs[32][70]:={ {1,11}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {9,28}, {6,32}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,32}, {9,26}, {9,27}, {5,11}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {9,25}, {7,16}, {7,26}, {1,12}, {2,32}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {10,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {9,18}, {10,17}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {5,27}, {5,26}, {8,18}, {4,18}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,24}, {3,31}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {7,18}, {10,16}, {5,16} }; // ET32.71 // Bipartite(9,23) Valencies [23,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 9381179834206580323123200000 EdgePairs[32][71]:={ {1,11}, {2,24}, {1,20}, {5,17}, {9,28}, {6,32}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {9,11}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,32}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {9,25}, {7,16}, {7,26}, {1,12}, {2,32}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,10}, {7,24}, {3,31}, {2,12}, {1,14}, {9,24}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET32.72 // Bipartite(8,24) Valencies [24,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 25016479557884214194995200000 EdgePairs[32][72]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,32}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {3,14}, {7,20}, {5,11}, {2,10}, {5,29}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {7,16}, {2,32}, {1,12}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET32.73 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 63429799040778240000 EdgePairs[32][73]:={ {13,21}, {19,28}, {9,32}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {4,31}, {6,15}, {8,21}, {21,30}, {3,19}, {14,31}, {5,15}, {15,27}, {24,32}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {5,32}, {7,30}, {6,9}, {8,31}, {13,27}, {14,29}, {6,14}, {16,21}, {24,28}, {6,32}, {11,29}, {11,17}, {1,12}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {7,11}, {12,20}, {23,31}, {1,13}, {12,26}, {13,30}, {3,10}, {7,27}, {8,9}, {2,10}, {3,9}, {10,26}, {2,17}, {12,31}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {24,30}, {15,30}, {2,15}, {12,23}, {22,25}, {13,20}, {16,25}, {24,31}, {6,18}, {1,29}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,19}, {1,26}, {14,32}, {3,17}, {7,15}, {8,22}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {5,12}, {6,27}, {2,30}, {4,9}, {6,12}, {4,21}, {17,29}, {13,17}, {20,25}, {7,19}, {4,32}, {1,30}, {16,18}, {2,13}, {13,18}, {19,27}, {8,10}, {8,15}, {14,28}, {11,21}, {8,17}, {16,29}, {3,30}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {3,24}, {14,23}, {6,16}, {13,25}, {21,25}, {21,31}, {19,30}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {5,14}, {3,29}, {17,31}, {12,17}, {2,23}, {22,29}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {20,31}, {3,25}, {17,28}, {22,30}, {2,27}, {12,30}, {6,30}, {2,12}, {1,22}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {22,31}, {6,19}, {20,30}, {2,20}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {6,11}, {13,29}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {10,25}, {12,29}, {6,31}, {11,32}, {15,24}, {21,32}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {23,27}, {4,15}, {18,31}, {6,23}, {16,31}, {15,17}, {4,29}, {1,32}, {24,29}, {19,29}, {8,32}, {24,27}, {7,24}, {10,28}, {9,24}, {5,31}, {17,25}, {2,19}, {6,20}, {5,23}, {20,32}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {2,11}, {13,32}, {14,26}, {23,32}, {11,30}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {8,11}, {2,31}, {14,19}, {18,27}, {20,28}, {16,27}, {3,14}, {5,26}, {19,25}, {3,11}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {5,9}, {11,19}, {4,12}, {20,27}, {8,14}, {7,10}, {11,31}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {14,18}, {5,21}, {21,27}, {21,29}, {23,30}, {6,28}, {16,23}, {19,32}, {1,15}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {12,32}, {15,31}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {22,32}, {3,12}, {7,13}, {14,17}, {16,19}, {10,32}, {17,32}, {12,19}, {23,26}, {21,26}, {22,28}, {8,25}, {2,9}, {16,32}, {2,32}, {12,21}, {2,14}, {11,26}, {15,25}, {5,30} }; // ET32.74 // Bipartite(7,25) Valencies [25,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 78176498618388169359360000000 EdgePairs[32][74]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,32}, {6,16}, {4,27}, {7,15}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {6,29}, {3,17}, {6,21}, {2,25}, {7,12}, {6,31}, {4,10}, {1,17}, {5,22}, {4,22}, {1,18}, {7,11}, {3,14}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,32}, {7,16}, {2,32}, {1,12}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {4,32}, {7,18}, {5,16} }; // ET32.75 // Bipartite(6,26) Valencies [26,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 290369852011156057620480000000 EdgePairs[32][75]:={ {1,11}, {2,24}, {1,20}, {5,17}, {6,16}, {6,32}, {4,27}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {6,29}, {3,17}, {3,7}, {6,21}, {2,25}, {6,31}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {1,31}, {3,12}, {1,22}, {6,12}, {6,30}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,32}, {2,32}, {1,12}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {3,16}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {5,8}, {6,25}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {4,17}, {4,32}, {5,16} }; // ET32.76 // Bipartite(5,27) Valencies [27,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1306664334050202259292160000000 EdgePairs[32][76]:={ {1,15}, {5,32}, {5,14}, {3,15}, {1,11}, {4,14}, {3,29}, {2,22}, {5,30}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {5,24}, {3,32}, {1,9}, {3,30}, {1,32}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {5,6}, {3,18}, {2,14}, {3,11}, {5,23}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {5,19}, {5,15}, {3,23}, {5,29}, {4,31}, {3,27}, {4,30}, {1,19}, {4,21}, {4,17}, {5,28}, {2,9}, {4,15}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {5,31}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {2,7}, {5,18}, {1,8}, {4,23}, {1,30}, {5,16}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET32.77 // Bipartite(4,28) Valencies [28,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7317320270681132652036096000000 EdgePairs[32][77]:={ {1,15}, {3,15}, {1,11}, {4,14}, {3,29}, {2,22}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {3,32}, {1,9}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {2,14}, {3,11}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {3,27}, {4,30}, {1,19}, {4,21}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,26}, {2,24}, {4,11}, {2,27}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {1,28}, {3,17}, {4,9}, {2,7}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET32.78 // Non-bipartite Valency 28 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 4438236667576320 EdgePairs[32][78]:={ {13,21}, {19,28}, {9,32}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {5,11}, {16,22}, {4,31}, {6,15}, {11,15}, {8,21}, {21,30}, {3,19}, {14,31}, {5,15}, {15,27}, {24,32}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {5,32}, {7,30}, {2,7}, {6,9}, {8,31}, {13,27}, {14,29}, {6,14}, {16,21}, {24,28}, {19,21}, {6,32}, {11,29}, {11,17}, {1,12}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {2,6}, {18,32}, {15,32}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {28,31}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {23,31}, {1,13}, {12,26}, {13,30}, {3,10}, {2,5}, {7,27}, {8,9}, {2,10}, {19,22}, {3,9}, {26,29}, {10,26}, {2,17}, {12,31}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {24,30}, {15,30}, {2,15}, {12,23}, {22,25}, {27,32}, {12,13}, {13,20}, {16,25}, {24,31}, {28,30}, {6,18}, {1,29}, {15,19}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {1,26}, {13,19}, {14,32}, {3,17}, {7,15}, {8,22}, {27,30}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {2,8}, {4,9}, {6,12}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {20,25}, {7,19}, {4,32}, {1,30}, {16,18}, {2,13}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,30}, {16,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {21,31}, {19,30}, {7,12}, {8,24}, {4,10}, {9,26}, {14,21}, {5,14}, {3,29}, {17,31}, {12,17}, {2,23}, {10,13}, {20,22}, {22,29}, {25,32}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {20,31}, {3,25}, {19,24}, {17,28}, {11,13}, {25,30}, {22,30}, {2,27}, {12,30}, {6,30}, {2,12}, {1,22}, {11,24}, {10,31}, {9,31}, {5,19}, {1,6}, {10,29}, {18,25}, {24,25}, {13,22}, {6,13}, {1,25}, {22,31}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {25,31}, {2,16}, {6,11}, {13,29}, {9,25}, {4,5}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {10,25}, {12,29}, {26,31}, {6,31}, {11,32}, {15,24}, {21,32}, {3,7}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {23,27}, {4,15}, {18,31}, {6,23}, {16,31}, {15,17}, {4,29}, {1,32}, {1,5}, {24,29}, {19,29}, {28,32}, {8,32}, {24,27}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {20,32}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {26,30}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {28,29}, {2,11}, {13,32}, {14,26}, {23,32}, {10,15}, {11,30}, {3,5}, {9,28}, {2,21}, {1,11}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {8,11}, {18,24}, {2,31}, {14,19}, {18,27}, {20,28}, {16,27}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {5,9}, {11,19}, {1,8}, {4,12}, {20,27}, {8,14}, {7,10}, {27,29}, {3,6}, {11,31}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {26,32}, {22,27}, {14,18}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {20,23}, {17,21}, {23,30}, {6,28}, {16,23}, {18,23}, {19,32}, {1,15}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {7,17}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {12,32}, {15,31}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,6}, {27,31}, {4,19}, {14,22}, {22,32}, {3,12}, {9,14}, {7,13}, {14,17}, {16,19}, {10,14}, {10,32}, {17,32}, {12,19}, {23,26}, {21,26}, {20,21}, {22,28}, {8,25}, {2,9}, {16,32}, {2,32}, {12,21}, {2,14}, {11,26}, {15,25}, {5,30} }; // ET32.79 // Bipartite(3,29) Valencies [29,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 53050571962438211727261696000000 EdgePairs[32][79]:={ {1,15}, {3,15}, {1,11}, {3,29}, {2,22}, {1,31}, {3,7}, {2,11}, {2,20}, {1,25}, {3,32}, {1,9}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {2,14}, {3,11}, {2,10}, {2,31}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {3,27}, {1,19}, {2,9}, {3,5}, {1,4}, {1,26}, {2,4}, {2,24}, {2,27}, {3,4}, {1,23}, {2,21}, {1,7}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {3,6}, {2,25}, {1,28}, {3,17}, {2,7}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET32.80 // Bipartite(2,30) Valencies [30,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 530505719624382117272616960000000 EdgePairs[32][80]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {1,31}, {2,12}, {2,4}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET32.81 // Non-bipartite Valency 30 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1371195958099968000 EdgePairs[32][81]:={ {13,25}, {15,28}, {15,17}, {10,17}, {3,29}, {20,26}, {9,18}, {16,28}, {5,13}, {4,26}, {20,25}, {14,29}, {2,4}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {26,27}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {14,15}, {23,29}, {8,26}, {10,29}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {8,24}, {8,11}, {12,27}, {17,22}, {21,31}, {3,13}, {2,21}, {7,26}, {11,27}, {18,28}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {4,5}, {15,20}, {17,25}, {3,32}, {3,27}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {17,32}, {21,30}, {16,23}, {3,14}, {9,22}, {5,20}, {22,32}, {1,20}, {18,27}, {7,14}, {15,24}, {10,23}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {24,30}, {16,30}, {5,27}, {9,31}, {3,6}, {7,23}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {10,14}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {9,26}, {18,20}, {6,12}, {7,31}, {13,18}, {1,29}, {10,19}, {12,19}, {15,27}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {13,19}, {9,29}, {2,22}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {1,17}, {20,23}, {9,14}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {17,28}, {23,32}, {5,21}, {22,24}, {13,26}, {11,24}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {10,11}, {1,13}, {13,32}, {10,24}, {2,25}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {12,24}, {18,19}, {14,28}, {2,3}, {12,20}, {16,29}, {1,11}, {15,30}, {3,19}, {2,16}, {18,25}, {14,19}, {21,27}, {9,13}, {21,23}, {15,29}, {4,15}, {4,29}, {8,25}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {19,23}, {11,16}, {1,4}, {7,25}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,30}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {6,32}, {15,31}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {1,19}, {2,10}, {6,17}, {19,29}, {11,14}, {7,12}, {13,20}, {13,21}, {3,11}, {4,10}, {11,23}, {3,5}, {15,19}, {8,16}, {20,21}, {8,9}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {8,15}, {4,14}, {24,28}, {11,28}, {6,25}, {11,17}, {15,18}, {24,29}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {4,31}, {2,15}, {30,32}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {20,30}, {2,29}, {14,21}, {3,21}, {19,27}, {26,30}, {2,6}, {13,30}, {9,24}, {24,32}, {4,6}, {6,20}, {11,15}, {6,26}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {15,21}, {12,30}, {1,8}, {2,32}, {19,26}, {12,14}, {4,23}, {27,30}, {8,13}, {16,21}, {6,27}, {15,32}, {6,30}, {11,25}, {17,27}, {2,17}, {25,31}, {16,18}, {5,14}, {11,22}, {9,16}, {16,32}, {9,32}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {26,29}, {1,21}, {9,15}, {6,21}, {8,12}, {7,20}, {16,19}, {23,27}, {27,31}, {7,18}, {10,21}, {28,30}, {5,17}, {1,24}, {19,25}, {6,8}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {26,28}, {4,8}, {29,31}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {12,31}, {1,15}, {27,29}, {12,29}, {7,19}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {6,29}, {2,31} }; // ET32.82 // Bipartite(1,31) Valencies [31,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 8222838654177922817725562880000000 EdgePairs[32][82]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,31}, {1,12}, {1,2}, {1,3}, {1,17}, {1,30}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,28}, {1,6}, {1,14}, {1,26}, {1,18}, {1,27}, {1,21}, {1,19}, {1,29}, {1,20}, {1,8}, {1,24}, {1,32}, {1,9}, {1,23}, {1,25} }; // ET32.83 // Non-bipartite Valency 31 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 263130836933693530167218012160000000 EdgePairs[32][83]:={ {13,25}, {15,28}, {15,17}, {10,17}, {3,29}, {20,26}, {9,18}, {16,28}, {5,13}, {4,26}, {20,25}, {14,29}, {2,4}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {11,12}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {15,16}, {26,27}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {14,15}, {23,29}, {8,26}, {10,29}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {8,24}, {8,11}, {12,27}, {17,22}, {21,31}, {3,13}, {2,21}, {7,26}, {11,27}, {18,28}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {4,5}, {15,20}, {9,10}, {17,18}, {17,25}, {3,32}, {3,27}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {17,32}, {16,23}, {21,30}, {3,14}, {25,26}, {9,22}, {5,20}, {22,32}, {1,20}, {18,27}, {7,14}, {23,24}, {15,24}, {10,23}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {24,30}, {16,30}, {5,27}, {9,31}, {3,6}, {7,23}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {10,14}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {9,26}, {18,20}, {6,12}, {7,31}, {13,18}, {1,29}, {21,22}, {10,19}, {12,19}, {15,27}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {13,19}, {9,29}, {2,22}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {1,17}, {20,23}, {9,14}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {31,32}, {17,28}, {23,32}, {5,21}, {22,24}, {13,26}, {11,24}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {10,11}, {1,13}, {13,32}, {10,24}, {2,25}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {12,24}, {18,19}, {3,4}, {14,28}, {2,3}, {12,20}, {16,29}, {1,11}, {15,30}, {3,19}, {2,16}, {18,25}, {14,19}, {21,27}, {7,8}, {9,13}, {21,23}, {15,29}, {4,15}, {4,29}, {8,25}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {19,23}, {11,16}, {1,4}, {7,25}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,30}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {5,6}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {6,32}, {15,31}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {1,19}, {2,10}, {6,17}, {19,29}, {11,14}, {7,12}, {13,20}, {13,21}, {3,11}, {4,10}, {11,23}, {3,5}, {15,19}, {8,16}, {20,21}, {8,9}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {8,15}, {4,14}, {24,28}, {11,28}, {6,25}, {11,17}, {15,18}, {24,29}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {4,31}, {2,15}, {30,32}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {20,30}, {2,29}, {14,21}, {3,21}, {19,27}, {26,30}, {2,6}, {13,30}, {9,24}, {24,32}, {1,2}, {4,6}, {6,20}, {11,15}, {6,26}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {19,20}, {2,23}, {15,21}, {12,30}, {1,8}, {2,32}, {19,26}, {12,14}, {4,23}, {27,30}, {8,13}, {16,21}, {6,27}, {15,32}, {29,30}, {6,30}, {11,25}, {17,27}, {2,17}, {25,31}, {16,18}, {5,14}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {26,29}, {1,21}, {13,14}, {6,21}, {9,15}, {8,12}, {7,20}, {16,19}, {23,27}, {27,31}, {7,18}, {10,21}, {28,30}, {5,17}, {1,24}, {19,25}, {6,8}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {26,28}, {4,8}, {29,31}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {12,31}, {1,15}, {27,29}, {12,29}, {7,19}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {6,29}, {2,31} }; // Total number of connected ET graphs of order 32 is 83 // ******************************************************************************************** // Order 33 // ET33.1 // Non-bipartite Valency 2 // Diameter 16 Girth 33 // Twin-free VT AT // Automorphism group of order 66 EdgePairs[33][1]:={ {19,32}, {11,22}, {4,17}, {1,14}, {5,18}, {11,32}, {8,29}, {1,24}, {3,23}, {10,31}, {12,23}, {20,33}, {7,21}, {6,27}, {2,22}, {6,16}, {14,26}, {12,33}, {18,30}, {17,29}, {16,28}, {5,26}, {10,24}, {9,30}, {8,19}, {4,25}, {21,31}, {2,15}, {13,25}, {3,13}, {9,20}, {7,28}, {15,27} }; // ET33.2 // Bipartite(11,22) Valencies [4,2] // Diameter 11 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 45056 EdgePairs[33][2]:={ {8,20}, {4,20}, {11,18}, {7,14}, {6,21}, {11,16}, {5,13}, {5,24}, {1,23}, {4,33}, {8,29}, {7,16}, {2,24}, {6,30}, {3,14}, {3,23}, {7,27}, {9,15}, {10,28}, {2,22}, {8,18}, {11,29}, {4,31}, {10,30}, {5,15}, {9,28}, {1,12}, {2,13}, {7,25}, {10,19}, {5,26}, {4,22}, {11,27}, {9,26}, {2,33}, {6,32}, {3,12}, {1,32}, {6,19}, {1,21}, {3,25}, {8,31}, {10,17}, {9,17} }; // ET33.3 // Non-bipartite Valency 4 // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 132 EdgePairs[33][3]:={ {3,22}, {8,28}, {9,19}, {1,14}, {8,20}, {1,24}, {17,28}, {21,33}, {2,24}, {14,26}, {9,21}, {12,33}, {6,26}, {11,24}, {8,21}, {13,25}, {12,32}, {13,26}, {15,27}, {3,23}, {11,23}, {8,29}, {10,33}, {7,30}, {5,16}, {6,16}, {9,29}, {4,18}, {16,30}, {5,25}, {1,15}, {10,31}, {10,23}, {4,27}, {11,32}, {6,27}, {2,15}, {18,30}, {3,14}, {12,24}, {4,17}, {15,25}, {7,20}, {7,19}, {4,25}, {12,22}, {14,27}, {19,32}, {7,28}, {21,31}, {5,18}, {16,28}, {3,13}, {6,17}, {5,26}, {18,29}, {9,30}, {19,31}, {10,22}, {2,13}, {20,32}, {1,23}, {20,33}, {17,29}, {11,31}, {2,22} }; // ET33.4 // Bipartite(15,18) Valencies [6,5] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 360 EdgePairs[33][4]:={ {3,22}, {1,26}, {5,33}, {12,27}, {8,19}, {11,16}, {8,28}, {9,23}, {14,19}, {14,31}, {8,20}, {5,24}, {12,18}, {2,24}, {7,31}, {13,16}, {5,27}, {10,32}, {13,25}, {11,29}, {6,30}, {11,23}, {1,31}, {3,24}, {6,32}, {11,33}, {9,32}, {4,30}, {2,21}, {8,27}, {5,23}, {13,32}, {15,21}, {7,27}, {4,33}, {7,32}, {2,16}, {4,18}, {5,31}, {10,16}, {2,31}, {1,16}, {3,28}, {15,19}, {8,33}, {13,33}, {14,22}, {3,17}, {15,30}, {9,27}, {4,20}, {3,30}, {6,21}, {3,18}, {15,17}, {7,25}, {1,18}, {15,25}, {10,29}, {12,29}, {7,21}, {12,26}, {7,20}, {9,22}, {4,25}, {2,28}, {2,19}, {14,23}, {5,18}, {13,24}, {14,20}, {10,28}, {10,22}, {11,26}, {9,26}, {12,28}, {15,26}, {1,22}, {11,19}, {10,20}, {6,29}, {1,25}, {8,17}, {6,23}, {13,17}, {9,17}, {6,24}, {12,21}, {14,30}, {4,29} }; // ET33.5 // Bipartite(15,18) Valencies [6,5] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 33592320 EdgePairs[33][5]:={ {5,33}, {15,32}, {12,27}, {4,24}, {8,19}, {11,16}, {8,28}, {13,19}, {10,27}, {7,16}, {5,24}, {8,31}, {6,33}, {2,30}, {1,29}, {13,31}, {2,29}, {9,20}, {2,24}, {14,26}, {12,33}, {5,27}, {8,16}, {15,20}, {11,28}, {6,31}, {11,20}, {13,25}, {8,25}, {13,26}, {15,27}, {4,31}, {3,23}, {10,33}, {3,29}, {9,32}, {7,30}, {4,30}, {5,21}, {13,32}, {15,21}, {4,18}, {10,16}, {9,24}, {1,16}, {7,18}, {3,17}, {2,18}, {3,25}, {11,32}, {11,22}, {3,19}, {12,23}, {6,27}, {14,32}, {6,21}, {3,31}, {13,20}, {5,30}, {7,22}, {12,29}, {8,22}, {1,17}, {4,25}, {6,19}, {1,28}, {9,18}, {14,23}, {2,17}, {7,28}, {5,18}, {6,25}, {15,33}, {2,23}, {14,20}, {9,30}, {10,28}, {10,22}, {11,26}, {9,26}, {10,21}, {14,29}, {15,26}, {1,22}, {1,23}, {4,19}, {12,17}, {14,17}, {7,24}, {12,21} }; // ET33.6 // Non-bipartite Valency 6 // Diameter 5 Girth 4 // Has twins VT AT // Automorphism group of order 7981535232 EdgePairs[33][6]:={ {3,22}, {2,14}, {8,19}, {8,28}, {9,19}, {1,14}, {8,20}, {1,24}, {17,28}, {9,20}, {21,33}, {2,24}, {14,26}, {9,21}, {12,33}, {5,27}, {6,26}, {11,24}, {8,21}, {10,32}, {13,25}, {12,32}, {13,26}, {15,27}, {3,23}, {11,23}, {4,16}, {3,24}, {12,31}, {8,29}, {10,33}, {11,33}, {7,30}, {5,16}, {6,16}, {18,28}, {9,29}, {4,18}, {16,30}, {5,25}, {1,15}, {10,31}, {10,23}, {3,15}, {4,27}, {11,32}, {11,22}, {5,17}, {12,23}, {6,27}, {2,15}, {18,30}, {3,14}, {20,31}, {12,24}, {4,17}, {15,25}, {7,21}, {10,24}, {7,20}, {7,19}, {6,18}, {4,25}, {19,33}, {12,22}, {14,27}, {19,32}, {7,28}, {21,31}, {5,18}, {16,28}, {6,25}, {3,13}, {6,17}, {17,30}, {5,26}, {2,23}, {18,29}, {1,13}, {9,30}, {19,31}, {10,22}, {13,27}, {4,26}, {15,26}, {1,22}, {2,13}, {20,32}, {9,28}, {1,23}, {21,32}, {8,30}, {20,33}, {17,29}, {11,31}, {14,25}, {16,29}, {2,22}, {7,29} }; // ET33.7 // Bipartite(9,24) Valencies [8,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 13759414272 EdgePairs[33][7]:={ {3,22}, {4,13}, {4,24}, {5,32}, {9,23}, {6,33}, {9,20}, {2,10}, {8,23}, {1,10}, {8,11}, {6,12}, {6,30}, {4,31}, {8,24}, {3,23}, {9,11}, {1,31}, {7,33}, {8,29}, {3,29}, {2,33}, {6,15}, {9,32}, {4,30}, {2,21}, {5,20}, {4,12}, {7,27}, {9,29}, {4,18}, {2,16}, {7,32}, {5,25}, {5,31}, {3,11}, {3,16}, {3,28}, {1,16}, {3,17}, {5,19}, {7,15}, {6,27}, {2,15}, {8,12}, {6,21}, {7,21}, {7,20}, {2,27}, {6,18}, {4,25}, {2,28}, {1,28}, {5,14}, {9,14}, {5,26}, {1,13}, {8,18}, {5,13}, {1,19}, {9,26}, {1,22}, {4,19}, {7,14}, {8,30}, {1,25}, {8,17}, {2,22}, {9,17}, {6,24}, {3,10}, {7,26} }; // ET33.8 // Bipartite(9,24) Valencies [8,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1769472 EdgePairs[33][8]:={ {3,32}, {2,14}, {4,13}, {5,32}, {2,26}, {3,12}, {6,33}, {2,30}, {1,29}, {1,30}, {9,25}, {7,31}, {5,27}, {8,23}, {6,14}, {6,26}, {8,11}, {5,10}, {8,21}, {8,15}, {6,12}, {8,25}, {5,15}, {3,23}, {3,24}, {7,33}, {3,20}, {5,16}, {8,27}, {6,16}, {4,32}, {5,20}, {7,10}, {3,11}, {9,24}, {2,31}, {1,16}, {8,33}, {9,10}, {5,28}, {2,18}, {9,12}, {4,20}, {3,19}, {8,13}, {2,15}, {6,21}, {3,31}, {4,17}, {1,18}, {7,22}, {7,21}, {9,13}, {2,27}, {7,19}, {1,17}, {4,25}, {9,22}, {2,19}, {1,28}, {9,18}, {7,17}, {9,30}, {4,26}, {6,28}, {4,14}, {1,23}, {1,11}, {5,22}, {6,24}, {4,29}, {7,29} }; // ET33.9 // Bipartite(6,27) Valencies [9,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 725594112 EdgePairs[33][9]:={ {3,32}, {1,26}, {2,14}, {5,33}, {3,12}, {5,24}, {2,32}, {5,29}, {2,24}, {6,26}, {4,11}, {4,10}, {3,21}, {6,31}, {6,12}, {5,11}, {4,7}, {6,30}, {5,15}, {3,23}, {4,16}, {2,33}, {5,20}, {1,7}, {5,31}, {1,16}, {3,28}, {2,18}, {4,20}, {3,19}, {3,30}, {2,15}, {3,14}, {6,21}, {1,18}, {1,27}, {4,28}, {2,27}, {1,17}, {4,25}, {6,22}, {6,17}, {2,23}, {1,8}, {5,13}, {2,9}, {1,9}, {4,19}, {5,22}, {1,25}, {6,13}, {6,8}, {3,10}, {4,29} }; // ET33.10 // Bipartite(11,22) Valencies [10,5] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 110 EdgePairs[33][10]:={ {10,19}, {5,32}, {11,15}, {3,15}, {11,17}, {8,31}, {6,18}, {11,23}, {3,29}, {2,22}, {6,14}, {11,33}, {1,31}, {4,27}, {10,27}, {11,29}, {2,20}, {4,16}, {6,13}, {9,12}, {6,32}, {7,27}, {9,21}, {3,30}, {1,32}, {7,23}, {7,15}, {5,13}, {2,28}, {8,14}, {9,17}, {5,21}, {2,29}, {3,19}, {10,30}, {4,12}, {8,22}, {2,14}, {5,33}, {2,23}, {8,33}, {10,25}, {1,22}, {6,33}, {1,16}, {10,13}, {4,33}, {8,18}, {8,21}, {4,28}, {2,13}, {10,31}, {1,12}, {4,29}, {10,16}, {7,25}, {3,22}, {5,15}, {8,26}, {8,17}, {7,14}, {3,27}, {6,26}, {6,15}, {1,19}, {7,30}, {9,25}, {4,25}, {2,24}, {5,22}, {6,19}, {1,23}, {2,21}, {5,27}, {11,19}, {7,18}, {5,20}, {9,28}, {10,14}, {3,28}, {11,31}, {3,26}, {8,16}, {5,31}, {9,24}, {3,12}, {11,25}, {9,26}, {4,18}, {7,32}, {7,21}, {11,20}, {5,12}, {3,17}, {10,20}, {6,24}, {9,32}, {10,26}, {9,16}, {7,17}, {4,23}, {11,24}, {1,30}, {4,13}, {2,30}, {1,18}, {9,20}, {1,24}, {8,29}, {6,28} }; // ET33.11 // Bipartite(11,22) Valencies [10,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1351680 EdgePairs[33][11]:={ {1,15}, {10,19}, {5,32}, {11,17}, {10,22}, {6,18}, {11,23}, {9,30}, {3,29}, {11,33}, {1,31}, {7,24}, {1,25}, {6,13}, {9,19}, {9,21}, {11,22}, {7,23}, {2,28}, {9,31}, {2,15}, {5,26}, {4,26}, {9,17}, {5,21}, {10,30}, {4,12}, {3,18}, {8,22}, {5,33}, {8,33}, {10,25}, {2,16}, {2,32}, {1,16}, {10,13}, {8,21}, {2,17}, {4,28}, {7,29}, {3,14}, {2,13}, {10,15}, {1,12}, {4,29}, {7,25}, {3,22}, {10,24}, {5,15}, {7,13}, {5,29}, {7,14}, {11,28}, {3,27}, {4,30}, {10,33}, {4,17}, {9,25}, {4,15}, {1,26}, {8,19}, {6,29}, {2,24}, {6,31}, {11,13}, {5,22}, {2,27}, {6,19}, {1,23}, {2,21}, {11,12}, {6,30}, {8,27}, {7,18}, {8,32}, {9,28}, {5,20}, {10,14}, {3,28}, {11,31}, {8,16}, {5,31}, {8,23}, {6,16}, {6,20}, {1,14}, {1,20}, {1,27}, {3,16}, {4,18}, {7,32}, {3,25}, {2,26}, {7,21}, {11,20}, {9,14}, {3,17}, {9,32}, {6,24}, {5,18}, {8,30}, {10,26}, {6,27}, {3,33}, {4,23}, {11,24}, {7,12}, {4,19}, {9,20}, {8,12} }; // ET33.12 // Non-bipartite Valency 10 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 330 EdgePairs[33][12]:={ {11,17}, {21,23}, {5,17}, {11,20}, {13,32}, {9,28}, {2,33}, {13,21}, {7,15}, {14,19}, {15,24}, {18,29}, {23,27}, {4,16}, {4,30}, {11,25}, {8,30}, {30,33}, {3,9}, {16,31}, {15,31}, {3,6}, {1,32}, {23,28}, {3,25}, {19,24}, {2,19}, {2,27}, {25,29}, {26,33}, {22,32}, {1,21}, {16,25}, {17,21}, {8,25}, {4,23}, {8,31}, {13,29}, {10,15}, {10,22}, {15,16}, {6,22}, {6,29}, {8,16}, {16,30}, {19,28}, {14,23}, {11,33}, {6,31}, {4,10}, {14,33}, {1,17}, {1,7}, {27,28}, {3,14}, {7,20}, {9,32}, {9,26}, {5,11}, {2,5}, {2,10}, {9,19}, {14,30}, {11,13}, {17,23}, {15,26}, {9,14}, {10,28}, {24,25}, {21,27}, {6,12}, {20,33}, {4,21}, {3,20}, {27,31}, {13,22}, {2,13}, {6,18}, {1,29}, {1,12}, {11,23}, {11,29}, {8,11}, {5,24}, {8,13}, {18,24}, {15,20}, {18,27}, {3,11}, {20,22}, {4,7}, {21,31}, {18,33}, {5,28}, {29,32}, {12,26}, {16,22}, {9,22}, {20,29}, {17,28}, {25,32}, {8,21}, {14,18}, {1,24}, {6,27}, {12,30}, {3,23}, {18,19}, {21,30}, {10,32}, {12,14}, {9,12}, {6,9}, {7,29}, {1,15}, {13,27}, {14,25}, {19,32}, {3,16}, {22,26}, {7,23}, {5,33}, {20,26}, {10,27}, {1,26}, {2,22}, {23,33}, {4,14}, {5,8}, {16,20}, {9,17}, {8,24}, {19,25}, {5,26}, {15,28}, {10,19}, {1,4}, {4,25}, {24,29}, {12,24}, {3,28}, {7,27}, {7,10}, {28,31}, {3,31}, {2,8}, {17,26}, {5,15}, {7,33}, {12,31}, {5,19}, {6,20}, {2,30}, {13,17}, {6,13}, {22,30}, {2,18}, {17,32}, {4,32}, {12,18}, {24,31}, {12,21}, {26,30}, {7,18}, {10,16} }; // ET33.13 // Bipartite(11,22) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1351680 EdgePairs[33][13]:={ {10,19}, {5,32}, {6,12}, {11,17}, {4,14}, {3,29}, {2,22}, {6,14}, {10,27}, {7,24}, {6,23}, {2,20}, {7,33}, {5,24}, {3,32}, {2,33}, {6,25}, {7,27}, {9,21}, {11,16}, {1,32}, {5,13}, {2,28}, {9,31}, {3,31}, {2,19}, {5,26}, {4,26}, {8,14}, {9,17}, {10,18}, {6,22}, {5,21}, {10,30}, {1,29}, {3,18}, {8,15}, {7,28}, {5,23}, {2,31}, {2,23}, {8,28}, {3,13}, {1,22}, {6,33}, {1,16}, {10,13}, {4,33}, {8,18}, {2,17}, {7,29}, {3,14}, {2,13}, {10,15}, {10,31}, {1,12}, {10,16}, {7,25}, {10,24}, {5,15}, {8,26}, {7,13}, {8,17}, {3,23}, {7,14}, {11,28}, {4,30}, {6,26}, {6,15}, {1,19}, {4,21}, {5,28}, {4,15}, {4,25}, {9,15}, {10,29}, {8,19}, {11,14}, {2,24}, {6,31}, {9,33}, {1,23}, {5,27}, {11,19}, {7,18}, {2,12}, {4,22}, {9,28}, {11,31}, {3,24}, {5,17}, {3,12}, {11,25}, {8,23}, {7,16}, {6,20}, {6,16}, {9,26}, {11,21}, {3,21}, {11,30}, {9,18}, {11,27}, {4,32}, {1,27}, {7,22}, {11,32}, {3,25}, {8,25}, {9,29}, {3,20}, {11,20}, {1,33}, {5,12}, {10,20}, {9,32}, {8,30}, {10,26}, {6,27}, {7,17}, {1,30}, {5,16}, {4,13}, {1,21}, {2,30}, {1,18}, {4,19}, {4,24}, {8,12}, {9,20}, {8,29}, {9,22} }; // ET33.14 // Bipartite(15,18) Valencies [12,10] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 360 EdgePairs[33][14]:={ {11,17}, {3,33}, {10,24}, {1,20}, {5,17}, {11,20}, {13,32}, {6,16}, {4,27}, {12,29}, {13,21}, {4,24}, {14,19}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {2,23}, {8,28}, {15,31}, {1,32}, {3,25}, {10,23}, {10,26}, {4,19}, {7,22}, {4,31}, {2,19}, {10,33}, {2,27}, {1,19}, {5,20}, {2,26}, {14,31}, {2,28}, {1,30}, {5,32}, {8,31}, {8,27}, {13,16}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {10,30}, {6,29}, {6,21}, {2,25}, {14,23}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {7,20}, {9,32}, {14,21}, {12,17}, {15,32}, {12,20}, {5,29}, {14,30}, {5,25}, {7,32}, {15,26}, {10,28}, {14,24}, {15,27}, {4,33}, {10,29}, {13,22}, {15,19}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {7,30}, {8,17}, {3,32}, {11,21}, {9,25}, {7,16}, {2,32}, {6,33}, {13,33}, {1,23}, {11,29}, {7,17}, {11,30}, {5,24}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {1,28}, {4,28}, {1,33}, {3,29}, {6,23}, {3,26}, {7,31}, {12,33}, {2,17}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {14,22}, {13,24}, {11,24}, {6,27}, {5,31}, {12,19}, {6,26}, {12,30}, {3,23}, {1,25}, {9,30}, {13,27}, {14,20}, {15,21}, {7,28}, {11,26}, {13,26}, {15,18}, {11,16}, {7,23}, {2,21}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {1,26}, {2,22}, {1,16}, {9,17}, {10,18}, {14,32}, {8,24}, {6,25}, {9,33}, {5,27}, {8,18}, {4,18}, {15,28}, {11,19}, {4,20}, {3,28}, {7,27}, {15,23}, {3,31}, {9,24}, {10,20}, {7,33}, {12,31}, {5,19}, {6,20}, {13,17}, {15,30}, {9,31}, {9,21}, {9,16}, {9,23}, {7,21}, {8,29}, {12,18}, {11,18}, {14,29}, {14,26}, {5,16} }; // ET33.15 // Bipartite(15,18) Valencies [12,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3869835264000000 EdgePairs[33][15]:={ {11,17}, {3,33}, {10,25}, {1,20}, {5,17}, {2,24}, {11,20}, {13,32}, {9,28}, {2,33}, {6,16}, {15,24}, {4,26}, {3,22}, {4,16}, {8,30}, {2,23}, {12,22}, {15,31}, {4,29}, {1,32}, {8,33}, {3,25}, {10,23}, {10,26}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {5,20}, {2,26}, {5,32}, {4,23}, {8,27}, {13,29}, {13,16}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {6,21}, {14,23}, {11,33}, {6,31}, {14,33}, {1,17}, {4,22}, {7,20}, {14,21}, {9,27}, {5,29}, {9,19}, {14,30}, {7,32}, {1,31}, {7,25}, {10,28}, {14,24}, {1,22}, {15,27}, {6,30}, {12,16}, {5,23}, {10,29}, {10,31}, {13,22}, {15,19}, {2,20}, {6,18}, {1,29}, {8,17}, {13,31}, {11,21}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {5,18}, {11,23}, {1,23}, {11,29}, {6,24}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {13,25}, {13,28}, {1,28}, {3,27}, {4,28}, {8,26}, {9,22}, {7,31}, {12,33}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {14,18}, {6,27}, {11,24}, {12,19}, {12,30}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {14,20}, {15,21}, {7,28}, {3,16}, {13,26}, {11,26}, {15,18}, {7,23}, {13,19}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {1,26}, {1,16}, {15,22}, {11,32}, {14,32}, {15,33}, {8,24}, {6,25}, {9,33}, {5,27}, {5,26}, {8,18}, {15,28}, {10,19}, {4,25}, {4,20}, {12,24}, {8,20}, {3,28}, {3,31}, {9,24}, {10,20}, {12,31}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {9,21}, {9,16}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {10,16} }; // ET33.16 // Bipartite(15,18) Valencies [12,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 33592320 EdgePairs[33][16]:={ {11,17}, {10,25}, {5,17}, {10,24}, {11,20}, {9,28}, {13,32}, {2,33}, {6,32}, {4,27}, {12,29}, {4,24}, {14,19}, {15,24}, {4,16}, {4,30}, {2,23}, {12,22}, {12,32}, {8,28}, {4,29}, {1,27}, {3,25}, {10,23}, {7,22}, {2,19}, {10,33}, {2,27}, {1,19}, {5,20}, {14,31}, {1,21}, {8,25}, {2,28}, {1,30}, {5,32}, {4,23}, {8,31}, {13,16}, {15,16}, {3,18}, {10,30}, {3,17}, {8,16}, {6,21}, {2,25}, {14,23}, {11,33}, {6,31}, {14,33}, {5,22}, {4,22}, {8,19}, {1,18}, {9,32}, {14,21}, {12,17}, {15,32}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {15,26}, {1,31}, {7,25}, {1,22}, {15,27}, {6,30}, {12,16}, {4,33}, {5,23}, {10,29}, {4,21}, {10,31}, {3,20}, {13,22}, {10,21}, {6,18}, {13,18}, {7,30}, {8,17}, {2,16}, {13,31}, {3,32}, {11,21}, {9,25}, {7,16}, {6,33}, {5,18}, {11,23}, {11,29}, {6,24}, {5,30}, {7,17}, {11,30}, {5,24}, {12,28}, {8,22}, {13,25}, {13,28}, {15,20}, {9,20}, {1,28}, {4,28}, {1,33}, {3,29}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {12,33}, {13,30}, {2,17}, {12,27}, {14,17}, {8,32}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {13,24}, {6,26}, {3,23}, {8,23}, {1,25}, {6,19}, {7,29}, {14,20}, {15,21}, {14,25}, {7,28}, {11,26}, {13,26}, {15,18}, {7,23}, {13,19}, {2,21}, {3,30}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {2,22}, {1,16}, {15,22}, {11,32}, {10,18}, {14,32}, {15,33}, {6,25}, {2,31}, {9,33}, {5,26}, {4,18}, {15,28}, {10,19}, {8,20}, {7,24}, {3,31}, {6,20}, {15,30}, {13,20}, {9,31}, {7,19}, {4,17}, {9,21}, {9,16}, {14,27}, {8,29}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {5,16} }; // ET33.17 // Bipartite(12,21) Valencies [14,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10618827964416000 EdgePairs[33][17]:={ {11,17}, {3,33}, {10,25}, {1,20}, {5,17}, {2,24}, {11,20}, {9,28}, {2,33}, {6,16}, {4,26}, {3,22}, {4,16}, {8,30}, {2,23}, {1,13}, {12,22}, {4,29}, {1,32}, {3,13}, {8,33}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {5,20}, {2,26}, {11,14}, {2,14}, {5,32}, {8,15}, {4,23}, {8,27}, {10,22}, {6,22}, {3,18}, {6,21}, {6,31}, {11,33}, {1,17}, {4,22}, {7,20}, {9,27}, {5,29}, {9,19}, {8,14}, {11,15}, {7,32}, {1,31}, {7,13}, {7,25}, {10,28}, {1,22}, {12,13}, {6,30}, {12,16}, {5,23}, {10,29}, {10,31}, {2,20}, {6,18}, {1,29}, {8,17}, {11,21}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {12,28}, {12,25}, {5,14}, {1,28}, {4,13}, {7,14}, {3,27}, {4,28}, {10,13}, {8,26}, {9,22}, {7,31}, {12,33}, {6,15}, {2,17}, {9,13}, {12,27}, {8,32}, {8,21}, {3,19}, {6,27}, {11,24}, {12,19}, {12,30}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {12,15}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {1,26}, {1,16}, {4,14}, {11,32}, {8,24}, {6,25}, {9,33}, {5,27}, {5,26}, {8,18}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {3,31}, {9,24}, {1,14}, {10,20}, {5,15}, {12,31}, {10,14}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,21}, {9,16}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {10,16} }; // ET33.18 // Bipartite(9,24) Valencies [16,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 84950623715328000 EdgePairs[33][18]:={ {9,13}, {7,19}, {5,32}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {4,14}, {1,11}, {9,30}, {5,30}, {1,31}, {2,11}, {2,20}, {1,25}, {4,16}, {6,13}, {9,12}, {5,24}, {2,33}, {6,25}, {7,31}, {9,19}, {9,21}, {3,30}, {1,32}, {7,23}, {3,10}, {9,31}, {3,31}, {9,10}, {2,18}, {2,15}, {5,26}, {4,26}, {8,14}, {6,22}, {7,11}, {5,21}, {2,29}, {3,19}, {1,29}, {3,18}, {7,28}, {8,15}, {7,10}, {2,14}, {5,33}, {5,23}, {4,20}, {9,27}, {2,23}, {1,10}, {7,26}, {8,33}, {1,17}, {3,13}, {1,22}, {2,32}, {6,33}, {1,16}, {6,21}, {2,17}, {8,18}, {8,21}, {4,28}, {7,29}, {4,29}, {7,25}, {3,22}, {5,15}, {7,20}, {8,26}, {7,13}, {8,17}, {5,29}, {7,14}, {4,31}, {3,27}, {6,15}, {1,19}, {8,11}, {4,17}, {9,25}, {4,25}, {9,15}, {1,26}, {2,24}, {6,31}, {9,33}, {4,11}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {6,30}, {8,27}, {2,12}, {4,22}, {5,20}, {8,32}, {9,28}, {3,28}, {3,24}, {5,17}, {9,24}, {3,12}, {8,20}, {8,23}, {6,16}, {7,16}, {3,21}, {1,14}, {9,18}, {4,32}, {1,20}, {5,11}, {7,22}, {3,16}, {1,13}, {3,25}, {7,32}, {2,26}, {5,12}, {1,28}, {6,24}, {5,18}, {8,30}, {6,27}, {9,16}, {3,33}, {7,17}, {4,23}, {4,13}, {2,30}, {4,19}, {4,10}, {8,12}, {8,29}, {6,28}, {9,22} }; // ET33.19 // Bipartite(9,24) Valencies [16,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 13759414272 EdgePairs[33][19]:={ {7,19}, {5,32}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {1,11}, {9,30}, {3,29}, {2,22}, {5,30}, {1,31}, {7,24}, {2,20}, {1,25}, {4,16}, {6,13}, {9,12}, {7,33}, {5,24}, {3,32}, {2,33}, {6,25}, {7,31}, {7,27}, {9,21}, {1,32}, {7,15}, {5,13}, {3,10}, {2,28}, {2,19}, {2,15}, {5,26}, {9,17}, {6,22}, {1,29}, {4,12}, {8,22}, {8,15}, {2,14}, {5,23}, {3,11}, {2,10}, {9,27}, {2,31}, {1,10}, {7,26}, {8,33}, {8,28}, {1,17}, {2,16}, {1,22}, {2,32}, {6,33}, {1,16}, {6,21}, {8,10}, {8,18}, {8,21}, {4,28}, {3,14}, {2,13}, {4,29}, {7,25}, {3,22}, {5,19}, {9,23}, {7,20}, {3,23}, {7,13}, {8,17}, {5,29}, {7,14}, {4,31}, {3,27}, {4,30}, {6,15}, {1,19}, {8,11}, {7,30}, {4,17}, {4,25}, {9,15}, {1,26}, {6,31}, {9,33}, {4,11}, {2,27}, {6,19}, {1,23}, {2,21}, {6,30}, {8,27}, {7,18}, {5,20}, {4,22}, {3,28}, {3,26}, {5,31}, {5,17}, {8,16}, {9,24}, {8,23}, {6,16}, {9,26}, {3,21}, {1,14}, {9,18}, {1,20}, {9,11}, {5,11}, {3,16}, {1,13}, {4,18}, {7,32}, {9,29}, {2,26}, {3,20}, {7,21}, {5,12}, {2,25}, {9,14}, {1,28}, {3,17}, {6,24}, {9,32}, {5,18}, {8,30}, {6,27}, {3,33}, {4,23}, {7,12}, {4,13}, {5,25}, {4,19}, {4,10}, {4,24}, {8,12}, {9,20}, {8,29}, {6,28} }; // ET33.20 // Bipartite(9,24) Valencies [16,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1769472 EdgePairs[33][20]:={ {1,15}, {5,14}, {3,15}, {8,24}, {8,31}, {6,10}, {6,18}, {3,29}, {2,22}, {5,30}, {1,31}, {6,17}, {4,27}, {2,11}, {7,24}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {2,33}, {6,32}, {6,25}, {7,27}, {9,19}, {9,21}, {3,30}, {1,32}, {7,15}, {7,23}, {5,13}, {3,10}, {2,28}, {9,31}, {5,26}, {8,14}, {9,17}, {6,22}, {7,11}, {5,21}, {2,29}, {4,12}, {3,18}, {8,22}, {7,28}, {5,33}, {5,23}, {2,10}, {6,11}, {9,27}, {2,23}, {1,10}, {7,26}, {8,28}, {3,13}, {2,16}, {1,22}, {2,32}, {4,33}, {2,17}, {8,10}, {8,18}, {4,28}, {3,14}, {2,13}, {1,12}, {7,25}, {3,22}, {5,19}, {9,23}, {7,20}, {8,26}, {7,13}, {8,17}, {5,29}, {7,14}, {4,31}, {3,27}, {4,30}, {6,15}, {1,19}, {4,21}, {7,30}, {4,15}, {9,15}, {1,26}, {8,19}, {6,29}, {2,24}, {6,31}, {9,33}, {4,11}, {6,19}, {2,21}, {6,30}, {7,18}, {2,12}, {4,22}, {8,32}, {9,28}, {3,28}, {3,26}, {5,31}, {5,17}, {8,16}, {8,20}, {6,20}, {7,16}, {9,26}, {3,21}, {1,14}, {1,20}, {1,27}, {9,11}, {5,11}, {3,16}, {1,13}, {4,18}, {3,25}, {7,32}, {9,29}, {1,33}, {5,12}, {2,25}, {9,14}, {3,17}, {9,32}, {5,18}, {8,30}, {6,27}, {9,16}, {3,33}, {4,23}, {7,12}, {1,21}, {5,25}, {4,19}, {4,10}, {4,24}, {8,12}, {9,20}, {1,24}, {8,29} }; // ET33.21 // Bipartite(16,17) Valencies [17,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7441973323855715893248000000 EdgePairs[33][21]:={ {13,21}, {15,33}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {16,22}, {4,31}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {5,32}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {9,18}, {10,17}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {16,25}, {15,19}, {1,29}, {6,18}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,19}, {14,32}, {1,26}, {3,17}, {8,22}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {4,21}, {13,17}, {7,19}, {4,32}, {16,18}, {1,30}, {13,18}, {14,28}, {11,21}, {8,17}, {16,29}, {16,17}, {3,30}, {2,24}, {11,23}, {3,24}, {14,33}, {14,23}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {12,17}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {10,25}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {6,23}, {16,31}, {15,17}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {2,21}, {4,27}, {5,24}, {15,29}, {2,22}, {16,20}, {2,31}, {14,19}, {1,33}, {16,27}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {7,25}, {7,22}, {6,26}, {14,18}, {5,21}, {6,28}, {16,23}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {5,18}, {1,23}, {10,24}, {11,20}, {15,18}, {10,27}, {5,17}, {16,33}, {7,17}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {14,17}, {16,19}, {10,32}, {12,19}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {15,25}, {5,33}, {5,30} }; // ET33.22 // Bipartite(6,27) Valencies [18,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2293666840313856000 EdgePairs[33][22]:={ {5,32}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {5,30}, {4,8}, {3,7}, {1,31}, {2,11}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {2,33}, {6,25}, {6,7}, {3,30}, {1,32}, {3,10}, {3,31}, {2,18}, {6,9}, {2,15}, {5,26}, {4,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {3,18}, {2,14}, {5,33}, {5,23}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {1,22}, {2,32}, {6,33}, {1,16}, {6,21}, {2,17}, {4,28}, {3,9}, {4,29}, {3,22}, {5,15}, {5,29}, {4,31}, {3,27}, {6,15}, {1,19}, {4,17}, {4,25}, {2,9}, {1,26}, {2,24}, {6,31}, {4,11}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {1,7}, {6,30}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,24}, {5,17}, {3,12}, {6,16}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {3,25}, {2,26}, {5,12}, {1,28}, {6,24}, {5,18}, {6,27}, {3,33}, {4,23}, {1,8}, {4,13}, {2,30}, {4,19}, {4,10}, {6,28} }; // ET33.23 // Bipartite(6,27) Valencies [18,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 725594112 EdgePairs[33][23]:={ {6,12}, {3,15}, {6,18}, {3,29}, {6,14}, {4,8}, {6,17}, {2,11}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {3,32}, {1,9}, {2,33}, {6,32}, {3,30}, {1,32}, {5,7}, {5,13}, {3,10}, {2,28}, {3,31}, {2,19}, {2,18}, {6,9}, {2,15}, {5,26}, {4,26}, {5,9}, {6,22}, {2,29}, {3,19}, {4,12}, {2,14}, {5,33}, {3,11}, {2,10}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {2,32}, {6,33}, {1,16}, {6,21}, {4,28}, {3,14}, {1,12}, {4,29}, {3,22}, {5,15}, {6,8}, {3,23}, {5,29}, {4,31}, {4,30}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {4,25}, {2,9}, {1,26}, {2,24}, {6,31}, {4,11}, {5,22}, {2,27}, {1,23}, {5,27}, {1,7}, {6,30}, {5,8}, {5,20}, {4,22}, {3,28}, {3,24}, {5,17}, {5,31}, {3,12}, {3,21}, {1,14}, {1,27}, {5,11}, {3,20}, {2,25}, {1,28}, {6,24}, {2,7}, {5,18}, {6,27}, {3,33}, {1,8}, {1,30}, {5,16}, {4,13}, {1,21}, {1,18}, {5,25}, {4,19}, {4,10} }; // ET33.24 // Bipartite(15,18) Valencies [18,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8372219989337680379904000000 EdgePairs[33][24]:={ {13,21}, {15,33}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {4,31}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {7,30}, {8,31}, {13,27}, {14,29}, {2,33}, {6,32}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {15,19}, {1,29}, {6,18}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {13,19}, {14,32}, {1,26}, {3,17}, {8,22}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {14,33}, {14,23}, {6,16}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {12,17}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {10,25}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,22}, {6,23}, {15,17}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {2,21}, {4,27}, {5,24}, {15,29}, {2,22}, {2,31}, {14,19}, {1,33}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {7,25}, {7,22}, {6,26}, {14,18}, {5,21}, {6,28}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {15,18}, {10,27}, {5,17}, {15,16}, {7,17}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {14,17}, {10,32}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {15,25}, {5,33}, {5,30} }; // ET33.25 // Bipartite(14,19) Valencies [19,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10604811986494395147878400000 EdgePairs[33][25]:={ {13,21}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {4,31}, {6,15}, {11,15}, {10,33}, {8,21}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {7,30}, {8,31}, {13,27}, {14,29}, {2,33}, {6,32}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {13,20}, {6,18}, {1,29}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {13,19}, {1,26}, {14,32}, {3,17}, {7,15}, {8,22}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {14,15}, {14,33}, {14,23}, {6,16}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {12,17}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,15}, {6,23}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {5,26}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {3,15}, {7,25}, {7,22}, {6,26}, {14,18}, {5,21}, {9,15}, {6,28}, {13,33}, {13,15}, {14,25}, {14,20}, {1,15}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {5,17}, {7,17}, {13,23}, {6,21}, {4,26}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {14,22}, {14,17}, {10,32}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {5,30} }; // ET33.26 // Bipartite(3,30) Valencies [20,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 286708355039232000000 EdgePairs[33][26]:={ {2,11}, {3,22}, {1,26}, {2,14}, {1,14}, {2,26}, {3,12}, {2,32}, {2,30}, {1,29}, {2,29}, {1,32}, {2,24}, {1,10}, {3,21}, {3,27}, {3,33}, {2,6}, {1,4}, {1,20}, {1,31}, {3,9}, {3,24}, {2,12}, {2,33}, {2,21}, {1,7}, {3,4}, {3,16}, {3,7}, {2,20}, {1,16}, {3,28}, {3,15}, {2,18}, {3,25}, {3,19}, {3,30}, {2,15}, {3,18}, {2,5}, {3,31}, {1,5}, {2,27}, {1,17}, {3,6}, {1,28}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,22}, {2,8}, {1,23}, {1,11}, {1,25}, {3,10} }; // ET33.27 // Bipartite(11,22) Valencies [20,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 81749606400 EdgePairs[33][27]:={ {11,17}, {3,33}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {1,13}, {8,28}, {4,29}, {1,32}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {11,12}, {2,28}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,27}, {8,31}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {11,33}, {1,17}, {5,22}, {4,22}, {1,18}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {11,13}, {11,15}, {1,31}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {11,21}, {9,25}, {7,26}, {1,12}, {6,33}, {2,32}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {11,24}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {5,33}, {10,17}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {5,27}, {8,18}, {4,18}, {11,19}, {10,19}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,24}, {3,31}, {1,14}, {9,24}, {10,20}, {7,33}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET33.28 // Bipartite(13,20) Valencies [20,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 15149731409277707354112000000 EdgePairs[33][28]:={ {11,17}, {3,33}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {13,32}, {2,33}, {6,16}, {6,32}, {4,27}, {12,29}, {13,21}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {4,29}, {1,32}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,27}, {8,31}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {6,31}, {11,33}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,32}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {11,15}, {1,31}, {11,22}, {9,14}, {7,25}, {10,28}, {11,31}, {1,22}, {6,30}, {4,33}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {13,22}, {10,21}, {2,20}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {3,32}, {11,21}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {13,33}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {13,28}, {5,14}, {9,20}, {4,15}, {1,28}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {12,33}, {6,15}, {13,30}, {2,17}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {10,32}, {12,14}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {13,27}, {7,28}, {3,16}, {11,26}, {13,26}, {7,23}, {11,16}, {13,19}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {13,14}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {3,31}, {1,14}, {9,24}, {10,20}, {5,15}, {7,33}, {12,31}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {13,17}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET33.29 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 239500800 EdgePairs[33][29]:={ {19,28}, {5,7}, {6,25}, {9,17}, {10,18}, {3,8}, {4,28}, {11,25}, {3,26}, {8,26}, {5,11}, {16,22}, {4,31}, {6,15}, {10,33}, {21,30}, {3,19}, {14,31}, {5,15}, {24,32}, {1,19}, {3,23}, {8,23}, {12,16}, {2,18}, {3,21}, {16,28}, {11,14}, {5,32}, {2,7}, {13,27}, {16,21}, {24,28}, {2,33}, {11,29}, {9,11}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {19,31}, {2,25}, {18,32}, {15,32}, {8,30}, {9,33}, {1,17}, {1,9}, {4,16}, {29,33}, {1,10}, {4,13}, {27,28}, {12,20}, {23,31}, {12,26}, {13,30}, {3,10}, {2,5}, {19,22}, {3,9}, {2,17}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {2,15}, {12,23}, {27,32}, {13,20}, {16,25}, {24,31}, {15,19}, {1,29}, {6,18}, {24,26}, {4,23}, {11,18}, {13,26}, {29,31}, {6,24}, {13,16}, {13,19}, {1,26}, {18,29}, {9,20}, {18,26}, {4,22}, {18,33}, {8,19}, {5,27}, {7,14}, {15,28}, {6,17}, {4,18}, {7,32}, {12,24}, {3,31}, {12,27}, {25,33}, {3,13}, {11,22}, {9,13}, {6,27}, {2,30}, {2,8}, {4,9}, {30,31}, {6,12}, {25,29}, {4,21}, {17,29}, {13,17}, {18,19}, {20,25}, {7,19}, {4,32}, {1,30}, {2,13}, {19,27}, {12,15}, {8,10}, {14,28}, {8,15}, {11,21}, {8,17}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {14,33}, {19,30}, {7,12}, {8,24}, {4,10}, {14,21}, {18,20}, {5,14}, {3,29}, {17,31}, {12,17}, {10,13}, {20,22}, {22,29}, {25,32}, {15,23}, {9,22}, {20,31}, {3,25}, {19,24}, {17,28}, {6,8}, {11,13}, {25,30}, {22,30}, {2,27}, {12,30}, {6,30}, {2,12}, {10,31}, {9,31}, {5,19}, {1,6}, {24,25}, {6,13}, {2,20}, {17,19}, {9,30}, {9,12}, {3,32}, {14,27}, {7,28}, {6,11}, {13,29}, {9,25}, {10,22}, {10,30}, {16,30}, {7,23}, {6,22}, {10,25}, {12,29}, {26,31}, {6,31}, {11,32}, {21,32}, {1,16}, {3,22}, {4,14}, {23,27}, {16,31}, {4,29}, {1,32}, {24,29}, {30,32}, {28,32}, {8,32}, {10,28}, {9,24}, {17,22}, {17,25}, {6,20}, {5,23}, {20,32}, {5,20}, {12,14}, {10,21}, {9,21}, {26,30}, {7,29}, {18,30}, {2,28}, {8,29}, {7,21}, {8,27}, {2,11}, {13,32}, {10,15}, {3,5}, {19,33}, {9,28}, {2,21}, {1,11}, {5,24}, {15,29}, {2,22}, {16,20}, {8,11}, {18,24}, {2,31}, {1,33}, {18,27}, {20,28}, {21,33}, {16,27}, {1,7}, {26,28}, {3,14}, {5,26}, {19,25}, {4,8}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {5,9}, {11,19}, {8,33}, {1,4}, {4,12}, {28,33}, {8,14}, {7,10}, {27,29}, {3,6}, {22,33}, {11,31}, {14,24}, {7,25}, {7,22}, {1,14}, {22,27}, {14,18}, {21,27}, {9,15}, {21,29}, {20,23}, {2,4}, {17,21}, {23,30}, {6,28}, {18,23}, {13,33}, {1,15}, {14,25}, {15,21}, {14,20}, {7,26}, {7,18}, {23,33}, {11,28}, {7,16}, {5,16}, {1,23}, {10,24}, {15,18}, {10,27}, {5,17}, {16,33}, {15,16}, {13,23}, {6,21}, {15,22}, {4,26}, {23,25}, {16,24}, {9,27}, {12,32}, {15,31}, {5,10}, {8,20}, {1,27}, {17,23}, {15,26}, {26,33}, {27,31}, {4,19}, {14,22}, {22,32}, {3,12}, {7,13}, {14,17}, {17,32}, {21,24}, {12,19}, {21,26}, {6,33}, {6,7}, {11,26}, {15,25}, {5,33}, {5,30}, {21,23} }; // ET33.30 // Bipartite(12,21) Valencies [21,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 24472643045756296495104000000 EdgePairs[33][30]:={ {11,17}, {3,33}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {12,29}, {7,15}, {4,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {12,22}, {12,32}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,27}, {8,31}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {6,31}, {11,33}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,32}, {12,17}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {11,13}, {11,15}, {1,31}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {11,31}, {1,22}, {12,13}, {6,30}, {4,33}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {11,21}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {12,28}, {12,25}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {12,33}, {6,15}, {2,17}, {9,13}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {5,31}, {6,27}, {11,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {10,32}, {12,14}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {5,13}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {3,31}, {1,14}, {9,24}, {10,20}, {5,15}, {7,33}, {12,31}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET33.31 // Bipartite(11,22) Valencies [22,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 44866512250553210241024000000 EdgePairs[33][31]:={ {11,17}, {3,33}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {5,20}, {2,26}, {1,21}, {11,14}, {8,25}, {11,12}, {2,28}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,27}, {8,31}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {11,33}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {11,13}, {11,15}, {1,31}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {11,31}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {11,21}, {9,25}, {7,16}, {7,26}, {1,12}, {6,33}, {2,32}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {11,24}, {6,26}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,24}, {3,31}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {7,33}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET33.32 // Non-bipartite Valency 22 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 381608820557217792000000 EdgePairs[33][32]:={ {15,33}, {19,28}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {11,25}, {4,28}, {3,26}, {8,26}, {17,33}, {4,31}, {6,15}, {11,15}, {10,33}, {8,21}, {21,30}, {3,19}, {14,31}, {5,15}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {5,32}, {7,30}, {8,31}, {13,27}, {14,29}, {6,14}, {2,33}, {6,32}, {11,29}, {11,17}, {1,12}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {20,24}, {1,13}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {20,29}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {2,15}, {12,23}, {22,25}, {16,25}, {6,18}, {1,29}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {1,26}, {14,32}, {3,17}, {7,15}, {8,22}, {18,29}, {9,29}, {9,20}, {18,26}, {4,22}, {18,33}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {10,12}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {6,12}, {19,23}, {4,21}, {17,29}, {20,25}, {7,19}, {4,32}, {1,30}, {2,13}, {19,27}, {8,15}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {3,24}, {14,33}, {14,23}, {6,16}, {11,33}, {13,25}, {21,25}, {21,31}, {19,30}, {7,12}, {8,24}, {9,26}, {5,14}, {3,29}, {17,31}, {2,23}, {10,13}, {22,29}, {10,19}, {15,23}, {9,22}, {9,19}, {20,31}, {3,25}, {19,24}, {17,28}, {11,13}, {22,30}, {2,27}, {12,30}, {6,30}, {2,12}, {4,33}, {1,22}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {6,13}, {1,25}, {22,31}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {9,12}, {3,32}, {14,27}, {7,28}, {2,16}, {13,29}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {10,25}, {12,29}, {6,31}, {11,32}, {15,24}, {21,32}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {4,15}, {18,31}, {6,23}, {16,31}, {4,29}, {1,32}, {19,29}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,25}, {2,19}, {6,20}, {5,23}, {20,32}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {19,33}, {9,28}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {18,24}, {2,31}, {1,33}, {18,27}, {20,28}, {21,33}, {16,27}, {3,14}, {5,26}, {19,25}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {4,12}, {20,27}, {8,14}, {22,33}, {11,31}, {20,33}, {14,24}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {22,27}, {22,23}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {20,23}, {6,28}, {16,23}, {18,23}, {19,32}, {13,33}, {1,15}, {14,25}, {11,12}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {22,24}, {10,24}, {11,20}, {10,27}, {5,17}, {16,33}, {7,17}, {13,23}, {17,27}, {6,21}, {4,26}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {22,32}, {3,12}, {9,14}, {7,13}, {10,14}, {10,32}, {17,32}, {21,24}, {21,26}, {22,28}, {8,25}, {16,32}, {6,33}, {2,32}, {2,14}, {11,26}, {5,33}, {15,25}, {5,30}, {21,23} }; // ET33.33 // Bipartite(10,23) Valencies [23,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 93811798342065803231232000000 EdgePairs[33][33]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {5,20}, {2,26}, {1,21}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,32}, {9,26}, {9,27}, {5,11}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {10,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {5,27}, {5,26}, {8,18}, {4,18}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {7,33}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {7,18}, {10,16}, {5,16} }; // ET33.34 // Bipartite(9,24) Valencies [24,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 225148316020957927754956800000 EdgePairs[33][34]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {9,11}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {7,20}, {3,14}, {9,32}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {2,31}, {9,33}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {7,33}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET33.35 // Bipartite(8,25) Valencies [25,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 625411988947105354874880000000 EdgePairs[33][35]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {4,10}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {3,14}, {7,20}, {5,11}, {2,10}, {5,29}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {7,33}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET33.36 // Bipartite(7,26) Valencies [26,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2032588964078092403343360000000 EdgePairs[33][36]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {6,29}, {3,17}, {6,21}, {2,25}, {7,12}, {6,31}, {4,10}, {1,17}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,32}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {7,33}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {7,19}, {4,17}, {7,21}, {4,32}, {7,18}, {5,16} }; // ET33.37 // Bipartite(6,27) Valencies [27,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7839986004301213555752960000000 EdgePairs[33][37]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {6,21}, {2,25}, {6,31}, {4,10}, {1,17}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {1,31}, {3,12}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,32}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {3,16}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {4,14}, {5,8}, {6,25}, {2,31}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {4,17}, {4,32}, {5,16} }; // ET33.38 // Bipartite(5,28) Valencies [28,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 36586601353405663260180480000000 EdgePairs[33][38]:={ {1,15}, {5,32}, {5,14}, {3,15}, {1,11}, {4,14}, {3,29}, {2,22}, {5,30}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {5,24}, {3,32}, {1,9}, {2,33}, {3,30}, {1,32}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {5,6}, {3,18}, {2,14}, {3,11}, {5,23}, {5,33}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {5,19}, {5,15}, {3,23}, {5,29}, {4,31}, {3,27}, {4,30}, {1,19}, {4,21}, {4,17}, {5,28}, {2,9}, {4,15}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {5,31}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {2,7}, {5,18}, {3,33}, {1,8}, {4,23}, {1,30}, {5,16}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET33.39 // Bipartite(4,29) Valencies [29,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 212202287849752846909046784000000 EdgePairs[33][39]:={ {1,15}, {3,15}, {1,11}, {4,14}, {3,29}, {2,22}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {3,32}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {2,14}, {3,11}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {3,27}, {4,30}, {1,19}, {4,21}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,26}, {2,24}, {4,11}, {2,27}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,17}, {4,9}, {2,7}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET33.40 // Bipartite(3,30) Valencies [30,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1591517158873146351817850880000000 EdgePairs[33][40]:={ {1,15}, {3,15}, {1,11}, {2,22}, {3,29}, {1,31}, {3,7}, {2,11}, {2,20}, {1,25}, {3,32}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {2,14}, {3,11}, {2,10}, {2,31}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {3,27}, {1,19}, {2,9}, {3,5}, {1,4}, {1,26}, {2,4}, {2,24}, {2,27}, {3,4}, {1,23}, {2,21}, {1,7}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,17}, {2,7}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET33.41 // Non-bipartite Valency 30 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 14481697524940800 EdgePairs[33][41]:={ {13,25}, {15,28}, {24,33}, {15,17}, {10,17}, {3,29}, {20,26}, {9,18}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {8,28}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {15,16}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {8,24}, {8,11}, {12,27}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {11,27}, {18,28}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {15,20}, {9,10}, {14,33}, {17,25}, {3,32}, {3,27}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {2,8}, {20,28}, {10,25}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {5,20}, {22,32}, {1,20}, {18,27}, {7,14}, {13,33}, {15,24}, {10,23}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {26,32}, {10,16}, {6,14}, {24,30}, {16,30}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {6,24}, {29,32}, {10,14}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {9,26}, {18,20}, {6,12}, {7,31}, {12,33}, {13,18}, {1,29}, {21,22}, {10,19}, {12,19}, {15,27}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {13,19}, {9,29}, {2,22}, {4,33}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {20,23}, {9,14}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {17,28}, {23,32}, {5,21}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {15,23}, {12,17}, {2,7}, {9,19}, {1,13}, {13,32}, {10,24}, {2,25}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {12,24}, {18,19}, {3,4}, {14,28}, {12,20}, {16,29}, {1,11}, {29,33}, {15,30}, {3,19}, {2,16}, {18,25}, {14,19}, {21,27}, {9,13}, {21,23}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {19,23}, {11,16}, {1,4}, {7,25}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,30}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {6,32}, {15,31}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {1,19}, {2,10}, {6,17}, {19,33}, {19,29}, {11,14}, {7,12}, {13,20}, {13,21}, {3,11}, {4,10}, {11,23}, {3,5}, {15,19}, {9,33}, {8,16}, {8,32}, {14,30}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {3,30}, {6,7}, {24,27}, {18,33}, {1,7}, {8,15}, {21,33}, {4,14}, {24,28}, {11,28}, {6,25}, {11,17}, {15,18}, {24,29}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {4,31}, {2,15}, {30,32}, {10,33}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {26,30}, {2,6}, {13,30}, {9,24}, {24,32}, {6,20}, {11,15}, {6,26}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {27,30}, {8,13}, {16,21}, {6,27}, {15,32}, {6,30}, {11,25}, {17,27}, {2,17}, {25,31}, {5,14}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {26,29}, {1,21}, {9,15}, {6,21}, {8,12}, {7,20}, {16,19}, {23,27}, {27,31}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {19,25}, {6,8}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {26,28}, {4,8}, {29,31}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {27,29}, {28,33}, {12,29}, {7,19}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {6,29}, {2,31} }; // ET33.42 // Bipartite(2,31) Valencies [31,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 16445677308355845635451125760000000 EdgePairs[33][42]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,33}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET33.43 // Bipartite(1,32) Valencies [32,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 263130836933693530167218012160000000 EdgePairs[33][43]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,31}, {1,12}, {1,2}, {1,33}, {1,3}, {1,17}, {1,30}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,28}, {1,6}, {1,14}, {1,26}, {1,18}, {1,27}, {1,21}, {1,19}, {1,29}, {1,20}, {1,8}, {1,24}, {1,32}, {1,9}, {1,23}, {1,25} }; // ET33.44 // Non-bipartite Valency 32 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 8683317618811886495518194401280000000 EdgePairs[33][44]:={ {13,25}, {15,28}, {24,33}, {15,17}, {10,17}, {3,29}, {9,18}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {11,12}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {15,16}, {26,27}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {8,24}, {8,11}, {12,27}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {11,27}, {18,28}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {4,5}, {15,20}, {9,10}, {17,18}, {14,33}, {17,25}, {3,32}, {3,27}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {25,26}, {9,22}, {5,20}, {22,32}, {1,20}, {18,27}, {7,14}, {13,33}, {23,24}, {15,24}, {10,23}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {24,30}, {16,30}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {10,14}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {9,26}, {18,20}, {6,12}, {7,31}, {12,33}, {13,18}, {1,29}, {21,22}, {10,19}, {12,19}, {15,27}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {13,19}, {9,29}, {2,22}, {4,33}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {9,14}, {20,23}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {31,32}, {17,28}, {23,32}, {5,21}, {22,24}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {10,11}, {1,13}, {13,32}, {10,24}, {2,25}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {12,24}, {18,19}, {3,4}, {14,28}, {2,3}, {12,20}, {16,29}, {1,11}, {29,33}, {15,30}, {3,19}, {2,16}, {18,25}, {14,19}, {21,27}, {7,8}, {9,13}, {21,23}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {19,23}, {11,16}, {1,4}, {7,25}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,30}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {5,6}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {6,32}, {15,31}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {1,19}, {2,10}, {6,17}, {19,33}, {19,29}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {4,10}, {11,23}, {3,5}, {15,19}, {9,33}, {8,16}, {20,21}, {8,9}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {3,30}, {6,7}, {24,27}, {18,33}, {1,7}, {8,15}, {21,33}, {4,14}, {24,28}, {11,28}, {6,25}, {11,17}, {15,18}, {24,29}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {4,31}, {2,15}, {30,32}, {10,33}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {1,2}, {4,6}, {6,20}, {11,15}, {6,26}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {19,20}, {2,23}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {27,30}, {8,13}, {16,21}, {6,27}, {15,32}, {29,30}, {6,30}, {11,25}, {17,27}, {2,17}, {25,31}, {16,18}, {5,14}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {26,29}, {1,21}, {13,14}, {6,21}, {9,15}, {8,12}, {7,20}, {16,19}, {23,27}, {27,31}, {7,18}, {10,21}, {3,33}, {28,30}, {5,17}, {1,24}, {19,25}, {6,8}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {26,28}, {4,8}, {29,31}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {27,29}, {28,33}, {12,29}, {7,19}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {6,29}, {2,31} }; // Total number of connected ET graphs of order 33 is 44 // ******************************************************************************************** // Order 34 // ET34.1 // Bipartite(17,17) Valencies [2,2] // Diameter 17 Girth 34 // Twin-free VT AT // Automorphism group of order 68 EdgePairs[34][1]:={ {1,20}, {7,26}, {6,28}, {7,30}, {4,24}, {8,28}, {5,21}, {14,25}, {2,19}, {3,18}, {3,21}, {11,31}, {12,29}, {16,20}, {13,31}, {10,33}, {12,33}, {4,19}, {8,32}, {11,34}, {13,27}, {15,22}, {17,23}, {6,24}, {5,26}, {9,34}, {2,23}, {1,18}, {9,30}, {14,29}, {17,22}, {16,25}, {15,27}, {10,32} }; // ET34.2 // Bipartite(17,17) Valencies [4,4] // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 136 EdgePairs[34][2]:={ {5,33}, {12,27}, {4,24}, {10,27}, {1,24}, {2,26}, {8,31}, {17,28}, {2,30}, {9,25}, {4,34}, {7,34}, {15,20}, {16,23}, {8,21}, {3,21}, {6,31}, {15,27}, {1,20}, {11,23}, {10,33}, {8,32}, {16,32}, {5,21}, {13,32}, {7,27}, {9,29}, {3,28}, {8,33}, {10,26}, {13,33}, {14,22}, {11,32}, {11,22}, {12,34}, {3,18}, {17,21}, {3,31}, {13,20}, {5,30}, {1,18}, {12,29}, {9,34}, {15,28}, {16,19}, {7,19}, {6,18}, {9,22}, {4,25}, {6,22}, {2,19}, {14,23}, {13,24}, {6,25}, {17,30}, {5,26}, {2,23}, {14,29}, {12,28}, {4,19}, {16,24}, {10,20}, {17,29}, {11,31}, {1,25}, {15,18}, {14,30}, {7,26} }; // ET34.3 // Non-bipartite Valency 4 // Diameter 8 Girth 4 // Has twins VT AT // Automorphism group of order 4456448 EdgePairs[34][3]:={ {2,14}, {8,19}, {1,14}, {8,20}, {1,24}, {21,33}, {2,24}, {14,26}, {9,21}, {9,31}, {12,33}, {5,27}, {11,24}, {10,32}, {13,25}, {13,26}, {15,27}, {11,23}, {4,16}, {8,29}, {11,33}, {9,32}, {7,30}, {16,27}, {10,31}, {3,16}, {3,15}, {5,28}, {3,25}, {5,17}, {12,34}, {12,23}, {6,27}, {18,30}, {20,31}, {12,24}, {3,26}, {15,28}, {4,15}, {7,20}, {21,34}, {7,19}, {6,18}, {9,22}, {4,25}, {22,34}, {11,34}, {19,32}, {22,33}, {5,18}, {16,28}, {6,17}, {17,30}, {2,23}, {18,29}, {1,13}, {19,31}, {10,22}, {10,21}, {4,26}, {2,13}, {6,28}, {20,32}, {1,23}, {8,30}, {17,29}, {14,25}, {7,29} }; // ET34.4 // Bipartite(17,17) Valencies [8,8] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 272 EdgePairs[34][4]:={ {7,19}, {16,25}, {13,25}, {16,34}, {14,25}, {15,23}, {10,22}, {6,18}, {9,30}, {12,19}, {14,34}, {2,22}, {17,27}, {5,30}, {11,33}, {16,30}, {7,24}, {11,29}, {6,23}, {2,20}, {13,24}, {5,34}, {7,33}, {12,31}, {12,22}, {7,31}, {16,23}, {7,27}, {13,27}, {3,30}, {1,32}, {15,29}, {3,34}, {9,31}, {14,20}, {2,19}, {17,18}, {5,26}, {4,26}, {10,18}, {15,32}, {5,21}, {10,23}, {15,28}, {14,27}, {3,18}, {7,28}, {12,21}, {17,31}, {5,33}, {5,23}, {10,34}, {15,22}, {13,33}, {8,33}, {7,26}, {8,28}, {10,25}, {2,32}, {6,21}, {8,21}, {9,34}, {10,31}, {4,29}, {16,19}, {3,22}, {14,28}, {5,19}, {8,26}, {5,29}, {4,31}, {2,34}, {10,33}, {14,26}, {1,19}, {11,18}, {12,28}, {17,33}, {12,29}, {4,25}, {13,22}, {15,26}, {12,23}, {6,31}, {2,27}, {1,23}, {2,21}, {16,27}, {6,30}, {15,18}, {11,19}, {13,32}, {8,32}, {3,28}, {3,24}, {9,24}, {11,25}, {8,20}, {6,20}, {3,21}, {11,30}, {17,21}, {11,27}, {4,32}, {13,21}, {17,34}, {1,20}, {7,22}, {4,18}, {8,25}, {3,25}, {9,29}, {17,29}, {13,23}, {2,26}, {11,20}, {1,33}, {14,29}, {1,28}, {9,32}, {6,24}, {8,30}, {17,28}, {10,26}, {6,27}, {15,30}, {16,32}, {16,31}, {12,20}, {1,18}, {4,19}, {14,24}, {4,24}, {9,20}, {1,24}, {9,22} }; // ET34.5 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 8912896 EdgePairs[34][5]:={ {1,15}, {7,19}, {13,25}, {10,21}, {14,25}, {3,15}, {12,26}, {10,22}, {11,23}, {6,18}, {9,30}, {14,34}, {2,22}, {11,33}, {6,17}, {16,30}, {4,16}, {12,31}, {13,34}, {12,33}, {6,25}, {19,31}, {7,27}, {13,27}, {9,21}, {19,33}, {15,29}, {9,31}, {22,33}, {12,25}, {2,15}, {5,26}, {4,26}, {10,23}, {15,28}, {10,30}, {14,27}, {3,18}, {8,22}, {7,28}, {11,34}, {14,33}, {17,31}, {2,14}, {17,30}, {20,33}, {2,23}, {13,33}, {8,28}, {13,26}, {2,16}, {1,22}, {1,16}, {12,34}, {8,21}, {7,29}, {2,13}, {10,31}, {14,28}, {9,23}, {10,24}, {5,19}, {7,20}, {3,23}, {16,29}, {6,26}, {14,26}, {21,33}, {7,30}, {4,17}, {5,28}, {4,15}, {4,25}, {10,29}, {8,19}, {11,26}, {12,24}, {12,23}, {2,24}, {6,19}, {18,32}, {1,23}, {2,21}, {16,27}, {5,27}, {8,27}, {5,20}, {11,31}, {20,32}, {3,26}, {3,24}, {5,17}, {9,24}, {11,25}, {22,34}, {13,28}, {8,20}, {6,20}, {1,14}, {18,29}, {19,34}, {11,32}, {7,22}, {15,27}, {3,16}, {1,13}, {4,18}, {18,30}, {16,28}, {9,29}, {3,25}, {17,29}, {10,32}, {20,34}, {7,21}, {12,32}, {18,31}, {21,34}, {3,17}, {20,31}, {9,32}, {17,32}, {5,18}, {8,30}, {19,32}, {6,27}, {15,30}, {4,23}, {11,24}, {1,21}, {5,25}, {4,24}, {1,24}, {8,29}, {9,22}, {6,28} }; // ET34.6 // Bipartite(16,18) Valencies [9,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1152 EdgePairs[34][6]:={ {16,25}, {16,34}, {5,32}, {10,21}, {13,29}, {14,25}, {15,23}, {8,31}, {8,24}, {12,26}, {6,18}, {9,30}, {12,19}, {3,29}, {11,33}, {1,31}, {4,27}, {16,30}, {2,20}, {13,24}, {14,19}, {1,25}, {12,17}, {12,31}, {12,22}, {16,18}, {3,32}, {13,34}, {6,32}, {7,31}, {6,25}, {7,27}, {12,18}, {16,20}, {6,34}, {2,18}, {5,26}, {4,26}, {6,22}, {15,32}, {13,20}, {5,21}, {15,28}, {10,30}, {3,19}, {14,27}, {1,34}, {11,34}, {14,33}, {16,21}, {5,33}, {5,23}, {10,34}, {15,22}, {9,27}, {2,31}, {2,23}, {8,33}, {7,26}, {8,28}, {1,17}, {13,26}, {1,22}, {16,17}, {8,21}, {4,33}, {7,29}, {4,29}, {9,23}, {5,19}, {7,20}, {3,23}, {10,33}, {11,18}, {12,28}, {7,30}, {15,33}, {9,25}, {10,29}, {15,26}, {12,23}, {2,24}, {2,27}, {6,19}, {14,17}, {2,21}, {16,27}, {14,22}, {5,27}, {10,28}, {15,18}, {11,19}, {14,31}, {14,23}, {4,22}, {3,28}, {11,31}, {5,17}, {9,24}, {11,25}, {13,28}, {8,23}, {6,20}, {11,21}, {3,21}, {10,17}, {11,27}, {4,32}, {13,21}, {7,22}, {8,25}, {3,25}, {9,29}, {2,26}, {10,32}, {3,20}, {1,33}, {14,29}, {1,28}, {3,17}, {9,32}, {6,24}, {5,18}, {8,30}, {10,26}, {13,31}, {4,34}, {7,34}, {13,19}, {15,30}, {16,32}, {7,17}, {11,24}, {1,30}, {2,30}, {1,18}, {12,20}, {15,24}, {4,19}, {4,24}, {9,20}, {8,29}, {9,22}, {6,28} }; // ET34.7 // Bipartite(16,18) Valencies [9,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 371504185344 EdgePairs[34][7]:={ {7,19}, {13,25}, {16,34}, {13,29}, {12,26}, {6,18}, {11,33}, {1,31}, {6,17}, {4,27}, {7,24}, {6,23}, {2,20}, {5,34}, {1,25}, {14,18}, {7,33}, {12,22}, {13,34}, {6,32}, {7,31}, {12,33}, {7,27}, {9,19}, {3,30}, {16,20}, {12,27}, {8,34}, {9,31}, {14,20}, {3,31}, {16,33}, {2,18}, {4,26}, {9,17}, {10,18}, {10,23}, {2,29}, {3,19}, {10,30}, {1,29}, {3,18}, {8,22}, {12,21}, {1,34}, {16,21}, {5,23}, {4,20}, {2,23}, {8,33}, {8,28}, {1,17}, {15,25}, {1,22}, {14,30}, {2,32}, {12,34}, {8,21}, {2,17}, {4,33}, {9,34}, {4,28}, {16,26}, {7,25}, {9,23}, {10,24}, {5,19}, {8,26}, {5,29}, {3,27}, {6,26}, {14,26}, {1,19}, {11,18}, {12,28}, {15,19}, {7,30}, {4,21}, {15,33}, {5,28}, {9,25}, {10,29}, {13,22}, {6,29}, {14,32}, {2,24}, {5,22}, {14,17}, {15,21}, {15,31}, {1,23}, {16,27}, {6,30}, {8,27}, {15,18}, {11,19}, {7,18}, {14,23}, {8,32}, {9,28}, {4,22}, {11,31}, {3,24}, {5,17}, {5,31}, {11,25}, {13,28}, {8,20}, {16,22}, {6,20}, {11,21}, {3,21}, {11,30}, {10,17}, {11,27}, {4,32}, {15,27}, {16,28}, {9,29}, {3,25}, {13,23}, {2,26}, {10,32}, {13,17}, {7,21}, {14,29}, {12,32}, {1,28}, {10,20}, {6,24}, {10,26}, {13,31}, {4,34}, {3,33}, {13,19}, {15,30}, {16,32}, {11,24}, {2,30}, {12,20}, {15,24}, {5,25}, {14,24}, {9,22} }; // ET34.8 // Bipartite(16,18) Valencies [9,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 573308928 EdgePairs[34][8]:={ {13,25}, {16,34}, {5,32}, {10,21}, {14,25}, {11,17}, {8,24}, {10,22}, {6,18}, {11,23}, {3,29}, {2,22}, {1,31}, {16,30}, {10,27}, {11,29}, {14,19}, {1,25}, {14,18}, {12,17}, {7,33}, {12,22}, {16,18}, {2,33}, {6,32}, {6,25}, {7,27}, {9,19}, {13,27}, {9,21}, {12,18}, {3,30}, {16,20}, {8,34}, {2,28}, {9,31}, {14,20}, {3,31}, {5,26}, {9,17}, {15,32}, {13,20}, {5,21}, {10,23}, {15,28}, {2,29}, {3,19}, {1,29}, {3,18}, {8,22}, {7,28}, {12,30}, {5,33}, {15,34}, {10,34}, {15,22}, {9,27}, {2,23}, {13,33}, {7,26}, {8,28}, {1,17}, {13,26}, {14,30}, {12,34}, {2,17}, {8,18}, {4,28}, {4,29}, {16,26}, {9,23}, {5,19}, {7,20}, {8,26}, {15,20}, {3,23}, {4,30}, {2,34}, {6,26}, {10,33}, {14,26}, {1,19}, {11,18}, {12,28}, {4,17}, {15,33}, {12,29}, {9,25}, {10,29}, {12,24}, {15,26}, {12,23}, {14,32}, {6,31}, {9,33}, {2,27}, {6,19}, {15,21}, {1,23}, {2,21}, {5,27}, {6,30}, {10,28}, {11,19}, {14,31}, {13,32}, {8,32}, {4,22}, {5,20}, {11,31}, {3,24}, {5,31}, {11,25}, {8,20}, {16,22}, {6,20}, {11,30}, {10,17}, {13,21}, {1,27}, {7,22}, {15,27}, {4,18}, {16,28}, {9,29}, {3,25}, {7,32}, {7,21}, {1,33}, {3,17}, {6,24}, {8,30}, {13,31}, {4,34}, {7,34}, {13,19}, {16,32}, {4,23}, {11,24}, {1,21}, {5,25}, {14,24}, {4,24}, {16,24} }; // ET34.9 // Bipartite(12,22) Valencies [11,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 7920 EdgePairs[34][9]:={ {10,19}, {7,19}, {5,14}, {11,17}, {8,31}, {4,14}, {12,19}, {3,29}, {5,30}, {6,23}, {2,20}, {4,16}, {12,15}, {12,17}, {12,31}, {5,24}, {3,32}, {2,33}, {12,33}, {7,27}, {9,21}, {12,18}, {1,32}, {11,22}, {12,27}, {7,23}, {7,15}, {2,28}, {3,34}, {12,25}, {3,31}, {6,34}, {2,19}, {2,18}, {2,15}, {8,14}, {8,13}, {9,17}, {6,22}, {5,21}, {10,23}, {3,19}, {10,30}, {3,18}, {8,22}, {8,15}, {1,34}, {12,30}, {5,23}, {4,20}, {10,34}, {7,26}, {8,28}, {10,25}, {2,16}, {1,22}, {6,33}, {10,13}, {2,17}, {3,14}, {2,13}, {10,31}, {4,29}, {10,16}, {7,25}, {5,19}, {9,23}, {10,24}, {7,13}, {8,17}, {5,29}, {7,14}, {4,30}, {6,26}, {6,15}, {10,33}, {11,18}, {4,21}, {5,28}, {12,29}, {9,25}, {4,15}, {4,25}, {11,26}, {6,29}, {11,14}, {6,31}, {9,33}, {11,13}, {2,21}, {5,27}, {5,20}, {4,22}, {8,32}, {3,28}, {11,31}, {3,26}, {8,16}, {5,17}, {3,24}, {9,24}, {11,25}, {8,23}, {6,20}, {9,26}, {11,27}, {1,27}, {3,16}, {1,13}, {4,18}, {7,32}, {9,29}, {2,26}, {7,21}, {11,20}, {1,33}, {12,32}, {1,28}, {10,20}, {9,32}, {8,30}, {4,34}, {6,27}, {9,16}, {7,34}, {11,24}, {1,30}, {1,21}, {1,18}, {1,24}, {6,28}, {9,22} }; // ET34.10 // Bipartite(10,24) Valencies [12,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 11466178560 EdgePairs[34][10]:={ {7,19}, {5,32}, {5,14}, {10,21}, {8,31}, {8,24}, {10,22}, {1,11}, {3,29}, {2,22}, {6,14}, {5,30}, {1,31}, {4,27}, {10,27}, {7,24}, {2,20}, {1,25}, {6,13}, {7,33}, {5,24}, {6,32}, {7,31}, {6,25}, {7,27}, {9,21}, {1,32}, {7,15}, {8,34}, {2,28}, {3,34}, {3,31}, {2,18}, {5,26}, {8,13}, {10,23}, {3,19}, {1,29}, {4,12}, {8,22}, {2,14}, {5,23}, {3,11}, {10,34}, {9,27}, {8,28}, {1,17}, {3,13}, {2,16}, {2,32}, {6,33}, {6,21}, {4,33}, {8,18}, {9,34}, {10,15}, {4,29}, {10,16}, {7,25}, {3,22}, {7,13}, {3,23}, {5,29}, {4,30}, {2,34}, {6,26}, {6,15}, {10,33}, {1,19}, {7,30}, {4,21}, {4,17}, {4,15}, {9,15}, {10,29}, {1,26}, {8,19}, {2,24}, {6,31}, {9,33}, {4,11}, {6,19}, {1,23}, {10,28}, {7,18}, {2,12}, {5,20}, {9,28}, {3,28}, {8,16}, {5,17}, {6,20}, {9,26}, {1,14}, {10,17}, {1,20}, {5,11}, {3,16}, {1,13}, {4,18}, {8,25}, {3,25}, {2,26}, {7,21}, {5,12}, {9,14}, {3,17}, {9,32}, {5,18}, {8,30}, {6,27}, {9,16}, {4,23}, {7,12}, {2,30}, {10,11}, {4,24}, {8,12}, {9,20}, {9,22} }; // ET34.11 // Bipartite(10,24) Valencies [12,5] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 491520 EdgePairs[34][11]:={ {9,13}, {6,12}, {5,14}, {8,31}, {10,22}, {1,11}, {9,30}, {5,30}, {1,31}, {10,27}, {2,20}, {5,34}, {4,16}, {7,33}, {5,24}, {2,33}, {6,32}, {7,27}, {9,21}, {3,30}, {7,15}, {8,34}, {3,34}, {3,31}, {2,19}, {2,15}, {5,26}, {8,14}, {8,13}, {9,17}, {3,19}, {3,18}, {8,22}, {2,14}, {3,11}, {4,20}, {10,34}, {2,31}, {7,26}, {10,12}, {2,32}, {6,33}, {1,16}, {6,21}, {4,28}, {7,29}, {3,14}, {2,13}, {10,15}, {1,12}, {4,29}, {10,16}, {7,25}, {3,22}, {9,23}, {10,24}, {5,15}, {8,26}, {7,13}, {3,23}, {5,29}, {7,14}, {6,15}, {1,19}, {8,11}, {7,30}, {4,17}, {9,25}, {4,25}, {10,29}, {8,19}, {6,31}, {9,33}, {4,11}, {5,22}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {10,28}, {7,18}, {4,22}, {8,32}, {9,28}, {3,26}, {3,24}, {5,17}, {3,12}, {8,20}, {8,23}, {6,16}, {6,20}, {9,18}, {10,17}, {4,32}, {9,11}, {8,25}, {9,29}, {2,26}, {10,32}, {7,21}, {1,33}, {5,12}, {2,25}, {1,28}, {10,20}, {6,24}, {5,18}, {4,34}, {6,27}, {9,16}, {7,17}, {4,23}, {1,30}, {4,13}, {1,21}, {1,18}, {1,24}, {6,28} }; // ET34.12 // Bipartite(6,28) Valencies [14,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 15485790781440000 EdgePairs[34][12]:={ {4,8}, {5,33}, {4,24}, {6,34}, {1,24}, {2,32}, {2,29}, {5,29}, {1,32}, {4,34}, {2,24}, {6,14}, {6,26}, {4,10}, {5,10}, {3,21}, {6,31}, {3,27}, {3,33}, {6,10}, {6,30}, {1,20}, {1,12}, {3,23}, {4,16}, {1,31}, {3,9}, {2,12}, {6,7}, {3,29}, {2,33}, {6,15}, {2,21}, {4,30}, {5,9}, {4,32}, {5,21}, {4,12}, {4,18}, {2,16}, {1,7}, {5,25}, {1,15}, {3,11}, {1,16}, {3,7}, {2,20}, {3,15}, {3,17}, {3,25}, {4,20}, {3,19}, {5,17}, {6,27}, {3,31}, {5,30}, {1,27}, {4,28}, {4,22}, {6,18}, {6,19}, {2,28}, {6,22}, {1,28}, {5,14}, {2,17}, {5,18}, {3,13}, {5,26}, {1,8}, {5,34}, {1,19}, {2,9}, {5,13}, {6,11}, {4,26}, {2,13}, {2,25}, {2,8}, {4,14}, {1,23}, {1,11}, {5,22}, {6,23} }; // ET34.13 // Bipartite(4,30) Valencies [15,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 71663616000000 EdgePairs[34][13]:={ {2,11}, {4,8}, {2,14}, {4,9}, {2,26}, {3,12}, {2,32}, {2,30}, {1,29}, {2,29}, {4,34}, {2,24}, {1,10}, {4,10}, {3,21}, {3,27}, {3,33}, {2,6}, {1,31}, {4,16}, {3,24}, {3,9}, {2,12}, {4,32}, {4,33}, {1,7}, {1,16}, {3,7}, {2,20}, {3,15}, {2,18}, {3,25}, {4,27}, {4,21}, {4,20}, {3,19}, {3,30}, {3,18}, {2,5}, {3,31}, {1,5}, {4,15}, {4,28}, {1,17}, {4,22}, {3,6}, {1,28}, {2,17}, {3,13}, {2,23}, {1,13}, {1,19}, {4,26}, {1,22}, {4,14}, {2,8}, {1,34}, {1,23}, {1,11}, {1,25} }; // ET34.14 // Bipartite(17,17) Valencies [16,16] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 711374856192000 EdgePairs[34][14]:={ {13,21}, {9,32}, {10,18}, {11,25}, {4,28}, {17,18}, {12,22}, {3,26}, {8,26}, {16,22}, {17,33}, {4,31}, {10,33}, {8,21}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {1,21}, {3,21}, {16,28}, {5,32}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {11,29}, {6,29}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {17,20}, {7,33}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {16,25}, {15,19}, {1,29}, {6,18}, {16,34}, {4,23}, {11,18}, {6,24}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {14,34}, {4,21}, {17,29}, {7,19}, {4,32}, {16,18}, {1,30}, {13,18}, {14,28}, {11,21}, {3,30}, {2,24}, {11,23}, {3,24}, {14,33}, {14,23}, {15,34}, {11,33}, {13,25}, {14,21}, {9,26}, {3,29}, {17,31}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {16,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {15,24}, {16,26}, {12,25}, {3,22}, {16,31}, {6,23}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {3,34}, {2,21}, {4,27}, {5,24}, {15,29}, {2,22}, {16,20}, {2,31}, {14,19}, {1,33}, {16,27}, {5,26}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {14,18}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {5,18}, {1,23}, {10,24}, {11,20}, {15,18}, {10,34}, {10,27}, {16,33}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,31}, {8,28}, {8,20}, {1,27}, {5,25}, {17,23}, {15,26}, {4,19}, {14,22}, {16,19}, {9,34}, {10,32}, {12,19}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {15,25}, {5,33}, {5,30} }; // ET34.15 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 17825792 EdgePairs[34][15]:={ {24,34}, {9,32}, {6,25}, {23,29}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {5,11}, {16,22}, {4,31}, {6,15}, {10,33}, {8,21}, {15,27}, {5,15}, {27,33}, {3,23}, {1,21}, {21,28}, {16,28}, {7,30}, {2,7}, {8,31}, {13,27}, {16,21}, {11,17}, {1,12}, {6,29}, {3,18}, {20,26}, {19,31}, {2,25}, {4,24}, {18,32}, {8,30}, {8,13}, {9,33}, {4,16}, {4,13}, {1,13}, {12,26}, {3,10}, {7,27}, {3,9}, {12,31}, {20,29}, {10,20}, {1,24}, {13,24}, {24,30}, {15,30}, {2,15}, {12,23}, {13,20}, {16,25}, {6,18}, {1,29}, {4,23}, {11,18}, {13,26}, {2,29}, {5,34}, {13,19}, {1,26}, {3,17}, {8,22}, {22,34}, {18,29}, {6,34}, {9,29}, {9,20}, {8,19}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {3,31}, {3,13}, {11,22}, {5,12}, {6,27}, {2,30}, {2,8}, {4,9}, {14,34}, {6,12}, {17,29}, {20,25}, {7,19}, {4,32}, {1,30}, {2,13}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,16}, {2,24}, {11,23}, {3,24}, {14,33}, {14,23}, {6,16}, {11,33}, {13,25}, {21,31}, {19,30}, {4,10}, {28,34}, {17,31}, {12,17}, {2,23}, {25,32}, {10,19}, {9,22}, {9,19}, {20,31}, {3,25}, {11,34}, {17,28}, {27,34}, {6,30}, {2,12}, {1,22}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {1,25}, {22,31}, {20,30}, {6,19}, {4,17}, {9,16}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {25,31}, {2,16}, {6,11}, {17,30}, {10,22}, {10,30}, {16,30}, {26,31}, {11,32}, {21,32}, {16,26}, {12,25}, {1,16}, {4,14}, {4,15}, {18,31}, {23,34}, {24,29}, {19,29}, {8,32}, {9,24}, {19,34}, {6,20}, {20,32}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {18,30}, {8,29}, {9,23}, {7,21}, {8,27}, {2,11}, {14,26}, {10,15}, {19,33}, {2,21}, {1,11}, {4,27}, {18,28}, {15,29}, {2,22}, {18,24}, {14,19}, {18,27}, {21,33}, {16,27}, {1,7}, {3,14}, {5,26}, {19,25}, {5,29}, {4,25}, {3,28}, {21,34}, {7,31}, {12,33}, {1,8}, {28,33}, {8,14}, {22,33}, {11,31}, {20,33}, {14,24}, {3,15}, {13,34}, {7,22}, {1,14}, {6,26}, {26,32}, {22,27}, {21,27}, {9,15}, {17,24}, {12,34}, {23,30}, {6,28}, {18,23}, {19,32}, {13,33}, {1,15}, {14,25}, {15,21}, {14,20}, {20,34}, {7,18}, {23,33}, {5,18}, {5,16}, {1,23}, {10,24}, {10,34}, {5,17}, {7,17}, {13,23}, {17,27}, {15,22}, {4,26}, {13,28}, {3,27}, {7,20}, {12,32}, {8,28}, {8,20}, {5,25}, {17,23}, {10,23}, {15,26}, {22,32}, {7,13}, {9,34}, {24,33}, {10,32}, {17,32}, {22,28}, {6,33}, {12,21}, {2,14}, {11,26}, {15,25}, {5,33}, {5,30} }; // ET34.16 // Bipartite(17,17) Valencies [17,17] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 253027093011094340370432000000 EdgePairs[34][16]:={ {13,21}, {15,33}, {9,32}, {6,25}, {5,22}, {10,18}, {11,25}, {4,28}, {17,18}, {12,22}, {3,26}, {8,26}, {16,22}, {17,33}, {4,31}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {5,32}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {11,29}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {16,25}, {15,19}, {1,29}, {6,18}, {16,34}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {14,34}, {4,21}, {17,29}, {7,19}, {4,32}, {16,18}, {1,30}, {13,18}, {14,28}, {11,21}, {16,29}, {3,30}, {2,24}, {11,23}, {3,24}, {14,33}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {17,31}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {6,23}, {16,31}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {15,29}, {2,22}, {16,20}, {2,31}, {14,19}, {1,33}, {16,27}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {14,18}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {5,18}, {1,23}, {10,24}, {11,20}, {15,18}, {10,34}, {10,27}, {16,33}, {13,23}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {16,19}, {9,34}, {10,32}, {17,32}, {12,19}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {15,25}, {5,33}, {5,30} }; // ET34.17 // Bipartite(16,18) Valencies [18,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 133955519829402886078464000000 EdgePairs[34][17]:={ {13,21}, {15,33}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {16,22}, {4,31}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {5,32}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {16,25}, {15,19}, {1,29}, {6,18}, {16,34}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {3,17}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {14,34}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {8,17}, {16,29}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {14,33}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {12,17}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {6,23}, {16,31}, {15,17}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {1,33}, {16,27}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {14,18}, {5,21}, {12,34}, {6,28}, {16,23}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {5,18}, {1,23}, {10,24}, {11,20}, {15,18}, {10,34}, {10,27}, {5,17}, {16,33}, {7,17}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {14,17}, {16,19}, {9,34}, {10,32}, {12,19}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {15,25}, {5,33}, {5,30} }; // ET34.18 // Bipartite(15,19) Valencies [19,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 159072179797415927218176000000 EdgePairs[34][18]:={ {13,21}, {15,33}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {4,31}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {7,30}, {8,31}, {13,27}, {14,29}, {2,33}, {6,32}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {6,18}, {1,29}, {15,19}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {3,17}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {14,34}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {14,33}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {12,17}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {13,29}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,22}, {6,23}, {15,17}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {2,31}, {14,19}, {1,33}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {14,18}, {5,21}, {12,34}, {6,28}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {15,16}, {7,17}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {14,17}, {9,34}, {10,32}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30} }; // ET34.19 // Bipartite(14,20) Valencies [20,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 212096239729887902957568000000 EdgePairs[34][19]:={ {13,21}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {4,31}, {6,15}, {11,15}, {10,33}, {8,21}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {7,30}, {8,31}, {13,27}, {14,29}, {2,33}, {6,32}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {13,20}, {6,18}, {1,29}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {13,19}, {1,26}, {14,32}, {3,17}, {7,15}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {14,34}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {14,15}, {14,33}, {14,23}, {6,16}, {11,33}, {13,25}, {8,24}, {9,26}, {14,21}, {3,29}, {12,17}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {13,29}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,15}, {6,23}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {5,26}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {3,15}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {14,18}, {5,21}, {9,15}, {12,34}, {6,28}, {13,33}, {13,15}, {1,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {13,23}, {6,21}, {4,26}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {14,22}, {14,17}, {9,34}, {10,32}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {5,30} }; // ET34.20 // Bipartite(13,21) Valencies [21,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 318144359594831854436352000000 EdgePairs[34][20]:={ {13,21}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {4,31}, {6,15}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {5,32}, {7,30}, {8,31}, {13,27}, {6,14}, {2,33}, {6,32}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {13,20}, {6,18}, {1,29}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {6,16}, {11,33}, {13,25}, {8,24}, {9,26}, {5,14}, {3,29}, {12,17}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {13,29}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {13,14}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {3,15}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {12,34}, {6,28}, {13,33}, {13,15}, {1,15}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {13,23}, {6,21}, {4,26}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {9,14}, {9,34}, {10,14}, {10,32}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {2,14}, {11,26}, {5,33}, {5,30} }; // ET34.21 // Bipartite(12,22) Valencies [22,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 538398147006638522892288000000 EdgePairs[34][21]:={ {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {4,31}, {6,15}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {5,32}, {7,30}, {8,31}, {6,14}, {2,33}, {6,32}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {12,20}, {1,13}, {12,26}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {2,15}, {12,23}, {12,13}, {6,18}, {1,29}, {4,23}, {11,18}, {6,24}, {2,29}, {5,34}, {1,26}, {3,17}, {7,15}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {6,27}, {2,30}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {6,16}, {11,33}, {8,24}, {9,26}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {11,13}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {12,34}, {6,28}, {1,15}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {7,13}, {9,14}, {9,34}, {10,14}, {10,32}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {2,14}, {11,26}, {5,33}, {5,30} }; // ET34.22 // Bipartite(11,23) Valencies [23,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1031929781762723835543552000000 EdgePairs[34][22]:={ {11,17}, {3,33}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {5,20}, {2,26}, {7,34}, {1,21}, {11,14}, {8,25}, {11,12}, {2,28}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,27}, {8,31}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {7,12}, {2,25}, {6,31}, {11,33}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {11,13}, {11,15}, {1,31}, {3,12}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {11,31}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {9,34}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {11,21}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {11,24}, {6,26}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {7,23}, {11,16}, {2,21}, {3,30}, {5,33}, {8,34}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {10,34}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {6,34}, {5,27}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {7,33}, {10,14}, {11,34}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET34.23 // Bipartite(10,24) Valencies [24,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2251483160209579277549568000000 EdgePairs[34][23]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {5,20}, {2,26}, {7,34}, {1,21}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {7,12}, {2,25}, {6,31}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {10,28}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {9,34}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {10,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {8,34}, {9,18}, {10,17}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {10,34}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {6,34}, {5,27}, {5,26}, {8,18}, {4,18}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {7,33}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {7,18}, {10,16}, {5,16} }; // ET34.24 // Bipartite(9,25) Valencies [25,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5628707900523948193873920000000 EdgePairs[34][24]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {7,34}, {1,21}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {9,11}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {7,12}, {2,25}, {6,31}, {4,10}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,11}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {9,34}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {8,34}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {2,31}, {9,33}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {7,33}, {5,19}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET34.25 // Bipartite(8,26) Valencies [26,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 16260711712624739226746880000000 EdgePairs[34][25]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {7,34}, {1,21}, {2,9}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,11}, {7,20}, {5,11}, {2,10}, {5,29}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {7,33}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {1,34}, {7,19}, {4,17}, {7,21}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET34.26 // Bipartite(7,27) Valencies [27,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 54879902030108494890270720000000 EdgePairs[34][26]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {5,20}, {2,26}, {7,34}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,32}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {7,33}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {1,34}, {7,19}, {4,17}, {7,21}, {4,32}, {7,18}, {5,16} }; // ET34.27 // Bipartite(6,28) Valencies [28,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 219519608120433979561082880000000 EdgePairs[34][27]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {2,26}, {1,21}, {2,9}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {6,21}, {3,34}, {2,25}, {6,31}, {4,10}, {2,34}, {1,17}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {1,31}, {3,12}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,32}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {3,16}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {1,34}, {4,17}, {4,32}, {5,16} }; // ET34.28 // Bipartite(5,29) Valencies [29,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1061011439248764234545233920000000 EdgePairs[34][28]:={ {1,15}, {5,32}, {5,14}, {3,15}, {1,11}, {4,14}, {3,29}, {2,22}, {5,30}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {5,34}, {1,25}, {4,16}, {5,24}, {3,32}, {1,9}, {2,33}, {3,30}, {1,32}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {5,6}, {3,18}, {1,34}, {2,14}, {3,11}, {5,23}, {5,33}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {5,19}, {5,15}, {3,23}, {5,29}, {4,31}, {3,27}, {2,34}, {4,30}, {1,19}, {4,21}, {4,17}, {5,28}, {2,9}, {4,15}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {5,31}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {2,7}, {5,18}, {4,34}, {3,33}, {1,8}, {4,23}, {1,30}, {5,16}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET34.29 // Bipartite(4,30) Valencies [30,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6366068635492585407271403520000000 EdgePairs[34][29]:={ {1,15}, {3,15}, {1,11}, {4,14}, {2,22}, {3,29}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {3,32}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {3,27}, {2,34}, {4,30}, {1,19}, {4,21}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,26}, {2,24}, {4,11}, {2,27}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,17}, {4,9}, {2,7}, {4,34}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET34.30 // Bipartite(3,31) Valencies [31,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 49337031925067536906353377280000000 EdgePairs[34][30]:={ {1,15}, {3,15}, {1,11}, {2,22}, {3,29}, {1,31}, {3,7}, {2,11}, {2,20}, {1,25}, {3,32}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {2,31}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {3,27}, {2,34}, {1,19}, {2,9}, {3,5}, {1,4}, {1,26}, {2,4}, {2,24}, {2,27}, {3,4}, {1,23}, {2,21}, {1,7}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,17}, {2,7}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET34.31 // Bipartite(2,32) Valencies [32,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 526261673867387060334436024320000000 EdgePairs[34][31]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,33}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {1,19}, {2,9}, {2,34}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET34.32 // Non-bipartite Valency 32 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 46620662575398912000 EdgePairs[34][32]:={ {13,25}, {15,28}, {24,33}, {15,17}, {10,17}, {3,29}, {9,18}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {8,24}, {8,11}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {4,5}, {15,20}, {23,34}, {14,33}, {17,25}, {3,32}, {3,27}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {7,14}, {13,33}, {15,24}, {10,23}, {22,27}, {30,34}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {9,26}, {18,20}, {6,12}, {7,31}, {12,33}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {9,14}, {20,23}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {17,28}, {23,32}, {5,21}, {22,24}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {10,11}, {1,13}, {13,32}, {10,24}, {2,25}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {12,24}, {18,19}, {14,28}, {2,3}, {12,20}, {16,29}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {2,16}, {18,25}, {14,19}, {21,27}, {9,13}, {21,23}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {9,34}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {6,32}, {15,31}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {1,19}, {2,10}, {6,17}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {8,9}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {4,6}, {6,20}, {11,15}, {6,26}, {12,34}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {27,30}, {8,13}, {16,21}, {6,27}, {15,32}, {6,30}, {11,25}, {17,27}, {2,17}, {25,31}, {16,18}, {5,14}, {11,22}, {9,16}, {16,32}, {9,32}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {8,12}, {7,20}, {16,19}, {23,27}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {26,28}, {4,8}, {29,31}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {27,29}, {28,33}, {12,29}, {7,19}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {6,29}, {2,31} }; // ET34.33 // Bipartite(1,33) Valencies [33,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 8683317618811886495518194401280000000 EdgePairs[34][33]:={ {1,5}, {1,4}, {1,7}, {1,16}, {1,31}, {1,12}, {1,2}, {1,33}, {1,3}, {1,17}, {1,30}, {1,13}, {1,22}, {1,10}, {1,15}, {1,11}, {1,28}, {1,6}, {1,14}, {1,26}, {1,34}, {1,18}, {1,27}, {1,21}, {1,19}, {1,29}, {1,20}, {1,8}, {1,24}, {1,32}, {1,9}, {1,23}, {1,25} }; // ET34.34 // Non-bipartite Valency 33 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 295232799039604140847618609643520000000 EdgePairs[34][34]:={ {13,25}, {15,28}, {24,33}, {15,17}, {10,17}, {3,29}, {9,18}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {11,12}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {15,16}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {8,24}, {8,11}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {4,5}, {15,20}, {9,10}, {17,18}, {23,34}, {14,33}, {17,25}, {3,32}, {3,27}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {25,26}, {9,22}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {7,14}, {13,33}, {23,24}, {15,24}, {10,23}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {9,26}, {18,20}, {6,12}, {7,31}, {12,33}, {13,18}, {1,29}, {2,34}, {21,22}, {10,19}, {12,19}, {15,27}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {9,14}, {20,23}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {31,32}, {17,28}, {23,32}, {5,21}, {22,24}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {10,11}, {1,13}, {13,32}, {10,24}, {2,25}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {12,24}, {18,19}, {3,4}, {14,28}, {2,3}, {12,20}, {16,29}, {1,11}, {29,33}, {33,34}, {15,30}, {24,34}, {3,19}, {2,16}, {14,19}, {18,25}, {21,27}, {7,8}, {9,13}, {21,23}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {5,6}, {9,34}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {6,32}, {15,31}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {1,19}, {2,10}, {6,17}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {8,9}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {1,2}, {4,6}, {6,20}, {11,15}, {6,26}, {12,34}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {19,20}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {27,30}, {8,13}, {16,21}, {6,27}, {15,32}, {29,30}, {6,30}, {11,25}, {17,27}, {2,17}, {25,31}, {16,18}, {5,14}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {26,29}, {1,21}, {13,14}, {6,21}, {9,15}, {19,34}, {8,12}, {7,20}, {16,19}, {23,27}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {26,28}, {4,8}, {29,31}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {27,29}, {28,33}, {12,29}, {7,19}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {6,29}, {2,31} }; // Total number of connected ET graphs of order 34 is 34 // ******************************************************************************************** // Order 35 // ET35.1 // Non-bipartite Valency 2 // Diameter 17 Girth 35 // Twin-free VT AT // Automorphism group of order 70 EdgePairs[35][1]:={ {8,20}, {5,28}, {25,32}, {9,16}, {21,33}, {20,27}, {9,32}, {1,29}, {23,35}, {3,15}, {22,34}, {6,18}, {19,26}, {12,24}, {10,33}, {5,12}, {24,31}, {1,13}, {4,27}, {15,22}, {18,30}, {2,30}, {7,35}, {17,29}, {16,28}, {4,11}, {3,26}, {11,23}, {14,21}, {13,25}, {10,17}, {8,31}, {6,34}, {7,19}, {2,14} }; // ET35.2 // Bipartite(14,21) Valencies [3,2] // Diameter 6 Girth 12 // Twin-free Non-VT Non-AT // Automorphism group of order 336 EdgePairs[35][2]:={ {5,28}, {13,19}, {4,20}, {8,33}, {3,24}, {3,16}, {11,22}, {7,30}, {6,15}, {7,23}, {11,25}, {8,28}, {5,18}, {5,27}, {2,19}, {9,32}, {12,23}, {1,29}, {1,15}, {12,31}, {2,25}, {8,16}, {3,35}, {13,31}, {10,30}, {4,27}, {10,22}, {11,21}, {6,24}, {13,20}, {2,35}, {14,29}, {14,21}, {14,32}, {4,26}, {9,33}, {1,26}, {9,17}, {10,18}, {6,34}, {12,17}, {7,34} }; // ET35.3 // Bipartite(15,20) Valencies [4,3] // Diameter 6 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[35][3]:={ {11,30}, {15,35}, {8,19}, {13,28}, {7,16}, {1,24}, {2,26}, {5,24}, {6,33}, {1,29}, {2,29}, {7,23}, {9,16}, {11,24}, {3,27}, {12,30}, {7,33}, {12,31}, {3,20}, {9,32}, {5,23}, {13,32}, {15,21}, {4,18}, {5,25}, {15,31}, {1,16}, {10,26}, {6,20}, {1,21}, {11,32}, {3,19}, {3,31}, {12,29}, {9,35}, {8,34}, {8,22}, {13,22}, {4,28}, {13,23}, {2,27}, {14,33}, {4,25}, {14,21}, {10,17}, {14,27}, {6,35}, {5,34}, {2,34}, {10,22}, {6,28}, {8,30}, {4,19}, {11,18}, {10,20}, {12,17}, {14,25}, {15,18}, {9,17}, {7,26} }; // ET35.4 // Bipartite(15,20) Valencies [4,3] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 122880 EdgePairs[35][4]:={ {3,32}, {3,22}, {1,26}, {15,35}, {5,33}, {12,27}, {6,34}, {8,31}, {14,18}, {11,17}, {5,29}, {9,16}, {12,33}, {6,26}, {8,21}, {8,25}, {11,27}, {15,29}, {1,31}, {3,24}, {2,33}, {11,21}, {4,30}, {6,16}, {5,23}, {13,32}, {7,27}, {7,32}, {1,16}, {15,19}, {10,34}, {5,19}, {2,18}, {1,21}, {4,20}, {12,23}, {13,20}, {15,25}, {7,22}, {10,29}, {8,35}, {10,24}, {13,22}, {4,25}, {2,28}, {10,19}, {3,34}, {9,18}, {2,23}, {14,20}, {7,17}, {9,26}, {4,35}, {9,28}, {13,30}, {14,28}, {12,17}, {11,31}, {6,24}, {14,30} }; // ET35.5 // Non-bipartite Valency 4 // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 140 EdgePairs[35][5]:={ {5,12}, {2,14}, {1,14}, {6,34}, {8,20}, {8,31}, {6,33}, {2,30}, {1,29}, {19,26}, {2,29}, {18,26}, {7,34}, {21,33}, {9,31}, {9,16}, {23,31}, {5,27}, {8,16}, {11,24}, {4,11}, {10,32}, {13,25}, {22,35}, {15,23}, {11,23}, {10,33}, {9,32}, {4,12}, {20,27}, {3,11}, {3,15}, {19,27}, {14,22}, {5,28}, {4,27}, {20,28}, {3,30}, {2,15}, {18,30}, {12,24}, {3,26}, {23,35}, {24,32}, {7,35}, {8,35}, {7,20}, {21,34}, {13,21}, {7,19}, {12,25}, {6,18}, {6,19}, {14,21}, {22,34}, {1,28}, {10,17}, {16,28}, {17,30}, {1,13}, {5,13}, {25,33}, {24,31}, {4,26}, {17,29}, {25,32}, {16,29}, {9,17}, {10,18}, {15,22} }; // ET35.6 // Non-bipartite Valency 4 // Diameter 3 Girth 6 // Twin-free VT AT // Automorphism group of order 5040 EdgePairs[35][6]:={ {3,22}, {15,35}, {2,14}, {19,24}, {6,34}, {11,15}, {21,33}, {27,29}, {7,31}, {20,23}, {21,22}, {31,33}, {11,20}, {10,32}, {2,6}, {25,28}, {8,24}, {10,12}, {8,29}, {20,24}, {30,31}, {4,6}, {16,27}, {4,12}, {5,7}, {4,18}, {1,7}, {1,15}, {3,28}, {16,18}, {9,12}, {2,3}, {29,33}, {34,35}, {10,14}, {5,6}, {8,12}, {26,32}, {1,3}, {27,28}, {23,34}, {9,13}, {22,23}, {11,13}, {16,19}, {18,21}, {20,25}, {14,33}, {9,22}, {4,25}, {28,32}, {25,31}, {2,19}, {10,17}, {24,26}, {21,26}, {19,30}, {30,35}, {32,35}, {5,26}, {1,8}, {5,13}, {9,30}, {7,17}, {16,17}, {13,27}, {29,34}, {11,14}, {15,18}, {17,23} }; // ET35.7 // Bipartite(10,25) Valencies [5,2] // Diameter 4 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 28800 EdgePairs[35][7]:={ {5,32}, {10,27}, {8,20}, {5,24}, {4,34}, {7,34}, {7,23}, {7,31}, {8,23}, {6,14}, {3,21}, {10,30}, {1,12}, {3,29}, {2,33}, {5,16}, {6,16}, {4,32}, {5,20}, {10,13}, {7,27}, {4,18}, {1,15}, {2,31}, {3,17}, {5,28}, {3,25}, {9,33}, {2,15}, {3,14}, {8,12}, {1,18}, {9,35}, {10,24}, {7,19}, {9,22}, {6,19}, {2,28}, {6,22}, {8,26}, {1,13}, {9,30}, {6,11}, {9,26}, {10,21}, {2,25}, {4,35}, {1,11}, {8,17}, {4,29} }; // ET35.8 // Bipartite(14,21) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 336 EdgePairs[35][8]:={ {3,22}, {12,20}, {12,27}, {4,24}, {11,16}, {13,19}, {4,23}, {5,32}, {6,34}, {11,15}, {2,26}, {12,18}, {6,33}, {2,29}, {5,29}, {9,20}, {7,34}, {13,34}, {9,31}, {9,16}, {12,33}, {1,33}, {5,27}, {8,16}, {11,28}, {8,15}, {14,34}, {4,31}, {3,23}, {1,31}, {3,24}, {7,33}, {12,31}, {3,29}, {6,15}, {11,21}, {4,30}, {2,21}, {8,32}, {13,32}, {7,27}, {10,16}, {9,24}, {10,26}, {11,35}, {1,21}, {3,25}, {5,17}, {14,32}, {6,21}, {7,25}, {3,26}, {8,35}, {10,24}, {7,20}, {13,23}, {1,17}, {4,22}, {13,15}, {6,19}, {9,18}, {14,23}, {14,27}, {2,17}, {7,28}, {5,18}, {5,35}, {8,18}, {2,35}, {1,19}, {9,30}, {10,28}, {11,26}, {14,29}, {1,22}, {6,28}, {10,25}, {13,30}, {8,30}, {4,19}, {10,20}, {12,17}, {14,25}, {2,22} }; // ET35.9 // Bipartite(14,21) Valencies [6,4] // Diameter 7 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 501645312 EdgePairs[35][9]:={ {3,22}, {10,15}, {5,32}, {9,23}, {6,34}, {14,19}, {14,31}, {8,20}, {12,18}, {1,29}, {2,30}, {13,34}, {14,26}, {9,21}, {9,16}, {7,31}, {11,28}, {12,16}, {8,15}, {13,25}, {12,30}, {12,32}, {1,20}, {3,24}, {7,33}, {8,29}, {3,29}, {6,32}, {11,33}, {11,21}, {13,18}, {2,21}, {8,27}, {5,16}, {5,23}, {13,32}, {4,33}, {2,16}, {5,25}, {1,15}, {10,31}, {3,15}, {6,20}, {3,17}, {11,35}, {4,21}, {12,23}, {6,27}, {3,31}, {13,20}, {5,30}, {10,29}, {9,35}, {8,34}, {8,22}, {10,24}, {1,27}, {4,28}, {7,19}, {6,18}, {12,25}, {14,33}, {2,28}, {10,17}, {5,18}, {6,25}, {2,23}, {2,35}, {14,24}, {7,17}, {9,30}, {10,22}, {11,26}, {13,27}, {4,26}, {1,22}, {4,35}, {1,34}, {9,28}, {4,19}, {11,19}, {14,17}, {7,24}, {7,26} }; // ET35.10 // Bipartite(14,21) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 645120 EdgePairs[35][10]:={ {3,32}, {5,33}, {12,20}, {12,27}, {13,19}, {13,28}, {9,23}, {14,19}, {7,16}, {1,24}, {8,31}, {2,30}, {5,29}, {11,17}, {11,25}, {4,34}, {9,21}, {9,31}, {9,16}, {12,33}, {5,27}, {6,26}, {8,15}, {11,20}, {10,32}, {13,26}, {6,30}, {8,24}, {3,23}, {1,31}, {7,33}, {3,29}, {6,15}, {2,21}, {8,27}, {5,21}, {5,20}, {2,16}, {7,32}, {1,15}, {2,31}, {3,28}, {10,23}, {3,17}, {11,35}, {4,20}, {11,22}, {14,32}, {3,18}, {4,17}, {7,25}, {1,18}, {10,29}, {12,29}, {13,35}, {8,34}, {12,26}, {1,27}, {7,19}, {4,22}, {14,33}, {13,15}, {4,25}, {6,19}, {9,22}, {11,34}, {10,17}, {6,35}, {5,26}, {2,23}, {8,18}, {14,24}, {9,30}, {10,28}, {6,28}, {4,35}, {1,34}, {13,30}, {14,25}, {14,16}, {2,22}, {7,24}, {10,18}, {12,21} }; // ET35.11 // Non-bipartite Valency 6 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 210 EdgePairs[35][11]:={ {7,19}, {16,34}, {14,21}, {13,25}, {20,27}, {3,15}, {8,31}, {11,23}, {6,18}, {12,19}, {24,26}, {11,33}, {4,27}, {10,27}, {11,29}, {2,20}, {6,13}, {27,34}, {25,32}, {26,33}, {17,35}, {16,23}, {5,7}, {4,6}, {3,10}, {3,31}, {6,34}, {23,30}, {15,32}, {21,28}, {13,20}, {10,23}, {15,28}, {14,27}, {1,29}, {8,15}, {12,30}, {1,34}, {2,14}, {5,33}, {20,33}, {15,22}, {17,24}, {19,26}, {14,16}, {13,26}, {10,12}, {12,34}, {8,21}, {7,29}, {22,29}, {7,25}, {18,25}, {13,35}, {7,14}, {30,32}, {24,31}, {10,33}, {21,33}, {1,19}, {11,18}, {4,21}, {4,17}, {2,35}, {5,28}, {2,9}, {28,35}, {7,35}, {12,24}, {2,24}, {4,11}, {5,22}, {25,27}, {1,23}, {14,31}, {3,26}, {22,34}, {8,20}, {9,26}, {10,17}, {4,32}, {9,11}, {3,16}, {1,13}, {18,30}, {16,28}, {3,25}, {17,29}, {15,17}, {29,31}, {5,12}, {18,31}, {9,32}, {6,24}, {5,18}, {8,30}, {19,32}, {20,22}, {9,16}, {23,35}, {19,21}, {1,8}, {2,30}, {9,22}, {6,28} }; // ET35.12 // Bipartite(7,28) Valencies [8,2] // Diameter 7 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 64210599936 EdgePairs[35][12]:={ {3,22}, {2,14}, {5,32}, {6,34}, {1,29}, {2,30}, {7,31}, {7,12}, {5,11}, {1,20}, {3,8}, {3,24}, {7,33}, {3,29}, {6,32}, {2,21}, {5,9}, {5,16}, {5,23}, {4,12}, {4,33}, {2,16}, {5,25}, {7,10}, {1,15}, {3,15}, {6,20}, {3,17}, {4,21}, {6,27}, {3,31}, {5,30}, {1,27}, {4,28}, {7,19}, {6,18}, {2,28}, {5,18}, {6,25}, {2,23}, {1,8}, {1,13}, {2,35}, {7,17}, {2,9}, {6,11}, {4,26}, {1,22}, {4,14}, {4,35}, {1,34}, {4,19}, {6,13}, {7,24}, {3,10}, {7,26} }; // ET35.13 // Bipartite(15,20) Valencies [8,6] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 619173642240 EdgePairs[35][13]:={ {10,19}, {4,35}, {5,32}, {14,25}, {8,31}, {10,22}, {9,30}, {2,22}, {1,31}, {13,18}, {10,27}, {11,29}, {2,20}, {5,34}, {14,18}, {12,17}, {12,22}, {5,24}, {7,27}, {11,16}, {12,27}, {14,35}, {15,29}, {14,20}, {12,25}, {3,31}, {6,34}, {15,32}, {1,29}, {3,18}, {1,34}, {11,34}, {12,30}, {13,16}, {14,33}, {15,34}, {10,34}, {4,20}, {15,22}, {13,33}, {8,33}, {8,28}, {13,26}, {14,30}, {2,32}, {1,16}, {6,21}, {8,21}, {8,18}, {2,17}, {4,33}, {4,28}, {7,25}, {14,28}, {9,23}, {10,24}, {5,19}, {7,20}, {8,26}, {3,23}, {5,29}, {4,30}, {6,26}, {1,19}, {15,19}, {7,30}, {2,35}, {12,35}, {9,25}, {4,25}, {10,29}, {1,26}, {11,26}, {6,29}, {7,35}, {6,31}, {9,33}, {5,22}, {2,27}, {6,19}, {5,27}, {9,35}, {11,19}, {14,23}, {9,28}, {3,28}, {11,31}, {3,26}, {8,16}, {5,17}, {13,28}, {8,23}, {11,21}, {6,16}, {3,21}, {9,18}, {10,17}, {13,21}, {7,22}, {15,27}, {3,16}, {4,18}, {7,32}, {13,23}, {10,32}, {15,17}, {2,25}, {12,32}, {6,24}, {13,31}, {3,33}, {7,17}, {4,23}, {11,24}, {2,30}, {1,21}, {12,20}, {15,24}, {9,20}, {1,24} }; // ET35.14 // Bipartite(15,20) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 955514880 EdgePairs[35][14]:={ {13,25}, {14,21}, {13,29}, {8,31}, {11,23}, {9,30}, {3,29}, {2,22}, {5,30}, {11,33}, {13,18}, {10,27}, {5,35}, {11,29}, {6,23}, {5,34}, {4,16}, {12,17}, {7,33}, {12,22}, {5,24}, {2,33}, {12,33}, {7,27}, {9,21}, {11,16}, {12,18}, {12,27}, {7,23}, {2,28}, {9,31}, {14,20}, {3,31}, {6,34}, {2,18}, {4,26}, {10,30}, {3,19}, {1,29}, {3,18}, {7,28}, {11,34}, {1,34}, {15,34}, {10,34}, {4,20}, {2,23}, {8,28}, {14,16}, {10,25}, {15,25}, {14,30}, {2,32}, {6,33}, {1,16}, {8,21}, {8,18}, {2,17}, {10,24}, {8,35}, {13,35}, {15,20}, {15,35}, {4,31}, {4,30}, {6,26}, {14,26}, {1,19}, {12,28}, {4,21}, {1,26}, {11,26}, {8,19}, {6,29}, {12,23}, {14,32}, {2,27}, {6,19}, {3,35}, {1,23}, {14,22}, {5,27}, {11,19}, {7,18}, {14,31}, {5,20}, {4,22}, {3,28}, {5,17}, {13,28}, {6,16}, {9,26}, {3,21}, {10,17}, {4,32}, {13,21}, {7,22}, {15,27}, {8,25}, {3,25}, {7,32}, {15,17}, {1,33}, {12,32}, {10,20}, {9,32}, {6,24}, {13,31}, {10,35}, {9,16}, {13,19}, {15,30}, {7,17}, {11,24}, {15,24}, {5,25}, {9,20}, {1,24}, {8,29}, {9,22} }; // ET35.15 // Bipartite(15,20) Valencies [8,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 737280 EdgePairs[35][15]:={ {10,19}, {4,35}, {5,32}, {13,29}, {14,25}, {15,23}, {11,17}, {8,31}, {8,24}, {10,22}, {11,23}, {6,18}, {9,30}, {2,22}, {5,30}, {11,33}, {1,31}, {6,17}, {10,27}, {13,24}, {14,19}, {14,18}, {4,16}, {7,33}, {12,31}, {13,34}, {2,33}, {6,32}, {12,33}, {7,27}, {9,19}, {13,27}, {11,16}, {12,18}, {3,30}, {1,32}, {14,35}, {7,23}, {8,34}, {15,29}, {2,28}, {12,25}, {3,31}, {2,18}, {4,26}, {6,22}, {3,18}, {8,22}, {12,21}, {11,34}, {5,33}, {5,23}, {4,20}, {2,23}, {14,16}, {10,25}, {1,22}, {2,32}, {1,16}, {8,21}, {9,34}, {7,25}, {14,28}, {5,19}, {7,20}, {8,35}, {5,29}, {3,27}, {2,34}, {4,30}, {6,26}, {14,26}, {12,28}, {15,19}, {7,30}, {15,33}, {12,35}, {4,25}, {10,29}, {1,26}, {11,26}, {7,35}, {15,26}, {12,23}, {2,24}, {5,22}, {15,21}, {15,31}, {8,32}, {9,28}, {5,20}, {3,28}, {9,24}, {15,16}, {6,16}, {3,21}, {9,18}, {10,17}, {11,27}, {13,21}, {1,20}, {8,25}, {9,29}, {10,32}, {13,17}, {3,20}, {14,29}, {3,17}, {13,31}, {4,34}, {10,35}, {6,27}, {13,19}, {7,17}, {11,24}, {1,30}, {1,21}, {4,24}, {9,20}, {6,28} }; // ET35.16 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1680 EdgePairs[35][16]:={ {1,15}, {10,19}, {7,19}, {13,25}, {14,21}, {20,27}, {24,33}, {5,14}, {14,25}, {15,23}, {3,15}, {8,31}, {11,23}, {6,18}, {3,29}, {20,28}, {4,27}, {6,17}, {16,30}, {25,34}, {2,11}, {13,24}, {7,33}, {25,32}, {19,27}, {6,32}, {7,31}, {22,35}, {21,35}, {3,30}, {11,22}, {8,34}, {5,13}, {2,28}, {9,31}, {22,33}, {12,25}, {6,34}, {2,15}, {5,26}, {4,26}, {9,17}, {10,18}, {2,29}, {1,29}, {4,12}, {12,21}, {2,14}, {3,11}, {17,30}, {10,34}, {15,22}, {23,32}, {19,30}, {19,26}, {6,33}, {4,28}, {3,14}, {2,13}, {10,31}, {1,12}, {10,16}, {25,33}, {7,20}, {8,35}, {8,17}, {5,29}, {16,29}, {24,31}, {3,27}, {4,30}, {10,33}, {21,33}, {5,28}, {4,15}, {8,19}, {13,22}, {18,27}, {7,35}, {12,24}, {12,23}, {9,33}, {4,11}, {6,19}, {15,21}, {25,31}, {16,27}, {14,22}, {5,27}, {9,35}, {7,18}, {14,23}, {8,32}, {3,26}, {8,16}, {23,31}, {3,12}, {11,25}, {22,34}, {24,32}, {8,20}, {24,35}, {7,16}, {6,20}, {21,32}, {1,14}, {18,29}, {9,18}, {10,17}, {20,26}, {13,21}, {1,27}, {5,11}, {1,13}, {18,30}, {16,28}, {17,29}, {20,29}, {2,26}, {10,32}, {5,12}, {1,28}, {21,34}, {17,26}, {9,32}, {6,35}, {17,28}, {23,34}, {9,16}, {22,31}, {7,34}, {23,35}, {11,24}, {1,30}, {19,28}, {4,13}, {2,30}, {15,24}, {9,20}, {18,26} }; // ET35.17 // Bipartite(14,21) Valencies [9,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6019743744 EdgePairs[35][17]:={ {1,15}, {4,35}, {14,21}, {13,29}, {12,26}, {9,30}, {12,19}, {14,34}, {11,33}, {6,17}, {10,27}, {13,24}, {5,34}, {1,25}, {12,15}, {12,22}, {3,32}, {2,33}, {12,33}, {7,27}, {9,19}, {1,32}, {12,27}, {14,35}, {7,23}, {3,34}, {9,31}, {14,20}, {3,31}, {2,19}, {5,26}, {4,26}, {9,17}, {10,18}, {6,22}, {14,27}, {1,29}, {3,18}, {8,22}, {8,15}, {7,28}, {5,33}, {10,34}, {2,31}, {2,23}, {14,16}, {10,25}, {2,16}, {1,22}, {14,30}, {1,16}, {6,21}, {12,34}, {4,33}, {8,18}, {2,17}, {4,28}, {10,31}, {14,28}, {9,23}, {10,24}, {5,19}, {5,15}, {7,20}, {13,35}, {5,29}, {11,28}, {3,27}, {6,15}, {11,18}, {7,30}, {4,21}, {12,29}, {4,25}, {11,26}, {13,22}, {6,29}, {7,35}, {2,24}, {9,33}, {6,31}, {5,22}, {1,23}, {5,27}, {11,19}, {14,23}, {8,32}, {5,20}, {8,16}, {3,24}, {9,24}, {11,25}, {13,28}, {8,23}, {7,16}, {9,26}, {11,21}, {10,17}, {4,32}, {13,21}, {11,32}, {4,18}, {8,25}, {3,25}, {2,26}, {10,32}, {13,17}, {3,20}, {7,21}, {13,15}, {3,17}, {10,20}, {6,35}, {6,24}, {8,30}, {13,31}, {9,16}, {7,34}, {1,30}, {11,35}, {2,30}, {1,18}, {12,20}, {4,19}, {8,29}, {6,28} }; // ET35.18 // Bipartite(14,21) Valencies [9,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 11757312 EdgePairs[35][18]:={ {1,15}, {10,19}, {7,19}, {14,21}, {11,15}, {10,21}, {10,22}, {6,18}, {9,30}, {5,30}, {11,33}, {4,27}, {11,29}, {5,34}, {1,25}, {12,15}, {12,17}, {7,33}, {12,31}, {12,22}, {13,34}, {2,33}, {6,32}, {6,25}, {13,27}, {9,21}, {12,18}, {1,32}, {11,22}, {14,35}, {3,34}, {9,31}, {12,25}, {3,31}, {6,34}, {2,19}, {9,17}, {13,20}, {3,19}, {1,29}, {7,28}, {11,34}, {13,16}, {5,23}, {4,20}, {2,31}, {2,23}, {8,33}, {7,26}, {2,16}, {1,22}, {1,16}, {6,21}, {2,17}, {8,18}, {10,15}, {7,25}, {14,28}, {9,23}, {5,15}, {8,26}, {13,35}, {5,29}, {4,31}, {3,27}, {10,33}, {4,17}, {12,29}, {13,30}, {4,25}, {10,29}, {8,19}, {11,26}, {7,35}, {12,24}, {2,24}, {5,22}, {14,17}, {1,23}, {14,22}, {5,27}, {9,35}, {10,28}, {11,19}, {7,18}, {14,31}, {8,32}, {9,28}, {5,20}, {3,26}, {8,16}, {3,24}, {9,24}, {13,28}, {8,23}, {6,20}, {11,27}, {4,32}, {13,21}, {14,15}, {4,18}, {8,25}, {7,32}, {13,23}, {2,26}, {3,20}, {7,21}, {11,20}, {14,29}, {12,32}, {3,17}, {6,35}, {8,30}, {10,26}, {4,34}, {10,35}, {6,27}, {9,16}, {3,33}, {1,30}, {5,16}, {2,30}, {1,18}, {14,24}, {4,24}, {6,28} }; // ET35.19 // Bipartite(10,25) Valencies [10,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 200 EdgePairs[35][19]:={ {1,15}, {9,13}, {5,32}, {6,12}, {3,15}, {6,18}, {4,14}, {1,11}, {3,29}, {4,27}, {6,17}, {5,35}, {7,24}, {5,34}, {9,12}, {2,33}, {7,31}, {6,25}, {7,27}, {3,30}, {3,34}, {9,31}, {5,26}, {8,13}, {6,22}, {5,21}, {10,23}, {2,29}, {3,19}, {10,30}, {1,29}, {8,22}, {7,28}, {2,14}, {5,33}, {4,20}, {10,34}, {6,11}, {2,31}, {8,28}, {2,16}, {1,16}, {6,21}, {10,13}, {8,21}, {4,33}, {10,31}, {1,12}, {4,29}, {10,16}, {7,25}, {7,20}, {8,26}, {3,23}, {2,34}, {6,15}, {1,19}, {4,17}, {2,35}, {4,15}, {8,19}, {7,35}, {2,24}, {4,11}, {2,27}, {6,19}, {1,23}, {5,27}, {10,28}, {7,18}, {8,32}, {9,28}, {5,20}, {3,26}, {5,17}, {9,24}, {8,23}, {6,20}, {3,21}, {1,14}, {9,18}, {9,11}, {7,22}, {1,13}, {4,18}, {8,25}, {7,32}, {10,32}, {9,14}, {3,17}, {10,26}, {10,35}, {9,16}, {3,33}, {1,30}, {2,30}, {5,25}, {4,24}, {8,12}, {9,22} }; // ET35.20 // Bipartite(10,25) Valencies [10,4] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7962624000000 EdgePairs[35][20]:={ {9,13}, {4,35}, {10,19}, {5,32}, {5,14}, {8,31}, {10,22}, {1,11}, {9,30}, {2,22}, {6,14}, {1,31}, {10,27}, {2,20}, {5,34}, {5,24}, {7,27}, {7,15}, {3,31}, {6,34}, {2,15}, {8,13}, {1,29}, {3,18}, {1,34}, {3,11}, {4,20}, {10,34}, {6,11}, {8,33}, {8,28}, {3,13}, {10,12}, {2,32}, {1,16}, {6,21}, {8,21}, {8,18}, {2,17}, {4,33}, {4,28}, {7,25}, {5,19}, {9,23}, {10,24}, {7,20}, {8,26}, {3,23}, {5,29}, {4,30}, {6,26}, {1,19}, {8,11}, {7,30}, {2,35}, {9,25}, {4,15}, {4,25}, {9,15}, {10,29}, {1,26}, {6,29}, {7,35}, {6,31}, {9,33}, {5,22}, {2,27}, {6,19}, {5,27}, {9,35}, {2,12}, {9,28}, {10,14}, {3,28}, {3,26}, {8,16}, {5,17}, {8,23}, {6,16}, {3,21}, {1,14}, {9,18}, {10,17}, {7,22}, {3,16}, {4,18}, {7,32}, {10,32}, {5,12}, {2,25}, {6,24}, {3,33}, {7,17}, {4,23}, {7,12}, {4,13}, {1,21}, {2,30}, {9,20}, {1,24} }; // ET35.21 // Bipartite(10,25) Valencies [10,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2985984000000 EdgePairs[35][21]:={ {7,19}, {5,14}, {8,31}, {6,18}, {9,30}, {1,11}, {2,22}, {6,14}, {5,30}, {1,31}, {5,35}, {7,24}, {6,23}, {2,20}, {5,34}, {4,16}, {6,13}, {5,24}, {3,32}, {7,27}, {9,21}, {9,31}, {6,34}, {2,15}, {4,26}, {10,18}, {10,23}, {10,30}, {1,29}, {3,18}, {8,22}, {1,34}, {3,13}, {10,25}, {2,32}, {6,33}, {1,16}, {10,13}, {8,21}, {2,17}, {4,33}, {4,28}, {7,29}, {10,15}, {3,22}, {5,19}, {5,15}, {8,26}, {3,23}, {8,17}, {5,29}, {7,14}, {4,31}, {3,27}, {10,33}, {1,19}, {8,11}, {4,21}, {2,35}, {9,25}, {9,15}, {1,26}, {6,29}, {4,11}, {2,27}, {6,19}, {8,27}, {9,35}, {10,28}, {2,12}, {5,20}, {8,32}, {3,28}, {8,16}, {3,12}, {9,26}, {1,14}, {9,11}, {7,22}, {4,18}, {7,32}, {2,25}, {3,17}, {10,20}, {6,24}, {10,35}, {9,16}, {7,34}, {3,33}, {7,17}, {4,23}, {7,12}, {4,13}, {1,21}, {2,30}, {5,25}, {9,20}, {8,12}, {1,24}, {6,28} }; // ET35.22 // Non-bipartite Valency 10 // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 5016453120000000 EdgePairs[35][22]:={ {1,11}, {25,31}, {6,32}, {6,16}, {4,27}, {13,21}, {16,26}, {15,24}, {18,29}, {4,26}, {4,30}, {11,25}, {16,27}, {21,32}, {6,17}, {1,13}, {12,22}, {20,27}, {4,29}, {3,13}, {8,33}, {1,27}, {3,15}, {2,15}, {25,33}, {10,33}, {2,27}, {21,35}, {2,26}, {7,34}, {22,32}, {2,28}, {2,14}, {1,30}, {9,35}, {20,30}, {8,31}, {16,29}, {15,25}, {8,16}, {16,30}, {19,28}, {23,32}, {14,23}, {6,31}, {8,19}, {3,14}, {7,20}, {14,21}, {9,32}, {19,26}, {19,30}, {22,34}, {5,11}, {5,29}, {9,19}, {19,29}, {22,35}, {7,32}, {3,12}, {23,34}, {11,22}, {14,24}, {25,34}, {10,31}, {9,34}, {13,22}, {24,32}, {2,13}, {6,18}, {1,29}, {8,17}, {18,30}, {11,21}, {7,16}, {23,35}, {6,33}, {1,12}, {11,23}, {5,30}, {17,30}, {7,17}, {17,27}, {13,23}, {12,25}, {13,25}, {20,28}, {8,35}, {5,14}, {18,26}, {9,20}, {4,15}, {4,13}, {1,28}, {18,27}, {24,34}, {3,11}, {3,27}, {4,28}, {21,31}, {3,29}, {3,26}, {21,33}, {5,28}, {24,35}, {7,31}, {25,35}, {17,28}, {20,29}, {5,12}, {25,32}, {8,32}, {12,23}, {14,22}, {13,24}, {11,24}, {22,33}, {10,32}, {17,29}, {6,19}, {1,15}, {22,31}, {2,11}, {15,21}, {14,25}, {10,35}, {3,30}, {8,34}, {9,18}, {20,26}, {10,17}, {2,29}, {18,28}, {1,26}, {23,33}, {4,14}, {15,22}, {10,34}, {9,17}, {10,18}, {9,33}, {6,34}, {5,27}, {5,26}, {8,18}, {10,19}, {4,11}, {4,12}, {5,13}, {8,20}, {3,28}, {12,24}, {15,23}, {23,31}, {21,34}, {2,12}, {1,14}, {10,20}, {17,26}, {5,15}, {7,33}, {6,20}, {7,35}, {2,30}, {9,31}, {7,19}, {24,33}, {6,35}, {9,16}, {16,28}, {19,27}, {24,31}, {12,21}, {7,18}, {10,16} }; // ET35.23 // Bipartite(5,30) Valencies [12,2] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1934917632000000 EdgePairs[35][23]:={ {5,12}, {1,26}, {4,8}, {4,13}, {4,23}, {5,32}, {1,14}, {1,24}, {5,24}, {2,32}, {2,30}, {1,29}, {5,29}, {2,10}, {5,27}, {4,10}, {3,21}, {1,6}, {3,33}, {3,8}, {3,23}, {1,31}, {2,12}, {4,30}, {5,9}, {5,7}, {4,18}, {4,33}, {2,7}, {3,11}, {3,16}, {3,28}, {2,20}, {1,16}, {5,19}, {1,21}, {4,20}, {5,17}, {2,15}, {3,18}, {3,31}, {3,26}, {4,15}, {4,28}, {2,27}, {3,6}, {4,25}, {5,14}, {2,17}, {3,13}, {5,34}, {2,35}, {1,19}, {1,9}, {2,25}, {4,35}, {1,34}, {1,11}, {5,22}, {2,22} }; // ET35.24 // Bipartite(5,30) Valencies [12,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7255941120 EdgePairs[35][24]:={ {1,26}, {1,14}, {1,24}, {5,24}, {2,32}, {1,29}, {1,33}, {5,27}, {4,11}, {4,10}, {5,10}, {3,21}, {1,6}, {5,15}, {4,31}, {3,8}, {4,16}, {3,9}, {2,12}, {3,29}, {2,33}, {4,6}, {4,30}, {4,32}, {4,12}, {5,20}, {5,7}, {5,25}, {2,7}, {3,11}, {1,16}, {3,28}, {3,15}, {2,18}, {3,25}, {4,21}, {4,20}, {3,19}, {5,17}, {3,18}, {3,31}, {5,30}, {2,27}, {4,22}, {2,28}, {5,14}, {2,17}, {2,23}, {5,34}, {1,13}, {5,35}, {1,19}, {1,9}, {4,26}, {2,13}, {2,8}, {1,34}, {1,23}, {2,22}, {3,35} }; // ET35.25 // Bipartite(7,28) Valencies [12,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 168 EdgePairs[35][25]:={ {5,12}, {1,26}, {4,8}, {4,9}, {4,23}, {5,32}, {6,34}, {1,24}, {2,32}, {2,30}, {1,29}, {2,29}, {1,32}, {2,10}, {6,14}, {4,10}, {3,21}, {3,27}, {7,13}, {5,11}, {6,10}, {1,12}, {5,15}, {3,8}, {3,23}, {4,16}, {1,31}, {7,33}, {2,33}, {6,15}, {3,20}, {5,9}, {7,30}, {6,16}, {5,21}, {4,12}, {4,33}, {3,11}, {2,31}, {1,16}, {3,28}, {7,18}, {6,20}, {1,21}, {5,28}, {3,19}, {3,30}, {5,17}, {6,27}, {2,15}, {3,31}, {1,18}, {7,22}, {1,27}, {7,20}, {4,28}, {7,19}, {3,34}, {5,18}, {3,13}, {6,25}, {6,17}, {6,35}, {2,23}, {1,8}, {5,35}, {2,34}, {2,9}, {5,13}, {7,17}, {6,11}, {4,26}, {2,25}, {4,14}, {4,35}, {4,19}, {7,14}, {1,25}, {5,22}, {2,22}, {7,24}, {6,24}, {7,26}, {7,29} }; // ET35.26 // Bipartite(7,28) Valencies [12,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 770527199232 EdgePairs[35][26]:={ {3,32}, {5,12}, {5,33}, {7,16}, {2,26}, {1,29}, {2,30}, {1,30}, {5,29}, {1,32}, {7,9}, {7,34}, {2,24}, {7,23}, {2,10}, {5,27}, {6,14}, {4,11}, {6,31}, {3,27}, {7,13}, {6,10}, {5,15}, {3,24}, {2,12}, {2,33}, {6,15}, {3,20}, {5,8}, {7,30}, {4,32}, {4,12}, {5,20}, {7,27}, {4,18}, {2,16}, {4,33}, {1,15}, {3,11}, {2,31}, {1,16}, {3,17}, {5,19}, {3,25}, {4,21}, {3,18}, {6,21}, {3,31}, {1,18}, {7,21}, {7,35}, {7,20}, {4,28}, {4,25}, {3,34}, {6,22}, {2,19}, {2,17}, {7,28}, {3,13}, {6,17}, {6,35}, {2,23}, {5,26}, {1,8}, {5,34}, {2,9}, {5,13}, {1,9}, {4,26}, {1,22}, {4,14}, {4,35}, {6,28}, {1,23}, {4,19}, {7,14}, {1,11}, {1,25}, {5,22}, {6,29}, {6,8}, {6,24}, {3,10} }; // ET35.27 // Bipartite(7,28) Valencies [12,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 688128 EdgePairs[35][27]:={ {1,26}, {4,8}, {4,13}, {5,32}, {6,34}, {7,16}, {2,26}, {5,24}, {2,30}, {2,29}, {5,29}, {1,32}, {7,34}, {7,31}, {1,33}, {6,26}, {4,11}, {5,10}, {3,21}, {6,12}, {7,13}, {3,33}, {6,10}, {1,12}, {5,15}, {3,23}, {1,31}, {3,24}, {3,9}, {2,12}, {6,32}, {5,9}, {7,30}, {5,23}, {7,27}, {2,16}, {4,33}, {5,31}, {3,11}, {3,16}, {2,20}, {6,20}, {4,27}, {3,25}, {1,21}, {5,28}, {3,19}, {3,30}, {5,17}, {6,27}, {2,15}, {1,18}, {7,21}, {7,35}, {4,15}, {7,20}, {4,28}, {1,17}, {4,22}, {6,18}, {4,25}, {5,14}, {7,28}, {5,18}, {6,25}, {2,23}, {1,8}, {2,34}, {2,9}, {1,19}, {7,17}, {6,11}, {1,22}, {4,14}, {2,8}, {1,35}, {4,19}, {7,14}, {2,22}, {6,13}, {6,24}, {3,10}, {3,35}, {4,29} }; // ET35.28 // Bipartite(14,21) Valencies [12,8] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 336 EdgePairs[35][28]:={ {11,17}, {2,24}, {1,20}, {11,20}, {9,28}, {2,33}, {6,16}, {6,32}, {12,29}, {13,21}, {7,15}, {5,34}, {14,19}, {4,26}, {4,16}, {11,25}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {4,29}, {1,27}, {10,23}, {2,15}, {2,19}, {10,33}, {2,27}, {3,35}, {5,20}, {13,35}, {12,35}, {2,28}, {12,34}, {1,30}, {9,35}, {14,28}, {8,31}, {8,27}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {10,30}, {3,17}, {3,34}, {2,25}, {11,33}, {6,31}, {14,33}, {5,22}, {8,19}, {1,18}, {9,32}, {9,26}, {9,27}, {9,19}, {14,30}, {5,25}, {7,32}, {11,22}, {14,24}, {6,30}, {12,16}, {4,33}, {5,23}, {10,29}, {4,21}, {10,31}, {3,20}, {13,22}, {10,21}, {13,18}, {1,29}, {8,17}, {2,16}, {13,31}, {3,32}, {9,25}, {7,16}, {7,26}, {2,32}, {13,33}, {14,15}, {1,23}, {11,29}, {5,30}, {7,17}, {11,30}, {12,28}, {12,25}, {13,25}, {13,28}, {4,15}, {1,28}, {3,27}, {6,23}, {8,26}, {9,22}, {7,31}, {14,17}, {8,21}, {3,19}, {1,24}, {14,18}, {14,22}, {13,24}, {11,24}, {6,27}, {5,31}, {12,19}, {6,26}, {12,30}, {8,23}, {3,21}, {7,29}, {1,15}, {13,27}, {1,35}, {14,20}, {3,16}, {10,35}, {7,23}, {3,30}, {5,33}, {8,34}, {10,27}, {1,26}, {4,34}, {10,34}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {5,26}, {4,18}, {11,19}, {4,25}, {4,20}, {12,24}, {8,20}, {3,28}, {14,35}, {7,24}, {3,31}, {5,15}, {11,34}, {6,20}, {5,21}, {9,15}, {2,18}, {1,34}, {7,19}, {4,17}, {6,35}, {9,23}, {7,21}, {8,29}, {4,32}, {11,18}, {12,21}, {14,26}, {7,18}, {5,16} }; // ET35.29 // Bipartite(14,21) Valencies [12,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6019743744 EdgePairs[35][29]:={ {3,33}, {10,24}, {11,20}, {13,32}, {2,33}, {6,16}, {6,32}, {4,27}, {12,29}, {13,21}, {7,15}, {11,35}, {11,25}, {6,17}, {2,23}, {12,22}, {4,29}, {1,32}, {8,33}, {10,26}, {7,22}, {2,19}, {10,33}, {2,27}, {1,19}, {3,35}, {13,35}, {2,26}, {14,31}, {7,34}, {12,35}, {8,25}, {8,15}, {8,31}, {13,16}, {11,28}, {3,17}, {6,21}, {3,34}, {2,25}, {14,23}, {6,31}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,20}, {9,32}, {9,26}, {9,27}, {5,29}, {9,19}, {14,30}, {11,15}, {1,31}, {11,22}, {10,28}, {14,24}, {1,22}, {6,30}, {12,16}, {5,23}, {4,21}, {10,31}, {3,20}, {9,34}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {11,21}, {4,35}, {9,25}, {7,16}, {2,32}, {14,15}, {11,29}, {6,24}, {5,30}, {7,17}, {13,23}, {12,28}, {8,22}, {13,25}, {13,28}, {9,20}, {4,15}, {3,27}, {4,28}, {1,33}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {7,31}, {12,33}, {13,30}, {14,17}, {8,32}, {3,19}, {1,24}, {12,23}, {14,22}, {13,24}, {12,19}, {12,30}, {14,34}, {3,21}, {1,25}, {7,29}, {1,15}, {6,28}, {12,15}, {9,30}, {14,20}, {10,35}, {7,23}, {5,33}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {4,34}, {10,34}, {11,32}, {8,24}, {6,25}, {9,33}, {5,26}, {8,18}, {4,18}, {10,19}, {4,25}, {4,20}, {3,28}, {7,27}, {7,24}, {3,31}, {10,20}, {5,15}, {11,34}, {5,19}, {5,21}, {2,30}, {13,17}, {5,35}, {2,18}, {6,35}, {9,16}, {9,23}, {14,27}, {8,29}, {4,32}, {11,18}, {12,21}, {14,29}, {5,16} }; // ET35.30 // Bipartite(15,20) Valencies [12,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 955514880 EdgePairs[35][30]:={ {11,17}, {2,24}, {1,20}, {5,17}, {11,20}, {13,32}, {2,33}, {4,27}, {12,29}, {14,19}, {4,26}, {3,22}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {15,31}, {4,29}, {1,27}, {3,25}, {10,26}, {4,19}, {7,22}, {2,19}, {3,35}, {13,35}, {7,34}, {1,21}, {12,35}, {8,25}, {12,34}, {1,30}, {5,32}, {9,35}, {4,23}, {13,16}, {10,22}, {15,16}, {3,18}, {11,28}, {8,16}, {15,29}, {6,21}, {3,34}, {2,25}, {14,23}, {11,33}, {6,31}, {2,34}, {14,33}, {1,17}, {5,22}, {9,29}, {1,18}, {15,32}, {9,26}, {9,27}, {5,29}, {9,19}, {14,30}, {7,32}, {15,26}, {1,31}, {7,25}, {11,31}, {10,28}, {2,35}, {15,27}, {6,30}, {4,33}, {10,29}, {10,31}, {3,20}, {13,22}, {15,19}, {10,21}, {14,16}, {6,18}, {13,18}, {3,32}, {11,21}, {4,35}, {9,25}, {2,32}, {6,33}, {5,18}, {11,23}, {1,23}, {6,24}, {11,30}, {12,25}, {8,22}, {13,25}, {8,35}, {13,28}, {9,20}, {1,28}, {1,33}, {15,17}, {6,23}, {3,26}, {5,28}, {8,26}, {7,31}, {12,33}, {13,30}, {14,17}, {8,32}, {1,24}, {12,23}, {13,24}, {11,24}, {6,27}, {5,31}, {12,19}, {10,32}, {7,29}, {6,28}, {9,30}, {14,20}, {15,21}, {14,25}, {3,16}, {13,26}, {15,18}, {7,23}, {2,21}, {3,30}, {8,34}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {2,22}, {15,22}, {9,17}, {10,18}, {8,24}, {2,31}, {9,33}, {6,34}, {5,27}, {5,26}, {8,18}, {15,28}, {10,19}, {4,25}, {4,20}, {12,24}, {8,20}, {3,28}, {14,35}, {7,24}, {7,33}, {12,31}, {11,34}, {13,34}, {5,19}, {6,20}, {7,35}, {5,21}, {13,20}, {1,34}, {7,19}, {4,17}, {9,16}, {9,23}, {7,21}, {14,27}, {11,18}, {12,21}, {14,29}, {14,26}, {10,16}, {5,16} }; // ET35.31 // Bipartite(15,20) Valencies [12,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 737280 EdgePairs[35][31]:={ {10,25}, {5,17}, {11,20}, {13,32}, {2,33}, {6,32}, {4,27}, {12,29}, {4,24}, {15,24}, {8,30}, {2,23}, {4,29}, {1,32}, {8,33}, {3,25}, {10,23}, {10,26}, {4,19}, {7,22}, {4,31}, {2,19}, {10,33}, {2,27}, {1,19}, {3,35}, {5,20}, {13,35}, {2,26}, {14,31}, {7,34}, {1,21}, {12,35}, {8,25}, {12,34}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {11,28}, {6,29}, {3,17}, {15,29}, {6,21}, {11,33}, {6,31}, {4,22}, {8,19}, {9,29}, {1,18}, {14,21}, {12,17}, {9,26}, {9,27}, {9,19}, {14,30}, {5,25}, {7,32}, {15,26}, {1,31}, {11,31}, {14,24}, {1,22}, {6,30}, {5,23}, {4,21}, {10,31}, {3,20}, {9,34}, {13,22}, {15,19}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {2,16}, {11,21}, {7,16}, {7,26}, {6,33}, {2,32}, {5,18}, {11,23}, {5,30}, {7,17}, {11,30}, {15,35}, {12,25}, {8,22}, {15,34}, {13,25}, {8,35}, {13,28}, {9,20}, {1,28}, {3,27}, {4,28}, {3,29}, {6,23}, {3,26}, {5,28}, {12,33}, {13,30}, {2,17}, {12,27}, {8,32}, {3,19}, {12,23}, {14,22}, {13,24}, {11,24}, {5,31}, {12,19}, {8,23}, {14,34}, {10,32}, {1,25}, {6,19}, {6,28}, {9,30}, {13,27}, {1,35}, {14,20}, {14,25}, {7,28}, {3,16}, {11,26}, {15,18}, {10,35}, {11,16}, {7,23}, {3,30}, {5,33}, {8,34}, {10,17}, {2,29}, {10,27}, {1,26}, {2,22}, {4,34}, {1,16}, {9,17}, {14,32}, {15,33}, {8,24}, {5,27}, {4,18}, {15,28}, {12,24}, {8,20}, {3,28}, {7,27}, {14,35}, {15,23}, {7,24}, {9,24}, {7,33}, {12,31}, {11,34}, {13,34}, {6,20}, {5,21}, {2,30}, {13,17}, {13,20}, {5,35}, {9,31}, {4,17}, {9,21}, {9,16}, {8,29}, {4,32}, {11,18}, {12,21}, {14,26}, {7,18}, {10,16} }; // ET35.32 // Non-bipartite Valency 12 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 50400 EdgePairs[35][32]:={ {2,24}, {5,17}, {17,35}, {4,27}, {12,29}, {13,21}, {7,15}, {16,33}, {4,26}, {4,16}, {8,30}, {1,13}, {30,33}, {3,6}, {20,27}, {24,27}, {3,25}, {3,15}, {10,23}, {17,34}, {2,15}, {4,31}, {2,19}, {25,33}, {10,33}, {1,19}, {3,35}, {13,35}, {14,31}, {26,33}, {7,34}, {17,24}, {12,35}, {2,9}, {18,21}, {8,25}, {12,34}, {2,14}, {5,32}, {8,15}, {16,23}, {28,35}, {8,31}, {13,16}, {9,11}, {16,29}, {10,22}, {19,21}, {11,28}, {6,29}, {8,16}, {2,25}, {11,33}, {2,34}, {5,22}, {4,22}, {1,18}, {7,20}, {14,21}, {9,32}, {19,26}, {15,32}, {16,24}, {9,26}, {9,27}, {12,20}, {22,34}, {2,10}, {19,22}, {22,35}, {7,25}, {10,28}, {25,28}, {2,35}, {15,27}, {20,33}, {23,26}, {5,23}, {4,21}, {3,20}, {24,32}, {2,20}, {14,16}, {6,18}, {1,29}, {7,30}, {24,26}, {13,31}, {18,30}, {23,35}, {6,33}, {5,18}, {11,23}, {1,23}, {11,29}, {6,24}, {17,30}, {8,11}, {5,7}, {12,25}, {1,9}, {13,25}, {20,28}, {8,35}, {18,26}, {19,31}, {1,28}, {3,11}, {7,14}, {20,22}, {4,7}, {15,17}, {1,33}, {10,13}, {26,34}, {10,12}, {6,23}, {3,10}, {22,29}, {3,26}, {21,33}, {30,32}, {5,28}, {8,26}, {18,31}, {29,32}, {9,22}, {13,30}, {4,6}, {5,12}, {25,32}, {14,17}, {8,21}, {1,24}, {14,22}, {11,24}, {17,25}, {12,19}, {20,23}, {12,30}, {21,29}, {10,32}, {18,25}, {17,29}, {3,21}, {9,12}, {6,19}, {7,29}, {6,28}, {6,14}, {16,34}, {19,32}, {3,16}, {13,26}, {15,18}, {3,30}, {5,33}, {10,17}, {2,29}, {10,27}, {15,22}, {5,8}, {29,31}, {9,17}, {14,32}, {15,33}, {10,18}, {6,34}, {27,35}, {5,27}, {15,28}, {11,19}, {4,11}, {1,8}, {4,12}, {5,13}, {8,20}, {12,24}, {28,31}, {15,23}, {25,27}, {23,31}, {7,24}, {3,31}, {21,34}, {1,14}, {11,34}, {7,35}, {2,30}, {6,13}, {13,20}, {22,30}, {27,34}, {9,31}, {1,34}, {7,19}, {21,28}, {4,17}, {9,21}, {9,16}, {16,28}, {18,35}, {20,32}, {14,27}, {4,32}, {19,27}, {24,31}, {11,18}, {14,26}, {23,30} }; // ET35.33 // Non-bipartite Valency 12 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 5040 EdgePairs[35][33]:={ {19,20}, {21,23}, {1,11}, {2,24}, {5,17}, {2,33}, {12,29}, {7,15}, {11,35}, {5,34}, {14,19}, {23,29}, {3,8}, {4,16}, {11,25}, {21,32}, {12,22}, {8,9}, {12,32}, {30,33}, {3,9}, {3,6}, {32,34}, {8,33}, {3,25}, {3,15}, {10,23}, {17,34}, {17,20}, {10,26}, {4,31}, {7,8}, {25,33}, {10,33}, {2,4}, {14,31}, {24,30}, {25,30}, {26,33}, {29,35}, {8,10}, {27,33}, {6,7}, {2,28}, {5,32}, {8,15}, {16,23}, {9,35}, {28,35}, {8,27}, {13,29}, {13,16}, {9,11}, {16,29}, {15,16}, {6,29}, {3,7}, {16,30}, {11,33}, {4,10}, {2,34}, {1,17}, {26,28}, {8,19}, {1,18}, {3,14}, {14,21}, {19,26}, {12,17}, {16,24}, {15,32}, {4,8}, {9,27}, {22,34}, {1,5}, {5,11}, {31,35}, {2,5}, {2,10}, {9,19}, {1,31}, {7,13}, {7,25}, {10,28}, {20,31}, {30,34}, {24,25}, {1,22}, {6,12}, {12,13}, {4,21}, {1,2}, {13,22}, {24,32}, {6,18}, {26,35}, {28,29}, {1,29}, {7,30}, {2,16}, {3,32}, {7,16}, {23,35}, {7,26}, {1,12}, {14,15}, {11,23}, {5,24}, {17,27}, {12,25}, {23,25}, {15,34}, {20,28}, {9,10}, {13,28}, {15,20}, {17,18}, {18,26}, {19,31}, {4,15}, {1,28}, {18,27}, {3,27}, {20,22}, {4,28}, {21,31}, {18,33}, {6,23}, {30,32}, {17,31}, {8,26}, {13,30}, {25,32}, {14,17}, {33,34}, {3,19}, {4,9}, {1,24}, {5,31}, {11,24}, {6,26}, {22,33}, {12,30}, {21,29}, {3,23}, {18,19}, {18,25}, {12,14}, {17,19}, {3,21}, {6,19}, {22,28}, {13,15}, {27,32}, {6,14}, {2,11}, {10,11}, {4,5}, {1,35}, {14,20}, {15,21}, {16,21}, {13,26}, {22,26}, {10,35}, {7,23}, {8,34}, {20,26}, {11,27}, {20,34}, {2,22}, {4,34}, {18,22}, {29,31}, {14,32}, {6,25}, {13,14}, {5,27}, {5,9}, {24,29}, {4,20}, {12,24}, {8,20}, {7,10}, {28,31}, {25,27}, {7,33}, {19,35}, {17,22}, {21,24}, {5,21}, {2,30}, {15,30}, {6,13}, {13,20}, {22,30}, {27,34}, {9,31}, {23,24}, {6,35}, {17,32}, {9,21}, {16,28}, {18,35}, {9,23}, {12,18}, {19,27}, {11,18}, {14,29}, {10,16} }; // ET35.34 // Non-bipartite Valency 14 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 32520160641024000000 EdgePairs[35][34]:={ {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {9,28}, {13,32}, {6,16}, {17,35}, {4,27}, {12,29}, {7,15}, {11,35}, {4,24}, {16,33}, {18,29}, {4,26}, {3,22}, {4,16}, {18,32}, {11,25}, {8,30}, {21,32}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {16,31}, {15,31}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {17,34}, {2,15}, {4,19}, {7,22}, {2,19}, {10,33}, {2,27}, {1,19}, {21,35}, {5,20}, {13,35}, {2,26}, {14,31}, {1,21}, {12,35}, {8,25}, {2,28}, {12,34}, {9,35}, {14,28}, {20,30}, {4,23}, {8,31}, {8,27}, {13,29}, {16,29}, {18,34}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {3,17}, {16,30}, {15,29}, {19,33}, {6,21}, {2,25}, {14,23}, {11,33}, {14,33}, {1,17}, {5,22}, {4,22}, {9,29}, {1,18}, {7,20}, {9,32}, {15,32}, {9,26}, {19,30}, {9,27}, {19,29}, {14,30}, {5,25}, {11,22}, {7,25}, {10,28}, {11,31}, {14,24}, {20,31}, {17,33}, {1,22}, {20,33}, {5,23}, {10,29}, {4,21}, {10,31}, {3,20}, {9,34}, {13,22}, {2,20}, {6,18}, {2,16}, {13,31}, {18,30}, {9,25}, {7,16}, {7,26}, {13,33}, {5,18}, {16,32}, {11,23}, {1,23}, {6,24}, {11,29}, {7,17}, {17,30}, {11,30}, {15,35}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {15,34}, {13,25}, {8,35}, {13,28}, {19,31}, {4,15}, {1,28}, {3,27}, {4,28}, {21,31}, {18,33}, {6,23}, {3,26}, {21,33}, {5,28}, {8,26}, {17,31}, {18,31}, {12,26}, {9,22}, {12,33}, {6,15}, {13,30}, {2,17}, {20,29}, {12,27}, {8,32}, {3,19}, {1,24}, {12,23}, {14,22}, {6,27}, {11,24}, {13,24}, {6,26}, {12,30}, {21,29}, {3,23}, {8,23}, {14,34}, {10,32}, {21,30}, {17,29}, {3,21}, {1,25}, {6,19}, {1,15}, {6,28}, {9,30}, {13,27}, {16,34}, {14,25}, {20,35}, {7,28}, {19,32}, {3,16}, {11,26}, {13,26}, {10,35}, {7,23}, {2,21}, {8,34}, {3,24}, {11,27}, {16,35}, {10,27}, {20,34}, {1,26}, {2,22}, {1,16}, {10,34}, {11,32}, {14,32}, {15,33}, {8,24}, {6,25}, {9,33}, {5,27}, {5,26}, {4,18}, {4,25}, {4,20}, {3,28}, {12,24}, {7,27}, {14,35}, {7,24}, {21,34}, {9,24}, {5,15}, {12,31}, {11,34}, {13,34}, {19,35}, {5,19}, {6,20}, {5,21}, {15,30}, {19,34}, {2,18}, {9,31}, {7,19}, {4,17}, {17,32}, {18,35}, {9,23}, {20,32}, {7,21}, {14,27}, {8,29}, {14,29}, {14,26}, {7,18}, {5,16} }; // ET35.35 // Bipartite(10,25) Valencies [15,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2985984000000 EdgePairs[35][35]:={ {3,33}, {10,24}, {1,20}, {2,24}, {9,28}, {6,32}, {6,16}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,30}, {6,17}, {1,13}, {4,29}, {3,13}, {3,25}, {3,15}, {10,23}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {10,33}, {3,35}, {2,26}, {2,14}, {1,30}, {6,11}, {8,31}, {8,27}, {9,11}, {10,22}, {6,22}, {3,18}, {8,16}, {6,21}, {2,25}, {7,12}, {6,31}, {2,34}, {4,22}, {8,19}, {1,18}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {5,29}, {8,14}, {7,32}, {7,13}, {7,25}, {10,28}, {2,35}, {6,12}, {6,30}, {5,23}, {10,29}, {3,20}, {2,20}, {1,29}, {7,30}, {8,17}, {2,16}, {4,35}, {5,18}, {1,23}, {7,17}, {8,11}, {5,24}, {8,22}, {5,14}, {4,15}, {1,28}, {3,11}, {1,33}, {10,13}, {10,12}, {3,26}, {5,28}, {8,26}, {9,22}, {6,15}, {9,13}, {8,32}, {8,21}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {10,32}, {3,21}, {1,25}, {9,12}, {1,15}, {2,11}, {1,35}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {8,34}, {9,18}, {10,17}, {2,29}, {10,27}, {4,34}, {4,14}, {10,34}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {5,26}, {10,19}, {4,25}, {4,12}, {4,20}, {5,13}, {3,28}, {7,27}, {3,31}, {1,14}, {7,33}, {10,14}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {9,31}, {1,34}, {4,17}, {6,35}, {9,21}, {9,16}, {9,23}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET35.36 // Bipartite(14,21) Valencies [15,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 645120 EdgePairs[35][36]:={ {11,17}, {3,33}, {10,25}, {1,20}, {5,17}, {2,24}, {9,28}, {13,32}, {2,33}, {6,16}, {6,32}, {4,27}, {12,29}, {7,15}, {11,35}, {4,26}, {3,22}, {4,16}, {11,25}, {8,30}, {2,23}, {12,22}, {4,29}, {8,33}, {1,27}, {3,25}, {3,15}, {4,19}, {7,22}, {2,19}, {10,33}, {1,19}, {3,35}, {5,20}, {2,26}, {14,31}, {12,35}, {2,28}, {1,30}, {8,15}, {9,35}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {10,30}, {6,29}, {8,16}, {3,34}, {2,25}, {14,23}, {11,33}, {2,34}, {14,33}, {1,17}, {5,22}, {8,19}, {1,18}, {9,32}, {14,21}, {12,17}, {9,26}, {12,20}, {5,29}, {9,19}, {14,30}, {5,25}, {11,15}, {7,32}, {1,31}, {10,28}, {14,24}, {2,35}, {1,22}, {6,30}, {4,33}, {12,16}, {5,23}, {10,29}, {4,21}, {10,31}, {3,20}, {9,34}, {13,22}, {10,21}, {2,20}, {6,18}, {13,18}, {7,30}, {8,17}, {3,32}, {11,21}, {4,35}, {9,25}, {7,26}, {2,32}, {5,18}, {14,15}, {11,23}, {6,24}, {11,29}, {7,17}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,25}, {8,35}, {13,28}, {9,20}, {4,15}, {3,27}, {1,33}, {3,29}, {6,23}, {5,28}, {8,26}, {7,31}, {13,30}, {2,17}, {14,17}, {1,24}, {14,18}, {12,23}, {14,22}, {5,31}, {6,27}, {13,24}, {6,26}, {12,19}, {10,32}, {3,21}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {9,30}, {13,27}, {1,35}, {7,28}, {3,16}, {11,26}, {13,26}, {10,35}, {11,16}, {7,23}, {13,19}, {2,21}, {3,30}, {8,34}, {11,27}, {10,27}, {1,26}, {4,34}, {1,16}, {10,34}, {11,32}, {9,17}, {14,32}, {8,24}, {6,25}, {2,31}, {9,33}, {6,34}, {8,18}, {4,18}, {11,19}, {4,25}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {3,31}, {9,24}, {10,20}, {5,15}, {7,33}, {12,31}, {11,34}, {13,34}, {5,19}, {6,20}, {5,21}, {2,30}, {13,20}, {5,35}, {9,31}, {1,34}, {4,17}, {9,21}, {9,23}, {7,21}, {14,27}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET35.37 // Bipartite(7,28) Valencies [16,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 770527199232 EdgePairs[35][37]:={ {1,15}, {4,35}, {5,14}, {6,10}, {6,18}, {4,14}, {1,11}, {6,14}, {5,30}, {4,8}, {4,27}, {1,31}, {6,17}, {2,11}, {5,35}, {7,24}, {6,23}, {2,20}, {1,25}, {2,33}, {6,32}, {6,25}, {7,31}, {7,27}, {1,32}, {7,15}, {7,23}, {3,10}, {3,34}, {3,31}, {2,19}, {2,18}, {6,9}, {5,26}, {5,9}, {5,21}, {3,19}, {1,29}, {7,10}, {5,23}, {5,33}, {4,20}, {6,11}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {6,21}, {4,28}, {7,29}, {3,14}, {2,13}, {1,12}, {4,29}, {5,19}, {5,15}, {7,20}, {7,13}, {5,29}, {3,27}, {2,34}, {1,19}, {4,21}, {7,30}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {6,31}, {4,11}, {5,22}, {7,8}, {2,27}, {3,35}, {6,30}, {5,8}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {6,16}, {7,16}, {3,21}, {7,9}, {4,32}, {7,22}, {4,18}, {2,26}, {3,20}, {1,33}, {5,12}, {2,25}, {3,17}, {6,24}, {6,35}, {4,34}, {3,33}, {7,34}, {7,17}, {1,8}, {5,16}, {4,13}, {2,30}, {1,18}, {1,24}, {6,28} }; // ET35.38 // Bipartite(15,20) Valencies [16,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7430083706880 EdgePairs[35][38]:={ {11,17}, {3,33}, {2,24}, {5,17}, {10,25}, {2,33}, {6,16}, {6,32}, {4,27}, {12,29}, {13,21}, {4,24}, {14,19}, {4,26}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {15,31}, {4,29}, {1,32}, {8,33}, {1,27}, {3,25}, {10,23}, {10,26}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {3,35}, {5,20}, {13,35}, {14,31}, {7,34}, {1,21}, {12,35}, {8,25}, {2,28}, {12,34}, {5,32}, {9,35}, {8,31}, {13,29}, {13,16}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {11,28}, {10,30}, {6,29}, {8,16}, {6,21}, {3,34}, {2,25}, {6,31}, {11,33}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {9,32}, {14,21}, {12,17}, {15,32}, {9,26}, {9,27}, {12,20}, {9,19}, {14,30}, {5,25}, {7,32}, {15,26}, {1,31}, {11,22}, {7,25}, {10,28}, {11,31}, {14,24}, {2,35}, {1,22}, {15,27}, {5,23}, {4,21}, {3,20}, {10,31}, {9,34}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {1,29}, {7,30}, {13,31}, {11,21}, {4,35}, {9,25}, {2,32}, {6,33}, {13,33}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {15,35}, {13,23}, {12,28}, {12,25}, {13,25}, {8,35}, {13,28}, {15,20}, {9,20}, {1,28}, {1,33}, {15,17}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {12,33}, {13,30}, {2,17}, {12,27}, {14,17}, {8,21}, {3,19}, {1,24}, {12,23}, {14,22}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {14,34}, {10,32}, {3,21}, {6,19}, {7,29}, {6,28}, {9,30}, {14,20}, {15,21}, {14,25}, {7,28}, {3,16}, {11,26}, {13,26}, {15,18}, {10,35}, {7,23}, {11,16}, {13,19}, {3,30}, {5,33}, {8,34}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {4,34}, {1,16}, {15,22}, {11,32}, {9,17}, {10,18}, {14,32}, {15,33}, {8,24}, {6,34}, {5,27}, {5,26}, {8,18}, {15,28}, {11,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {14,35}, {15,23}, {7,24}, {3,31}, {9,24}, {10,20}, {7,33}, {11,34}, {13,34}, {7,35}, {5,21}, {2,30}, {15,30}, {13,20}, {5,35}, {2,18}, {9,31}, {1,34}, {7,19}, {4,17}, {9,21}, {9,16}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET35.39 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 40320 EdgePairs[35][39]:={ {5,7}, {6,25}, {23,29}, {19,26}, {3,8}, {4,28}, {11,25}, {9,10}, {17,18}, {12,22}, {8,26}, {5,11}, {1,3}, {4,31}, {11,15}, {10,33}, {33,34}, {5,6}, {3,19}, {14,31}, {24,32}, {27,33}, {3,23}, {3,21}, {16,28}, {11,14}, {1,35}, {5,32}, {7,30}, {21,22}, {13,27}, {14,29}, {6,14}, {16,21}, {19,20}, {10,11}, {2,33}, {11,35}, {1,12}, {9,11}, {11,27}, {6,29}, {2,34}, {20,26}, {10,17}, {19,31}, {2,6}, {15,32}, {8,12}, {1,17}, {4,16}, {29,33}, {28,31}, {20,24}, {27,28}, {13,30}, {2,5}, {8,9}, {2,10}, {3,9}, {10,26}, {17,20}, {7,33}, {24,30}, {1,24}, {15,30}, {27,32}, {12,13}, {13,20}, {26,35}, {18,35}, {9,35}, {6,18}, {1,29}, {10,35}, {24,26}, {11,18}, {13,26}, {29,31}, {13,16}, {5,34}, {14,32}, {7,15}, {22,34}, {6,34}, {18,26}, {18,33}, {8,19}, {1,18}, {5,27}, {32,35}, {4,18}, {10,12}, {12,24}, {1,31}, {25,33}, {9,13}, {2,30}, {4,9}, {30,31}, {6,12}, {4,21}, {18,19}, {20,25}, {16,18}, {1,2}, {19,27}, {8,10}, {8,15}, {34,35}, {16,29}, {10,16}, {16,17}, {2,24}, {11,23}, {22,26}, {14,15}, {14,33}, {15,34}, {11,33}, {18,22}, {21,31}, {19,30}, {8,24}, {31,33}, {4,10}, {14,21}, {17,31}, {12,17}, {20,22}, {25,32}, {9,22}, {9,19}, {20,31}, {3,25}, {19,24}, {11,13}, {25,30}, {22,30}, {27,34}, {12,30}, {1,22}, {11,24}, {9,31}, {7,8}, {18,25}, {24,25}, {13,22}, {6,13}, {23,35}, {6,19}, {17,19}, {9,30}, {9,12}, {3,32}, {25,31}, {12,18}, {2,16}, {13,29}, {8,34}, {4,5}, {16,30}, {7,23}, {4,34}, {15,35}, {12,29}, {21,32}, {3,7}, {12,25}, {3,22}, {4,15}, {6,23}, {23,34}, {13,14}, {1,5}, {2,3}, {24,29}, {30,32}, {28,32}, {10,28}, {5,31}, {17,22}, {2,19}, {12,14}, {18,21}, {9,21}, {2,28}, {8,29}, {9,23}, {8,27}, {28,29}, {2,11}, {1,11}, {30,35}, {5,24}, {2,22}, {14,19}, {20,28}, {21,33}, {18,27}, {16,27}, {1,7}, {26,28}, {3,14}, {5,26}, {4,8}, {4,25}, {3,28}, {31,35}, {7,31}, {5,9}, {8,33}, {30,33}, {1,8}, {4,12}, {17,34}, {7,10}, {27,29}, {3,6}, {22,33}, {19,35}, {3,15}, {7,25}, {6,26}, {26,32}, {30,34}, {22,23}, {5,21}, {21,29}, {20,23}, {2,4}, {28,35}, {16,23}, {13,15}, {15,21}, {14,20}, {1,15}, {20,34}, {7,26}, {7,16}, {11,20}, {15,18}, {5,17}, {15,16}, {7,17}, {17,27}, {15,20}, {13,28}, {1,28}, {23,25}, {16,24}, {3,27}, {9,27}, {12,32}, {4,20}, {8,20}, {5,13}, {25,27}, {32,34}, {17,23}, {10,23}, {26,33}, {4,6}, {29,35}, {7,13}, {14,17}, {25,28}, {16,19}, {10,14}, {10,32}, {21,24}, {17,32}, {6,35}, {29,34}, {21,26}, {22,28}, {23,24}, {6,7}, {2,14}, {21,23} }; // ET35.40 // Bipartite(5,30) Valencies [18,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7255941120 EdgePairs[35][40]:={ {2,11}, {3,22}, {3,32}, {5,12}, {2,14}, {4,13}, {4,9}, {4,23}, {5,32}, {1,14}, {1,24}, {3,12}, {2,32}, {1,30}, {2,29}, {5,29}, {2,24}, {1,33}, {5,27}, {1,10}, {4,10}, {5,11}, {4,7}, {1,20}, {3,8}, {1,31}, {4,16}, {3,24}, {2,12}, {2,33}, {3,20}, {5,8}, {2,21}, {4,6}, {4,30}, {5,9}, {5,16}, {5,21}, {5,7}, {4,33}, {1,7}, {5,31}, {2,31}, {3,16}, {3,28}, {3,15}, {5,19}, {1,21}, {3,25}, {4,27}, {5,28}, {4,20}, {3,30}, {5,17}, {5,6}, {2,15}, {3,14}, {3,18}, {4,17}, {1,18}, {3,26}, {4,15}, {1,27}, {1,17}, {3,6}, {4,25}, {3,34}, {2,19}, {1,28}, {5,18}, {2,23}, {5,26}, {1,8}, {1,13}, {2,35}, {2,34}, {2,9}, {4,26}, {2,13}, {2,25}, {4,35}, {1,34}, {1,23}, {4,19}, {1,11}, {5,22}, {2,22}, {3,10}, {3,35}, {4,29} }; // ET35.41 // Bipartite(14,21) Valencies [18,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 180592312320 EdgePairs[35][41]:={ {3,33}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {2,33}, {6,16}, {4,27}, {12,29}, {13,21}, {7,15}, {11,35}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {4,29}, {1,32}, {8,33}, {1,27}, {3,25}, {3,15}, {10,26}, {4,19}, {7,22}, {2,19}, {1,19}, {2,27}, {10,33}, {3,35}, {13,35}, {2,26}, {14,31}, {7,34}, {12,35}, {8,25}, {2,28}, {1,30}, {5,32}, {8,15}, {9,35}, {14,28}, {4,23}, {8,27}, {8,31}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {2,25}, {14,23}, {6,31}, {11,33}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,20}, {9,32}, {14,21}, {12,17}, {9,26}, {9,27}, {5,29}, {9,19}, {14,30}, {5,25}, {7,32}, {11,15}, {1,31}, {11,22}, {7,25}, {10,28}, {14,24}, {2,35}, {1,22}, {6,30}, {4,33}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {9,34}, {13,22}, {10,21}, {2,20}, {14,16}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {3,32}, {11,21}, {4,35}, {9,25}, {7,16}, {2,32}, {6,33}, {13,33}, {5,18}, {14,15}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {8,22}, {13,28}, {9,20}, {4,15}, {3,27}, {4,28}, {1,33}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {12,26}, {7,31}, {12,33}, {6,15}, {13,30}, {2,17}, {14,17}, {8,32}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {5,31}, {6,27}, {13,24}, {6,26}, {12,19}, {12,30}, {8,23}, {14,34}, {10,32}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {12,15}, {9,30}, {13,27}, {14,20}, {14,25}, {7,28}, {11,26}, {13,26}, {10,35}, {7,23}, {11,16}, {13,19}, {2,21}, {5,33}, {8,34}, {9,18}, {10,17}, {3,24}, {11,27}, {10,27}, {1,26}, {4,34}, {1,16}, {10,34}, {11,32}, {9,17}, {10,18}, {14,32}, {8,24}, {2,31}, {9,33}, {6,34}, {5,26}, {8,18}, {4,18}, {11,19}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {14,35}, {7,24}, {3,31}, {9,24}, {10,20}, {5,15}, {12,31}, {11,34}, {13,34}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {13,17}, {13,20}, {5,35}, {2,18}, {1,34}, {9,31}, {6,35}, {9,16}, {9,21}, {9,23}, {7,21}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {7,18}, {5,16} }; // ET35.42 // Bipartite(17,18) Valencies [18,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2277243837099849063333888000000 EdgePairs[35][42]:={ {13,21}, {15,33}, {9,32}, {6,25}, {5,22}, {10,18}, {11,25}, {4,28}, {17,18}, {12,22}, {3,26}, {8,26}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {16,25}, {9,35}, {15,19}, {1,29}, {6,18}, {16,34}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {4,21}, {17,29}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {16,29}, {3,30}, {2,24}, {11,23}, {3,24}, {14,33}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {17,31}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {6,23}, {16,31}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {15,29}, {2,22}, {16,20}, {2,31}, {14,19}, {1,33}, {16,27}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {15,18}, {10,34}, {10,27}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {16,19}, {9,34}, {10,32}, {12,35}, {6,35}, {17,32}, {12,19}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {15,25}, {5,33}, {5,30} }; // ET35.43 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 40320 EdgePairs[35][43]:={ {13,21}, {24,34}, {15,33}, {19,28}, {9,32}, {5,22}, {10,18}, {9,17}, {3,26}, {16,22}, {2,35}, {17,33}, {6,15}, {3,35}, {8,21}, {21,30}, {15,27}, {5,15}, {1,19}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {21,28}, {2,7}, {6,9}, {8,31}, {24,28}, {19,21}, {6,32}, {17,35}, {11,29}, {11,17}, {1,20}, {3,18}, {8,16}, {9,18}, {12,28}, {2,25}, {4,24}, {18,32}, {32,33}, {4,30}, {8,13}, {8,30}, {9,33}, {1,9}, {1,10}, {4,13}, {7,11}, {12,20}, {23,31}, {1,13}, {12,26}, {3,10}, {7,27}, {19,22}, {25,34}, {26,29}, {2,17}, {33,35}, {12,31}, {20,29}, {23,28}, {10,20}, {17,26}, {13,24}, {2,15}, {12,23}, {22,25}, {16,25}, {24,31}, {20,35}, {28,30}, {15,19}, {16,34}, {4,23}, {6,24}, {2,29}, {13,19}, {1,26}, {3,17}, {8,22}, {27,30}, {18,29}, {9,29}, {9,20}, {4,22}, {29,32}, {7,14}, {15,28}, {6,17}, {5,28}, {6,10}, {4,7}, {8,18}, {14,35}, {7,32}, {3,31}, {12,27}, {25,26}, {3,13}, {11,22}, {5,12}, {6,27}, {2,8}, {5,35}, {14,34}, {19,23}, {25,29}, {17,29}, {13,17}, {7,19}, {4,32}, {1,30}, {2,13}, {13,18}, {12,15}, {14,28}, {11,21}, {8,17}, {3,30}, {3,16}, {11,16}, {3,24}, {14,23}, {6,16}, {13,25}, {21,25}, {7,12}, {9,26}, {18,20}, {5,14}, {28,34}, {3,29}, {2,23}, {10,13}, {22,29}, {10,19}, {15,23}, {4,11}, {11,34}, {17,28}, {6,8}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {7,34}, {10,31}, {5,19}, {1,6}, {10,29}, {1,25}, {22,31}, {20,30}, {2,20}, {9,16}, {4,17}, {13,31}, {14,27}, {7,28}, {6,11}, {9,25}, {17,30}, {10,22}, {10,30}, {6,22}, {10,25}, {26,31}, {6,31}, {11,32}, {15,24}, {16,26}, {1,16}, {27,35}, {4,14}, {5,8}, {23,27}, {24,35}, {31,32}, {18,31}, {16,31}, {15,17}, {4,29}, {1,32}, {26,27}, {19,29}, {8,32}, {24,27}, {7,24}, {9,24}, {29,30}, {17,25}, {19,34}, {6,20}, {5,23}, {20,32}, {5,20}, {2,26}, {10,21}, {26,30}, {7,29}, {18,30}, {7,21}, {14,16}, {3,33}, {13,32}, {14,26}, {23,32}, {10,15}, {11,30}, {3,5}, {19,33}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {15,29}, {16,20}, {8,11}, {18,24}, {2,31}, {1,33}, {19,25}, {3,11}, {5,29}, {14,30}, {21,34}, {12,33}, {11,19}, {1,4}, {20,27}, {21,35}, {28,33}, {31,34}, {8,14}, {11,31}, {20,33}, {14,24}, {13,34}, {7,22}, {1,14}, {1,34}, {22,27}, {13,35}, {14,18}, {21,27}, {9,15}, {17,24}, {12,34}, {17,21}, {23,30}, {6,28}, {18,23}, {4,35}, {19,32}, {13,33}, {14,25}, {11,12}, {7,18}, {23,33}, {11,28}, {5,18}, {5,16}, {1,23}, {16,35}, {22,24}, {10,24}, {10,27}, {10,34}, {16,33}, {3,4}, {13,23}, {8,35}, {6,21}, {15,22}, {4,26}, {26,34}, {7,20}, {7,9}, {25,35}, {22,35}, {15,31}, {5,10}, {8,28}, {1,27}, {5,25}, {15,26}, {27,31}, {4,19}, {14,22}, {22,32}, {3,12}, {9,14}, {9,34}, {24,33}, {12,35}, {12,19}, {23,26}, {20,21}, {8,25}, {2,9}, {16,32}, {2,32}, {12,21}, {6,33}, {18,34}, {11,26}, {15,25}, {5,33}, {5,30} }; // ET35.44 // Bipartite(16,19) Valencies [19,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2545154876758654835490816000000 EdgePairs[35][44]:={ {13,21}, {15,33}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {16,22}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {16,25}, {9,35}, {15,19}, {1,29}, {6,18}, {16,34}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {3,17}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {8,17}, {16,29}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {14,33}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {12,17}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {6,23}, {16,31}, {15,17}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {1,33}, {16,27}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {15,18}, {10,34}, {10,27}, {5,17}, {16,33}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {14,17}, {16,19}, {9,34}, {10,32}, {12,35}, {6,35}, {12,19}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30} }; // ET35.45 // Bipartite(10,25) Valencies [20,8] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 28800 EdgePairs[35][45]:={ {1,11}, {5,17}, {1,20}, {10,24}, {10,25}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {3,22}, {4,16}, {4,30}, {6,17}, {2,23}, {1,13}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {2,19}, {2,27}, {10,33}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {9,35}, {8,27}, {8,31}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {3,17}, {6,21}, {3,34}, {7,12}, {6,31}, {2,34}, {1,17}, {5,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {9,32}, {9,26}, {9,27}, {5,29}, {9,19}, {8,14}, {5,25}, {3,12}, {7,13}, {9,14}, {7,25}, {10,28}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {10,29}, {10,31}, {9,34}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {9,25}, {7,16}, {7,26}, {1,12}, {2,32}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {8,35}, {5,14}, {9,20}, {4,15}, {1,28}, {3,11}, {3,27}, {4,28}, {1,33}, {10,13}, {10,12}, {3,29}, {6,23}, {5,28}, {8,26}, {9,22}, {7,31}, {2,17}, {9,13}, {8,21}, {3,19}, {5,31}, {6,26}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {7,28}, {3,16}, {10,35}, {7,23}, {5,33}, {9,18}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {10,34}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {6,34}, {5,27}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {3,28}, {8,20}, {7,24}, {3,31}, {1,14}, {9,24}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {5,35}, {9,31}, {7,19}, {4,17}, {9,16}, {7,21}, {8,29}, {4,32}, {10,16} }; // ET35.46 // Bipartite(10,25) Valencies [20,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 95551488000000 EdgePairs[35][46]:={ {1,11}, {3,33}, {2,24}, {5,17}, {10,25}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {4,24}, {4,26}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {3,35}, {5,20}, {7,34}, {1,21}, {8,25}, {2,28}, {2,14}, {5,32}, {6,11}, {8,15}, {9,35}, {8,31}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {8,16}, {6,21}, {3,34}, {7,12}, {2,25}, {6,31}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {9,19}, {8,14}, {5,25}, {7,32}, {1,31}, {7,13}, {9,14}, {7,25}, {10,28}, {2,35}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {10,31}, {9,34}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {4,35}, {9,25}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {8,13}, {8,35}, {9,20}, {4,15}, {1,28}, {3,11}, {7,14}, {1,33}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {2,17}, {5,12}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {10,32}, {3,21}, {6,19}, {9,12}, {7,29}, {6,28}, {6,14}, {9,30}, {10,11}, {7,28}, {3,16}, {10,35}, {7,23}, {3,30}, {5,33}, {8,34}, {10,17}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {9,17}, {10,18}, {8,24}, {6,34}, {5,27}, {5,26}, {8,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,24}, {3,31}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {7,33}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {9,16}, {9,21}, {8,29}, {4,32}, {7,18}, {10,16}, {5,16} }; // ET35.47 // Bipartite(15,20) Valencies [20,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3181443595948318544363520000000 EdgePairs[35][47]:={ {13,21}, {15,33}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {9,35}, {6,18}, {1,29}, {15,19}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {13,19}, {1,26}, {14,32}, {3,17}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {14,33}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {12,17}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {13,29}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,22}, {6,23}, {15,17}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {2,31}, {14,19}, {1,33}, {5,26}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {15,16}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {14,17}, {9,34}, {10,32}, {12,35}, {6,35}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30} }; // ET35.48 // Bipartite(14,21) Valencies [21,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4454021034327645962108928000000 EdgePairs[35][48]:={ {13,21}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {13,20}, {9,35}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {13,19}, {1,26}, {14,32}, {3,17}, {7,15}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {14,15}, {14,33}, {14,23}, {6,16}, {11,33}, {13,25}, {8,24}, {9,26}, {14,21}, {3,29}, {12,17}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {13,29}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,15}, {6,23}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {5,26}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {3,15}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {13,15}, {1,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {14,22}, {14,17}, {9,34}, {10,32}, {12,35}, {6,35}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {5,30} }; // ET35.49 // Bipartite(13,22) Valencies [22,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6999175911086300797599744000000 EdgePairs[35][49]:={ {13,21}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {13,27}, {6,14}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {13,20}, {9,35}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {13,19}, {1,26}, {3,17}, {7,15}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {6,16}, {11,33}, {13,25}, {8,24}, {9,26}, {5,14}, {3,29}, {12,17}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {13,14}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {3,15}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {13,15}, {1,15}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {9,14}, {9,34}, {10,14}, {10,32}, {12,35}, {6,35}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {2,14}, {11,26}, {5,33}, {5,30} }; // ET35.50 // Bipartite(12,23) Valencies [23,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12383157381152686026522624000000 EdgePairs[35][50]:={ {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {6,14}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {12,20}, {1,13}, {12,26}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {2,15}, {12,23}, {12,13}, {9,35}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {6,24}, {2,29}, {5,34}, {1,26}, {3,17}, {7,15}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {6,27}, {2,30}, {5,35}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {6,16}, {11,33}, {8,24}, {9,26}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {11,13}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {7,13}, {9,14}, {9,34}, {10,14}, {10,32}, {12,35}, {6,35}, {12,19}, {8,25}, {2,32}, {12,21}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30} }; // ET35.51 // Bipartite(5,30) Valencies [24,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23219011584000000 EdgePairs[35][51]:={ {4,35}, {5,32}, {3,15}, {4,14}, {1,11}, {3,29}, {2,22}, {5,30}, {1,31}, {4,27}, {5,35}, {2,20}, {4,16}, {1,9}, {2,33}, {3,30}, {1,32}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {5,6}, {3,18}, {1,34}, {2,14}, {3,11}, {5,23}, {5,33}, {2,10}, {4,20}, {2,23}, {4,7}, {1,17}, {3,13}, {1,22}, {2,32}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {4,29}, {3,9}, {5,15}, {3,23}, {4,31}, {4,30}, {2,34}, {1,19}, {4,21}, {4,17}, {2,35}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {3,35}, {1,23}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {5,31}, {3,21}, {1,14}, {4,32}, {2,8}, {1,27}, {5,11}, {3,16}, {1,13}, {5,10}, {3,25}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {5,12}, {1,28}, {4,9}, {2,7}, {5,18}, {4,34}, {3,33}, {1,8}, {5,16}, {2,30}, {1,21}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET35.52 // Bipartite(7,28) Valencies [24,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23115815976960 EdgePairs[35][52]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {4,27}, {7,15}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {4,19}, {7,22}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {2,26}, {7,34}, {2,9}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {6,22}, {3,18}, {6,29}, {3,17}, {6,21}, {3,34}, {2,25}, {6,31}, {2,34}, {1,17}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {7,30}, {2,16}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {7,28}, {7,23}, {2,21}, {5,33}, {3,24}, {1,26}, {4,34}, {1,16}, {4,14}, {5,8}, {7,9}, {2,31}, {6,34}, {6,10}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {5,15}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {6,35}, {7,21}, {4,32}, {7,18}, {5,16} }; // ET35.53 // Bipartite(11,24) Valencies [24,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 24766314762305372053045248000000 EdgePairs[35][53]:={ {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {6,14}, {2,33}, {6,32}, {11,29}, {11,35}, {11,17}, {1,12}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {1,13}, {7,27}, {10,26}, {2,17}, {7,33}, {10,20}, {1,24}, {2,15}, {9,35}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {6,24}, {2,29}, {5,34}, {1,26}, {3,17}, {7,15}, {8,22}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {5,35}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {11,21}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {3,24}, {6,16}, {11,33}, {7,12}, {8,24}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {11,13}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {5,29}, {4,25}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {3,12}, {9,14}, {7,13}, {9,34}, {10,14}, {10,32}, {6,35}, {8,25}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30} }; // ET35.54 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 604800 EdgePairs[35][54]:={ {13,21}, {15,33}, {19,28}, {5,7}, {9,32}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {11,25}, {4,28}, {3,26}, {8,26}, {5,11}, {16,22}, {2,35}, {17,33}, {4,31}, {6,15}, {3,35}, {10,33}, {8,21}, {21,30}, {5,6}, {3,19}, {14,31}, {15,27}, {24,32}, {1,19}, {27,33}, {12,16}, {3,20}, {2,18}, {3,21}, {16,28}, {21,28}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {6,14}, {24,28}, {10,11}, {19,21}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {11,17}, {1,12}, {9,11}, {11,27}, {6,29}, {1,20}, {8,16}, {10,17}, {9,18}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {2,6}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,12}, {1,17}, {1,9}, {4,16}, {29,33}, {28,31}, {1,10}, {4,13}, {20,24}, {7,11}, {12,20}, {23,31}, {1,13}, {12,26}, {13,30}, {3,10}, {2,10}, {19,22}, {3,9}, {25,34}, {10,26}, {7,33}, {12,31}, {20,29}, {17,26}, {1,24}, {13,24}, {24,30}, {2,15}, {12,23}, {13,20}, {26,35}, {18,35}, {16,25}, {24,31}, {9,35}, {6,18}, {1,29}, {15,19}, {16,34}, {24,26}, {4,23}, {11,18}, {13,26}, {29,31}, {6,24}, {13,16}, {2,29}, {5,34}, {13,19}, {14,32}, {3,17}, {7,15}, {8,22}, {22,34}, {18,29}, {6,34}, {9,20}, {18,26}, {4,22}, {29,32}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {4,7}, {4,18}, {14,35}, {10,12}, {12,24}, {3,31}, {25,33}, {25,26}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {2,8}, {30,31}, {6,12}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {7,19}, {4,32}, {1,30}, {2,13}, {19,27}, {8,15}, {14,28}, {8,17}, {16,29}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {3,24}, {14,33}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {19,30}, {8,24}, {4,10}, {9,26}, {14,21}, {5,14}, {28,34}, {3,29}, {17,31}, {2,23}, {10,13}, {20,22}, {22,29}, {25,32}, {10,19}, {15,23}, {9,22}, {4,11}, {20,31}, {3,25}, {11,34}, {17,28}, {7,35}, {22,30}, {27,34}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {6,13}, {1,25}, {22,31}, {23,35}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {9,12}, {3,32}, {14,27}, {7,28}, {12,18}, {25,31}, {2,16}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {7,23}, {16,30}, {6,22}, {12,29}, {11,32}, {15,24}, {21,32}, {3,7}, {12,25}, {27,35}, {3,22}, {5,8}, {23,27}, {24,35}, {4,15}, {18,31}, {6,23}, {15,17}, {23,34}, {1,32}, {30,32}, {28,32}, {8,32}, {24,27}, {7,24}, {10,28}, {5,31}, {17,25}, {2,19}, {6,20}, {5,23}, {20,32}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,27}, {2,11}, {13,32}, {14,26}, {23,32}, {11,30}, {19,33}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {15,29}, {8,11}, {18,24}, {2,31}, {1,33}, {18,27}, {20,28}, {21,33}, {16,27}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {4,8}, {5,29}, {4,25}, {14,30}, {21,34}, {7,31}, {12,33}, {5,9}, {11,19}, {30,33}, {1,8}, {4,12}, {17,34}, {20,27}, {21,35}, {8,14}, {3,6}, {22,33}, {20,33}, {19,35}, {3,15}, {13,34}, {7,25}, {1,14}, {26,32}, {1,34}, {30,34}, {13,35}, {14,18}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {20,23}, {12,34}, {17,21}, {28,35}, {23,30}, {6,28}, {16,23}, {4,35}, {19,32}, {1,15}, {14,20}, {14,25}, {15,21}, {20,34}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {15,16}, {8,35}, {15,22}, {4,26}, {1,28}, {26,34}, {16,24}, {3,27}, {7,20}, {9,27}, {22,35}, {15,31}, {4,20}, {8,20}, {1,27}, {5,13}, {25,27}, {17,23}, {10,23}, {15,26}, {26,33}, {4,6}, {27,31}, {14,22}, {29,35}, {3,12}, {7,13}, {14,17}, {25,28}, {10,14}, {24,33}, {10,32}, {12,35}, {6,35}, {12,19}, {23,26}, {20,21}, {22,28}, {8,25}, {2,9}, {16,32}, {6,33}, {12,21}, {2,14}, {18,34}, {5,33} }; // ET35.55 // Bipartite(10,25) Valencies [25,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 56287079005239481938739200000000 EdgePairs[35][55]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {10,24}, {10,25}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {9,35}, {4,23}, {8,27}, {8,31}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,11}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {10,28}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {9,34}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {8,35}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {10,32}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {10,11}, {1,35}, {7,28}, {3,16}, {10,35}, {7,23}, {2,21}, {3,30}, {5,33}, {8,34}, {9,18}, {10,17}, {3,24}, {2,29}, {10,27}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {10,34}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {6,34}, {5,27}, {5,26}, {8,18}, {4,18}, {4,25}, {10,19}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {7,33}, {10,14}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {6,35}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {7,18}, {10,16}, {5,16} }; // ET35.56 // Bipartite(9,26) Valencies [26,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 146346405413622653040721920000000 EdgePairs[35][56]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {9,35}, {4,23}, {8,27}, {8,31}, {9,11}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,11}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {9,34}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {8,35}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {1,35}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {8,34}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {2,31}, {9,33}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {6,35}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET35.57 // Bipartite(8,27) Valencies [27,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 439039216240867959122165760000000 EdgePairs[35][57]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {2,9}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {3,17}, {6,29}, {8,16}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,11}, {7,20}, {5,11}, {2,10}, {5,29}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {7,19}, {4,17}, {6,35}, {7,21}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET35.58 // Bipartite(7,28) Valencies [28,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1536637256843037856927580160000000 EdgePairs[35][58]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {7,19}, {4,17}, {6,35}, {7,21}, {4,32}, {7,18}, {5,16} }; // ET35.59 // Non-bipartite Valency 28 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 390241927692288000000 EdgePairs[35][59]:={ {13,25}, {15,28}, {24,33}, {10,17}, {3,29}, {20,26}, {9,18}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {26,33}, {2,20}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,31}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {8,24}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {11,27}, {18,28}, {4,34}, {13,29}, {10,22}, {25,29}, {25,32}, {20,29}, {12,22}, {23,34}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {13,15}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {7,14}, {13,33}, {18,35}, {10,23}, {15,24}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {26,32}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {5,27}, {9,31}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {6,24}, {19,35}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {9,26}, {6,12}, {7,31}, {12,33}, {13,18}, {1,29}, {2,34}, {21,22}, {10,19}, {12,19}, {15,27}, {14,35}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {9,28}, {6,13}, {11,19}, {19,24}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {20,23}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {10,28}, {15,23}, {12,17}, {9,19}, {13,35}, {1,13}, {13,32}, {10,24}, {2,25}, {17,23}, {21,29}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {12,20}, {16,29}, {1,11}, {15,30}, {24,34}, {3,19}, {2,16}, {18,25}, {14,19}, {21,27}, {7,8}, {7,35}, {21,23}, {15,29}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {7,25}, {24,35}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {9,34}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {19,33}, {19,29}, {3,34}, {13,20}, {7,12}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {9,33}, {8,16}, {20,35}, {8,32}, {14,30}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {3,30}, {18,33}, {8,15}, {21,33}, {10,34}, {4,14}, {11,28}, {6,25}, {28,34}, {11,17}, {24,29}, {17,34}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {13,24}, {6,16}, {20,34}, {25,34}, {4,31}, {2,15}, {10,33}, {13,34}, {20,24}, {18,24}, {21,24}, {8,23}, {20,30}, {2,29}, {14,21}, {3,21}, {19,27}, {26,30}, {13,30}, {9,24}, {24,32}, {6,20}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {4,23}, {22,34}, {27,30}, {6,27}, {15,32}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {22,35}, {26,29}, {1,21}, {19,34}, {6,21}, {9,15}, {7,20}, {27,31}, {7,18}, {10,21}, {3,33}, {27,35}, {28,30}, {5,17}, {1,24}, {19,25}, {6,8}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {4,8}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {27,29}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {6,29}, {2,31} }; // ET35.60 // Bipartite(6,29) Valencies [29,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6366068635492585407271403520000000 EdgePairs[35][60]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {1,21}, {2,9}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {6,21}, {3,34}, {2,25}, {6,31}, {4,10}, {2,34}, {1,17}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {3,16}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {4,17}, {6,35}, {4,32}, {5,16} }; // ET35.61 // Bipartite(5,30) Valencies [30,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31830343177462927036357017600000000 EdgePairs[35][61]:={ {1,15}, {4,35}, {5,32}, {5,14}, {3,15}, {1,11}, {4,14}, {3,29}, {2,22}, {5,30}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {5,35}, {2,20}, {5,34}, {1,25}, {4,16}, {5,24}, {3,32}, {1,9}, {2,33}, {3,30}, {1,32}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {5,6}, {3,18}, {1,34}, {2,14}, {3,11}, {5,23}, {5,33}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {5,19}, {5,15}, {3,23}, {5,29}, {4,31}, {3,27}, {2,34}, {4,30}, {1,19}, {4,21}, {2,35}, {4,17}, {5,28}, {2,9}, {4,15}, {4,25}, {1,35}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {3,35}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {3,24}, {5,17}, {5,31}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {4,18}, {5,10}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {5,12}, {1,28}, {3,17}, {4,9}, {2,7}, {5,18}, {4,34}, {3,33}, {1,8}, {4,23}, {1,30}, {5,16}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET35.62 // Non-bipartite Valency 30 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1805923123200000000 EdgePairs[35][62]:={ {13,25}, {15,28}, {24,33}, {15,17}, {10,17}, {3,29}, {9,18}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {8,28}, {5,32}, {4,24}, {8,31}, {7,24}, {15,16}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {2,30}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {4,30}, {21,35}, {8,24}, {8,11}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {11,27}, {18,28}, {4,34}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {15,20}, {23,34}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {25,26}, {9,22}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {7,14}, {13,33}, {18,35}, {10,23}, {15,24}, {22,27}, {30,34}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {9,26}, {6,12}, {7,31}, {12,33}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {9,28}, {6,13}, {11,19}, {19,24}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {1,28}, {14,18}, {27,33}, {1,17}, {9,14}, {20,23}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {13,35}, {10,11}, {1,13}, {13,32}, {10,24}, {2,25}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {12,20}, {16,29}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {2,16}, {18,25}, {14,19}, {21,27}, {7,35}, {9,13}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {7,25}, {24,35}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {5,6}, {9,34}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {19,33}, {19,29}, {3,34}, {13,20}, {7,12}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,32}, {14,30}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {3,30}, {24,27}, {18,33}, {1,7}, {8,15}, {21,33}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {15,18}, {24,29}, {17,34}, {4,16}, {12,26}, {10,30}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {6,16}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {20,24}, {18,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {2,6}, {13,30}, {9,24}, {24,32}, {4,6}, {6,20}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {4,23}, {22,34}, {8,13}, {16,21}, {6,27}, {15,32}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {1,21}, {9,15}, {6,21}, {19,34}, {8,12}, {7,20}, {23,27}, {27,31}, {7,18}, {10,21}, {3,33}, {27,35}, {5,17}, {1,24}, {19,25}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {4,8}, {29,31}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {29,35}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {6,29}, {2,31} }; // ET35.63 // Bipartite(4,31) Valencies [31,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 197348127700270147625413509120000000 EdgePairs[35][63]:={ {1,15}, {4,35}, {3,15}, {1,11}, {4,14}, {2,22}, {3,29}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {3,32}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {3,27}, {2,34}, {4,30}, {1,19}, {4,21}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,35}, {1,26}, {2,24}, {4,11}, {2,27}, {3,35}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,17}, {4,9}, {2,7}, {4,34}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET35.64 // Bipartite(3,32) Valencies [32,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1578785021602161181003308072960000000 EdgePairs[35][64]:={ {1,15}, {3,15}, {1,11}, {2,22}, {3,29}, {1,31}, {3,7}, {2,11}, {2,20}, {1,25}, {3,32}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {2,31}, {2,23}, {1,10}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {3,27}, {2,34}, {1,19}, {2,35}, {2,9}, {3,5}, {1,4}, {1,35}, {1,26}, {2,4}, {2,24}, {2,27}, {3,4}, {3,35}, {1,23}, {2,21}, {1,7}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,17}, {2,7}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET35.65 // Bipartite(2,33) Valencies [33,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 17366635237623772991036388802560000000 EdgePairs[35][65]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,33}, {1,10}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET35.66 // Bipartite(1,34) Valencies [34,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 295232799039604140847618609643520000000 EdgePairs[35][66]:={ {1,4}, {1,20}, {1,3}, {1,34}, {1,30}, {1,14}, {1,23}, {1,33}, {1,24}, {1,7}, {1,27}, {1,29}, {1,35}, {1,5}, {1,15}, {1,22}, {1,28}, {1,16}, {1,10}, {1,12}, {1,13}, {1,17}, {1,2}, {1,11}, {1,19}, {1,18}, {1,25}, {1,32}, {1,21}, {1,9}, {1,26}, {1,31}, {1,6}, {1,8} }; // ET35.67 // Non-bipartite Valency 34 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 10333147966386144929666651337523200000000 EdgePairs[35][67]:={ {13,25}, {15,28}, {24,33}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {11,12}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {15,16}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {8,24}, {8,11}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {4,5}, {15,20}, {9,10}, {17,18}, {23,34}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {25,26}, {9,22}, {31,35}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {7,14}, {13,33}, {23,24}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {9,26}, {18,20}, {6,12}, {7,31}, {12,33}, {13,18}, {1,29}, {2,34}, {21,22}, {10,19}, {12,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {9,14}, {20,23}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {1,35}, {31,32}, {17,28}, {23,32}, {26,35}, {5,21}, {22,24}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {13,35}, {10,11}, {1,13}, {13,32}, {10,24}, {2,25}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {3,4}, {18,19}, {14,28}, {2,3}, {12,20}, {16,29}, {1,11}, {29,33}, {33,34}, {15,30}, {24,34}, {3,19}, {2,16}, {14,19}, {18,25}, {21,27}, {7,8}, {7,35}, {9,13}, {21,23}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {24,35}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {5,6}, {9,34}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {1,2}, {4,6}, {6,20}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {19,20}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {27,30}, {8,13}, {16,21}, {6,27}, {15,32}, {29,30}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {33,35}, {25,31}, {16,18}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {26,29}, {1,21}, {13,14}, {6,21}, {9,15}, {19,34}, {8,12}, {7,20}, {16,19}, {23,27}, {34,35}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {27,35}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {26,28}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {29,35}, {27,29}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {6,29}, {2,31} }; // Total number of connected ET graphs of order 35 is 67 // ******************************************************************************************** // Order 36 // ET36.1 // Bipartite(18,18) Valencies [2,2] // Diameter 18 Girth 36 // Twin-free VT AT // Automorphism group of order 72 EdgePairs[36][1]:={ {4,34}, {18,22}, {4,30}, {9,19}, {14,36}, {8,29}, {6,35}, {2,24}, {7,20}, {9,23}, {18,27}, {13,35}, {10,28}, {11,26}, {5,33}, {12,30}, {2,28}, {12,24}, {15,33}, {3,32}, {8,27}, {7,25}, {10,22}, {11,21}, {17,23}, {17,20}, {6,31}, {16,31}, {1,19}, {3,26}, {14,32}, {1,21}, {5,36}, {15,29}, {16,25}, {13,34} }; // ET36.2 // Bipartite(12,24) Valencies [4,2] // Diameter 6 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 48 EdgePairs[36][2]:={ {3,32}, {11,30}, {1,26}, {2,14}, {4,13}, {5,36}, {9,19}, {4,36}, {6,33}, {1,29}, {7,34}, {7,23}, {9,31}, {9,16}, {6,14}, {11,24}, {10,32}, {3,33}, {8,25}, {2,21}, {8,27}, {5,21}, {10,16}, {5,25}, {2,31}, {3,15}, {7,18}, {6,20}, {11,35}, {5,19}, {4,27}, {7,15}, {4,17}, {3,26}, {12,29}, {9,35}, {10,24}, {2,28}, {11,34}, {6,22}, {12,22}, {1,13}, {8,18}, {12,28}, {1,23}, {8,30}, {10,20}, {12,17} }; // ET36.3 // Bipartite(12,24) Valencies [4,2] // Diameter 6 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 768 EdgePairs[36][3]:={ {5,28}, {3,29}, {3,20}, {8,35}, {1,14}, {5,18}, {7,27}, {9,22}, {8,23}, {2,36}, {7,33}, {4,16}, {6,18}, {11,31}, {1,16}, {7,36}, {10,25}, {2,31}, {2,28}, {10,30}, {10,33}, {5,15}, {11,34}, {3,32}, {4,27}, {1,13}, {5,23}, {11,21}, {6,24}, {7,35}, {10,19}, {12,20}, {11,24}, {12,21}, {4,22}, {1,19}, {8,13}, {9,26}, {6,32}, {9,25}, {6,26}, {12,15}, {4,29}, {3,30}, {8,34}, {9,17}, {12,17}, {2,14} }; // ET36.4 // Bipartite(12,24) Valencies [4,2] // Diameter 12 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 98304 EdgePairs[36][4]:={ {6,20}, {8,20}, {5,34}, {4,34}, {3,16}, {6,33}, {11,36}, {3,29}, {6,21}, {7,30}, {12,16}, {1,14}, {5,21}, {9,27}, {2,17}, {4,23}, {12,27}, {10,13}, {9,15}, {5,22}, {5,33}, {10,25}, {7,31}, {3,17}, {8,32}, {1,13}, {12,28}, {2,30}, {2,18}, {7,18}, {11,24}, {4,22}, {10,24}, {3,28}, {1,25}, {8,19}, {9,26}, {11,23}, {9,14}, {4,35}, {6,32}, {11,35}, {2,29}, {12,15}, {8,31}, {1,26}, {10,36}, {7,19} }; // ET36.5 // Bipartite(18,18) Valencies [4,4] // Diameter 6 Girth 4 // Twin-free VT AT // Automorphism group of order 288 EdgePairs[36][5]:={ {3,32}, {15,32}, {12,27}, {5,36}, {13,19}, {8,20}, {2,26}, {8,31}, {6,33}, {13,31}, {1,29}, {1,30}, {11,25}, {16,34}, {4,34}, {7,34}, {14,26}, {9,21}, {8,23}, {15,20}, {11,28}, {18,33}, {12,32}, {12,30}, {6,30}, {2,36}, {11,23}, {3,24}, {10,33}, {6,32}, {3,20}, {7,30}, {5,23}, {5,21}, {18,28}, {7,27}, {9,29}, {5,25}, {9,24}, {2,20}, {10,26}, {14,36}, {14,22}, {17,36}, {17,27}, {18,19}, {17,21}, {12,24}, {16,21}, {18,31}, {7,22}, {16,25}, {13,35}, {9,35}, {8,35}, {4,28}, {4,22}, {4,25}, {6,19}, {14,27}, {15,33}, {2,23}, {13,29}, {10,28}, {1,19}, {10,22}, {15,26}, {1,34}, {11,31}, {16,29}, {17,24}, {3,35} }; // ET36.6 // Bipartite(18,18) Valencies [4,4] // Diameter 6 Girth 4 // Twin-free VT AT // Automorphism group of order 144 EdgePairs[36][6]:={ {18,32}, {14,19}, {5,24}, {15,36}, {13,31}, {11,25}, {5,29}, {1,32}, {13,34}, {2,24}, {7,23}, {9,21}, {12,33}, {6,26}, {16,23}, {18,33}, {13,26}, {17,25}, {6,36}, {6,32}, {16,33}, {17,35}, {3,20}, {8,32}, {8,27}, {4,33}, {2,31}, {10,23}, {2,20}, {14,22}, {5,28}, {3,25}, {4,27}, {15,30}, {9,36}, {9,27}, {4,21}, {18,19}, {6,21}, {12,19}, {15,25}, {10,29}, {12,29}, {11,36}, {16,22}, {1,27}, {7,20}, {18,21}, {4,22}, {17,31}, {3,34}, {8,26}, {14,23}, {15,34}, {7,28}, {5,35}, {2,34}, {9,30}, {1,19}, {11,26}, {12,28}, {1,22}, {13,30}, {14,28}, {8,30}, {10,20}, {11,31}, {16,29}, {10,35}, {7,24}, {17,24}, {3,35} }; // ET36.7 // Bipartite(18,18) Valencies [4,4] // Diameter 4 Girth 6 // Twin-free VT AT // Automorphism group of order 144 EdgePairs[36][7]:={ {5,33}, {9,23}, {6,34}, {10,27}, {14,31}, {17,34}, {2,26}, {4,36}, {8,31}, {15,36}, {2,30}, {11,25}, {12,33}, {8,23}, {6,31}, {11,20}, {16,31}, {11,27}, {15,29}, {15,27}, {1,20}, {17,22}, {2,36}, {3,24}, {3,29}, {8,32}, {13,32}, {18,28}, {7,27}, {5,25}, {9,24}, {13,33}, {8,36}, {1,21}, {3,25}, {11,32}, {9,33}, {4,20}, {18,30}, {12,19}, {16,21}, {5,30}, {7,22}, {16,25}, {9,34}, {12,26}, {4,28}, {13,21}, {7,19}, {4,22}, {6,19}, {15,34}, {18,23}, {6,35}, {17,32}, {18,29}, {13,29}, {14,20}, {2,35}, {14,24}, {10,28}, {1,19}, {10,21}, {12,28}, {1,23}, {17,26}, {5,22}, {7,24}, {10,35}, {14,30}, {16,26}, {3,35} }; // ET36.8 // Bipartite(18,18) Valencies [4,4] // Diameter 9 Girth 4 // Has twins VT AT // Automorphism group of order 9437184 EdgePairs[36][8]:={ {8,19}, {8,28}, {4,23}, {18,22}, {4,36}, {15,36}, {17,28}, {2,32}, {6,33}, {1,30}, {2,29}, {9,20}, {14,26}, {9,31}, {7,31}, {3,21}, {11,20}, {16,31}, {11,29}, {15,24}, {10,30}, {12,30}, {15,27}, {14,34}, {8,24}, {11,23}, {6,36}, {4,32}, {13,32}, {9,29}, {5,25}, {2,20}, {8,33}, {17,19}, {13,36}, {4,27}, {3,25}, {1,21}, {11,32}, {14,35}, {3,30}, {12,34}, {6,27}, {18,31}, {7,22}, {16,35}, {7,35}, {16,22}, {13,23}, {12,25}, {9,22}, {10,19}, {3,34}, {1,28}, {15,33}, {5,26}, {2,23}, {18,29}, {5,34}, {5,35}, {17,33}, {10,28}, {1,19}, {10,21}, {13,27}, {18,20}, {14,25}, {17,24}, {6,24}, {12,21}, {16,26}, {7,26} }; // ET36.9 // Bipartite(18,18) Valencies [4,4] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 36864 EdgePairs[36][9]:={ {15,35}, {18,32}, {12,27}, {8,19}, {8,28}, {6,34}, {17,28}, {5,29}, {18,26}, {14,26}, {12,33}, {15,20}, {11,20}, {3,27}, {3,33}, {11,27}, {14,34}, {1,31}, {12,31}, {9,32}, {11,21}, {4,30}, {7,36}, {2,21}, {5,23}, {4,32}, {13,32}, {16,36}, {18,28}, {9,24}, {10,31}, {10,23}, {2,20}, {8,33}, {12,36}, {6,20}, {17,19}, {11,22}, {3,31}, {16,21}, {15,25}, {7,21}, {13,35}, {13,22}, {2,27}, {4,22}, {10,19}, {14,23}, {15,34}, {6,25}, {6,35}, {17,30}, {5,26}, {5,34}, {17,33}, {1,19}, {18,24}, {9,26}, {14,29}, {4,35}, {10,25}, {9,28}, {1,23}, {13,30}, {8,30}, {16,24}, {1,25}, {16,29}, {2,22}, {7,24}, {3,36}, {7,29} }; // ET36.10 // Non-bipartite Valency 4 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 9216 EdgePairs[36][10]:={ {18,32}, {4,24}, {9,19}, {5,32}, {19,29}, {2,26}, {2,24}, {14,26}, {7,31}, {8,16}, {21,35}, {3,21}, {11,20}, {6,31}, {3,27}, {13,25}, {15,27}, {5,15}, {10,36}, {3,23}, {11,33}, {8,32}, {6,16}, {20,30}, {24,35}, {10,34}, {12,36}, {11,35}, {1,21}, {9,33}, {23,36}, {7,15}, {12,34}, {8,13}, {23,33}, {20,31}, {12,19}, {5,30}, {3,26}, {15,25}, {9,35}, {4,28}, {21,34}, {2,27}, {4,22}, {4,25}, {17,31}, {1,28}, {19,32}, {5,14}, {22,33}, {16,28}, {22,36}, {17,30}, {18,29}, {13,27}, {24,34}, {1,23}, {14,28}, {7,14}, {8,30}, {11,18}, {10,20}, {12,17}, {6,29}, {1,25}, {2,22}, {6,13}, {10,18}, {9,17}, {16,26}, {7,29} }; // ET36.11 // Non-bipartite Valency 4 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 144 EdgePairs[36][11]:={ {3,22}, {1,26}, {4,24}, {7,16}, {13,31}, {11,17}, {18,26}, {4,34}, {12,33}, {1,33}, {3,27}, {19,25}, {12,30}, {15,29}, {18,34}, {10,36}, {14,34}, {6,15}, {17,35}, {11,21}, {8,27}, {16,32}, {16,36}, {9,29}, {7,32}, {5,31}, {1,15}, {22,29}, {10,31}, {3,16}, {6,20}, {11,35}, {1,21}, {11,32}, {20,28}, {12,23}, {17,27}, {12,19}, {7,25}, {9,34}, {13,35}, {10,24}, {7,19}, {9,22}, {4,25}, {19,33}, {2,28}, {9,18}, {5,18}, {21,26}, {15,33}, {5,26}, {2,23}, {22,27}, {8,14}, {2,35}, {5,13}, {23,30}, {24,31}, {2,13}, {6,28}, {4,14}, {21,32}, {8,30}, {10,20}, {23,28}, {6,29}, {8,17}, {24,25}, {20,36}, {3,36}, {14,30} }; // ET36.12 // Bipartite(16,20) Valencies [5,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 160 EdgePairs[36][12]:={ {3,22}, {11,30}, {1,26}, {5,33}, {12,27}, {4,24}, {13,28}, {10,27}, {14,19}, {2,26}, {12,18}, {2,30}, {13,31}, {1,30}, {11,17}, {4,34}, {2,24}, {9,31}, {3,33}, {8,25}, {1,20}, {15,23}, {3,29}, {6,32}, {3,20}, {7,36}, {16,32}, {5,23}, {5,21}, {13,32}, {5,20}, {7,27}, {9,29}, {4,18}, {15,31}, {8,33}, {10,26}, {7,18}, {13,36}, {9,36}, {11,32}, {11,22}, {5,17}, {12,23}, {6,21}, {15,17}, {10,29}, {9,34}, {8,35}, {8,22}, {16,22}, {1,27}, {7,20}, {4,28}, {13,21}, {16,19}, {1,17}, {12,25}, {14,33}, {14,21}, {10,19}, {15,34}, {7,28}, {12,35}, {6,35}, {2,35}, {2,34}, {9,26}, {10,25}, {14,28}, {8,30}, {4,19}, {16,24}, {11,31}, {14,25}, {15,18}, {16,29}, {6,23}, {6,24}, {3,36} }; // ET36.13 // Bipartite(16,20) Valencies [5,4] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 5760 EdgePairs[36][13]:={ {8,19}, {5,36}, {9,23}, {8,20}, {12,18}, {1,29}, {2,30}, {14,18}, {9,25}, {4,34}, {13,34}, {2,24}, {11,28}, {16,23}, {3,21}, {3,27}, {10,32}, {3,33}, {11,29}, {10,30}, {13,26}, {6,30}, {1,20}, {10,36}, {15,23}, {4,31}, {1,31}, {7,33}, {11,33}, {9,32}, {13,18}, {2,21}, {8,32}, {8,27}, {15,31}, {9,24}, {10,31}, {10,26}, {12,36}, {5,28}, {3,25}, {1,21}, {11,32}, {5,17}, {6,27}, {12,19}, {12,24}, {16,21}, {12,29}, {7,35}, {8,22}, {7,20}, {16,19}, {1,17}, {4,25}, {11,34}, {16,28}, {6,35}, {15,33}, {14,20}, {5,35}, {2,34}, {13,27}, {4,35}, {14,28}, {4,19}, {14,25}, {6,29}, {5,22}, {15,18}, {6,23}, {2,22}, {13,17}, {7,24}, {9,17}, {3,36}, {14,30}, {15,22}, {16,26}, {7,26} }; // ET36.14 // Non-bipartite Valency 5 // Diameter 3 Girth 5 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[36][14]:={ {3,22}, {26,31}, {8,19}, {27,33}, {6,34}, {14,19}, {24,29}, {4,36}, {8,31}, {13,31}, {1,30}, {9,25}, {11,17}, {16,34}, {1,32}, {2,24}, {14,26}, {9,21}, {5,27}, {6,26}, {12,16}, {4,11}, {5,10}, {11,20}, {25,34}, {3,33}, {19,25}, {12,32}, {10,30}, {19,35}, {28,35}, {1,20}, {15,23}, {30,36}, {4,16}, {3,9}, {2,12}, {6,7}, {17,35}, {11,33}, {8,27}, {5,23}, {16,27}, {18,28}, {21,27}, {1,15}, {2,31}, {3,28}, {10,34}, {24,33}, {9,36}, {20,28}, {23,36}, {7,15}, {12,23}, {10,14}, {14,32}, {3,14}, {6,21}, {17,21}, {13,20}, {15,25}, {7,22}, {22,31}, {7,35}, {10,24}, {16,22}, {20,34}, {29,32}, {9,13}, {6,18}, {2,17}, {15,33}, {17,30}, {1,8}, {13,29}, {5,35}, {8,18}, {5,13}, {18,24}, {11,26}, {23,26}, {12,28}, {2,25}, {21,32}, {4,19}, {22,30}, {18,36}, {4,29}, {7,29} }; // ET36.15 // Bipartite(9,27) Valencies [6,2] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 1296 EdgePairs[36][15]:={ {5,33}, {4,24}, {6,34}, {9,23}, {4,36}, {2,32}, {4,34}, {1,32}, {2,24}, {1,10}, {6,14}, {4,11}, {3,21}, {8,15}, {7,13}, {8,25}, {5,11}, {9,15}, {7,33}, {2,12}, {3,29}, {7,30}, {8,10}, {2,31}, {3,16}, {1,16}, {6,20}, {8,36}, {4,27}, {9,12}, {4,21}, {9,27}, {3,18}, {3,31}, {3,26}, {7,20}, {9,22}, {6,19}, {2,19}, {1,28}, {5,14}, {6,25}, {5,26}, {5,35}, {8,18}, {7,17}, {2,13}, {6,28}, {1,35}, {1,23}, {8,30}, {5,22}, {9,17}, {7,29} }; // ET36.16 // Bipartite(9,27) Valencies [6,2] // Diameter 9 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 181398528 EdgePairs[36][16]:={ {2,11}, {1,26}, {3,12}, {4,36}, {6,33}, {2,29}, {5,29}, {4,34}, {7,23}, {9,31}, {7,12}, {8,23}, {8,16}, {1,10}, {6,26}, {3,21}, {8,25}, {5,11}, {9,15}, {2,36}, {4,16}, {6,15}, {7,30}, {8,32}, {5,20}, {4,18}, {7,32}, {5,31}, {9,24}, {2,20}, {3,28}, {4,27}, {2,18}, {9,33}, {3,19}, {3,30}, {7,21}, {8,34}, {9,13}, {2,27}, {1,17}, {4,25}, {9,22}, {1,28}, {6,35}, {6,17}, {8,14}, {5,13}, {1,19}, {1,35}, {7,14}, {5,22}, {6,24}, {3,10} }; // ET36.17 // Bipartite(12,24) Valencies [6,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[36][17]:={ {3,32}, {11,30}, {1,26}, {4,24}, {1,14}, {10,27}, {2,26}, {9,25}, {5,29}, {4,34}, {1,32}, {8,23}, {11,24}, {12,16}, {8,15}, {9,15}, {6,30}, {3,23}, {7,33}, {12,31}, {6,36}, {3,29}, {2,33}, {3,20}, {4,30}, {7,36}, {5,16}, {8,27}, {8,32}, {5,21}, {5,20}, {10,16}, {9,24}, {10,31}, {10,23}, {8,36}, {11,35}, {5,28}, {2,18}, {9,27}, {9,33}, {4,20}, {11,22}, {7,15}, {5,17}, {8,13}, {12,14}, {3,18}, {12,19}, {4,17}, {1,18}, {10,29}, {7,21}, {12,26}, {7,19}, {4,25}, {9,22}, {3,34}, {2,19}, {7,28}, {6,35}, {6,17}, {1,13}, {2,34}, {10,22}, {6,28}, {2,25}, {1,35}, {11,14}, {11,31}, {6,13}, {12,21} }; // ET36.18 // Bipartite(12,24) Valencies [6,3] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 80621568 EdgePairs[36][18]:={ {11,30}, {4,24}, {6,34}, {9,23}, {8,31}, {2,32}, {1,29}, {2,24}, {9,31}, {1,33}, {8,23}, {6,26}, {12,16}, {8,15}, {3,27}, {7,13}, {8,25}, {11,27}, {12,32}, {9,15}, {10,36}, {2,36}, {3,23}, {4,16}, {6,36}, {10,33}, {4,30}, {4,32}, {7,27}, {2,16}, {2,20}, {3,15}, {8,33}, {6,20}, {11,35}, {1,21}, {11,22}, {3,19}, {3,31}, {12,13}, {12,24}, {5,30}, {12,29}, {9,34}, {7,21}, {7,35}, {1,17}, {7,19}, {6,18}, {4,22}, {2,28}, {9,18}, {10,17}, {5,14}, {5,18}, {5,26}, {5,34}, {1,13}, {10,28}, {9,26}, {6,28}, {4,14}, {10,25}, {11,19}, {10,20}, {11,14}, {5,22}, {1,25}, {8,17}, {12,21}, {3,35}, {7,29} }; // ET36.19 // Bipartite(12,24) Valencies [6,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 294912 EdgePairs[36][19]:={ {3,32}, {11,30}, {4,24}, {7,16}, {4,36}, {12,18}, {1,30}, {9,20}, {11,17}, {4,34}, {1,32}, {2,24}, {5,27}, {8,23}, {6,14}, {6,26}, {12,16}, {8,21}, {3,21}, {6,31}, {3,33}, {11,29}, {12,30}, {9,15}, {1,20}, {5,15}, {2,36}, {6,36}, {10,33}, {3,20}, {9,32}, {7,27}, {5,25}, {10,16}, {8,33}, {10,26}, {9,27}, {3,19}, {7,15}, {10,14}, {12,23}, {3,31}, {4,17}, {1,18}, {9,34}, {8,34}, {8,22}, {8,35}, {4,22}, {6,19}, {9,22}, {5,14}, {7,28}, {12,35}, {5,26}, {2,23}, {1,13}, {2,35}, {5,13}, {7,17}, {10,28}, {10,21}, {12,28}, {2,13}, {2,25}, {11,19}, {11,18}, {11,31}, {1,25}, {6,24}, {4,29}, {7,29} }; // ET36.20 // Bipartite(18,18) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 432 EdgePairs[36][20]:={ {4,35}, {16,34}, {14,21}, {13,29}, {14,25}, {10,22}, {14,34}, {12,19}, {3,29}, {5,30}, {6,36}, {4,27}, {10,27}, {8,36}, {5,35}, {2,20}, {5,24}, {3,32}, {6,32}, {2,33}, {9,19}, {3,30}, {18,23}, {7,23}, {18,21}, {3,34}, {9,31}, {6,22}, {13,20}, {5,21}, {10,23}, {14,27}, {1,29}, {1,34}, {17,30}, {10,34}, {15,22}, {13,33}, {17,24}, {8,33}, {7,26}, {8,28}, {1,36}, {1,22}, {4,33}, {15,36}, {4,28}, {16,35}, {16,19}, {14,28}, {5,29}, {4,31}, {1,19}, {7,30}, {15,33}, {2,35}, {12,29}, {13,30}, {12,35}, {9,25}, {18,19}, {8,19}, {11,26}, {13,22}, {7,35}, {15,26}, {12,23}, {2,24}, {9,33}, {11,36}, {2,27}, {15,31}, {18,28}, {11,31}, {5,31}, {9,24}, {11,25}, {8,20}, {11,21}, {6,20}, {11,27}, {16,28}, {8,25}, {3,25}, {9,29}, {13,23}, {2,26}, {10,32}, {7,21}, {12,32}, {3,36}, {18,31}, {17,26}, {17,32}, {18,22}, {10,26}, {17,20}, {6,27}, {7,34}, {15,30}, {16,32}, {4,23}, {1,21}, {12,20}, {14,24}, {17,25}, {6,28}, {16,24} }; // ET36.21 // Bipartite(18,18) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 10368 EdgePairs[36][21]:={ {7,19}, {16,25}, {16,34}, {5,32}, {15,23}, {13,29}, {8,24}, {11,23}, {9,30}, {12,19}, {11,33}, {16,30}, {10,27}, {6,23}, {14,19}, {5,34}, {7,33}, {12,31}, {12,22}, {13,34}, {17,35}, {7,27}, {1,32}, {2,28}, {3,34}, {9,31}, {4,26}, {13,20}, {1,29}, {18,24}, {14,33}, {17,31}, {16,21}, {17,23}, {10,34}, {2,31}, {2,23}, {7,26}, {10,25}, {15,25}, {14,30}, {6,33}, {8,21}, {9,34}, {15,36}, {16,26}, {3,22}, {14,28}, {13,35}, {3,27}, {4,30}, {1,19}, {4,21}, {17,33}, {10,29}, {18,19}, {11,26}, {13,22}, {6,29}, {18,27}, {17,36}, {12,24}, {15,26}, {14,32}, {2,24}, {3,35}, {9,35}, {10,28}, {18,28}, {14,31}, {5,20}, {9,28}, {4,22}, {5,36}, {3,26}, {5,31}, {12,36}, {8,20}, {8,23}, {11,21}, {18,29}, {11,30}, {13,21}, {1,20}, {15,27}, {8,25}, {7,32}, {10,32}, {1,33}, {2,25}, {3,36}, {6,35}, {18,22}, {17,20}, {6,27}, {16,32}, {7,36}, {11,35}, {2,30}, {1,21}, {12,20}, {15,24}, {5,25}, {4,19}, {4,24}, {8,29}, {9,22}, {6,28} }; // ET36.22 // Bipartite(18,18) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 216 EdgePairs[36][22]:={ {10,19}, {16,25}, {5,32}, {10,21}, {14,25}, {8,24}, {2,22}, {1,31}, {4,27}, {8,36}, {5,35}, {11,29}, {6,23}, {2,20}, {5,34}, {12,31}, {3,32}, {17,35}, {12,33}, {9,19}, {3,30}, {11,22}, {16,20}, {12,27}, {18,23}, {7,23}, {18,21}, {2,28}, {3,34}, {9,31}, {15,32}, {13,20}, {10,23}, {15,28}, {2,29}, {8,22}, {7,28}, {14,33}, {17,30}, {15,34}, {7,26}, {13,26}, {14,30}, {6,33}, {12,34}, {9,34}, {7,29}, {4,28}, {4,29}, {16,19}, {15,35}, {6,26}, {1,19}, {7,30}, {4,21}, {2,35}, {17,33}, {4,25}, {11,26}, {13,22}, {18,27}, {12,24}, {6,31}, {9,33}, {5,22}, {11,36}, {6,19}, {18,32}, {15,21}, {1,23}, {6,30}, {10,28}, {9,35}, {8,27}, {14,31}, {8,32}, {5,20}, {5,36}, {3,26}, {11,25}, {16,22}, {11,30}, {17,34}, {1,27}, {15,27}, {8,25}, {17,29}, {13,23}, {13,36}, {7,21}, {14,29}, {12,32}, {2,25}, {3,36}, {10,20}, {18,36}, {17,28}, {10,35}, {13,19}, {3,33}, {16,31}, {1,21}, {14,24}, {4,24}, {9,20}, {18,26}, {1,24}, {16,24} }; // ET36.23 // Bipartite(18,18) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 4320 EdgePairs[36][23]:={ {16,34}, {14,21}, {13,29}, {12,26}, {17,27}, {5,30}, {16,30}, {7,24}, {13,24}, {17,19}, {12,22}, {5,24}, {13,34}, {2,33}, {6,32}, {7,31}, {6,25}, {13,27}, {9,21}, {14,35}, {14,20}, {4,26}, {6,22}, {5,21}, {10,30}, {3,19}, {1,29}, {11,34}, {1,34}, {16,21}, {17,23}, {5,23}, {4,20}, {15,22}, {9,27}, {10,36}, {2,23}, {13,33}, {2,31}, {17,24}, {8,33}, {8,28}, {1,36}, {18,33}, {10,25}, {15,25}, {1,22}, {2,32}, {4,33}, {16,26}, {10,24}, {7,20}, {18,25}, {8,35}, {5,29}, {10,33}, {15,19}, {12,28}, {4,36}, {12,29}, {9,25}, {1,35}, {8,19}, {17,36}, {15,26}, {18,35}, {12,23}, {14,32}, {2,27}, {17,22}, {14,36}, {15,31}, {11,19}, {14,23}, {3,28}, {11,31}, {3,24}, {5,31}, {13,28}, {8,23}, {11,21}, {9,26}, {18,20}, {3,21}, {18,29}, {11,27}, {7,22}, {16,28}, {9,29}, {3,25}, {7,32}, {2,26}, {10,32}, {3,20}, {18,31}, {6,35}, {8,30}, {9,36}, {4,34}, {6,27}, {7,34}, {15,30}, {16,32}, {1,30}, {11,35}, {12,20}, {4,19}, {6,28} }; // ET36.24 // Bipartite(18,18) Valencies [6,6] // Diameter 6 Girth 4 // Has twins VT AT // Automorphism group of order 52242776064 EdgePairs[36][24]:={ {7,19}, {13,25}, {16,34}, {10,21}, {14,25}, {8,31}, {10,22}, {11,23}, {6,36}, {1,31}, {4,27}, {10,27}, {5,35}, {7,24}, {11,29}, {6,23}, {2,20}, {14,19}, {13,24}, {5,34}, {1,25}, {3,32}, {17,35}, {7,31}, {9,21}, {11,22}, {18,23}, {14,20}, {16,33}, {2,19}, {15,32}, {18,24}, {12,30}, {11,34}, {16,21}, {17,23}, {5,23}, {10,34}, {9,27}, {2,31}, {1,36}, {2,32}, {4,33}, {4,28}, {7,25}, {15,20}, {8,26}, {5,29}, {11,28}, {3,27}, {14,26}, {10,33}, {1,19}, {7,30}, {4,21}, {15,33}, {5,28}, {13,30}, {12,35}, {12,29}, {8,19}, {6,29}, {12,24}, {15,26}, {18,35}, {12,23}, {14,32}, {9,33}, {5,22}, {17,22}, {15,21}, {16,27}, {6,30}, {10,28}, {14,31}, {8,32}, {4,22}, {3,26}, {12,36}, {8,20}, {16,22}, {9,26}, {3,21}, {18,29}, {17,34}, {15,27}, {18,30}, {16,28}, {8,25}, {17,29}, {2,26}, {13,36}, {3,20}, {2,25}, {18,36}, {9,32}, {6,24}, {6,35}, {17,28}, {13,31}, {4,34}, {13,19}, {3,33}, {7,36}, {1,30}, {11,35}, {9,20}, {1,24} }; // ET36.25 // Bipartite(18,18) Valencies [6,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1719926784 EdgePairs[36][25]:={ {10,19}, {7,19}, {14,21}, {5,32}, {13,29}, {10,22}, {11,23}, {17,27}, {8,36}, {5,34}, {12,33}, {6,25}, {16,23}, {14,35}, {9,31}, {12,25}, {3,31}, {6,34}, {13,20}, {10,23}, {14,27}, {1,29}, {18,24}, {7,28}, {11,34}, {17,23}, {5,23}, {15,22}, {18,33}, {14,30}, {6,33}, {12,34}, {2,36}, {8,21}, {4,28}, {7,29}, {10,31}, {16,19}, {3,22}, {7,20}, {18,25}, {8,35}, {15,35}, {8,26}, {4,31}, {18,34}, {14,26}, {1,19}, {7,30}, {15,33}, {2,35}, {12,29}, {13,30}, {6,29}, {17,36}, {12,24}, {15,26}, {9,33}, {11,36}, {2,27}, {14,36}, {15,31}, {3,35}, {2,21}, {5,27}, {8,27}, {10,28}, {9,35}, {4,22}, {5,36}, {3,26}, {3,24}, {9,24}, {11,25}, {13,28}, {16,22}, {6,20}, {9,26}, {18,20}, {18,29}, {11,27}, {4,32}, {13,21}, {17,34}, {1,20}, {11,32}, {16,28}, {2,26}, {10,32}, {7,21}, {1,28}, {6,24}, {17,32}, {8,30}, {13,19}, {16,32}, {3,33}, {4,23}, {1,30}, {16,31}, {2,30}, {1,21}, {12,20}, {15,24}, {5,25}, {4,19}, {17,25}, {9,22} }; // ET36.26 // Bipartite(18,18) Valencies [6,6] // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 56623104 EdgePairs[36][26]:={ {10,19}, {4,35}, {7,19}, {14,21}, {10,21}, {16,36}, {8,24}, {11,23}, {5,30}, {11,29}, {2,20}, {13,24}, {1,25}, {12,31}, {12,22}, {3,32}, {16,23}, {7,27}, {7,23}, {8,34}, {3,34}, {9,31}, {14,20}, {12,25}, {3,31}, {4,26}, {6,22}, {5,21}, {2,29}, {14,27}, {10,30}, {18,24}, {7,28}, {1,34}, {10,34}, {15,22}, {9,27}, {13,33}, {2,23}, {17,24}, {8,33}, {18,33}, {13,26}, {10,25}, {14,30}, {2,32}, {12,34}, {6,21}, {4,33}, {4,28}, {16,19}, {3,22}, {15,35}, {13,35}, {3,23}, {5,29}, {6,26}, {1,19}, {2,35}, {17,33}, {11,26}, {18,27}, {15,26}, {12,23}, {6,31}, {9,33}, {14,36}, {15,21}, {15,31}, {16,27}, {5,27}, {6,30}, {10,28}, {5,20}, {5,36}, {9,24}, {13,28}, {8,20}, {17,34}, {11,32}, {16,28}, {8,25}, {3,25}, {7,32}, {17,29}, {2,26}, {11,20}, {14,29}, {12,32}, {1,28}, {18,31}, {18,36}, {6,35}, {18,22}, {9,36}, {17,20}, {13,19}, {15,30}, {16,32}, {7,36}, {1,30}, {11,35}, {1,21}, {4,19}, {4,24}, {17,25}, {8,29}, {9,22} }; // ET36.27 // Bipartite(18,18) Valencies [6,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 55296 EdgePairs[36][27]:={ {10,19}, {4,35}, {16,36}, {8,24}, {10,22}, {11,23}, {11,33}, {10,27}, {2,20}, {2,33}, {6,32}, {17,35}, {7,31}, {6,25}, {7,27}, {9,21}, {16,20}, {12,27}, {18,21}, {3,34}, {14,20}, {12,25}, {6,34}, {5,26}, {15,32}, {15,28}, {18,24}, {8,22}, {14,33}, {1,34}, {16,21}, {17,23}, {5,33}, {17,30}, {15,34}, {10,34}, {2,31}, {2,23}, {17,24}, {7,26}, {15,25}, {1,22}, {6,33}, {12,34}, {16,26}, {14,28}, {7,20}, {8,35}, {13,35}, {3,23}, {5,29}, {4,31}, {3,27}, {4,30}, {14,26}, {1,19}, {15,19}, {4,21}, {15,33}, {5,28}, {13,30}, {1,35}, {1,26}, {12,24}, {12,23}, {5,22}, {6,19}, {17,22}, {18,32}, {16,27}, {14,22}, {18,28}, {13,32}, {5,20}, {9,28}, {11,31}, {3,24}, {9,24}, {11,25}, {12,36}, {8,23}, {18,29}, {11,30}, {4,32}, {13,21}, {1,27}, {9,29}, {3,25}, {17,29}, {11,20}, {7,21}, {14,29}, {2,25}, {3,36}, {18,36}, {9,32}, {8,30}, {13,31}, {9,36}, {10,26}, {10,35}, {13,19}, {7,36}, {16,31}, {2,30}, {4,19}, {8,29}, {6,28} }; // ET36.28 // Non-bipartite Valency 6 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 432 EdgePairs[36][28]:={ {11,15}, {6,12}, {13,29}, {11,17}, {12,26}, {9,30}, {27,32}, {1,31}, {3,7}, {32,35}, {10,27}, {23,25}, {7,24}, {17,19}, {5,34}, {9,12}, {12,14}, {27,29}, {13,34}, {28,34}, {21,35}, {12,18}, {6,7}, {14,35}, {22,28}, {14,20}, {2,18}, {4,26}, {8,13}, {33,34}, {5,21}, {15,28}, {1,34}, {7,10}, {16,21}, {17,23}, {8,28}, {14,16}, {1,17}, {1,22}, {14,30}, {2,32}, {2,36}, {10,13}, {15,36}, {7,29}, {10,16}, {25,33}, {20,24}, {3,23}, {7,14}, {26,31}, {30,32}, {25,28}, {26,30}, {10,33}, {8,11}, {15,19}, {4,36}, {17,33}, {2,9}, {3,5}, {9,15}, {1,4}, {23,29}, {2,24}, {4,11}, {3,35}, {29,35}, {15,18}, {5,8}, {11,31}, {24,30}, {11,25}, {31,36}, {21,23}, {8,23}, {30,36}, {2,6}, {18,20}, {6,20}, {19,22}, {20,26}, {19,34}, {13,21}, {3,16}, {28,31}, {5,10}, {22,26}, {13,17}, {24,27}, {12,32}, {18,31}, {4,9}, {6,35}, {18,22}, {20,36}, {6,27}, {19,25}, {3,33}, {16,32}, {1,8}, {29,33}, {5,25}, {4,19}, {21,27}, {16,24}, {9,22} }; // ET36.29 // Non-bipartite Valency 6 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 432 EdgePairs[36][29]:={ {6,12}, {13,29}, {12,26}, {26,28}, {27,32}, {11,33}, {32,35}, {10,27}, {23,25}, {7,24}, {5,34}, {12,17}, {12,31}, {3,32}, {13,34}, {1,9}, {1,5}, {11,16}, {16,20}, {19,23}, {22,28}, {18,23}, {14,35}, {14,20}, {16,33}, {9,10}, {8,13}, {10,18}, {7,11}, {5,9}, {33,34}, {5,21}, {15,28}, {3,18}, {1,34}, {17,31}, {20,35}, {2,31}, {17,24}, {4,7}, {14,16}, {1,22}, {14,30}, {1,16}, {2,36}, {2,17}, {15,36}, {10,15}, {25,33}, {6,8}, {25,29}, {3,23}, {7,14}, {26,31}, {28,36}, {30,32}, {6,26}, {15,19}, {4,36}, {7,30}, {4,25}, {9,15}, {18,19}, {23,29}, {11,14}, {2,4}, {2,24}, {4,11}, {30,35}, {18,32}, {3,35}, {5,27}, {15,18}, {9,28}, {24,30}, {19,36}, {11,25}, {27,30}, {31,36}, {8,23}, {16,22}, {6,20}, {17,21}, {20,26}, {13,21}, {28,31}, {5,10}, {22,26}, {10,32}, {3,8}, {13,17}, {24,27}, {1,33}, {3,6}, {21,34}, {6,35}, {2,7}, {19,25}, {20,22}, {29,33}, {21,24}, {4,19}, {12,13}, {8,12}, {29,34}, {8,29}, {21,27}, {9,22} }; // ET36.30 // Non-bipartite Valency 6 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 216 EdgePairs[36][30]:={ {6,12}, {13,29}, {12,26}, {27,32}, {4,8}, {4,27}, {12,16}, {32,35}, {10,27}, {23,25}, {7,24}, {5,34}, {12,15}, {20,23}, {13,34}, {2,33}, {12,33}, {6,25}, {16,23}, {19,24}, {1,32}, {22,28}, {14,35}, {5,7}, {18,21}, {14,20}, {3,31}, {6,9}, {5,26}, {8,13}, {33,34}, {5,21}, {15,28}, {18,24}, {7,28}, {1,34}, {18,33}, {14,16}, {2,16}, {1,22}, {14,30}, {2,36}, {8,10}, {15,36}, {10,31}, {3,9}, {25,33}, {16,19}, {3,23}, {7,14}, {26,31}, {30,32}, {11,18}, {15,19}, {4,36}, {9,15}, {23,29}, {28,35}, {30,34}, {2,24}, {11,13}, {4,11}, {17,22}, {3,4}, {3,35}, {27,28}, {1,7}, {15,18}, {10,14}, {24,30}, {21,22}, {11,25}, {31,36}, {8,23}, {6,20}, {26,29}, {21,36}, {10,17}, {20,26}, {13,21}, {2,8}, {25,30}, {9,11}, {11,32}, {28,31}, {5,10}, {22,26}, {29,36}, {9,29}, {20,34}, {13,17}, {24,27}, {3,17}, {6,35}, {17,32}, {8,30}, {17,20}, {19,25}, {19,35}, {7,12}, {16,31}, {1,6}, {1,18}, {29,33}, {4,19}, {2,5}, {21,27}, {9,22} }; // ET36.31 // Bipartite(8,28) Valencies [7,2] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 40320 EdgePairs[36][31]:={ {1,26}, {4,13}, {5,36}, {6,34}, {1,24}, {2,30}, {5,29}, {1,33}, {3,21}, {6,12}, {7,13}, {5,11}, {1,31}, {7,33}, {2,12}, {6,32}, {6,16}, {4,32}, {5,23}, {8,10}, {7,27}, {5,25}, {3,16}, {3,28}, {2,20}, {3,15}, {4,21}, {7,15}, {5,17}, {6,27}, {3,31}, {7,22}, {8,34}, {8,22}, {7,20}, {1,17}, {4,25}, {2,28}, {8,26}, {5,18}, {2,23}, {2,35}, {8,14}, {8,18}, {1,19}, {2,9}, {6,11}, {1,9}, {4,14}, {4,35}, {4,19}, {8,30}, {6,24}, {3,10}, {3,36}, {7,29} }; // ET36.32 // Non-bipartite Valency 7 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 504 EdgePairs[36][32]:={ {20,27}, {11,15}, {6,12}, {28,33}, {16,36}, {13,29}, {12,26}, {6,10}, {11,23}, {1,11}, {12,19}, {6,14}, {12,16}, {2,20}, {2,3}, {14,18}, {12,15}, {27,29}, {5,24}, {19,27}, {17,35}, {28,34}, {22,35}, {13,27}, {19,24}, {1,32}, {12,27}, {18,23}, {7,23}, {14,20}, {29,30}, {6,34}, {17,18}, {4,26}, {8,13}, {10,18}, {7,11}, {13,20}, {15,28}, {14,27}, {18,24}, {8,15}, {14,33}, {1,34}, {22,25}, {17,31}, {17,23}, {5,23}, {17,30}, {10,34}, {20,35}, {2,23}, {1,10}, {8,33}, {19,30}, {8,28}, {18,33}, {2,16}, {1,22}, {30,31}, {8,21}, {9,34}, {3,14}, {16,26}, {5,19}, {10,24}, {5,15}, {19,29}, {21,33}, {8,11}, {4,21}, {2,35}, {17,33}, {9,25}, {4,25}, {9,15}, {13,22}, {15,26}, {6,31}, {11,13}, {30,35}, {3,4}, {21,29}, {1,7}, {9,28}, {10,14}, {3,26}, {22,34}, {24,32}, {31,36}, {30,36}, {7,16}, {9,26}, {6,16}, {21,32}, {3,21}, {21,36}, {4,32}, {24,25}, {25,30}, {5,11}, {1,13}, {31,34}, {28,31}, {29,36}, {7,32}, {2,26}, {10,32}, {3,20}, {25,35}, {5,12}, {4,9}, {17,28}, {5,18}, {2,7}, {32,36}, {6,27}, {19,25}, {20,22}, {3,33}, {23,35}, {7,36}, {16,31}, {4,24}, {8,29}, {9,22} }; // ET36.33 // Bipartite(12,24) Valencies [8,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 768 EdgePairs[36][33]:={ {9,13}, {4,35}, {10,19}, {7,19}, {3,15}, {8,31}, {8,24}, {11,23}, {6,18}, {2,22}, {6,14}, {5,30}, {11,33}, {10,27}, {8,36}, {2,20}, {1,25}, {4,16}, {12,15}, {12,17}, {7,33}, {12,31}, {5,24}, {3,32}, {6,32}, {11,22}, {7,15}, {2,28}, {3,34}, {3,31}, {6,34}, {2,19}, {4,26}, {9,17}, {10,18}, {12,21}, {2,23}, {8,33}, {10,25}, {2,16}, {1,16}, {10,13}, {2,17}, {7,29}, {3,14}, {10,15}, {4,29}, {5,19}, {8,35}, {3,23}, {11,28}, {4,30}, {6,26}, {10,33}, {7,30}, {4,21}, {12,29}, {1,35}, {1,26}, {12,23}, {2,27}, {11,36}, {7,18}, {8,32}, {9,28}, {4,22}, {5,20}, {10,14}, {5,31}, {5,17}, {9,24}, {12,36}, {6,20}, {9,26}, {3,21}, {1,14}, {9,18}, {11,27}, {1,27}, {11,32}, {7,22}, {1,13}, {8,25}, {9,29}, {3,20}, {6,24}, {8,30}, {9,36}, {4,34}, {7,34}, {5,16}, {11,35}, {1,21}, {5,25}, {12,13}, {6,28} }; // ET36.34 // Bipartite(12,24) Valencies [8,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 768 EdgePairs[36][34]:={ {9,13}, {7,19}, {5,32}, {3,15}, {8,31}, {12,26}, {10,22}, {11,23}, {2,22}, {1,31}, {6,17}, {8,36}, {6,23}, {2,20}, {5,34}, {1,25}, {6,13}, {7,33}, {12,14}, {9,21}, {12,18}, {3,30}, {11,22}, {7,15}, {8,34}, {3,34}, {6,34}, {2,19}, {9,17}, {10,18}, {12,21}, {12,30}, {5,33}, {9,27}, {2,23}, {8,33}, {8,28}, {2,16}, {1,16}, {10,13}, {2,17}, {7,29}, {3,14}, {10,15}, {10,16}, {4,29}, {5,19}, {8,35}, {3,23}, {11,28}, {4,31}, {4,30}, {10,33}, {6,15}, {4,36}, {4,21}, {7,30}, {12,35}, {4,25}, {11,26}, {6,29}, {11,36}, {3,35}, {8,27}, {10,28}, {7,18}, {8,32}, {5,20}, {10,14}, {3,24}, {5,17}, {5,31}, {11,25}, {9,26}, {1,14}, {9,18}, {11,27}, {7,22}, {1,13}, {9,29}, {2,26}, {3,20}, {2,25}, {12,32}, {1,28}, {9,32}, {6,24}, {6,27}, {7,36}, {5,16}, {11,35}, {1,21}, {12,20}, {4,19}, {4,24}, {1,24} }; // ET36.35 // Bipartite(12,24) Valencies [8,4] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 146767085568 EdgePairs[36][35]:={ {4,35}, {7,19}, {11,17}, {3,15}, {10,22}, {11,23}, {6,18}, {12,19}, {5,30}, {6,36}, {1,31}, {5,35}, {11,29}, {2,20}, {1,25}, {4,16}, {6,13}, {12,31}, {5,24}, {2,33}, {7,31}, {6,25}, {9,21}, {12,18}, {1,32}, {3,34}, {12,25}, {2,15}, {8,14}, {10,23}, {8,15}, {12,30}, {2,14}, {5,23}, {10,34}, {9,27}, {8,33}, {7,26}, {2,32}, {8,21}, {9,34}, {4,28}, {10,16}, {4,29}, {7,25}, {3,22}, {7,20}, {8,26}, {7,13}, {5,29}, {7,14}, {3,27}, {1,19}, {11,18}, {4,17}, {9,15}, {10,29}, {1,26}, {12,24}, {6,31}, {9,33}, {11,36}, {6,19}, {2,27}, {2,21}, {6,30}, {10,28}, {8,27}, {8,32}, {9,28}, {4,22}, {3,28}, {5,36}, {5,17}, {12,36}, {8,20}, {3,21}, {1,14}, {11,30}, {10,17}, {1,20}, {3,16}, {1,13}, {7,32}, {2,26}, {6,24}, {5,18}, {4,34}, {10,35}, {9,16}, {3,33}, {4,23}, {11,24}, {11,35}, {12,13}, {9,22} }; // ET36.36 // Bipartite(12,24) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 9172942848 EdgePairs[36][36]:={ {7,19}, {10,21}, {3,15}, {8,24}, {9,30}, {2,22}, {1,31}, {6,17}, {12,16}, {10,27}, {8,36}, {7,24}, {6,23}, {2,20}, {5,34}, {1,25}, {4,16}, {12,17}, {12,22}, {7,31}, {2,28}, {3,31}, {8,14}, {9,17}, {5,21}, {3,19}, {1,29}, {2,14}, {5,33}, {1,17}, {3,13}, {2,16}, {2,32}, {6,33}, {6,21}, {12,34}, {8,18}, {4,28}, {10,15}, {7,25}, {9,23}, {5,15}, {8,26}, {7,13}, {3,27}, {2,34}, {4,30}, {10,33}, {6,15}, {1,19}, {12,28}, {4,36}, {7,30}, {5,28}, {12,29}, {12,35}, {1,35}, {11,26}, {11,14}, {6,29}, {12,23}, {11,13}, {5,22}, {1,23}, {5,27}, {9,35}, {11,19}, {7,18}, {8,32}, {4,22}, {10,14}, {11,31}, {9,24}, {11,25}, {8,20}, {3,21}, {9,18}, {11,32}, {1,13}, {4,18}, {9,29}, {3,25}, {2,26}, {10,32}, {11,20}, {10,20}, {6,35}, {8,30}, {10,26}, {9,36}, {4,34}, {6,27}, {3,33}, {7,36}, {5,16}, {4,24} }; // ET36.37 // Bipartite(12,24) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12582912 EdgePairs[36][37]:={ {1,15}, {7,19}, {3,15}, {9,30}, {4,14}, {12,19}, {3,29}, {2,22}, {5,30}, {11,33}, {12,16}, {1,31}, {2,20}, {1,25}, {4,16}, {12,31}, {5,24}, {6,32}, {7,31}, {12,33}, {7,27}, {3,30}, {7,23}, {7,15}, {8,34}, {5,13}, {3,34}, {8,14}, {4,26}, {9,17}, {5,21}, {3,18}, {8,22}, {12,21}, {2,14}, {5,33}, {9,27}, {10,36}, {2,23}, {2,32}, {6,33}, {6,21}, {9,34}, {4,28}, {10,16}, {4,29}, {7,25}, {3,22}, {10,24}, {8,35}, {8,26}, {7,13}, {3,27}, {2,34}, {1,19}, {11,18}, {12,28}, {4,36}, {4,17}, {2,35}, {9,15}, {10,29}, {1,35}, {7,35}, {6,31}, {11,13}, {11,36}, {6,19}, {1,23}, {10,28}, {8,32}, {10,14}, {5,36}, {11,25}, {8,20}, {8,23}, {11,21}, {6,20}, {6,16}, {11,30}, {9,18}, {10,17}, {1,27}, {1,13}, {9,29}, {2,26}, {12,32}, {3,17}, {5,18}, {10,26}, {11,24}, {12,20}, {5,25}, {4,24}, {9,22}, {6,28} }; // ET36.38 // Bipartite(12,24) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1572864 EdgePairs[36][38]:={ {11,15}, {10,22}, {11,23}, {12,19}, {6,14}, {5,30}, {11,33}, {6,17}, {12,16}, {10,27}, {7,24}, {6,23}, {5,34}, {1,25}, {12,17}, {12,31}, {3,32}, {9,21}, {5,13}, {2,28}, {3,34}, {3,31}, {6,34}, {2,19}, {2,15}, {8,13}, {6,22}, {3,19}, {8,15}, {10,34}, {10,36}, {2,31}, {2,16}, {1,16}, {2,36}, {4,33}, {7,29}, {10,15}, {4,29}, {7,25}, {3,22}, {5,19}, {10,24}, {7,20}, {8,35}, {7,13}, {4,30}, {6,26}, {11,18}, {12,28}, {4,36}, {4,21}, {4,17}, {12,29}, {12,35}, {1,26}, {6,29}, {12,23}, {2,24}, {9,33}, {5,22}, {2,27}, {8,27}, {8,32}, {9,28}, {10,14}, {5,31}, {8,20}, {8,23}, {11,21}, {9,26}, {3,21}, {1,14}, {11,30}, {11,27}, {1,13}, {4,18}, {8,25}, {7,32}, {3,20}, {9,14}, {1,28}, {9,32}, {6,35}, {5,18}, {10,26}, {9,16}, {3,33}, {7,36}, {7,17}, {1,30}, {11,35}, {1,18}, {5,25}, {4,24}, {9,20} }; // ET36.39 // Bipartite(12,24) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 196608 EdgePairs[36][39]:={ {9,13}, {5,14}, {10,21}, {8,31}, {6,18}, {4,14}, {3,29}, {11,33}, {12,16}, {6,17}, {4,27}, {7,24}, {1,25}, {12,15}, {7,33}, {3,32}, {6,32}, {12,18}, {1,32}, {11,22}, {12,27}, {7,23}, {2,28}, {3,34}, {12,25}, {3,31}, {5,26}, {4,26}, {10,18}, {10,23}, {10,30}, {3,19}, {11,34}, {1,34}, {12,30}, {2,14}, {9,27}, {2,23}, {8,33}, {7,26}, {8,28}, {2,16}, {1,22}, {8,21}, {8,18}, {9,34}, {2,13}, {4,29}, {3,22}, {5,19}, {5,29}, {7,14}, {10,33}, {6,15}, {12,28}, {4,36}, {4,17}, {2,35}, {5,28}, {9,25}, {4,15}, {9,15}, {1,35}, {8,19}, {6,29}, {7,35}, {11,36}, {1,23}, {6,30}, {11,19}, {11,31}, {8,16}, {5,17}, {5,31}, {9,24}, {11,21}, {6,20}, {1,20}, {1,13}, {2,26}, {10,32}, {3,20}, {7,21}, {2,25}, {3,17}, {10,20}, {8,30}, {9,36}, {6,27}, {10,35}, {7,36}, {11,24}, {5,16}, {4,24}, {12,13}, {9,22} }; // ET36.40 // Bipartite(12,24) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 196608 EdgePairs[36][40]:={ {5,32}, {11,15}, {10,21}, {4,14}, {12,19}, {6,36}, {12,16}, {6,17}, {5,35}, {2,20}, {1,25}, {12,15}, {12,31}, {6,32}, {7,27}, {11,22}, {12,27}, {7,23}, {7,15}, {8,34}, {2,28}, {3,34}, {3,31}, {4,26}, {8,13}, {2,29}, {3,19}, {1,29}, {8,22}, {11,34}, {1,34}, {5,23}, {9,27}, {10,36}, {8,33}, {7,26}, {1,17}, {10,25}, {2,16}, {1,22}, {2,32}, {6,33}, {6,21}, {10,13}, {8,21}, {8,18}, {2,17}, {4,33}, {3,14}, {2,13}, {10,16}, {4,29}, {3,22}, {9,23}, {10,24}, {5,19}, {3,23}, {7,14}, {4,30}, {10,33}, {11,18}, {12,28}, {7,30}, {4,21}, {4,17}, {5,28}, {9,15}, {1,26}, {6,29}, {7,35}, {12,24}, {3,35}, {9,35}, {10,28}, {11,19}, {7,18}, {5,20}, {11,31}, {3,26}, {5,31}, {9,24}, {12,36}, {6,20}, {1,14}, {11,30}, {11,27}, {1,13}, {4,18}, {8,25}, {2,25}, {9,32}, {6,24}, {8,30}, {9,36}, {5,16}, {9,20} }; // ET36.41 // Bipartite(18,18) Valencies [8,8] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 576 EdgePairs[36][41]:={ {10,24}, {1,20}, {2,24}, {13,32}, {2,33}, {6,32}, {17,36}, {4,27}, {11,35}, {5,34}, {14,19}, {16,26}, {18,29}, {3,22}, {4,30}, {16,27}, {15,31}, {4,29}, {8,33}, {1,27}, {3,25}, {10,26}, {17,20}, {7,22}, {1,19}, {2,26}, {7,34}, {17,24}, {1,21}, {7,36}, {17,21}, {8,25}, {2,28}, {12,34}, {1,30}, {16,23}, {8,27}, {13,29}, {18,34}, {10,22}, {6,22}, {15,29}, {6,21}, {2,25}, {14,33}, {2,34}, {8,19}, {7,20}, {14,36}, {16,24}, {9,27}, {12,20}, {12,36}, {7,32}, {1,31}, {10,28}, {14,24}, {11,31}, {17,33}, {1,22}, {6,30}, {4,33}, {5,23}, {10,29}, {3,20}, {9,34}, {13,22}, {15,19}, {10,21}, {13,31}, {18,30}, {11,21}, {4,35}, {9,25}, {2,32}, {16,32}, {11,23}, {11,29}, {5,24}, {13,23}, {12,28}, {12,25}, {13,25}, {13,28}, {9,20}, {18,26}, {15,36}, {5,28}, {17,31}, {8,26}, {12,26}, {16,22}, {7,31}, {13,30}, {4,36}, {8,21}, {3,19}, {5,31}, {17,25}, {11,24}, {6,27}, {12,19}, {6,26}, {12,30}, {3,23}, {8,23}, {18,19}, {3,21}, {18,23}, {9,30}, {1,35}, {14,20}, {16,34}, {15,21}, {7,28}, {10,35}, {6,36}, {5,33}, {3,24}, {2,29}, {11,27}, {4,34}, {10,36}, {18,22}, {11,32}, {16,20}, {15,33}, {6,25}, {9,33}, {15,28}, {3,28}, {14,35}, {5,19}, {7,35}, {15,30}, {5,35}, {9,31}, {17,32}, {18,35}, {9,23}, {14,27}, {8,29}, {4,32}, {14,26} }; // ET36.42 // Bipartite(18,18) Valencies [8,8] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 37748736 EdgePairs[36][42]:={ {10,19}, {7,19}, {13,25}, {14,21}, {5,32}, {10,21}, {16,36}, {8,24}, {12,26}, {10,22}, {11,23}, {5,30}, {6,36}, {1,31}, {4,27}, {5,35}, {7,24}, {11,29}, {2,20}, {13,24}, {17,19}, {1,25}, {7,33}, {5,24}, {3,32}, {13,34}, {17,35}, {7,31}, {7,27}, {13,27}, {12,27}, {14,35}, {18,23}, {15,29}, {2,28}, {3,34}, {9,31}, {12,25}, {16,33}, {2,19}, {5,26}, {6,22}, {5,21}, {2,29}, {10,30}, {7,28}, {1,34}, {14,33}, {5,33}, {5,23}, {10,34}, {15,22}, {2,23}, {13,33}, {17,24}, {8,33}, {8,28}, {10,25}, {1,22}, {14,30}, {2,32}, {12,34}, {4,33}, {9,34}, {15,36}, {10,31}, {16,19}, {9,23}, {18,25}, {8,35}, {8,26}, {15,20}, {15,35}, {3,23}, {11,28}, {3,27}, {4,30}, {18,34}, {6,26}, {14,26}, {1,19}, {4,36}, {4,21}, {17,33}, {12,35}, {13,30}, {9,25}, {4,25}, {8,19}, {6,29}, {15,26}, {12,23}, {14,32}, {6,31}, {18,32}, {3,35}, {15,31}, {2,21}, {16,27}, {10,28}, {11,19}, {14,23}, {3,26}, {12,36}, {8,20}, {16,22}, {11,21}, {6,20}, {18,20}, {18,29}, {11,30}, {13,21}, {11,32}, {7,22}, {15,27}, {16,28}, {9,29}, {3,25}, {17,29}, {13,36}, {11,20}, {12,32}, {1,28}, {3,36}, {18,31}, {17,26}, {9,32}, {6,35}, {18,22}, {17,28}, {17,20}, {4,34}, {6,27}, {7,36}, {1,30}, {16,31}, {2,30}, {1,21}, {14,24}, {4,24}, {9,20}, {8,29}, {9,22}, {16,24} }; // ET36.43 // Bipartite(18,18) Valencies [8,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 73728 EdgePairs[36][43]:={ {10,19}, {13,25}, {14,21}, {16,34}, {16,36}, {8,31}, {12,26}, {12,19}, {6,36}, {11,33}, {10,27}, {5,35}, {7,24}, {11,29}, {2,20}, {1,25}, {5,24}, {13,34}, {2,33}, {6,32}, {7,27}, {9,21}, {3,30}, {1,32}, {16,20}, {14,35}, {18,23}, {18,21}, {3,34}, {9,31}, {12,25}, {6,34}, {2,19}, {15,32}, {13,20}, {5,21}, {10,23}, {15,28}, {2,29}, {3,19}, {1,29}, {8,22}, {12,30}, {14,33}, {17,31}, {17,23}, {5,33}, {5,23}, {17,30}, {15,34}, {4,20}, {9,27}, {2,31}, {13,33}, {7,26}, {8,28}, {10,25}, {6,21}, {12,34}, {2,36}, {4,33}, {7,29}, {15,36}, {16,26}, {14,28}, {9,23}, {10,24}, {7,20}, {18,25}, {8,26}, {16,29}, {4,30}, {10,33}, {1,19}, {12,28}, {15,19}, {4,21}, {2,35}, {5,28}, {12,35}, {13,30}, {9,25}, {4,25}, {10,29}, {13,22}, {18,27}, {12,24}, {18,35}, {6,31}, {5,22}, {6,19}, {11,36}, {17,22}, {14,36}, {15,21}, {3,35}, {15,31}, {1,23}, {16,27}, {14,22}, {9,35}, {11,19}, {13,32}, {14,23}, {8,32}, {4,22}, {3,28}, {11,31}, {5,36}, {3,26}, {3,24}, {8,23}, {16,22}, {9,26}, {18,20}, {11,30}, {4,32}, {13,21}, {1,27}, {7,22}, {15,27}, {3,25}, {17,29}, {10,32}, {11,20}, {1,33}, {18,31}, {17,26}, {17,32}, {8,30}, {17,28}, {4,34}, {6,27}, {7,34}, {7,36}, {11,35}, {2,30}, {14,24}, {9,20}, {18,26}, {1,24}, {8,29}, {6,28}, {16,24} }; // ET36.44 // Bipartite(18,18) Valencies [8,8] // Diameter 3 Girth 4 // Twin-free VT Non-AT // Automorphism group of order 144 EdgePairs[36][44]:={ {7,19}, {13,25}, {14,21}, {16,34}, {5,32}, {13,29}, {14,25}, {8,31}, {9,30}, {3,29}, {1,31}, {4,27}, {7,24}, {2,20}, {13,24}, {5,34}, {17,19}, {12,22}, {3,32}, {2,33}, {7,27}, {9,21}, {3,30}, {1,32}, {11,22}, {16,20}, {12,27}, {14,35}, {18,23}, {18,21}, {15,29}, {2,28}, {9,31}, {14,20}, {12,25}, {3,31}, {16,33}, {6,34}, {2,19}, {5,26}, {15,32}, {15,28}, {10,30}, {1,29}, {7,28}, {12,21}, {14,33}, {17,23}, {5,33}, {5,23}, {17,30}, {15,34}, {10,34}, {10,36}, {2,31}, {13,33}, {8,28}, {10,25}, {13,26}, {12,34}, {8,21}, {7,29}, {4,29}, {7,25}, {3,22}, {5,19}, {10,24}, {18,25}, {8,35}, {15,20}, {11,28}, {18,34}, {6,26}, {1,19}, {4,36}, {2,35}, {17,33}, {12,35}, {4,25}, {10,29}, {1,26}, {7,35}, {17,36}, {15,26}, {18,35}, {12,23}, {2,24}, {9,33}, {5,22}, {11,36}, {6,19}, {2,27}, {17,22}, {15,31}, {1,23}, {16,27}, {5,27}, {6,30}, {11,19}, {14,31}, {14,23}, {8,32}, {4,22}, {3,28}, {9,24}, {8,23}, {16,22}, {11,21}, {6,20}, {18,20}, {3,21}, {11,30}, {17,21}, {11,27}, {4,32}, {18,30}, {8,25}, {13,23}, {13,36}, {1,33}, {12,32}, {1,28}, {3,36}, {10,20}, {17,26}, {6,35}, {10,26}, {9,36}, {4,34}, {6,27}, {13,19}, {15,30}, {16,32}, {7,36}, {11,35}, {16,31}, {14,24}, {4,24}, {9,20}, {18,26}, {8,29}, {9,22}, {6,28}, {16,24} }; // ET36.45 // Non-bipartite Valency 8 // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 47552535724032 EdgePairs[36][45]:={ {10,19}, {16,25}, {13,25}, {5,32}, {24,33}, {5,14}, {14,25}, {11,17}, {8,31}, {12,19}, {2,22}, {6,14}, {5,30}, {11,33}, {4,27}, {23,33}, {1,25}, {6,13}, {12,17}, {6,32}, {7,31}, {12,33}, {19,31}, {22,35}, {9,19}, {13,27}, {21,35}, {12,18}, {22,36}, {7,15}, {5,13}, {2,28}, {22,33}, {24,34}, {8,14}, {4,26}, {8,13}, {9,17}, {10,18}, {15,28}, {14,27}, {8,15}, {11,34}, {17,31}, {17,30}, {10,34}, {10,36}, {2,23}, {19,30}, {13,26}, {15,25}, {1,22}, {12,34}, {9,34}, {7,29}, {4,28}, {16,26}, {3,22}, {14,28}, {5,15}, {7,13}, {3,23}, {5,29}, {7,14}, {19,29}, {3,27}, {10,33}, {6,15}, {14,26}, {21,33}, {11,18}, {7,30}, {4,21}, {12,35}, {4,25}, {1,26}, {6,29}, {15,26}, {2,24}, {9,33}, {6,31}, {2,27}, {11,36}, {18,32}, {1,23}, {2,21}, {16,27}, {6,30}, {9,35}, {11,19}, {8,32}, {4,22}, {3,28}, {20,32}, {3,26}, {8,16}, {5,31}, {3,24}, {12,36}, {22,34}, {13,28}, {24,35}, {20,30}, {7,16}, {6,16}, {3,21}, {18,29}, {21,36}, {9,18}, {10,17}, {1,27}, {15,27}, {18,30}, {16,28}, {7,32}, {3,25}, {17,29}, {20,29}, {2,26}, {11,20}, {2,25}, {1,28}, {18,31}, {21,34}, {10,20}, {20,31}, {17,32}, {8,30}, {9,36}, {19,32}, {23,34}, {10,35}, {23,35}, {4,23}, {5,16}, {11,35}, {1,21}, {23,36}, {12,20}, {4,24}, {9,20}, {1,24}, {8,29}, {24,36} }; // ET36.46 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 288 EdgePairs[36][46]:={ {9,13}, {7,19}, {13,25}, {16,34}, {20,27}, {24,33}, {16,36}, {3,15}, {8,24}, {12,26}, {10,22}, {9,30}, {14,34}, {6,36}, {1,31}, {6,17}, {5,35}, {11,29}, {2,20}, {5,34}, {4,16}, {12,15}, {7,33}, {12,31}, {12,14}, {12,22}, {24,29}, {2,33}, {19,31}, {7,27}, {22,35}, {13,27}, {9,21}, {11,16}, {3,30}, {12,27}, {7,23}, {8,34}, {3,34}, {9,31}, {22,33}, {3,31}, {2,15}, {23,30}, {10,23}, {2,29}, {20,25}, {1,34}, {12,30}, {17,31}, {2,14}, {5,23}, {23,32}, {9,27}, {13,33}, {7,26}, {8,28}, {19,26}, {10,25}, {15,25}, {2,32}, {6,33}, {1,16}, {6,21}, {2,36}, {8,21}, {2,17}, {4,33}, {3,14}, {10,15}, {22,29}, {4,29}, {16,26}, {14,28}, {5,19}, {18,25}, {8,35}, {13,35}, {15,35}, {8,17}, {11,28}, {19,29}, {24,31}, {6,26}, {14,26}, {1,19}, {4,36}, {15,33}, {5,28}, {10,29}, {1,35}, {18,27}, {12,23}, {11,13}, {21,30}, {5,22}, {18,32}, {14,36}, {3,35}, {10,28}, {7,18}, {10,14}, {20,32}, {9,24}, {11,25}, {8,20}, {24,35}, {20,30}, {11,21}, {9,26}, {6,20}, {21,32}, {21,36}, {4,32}, {11,32}, {7,22}, {15,27}, {1,13}, {4,18}, {18,30}, {16,28}, {8,25}, {17,29}, {10,32}, {3,20}, {21,34}, {3,17}, {17,26}, {6,24}, {5,18}, {17,28}, {23,34}, {6,27}, {9,16}, {22,31}, {7,36}, {11,24}, {1,30}, {19,28}, {4,13}, {23,36}, {1,18}, {5,25}, {4,19} }; // ET36.47 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 288 EdgePairs[36][47]:={ {11,17}, {3,33}, {10,24}, {5,17}, {2,24}, {11,20}, {2,33}, {17,36}, {4,27}, {11,35}, {4,24}, {4,26}, {3,22}, {23,29}, {4,16}, {12,22}, {15,31}, {24,27}, {1,27}, {23,28}, {3,25}, {3,15}, {17,34}, {10,33}, {5,20}, {13,35}, {24,30}, {22,32}, {2,28}, {5,32}, {8,15}, {9,35}, {8,27}, {13,29}, {10,30}, {16,30}, {15,29}, {2,25}, {6,31}, {2,36}, {8,19}, {9,29}, {3,14}, {7,20}, {14,36}, {9,32}, {12,36}, {5,29}, {9,19}, {8,14}, {14,30}, {7,13}, {7,25}, {22,27}, {24,25}, {1,22}, {20,33}, {6,30}, {23,26}, {4,21}, {21,26}, {10,31}, {9,34}, {24,32}, {10,21}, {2,13}, {6,18}, {7,30}, {2,16}, {13,31}, {11,21}, {4,35}, {7,16}, {13,33}, {16,32}, {1,23}, {11,29}, {7,17}, {15,35}, {17,27}, {20,28}, {18,26}, {4,13}, {21,31}, {18,33}, {8,26}, {9,22}, {7,31}, {12,33}, {6,15}, {22,25}, {8,32}, {12,23}, {11,24}, {17,25}, {12,19}, {12,30}, {21,29}, {14,34}, {3,23}, {6,19}, {19,36}, {1,15}, {6,28}, {6,14}, {1,35}, {16,34}, {20,35}, {7,28}, {16,36}, {2,21}, {9,18}, {20,26}, {10,17}, {18,28}, {1,26}, {4,34}, {10,36}, {11,32}, {15,33}, {14,32}, {6,25}, {5,27}, {19,25}, {5,26}, {8,18}, {5,13}, {3,28}, {23,31}, {1,14}, {10,20}, {12,31}, {11,34}, {19,34}, {22,30}, {1,34}, {21,28}, {3,36}, {18,35}, {9,23}, {8,29}, {19,27}, {12,18}, {5,16} }; // ET36.48 // Non-bipartite Valency 8 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 4608 EdgePairs[36][48]:={ {5,32}, {10,21}, {28,33}, {15,23}, {16,36}, {3,15}, {12,26}, {6,10}, {4,14}, {4,8}, {6,17}, {3,7}, {13,18}, {32,35}, {2,11}, {14,19}, {13,24}, {4,16}, {27,34}, {25,32}, {20,21}, {27,29}, {16,18}, {13,34}, {1,9}, {7,31}, {21,26}, {1,5}, {11,22}, {16,20}, {30,33}, {19,23}, {18,21}, {4,6}, {3,34}, {16,33}, {2,15}, {28,32}, {5,9}, {21,28}, {13,20}, {27,31}, {10,23}, {18,24}, {12,21}, {14,33}, {22,25}, {17,31}, {16,21}, {17,23}, {17,30}, {2,10}, {15,34}, {6,11}, {15,22}, {9,27}, {1,36}, {3,13}, {1,16}, {8,10}, {8,18}, {4,33}, {2,13}, {1,12}, {3,9}, {25,33}, {5,19}, {7,20}, {20,24}, {15,35}, {13,35}, {5,29}, {26,31}, {19,29}, {2,34}, {8,11}, {12,28}, {15,19}, {4,36}, {7,30}, {2,35}, {9,25}, {3,5}, {8,19}, {28,35}, {22,27}, {12,23}, {6,31}, {4,11}, {30,35}, {17,22}, {18,32}, {14,36}, {14,17}, {3,35}, {14,22}, {27,36}, {6,30}, {10,28}, {1,7}, {14,23}, {8,32}, {9,24}, {3,12}, {11,25}, {31,36}, {20,30}, {28,30}, {2,6}, {6,20}, {32,33}, {1,14}, {18,29}, {26,29}, {19,22}, {7,9}, {11,27}, {13,21}, {24,25}, {2,8}, {25,30}, {31,34}, {29,36}, {15,17}, {24,27}, {25,35}, {1,33}, {5,12}, {23,28}, {26,36}, {20,31}, {5,18}, {10,26}, {19,32}, {26,34}, {23,26}, {7,17}, {11,24}, {7,12}, {4,10}, {29,34}, {8,29}, {9,22}, {16,24} }; // ET36.49 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 4608 EdgePairs[36][49]:={ {1,15}, {4,35}, {7,19}, {16,34}, {14,21}, {6,12}, {8,31}, {10,22}, {11,23}, {6,18}, {1,11}, {14,34}, {5,30}, {24,26}, {27,32}, {10,27}, {25,34}, {23,25}, {23,27}, {27,35}, {14,18}, {26,33}, {12,22}, {20,23}, {2,33}, {6,32}, {16,23}, {19,31}, {4,5}, {28,34}, {9,21}, {19,24}, {21,25}, {12,27}, {14,35}, {18,23}, {22,28}, {3,10}, {14,20}, {12,25}, {6,9}, {26,35}, {7,11}, {4,12}, {1,34}, {7,10}, {2,14}, {27,33}, {3,11}, {13,33}, {17,24}, {1,10}, {19,30}, {4,7}, {10,25}, {2,16}, {16,17}, {28,29}, {2,36}, {15,36}, {7,29}, {3,14}, {16,35}, {26,32}, {16,19}, {9,23}, {10,24}, {31,35}, {15,20}, {25,29}, {8,17}, {28,36}, {11,28}, {26,30}, {15,33}, {32,34}, {4,15}, {2,9}, {1,35}, {11,26}, {13,22}, {6,29}, {30,34}, {12,24}, {6,19}, {15,21}, {29,35}, {25,31}, {15,18}, {7,18}, {8,9}, {2,12}, {9,28}, {5,20}, {20,32}, {5,31}, {5,17}, {27,30}, {8,20}, {16,22}, {30,36}, {11,21}, {9,26}, {17,21}, {5,11}, {3,16}, {1,13}, {18,30}, {28,31}, {5,10}, {22,26}, {7,32}, {17,29}, {20,29}, {13,23}, {13,36}, {3,8}, {13,17}, {3,6}, {3,36}, {18,31}, {4,9}, {17,32}, {18,22}, {2,7}, {8,30}, {32,36}, {4,34}, {20,22}, {13,19}, {3,33}, {19,21}, {1,8}, {31,33}, {4,13}, {1,6}, {15,24}, {29,33}, {14,24}, {2,5}, {25,36}, {8,12}, {24,28}, {21,27} }; // ET36.50 // Bipartite(9,27) Valencies [9,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1296 EdgePairs[36][50]:={ {2,11}, {3,22}, {4,24}, {5,32}, {9,19}, {1,14}, {6,34}, {7,11}, {8,20}, {2,26}, {8,31}, {6,33}, {2,29}, {5,29}, {2,24}, {7,12}, {8,16}, {1,10}, {4,11}, {4,10}, {8,21}, {7,13}, {3,33}, {8,25}, {6,30}, {1,20}, {5,15}, {4,16}, {6,36}, {2,33}, {9,32}, {4,30}, {2,21}, {8,27}, {8,32}, {5,23}, {5,20}, {4,12}, {4,18}, {7,10}, {2,31}, {1,16}, {3,28}, {3,17}, {5,19}, {4,27}, {3,25}, {9,12}, {9,36}, {4,21}, {9,27}, {7,15}, {2,15}, {3,14}, {3,31}, {1,18}, {7,22}, {9,34}, {9,35}, {8,35}, {7,19}, {6,18}, {9,22}, {1,28}, {8,26}, {2,17}, {5,26}, {5,34}, {1,13}, {5,13}, {7,17}, {9,30}, {6,28}, {1,23}, {7,14}, {1,25}, {6,29}, {6,23}, {6,24}, {3,36}, {3,35} }; // ET36.51 // Bipartite(9,27) Valencies [9,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1088391168 EdgePairs[36][51]:={ {2,11}, {3,32}, {5,12}, {2,14}, {4,24}, {9,23}, {8,20}, {2,26}, {4,36}, {8,31}, {2,32}, {2,29}, {9,25}, {5,29}, {9,16}, {7,12}, {1,10}, {6,26}, {8,11}, {6,31}, {8,15}, {3,33}, {5,11}, {8,24}, {3,23}, {1,31}, {3,24}, {6,36}, {8,29}, {9,32}, {4,30}, {7,30}, {5,16}, {5,21}, {4,12}, {5,20}, {4,33}, {4,18}, {5,25}, {7,10}, {1,16}, {3,28}, {2,20}, {3,15}, {8,33}, {4,27}, {9,36}, {4,21}, {9,27}, {3,19}, {8,13}, {6,27}, {3,14}, {5,30}, {9,34}, {7,21}, {7,35}, {8,22}, {4,15}, {7,19}, {6,18}, {6,22}, {1,28}, {9,18}, {2,17}, {7,28}, {9,14}, {6,17}, {6,35}, {2,23}, {5,34}, {1,13}, {2,35}, {1,19}, {7,17}, {1,22}, {1,34}, {1,25}, {6,13}, {3,10}, {7,26} }; // ET36.52 // Non-bipartite Valency 9 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 648 EdgePairs[36][52]:={ {21,23}, {3,33}, {10,25}, {1,20}, {2,24}, {17,36}, {4,27}, {13,21}, {7,15}, {5,34}, {8,12}, {16,33}, {3,22}, {1,10}, {18,32}, {16,27}, {30,33}, {3,9}, {8,28}, {15,31}, {3,6}, {1,32}, {19,24}, {4,31}, {2,19}, {25,33}, {13,35}, {25,30}, {17,24}, {7,36}, {17,21}, {6,7}, {5,32}, {9,35}, {20,30}, {4,23}, {13,29}, {13,16}, {10,15}, {3,18}, {11,28}, {32,36}, {23,32}, {26,28}, {5,22}, {9,29}, {7,11}, {14,36}, {4,8}, {31,35}, {5,11}, {2,5}, {28,34}, {27,29}, {29,36}, {8,14}, {19,29}, {14,30}, {5,25}, {11,13}, {3,12}, {22,27}, {2,35}, {25,34}, {4,21}, {10,29}, {27,31}, {10,31}, {15,19}, {26,35}, {24,26}, {7,30}, {1,29}, {8,17}, {11,21}, {4,35}, {9,25}, {7,16}, {13,33}, {6,33}, {30,35}, {1,23}, {6,24}, {21,25}, {23,25}, {15,34}, {27,36}, {9,10}, {5,14}, {18,26}, {4,13}, {20,22}, {17,31}, {8,26}, {29,32}, {16,22}, {9,22}, {12,33}, {6,15}, {2,17}, {9,13}, {12,27}, {14,17}, {33,34}, {14,22}, {13,24}, {17,25}, {12,19}, {6,26}, {12,30}, {18,19}, {12,14}, {3,21}, {2,7}, {22,28}, {26,32}, {18,23}, {22,31}, {2,11}, {14,20}, {16,34}, {20,35}, {11,26}, {15,18}, {11,16}, {7,23}, {6,36}, {8,34}, {9,18}, {20,26}, {10,17}, {1,16}, {11,32}, {16,20}, {14,32}, {8,24}, {2,31}, {6,10}, {15,28}, {5,9}, {1,4}, {24,29}, {1,8}, {4,12}, {3,28}, {7,27}, {28,31}, {15,23}, {21,36}, {10,20}, {5,19}, {6,20}, {2,30}, {19,34}, {1,34}, {24,33}, {21,28}, {3,36}, {18,35}, {19,27}, {12,18}, {23,30} }; // ET36.53 // Non-bipartite Valency 9 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1296 EdgePairs[36][53]:={ {1,11}, {3,33}, {10,25}, {1,20}, {13,32}, {9,28}, {25,31}, {17,35}, {4,27}, {12,29}, {7,15}, {14,19}, {16,33}, {16,26}, {23,27}, {18,32}, {8,30}, {2,23}, {30,33}, {20,27}, {1,32}, {4,19}, {2,19}, {5,20}, {14,31}, {26,33}, {29,35}, {17,24}, {11,14}, {17,21}, {8,25}, {6,11}, {20,30}, {13,29}, {13,16}, {18,34}, {32,36}, {3,17}, {3,7}, {8,16}, {6,21}, {3,34}, {6,31}, {4,10}, {2,36}, {4,22}, {1,18}, {12,17}, {9,27}, {27,30}, {1,5}, {31,35}, {26,29}, {8,14}, {19,29}, {14,30}, {19,22}, {5,25}, {10,28}, {25,28}, {30,34}, {24,25}, {1,22}, {25,34}, {21,26}, {10,31}, {9,34}, {24,32}, {26,35}, {2,16}, {11,21}, {8,36}, {3,4}, {7,26}, {2,6}, {8,11}, {11,30}, {5,24}, {17,27}, {1,9}, {27,36}, {1,28}, {4,7}, {10,13}, {6,23}, {3,10}, {15,36}, {17,31}, {29,32}, {16,22}, {9,22}, {12,33}, {4,36}, {9,13}, {12,27}, {5,12}, {14,17}, {33,34}, {28,36}, {14,22}, {13,24}, {12,19}, {6,26}, {22,33}, {20,23}, {18,19}, {18,25}, {3,21}, {9,12}, {22,28}, {6,9}, {7,29}, {27,32}, {12,15}, {18,23}, {1,35}, {15,21}, {20,35}, {11,26}, {15,18}, {22,26}, {16,36}, {7,23}, {3,30}, {5,33}, {3,24}, {2,29}, {4,14}, {5,8}, {11,32}, {16,20}, {15,33}, {9,17}, {8,24}, {2,31}, {6,34}, {19,25}, {15,28}, {24,29}, {7,10}, {28,31}, {15,23}, {14,35}, {21,36}, {23,31}, {2,12}, {2,8}, {10,20}, {5,15}, {13,34}, {7,35}, {21,24}, {19,34}, {6,13}, {13,20}, {5,35}, {21,28}, {4,32}, {11,18}, {23,30}, {7,18}, {10,16} }; // ET36.54 // Non-bipartite Valency 9 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1296 EdgePairs[36][54]:={ {16,25}, {16,34}, {5,32}, {10,21}, {15,23}, {8,24}, {6,10}, {9,30}, {1,11}, {6,14}, {11,33}, {4,8}, {4,27}, {32,35}, {10,27}, {25,34}, {8,36}, {6,23}, {27,35}, {14,19}, {14,18}, {12,15}, {22,30}, {12,31}, {25,32}, {5,24}, {13,34}, {16,23}, {28,34}, {7,27}, {19,24}, {11,16}, {12,18}, {3,30}, {7,23}, {5,7}, {5,13}, {22,33}, {12,25}, {3,31}, {16,33}, {9,10}, {2,19}, {6,9}, {7,11}, {15,32}, {21,28}, {13,20}, {5,21}, {2,29}, {4,12}, {18,24}, {3,18}, {20,25}, {8,15}, {14,33}, {16,21}, {27,33}, {2,10}, {20,35}, {2,23}, {19,30}, {8,28}, {19,26}, {2,32}, {1,16}, {4,33}, {2,17}, {9,34}, {7,29}, {3,9}, {3,22}, {8,26}, {15,35}, {25,29}, {7,13}, {8,17}, {26,31}, {30,32}, {26,30}, {2,34}, {6,26}, {33,36}, {12,29}, {9,25}, {4,15}, {3,5}, {18,19}, {1,35}, {11,26}, {23,29}, {13,22}, {18,27}, {2,4}, {7,35}, {17,36}, {22,27}, {18,35}, {6,31}, {11,13}, {30,35}, {17,22}, {14,36}, {15,21}, {27,28}, {10,28}, {11,19}, {7,18}, {4,22}, {10,14}, {5,36}, {23,31}, {3,12}, {24,32}, {13,28}, {21,23}, {15,16}, {6,20}, {3,21}, {11,30}, {21,36}, {10,17}, {19,34}, {24,25}, {1,20}, {5,11}, {31,34}, {28,31}, {29,36}, {20,29}, {10,32}, {13,17}, {1,33}, {14,29}, {9,14}, {1,28}, {3,36}, {18,31}, {26,36}, {17,26}, {6,35}, {17,32}, {2,7}, {13,31}, {17,20}, {4,34}, {20,22}, {9,16}, {23,26}, {15,30}, {1,8}, {12,20}, {1,6}, {29,33}, {5,25}, {4,19}, {14,24}, {8,12}, {1,24}, {24,28}, {9,22}, {21,27} }; // ET36.55 // Bipartite(6,30) Valencies [10,2] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 35831808000000 EdgePairs[36][55]:={ {5,12}, {3,22}, {1,26}, {2,14}, {5,36}, {4,23}, {1,14}, {2,26}, {5,24}, {2,32}, {5,29}, {4,34}, {1,32}, {4,11}, {4,10}, {3,21}, {6,31}, {3,27}, {6,12}, {3,33}, {5,11}, {6,30}, {1,20}, {4,16}, {1,31}, {3,9}, {6,36}, {6,7}, {2,33}, {2,21}, {5,23}, {1,7}, {3,16}, {3,28}, {2,20}, {3,15}, {5,17}, {2,15}, {4,17}, {5,30}, {4,28}, {2,27}, {4,22}, {6,18}, {6,19}, {3,34}, {5,18}, {6,25}, {1,8}, {1,13}, {5,35}, {1,19}, {2,9}, {4,35}, {2,8}, {1,25}, {6,13}, {6,24}, {3,10}, {4,29} }; // ET36.56 // Bipartite(6,30) Valencies [10,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23592960 EdgePairs[36][56]:={ {4,24}, {4,9}, {5,36}, {5,32}, {1,14}, {1,29}, {6,33}, {4,34}, {1,32}, {2,24}, {6,26}, {4,10}, {6,31}, {6,12}, {5,15}, {3,8}, {3,23}, {1,31}, {6,36}, {2,33}, {6,16}, {5,21}, {4,12}, {5,20}, {1,7}, {2,7}, {3,11}, {1,16}, {3,28}, {2,20}, {3,15}, {5,19}, {4,27}, {3,25}, {2,18}, {5,17}, {3,30}, {6,27}, {6,21}, {3,26}, {5,30}, {1,17}, {6,18}, {4,25}, {1,28}, {3,13}, {2,23}, {5,34}, {1,13}, {5,35}, {2,35}, {2,9}, {6,11}, {1,22}, {4,14}, {2,8}, {4,19}, {2,22}, {3,10}, {4,29} }; // ET36.57 // Bipartite(12,24) Valencies [10,5] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 983040 EdgePairs[36][57]:={ {10,19}, {4,35}, {11,15}, {8,24}, {12,26}, {10,22}, {3,29}, {11,33}, {4,27}, {6,17}, {12,16}, {8,36}, {5,35}, {2,20}, {1,25}, {6,13}, {12,14}, {5,24}, {3,32}, {6,25}, {9,19}, {11,16}, {12,18}, {11,22}, {8,34}, {2,28}, {9,31}, {3,31}, {2,15}, {8,14}, {5,21}, {3,19}, {8,22}, {11,34}, {12,30}, {5,33}, {5,23}, {10,34}, {9,27}, {2,23}, {8,33}, {10,25}, {2,16}, {2,32}, {6,33}, {6,21}, {10,13}, {8,21}, {9,34}, {7,29}, {3,14}, {2,13}, {10,31}, {10,16}, {4,29}, {7,25}, {5,19}, {7,20}, {8,26}, {7,13}, {8,17}, {3,23}, {11,28}, {4,30}, {6,15}, {11,18}, {12,28}, {4,36}, {7,30}, {4,17}, {2,35}, {5,28}, {4,15}, {9,15}, {1,35}, {1,26}, {6,29}, {12,24}, {6,31}, {2,27}, {6,19}, {3,35}, {1,23}, {10,28}, {7,18}, {10,14}, {5,36}, {3,26}, {5,31}, {9,24}, {12,36}, {11,21}, {1,14}, {11,30}, {11,27}, {7,22}, {1,13}, {4,18}, {7,32}, {3,20}, {1,33}, {2,25}, {12,32}, {3,17}, {9,32}, {10,26}, {9,36}, {6,27}, {7,34}, {7,17}, {4,23}, {1,30}, {5,16}, {1,21}, {1,18}, {12,20}, {4,24}, {9,20}, {8,29}, {9,22} }; // ET36.58 // Bipartite(16,20) Valencies [10,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1920 EdgePairs[36][58]:={ {2,24}, {1,20}, {11,20}, {13,32}, {4,27}, {12,29}, {13,21}, {5,34}, {14,19}, {15,24}, {16,26}, {16,33}, {16,27}, {6,17}, {2,23}, {15,31}, {4,29}, {1,32}, {10,26}, {4,19}, {7,22}, {4,31}, {2,19}, {10,33}, {3,35}, {2,26}, {7,34}, {16,25}, {12,35}, {7,36}, {8,25}, {2,28}, {12,34}, {1,30}, {16,23}, {14,28}, {9,35}, {4,23}, {8,31}, {8,27}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {11,33}, {6,31}, {14,33}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {9,29}, {7,20}, {14,21}, {16,24}, {12,20}, {12,36}, {9,19}, {14,30}, {5,25}, {7,32}, {15,26}, {1,31}, {11,22}, {10,28}, {14,24}, {15,27}, {6,30}, {4,33}, {5,23}, {10,31}, {9,34}, {15,19}, {10,21}, {13,18}, {1,29}, {8,17}, {13,31}, {11,21}, {9,25}, {8,36}, {2,32}, {7,26}, {5,18}, {1,23}, {11,29}, {5,30}, {7,17}, {15,35}, {12,25}, {8,22}, {13,25}, {3,27}, {15,17}, {1,33}, {3,29}, {6,23}, {13,36}, {8,26}, {9,22}, {13,30}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {1,24}, {13,24}, {14,34}, {3,23}, {1,25}, {6,28}, {9,30}, {15,21}, {16,34}, {16,17}, {7,28}, {13,26}, {10,35}, {7,23}, {6,36}, {5,33}, {3,24}, {11,27}, {16,35}, {11,32}, {9,17}, {14,32}, {10,18}, {15,33}, {16,20}, {9,36}, {5,26}, {15,28}, {4,18}, {4,25}, {12,24}, {3,28}, {7,27}, {3,31}, {10,20}, {11,34}, {5,19}, {6,20}, {2,30}, {13,20}, {5,35}, {2,18}, {6,35}, {9,21}, {3,36}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29} }; // ET36.59 // Bipartite(16,20) Valencies [10,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 550376570880000 EdgePairs[36][59]:={ {10,25}, {1,20}, {5,17}, {11,20}, {13,32}, {9,28}, {2,33}, {11,36}, {4,27}, {13,21}, {11,35}, {15,24}, {16,26}, {4,26}, {4,30}, {16,27}, {8,30}, {6,17}, {12,22}, {16,31}, {15,31}, {1,32}, {10,26}, {16,19}, {4,19}, {4,31}, {10,33}, {3,35}, {5,20}, {2,26}, {1,21}, {16,18}, {12,35}, {7,36}, {12,34}, {5,32}, {16,23}, {4,23}, {8,31}, {8,27}, {13,29}, {10,22}, {6,22}, {11,28}, {10,30}, {6,29}, {16,30}, {6,21}, {2,25}, {14,33}, {2,34}, {1,17}, {4,22}, {8,19}, {9,29}, {7,20}, {14,21}, {9,32}, {15,32}, {5,29}, {14,30}, {5,25}, {7,32}, {11,31}, {15,27}, {6,30}, {10,29}, {3,20}, {15,19}, {10,21}, {6,18}, {1,29}, {3,32}, {4,35}, {9,25}, {13,33}, {6,33}, {11,23}, {15,35}, {5,24}, {8,22}, {13,25}, {8,35}, {13,28}, {15,20}, {9,20}, {1,28}, {3,27}, {1,33}, {15,36}, {13,36}, {5,28}, {8,26}, {12,26}, {16,22}, {7,31}, {2,17}, {12,27}, {14,17}, {3,19}, {14,18}, {1,24}, {12,23}, {14,22}, {13,24}, {11,24}, {12,19}, {6,26}, {12,30}, {14,34}, {8,23}, {3,23}, {5,36}, {1,25}, {16,34}, {14,25}, {7,28}, {7,23}, {2,21}, {8,34}, {5,33}, {10,17}, {3,24}, {2,29}, {11,27}, {16,35}, {2,22}, {4,34}, {10,34}, {11,32}, {9,17}, {10,18}, {6,25}, {9,33}, {9,36}, {6,34}, {8,18}, {15,28}, {4,18}, {11,19}, {3,28}, {7,27}, {15,23}, {7,24}, {3,31}, {9,24}, {12,31}, {7,35}, {5,21}, {2,30}, {13,17}, {13,20}, {2,18}, {7,19}, {9,21}, {3,36}, {12,18}, {1,36}, {14,29}, {14,26} }; // ET36.60 // Bipartite(16,20) Valencies [10,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1966080 EdgePairs[36][60]:={ {10,24}, {11,20}, {6,32}, {4,27}, {15,24}, {16,26}, {16,33}, {4,26}, {4,30}, {12,22}, {12,32}, {4,29}, {8,33}, {1,27}, {10,23}, {4,19}, {7,22}, {2,19}, {10,33}, {2,27}, {1,19}, {5,20}, {13,35}, {14,31}, {2,26}, {1,21}, {12,35}, {7,36}, {8,25}, {2,28}, {12,34}, {5,32}, {16,23}, {14,28}, {9,35}, {4,23}, {8,31}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {16,30}, {6,21}, {2,25}, {6,31}, {1,17}, {2,36}, {5,22}, {9,29}, {7,20}, {14,21}, {9,32}, {16,24}, {9,26}, {12,36}, {5,29}, {9,19}, {7,32}, {15,26}, {1,31}, {11,22}, {11,31}, {14,24}, {2,35}, {15,27}, {4,33}, {5,23}, {10,31}, {3,20}, {10,21}, {6,18}, {1,29}, {7,30}, {11,21}, {9,25}, {13,33}, {7,26}, {16,32}, {1,23}, {5,30}, {11,30}, {13,23}, {12,28}, {12,25}, {8,22}, {15,34}, {13,25}, {8,35}, {15,20}, {3,27}, {15,17}, {1,33}, {3,29}, {13,36}, {15,36}, {12,26}, {16,22}, {9,22}, {2,17}, {4,36}, {14,17}, {8,32}, {8,21}, {3,19}, {14,18}, {13,24}, {11,24}, {5,31}, {14,34}, {8,23}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {13,27}, {1,35}, {16,34}, {14,25}, {7,28}, {13,26}, {15,18}, {16,36}, {3,30}, {5,33}, {8,34}, {10,17}, {2,29}, {10,27}, {10,34}, {11,32}, {16,20}, {8,24}, {6,25}, {9,33}, {9,36}, {15,28}, {4,20}, {12,24}, {3,28}, {14,35}, {3,31}, {10,20}, {13,34}, {11,34}, {5,19}, {5,21}, {13,17}, {15,30}, {2,18}, {7,19}, {4,17}, {6,35}, {9,23}, {14,27}, {12,18}, {11,18}, {7,18} }; // ET36.61 // Bipartite(18,18) Valencies [10,10] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 8640 EdgePairs[36][61]:={ {10,25}, {1,20}, {2,24}, {9,28}, {2,33}, {6,32}, {4,27}, {12,29}, {5,34}, {14,19}, {15,24}, {16,33}, {18,29}, {4,30}, {11,25}, {16,27}, {12,32}, {16,31}, {8,33}, {1,27}, {10,23}, {17,34}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {13,35}, {2,26}, {17,24}, {16,25}, {12,35}, {7,36}, {17,21}, {18,21}, {8,25}, {12,34}, {1,30}, {5,32}, {16,23}, {4,23}, {8,27}, {18,34}, {10,22}, {10,30}, {6,29}, {16,30}, {15,29}, {6,21}, {3,34}, {6,31}, {14,33}, {2,34}, {8,19}, {9,29}, {7,20}, {14,21}, {9,32}, {15,32}, {18,20}, {12,36}, {5,29}, {14,30}, {5,25}, {15,26}, {1,31}, {11,22}, {7,25}, {14,24}, {10,28}, {17,33}, {1,22}, {4,33}, {10,31}, {3,20}, {9,34}, {13,22}, {3,32}, {4,35}, {13,33}, {2,32}, {11,29}, {5,30}, {17,30}, {15,35}, {11,30}, {17,27}, {13,23}, {12,28}, {8,22}, {13,25}, {18,24}, {15,20}, {13,28}, {9,20}, {18,26}, {1,28}, {18,36}, {4,28}, {1,33}, {6,23}, {3,26}, {15,36}, {13,36}, {18,31}, {12,26}, {16,22}, {7,31}, {13,30}, {8,32}, {8,21}, {12,23}, {14,22}, {11,24}, {17,25}, {6,26}, {17,29}, {3,21}, {6,28}, {18,23}, {1,35}, {15,21}, {14,25}, {7,28}, {11,26}, {10,35}, {7,23}, {13,19}, {16,36}, {2,21}, {8,34}, {5,33}, {3,24}, {11,27}, {16,35}, {10,27}, {2,22}, {10,36}, {11,32}, {16,20}, {14,32}, {8,24}, {9,36}, {6,34}, {5,27}, {5,26}, {15,28}, {11,19}, {10,19}, {4,25}, {4,20}, {12,24}, {3,28}, {7,27}, {15,23}, {3,31}, {9,24}, {17,26}, {7,33}, {12,31}, {11,34}, {5,19}, {6,20}, {17,22}, {5,21}, {2,30}, {13,20}, {9,31}, {7,19}, {6,35}, {9,21}, {3,36}, {18,35}, {9,23}, {8,29}, {1,36}, {14,29}, {14,26} }; // ET36.62 // Non-bipartite Valency 10 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[36][62]:={ {11,20}, {2,33}, {6,32}, {7,15}, {4,24}, {15,24}, {18,29}, {3,22}, {23,29}, {23,27}, {1,10}, {16,27}, {26,31}, {6,17}, {1,13}, {12,22}, {12,32}, {16,31}, {4,29}, {10,23}, {10,26}, {17,20}, {2,15}, {16,19}, {7,22}, {25,33}, {1,19}, {2,27}, {3,35}, {21,35}, {13,35}, {24,30}, {22,32}, {16,25}, {2,9}, {7,36}, {17,21}, {8,25}, {27,33}, {2,14}, {1,30}, {16,23}, {6,11}, {9,35}, {20,30}, {28,35}, {13,29}, {18,34}, {3,18}, {8,16}, {23,32}, {19,33}, {3,34}, {14,33}, {1,7}, {14,21}, {14,36}, {15,32}, {9,27}, {28,34}, {29,36}, {19,29}, {14,30}, {6,8}, {11,13}, {15,26}, {1,31}, {3,12}, {10,28}, {14,24}, {11,31}, {22,27}, {17,33}, {1,22}, {4,33}, {5,23}, {4,21}, {21,26}, {13,22}, {2,20}, {7,30}, {11,21}, {9,25}, {7,26}, {2,32}, {5,18}, {30,35}, {11,29}, {6,24}, {17,30}, {7,17}, {5,7}, {13,23}, {12,28}, {13,25}, {27,36}, {8,35}, {15,20}, {9,20}, {4,15}, {1,28}, {18,27}, {24,34}, {21,31}, {26,34}, {3,10}, {3,26}, {15,36}, {5,28}, {18,31}, {29,32}, {12,33}, {4,36}, {17,28}, {9,13}, {5,12}, {22,25}, {25,32}, {8,21}, {4,9}, {5,31}, {6,27}, {12,19}, {12,30}, {3,23}, {18,19}, {10,32}, {12,14}, {19,36}, {12,15}, {6,14}, {20,35}, {3,16}, {11,16}, {7,23}, {6,36}, {2,21}, {3,30}, {8,34}, {9,18}, {10,17}, {20,26}, {2,29}, {11,27}, {16,35}, {20,34}, {23,33}, {10,36}, {1,16}, {18,22}, {8,24}, {6,25}, {19,25}, {5,26}, {8,18}, {15,28}, {10,19}, {4,25}, {4,11}, {5,13}, {9,24}, {2,8}, {30,31}, {7,33}, {13,34}, {10,14}, {11,34}, {5,19}, {6,20}, {5,35}, {22,36}, {9,31}, {1,34}, {21,28}, {4,17}, {17,32}, {8,29}, {24,28}, {24,31}, {14,26} }; // ET36.63 // Non-bipartite Valency 10 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[36][63]:={ {1,11}, {9,28}, {25,31}, {6,16}, {17,36}, {11,36}, {12,29}, {11,35}, {5,34}, {4,26}, {23,27}, {1,10}, {4,30}, {3,13}, {8,33}, {24,27}, {1,27}, {23,28}, {17,20}, {2,19}, {10,33}, {1,19}, {5,20}, {13,35}, {14,31}, {26,33}, {29,35}, {7,34}, {1,21}, {12,35}, {11,14}, {2,9}, {18,21}, {8,25}, {2,28}, {16,23}, {8,15}, {20,30}, {4,23}, {16,29}, {10,22}, {6,22}, {3,18}, {11,28}, {16,30}, {6,31}, {14,33}, {1,17}, {4,22}, {19,26}, {12,17}, {22,34}, {12,36}, {5,29}, {8,14}, {19,29}, {14,30}, {6,8}, {11,15}, {15,26}, {7,13}, {7,25}, {14,24}, {30,34}, {2,35}, {15,27}, {20,33}, {10,29}, {3,20}, {9,34}, {13,22}, {15,19}, {24,32}, {2,13}, {4,35}, {7,16}, {23,35}, {7,26}, {2,32}, {16,32}, {11,23}, {21,25}, {11,30}, {15,35}, {5,24}, {5,7}, {15,34}, {13,25}, {15,20}, {13,28}, {19,31}, {18,26}, {9,20}, {18,27}, {3,11}, {4,7}, {26,36}, {1,33}, {10,13}, {18,33}, {6,23}, {3,10}, {22,29}, {3,26}, {30,32}, {5,28}, {8,26}, {18,31}, {9,22}, {7,31}, {6,15}, {25,35}, {17,28}, {12,27}, {5,12}, {8,32}, {8,21}, {28,36}, {14,22}, {13,24}, {17,25}, {6,27}, {28,33}, {10,32}, {21,30}, {20,25}, {17,19}, {1,25}, {6,9}, {27,32}, {18,23}, {9,30}, {16,21}, {20,35}, {19,32}, {22,26}, {16,36}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {3,24}, {2,29}, {10,27}, {23,33}, {4,14}, {29,31}, {9,17}, {8,24}, {6,25}, {11,19}, {4,12}, {12,24}, {21,36}, {3,31}, {21,34}, {1,14}, {2,8}, {10,20}, {5,15}, {13,34}, {2,18}, {22,36}, {27,34}, {9,31}, {1,34}, {7,19}, {4,17}, {17,32}, {3,36}, {4,32}, {12,18}, {24,28}, {24,31}, {12,21}, {14,29}, {10,16}, {5,16} }; // ET36.64 // Non-bipartite Valency 10 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1036800 EdgePairs[36][64]:={ {10,24}, {1,20}, {13,32}, {11,36}, {11,35}, {14,19}, {15,24}, {18,29}, {3,22}, {23,27}, {11,25}, {8,30}, {1,13}, {12,32}, {3,9}, {29,33}, {3,6}, {3,15}, {19,24}, {17,34}, {25,33}, {5,20}, {24,30}, {22,32}, {1,21}, {16,18}, {2,9}, {18,21}, {27,33}, {1,30}, {14,28}, {20,30}, {9,35}, {4,23}, {8,27}, {16,29}, {32,36}, {3,17}, {19,28}, {6,21}, {3,34}, {7,12}, {14,23}, {31,33}, {2,34}, {1,18}, {27,28}, {16,24}, {19,30}, {22,34}, {25,36}, {26,27}, {28,34}, {27,29}, {29,36}, {14,30}, {19,22}, {5,25}, {7,32}, {17,23}, {15,26}, {3,12}, {11,22}, {7,13}, {14,24}, {6,12}, {12,13}, {20,33}, {23,26}, {4,33}, {21,26}, {10,31}, {27,31}, {1,2}, {9,34}, {15,19}, {2,13}, {2,20}, {26,35}, {29,34}, {28,29}, {1,29}, {13,31}, {23,35}, {6,33}, {14,15}, {11,23}, {7,17}, {8,11}, {5,24}, {8,13}, {9,10}, {8,35}, {17,18}, {7,14}, {4,7}, {18,36}, {10,13}, {10,12}, {2,3}, {3,26}, {24,35}, {8,26}, {12,26}, {9,22}, {31,34}, {7,31}, {6,15}, {13,30}, {2,17}, {4,6}, {22,25}, {25,32}, {14,17}, {33,34}, {14,18}, {6,26}, {28,33}, {21,29}, {8,23}, {10,32}, {20,25}, {3,21}, {19,36}, {12,15}, {18,23}, {4,5}, {15,21}, {16,21}, {19,32}, {28,30}, {11,26}, {10,35}, {16,36}, {7,23}, {5,33}, {16,35}, {11,27}, {2,22}, {1,16}, {4,14}, {29,31}, {11,32}, {9,17}, {6,25}, {31,32}, {27,35}, {5,10}, {19,25}, {15,28}, {4,18}, {5,9}, {11,19}, {4,25}, {1,8}, {4,20}, {8,20}, {7,10}, {28,31}, {5,6}, {21,36}, {9,24}, {2,8}, {12,31}, {6,20}, {17,22}, {2,30}, {15,30}, {13,20}, {5,35}, {22,36}, {27,34}, {4,17}, {9,16}, {24,28}, {12,21}, {1,36}, {7,18}, {10,16}, {5,16} }; // ET36.65 // Bipartite(9,27) Valencies [12,4] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1296 EdgePairs[36][65]:={ {1,15}, {4,35}, {9,13}, {5,32}, {8,24}, {6,10}, {6,18}, {1,11}, {9,30}, {3,29}, {2,22}, {5,30}, {6,36}, {1,31}, {4,27}, {2,11}, {8,36}, {7,24}, {6,23}, {2,20}, {5,34}, {1,25}, {9,12}, {2,33}, {6,32}, {9,19}, {9,21}, {3,30}, {7,23}, {8,34}, {9,31}, {3,31}, {2,19}, {9,10}, {8,14}, {8,13}, {7,11}, {6,22}, {4,12}, {3,18}, {8,22}, {2,14}, {5,33}, {4,20}, {6,11}, {2,23}, {1,10}, {7,26}, {8,28}, {1,17}, {2,16}, {1,16}, {6,21}, {8,10}, {2,17}, {4,33}, {4,28}, {7,29}, {5,19}, {9,23}, {5,15}, {8,26}, {7,13}, {5,29}, {7,14}, {4,31}, {9,25}, {4,15}, {9,15}, {1,26}, {7,35}, {3,35}, {5,27}, {8,27}, {7,18}, {2,12}, {3,28}, {5,36}, {8,16}, {5,17}, {3,24}, {3,12}, {6,16}, {4,32}, {1,20}, {1,13}, {7,32}, {3,25}, {2,26}, {3,20}, {7,21}, {1,33}, {9,14}, {3,36}, {3,17}, {6,35}, {5,18}, {4,34}, {6,27}, {7,34}, {2,30}, {1,21}, {5,25}, {4,19}, {4,24}, {8,29}, {6,28}, {9,22} }; // ET36.66 // Bipartite(9,27) Valencies [12,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 725594112 EdgePairs[36][66]:={ {9,13}, {7,19}, {5,32}, {5,14}, {8,24}, {1,11}, {9,30}, {3,29}, {6,14}, {5,30}, {4,27}, {6,17}, {2,11}, {6,23}, {2,20}, {1,25}, {4,16}, {6,13}, {9,12}, {3,32}, {2,33}, {6,32}, {7,31}, {6,25}, {7,27}, {9,21}, {3,10}, {9,31}, {3,31}, {6,34}, {2,18}, {2,15}, {8,14}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {8,15}, {7,28}, {1,34}, {7,10}, {5,23}, {3,11}, {1,10}, {8,33}, {1,17}, {3,13}, {1,16}, {2,36}, {8,21}, {2,17}, {4,33}, {4,28}, {9,34}, {3,14}, {3,22}, {8,35}, {8,26}, {7,13}, {8,17}, {3,23}, {5,29}, {6,26}, {1,19}, {4,36}, {7,30}, {2,35}, {9,25}, {4,15}, {4,25}, {9,15}, {1,35}, {1,26}, {2,24}, {6,31}, {9,33}, {2,27}, {5,27}, {7,18}, {5,20}, {8,32}, {3,28}, {5,36}, {9,24}, {8,23}, {6,16}, {1,20}, {5,11}, {7,22}, {4,18}, {2,26}, {3,20}, {7,21}, {5,12}, {1,28}, {6,35}, {5,18}, {8,30}, {4,34}, {9,16}, {7,36}, {7,12}, {4,19}, {4,10}, {4,24}, {8,12}, {9,22} }; // ET36.67 // Bipartite(12,24) Valencies [12,6] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[36][67]:={ {9,13}, {5,14}, {10,21}, {12,26}, {10,22}, {6,18}, {4,14}, {9,30}, {2,22}, {5,30}, {6,36}, {1,31}, {12,16}, {10,27}, {6,23}, {11,29}, {1,25}, {6,13}, {12,17}, {7,33}, {12,31}, {12,14}, {12,22}, {5,24}, {3,32}, {2,33}, {7,27}, {9,19}, {9,21}, {12,18}, {3,30}, {1,32}, {8,34}, {3,34}, {12,25}, {3,31}, {6,34}, {2,18}, {4,26}, {8,13}, {3,19}, {8,15}, {12,21}, {5,33}, {5,23}, {9,27}, {2,23}, {10,36}, {8,28}, {2,32}, {6,33}, {1,16}, {2,17}, {8,21}, {4,28}, {7,29}, {2,13}, {10,15}, {10,16}, {7,25}, {10,24}, {5,15}, {7,20}, {8,17}, {7,14}, {4,31}, {11,28}, {3,27}, {2,34}, {4,30}, {6,15}, {1,19}, {11,18}, {7,30}, {2,35}, {12,29}, {4,15}, {9,15}, {10,29}, {1,35}, {8,19}, {11,26}, {6,29}, {11,14}, {7,35}, {12,23}, {5,22}, {2,27}, {11,36}, {1,23}, {2,21}, {5,27}, {9,35}, {10,28}, {11,19}, {7,18}, {4,22}, {3,28}, {11,31}, {5,36}, {3,26}, {3,24}, {5,31}, {8,16}, {8,20}, {6,16}, {10,17}, {1,20}, {11,32}, {1,13}, {4,18}, {3,25}, {8,25}, {2,26}, {10,32}, {11,20}, {1,33}, {9,14}, {3,17}, {6,35}, {6,24}, {9,32}, {8,30}, {9,36}, {10,26}, {4,34}, {7,34}, {3,33}, {7,36}, {7,17}, {4,23}, {11,24}, {5,16}, {11,35}, {4,13}, {1,21}, {12,20}, {5,25}, {4,19}, {9,20}, {1,24}, {8,29}, {6,28}, {9,22} }; // ET36.68 // Bipartite(12,24) Valencies [12,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 2304 EdgePairs[36][68]:={ {4,35}, {10,19}, {11,15}, {5,14}, {8,24}, {6,18}, {4,14}, {9,30}, {6,17}, {12,16}, {10,27}, {8,36}, {6,23}, {4,16}, {6,13}, {7,33}, {12,14}, {5,24}, {3,32}, {2,33}, {6,32}, {12,33}, {9,19}, {11,16}, {1,32}, {12,27}, {7,23}, {7,15}, {5,13}, {8,34}, {3,34}, {3,31}, {2,19}, {5,26}, {9,17}, {10,23}, {3,19}, {8,22}, {12,21}, {12,30}, {2,14}, {5,33}, {10,34}, {2,31}, {2,23}, {8,28}, {1,36}, {1,17}, {3,13}, {1,16}, {6,21}, {12,34}, {2,36}, {2,17}, {4,28}, {7,29}, {2,13}, {10,15}, {10,31}, {4,29}, {7,25}, {3,22}, {9,23}, {10,24}, {5,15}, {7,20}, {8,35}, {8,26}, {7,13}, {8,17}, {5,29}, {4,31}, {11,28}, {2,34}, {6,15}, {1,19}, {11,18}, {4,36}, {4,21}, {7,30}, {4,17}, {12,29}, {12,35}, {9,25}, {4,25}, {9,15}, {1,26}, {6,29}, {12,24}, {6,31}, {9,33}, {5,22}, {2,27}, {2,21}, {9,35}, {10,28}, {11,19}, {5,20}, {4,22}, {8,32}, {10,14}, {3,28}, {3,26}, {5,31}, {11,25}, {12,36}, {8,23}, {9,26}, {11,21}, {11,30}, {9,18}, {11,27}, {1,27}, {7,22}, {11,32}, {3,16}, {1,13}, {4,18}, {7,32}, {3,25}, {3,20}, {7,21}, {11,20}, {1,33}, {2,25}, {9,14}, {3,36}, {10,20}, {6,24}, {5,18}, {8,30}, {10,26}, {6,27}, {10,35}, {7,34}, {1,30}, {5,16}, {11,35}, {1,18}, {12,20}, {1,24}, {8,29}, {6,28}, {9,22} }; // ET36.69 // Bipartite(12,24) Valencies [12,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2786281390080000 EdgePairs[36][69]:={ {4,35}, {9,13}, {7,19}, {5,32}, {11,15}, {10,21}, {3,15}, {8,31}, {12,26}, {10,22}, {6,18}, {11,23}, {4,14}, {12,19}, {2,22}, {6,14}, {4,27}, {6,17}, {7,24}, {1,25}, {6,13}, {12,15}, {12,31}, {12,14}, {12,22}, {5,24}, {3,32}, {2,33}, {7,31}, {6,25}, {7,27}, {9,21}, {11,16}, {12,18}, {1,32}, {12,27}, {7,23}, {7,15}, {5,13}, {8,34}, {3,31}, {6,34}, {2,18}, {8,14}, {4,26}, {9,17}, {10,18}, {6,22}, {5,21}, {2,29}, {3,19}, {10,30}, {1,29}, {8,22}, {7,28}, {8,15}, {12,30}, {2,14}, {5,33}, {10,34}, {1,36}, {1,17}, {10,25}, {6,33}, {1,16}, {6,21}, {12,34}, {10,13}, {2,17}, {8,18}, {2,13}, {7,20}, {8,35}, {8,26}, {3,23}, {5,29}, {4,31}, {11,28}, {3,27}, {2,34}, {4,30}, {6,26}, {10,33}, {5,28}, {12,35}, {9,25}, {4,15}, {10,29}, {8,19}, {6,29}, {7,35}, {12,23}, {9,33}, {11,36}, {3,35}, {2,21}, {6,30}, {8,27}, {11,19}, {5,20}, {4,22}, {9,28}, {10,14}, {3,28}, {11,31}, {5,36}, {3,24}, {5,17}, {9,24}, {8,23}, {7,16}, {10,17}, {11,27}, {1,20}, {11,32}, {3,16}, {1,13}, {4,18}, {7,32}, {9,29}, {2,26}, {3,20}, {11,20}, {1,33}, {2,25}, {1,28}, {3,36}, {9,32}, {8,30}, {9,36}, {10,26}, {4,34}, {9,16}, {7,36}, {4,23}, {11,24}, {5,16}, {11,35}, {2,30}, {1,21}, {5,25}, {4,19}, {9,20}, {1,24} }; // ET36.70 // Bipartite(12,24) Valencies [12,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 412782428160000 EdgePairs[36][70]:={ {9,13}, {5,32}, {11,15}, {3,15}, {8,31}, {10,22}, {11,23}, {4,14}, {3,29}, {2,22}, {6,36}, {6,17}, {12,16}, {5,35}, {1,25}, {4,16}, {6,13}, {12,17}, {7,33}, {5,24}, {6,32}, {6,25}, {12,33}, {9,19}, {9,21}, {11,16}, {8,34}, {9,31}, {12,25}, {3,31}, {2,19}, {2,18}, {2,15}, {8,14}, {4,26}, {9,17}, {10,18}, {3,19}, {10,30}, {1,29}, {8,22}, {8,15}, {12,21}, {1,34}, {2,14}, {5,23}, {4,20}, {10,34}, {9,27}, {2,31}, {2,23}, {10,36}, {7,26}, {1,17}, {3,13}, {1,22}, {6,33}, {6,21}, {8,18}, {4,28}, {7,29}, {10,16}, {7,25}, {5,19}, {9,23}, {10,24}, {5,15}, {8,35}, {8,26}, {7,13}, {3,23}, {7,14}, {11,28}, {3,27}, {2,34}, {4,30}, {12,28}, {4,36}, {7,30}, {2,35}, {5,28}, {12,29}, {9,25}, {9,15}, {1,26}, {8,19}, {6,29}, {12,24}, {9,33}, {2,27}, {11,36}, {3,35}, {5,27}, {8,27}, {9,35}, {10,28}, {11,19}, {7,18}, {5,20}, {4,22}, {10,14}, {11,31}, {5,36}, {5,31}, {12,36}, {8,23}, {6,16}, {6,20}, {3,21}, {1,14}, {11,27}, {4,32}, {7,22}, {11,32}, {1,13}, {4,18}, {3,25}, {9,29}, {2,26}, {10,32}, {7,21}, {11,20}, {1,33}, {12,32}, {3,17}, {10,20}, {6,24}, {8,30}, {10,26}, {4,34}, {7,34}, {3,33}, {7,17}, {11,24}, {1,30}, {5,16}, {11,35}, {2,30}, {1,21}, {1,18}, {12,20}, {4,24}, {12,13}, {6,28} }; // ET36.71 // Bipartite(12,24) Valencies [12,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5944066965504 EdgePairs[36][71]:={ {1,15}, {4,35}, {9,13}, {10,19}, {11,15}, {3,15}, {11,17}, {8,24}, {10,22}, {11,23}, {9,30}, {3,29}, {2,22}, {6,14}, {5,30}, {11,33}, {1,31}, {12,16}, {8,36}, {11,29}, {2,20}, {1,25}, {4,16}, {6,13}, {12,17}, {7,33}, {12,22}, {5,24}, {3,32}, {6,32}, {6,25}, {7,27}, {9,19}, {9,21}, {12,18}, {7,23}, {7,15}, {5,13}, {8,34}, {2,28}, {9,31}, {6,34}, {2,19}, {6,22}, {5,21}, {8,22}, {12,30}, {2,14}, {5,33}, {10,34}, {9,27}, {2,31}, {7,26}, {8,28}, {1,36}, {10,25}, {2,16}, {2,32}, {12,34}, {10,13}, {8,18}, {4,28}, {7,29}, {3,14}, {2,13}, {10,31}, {4,29}, {10,16}, {5,19}, {5,15}, {7,20}, {8,35}, {3,23}, {8,17}, {7,14}, {3,27}, {2,34}, {4,30}, {6,26}, {1,19}, {12,28}, {4,36}, {4,17}, {12,29}, {12,35}, {9,25}, {9,15}, {11,26}, {11,14}, {7,35}, {12,24}, {12,23}, {6,31}, {9,33}, {6,19}, {3,35}, {5,27}, {10,28}, {4,22}, {10,14}, {5,36}, {3,26}, {8,16}, {5,31}, {9,24}, {12,36}, {8,23}, {6,16}, {6,20}, {11,21}, {3,21}, {9,18}, {11,27}, {1,27}, {11,32}, {1,13}, {4,18}, {7,32}, {2,26}, {10,32}, {3,20}, {7,21}, {11,20}, {1,33}, {2,25}, {3,17}, {10,20}, {5,18}, {8,30}, {9,36}, {10,26}, {4,34}, {3,33}, {7,17}, {4,23}, {1,30}, {11,35}, {1,21}, {1,18}, {5,25}, {4,24}, {1,24}, {8,29}, {6,28} }; // ET36.72 // Bipartite(12,24) Valencies [12,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5159780352 EdgePairs[36][72]:={ {11,17}, {3,33}, {10,25}, {5,17}, {2,24}, {6,32}, {6,16}, {4,27}, {7,15}, {11,35}, {4,26}, {11,25}, {2,23}, {1,13}, {12,22}, {12,32}, {8,28}, {1,32}, {3,13}, {3,25}, {3,15}, {10,26}, {2,15}, {4,19}, {7,22}, {10,33}, {2,26}, {1,21}, {11,14}, {12,35}, {2,28}, {1,30}, {8,15}, {8,31}, {6,22}, {3,18}, {3,17}, {8,16}, {3,34}, {11,33}, {2,34}, {2,36}, {5,22}, {9,29}, {9,26}, {12,20}, {12,36}, {5,29}, {5,25}, {11,13}, {7,32}, {1,31}, {11,22}, {7,13}, {10,28}, {1,22}, {6,30}, {4,33}, {12,16}, {9,34}, {2,20}, {1,29}, {7,30}, {2,16}, {11,21}, {4,35}, {9,25}, {7,16}, {8,36}, {2,32}, {1,23}, {11,29}, {6,24}, {5,30}, {11,30}, {12,28}, {5,14}, {7,14}, {4,28}, {3,29}, {3,26}, {8,26}, {7,31}, {4,36}, {9,13}, {12,27}, {8,32}, {1,24}, {6,27}, {12,19}, {12,30}, {3,23}, {8,23}, {12,14}, {3,21}, {6,19}, {7,29}, {1,15}, {6,28}, {6,14}, {10,35}, {7,23}, {6,36}, {8,34}, {5,33}, {9,18}, {10,17}, {11,27}, {10,27}, {4,34}, {10,36}, {1,16}, {10,34}, {9,17}, {10,18}, {8,24}, {2,31}, {9,33}, {5,27}, {8,18}, {4,18}, {11,19}, {10,19}, {4,25}, {4,20}, {5,13}, {8,20}, {12,24}, {7,24}, {3,31}, {1,14}, {10,20}, {5,19}, {6,20}, {5,21}, {9,15}, {5,35}, {2,18}, {9,31}, {4,17}, {6,35}, {9,21}, {9,23}, {7,21} }; // ET36.73 // Bipartite(12,24) Valencies [12,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 322486272 EdgePairs[36][73]:={ {11,17}, {3,33}, {10,25}, {2,24}, {10,24}, {9,28}, {4,27}, {7,15}, {11,35}, {5,34}, {4,24}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {12,22}, {12,32}, {4,29}, {3,25}, {3,15}, {2,15}, {4,19}, {2,19}, {10,33}, {2,27}, {5,20}, {7,34}, {1,21}, {2,28}, {12,34}, {1,30}, {8,15}, {9,35}, {8,31}, {8,27}, {3,17}, {11,33}, {6,31}, {1,17}, {2,36}, {4,22}, {8,19}, {1,18}, {3,14}, {9,27}, {12,20}, {12,36}, {5,29}, {9,19}, {8,14}, {11,15}, {7,32}, {11,13}, {7,13}, {9,14}, {10,28}, {11,31}, {2,35}, {1,22}, {12,16}, {4,21}, {10,29}, {10,21}, {2,20}, {6,18}, {1,29}, {2,16}, {3,32}, {11,21}, {4,35}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {5,18}, {11,23}, {11,29}, {12,28}, {8,22}, {8,35}, {9,20}, {4,13}, {1,33}, {10,13}, {6,23}, {5,28}, {8,26}, {12,26}, {9,22}, {7,31}, {6,15}, {6,26}, {12,30}, {3,23}, {8,23}, {10,32}, {12,14}, {5,36}, {1,25}, {7,29}, {6,28}, {9,30}, {3,16}, {7,23}, {6,36}, {3,30}, {8,34}, {10,17}, {3,24}, {11,27}, {1,26}, {10,36}, {4,14}, {9,17}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {5,27}, {5,26}, {8,18}, {11,19}, {5,13}, {12,24}, {7,24}, {3,31}, {1,14}, {10,20}, {5,19}, {6,20}, {5,21}, {5,35}, {1,34}, {7,21}, {4,32}, {12,18}, {7,18}, {10,16} }; // ET36.74 // Bipartite(12,24) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 589824 EdgePairs[36][74]:={ {3,33}, {10,25}, {1,20}, {10,24}, {6,32}, {5,34}, {4,26}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {12,22}, {4,29}, {1,32}, {8,33}, {4,19}, {7,22}, {4,31}, {2,19}, {10,33}, {5,20}, {7,34}, {7,36}, {2,28}, {12,34}, {5,32}, {8,15}, {9,35}, {4,23}, {8,27}, {10,15}, {3,18}, {6,29}, {3,17}, {6,21}, {2,25}, {11,33}, {1,17}, {5,22}, {4,22}, {3,14}, {9,32}, {9,26}, {9,27}, {12,36}, {8,14}, {11,15}, {11,13}, {11,22}, {7,13}, {9,14}, {7,25}, {11,31}, {10,28}, {2,35}, {1,22}, {12,16}, {5,23}, {10,31}, {3,20}, {10,21}, {2,13}, {2,20}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {11,21}, {4,35}, {7,16}, {2,32}, {6,33}, {6,24}, {11,30}, {12,28}, {8,35}, {5,14}, {9,20}, {1,28}, {4,13}, {10,13}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {6,15}, {2,17}, {12,27}, {8,21}, {5,31}, {6,27}, {12,19}, {12,30}, {8,23}, {3,21}, {1,25}, {12,15}, {9,30}, {7,28}, {6,36}, {3,30}, {9,18}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {4,34}, {10,36}, {1,16}, {4,14}, {2,31}, {9,36}, {5,26}, {8,18}, {11,19}, {10,19}, {4,25}, {12,24}, {7,24}, {9,24}, {1,14}, {7,33}, {12,31}, {11,34}, {5,19}, {6,20}, {9,15}, {5,35}, {1,34}, {4,17}, {6,35}, {3,36}, {9,23}, {7,21}, {8,29}, {12,18}, {11,18}, {7,18}, {10,16}, {5,16} }; // ET36.75 // Bipartite(12,24) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2359296 EdgePairs[36][75]:={ {1,15}, {4,35}, {9,13}, {10,19}, {5,32}, {11,15}, {5,14}, {8,31}, {11,23}, {9,30}, {12,19}, {3,29}, {6,36}, {1,31}, {6,17}, {4,27}, {10,27}, {6,23}, {5,34}, {7,33}, {12,31}, {12,22}, {5,24}, {3,32}, {2,33}, {7,27}, {11,16}, {12,18}, {3,30}, {11,22}, {7,23}, {7,15}, {5,13}, {3,34}, {2,19}, {2,18}, {5,26}, {8,14}, {9,17}, {5,21}, {1,29}, {3,18}, {8,15}, {7,28}, {1,34}, {11,34}, {12,30}, {2,14}, {5,33}, {2,31}, {2,23}, {10,36}, {8,28}, {1,17}, {10,25}, {1,22}, {6,33}, {6,21}, {12,34}, {10,13}, {8,18}, {2,13}, {10,15}, {10,31}, {4,29}, {7,25}, {3,22}, {10,24}, {7,20}, {8,26}, {7,13}, {11,28}, {4,30}, {1,19}, {4,17}, {2,35}, {12,35}, {9,25}, {4,15}, {4,25}, {10,29}, {1,26}, {8,19}, {11,26}, {6,29}, {11,14}, {7,35}, {12,24}, {12,23}, {6,31}, {5,22}, {6,19}, {11,36}, {2,21}, {8,27}, {5,20}, {4,22}, {8,32}, {9,28}, {3,28}, {5,36}, {8,16}, {9,24}, {12,36}, {8,20}, {7,16}, {6,16}, {9,26}, {3,21}, {1,14}, {9,18}, {10,17}, {11,27}, {1,27}, {3,16}, {4,18}, {7,32}, {9,29}, {2,26}, {10,32}, {3,20}, {7,21}, {1,33}, {2,25}, {9,14}, {12,32}, {3,17}, {10,20}, {6,35}, {6,24}, {8,30}, {9,36}, {4,34}, {9,16}, {3,33}, {4,23}, {11,24}, {11,35}, {4,13}, {1,21}, {2,30}, {12,20}, {5,25}, {6,28} }; // ET36.76 // Bipartite(12,24) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2359296 EdgePairs[36][76]:={ {11,15}, {8,24}, {8,31}, {12,26}, {10,22}, {11,23}, {12,19}, {3,29}, {5,30}, {6,36}, {4,27}, {12,16}, {10,27}, {8,36}, {5,35}, {6,23}, {2,20}, {12,17}, {7,33}, {12,31}, {12,14}, {5,24}, {3,32}, {2,33}, {6,32}, {12,33}, {9,21}, {11,16}, {12,18}, {1,32}, {7,23}, {5,13}, {8,34}, {2,19}, {2,15}, {8,14}, {9,17}, {8,22}, {12,21}, {1,34}, {12,30}, {2,14}, {5,23}, {4,20}, {10,34}, {9,27}, {2,31}, {10,36}, {8,33}, {1,36}, {3,13}, {10,25}, {1,22}, {2,32}, {1,16}, {10,13}, {8,21}, {9,34}, {2,13}, {10,15}, {4,29}, {7,25}, {5,19}, {9,23}, {10,24}, {7,20}, {8,35}, {8,26}, {7,13}, {5,29}, {4,31}, {11,28}, {4,30}, {6,15}, {11,18}, {12,28}, {7,30}, {4,17}, {12,29}, {4,15}, {9,15}, {10,29}, {1,26}, {8,19}, {11,26}, {11,14}, {7,35}, {6,31}, {9,33}, {11,13}, {2,27}, {6,19}, {2,21}, {9,35}, {7,18}, {4,22}, {9,28}, {10,14}, {3,28}, {5,36}, {3,24}, {5,17}, {5,31}, {11,25}, {8,23}, {6,16}, {6,20}, {3,21}, {1,14}, {11,30}, {10,17}, {11,27}, {4,32}, {1,20}, {7,22}, {3,16}, {4,18}, {7,32}, {3,25}, {9,29}, {2,26}, {3,20}, {7,21}, {2,25}, {1,28}, {3,36}, {3,17}, {6,35}, {6,24}, {5,18}, {10,26}, {4,34}, {6,27}, {9,16}, {7,34}, {3,33}, {1,30}, {11,35}, {1,18}, {5,25}, {4,19}, {1,24}, {6,28}, {9,22} }; // ET36.77 // Bipartite(18,18) Valencies [12,12] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 10368 EdgePairs[36][77]:={ {10,25}, {1,20}, {2,24}, {10,24}, {11,20}, {13,32}, {2,33}, {11,36}, {12,29}, {11,35}, {4,24}, {16,33}, {4,26}, {3,22}, {18,32}, {4,30}, {16,27}, {8,30}, {12,22}, {12,32}, {8,28}, {16,31}, {4,29}, {1,32}, {3,25}, {10,23}, {10,26}, {17,34}, {4,19}, {16,19}, {7,22}, {2,19}, {10,33}, {2,27}, {1,19}, {3,35}, {5,20}, {13,35}, {2,26}, {14,31}, {7,34}, {1,21}, {17,24}, {16,25}, {12,35}, {18,21}, {8,25}, {2,28}, {12,34}, {1,30}, {5,32}, {9,35}, {4,23}, {8,31}, {13,29}, {16,29}, {15,25}, {11,28}, {10,30}, {6,29}, {6,21}, {3,34}, {2,25}, {14,23}, {6,31}, {14,33}, {2,36}, {5,22}, {4,22}, {8,19}, {9,29}, {7,20}, {9,32}, {14,21}, {15,32}, {9,26}, {18,20}, {9,27}, {12,20}, {9,19}, {14,30}, {5,25}, {15,26}, {17,23}, {1,31}, {11,22}, {7,25}, {10,28}, {14,24}, {17,33}, {6,30}, {5,23}, {10,31}, {13,22}, {15,19}, {10,21}, {2,20}, {13,31}, {18,30}, {11,21}, {4,35}, {8,36}, {6,33}, {2,32}, {7,26}, {1,23}, {11,29}, {17,30}, {11,30}, {5,24}, {12,25}, {8,22}, {15,34}, {13,25}, {18,24}, {8,35}, {13,28}, {15,20}, {9,20}, {18,26}, {18,27}, {3,27}, {18,36}, {4,28}, {1,33}, {3,29}, {13,36}, {15,36}, {17,31}, {16,22}, {12,33}, {13,30}, {17,28}, {8,32}, {8,21}, {12,23}, {13,24}, {6,27}, {5,31}, {17,25}, {12,19}, {6,26}, {3,23}, {8,23}, {14,34}, {10,32}, {17,29}, {5,36}, {3,21}, {17,19}, {6,19}, {7,29}, {6,28}, {18,23}, {9,30}, {13,27}, {1,35}, {14,20}, {15,21}, {16,34}, {16,21}, {7,28}, {11,26}, {7,23}, {13,19}, {16,36}, {6,36}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {11,27}, {16,35}, {18,28}, {10,27}, {1,26}, {2,22}, {4,34}, {10,36}, {15,22}, {18,22}, {15,33}, {16,20}, {6,25}, {9,33}, {9,36}, {6,34}, {5,27}, {15,28}, {11,19}, {4,20}, {12,24}, {3,28}, {7,27}, {14,35}, {15,23}, {7,24}, {3,31}, {9,24}, {17,26}, {7,33}, {12,31}, {11,34}, {5,21}, {5,35}, {9,31}, {1,34}, {17,32}, {18,35}, {7,21}, {14,27}, {4,32}, {1,36}, {14,29}, {14,26} }; // ET36.78 // Bipartite(18,18) Valencies [12,12] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 4320 EdgePairs[36][78]:={ {10,24}, {1,20}, {2,24}, {2,33}, {6,32}, {11,36}, {4,27}, {12,29}, {13,21}, {5,34}, {4,24}, {14,19}, {15,24}, {3,22}, {18,32}, {4,30}, {11,25}, {16,27}, {8,30}, {2,23}, {12,32}, {8,28}, {16,31}, {15,31}, {4,29}, {3,25}, {10,23}, {10,26}, {17,20}, {17,34}, {4,19}, {16,19}, {4,31}, {2,19}, {2,27}, {5,20}, {13,35}, {2,26}, {14,31}, {7,34}, {16,25}, {12,35}, {7,36}, {17,21}, {18,21}, {8,25}, {12,34}, {1,30}, {5,32}, {16,23}, {9,35}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {16,29}, {10,22}, {6,22}, {15,25}, {3,34}, {11,33}, {2,34}, {14,33}, {5,22}, {8,19}, {7,20}, {9,32}, {14,21}, {15,32}, {16,24}, {12,20}, {5,29}, {9,19}, {5,25}, {15,26}, {17,23}, {1,31}, {11,22}, {7,25}, {11,31}, {10,28}, {2,35}, {17,33}, {1,22}, {15,27}, {4,33}, {4,21}, {10,31}, {3,20}, {9,34}, {13,22}, {10,21}, {1,29}, {18,30}, {3,32}, {11,21}, {7,26}, {6,33}, {2,32}, {1,23}, {11,29}, {5,30}, {17,30}, {11,30}, {5,24}, {17,27}, {13,23}, {12,28}, {12,25}, {8,22}, {15,34}, {18,24}, {13,28}, {15,20}, {9,20}, {18,26}, {1,28}, {3,27}, {18,36}, {4,28}, {1,33}, {18,33}, {6,23}, {13,36}, {15,36}, {8,26}, {18,31}, {16,22}, {9,22}, {12,33}, {13,30}, {4,36}, {17,28}, {8,32}, {3,19}, {12,23}, {14,22}, {13,24}, {6,27}, {5,31}, {12,19}, {6,26}, {12,30}, {8,23}, {18,19}, {10,32}, {18,25}, {17,29}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {1,35}, {14,20}, {16,34}, {14,25}, {7,28}, {13,26}, {11,26}, {10,35}, {13,19}, {16,36}, {6,36}, {2,21}, {3,30}, {3,24}, {2,29}, {11,27}, {16,35}, {18,28}, {10,27}, {1,26}, {10,36}, {14,32}, {15,33}, {16,20}, {8,24}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {5,26}, {11,19}, {4,20}, {12,24}, {3,28}, {7,27}, {14,35}, {15,23}, {7,24}, {10,20}, {17,26}, {7,33}, {13,34}, {11,34}, {7,35}, {17,22}, {5,21}, {15,30}, {5,35}, {9,31}, {6,35}, {17,32}, {9,21}, {3,36}, {18,35}, {9,23}, {7,21}, {14,27}, {8,29}, {1,36}, {14,29} }; // ET36.79 // Bipartite(18,18) Valencies [12,12] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 1671768834048000000 EdgePairs[36][79]:={ {3,33}, {10,25}, {10,24}, {11,20}, {6,32}, {17,35}, {4,27}, {12,29}, {13,21}, {11,35}, {5,34}, {4,24}, {14,19}, {15,24}, {16,33}, {18,29}, {18,32}, {4,30}, {11,25}, {16,27}, {2,23}, {12,32}, {8,28}, {16,31}, {1,27}, {17,20}, {17,34}, {4,19}, {16,19}, {7,22}, {4,31}, {2,19}, {10,33}, {1,19}, {3,35}, {5,20}, {2,26}, {14,31}, {7,34}, {1,21}, {16,25}, {12,35}, {7,36}, {18,21}, {8,25}, {2,28}, {1,30}, {5,32}, {9,35}, {14,28}, {8,31}, {10,22}, {11,28}, {10,30}, {6,29}, {16,30}, {15,29}, {6,21}, {2,25}, {14,23}, {2,34}, {5,22}, {4,22}, {8,19}, {9,29}, {9,32}, {15,32}, {16,24}, {9,26}, {18,20}, {9,27}, {12,20}, {12,36}, {5,29}, {5,25}, {15,26}, {17,23}, {1,31}, {11,22}, {7,25}, {11,31}, {10,28}, {2,35}, {1,22}, {15,27}, {6,30}, {4,33}, {5,23}, {4,21}, {10,31}, {3,20}, {13,22}, {10,21}, {2,20}, {7,30}, {13,31}, {18,30}, {3,32}, {2,32}, {6,33}, {13,33}, {11,23}, {11,29}, {6,24}, {15,35}, {8,22}, {13,25}, {18,24}, {8,35}, {13,28}, {15,20}, {9,20}, {18,26}, {1,28}, {18,27}, {3,27}, {18,36}, {4,28}, {1,33}, {18,33}, {3,29}, {6,23}, {3,26}, {5,28}, {13,36}, {15,36}, {8,26}, {17,31}, {12,26}, {16,22}, {7,31}, {12,33}, {13,30}, {4,36}, {17,28}, {12,27}, {8,32}, {1,24}, {12,23}, {14,22}, {5,31}, {6,27}, {13,24}, {17,25}, {6,26}, {12,30}, {3,23}, {8,23}, {14,34}, {17,29}, {3,21}, {17,19}, {1,25}, {18,23}, {9,30}, {13,27}, {14,20}, {15,21}, {16,34}, {14,25}, {16,21}, {7,28}, {11,26}, {13,19}, {16,36}, {6,36}, {3,30}, {8,34}, {3,24}, {2,29}, {10,27}, {2,22}, {4,34}, {10,36}, {10,34}, {11,32}, {14,32}, {15,33}, {2,31}, {9,33}, {9,36}, {5,26}, {11,19}, {10,19}, {4,25}, {12,24}, {8,20}, {7,27}, {14,35}, {15,23}, {7,24}, {9,24}, {17,26}, {7,33}, {11,34}, {13,34}, {5,19}, {6,20}, {17,22}, {15,30}, {5,35}, {1,34}, {7,19}, {6,35}, {17,32}, {9,21}, {3,36}, {16,28}, {18,35}, {9,23}, {7,21}, {8,29}, {12,21}, {1,36}, {14,29}, {14,26} }; // ET36.80 // Bipartite(18,18) Valencies [12,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1719926784 EdgePairs[36][80]:={ {3,33}, {10,25}, {1,20}, {10,24}, {11,20}, {11,36}, {17,36}, {12,29}, {13,21}, {5,34}, {4,24}, {14,19}, {15,24}, {16,33}, {18,29}, {3,22}, {11,25}, {8,30}, {2,23}, {8,28}, {16,31}, {15,31}, {4,29}, {3,25}, {10,23}, {17,20}, {17,34}, {4,19}, {16,19}, {7,22}, {4,31}, {2,19}, {10,33}, {2,27}, {1,19}, {3,35}, {5,20}, {13,35}, {2,26}, {14,31}, {1,21}, {16,25}, {12,35}, {17,21}, {18,21}, {2,28}, {12,34}, {1,30}, {5,32}, {16,23}, {9,35}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {16,29}, {18,34}, {10,22}, {15,25}, {11,28}, {6,29}, {6,21}, {3,34}, {14,23}, {2,36}, {4,22}, {8,19}, {7,20}, {9,32}, {14,21}, {14,36}, {15,32}, {16,24}, {9,26}, {18,20}, {9,27}, {12,20}, {12,36}, {5,29}, {14,30}, {5,25}, {15,26}, {17,23}, {1,31}, {10,28}, {2,35}, {1,22}, {15,27}, {6,30}, {4,33}, {5,23}, {10,29}, {10,31}, {9,34}, {13,22}, {1,29}, {7,30}, {13,31}, {18,30}, {3,32}, {11,21}, {9,25}, {8,36}, {6,33}, {2,32}, {7,26}, {13,33}, {16,32}, {11,23}, {11,29}, {6,24}, {5,30}, {17,30}, {11,30}, {15,35}, {17,27}, {12,25}, {8,22}, {15,34}, {18,24}, {8,35}, {13,28}, {18,26}, {1,28}, {18,27}, {3,27}, {18,36}, {4,28}, {1,33}, {18,33}, {3,26}, {5,28}, {15,36}, {8,26}, {12,26}, {16,22}, {9,22}, {7,31}, {12,33}, {13,30}, {17,28}, {12,27}, {8,32}, {8,21}, {1,24}, {14,22}, {6,27}, {13,24}, {17,25}, {6,26}, {12,30}, {3,23}, {8,23}, {10,32}, {18,25}, {17,29}, {5,36}, {17,19}, {7,29}, {1,35}, {16,34}, {7,28}, {13,26}, {13,19}, {6,36}, {2,21}, {3,24}, {11,27}, {1,26}, {2,22}, {4,34}, {10,34}, {15,22}, {11,32}, {14,32}, {15,33}, {16,20}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {5,27}, {11,19}, {10,19}, {4,25}, {4,20}, {12,24}, {14,35}, {15,23}, {7,24}, {3,31}, {9,24}, {10,20}, {7,33}, {11,34}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {13,20}, {9,31}, {7,19}, {6,35}, {17,32}, {3,36}, {16,28}, {18,35}, {9,23}, {7,21}, {14,27}, {4,32}, {12,21}, {14,26} }; // ET36.81 // Bipartite(18,18) Valencies [12,12] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 56623104 EdgePairs[36][81]:={ {3,33}, {10,25}, {10,24}, {11,20}, {13,32}, {6,32}, {17,35}, {4,27}, {12,29}, {13,21}, {11,35}, {5,34}, {14,19}, {16,33}, {18,29}, {3,22}, {18,32}, {4,30}, {11,25}, {16,27}, {8,30}, {2,23}, {12,22}, {15,31}, {4,29}, {8,33}, {1,27}, {17,20}, {17,34}, {16,19}, {4,31}, {2,19}, {10,33}, {1,19}, {3,35}, {2,26}, {7,34}, {1,21}, {17,24}, {16,25}, {12,35}, {7,36}, {17,21}, {18,21}, {8,25}, {2,28}, {1,30}, {5,32}, {16,23}, {9,35}, {14,28}, {4,23}, {8,31}, {13,29}, {16,29}, {10,22}, {6,22}, {11,28}, {10,30}, {6,21}, {14,23}, {2,25}, {6,31}, {2,34}, {14,33}, {4,22}, {9,29}, {7,20}, {14,21}, {9,32}, {15,32}, {16,24}, {9,26}, {18,20}, {9,27}, {12,20}, {12,36}, {14,30}, {5,25}, {7,32}, {15,26}, {1,31}, {11,22}, {7,25}, {11,31}, {10,28}, {14,24}, {2,35}, {17,33}, {1,22}, {15,27}, {6,30}, {5,23}, {4,21}, {10,31}, {3,20}, {13,22}, {15,19}, {10,21}, {2,20}, {13,31}, {18,30}, {2,32}, {16,32}, {11,23}, {11,29}, {5,30}, {17,30}, {15,35}, {5,24}, {13,23}, {12,28}, {8,22}, {13,25}, {18,24}, {8,35}, {9,20}, {18,26}, {1,28}, {18,27}, {3,27}, {18,36}, {1,33}, {18,33}, {3,29}, {6,23}, {3,26}, {5,28}, {13,36}, {15,36}, {8,26}, {17,31}, {12,26}, {12,33}, {13,30}, {4,36}, {12,27}, {8,21}, {3,19}, {1,24}, {6,27}, {17,25}, {12,19}, {6,26}, {14,34}, {17,29}, {1,25}, {6,19}, {7,29}, {6,28}, {18,23}, {9,30}, {13,27}, {15,21}, {16,34}, {14,25}, {7,28}, {11,26}, {7,23}, {16,36}, {6,36}, {8,34}, {5,33}, {3,24}, {2,29}, {10,27}, {2,22}, {4,34}, {10,36}, {10,34}, {15,22}, {11,32}, {14,32}, {16,20}, {8,24}, {2,31}, {9,33}, {9,36}, {5,26}, {15,28}, {11,19}, {10,19}, {4,25}, {4,20}, {12,24}, {8,20}, {3,28}, {7,27}, {14,35}, {15,23}, {7,24}, {3,31}, {9,24}, {17,26}, {7,33}, {12,31}, {13,34}, {11,34}, {5,19}, {17,22}, {5,21}, {15,30}, {13,20}, {5,35}, {1,34}, {7,19}, {6,35}, {9,21}, {3,36}, {16,28}, {18,35}, {9,23}, {8,29}, {4,32}, {1,36}, {14,26} }; // ET36.82 // Non-bipartite Valency 12 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 104485552128 EdgePairs[36][82]:={ {11,17}, {3,33}, {10,25}, {1,20}, {10,24}, {13,32}, {17,35}, {11,36}, {4,27}, {12,29}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {23,27}, {4,16}, {18,32}, {11,25}, {16,27}, {8,30}, {21,32}, {6,17}, {2,23}, {12,32}, {8,28}, {15,31}, {4,29}, {3,13}, {8,33}, {3,25}, {3,15}, {2,15}, {7,22}, {2,19}, {10,33}, {2,27}, {5,20}, {2,26}, {14,31}, {7,34}, {1,21}, {16,25}, {12,35}, {8,25}, {12,34}, {1,30}, {5,32}, {9,35}, {14,28}, {8,31}, {18,34}, {6,22}, {11,28}, {10,30}, {3,17}, {8,16}, {16,30}, {23,32}, {15,29}, {11,33}, {6,31}, {2,34}, {14,33}, {9,29}, {1,18}, {9,32}, {9,26}, {19,30}, {9,27}, {12,20}, {5,29}, {9,19}, {8,14}, {22,35}, {11,15}, {7,32}, {11,13}, {15,26}, {1,31}, {23,34}, {11,22}, {7,13}, {10,28}, {11,31}, {20,31}, {2,35}, {17,33}, {23,36}, {21,27}, {20,33}, {6,30}, {12,16}, {4,21}, {10,31}, {9,34}, {10,21}, {2,13}, {24,26}, {18,30}, {4,35}, {8,36}, {6,33}, {2,32}, {7,26}, {5,18}, {16,32}, {11,23}, {7,17}, {11,30}, {15,35}, {21,25}, {5,24}, {23,25}, {13,25}, {20,28}, {5,14}, {1,28}, {18,27}, {18,36}, {1,33}, {6,23}, {22,29}, {13,36}, {24,35}, {17,31}, {12,26}, {9,22}, {6,15}, {13,30}, {2,17}, {17,28}, {20,29}, {9,13}, {12,27}, {8,21}, {3,19}, {1,24}, {22,33}, {3,23}, {18,25}, {21,30}, {12,14}, {17,29}, {1,25}, {6,19}, {22,28}, {7,29}, {19,36}, {6,28}, {22,31}, {13,27}, {16,34}, {20,35}, {19,32}, {22,26}, {7,23}, {16,36}, {6,36}, {3,30}, {20,26}, {2,29}, {2,22}, {4,34}, {10,36}, {1,16}, {4,14}, {9,17}, {10,18}, {15,33}, {8,24}, {6,25}, {5,27}, {19,25}, {5,26}, {8,18}, {4,18}, {15,28}, {11,19}, {24,29}, {4,20}, {12,24}, {8,20}, {3,28}, {7,27}, {14,35}, {21,36}, {3,31}, {21,34}, {1,14}, {10,20}, {17,26}, {10,14}, {13,34}, {7,35}, {5,21}, {9,15}, {19,34}, {6,13}, {5,35}, {7,19}, {24,33}, {3,36}, {9,23}, {4,32}, {12,18}, {19,27}, {24,28}, {24,31}, {12,21}, {1,36}, {14,29}, {14,26}, {23,30}, {10,16}, {5,16} }; // ET36.83 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1728 EdgePairs[36][83]:={ {11,17}, {3,33}, {10,25}, {2,24}, {9,28}, {25,31}, {2,33}, {4,27}, {5,34}, {14,19}, {8,12}, {16,33}, {3,22}, {23,29}, {23,27}, {18,32}, {8,30}, {26,31}, {32,35}, {2,23}, {12,32}, {3,9}, {29,33}, {16,31}, {3,6}, {20,27}, {1,32}, {32,34}, {24,27}, {23,28}, {19,24}, {10,26}, {17,20}, {16,19}, {4,19}, {25,33}, {10,33}, {3,35}, {2,4}, {25,29}, {24,30}, {25,30}, {29,35}, {17,24}, {2,9}, {21,22}, {18,21}, {8,10}, {27,33}, {16,23}, {6,11}, {8,15}, {28,35}, {13,29}, {13,16}, {9,11}, {15,16}, {3,18}, {3,17}, {3,7}, {6,21}, {3,34}, {7,12}, {11,33}, {4,10}, {2,36}, {1,7}, {26,28}, {9,29}, {1,18}, {27,28}, {7,11}, {14,21}, {19,26}, {4,8}, {18,20}, {27,30}, {1,5}, {31,35}, {2,5}, {28,34}, {29,36}, {26,29}, {14,30}, {6,8}, {11,15}, {11,13}, {1,31}, {7,13}, {9,14}, {11,31}, {30,34}, {2,35}, {1,22}, {21,27}, {6,12}, {12,16}, {13,18}, {7,30}, {24,26}, {2,16}, {2,32}, {3,4}, {30,36}, {15,35}, {21,25}, {5,7}, {12,25}, {23,25}, {8,13}, {8,22}, {18,24}, {9,10}, {13,28}, {15,20}, {7,14}, {20,22}, {4,7}, {15,17}, {10,13}, {31,36}, {18,33}, {30,32}, {15,36}, {13,36}, {17,31}, {29,32}, {16,22}, {9,22}, {2,17}, {4,36}, {12,27}, {5,12}, {22,25}, {14,17}, {33,34}, {14,18}, {1,24}, {6,26}, {28,33}, {20,23}, {14,34}, {8,23}, {3,23}, {10,32}, {12,14}, {17,19}, {22,28}, {6,9}, {26,32}, {19,36}, {27,32}, {12,15}, {18,23}, {33,36}, {15,21}, {16,21}, {20,35}, {7,28}, {11,26}, {22,26}, {7,23}, {13,19}, {6,36}, {10,17}, {20,26}, {11,27}, {20,34}, {4,34}, {1,16}, {6,25}, {5,27}, {5,10}, {19,25}, {5,26}, {15,28}, {5,9}, {4,25}, {4,11}, {1,8}, {24,29}, {4,20}, {28,31}, {14,35}, {21,36}, {7,24}, {3,31}, {21,34}, {9,24}, {2,8}, {1,6}, {30,31}, {12,31}, {13,34}, {10,14}, {19,35}, {5,19}, {6,20}, {17,22}, {21,24}, {5,21}, {9,15}, {15,30}, {13,20}, {5,35}, {22,30}, {1,34}, {19,23}, {6,35}, {17,32}, {8,29}, {12,18}, {11,18}, {1,36}, {14,29}, {10,16} }; // ET36.84 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 432 EdgePairs[36][84]:={ {11,17}, {21,23}, {10,25}, {2,24}, {9,28}, {2,33}, {7,15}, {5,34}, {14,19}, {8,12}, {16,33}, {4,26}, {23,27}, {18,32}, {11,25}, {26,31}, {32,35}, {12,32}, {30,33}, {3,9}, {8,28}, {29,33}, {3,6}, {20,27}, {23,28}, {19,24}, {17,20}, {16,19}, {4,19}, {7,22}, {25,33}, {10,33}, {28,32}, {21,35}, {25,29}, {13,35}, {24,30}, {26,33}, {29,35}, {11,14}, {21,22}, {18,21}, {8,15}, {6,11}, {13,29}, {13,16}, {10,15}, {15,16}, {32,36}, {3,17}, {3,7}, {6,21}, {3,34}, {4,10}, {2,34}, {26,28}, {1,18}, {7,11}, {14,21}, {14,36}, {19,26}, {12,17}, {16,24}, {4,8}, {18,20}, {27,30}, {1,5}, {5,11}, {31,35}, {2,5}, {28,34}, {27,29}, {29,36}, {8,14}, {14,30}, {6,8}, {5,25}, {11,13}, {17,23}, {1,31}, {7,13}, {9,14}, {11,31}, {25,28}, {22,27}, {30,34}, {2,35}, {17,33}, {24,25}, {1,22}, {12,13}, {21,26}, {10,31}, {27,31}, {13,18}, {7,30}, {24,26}, {3,32}, {4,35}, {2,32}, {3,4}, {16,32}, {1,23}, {30,35}, {2,6}, {15,35}, {8,11}, {21,25}, {5,7}, {23,25}, {1,9}, {18,24}, {9,10}, {13,28}, {15,20}, {20,22}, {4,7}, {15,17}, {1,33}, {22,29}, {30,32}, {15,36}, {17,31}, {18,31}, {12,26}, {16,22}, {9,22}, {31,34}, {12,33}, {2,17}, {9,13}, {12,27}, {5,12}, {25,32}, {14,17}, {33,34}, {14,18}, {28,36}, {6,27}, {6,26}, {14,34}, {8,23}, {3,23}, {20,25}, {17,19}, {5,36}, {2,7}, {9,12}, {22,28}, {6,9}, {7,29}, {19,36}, {27,32}, {12,15}, {18,23}, {9,30}, {1,35}, {33,36}, {15,21}, {16,21}, {3,16}, {11,26}, {22,26}, {11,16}, {13,19}, {7,23}, {6,36}, {3,24}, {10,27}, {20,34}, {2,22}, {4,34}, {1,16}, {29,31}, {11,32}, {10,18}, {8,24}, {20,24}, {20,36}, {6,10}, {5,27}, {15,28}, {5,9}, {4,25}, {1,4}, {1,8}, {24,29}, {4,12}, {4,20}, {7,10}, {28,31}, {3,31}, {21,34}, {9,24}, {2,8}, {13,34}, {10,14}, {19,35}, {5,19}, {6,20}, {17,22}, {5,21}, {15,30}, {13,20}, {2,18}, {19,23}, {6,35}, {3,36}, {8,29}, {12,18}, {19,27}, {1,36}, {14,29}, {23,30}, {26,30}, {10,16} }; // ET36.85 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT Non-AT // Automorphism group of order 432 EdgePairs[36][85]:={ {21,23}, {1,11}, {2,24}, {9,28}, {2,33}, {6,32}, {17,36}, {8,12}, {16,26}, {15,24}, {4,26}, {16,27}, {8,30}, {26,31}, {30,33}, {3,9}, {29,33}, {16,31}, {20,27}, {32,34}, {17,20}, {28,32}, {25,29}, {14,31}, {26,33}, {7,34}, {1,21}, {2,9}, {18,21}, {8,25}, {16,23}, {8,15}, {28,35}, {3,5}, {10,15}, {15,16}, {6,22}, {3,17}, {8,16}, {19,28}, {23,32}, {3,34}, {14,23}, {11,33}, {1,17}, {1,7}, {4,22}, {9,29}, {27,28}, {14,36}, {19,26}, {12,17}, {19,30}, {12,20}, {27,30}, {2,10}, {26,29}, {8,14}, {14,30}, {6,8}, {5,25}, {11,13}, {17,23}, {1,31}, {7,13}, {22,27}, {30,34}, {2,35}, {17,33}, {1,22}, {21,27}, {12,13}, {25,34}, {23,26}, {5,23}, {10,29}, {4,21}, {10,31}, {3,20}, {15,19}, {24,32}, {13,18}, {29,34}, {1,29}, {7,30}, {24,26}, {2,16}, {4,35}, {9,25}, {8,36}, {3,4}, {2,32}, {7,26}, {13,33}, {1,23}, {11,29}, {2,6}, {7,17}, {8,11}, {5,24}, {13,23}, {12,28}, {12,25}, {15,34}, {18,24}, {27,36}, {9,10}, {13,28}, {4,15}, {1,28}, {3,11}, {20,22}, {4,7}, {18,36}, {26,36}, {15,17}, {18,31}, {12,26}, {9,22}, {31,34}, {25,35}, {33,35}, {20,29}, {9,13}, {22,25}, {25,32}, {3,19}, {4,9}, {14,18}, {28,36}, {5,31}, {17,25}, {6,26}, {22,33}, {12,30}, {21,29}, {18,19}, {18,25}, {6,19}, {27,32}, {22,31}, {1,35}, {33,36}, {14,20}, {16,34}, {15,21}, {20,35}, {11,16}, {6,36}, {2,21}, {3,30}, {5,33}, {10,17}, {3,24}, {16,35}, {11,27}, {10,27}, {4,14}, {15,22}, {5,8}, {18,22}, {11,32}, {16,20}, {14,32}, {15,33}, {8,24}, {20,24}, {9,36}, {6,34}, {6,10}, {5,27}, {5,10}, {19,25}, {15,28}, {11,19}, {10,19}, {4,11}, {1,8}, {24,29}, {4,12}, {5,13}, {7,27}, {7,10}, {28,31}, {14,35}, {21,36}, {7,24}, {3,31}, {21,34}, {2,12}, {1,6}, {12,31}, {13,34}, {10,14}, {19,35}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {13,20}, {5,35}, {2,18}, {22,30}, {19,23}, {17,32}, {3,36}, {9,16}, {9,23}, {4,32}, {24,28}, {11,18}, {12,21}, {14,29}, {23,30}, {7,18} }; // ET36.86 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 432 EdgePairs[36][86]:={ {3,33}, {10,25}, {1,20}, {11,20}, {13,32}, {25,31}, {17,35}, {4,27}, {13,21}, {7,15}, {5,34}, {14,19}, {4,24}, {16,33}, {3,22}, {23,29}, {3,8}, {23,27}, {1,10}, {18,32}, {11,25}, {32,35}, {2,23}, {12,32}, {8,28}, {15,31}, {1,32}, {24,27}, {23,28}, {19,24}, {10,26}, {17,34}, {4,19}, {16,19}, {7,22}, {4,31}, {2,19}, {25,33}, {10,33}, {1,19}, {2,4}, {5,20}, {13,35}, {25,30}, {29,35}, {17,24}, {11,14}, {21,22}, {17,21}, {27,33}, {6,7}, {2,28}, {6,11}, {9,35}, {20,30}, {4,23}, {8,27}, {13,29}, {13,16}, {9,11}, {18,34}, {3,18}, {11,28}, {10,30}, {32,36}, {3,7}, {15,29}, {7,12}, {6,31}, {2,34}, {2,36}, {26,28}, {1,18}, {7,11}, {14,21}, {15,32}, {16,24}, {9,26}, {9,27}, {1,5}, {5,11}, {31,35}, {2,5}, {29,36}, {19,22}, {11,15}, {3,12}, {9,14}, {10,28}, {14,24}, {25,28}, {24,25}, {6,12}, {12,16}, {4,33}, {21,26}, {27,31}, {9,34}, {13,22}, {10,21}, {2,20}, {14,16}, {26,35}, {8,17}, {13,31}, {3,32}, {11,21}, {6,33}, {1,12}, {16,32}, {30,36}, {30,35}, {6,24}, {15,35}, {11,30}, {21,25}, {17,27}, {5,7}, {23,25}, {8,22}, {20,28}, {8,35}, {5,14}, {18,26}, {18,27}, {7,14}, {1,33}, {26,34}, {31,36}, {18,33}, {3,29}, {3,10}, {6,23}, {22,29}, {30,32}, {13,36}, {15,36}, {8,26}, {29,32}, {16,22}, {12,33}, {6,15}, {13,30}, {4,36}, {5,12}, {14,17}, {14,22}, {13,24}, {6,27}, {3,23}, {8,23}, {10,32}, {21,30}, {12,14}, {20,25}, {5,36}, {17,19}, {2,7}, {9,12}, {22,28}, {6,9}, {7,29}, {19,36}, {12,15}, {6,14}, {16,21}, {7,28}, {3,16}, {11,26}, {7,23}, {13,19}, {8,34}, {9,18}, {20,26}, {2,29}, {20,34}, {2,22}, {23,33}, {4,34}, {1,16}, {29,31}, {9,17}, {10,18}, {6,25}, {20,36}, {27,35}, {8,18}, {5,9}, {4,25}, {1,4}, {4,20}, {3,28}, {23,31}, {2,8}, {10,20}, {17,26}, {30,31}, {5,15}, {5,19}, {17,22}, {21,24}, {9,15}, {13,17}, {15,30}, {19,34}, {27,34}, {1,34}, {21,28}, {24,33}, {18,35}, {8,29}, {12,18}, {24,31}, {1,36}, {26,30}, {10,16} }; // ET36.87 // Bipartite(8,28) Valencies [14,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 336 EdgePairs[36][87]:={ {7,19}, {5,32}, {6,12}, {3,15}, {8,24}, {6,18}, {2,22}, {6,14}, {5,30}, {5,35}, {7,24}, {6,23}, {2,20}, {4,16}, {6,13}, {5,24}, {3,32}, {1,9}, {6,25}, {7,27}, {3,30}, {1,32}, {7,23}, {7,15}, {8,34}, {3,34}, {2,18}, {6,9}, {5,26}, {4,26}, {8,14}, {3,19}, {8,22}, {7,28}, {5,33}, {3,11}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {8,33}, {8,28}, {1,36}, {3,13}, {1,22}, {2,32}, {6,33}, {1,16}, {6,21}, {2,36}, {2,17}, {8,10}, {8,18}, {7,29}, {3,14}, {2,13}, {1,12}, {4,29}, {8,35}, {4,31}, {3,27}, {2,34}, {6,15}, {1,19}, {8,11}, {4,36}, {4,21}, {7,30}, {4,17}, {4,15}, {1,35}, {1,26}, {6,29}, {7,35}, {6,31}, {4,11}, {1,23}, {2,21}, {5,27}, {7,18}, {8,9}, {4,22}, {3,28}, {3,26}, {5,31}, {5,17}, {8,20}, {6,16}, {3,21}, {1,14}, {5,11}, {1,13}, {5,10}, {8,25}, {3,20}, {5,12}, {2,25}, {1,28}, {4,9}, {6,27}, {3,33}, {7,34}, {7,36}, {7,17}, {7,12}, {5,16}, {2,30}, {5,25}, {4,19}, {4,24}, {8,29} }; // ET36.88 // Bipartite(8,28) Valencies [14,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 82590884167680000 EdgePairs[36][88]:={ {4,35}, {7,19}, {5,32}, {3,15}, {8,31}, {6,10}, {6,18}, {4,14}, {2,22}, {6,14}, {4,27}, {6,17}, {7,24}, {1,25}, {6,13}, {5,24}, {3,32}, {1,9}, {2,33}, {6,25}, {7,31}, {7,27}, {1,32}, {7,15}, {7,23}, {5,13}, {8,34}, {3,31}, {6,34}, {2,18}, {6,9}, {4,26}, {8,14}, {5,9}, {6,22}, {7,11}, {5,21}, {2,29}, {3,19}, {1,29}, {8,22}, {7,28}, {8,15}, {2,14}, {5,33}, {3,11}, {2,10}, {1,36}, {1,17}, {6,33}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {2,13}, {1,12}, {7,20}, {8,35}, {8,26}, {3,23}, {5,29}, {4,31}, {3,27}, {2,34}, {4,30}, {6,26}, {8,11}, {5,28}, {4,15}, {2,9}, {8,19}, {6,29}, {7,35}, {4,11}, {3,35}, {2,21}, {6,30}, {8,27}, {5,20}, {4,22}, {3,28}, {5,36}, {3,24}, {5,17}, {3,12}, {8,23}, {7,16}, {1,20}, {3,16}, {1,13}, {4,18}, {7,32}, {2,26}, {3,20}, {1,33}, {5,12}, {2,25}, {1,28}, {3,36}, {8,30}, {4,34}, {7,36}, {4,23}, {5,16}, {7,12}, {2,30}, {1,21}, {5,25}, {4,19}, {4,10}, {1,24} }; // ET36.89 // Bipartite(8,28) Valencies [14,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 22020096 EdgePairs[36][89]:={ {4,35}, {7,19}, {5,14}, {3,15}, {8,24}, {3,29}, {6,36}, {4,27}, {6,17}, {2,11}, {8,36}, {7,24}, {6,23}, {2,20}, {6,13}, {7,33}, {3,32}, {1,9}, {6,25}, {7,31}, {1,32}, {8,34}, {3,10}, {2,28}, {6,34}, {2,18}, {6,9}, {2,15}, {5,26}, {4,26}, {8,14}, {7,11}, {6,22}, {5,9}, {2,29}, {3,19}, {4,12}, {3,18}, {8,22}, {7,28}, {7,10}, {2,14}, {5,33}, {3,11}, {5,23}, {4,20}, {6,11}, {2,23}, {8,28}, {3,13}, {2,32}, {1,16}, {8,10}, {8,18}, {1,12}, {4,29}, {7,25}, {3,22}, {5,19}, {5,15}, {8,26}, {5,29}, {7,14}, {4,31}, {3,27}, {2,34}, {1,19}, {4,21}, {7,30}, {4,17}, {2,35}, {5,28}, {4,15}, {2,9}, {1,35}, {1,26}, {7,35}, {6,31}, {5,22}, {1,23}, {2,21}, {6,30}, {8,32}, {5,36}, {3,24}, {5,17}, {5,31}, {8,16}, {8,20}, {7,16}, {6,20}, {6,16}, {1,27}, {1,13}, {3,25}, {7,21}, {1,33}, {5,12}, {2,25}, {3,36}, {8,30}, {4,34}, {6,27}, {3,33}, {7,17}, {1,30}, {4,13}, {1,21}, {1,18}, {4,10}, {4,24}, {8,12} }; // ET36.90 // Bipartite(15,21) Valencies [14,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1327353495552000000 EdgePairs[36][90]:={ {11,17}, {3,33}, {10,25}, {1,20}, {5,17}, {2,24}, {11,20}, {9,28}, {13,32}, {2,33}, {6,16}, {11,36}, {11,35}, {15,24}, {4,26}, {3,22}, {4,16}, {8,30}, {2,23}, {12,22}, {15,31}, {4,29}, {1,32}, {8,33}, {3,25}, {10,23}, {10,26}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {5,20}, {13,35}, {2,26}, {7,34}, {12,34}, {5,32}, {4,23}, {8,27}, {13,29}, {13,16}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {6,21}, {3,34}, {14,23}, {6,31}, {11,33}, {14,33}, {1,17}, {2,36}, {4,22}, {7,20}, {14,21}, {14,36}, {9,27}, {12,36}, {5,29}, {9,19}, {14,30}, {7,32}, {1,31}, {7,25}, {10,28}, {14,24}, {2,35}, {1,22}, {15,27}, {6,30}, {12,16}, {5,23}, {10,29}, {10,31}, {9,34}, {13,22}, {15,19}, {2,20}, {6,18}, {1,29}, {8,17}, {13,31}, {11,21}, {4,35}, {9,25}, {7,16}, {8,36}, {6,33}, {2,32}, {7,26}, {5,18}, {11,23}, {1,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {13,23}, {12,28}, {12,25}, {15,34}, {13,25}, {8,35}, {13,28}, {1,28}, {3,27}, {4,28}, {15,36}, {8,26}, {9,22}, {7,31}, {12,33}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {14,18}, {6,27}, {11,24}, {12,19}, {12,30}, {8,23}, {10,32}, {5,36}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {1,35}, {14,20}, {15,21}, {7,28}, {3,16}, {11,26}, {13,26}, {15,18}, {10,35}, {7,23}, {13,19}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {1,26}, {4,34}, {1,16}, {10,34}, {15,22}, {11,32}, {14,32}, {15,33}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {5,27}, {5,26}, {8,18}, {15,28}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {14,35}, {3,31}, {9,24}, {10,20}, {12,31}, {13,34}, {7,35}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {5,35}, {2,18}, {9,31}, {1,34}, {7,19}, {4,17}, {9,21}, {9,16}, {3,36}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {10,16} }; // ET36.91 // Non-bipartite Valency 14 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 362880 EdgePairs[36][91]:={ {35,36}, {11,17}, {19,20}, {10,25}, {11,20}, {13,32}, {25,31}, {2,33}, {6,32}, {11,36}, {7,15}, {11,35}, {8,12}, {14,19}, {15,24}, {3,22}, {4,16}, {4,30}, {8,30}, {26,31}, {6,17}, {30,33}, {3,6}, {15,31}, {4,29}, {3,13}, {34,36}, {24,27}, {1,27}, {23,28}, {3,25}, {3,15}, {10,23}, {17,20}, {2,15}, {16,19}, {7,22}, {7,8}, {2,27}, {20,21}, {14,31}, {26,33}, {29,35}, {7,34}, {22,32}, {1,21}, {17,24}, {2,9}, {17,21}, {18,21}, {27,33}, {6,7}, {24,36}, {12,34}, {5,32}, {14,28}, {20,30}, {28,35}, {8,31}, {9,11}, {16,29}, {18,34}, {19,21}, {6,22}, {15,25}, {6,29}, {3,17}, {3,7}, {23,32}, {15,29}, {2,25}, {7,12}, {14,23}, {11,33}, {8,19}, {1,18}, {7,20}, {9,32}, {19,26}, {4,8}, {18,20}, {12,20}, {1,5}, {25,36}, {2,5}, {12,36}, {5,29}, {26,27}, {9,19}, {8,14}, {19,22}, {1,31}, {3,12}, {10,28}, {25,28}, {30,34}, {23,36}, {15,27}, {21,27}, {12,13}, {6,30}, {23,26}, {27,31}, {1,2}, {10,21}, {2,13}, {14,16}, {26,35}, {28,29}, {1,29}, {7,30}, {24,26}, {18,30}, {11,21}, {4,35}, {2,32}, {6,33}, {13,33}, {6,24}, {5,30}, {2,6}, {7,17}, {32,33}, {21,25}, {13,23}, {12,28}, {12,25}, {23,25}, {8,22}, {13,25}, {27,36}, {9,10}, {13,28}, {5,14}, {9,20}, {19,31}, {1,28}, {18,27}, {24,34}, {4,7}, {26,36}, {4,28}, {15,17}, {21,31}, {10,13}, {26,34}, {10,12}, {3,29}, {3,10}, {22,29}, {30,32}, {5,28}, {13,36}, {24,35}, {8,26}, {18,31}, {6,15}, {13,30}, {33,35}, {9,13}, {8,32}, {33,34}, {12,23}, {22,23}, {28,36}, {14,22}, {11,24}, {12,30}, {3,23}, {8,23}, {18,25}, {17,29}, {17,19}, {1,25}, {6,9}, {26,32}, {7,29}, {1,15}, {22,31}, {9,30}, {10,11}, {4,5}, {1,35}, {33,36}, {15,21}, {16,17}, {16,21}, {19,32}, {22,24}, {11,26}, {15,18}, {22,26}, {11,16}, {2,21}, {8,34}, {5,33}, {10,17}, {3,24}, {11,27}, {16,35}, {20,34}, {4,34}, {10,36}, {1,16}, {4,14}, {15,22}, {9,17}, {14,32}, {16,20}, {31,32}, {2,31}, {9,33}, {27,35}, {8,18}, {4,18}, {5,9}, {11,19}, {10,19}, {1,4}, {24,29}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {14,35}, {25,27}, {5,6}, {23,31}, {7,24}, {1,14}, {10,20}, {11,34}, {17,22}, {2,30}, {6,13}, {5,35}, {2,18}, {27,34}, {19,23}, {24,33}, {9,21}, {9,16}, {3,36}, {16,28}, {34,35}, {12,18}, {14,29}, {14,26}, {7,18}, {10,16}, {5,16} }; // ET36.92 // Non-bipartite Valency 14 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 12096 EdgePairs[36][92]:={ {11,17}, {21,23}, {1,11}, {10,24}, {5,17}, {2,24}, {11,20}, {13,32}, {25,31}, {11,36}, {17,36}, {15,24}, {4,26}, {3,8}, {23,27}, {4,16}, {1,10}, {18,32}, {2,23}, {1,13}, {12,22}, {12,32}, {30,33}, {3,9}, {20,27}, {8,33}, {23,28}, {3,25}, {10,26}, {17,34}, {4,19}, {7,22}, {4,31}, {2,19}, {25,33}, {10,33}, {2,4}, {24,30}, {25,30}, {17,24}, {7,36}, {8,25}, {12,34}, {5,32}, {6,11}, {8,15}, {16,23}, {14,28}, {13,29}, {10,15}, {15,16}, {15,25}, {3,18}, {11,28}, {10,30}, {32,36}, {6,29}, {3,17}, {3,7}, {16,30}, {6,21}, {14,23}, {4,10}, {14,33}, {1,7}, {9,32}, {16,24}, {19,30}, {9,27}, {27,30}, {1,5}, {31,35}, {2,5}, {26,27}, {9,19}, {29,36}, {26,29}, {19,29}, {19,22}, {22,35}, {11,15}, {11,13}, {15,26}, {23,34}, {7,13}, {9,14}, {10,28}, {11,31}, {14,24}, {25,28}, {17,33}, {21,27}, {6,12}, {12,13}, {6,30}, {12,16}, {4,33}, {10,29}, {21,26}, {1,2}, {13,22}, {9,34}, {24,32}, {2,20}, {6,18}, {13,18}, {29,34}, {28,29}, {8,17}, {2,16}, {13,31}, {9,25}, {7,16}, {6,33}, {1,12}, {16,32}, {11,23}, {30,35}, {2,6}, {17,30}, {32,33}, {11,30}, {15,35}, {21,25}, {13,23}, {12,28}, {12,25}, {8,13}, {1,9}, {20,28}, {8,35}, {18,26}, {7,14}, {3,27}, {20,22}, {4,7}, {21,31}, {26,34}, {18,33}, {3,29}, {2,3}, {3,26}, {1,3}, {21,33}, {5,28}, {15,36}, {17,31}, {18,31}, {12,26}, {31,34}, {7,31}, {13,30}, {2,17}, {20,29}, {5,12}, {22,25}, {14,17}, {8,32}, {28,36}, {14,22}, {13,24}, {5,31}, {12,30}, {21,29}, {8,23}, {14,34}, {12,14}, {20,25}, {5,36}, {6,9}, {26,32}, {7,29}, {19,36}, {27,32}, {1,15}, {18,23}, {33,36}, {14,20}, {15,21}, {16,34}, {20,35}, {3,16}, {11,26}, {22,26}, {10,35}, {13,19}, {16,36}, {6,36}, {2,21}, {3,30}, {8,34}, {9,18}, {11,27}, {16,35}, {18,28}, {2,22}, {23,33}, {4,34}, {15,22}, {5,8}, {18,22}, {10,18}, {20,24}, {9,36}, {6,34}, {27,35}, {5,27}, {5,10}, {19,25}, {10,19}, {1,4}, {4,25}, {4,11}, {1,8}, {24,29}, {4,20}, {3,28}, {8,20}, {7,27}, {28,31}, {15,23}, {9,24}, {1,14}, {1,6}, {17,26}, {7,33}, {10,14}, {5,19}, {6,20}, {7,35}, {17,22}, {21,24}, {5,21}, {9,15}, {19,34}, {5,35}, {2,18}, {22,36}, {9,31}, {19,23}, {6,35}, {16,28}, {18,35}, {20,32}, {7,21}, {14,27}, {34,35}, {8,29}, {4,32}, {19,27}, {24,31}, {12,21} }; // ET36.93 // Bipartite(6,30) Valencies [15,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3627970560 EdgePairs[36][93]:={ {4,35}, {5,32}, {6,18}, {1,11}, {3,29}, {6,14}, {5,30}, {6,36}, {4,8}, {4,27}, {3,7}, {1,31}, {2,11}, {5,35}, {2,20}, {3,32}, {1,9}, {2,33}, {6,25}, {5,13}, {2,28}, {3,34}, {6,34}, {2,18}, {6,9}, {5,26}, {3,19}, {1,29}, {4,12}, {2,14}, {5,33}, {5,23}, {2,10}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {1,17}, {3,13}, {1,16}, {4,28}, {3,14}, {2,13}, {3,9}, {3,22}, {5,15}, {6,8}, {3,23}, {4,31}, {3,27}, {2,34}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {4,15}, {4,25}, {1,26}, {6,29}, {2,24}, {4,11}, {5,22}, {6,19}, {2,21}, {1,7}, {5,20}, {4,22}, {5,36}, {3,24}, {3,12}, {6,16}, {4,32}, {2,8}, {1,20}, {1,27}, {4,18}, {5,10}, {5,12}, {3,17}, {6,24}, {6,35}, {3,33}, {1,30}, {5,16}, {2,30}, {1,21}, {5,25}, {6,28} }; // ET36.94 // Bipartite(16,20) Valencies [15,12] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 5760 EdgePairs[36][94]:={ {3,33}, {10,25}, {2,24}, {10,24}, {11,20}, {9,28}, {13,32}, {11,36}, {4,27}, {12,29}, {11,35}, {5,34}, {14,19}, {15,24}, {16,26}, {16,33}, {4,26}, {3,22}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {16,31}, {15,31}, {1,27}, {3,25}, {10,23}, {10,26}, {16,19}, {7,22}, {4,31}, {2,19}, {2,27}, {10,33}, {5,20}, {2,26}, {14,31}, {7,34}, {16,25}, {12,35}, {8,25}, {2,28}, {12,34}, {1,30}, {5,32}, {9,35}, {4,23}, {8,27}, {16,29}, {3,18}, {11,28}, {6,29}, {3,17}, {16,30}, {15,29}, {6,21}, {2,25}, {14,23}, {6,31}, {11,33}, {2,34}, {14,33}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {7,20}, {9,32}, {14,21}, {14,36}, {12,17}, {15,32}, {16,24}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {14,30}, {5,25}, {7,32}, {1,31}, {11,22}, {7,25}, {10,28}, {14,24}, {2,35}, {1,22}, {15,27}, {6,30}, {4,33}, {5,23}, {10,29}, {4,21}, {13,22}, {10,21}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {13,31}, {3,32}, {11,21}, {4,35}, {9,25}, {8,36}, {6,33}, {2,32}, {13,33}, {5,18}, {16,32}, {1,23}, {11,23}, {7,17}, {11,30}, {15,35}, {13,23}, {12,28}, {8,22}, {15,34}, {13,28}, {15,20}, {9,20}, {3,27}, {4,28}, {1,33}, {15,17}, {3,29}, {5,28}, {13,36}, {15,36}, {8,26}, {12,26}, {16,22}, {9,22}, {7,31}, {12,33}, {13,30}, {2,17}, {4,36}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {3,23}, {8,23}, {10,32}, {5,36}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {1,35}, {14,20}, {15,21}, {16,34}, {16,21}, {13,26}, {15,18}, {10,35}, {7,23}, {13,19}, {16,36}, {6,36}, {2,21}, {8,34}, {9,18}, {10,17}, {3,24}, {11,27}, {16,35}, {1,26}, {10,36}, {10,34}, {15,22}, {9,17}, {10,18}, {14,32}, {8,24}, {6,25}, {2,31}, {9,33}, {6,34}, {5,27}, {5,26}, {15,28}, {11,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {14,35}, {3,31}, {9,24}, {10,20}, {7,33}, {12,31}, {11,34}, {13,34}, {5,19}, {6,20}, {7,35}, {2,30}, {13,17}, {15,30}, {13,20}, {5,35}, {2,18}, {1,34}, {7,19}, {4,17}, {3,36}, {16,28}, {7,21}, {14,27}, {8,29}, {4,32}, {11,18}, {1,36}, {12,21}, {14,29}, {14,26}, {7,18} }; // ET36.95 // Bipartite(16,20) Valencies [15,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1651129712640000 EdgePairs[36][95]:={ {10,25}, {1,20}, {5,17}, {11,20}, {9,28}, {13,32}, {2,33}, {11,36}, {4,27}, {12,29}, {13,21}, {11,35}, {5,34}, {4,24}, {14,19}, {15,24}, {16,33}, {3,22}, {16,27}, {6,17}, {2,23}, {12,32}, {8,28}, {16,31}, {15,31}, {4,29}, {1,32}, {8,33}, {10,23}, {10,26}, {4,19}, {16,19}, {7,22}, {4,31}, {2,19}, {10,33}, {2,27}, {3,35}, {5,20}, {2,26}, {14,31}, {7,34}, {1,21}, {16,25}, {12,35}, {7,36}, {8,25}, {1,30}, {5,32}, {16,23}, {4,23}, {8,31}, {8,27}, {13,29}, {16,29}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {6,21}, {3,34}, {2,25}, {14,23}, {6,31}, {2,34}, {14,33}, {1,17}, {5,22}, {8,19}, {9,29}, {1,18}, {7,20}, {9,32}, {14,21}, {12,17}, {15,32}, {16,24}, {9,26}, {12,20}, {12,36}, {5,29}, {14,30}, {5,25}, {7,32}, {15,26}, {11,22}, {11,31}, {2,35}, {1,22}, {15,27}, {6,30}, {4,33}, {4,21}, {10,29}, {10,31}, {3,20}, {9,34}, {13,22}, {15,19}, {10,21}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {3,32}, {4,35}, {9,25}, {8,36}, {6,33}, {7,26}, {13,33}, {5,18}, {16,32}, {11,23}, {5,30}, {11,30}, {15,35}, {5,24}, {12,28}, {12,25}, {15,34}, {13,25}, {8,35}, {13,28}, {15,20}, {9,20}, {1,28}, {3,27}, {4,28}, {1,33}, {6,23}, {3,26}, {5,28}, {13,36}, {15,36}, {9,22}, {7,31}, {12,33}, {13,30}, {2,17}, {4,36}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {3,23}, {8,23}, {14,34}, {5,36}, {1,25}, {6,19}, {9,30}, {14,25}, {16,17}, {16,21}, {7,28}, {11,26}, {13,26}, {15,18}, {10,35}, {7,23}, {16,36}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {16,35}, {10,27}, {1,26}, {2,22}, {10,34}, {15,22}, {11,32}, {9,17}, {10,18}, {16,20}, {8,24}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {5,26}, {15,28}, {11,19}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {14,35}, {15,23}, {7,24}, {3,31}, {9,24}, {12,31}, {11,34}, {13,34}, {7,35}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {2,18}, {1,34}, {7,19}, {4,17}, {6,35}, {9,21}, {3,36}, {16,28}, {14,27}, {8,29}, {4,32}, {11,18}, {1,36}, {12,21}, {14,29}, {14,26}, {7,18} }; // ET36.96 // Bipartite(18,18) Valencies [15,15] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 3134566563840 EdgePairs[36][96]:={ {13,21}, {15,33}, {14,36}, {6,25}, {5,22}, {11,25}, {4,28}, {8,26}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {8,21}, {3,19}, {15,27}, {1,19}, {3,23}, {8,23}, {1,21}, {3,21}, {16,28}, {5,32}, {7,30}, {13,27}, {14,29}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {2,34}, {4,24}, {18,32}, {4,30}, {8,30}, {9,33}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {15,19}, {16,34}, {10,35}, {4,23}, {13,26}, {6,24}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {2,36}, {8,22}, {18,29}, {9,36}, {9,29}, {18,26}, {4,22}, {18,33}, {18,36}, {5,27}, {15,28}, {5,28}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {14,21}, {18,20}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {2,27}, {12,30}, {6,30}, {1,22}, {7,34}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {17,19}, {9,30}, {14,27}, {7,28}, {8,34}, {9,25}, {10,22}, {10,30}, {16,30}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {16,26}, {12,25}, {3,22}, {18,31}, {16,31}, {6,23}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {9,21}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {9,28}, {3,34}, {2,21}, {15,29}, {2,22}, {16,20}, {18,24}, {1,33}, {18,27}, {12,36}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {5,21}, {17,21}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {15,21}, {7,26}, {11,28}, {16,35}, {10,24}, {11,20}, {10,34}, {17,27}, {8,35}, {6,21}, {15,22}, {4,26}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {4,19}, {14,22}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {15,25}, {5,33} }; // ET36.97 // Non-bipartite Valency 15 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 261213880320 EdgePairs[36][97]:={ {24,34}, {15,33}, {19,28}, {14,36}, {5,7}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {5,11}, {16,22}, {2,35}, {6,15}, {11,15}, {10,33}, {8,21}, {3,19}, {14,31}, {24,32}, {1,19}, {27,33}, {12,16}, {1,21}, {3,21}, {21,28}, {11,14}, {5,32}, {2,7}, {6,9}, {13,27}, {14,29}, {6,14}, {24,28}, {17,35}, {11,29}, {1,12}, {27,36}, {3,18}, {8,16}, {2,34}, {8,30}, {8,13}, {1,9}, {4,16}, {4,13}, {23,31}, {13,30}, {2,10}, {3,9}, {23,36}, {10,26}, {2,17}, {17,20}, {7,33}, {10,20}, {1,24}, {22,25}, {12,13}, {13,20}, {26,35}, {16,25}, {9,35}, {1,36}, {15,19}, {6,18}, {16,34}, {24,26}, {4,23}, {11,18}, {6,24}, {30,36}, {2,29}, {5,34}, {20,36}, {7,15}, {18,29}, {18,26}, {4,22}, {18,36}, {18,33}, {29,32}, {8,19}, {1,18}, {7,14}, {15,28}, {5,28}, {4,7}, {12,24}, {1,31}, {3,31}, {25,33}, {12,27}, {11,22}, {9,13}, {6,27}, {5,35}, {30,31}, {3,36}, {6,12}, {18,19}, {20,25}, {4,32}, {1,30}, {2,13}, {14,28}, {6,36}, {8,17}, {11,36}, {3,30}, {11,23}, {3,24}, {10,36}, {14,33}, {11,33}, {13,25}, {8,24}, {4,10}, {14,21}, {28,34}, {12,17}, {2,23}, {4,11}, {9,19}, {20,31}, {3,25}, {6,8}, {22,30}, {12,30}, {6,30}, {10,31}, {10,29}, {13,22}, {1,25}, {22,31}, {20,30}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {7,28}, {25,31}, {2,16}, {8,34}, {9,25}, {17,30}, {10,22}, {16,30}, {7,23}, {4,34}, {6,31}, {15,24}, {21,32}, {12,25}, {23,27}, {24,35}, {18,31}, {4,29}, {24,29}, {19,29}, {28,32}, {8,32}, {10,28}, {9,24}, {17,22}, {17,25}, {19,34}, {5,23}, {5,20}, {2,26}, {18,21}, {9,21}, {7,29}, {2,28}, {8,27}, {3,33}, {2,11}, {13,32}, {14,26}, {10,15}, {18,28}, {15,29}, {2,22}, {16,20}, {18,24}, {25,36}, {14,19}, {1,33}, {16,27}, {3,14}, {5,26}, {5,29}, {21,34}, {7,31}, {30,33}, {1,8}, {20,27}, {21,35}, {17,34}, {22,33}, {11,31}, {20,33}, {14,24}, {19,35}, {3,15}, {13,34}, {7,22}, {1,14}, {26,32}, {22,27}, {13,35}, {21,29}, {12,34}, {28,35}, {23,30}, {16,23}, {4,35}, {19,32}, {1,15}, {15,21}, {7,26}, {7,18}, {23,33}, {11,28}, {5,16}, {16,35}, {11,20}, {5,17}, {17,27}, {8,35}, {13,23}, {6,21}, {4,26}, {26,34}, {23,25}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {5,10}, {4,20}, {1,27}, {5,13}, {17,23}, {10,23}, {15,26}, {22,36}, {27,31}, {29,35}, {3,12}, {9,34}, {10,14}, {12,35}, {7,36}, {17,32}, {29,34}, {12,19}, {21,26}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26} }; // ET36.98 // Non-bipartite Valency 15 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 51840 EdgePairs[36][98]:={ {14,36}, {9,32}, {5,22}, {9,17}, {17,18}, {8,26}, {16,22}, {2,35}, {3,35}, {8,21}, {33,34}, {5,6}, {24,32}, {1,19}, {24,36}, {8,23}, {1,21}, {1,35}, {7,30}, {13,27}, {14,29}, {16,21}, {24,28}, {19,21}, {10,11}, {17,35}, {11,17}, {9,11}, {6,29}, {27,36}, {3,18}, {2,34}, {10,17}, {2,25}, {18,32}, {15,32}, {8,30}, {9,33}, {1,9}, {4,16}, {4,13}, {27,28}, {20,24}, {7,11}, {23,31}, {3,10}, {2,5}, {2,10}, {19,22}, {26,29}, {2,17}, {7,33}, {12,31}, {20,29}, {17,26}, {15,30}, {22,25}, {27,32}, {12,13}, {13,20}, {26,35}, {24,31}, {28,30}, {1,36}, {6,18}, {16,34}, {29,31}, {5,34}, {13,19}, {1,26}, {3,17}, {20,36}, {9,36}, {9,29}, {18,26}, {4,22}, {7,14}, {6,10}, {4,18}, {14,35}, {10,12}, {7,32}, {1,31}, {3,31}, {25,33}, {12,27}, {5,12}, {6,27}, {2,30}, {2,8}, {6,12}, {19,23}, {13,17}, {18,19}, {20,25}, {7,19}, {1,30}, {13,18}, {19,27}, {12,15}, {8,10}, {34,35}, {16,29}, {11,36}, {10,16}, {3,30}, {11,23}, {11,16}, {10,36}, {3,24}, {15,34}, {11,33}, {21,31}, {7,12}, {31,33}, {14,21}, {18,20}, {9,26}, {17,31}, {12,17}, {13,36}, {2,23}, {22,29}, {25,32}, {4,11}, {3,25}, {6,8}, {11,13}, {25,30}, {2,27}, {4,33}, {2,12}, {7,34}, {11,24}, {9,31}, {18,25}, {24,25}, {20,30}, {6,19}, {9,12}, {7,28}, {12,18}, {2,16}, {9,25}, {4,5}, {10,22}, {10,30}, {6,22}, {4,34}, {6,31}, {15,24}, {16,26}, {27,35}, {3,22}, {5,8}, {23,27}, {4,15}, {23,34}, {13,14}, {4,36}, {1,32}, {24,29}, {30,32}, {28,32}, {24,27}, {9,24}, {17,25}, {5,20}, {2,26}, {18,21}, {10,21}, {7,29}, {8,36}, {8,27}, {3,33}, {28,29}, {10,15}, {19,33}, {30,35}, {18,28}, {2,22}, {8,11}, {14,19}, {20,28}, {1,33}, {12,36}, {26,28}, {19,25}, {5,26}, {3,11}, {5,29}, {14,30}, {3,28}, {31,35}, {5,9}, {8,33}, {30,33}, {1,4}, {1,8}, {31,34}, {7,10}, {3,6}, {3,15}, {13,34}, {1,14}, {26,32}, {22,27}, {30,34}, {13,35}, {21,29}, {20,23}, {12,34}, {17,21}, {28,35}, {6,28}, {16,23}, {4,35}, {19,32}, {1,15}, {14,25}, {15,21}, {14,20}, {20,34}, {23,33}, {11,28}, {7,16}, {5,18}, {22,24}, {15,18}, {3,4}, {15,16}, {13,23}, {6,21}, {4,26}, {15,20}, {13,28}, {23,25}, {16,24}, {7,9}, {12,32}, {15,36}, {22,35}, {15,31}, {8,28}, {8,20}, {1,27}, {5,25}, {17,23}, {22,36}, {27,31}, {4,19}, {14,22}, {29,35}, {7,13}, {9,14}, {14,17}, {16,19}, {5,36}, {10,14}, {29,34}, {21,26}, {20,21}, {23,24}, {16,32}, {6,33}, {2,32}, {6,7}, {11,26}, {5,33}, {21,23} }; // ET36.99 // Bipartite(4,32) Valencies [16,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 21143266346926080000 EdgePairs[36][99]:={ {3,32}, {2,14}, {4,23}, {1,24}, {3,12}, {2,26}, {1,29}, {2,30}, {2,29}, {1,32}, {4,34}, {2,10}, {1,33}, {4,11}, {4,10}, {1,36}, {3,27}, {2,6}, {4,7}, {1,20}, {1,12}, {4,31}, {3,8}, {3,23}, {3,24}, {2,33}, {3,20}, {2,21}, {4,6}, {4,30}, {4,18}, {3,11}, {3,16}, {3,7}, {3,28}, {1,16}, {3,15}, {2,18}, {1,21}, {4,27}, {3,19}, {2,5}, {3,31}, {1,5}, {4,15}, {1,17}, {4,22}, {1,28}, {2,17}, {1,8}, {1,13}, {2,34}, {2,9}, {1,9}, {4,26}, {2,13}, {2,25}, {4,14}, {4,35}, {4,19}, {1,25}, {2,22}, {3,36}, {3,35} }; // ET36.100 // Bipartite(12,24) Valencies [16,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5436839917780992000 EdgePairs[36][100]:={ {11,17}, {3,33}, {2,24}, {1,20}, {5,17}, {10,25}, {11,20}, {9,28}, {2,33}, {6,16}, {11,36}, {11,35}, {4,26}, {3,22}, {4,16}, {8,30}, {2,23}, {1,13}, {12,22}, {4,29}, {1,32}, {3,13}, {8,33}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {5,20}, {2,26}, {7,34}, {11,14}, {12,34}, {2,14}, {5,32}, {8,15}, {4,23}, {8,27}, {10,22}, {6,22}, {3,18}, {6,21}, {3,34}, {6,31}, {11,33}, {1,17}, {2,36}, {4,22}, {7,20}, {9,27}, {12,36}, {5,29}, {9,19}, {8,14}, {7,32}, {11,15}, {1,31}, {7,13}, {7,25}, {10,28}, {2,35}, {1,22}, {12,13}, {6,30}, {12,16}, {5,23}, {10,29}, {10,31}, {9,34}, {2,20}, {6,18}, {1,29}, {8,17}, {11,21}, {4,35}, {9,25}, {7,16}, {8,36}, {6,33}, {2,32}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {12,28}, {12,25}, {8,35}, {5,14}, {1,28}, {4,13}, {7,14}, {3,27}, {4,28}, {10,13}, {8,26}, {9,22}, {7,31}, {12,33}, {6,15}, {2,17}, {9,13}, {12,27}, {8,32}, {8,21}, {3,19}, {6,27}, {11,24}, {12,19}, {12,30}, {8,23}, {10,32}, {5,36}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {12,15}, {9,30}, {1,35}, {7,28}, {3,16}, {11,26}, {10,35}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {1,26}, {4,34}, {1,16}, {4,14}, {10,34}, {11,32}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {5,27}, {5,26}, {8,18}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {3,31}, {9,24}, {1,14}, {10,20}, {5,15}, {12,31}, {10,14}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {5,35}, {2,18}, {9,31}, {1,34}, {7,19}, {4,17}, {9,21}, {9,16}, {3,36}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {10,16} }; // ET36.101 // Bipartite(18,18) Valencies [16,16] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 190253629440 EdgePairs[36][101]:={ {13,21}, {15,33}, {14,36}, {9,32}, {5,22}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {16,22}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {1,21}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {6,29}, {11,27}, {2,34}, {12,28}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {12,20}, {12,26}, {13,30}, {10,26}, {17,20}, {7,33}, {12,31}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {15,19}, {16,34}, {10,35}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {2,36}, {8,22}, {18,29}, {9,36}, {9,29}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {5,27}, {15,28}, {5,28}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {6,27}, {2,30}, {14,34}, {3,36}, {4,21}, {17,29}, {7,19}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {14,23}, {11,33}, {18,22}, {13,25}, {14,21}, {9,26}, {18,20}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {18,31}, {6,23}, {16,31}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {11,30}, {3,34}, {2,21}, {4,27}, {5,24}, {15,29}, {16,20}, {18,24}, {14,19}, {1,33}, {18,27}, {12,36}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {17,34}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {12,34}, {17,21}, {6,28}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {16,19}, {5,36}, {9,34}, {10,32}, {12,35}, {6,35}, {17,32}, {12,19}, {8,25}, {16,32}, {6,33}, {2,32}, {18,34}, {11,26}, {5,33}, {5,30} }; // ET36.102 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 190210142896128 EdgePairs[36][102]:={ {24,34}, {15,33}, {19,28}, {14,36}, {9,32}, {6,25}, {23,29}, {5,22}, {19,26}, {11,25}, {12,22}, {8,26}, {2,35}, {4,31}, {3,35}, {11,15}, {8,21}, {21,30}, {3,19}, {15,27}, {24,32}, {1,19}, {24,36}, {8,23}, {12,16}, {3,20}, {2,18}, {16,28}, {11,14}, {1,35}, {13,27}, {2,33}, {11,29}, {11,27}, {1,20}, {3,18}, {2,34}, {20,26}, {12,28}, {19,31}, {18,32}, {4,30}, {1,17}, {4,16}, {4,13}, {23,31}, {1,13}, {12,26}, {7,27}, {23,36}, {10,26}, {2,17}, {7,33}, {12,31}, {20,29}, {17,26}, {24,30}, {2,15}, {12,23}, {12,13}, {16,25}, {24,31}, {1,36}, {6,18}, {1,29}, {16,34}, {13,26}, {6,24}, {2,29}, {5,34}, {3,17}, {2,36}, {8,22}, {22,34}, {18,29}, {6,34}, {9,29}, {18,26}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {17,29}, {20,25}, {7,19}, {4,32}, {1,30}, {2,13}, {19,27}, {12,15}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {11,23}, {11,16}, {14,33}, {15,34}, {13,25}, {21,31}, {19,30}, {8,24}, {9,26}, {3,29}, {17,31}, {13,36}, {10,13}, {22,29}, {9,22}, {20,31}, {17,28}, {11,13}, {7,35}, {22,30}, {12,30}, {4,33}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {22,31}, {23,35}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {9,30}, {3,32}, {14,27}, {7,28}, {2,16}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {11,32}, {21,32}, {16,26}, {12,25}, {1,16}, {4,14}, {24,35}, {4,15}, {18,31}, {6,23}, {23,34}, {4,36}, {4,29}, {1,32}, {24,29}, {19,29}, {7,24}, {10,28}, {9,24}, {17,25}, {2,19}, {6,20}, {5,23}, {20,32}, {5,20}, {12,14}, {10,21}, {9,21}, {18,30}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {14,26}, {23,32}, {10,15}, {11,30}, {9,28}, {3,34}, {18,28}, {5,24}, {2,31}, {18,27}, {1,33}, {20,28}, {21,33}, {16,27}, {3,14}, {5,26}, {19,25}, {21,34}, {8,33}, {20,27}, {21,35}, {22,33}, {11,31}, {3,15}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {9,15}, {21,29}, {23,30}, {6,28}, {4,35}, {19,32}, {13,33}, {1,15}, {14,25}, {7,26}, {7,18}, {23,33}, {11,28}, {5,18}, {16,35}, {10,24}, {10,27}, {5,17}, {16,33}, {7,17}, {8,35}, {17,27}, {6,21}, {13,28}, {7,20}, {9,27}, {12,32}, {15,36}, {22,35}, {21,36}, {8,28}, {4,20}, {8,20}, {5,25}, {10,23}, {15,26}, {22,36}, {4,19}, {22,32}, {9,14}, {5,36}, {10,14}, {24,33}, {10,32}, {7,36}, {6,35}, {17,32}, {8,25}, {6,33}, {12,21}, {2,32}, {2,14}, {11,26}, {15,25}, {5,33} }; // ET36.103 // Bipartite(18,18) Valencies [17,17] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 12804747411456000 EdgePairs[36][103]:={ {13,21}, {15,33}, {14,36}, {9,32}, {5,22}, {11,25}, {4,28}, {12,22}, {3,26}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {1,21}, {3,21}, {16,28}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {12,20}, {12,26}, {7,27}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {15,19}, {1,29}, {16,34}, {10,35}, {4,23}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {2,36}, {8,22}, {6,34}, {9,29}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {5,27}, {15,28}, {5,28}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {8,24}, {14,21}, {9,26}, {18,20}, {3,29}, {17,31}, {13,36}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {18,31}, {6,23}, {16,31}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {15,29}, {2,22}, {16,20}, {18,24}, {2,31}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {17,21}, {6,28}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,28}, {1,23}, {16,35}, {11,20}, {10,27}, {10,34}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {16,19}, {5,36}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {15,25}, {5,33}, {5,30} }; // ET36.104 // Non-bipartite Valency 17 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 4896 EdgePairs[36][104]:={ {13,21}, {24,34}, {9,32}, {9,17}, {10,18}, {19,26}, {3,8}, {4,28}, {12,22}, {16,22}, {2,35}, {4,31}, {6,15}, {10,33}, {8,21}, {3,19}, {1,19}, {24,36}, {2,18}, {3,21}, {21,28}, {6,9}, {8,31}, {13,27}, {14,29}, {24,28}, {6,32}, {17,35}, {11,35}, {11,29}, {11,17}, {1,12}, {9,11}, {11,27}, {27,36}, {3,18}, {8,16}, {2,34}, {12,28}, {19,31}, {18,32}, {32,33}, {15,32}, {8,30}, {8,12}, {1,17}, {29,33}, {1,10}, {7,11}, {1,13}, {13,30}, {2,5}, {7,27}, {8,9}, {19,22}, {3,9}, {26,29}, {17,20}, {33,35}, {7,33}, {20,29}, {1,24}, {13,24}, {15,30}, {2,15}, {13,20}, {26,35}, {16,25}, {24,31}, {1,36}, {1,29}, {10,35}, {24,26}, {4,23}, {29,31}, {6,24}, {5,34}, {14,32}, {20,36}, {7,15}, {22,34}, {27,30}, {18,29}, {9,36}, {9,29}, {9,20}, {18,26}, {4,22}, {18,36}, {18,33}, {8,19}, {5,27}, {15,28}, {6,17}, {4,7}, {14,35}, {10,12}, {7,32}, {12,24}, {1,31}, {25,33}, {3,13}, {5,12}, {2,30}, {2,8}, {3,36}, {13,17}, {18,19}, {20,25}, {19,27}, {12,15}, {14,28}, {11,21}, {8,17}, {16,29}, {16,17}, {3,30}, {3,16}, {11,23}, {22,26}, {11,16}, {3,24}, {14,33}, {14,23}, {15,34}, {11,33}, {21,25}, {13,25}, {21,31}, {19,30}, {8,24}, {4,10}, {9,26}, {5,14}, {17,31}, {29,36}, {13,36}, {2,23}, {10,13}, {25,32}, {10,19}, {9,22}, {3,25}, {19,24}, {17,28}, {34,36}, {11,13}, {25,30}, {22,30}, {27,34}, {2,27}, {12,30}, {6,30}, {1,22}, {10,31}, {1,6}, {6,13}, {1,25}, {23,35}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {3,32}, {12,18}, {6,11}, {8,34}, {4,5}, {17,30}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {26,31}, {15,24}, {12,25}, {1,16}, {4,14}, {5,8}, {23,27}, {4,15}, {16,31}, {4,29}, {2,3}, {24,29}, {30,32}, {26,27}, {28,32}, {9,24}, {5,31}, {17,22}, {17,25}, {5,23}, {20,32}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {7,29}, {14,16}, {3,33}, {28,29}, {2,11}, {16,36}, {14,26}, {23,32}, {10,15}, {19,33}, {9,28}, {2,21}, {30,35}, {18,24}, {25,36}, {14,19}, {20,28}, {21,33}, {1,33}, {18,27}, {12,36}, {16,27}, {1,7}, {3,11}, {5,29}, {31,35}, {1,4}, {4,12}, {17,34}, {21,35}, {28,33}, {31,34}, {8,14}, {7,10}, {3,6}, {11,31}, {19,35}, {13,34}, {7,22}, {6,26}, {22,27}, {30,34}, {14,18}, {22,23}, {5,21}, {21,29}, {20,23}, {12,34}, {28,35}, {23,30}, {6,28}, {16,23}, {4,35}, {13,15}, {15,21}, {20,34}, {7,26}, {7,18}, {23,33}, {5,18}, {5,16}, {11,20}, {15,18}, {10,27}, {16,33}, {8,35}, {32,36}, {4,26}, {15,20}, {1,28}, {26,34}, {23,25}, {3,27}, {7,20}, {12,32}, {5,10}, {8,28}, {4,20}, {5,25}, {17,23}, {10,23}, {15,26}, {22,36}, {27,31}, {22,32}, {14,22}, {7,13}, {9,14}, {25,28}, {16,19}, {5,36}, {9,34}, {7,36}, {21,24}, {6,35}, {12,19}, {20,21}, {8,25}, {2,9}, {6,33}, {2,32}, {6,7}, {2,14}, {11,26} }; // ET36.105 // Bipartite(9,27) Valencies [18,6] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1296 EdgePairs[36][105]:={ {3,33}, {5,17}, {1,20}, {9,28}, {6,32}, {6,16}, {4,27}, {7,15}, {4,24}, {8,12}, {4,26}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,31}, {1,19}, {2,27}, {3,35}, {5,20}, {7,34}, {1,21}, {8,10}, {2,28}, {2,14}, {5,32}, {8,15}, {9,35}, {4,23}, {8,31}, {8,27}, {9,11}, {6,22}, {3,18}, {6,29}, {8,16}, {6,21}, {3,34}, {7,12}, {2,25}, {6,31}, {4,10}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {7,11}, {3,14}, {9,32}, {9,26}, {5,11}, {2,10}, {9,19}, {8,14}, {5,25}, {7,13}, {7,25}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {9,34}, {2,13}, {2,20}, {1,29}, {7,30}, {2,16}, {3,32}, {8,36}, {1,12}, {6,33}, {5,30}, {7,17}, {8,11}, {8,13}, {8,22}, {7,14}, {3,27}, {1,33}, {3,29}, {6,23}, {5,28}, {8,26}, {9,22}, {2,17}, {4,36}, {5,12}, {8,32}, {3,19}, {1,24}, {6,27}, {6,26}, {1,25}, {9,12}, {7,29}, {6,28}, {2,11}, {9,30}, {1,35}, {7,23}, {6,36}, {3,30}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {5,10}, {5,26}, {8,18}, {4,18}, {4,11}, {4,12}, {5,13}, {8,20}, {3,28}, {7,10}, {7,24}, {3,31}, {9,24}, {1,14}, {5,15}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {9,15}, {5,35}, {2,18}, {9,31}, {7,19}, {4,17}, {6,35}, {9,21}, {3,36}, {9,23}, {7,21}, {1,36}, {7,18}, {5,16} }; // ET36.106 // Bipartite(9,27) Valencies [18,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 61929004688474112000 EdgePairs[36][106]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {8,30}, {2,23}, {1,13}, {4,29}, {1,32}, {3,13}, {8,33}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {5,20}, {2,26}, {7,34}, {2,14}, {5,32}, {8,15}, {4,23}, {8,27}, {6,22}, {3,18}, {6,21}, {3,34}, {6,31}, {4,10}, {1,17}, {2,36}, {4,22}, {7,11}, {7,20}, {9,27}, {5,11}, {5,29}, {9,19}, {8,14}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {5,23}, {9,34}, {2,20}, {6,18}, {1,29}, {8,17}, {4,35}, {9,25}, {7,16}, {8,36}, {6,33}, {2,32}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {9,10}, {8,35}, {5,14}, {1,28}, {4,13}, {7,14}, {3,27}, {4,28}, {3,10}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {6,27}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {6,28}, {2,11}, {9,30}, {1,35}, {7,28}, {3,16}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {3,24}, {2,29}, {1,26}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {6,10}, {5,27}, {5,26}, {8,18}, {4,25}, {4,11}, {4,20}, {3,28}, {8,20}, {7,10}, {3,31}, {2,12}, {1,14}, {9,24}, {5,15}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {3,36}, {9,16}, {9,21}, {8,29}, {4,32} }; // ET36.107 // Bipartite(9,27) Valencies [18,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1088391168 EdgePairs[36][107]:={ {1,11}, {3,33}, {1,20}, {9,28}, {6,32}, {6,16}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {1,10}, {4,30}, {8,30}, {6,17}, {4,29}, {1,32}, {3,13}, {8,33}, {3,15}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {1,30}, {5,32}, {8,15}, {8,27}, {3,18}, {3,17}, {6,21}, {2,25}, {4,10}, {2,34}, {2,36}, {5,22}, {4,22}, {7,11}, {7,20}, {3,14}, {9,27}, {5,11}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {7,13}, {7,25}, {2,35}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {9,34}, {2,13}, {2,20}, {6,18}, {1,29}, {8,17}, {2,16}, {3,32}, {4,35}, {9,25}, {7,16}, {7,26}, {1,12}, {8,36}, {5,18}, {1,23}, {7,17}, {8,11}, {5,24}, {8,35}, {9,10}, {5,14}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {1,33}, {6,23}, {3,10}, {3,26}, {8,26}, {9,22}, {7,31}, {2,17}, {9,13}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {5,36}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {7,28}, {7,23}, {6,36}, {2,21}, {5,33}, {9,18}, {3,24}, {2,29}, {2,22}, {1,16}, {8,24}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {6,10}, {5,27}, {8,18}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {3,28}, {7,10}, {3,31}, {2,12}, {1,14}, {9,24}, {5,15}, {7,35}, {2,30}, {9,15}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {6,35}, {3,36}, {9,16}, {9,21}, {8,29}, {5,16} }; // ET36.108 // Bipartite(12,24) Valencies [18,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8358844170240000 EdgePairs[36][108]:={ {5,17}, {1,20}, {10,25}, {11,20}, {9,28}, {2,33}, {11,36}, {4,27}, {12,29}, {7,15}, {11,35}, {5,34}, {4,24}, {3,22}, {4,16}, {6,17}, {2,23}, {1,13}, {12,32}, {8,28}, {4,29}, {1,32}, {8,33}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {2,27}, {10,33}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {11,14}, {12,35}, {7,36}, {8,25}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,31}, {8,27}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {8,16}, {6,21}, {3,34}, {2,25}, {6,31}, {2,34}, {1,17}, {5,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,20}, {9,32}, {12,17}, {9,26}, {12,20}, {12,36}, {5,29}, {5,25}, {7,32}, {11,15}, {11,22}, {9,14}, {11,31}, {2,35}, {1,22}, {12,13}, {6,30}, {4,33}, {12,16}, {4,21}, {10,29}, {3,20}, {10,31}, {9,34}, {2,13}, {10,21}, {6,18}, {1,29}, {7,30}, {8,17}, {3,32}, {4,35}, {9,25}, {7,16}, {8,36}, {6,33}, {7,26}, {5,18}, {11,23}, {5,30}, {11,30}, {5,24}, {12,28}, {12,25}, {8,13}, {8,35}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {6,23}, {3,26}, {5,28}, {9,22}, {7,31}, {12,33}, {6,15}, {2,17}, {4,36}, {9,13}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {6,26}, {12,19}, {3,23}, {8,23}, {5,36}, {1,25}, {6,19}, {12,15}, {6,14}, {9,30}, {7,28}, {3,16}, {11,26}, {10,35}, {7,23}, {11,16}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {10,34}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {5,26}, {11,19}, {4,25}, {10,19}, {4,20}, {5,13}, {8,20}, {3,28}, {12,24}, {7,27}, {7,24}, {3,31}, {9,24}, {1,14}, {12,31}, {10,14}, {11,34}, {7,35}, {5,21}, {2,30}, {6,13}, {2,18}, {1,34}, {7,19}, {4,17}, {6,35}, {9,21}, {9,16}, {3,36}, {8,29}, {4,32}, {11,18}, {1,36}, {12,21}, {7,18}, {5,16} }; // ET36.109 // Bipartite(18,18) Valencies [18,18] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 81980778135594566280019968000000 EdgePairs[36][109]:={ {13,21}, {15,33}, {14,36}, {9,32}, {6,25}, {5,22}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {1,21}, {3,21}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {15,19}, {1,29}, {16,34}, {10,35}, {4,23}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {2,36}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {5,27}, {15,28}, {5,28}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {8,24}, {14,21}, {9,26}, {18,20}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {18,31}, {6,23}, {16,31}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {14,19}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {5,36}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {15,25}, {5,33}, {5,30} }; // ET36.110 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 313456656384 EdgePairs[36][110]:={ {13,21}, {14,36}, {5,7}, {6,25}, {23,29}, {10,18}, {19,26}, {3,8}, {11,25}, {9,10}, {5,11}, {16,22}, {2,35}, {17,33}, {3,35}, {11,15}, {10,33}, {33,34}, {27,33}, {3,23}, {8,23}, {12,16}, {2,18}, {11,14}, {1,35}, {7,30}, {2,7}, {6,9}, {21,22}, {14,29}, {16,21}, {24,28}, {2,33}, {11,17}, {9,11}, {11,27}, {3,18}, {2,34}, {20,26}, {10,17}, {18,32}, {2,6}, {8,30}, {8,13}, {8,12}, {1,17}, {1,9}, {29,33}, {28,31}, {20,24}, {27,28}, {7,11}, {31,36}, {12,26}, {13,30}, {2,5}, {19,22}, {3,9}, {26,29}, {10,26}, {2,17}, {17,20}, {33,35}, {12,31}, {23,28}, {1,24}, {24,30}, {15,30}, {22,25}, {27,32}, {12,13}, {13,20}, {20,35}, {1,36}, {15,19}, {24,26}, {11,18}, {29,31}, {30,36}, {13,16}, {5,34}, {13,19}, {3,17}, {20,36}, {2,36}, {7,15}, {8,22}, {27,30}, {6,34}, {9,29}, {18,33}, {29,32}, {1,18}, {5,27}, {7,14}, {15,28}, {32,35}, {6,10}, {4,7}, {14,35}, {1,31}, {3,31}, {12,27}, {25,33}, {9,13}, {5,12}, {6,27}, {2,8}, {5,35}, {4,9}, {14,34}, {30,31}, {3,36}, {6,12}, {19,23}, {25,29}, {4,21}, {13,17}, {18,19}, {20,25}, {13,18}, {19,27}, {12,15}, {8,10}, {14,28}, {8,15}, {6,36}, {10,16}, {3,16}, {2,24}, {22,26}, {11,16}, {3,24}, {15,34}, {11,33}, {18,22}, {21,25}, {7,12}, {8,24}, {4,10}, {18,20}, {14,21}, {28,34}, {17,31}, {12,17}, {29,36}, {13,36}, {2,23}, {10,13}, {20,22}, {22,29}, {25,32}, {9,22}, {4,11}, {19,24}, {6,8}, {11,13}, {25,30}, {22,30}, {1,22}, {10,31}, {5,19}, {1,6}, {24,25}, {6,19}, {17,19}, {9,30}, {9,12}, {3,32}, {7,28}, {12,18}, {25,31}, {2,16}, {6,11}, {13,29}, {7,23}, {4,34}, {10,25}, {15,35}, {26,31}, {11,32}, {3,7}, {12,25}, {1,16}, {3,22}, {5,8}, {23,27}, {18,31}, {16,31}, {15,17}, {4,36}, {1,32}, {1,5}, {24,29}, {30,32}, {28,32}, {24,27}, {7,24}, {9,24}, {17,22}, {19,34}, {6,20}, {5,20}, {12,14}, {18,21}, {26,30}, {7,29}, {8,29}, {9,23}, {14,16}, {3,33}, {10,15}, {3,5}, {9,28}, {3,34}, {4,27}, {30,35}, {15,29}, {2,22}, {16,20}, {8,11}, {18,24}, {2,31}, {14,19}, {1,33}, {1,7}, {26,28}, {19,25}, {5,26}, {4,8}, {4,25}, {14,30}, {21,34}, {31,35}, {12,33}, {5,9}, {30,33}, {1,4}, {4,12}, {1,8}, {20,27}, {21,35}, {28,33}, {28,36}, {31,34}, {8,14}, {7,10}, {27,29}, {3,6}, {11,31}, {19,35}, {13,34}, {7,22}, {6,26}, {26,32}, {22,27}, {1,34}, {30,34}, {13,35}, {14,18}, {21,27}, {5,21}, {9,15}, {17,24}, {20,23}, {2,4}, {17,21}, {19,36}, {28,35}, {23,30}, {16,23}, {18,23}, {4,35}, {14,20}, {15,21}, {20,34}, {1,23}, {15,18}, {10,27}, {16,33}, {3,4}, {15,16}, {32,36}, {6,21}, {4,26}, {15,20}, {13,28}, {23,25}, {16,24}, {12,32}, {15,36}, {21,36}, {5,10}, {8,28}, {4,20}, {5,25}, {32,34}, {17,23}, {26,33}, {27,31}, {4,19}, {29,35}, {7,13}, {9,14}, {14,17}, {25,28}, {16,19}, {5,36}, {10,14}, {10,32}, {21,24}, {17,32}, {6,35}, {29,34}, {23,26}, {21,26}, {22,28}, {2,9}, {16,32}, {2,32}, {6,7}, {11,26}, {33,36}, {21,23} }; // ET36.111 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1296 EdgePairs[36][111]:={ {13,21}, {15,33}, {19,28}, {6,25}, {5,22}, {10,18}, {9,17}, {3,8}, {11,25}, {16,22}, {2,35}, {17,33}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {21,30}, {33,34}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {11,14}, {7,30}, {21,22}, {2,33}, {17,35}, {6,32}, {11,29}, {11,17}, {1,12}, {9,11}, {11,27}, {27,36}, {8,16}, {9,18}, {20,26}, {12,28}, {4,24}, {18,32}, {2,6}, {8,30}, {8,13}, {1,17}, {1,9}, {1,10}, {4,13}, {20,24}, {31,36}, {12,26}, {13,30}, {3,10}, {2,5}, {19,22}, {26,29}, {10,26}, {33,35}, {23,28}, {10,20}, {13,24}, {24,30}, {22,25}, {27,32}, {12,13}, {26,35}, {24,31}, {9,35}, {1,36}, {15,19}, {1,29}, {24,26}, {4,23}, {11,18}, {29,31}, {6,24}, {30,36}, {13,16}, {5,34}, {13,19}, {14,32}, {3,17}, {2,36}, {20,36}, {7,15}, {8,22}, {27,30}, {9,36}, {6,34}, {9,29}, {18,26}, {18,36}, {18,33}, {29,32}, {1,18}, {5,27}, {7,14}, {15,28}, {4,7}, {8,18}, {14,35}, {1,31}, {12,27}, {25,33}, {9,13}, {5,12}, {6,27}, {2,30}, {2,8}, {5,35}, {4,9}, {14,34}, {30,31}, {6,12}, {19,23}, {4,21}, {4,32}, {1,30}, {13,18}, {19,27}, {8,10}, {14,28}, {11,21}, {6,36}, {10,16}, {3,16}, {2,24}, {22,26}, {3,24}, {14,23}, {15,34}, {18,22}, {21,25}, {7,12}, {4,10}, {18,20}, {9,26}, {14,21}, {5,14}, {3,29}, {17,31}, {12,17}, {13,36}, {10,13}, {22,29}, {10,19}, {4,11}, {6,8}, {25,30}, {27,34}, {12,30}, {2,12}, {1,22}, {7,34}, {10,31}, {5,19}, {10,29}, {18,25}, {6,13}, {22,31}, {6,19}, {20,30}, {2,20}, {17,19}, {9,12}, {3,32}, {7,28}, {25,31}, {2,16}, {6,11}, {8,34}, {13,29}, {10,30}, {6,22}, {10,25}, {11,32}, {15,24}, {3,7}, {16,26}, {4,14}, {5,8}, {23,27}, {16,31}, {15,17}, {4,36}, {1,32}, {1,5}, {24,29}, {19,29}, {28,32}, {24,27}, {7,24}, {9,24}, {5,31}, {17,25}, {5,23}, {5,20}, {12,14}, {18,21}, {2,28}, {8,29}, {9,23}, {14,16}, {8,27}, {3,33}, {2,11}, {16,36}, {13,32}, {23,32}, {10,15}, {9,28}, {3,34}, {2,21}, {15,29}, {2,22}, {16,20}, {8,11}, {25,36}, {2,31}, {20,28}, {16,27}, {1,7}, {26,28}, {19,25}, {5,26}, {3,11}, {4,25}, {14,30}, {3,28}, {21,34}, {31,35}, {12,33}, {5,9}, {30,33}, {1,4}, {17,34}, {20,27}, {21,35}, {28,33}, {28,36}, {8,14}, {7,10}, {27,29}, {3,6}, {11,31}, {19,35}, {7,25}, {7,22}, {26,32}, {1,34}, {30,34}, {13,35}, {9,15}, {21,29}, {17,24}, {20,23}, {17,21}, {19,36}, {28,35}, {23,30}, {18,23}, {4,35}, {13,33}, {14,20}, {20,34}, {7,26}, {23,33}, {11,28}, {7,16}, {1,23}, {16,35}, {11,20}, {15,18}, {3,4}, {7,17}, {8,35}, {13,23}, {17,27}, {32,36}, {6,21}, {15,22}, {4,26}, {15,20}, {26,34}, {23,25}, {16,24}, {9,27}, {12,32}, {15,36}, {25,35}, {15,31}, {5,10}, {4,20}, {32,34}, {17,23}, {26,33}, {27,31}, {14,22}, {22,32}, {29,35}, {14,17}, {25,28}, {16,19}, {24,33}, {7,36}, {21,24}, {29,34}, {12,19}, {21,26}, {22,28}, {8,25}, {2,9}, {16,32}, {6,33}, {12,21}, {6,7}, {18,34}, {5,33} }; // ET36.112 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1296 EdgePairs[36][112]:={ {13,21}, {19,28}, {14,36}, {5,7}, {23,29}, {5,22}, {10,18}, {9,10}, {5,11}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {11,15}, {10,33}, {21,30}, {33,34}, {5,15}, {24,32}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {3,21}, {21,28}, {5,32}, {6,9}, {21,22}, {14,29}, {6,14}, {24,28}, {2,33}, {17,35}, {11,29}, {1,12}, {11,27}, {1,20}, {9,18}, {10,17}, {20,26}, {12,28}, {4,24}, {18,32}, {2,6}, {15,32}, {8,30}, {8,13}, {29,33}, {1,10}, {20,24}, {27,28}, {7,11}, {31,36}, {23,31}, {13,30}, {7,27}, {2,10}, {19,22}, {3,9}, {25,34}, {10,26}, {2,17}, {12,31}, {20,29}, {10,20}, {13,24}, {24,30}, {15,30}, {22,25}, {27,32}, {12,13}, {26,35}, {18,35}, {16,25}, {9,35}, {1,36}, {15,19}, {16,34}, {24,26}, {11,18}, {29,31}, {17,36}, {6,24}, {30,36}, {13,16}, {2,29}, {5,34}, {13,19}, {14,32}, {3,17}, {2,36}, {20,36}, {7,15}, {26,36}, {9,29}, {18,26}, {4,22}, {1,18}, {7,14}, {32,35}, {6,10}, {8,18}, {1,31}, {12,27}, {25,33}, {9,13}, {6,27}, {2,8}, {5,35}, {4,9}, {14,34}, {30,31}, {6,12}, {25,29}, {4,21}, {4,32}, {1,30}, {13,18}, {19,27}, {8,10}, {14,28}, {8,15}, {11,21}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {22,26}, {11,16}, {3,24}, {14,33}, {14,23}, {11,33}, {18,22}, {21,25}, {7,12}, {8,24}, {14,21}, {18,20}, {9,26}, {28,34}, {3,29}, {12,17}, {22,29}, {10,19}, {9,22}, {4,11}, {19,24}, {11,13}, {7,35}, {25,30}, {27,34}, {12,30}, {1,22}, {1,6}, {5,19}, {10,29}, {6,13}, {22,31}, {6,19}, {20,30}, {13,31}, {9,16}, {17,19}, {9,30}, {9,12}, {3,32}, {7,28}, {25,31}, {8,34}, {9,25}, {10,30}, {7,23}, {4,34}, {10,25}, {15,35}, {6,31}, {15,24}, {3,7}, {16,26}, {12,25}, {1,16}, {27,35}, {4,14}, {5,8}, {23,27}, {4,15}, {18,31}, {16,31}, {6,23}, {15,17}, {4,36}, {1,32}, {1,5}, {30,32}, {19,29}, {28,32}, {24,27}, {9,24}, {17,25}, {19,34}, {2,19}, {6,20}, {5,23}, {12,14}, {18,21}, {26,30}, {7,29}, {2,28}, {8,36}, {8,27}, {3,33}, {2,11}, {16,36}, {10,15}, {3,5}, {3,34}, {2,21}, {4,27}, {30,35}, {15,29}, {2,22}, {16,20}, {8,11}, {25,36}, {2,31}, {18,27}, {1,7}, {26,28}, {19,25}, {5,26}, {3,11}, {4,8}, {4,25}, {31,35}, {1,8}, {4,12}, {20,27}, {21,35}, {28,33}, {28,36}, {27,29}, {11,31}, {19,35}, {13,34}, {7,22}, {6,26}, {26,32}, {1,34}, {13,35}, {14,18}, {5,21}, {17,24}, {20,23}, {2,4}, {17,21}, {23,30}, {18,23}, {13,33}, {14,20}, {20,34}, {7,26}, {23,33}, {11,28}, {7,16}, {1,23}, {11,20}, {16,33}, {3,4}, {15,16}, {7,17}, {13,23}, {17,27}, {15,22}, {15,20}, {13,28}, {1,28}, {23,25}, {16,24}, {12,32}, {15,36}, {21,36}, {15,31}, {5,10}, {8,28}, {4,20}, {5,13}, {5,25}, {32,34}, {17,23}, {26,33}, {27,31}, {14,22}, {22,32}, {29,35}, {3,12}, {9,14}, {14,17}, {16,19}, {9,34}, {10,14}, {24,33}, {10,32}, {7,36}, {6,35}, {17,32}, {29,34}, {12,19}, {21,26}, {22,28}, {8,25}, {2,9}, {6,33}, {12,21}, {6,7}, {18,34}, {11,26}, {33,36}, {5,33}, {21,23} }; // ET36.113 // Bipartite(17,19) Valencies [19,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 43267632904897132203343872000000 EdgePairs[36][113]:={ {13,21}, {15,33}, {14,36}, {9,32}, {6,25}, {5,22}, {10,18}, {11,25}, {4,28}, {17,18}, {12,22}, {3,26}, {8,26}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {16,34}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {6,23}, {16,31}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {1,33}, {12,36}, {16,27}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {5,36}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30} }; // ET36.114 // Bipartite(6,30) Valencies [20,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2293666840313856000000 EdgePairs[36][114]:={ {4,35}, {5,32}, {6,12}, {5,14}, {3,15}, {6,10}, {6,18}, {4,14}, {1,11}, {5,30}, {6,36}, {4,8}, {3,7}, {1,31}, {2,11}, {5,35}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {2,33}, {6,25}, {6,7}, {3,30}, {1,32}, {3,10}, {3,34}, {3,31}, {6,34}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {3,18}, {1,34}, {2,14}, {5,23}, {5,33}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {1,22}, {2,32}, {6,33}, {1,16}, {6,21}, {2,36}, {2,17}, {4,28}, {3,9}, {4,29}, {3,22}, {5,15}, {5,29}, {4,31}, {3,27}, {6,15}, {1,19}, {4,17}, {2,35}, {4,25}, {2,9}, {1,35}, {1,26}, {2,24}, {6,31}, {4,11}, {2,27}, {6,19}, {1,23}, {2,21}, {5,27}, {1,7}, {6,30}, {5,8}, {2,12}, {4,22}, {5,20}, {3,28}, {5,36}, {3,24}, {5,17}, {3,12}, {6,16}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {5,11}, {3,16}, {1,13}, {3,25}, {2,26}, {5,12}, {1,28}, {3,36}, {6,24}, {5,18}, {4,34}, {6,27}, {3,33}, {4,23}, {1,8}, {4,13}, {2,30}, {4,19}, {4,10}, {6,28} }; // ET36.115 // Bipartite(6,30) Valencies [20,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23592960 EdgePairs[36][115]:={ {1,15}, {4,35}, {5,32}, {6,12}, {5,14}, {6,10}, {6,18}, {4,14}, {1,11}, {5,30}, {6,36}, {4,8}, {4,27}, {3,7}, {6,17}, {2,11}, {5,35}, {6,23}, {2,20}, {5,34}, {1,25}, {4,16}, {5,24}, {3,32}, {2,33}, {6,32}, {6,25}, {6,7}, {3,10}, {2,28}, {3,34}, {3,31}, {2,18}, {5,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {1,34}, {2,14}, {3,11}, {5,33}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {3,13}, {2,16}, {1,22}, {2,32}, {6,33}, {6,21}, {2,17}, {4,28}, {2,13}, {3,9}, {4,29}, {3,22}, {5,19}, {5,15}, {6,8}, {5,29}, {4,31}, {3,27}, {4,30}, {6,15}, {1,19}, {2,35}, {4,15}, {2,9}, {1,26}, {2,24}, {6,31}, {1,23}, {5,27}, {1,7}, {6,30}, {4,22}, {5,20}, {3,28}, {3,26}, {5,36}, {3,24}, {5,17}, {3,12}, {6,16}, {6,20}, {3,21}, {1,14}, {2,8}, {5,11}, {3,16}, {1,13}, {3,25}, {2,26}, {1,33}, {5,12}, {2,25}, {1,28}, {3,36}, {3,17}, {4,9}, {6,35}, {5,18}, {4,34}, {6,27}, {4,23}, {1,8}, {1,30}, {4,13}, {1,21}, {1,18}, {4,19}, {4,24} }; // ET36.116 // Bipartite(12,24) Valencies [20,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8806025134080 EdgePairs[36][116]:={ {11,17}, {3,33}, {2,24}, {5,17}, {10,25}, {11,20}, {6,32}, {6,16}, {11,36}, {4,27}, {7,15}, {11,35}, {5,34}, {4,26}, {4,16}, {8,30}, {2,23}, {1,13}, {12,22}, {12,32}, {8,28}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {10,33}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {11,14}, {7,36}, {8,25}, {2,28}, {12,34}, {2,14}, {1,30}, {5,32}, {9,35}, {4,23}, {8,31}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {3,17}, {8,16}, {6,21}, {2,25}, {6,31}, {11,33}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {9,32}, {9,26}, {9,27}, {12,20}, {12,36}, {5,29}, {9,19}, {8,14}, {11,15}, {1,31}, {11,22}, {7,13}, {9,14}, {7,25}, {10,28}, {2,35}, {1,22}, {12,13}, {6,30}, {4,33}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {11,21}, {4,35}, {9,25}, {7,16}, {2,32}, {6,33}, {8,36}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {12,28}, {12,25}, {8,13}, {8,22}, {8,35}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,27}, {4,28}, {1,33}, {10,13}, {3,29}, {3,26}, {5,28}, {8,26}, {12,26}, {7,31}, {12,33}, {6,15}, {2,17}, {9,13}, {12,27}, {8,32}, {3,19}, {1,24}, {6,27}, {11,24}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {10,32}, {12,14}, {5,36}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {1,35}, {7,28}, {11,26}, {10,35}, {7,23}, {11,16}, {6,36}, {3,30}, {5,33}, {8,34}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {2,22}, {4,34}, {1,16}, {4,14}, {10,34}, {11,32}, {9,17}, {8,24}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {5,27}, {5,26}, {8,18}, {4,25}, {10,19}, {4,20}, {8,20}, {12,24}, {7,27}, {7,24}, {3,31}, {9,24}, {10,20}, {5,15}, {7,33}, {12,31}, {10,14}, {11,34}, {6,20}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {3,36}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {12,18}, {11,18}, {1,36}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET36.117 // Bipartite(16,20) Valencies [20,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 50903097535173096709816320000000 EdgePairs[36][117]:={ {13,21}, {15,33}, {14,36}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {16,22}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {16,34}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {5,34}, {13,19}, {1,26}, {14,32}, {3,17}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {6,23}, {16,31}, {15,17}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {1,33}, {12,36}, {16,27}, {5,26}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {14,17}, {5,36}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {12,19}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30} }; // ET36.118 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1132462080 EdgePairs[36][118]:={ {13,21}, {24,34}, {14,36}, {5,7}, {9,32}, {6,25}, {23,29}, {9,17}, {10,18}, {19,26}, {12,22}, {3,26}, {8,26}, {5,11}, {17,33}, {3,35}, {11,15}, {8,21}, {15,27}, {24,32}, {1,19}, {27,33}, {3,23}, {8,23}, {12,16}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {5,32}, {7,30}, {2,7}, {14,29}, {6,14}, {24,28}, {2,33}, {6,32}, {11,29}, {11,27}, {1,20}, {27,36}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {20,26}, {12,28}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {1,9}, {4,16}, {1,10}, {12,20}, {23,31}, {1,13}, {13,30}, {3,10}, {2,10}, {3,9}, {25,34}, {10,26}, {17,20}, {7,33}, {12,31}, {20,29}, {23,28}, {10,20}, {13,24}, {24,30}, {2,15}, {22,25}, {12,13}, {16,25}, {24,31}, {20,35}, {9,35}, {15,19}, {1,29}, {6,18}, {10,35}, {4,23}, {13,26}, {29,31}, {6,24}, {30,36}, {2,29}, {3,17}, {20,36}, {7,15}, {8,22}, {18,29}, {9,36}, {9,20}, {4,22}, {18,33}, {29,32}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {1,31}, {12,27}, {25,33}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {2,8}, {5,35}, {4,9}, {14,34}, {30,31}, {3,36}, {6,12}, {4,21}, {17,29}, {18,19}, {20,25}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {3,30}, {3,16}, {22,26}, {11,16}, {10,36}, {3,24}, {14,33}, {14,23}, {11,33}, {18,22}, {13,25}, {21,25}, {21,31}, {19,30}, {8,24}, {4,10}, {9,26}, {14,21}, {18,20}, {5,14}, {28,34}, {3,29}, {17,31}, {29,36}, {13,36}, {10,13}, {25,32}, {10,19}, {15,23}, {4,11}, {9,19}, {3,25}, {11,34}, {17,28}, {6,8}, {7,35}, {11,13}, {27,34}, {2,27}, {12,30}, {4,33}, {1,22}, {7,34}, {10,31}, {9,31}, {5,19}, {13,22}, {6,13}, {22,31}, {6,19}, {20,30}, {2,20}, {4,17}, {17,19}, {25,31}, {2,16}, {6,11}, {8,34}, {13,29}, {9,25}, {17,30}, {7,23}, {4,34}, {10,25}, {15,35}, {12,29}, {26,31}, {6,31}, {11,32}, {15,24}, {21,32}, {16,26}, {1,16}, {27,35}, {3,22}, {5,8}, {23,27}, {4,15}, {18,31}, {6,23}, {16,31}, {23,34}, {4,36}, {4,29}, {1,32}, {24,29}, {30,32}, {19,29}, {24,27}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {19,34}, {2,19}, {6,20}, {5,23}, {5,20}, {12,14}, {18,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {3,33}, {16,36}, {14,26}, {23,32}, {11,30}, {19,33}, {9,28}, {3,34}, {2,21}, {30,35}, {18,28}, {5,24}, {2,22}, {16,20}, {2,31}, {1,33}, {18,27}, {16,27}, {1,7}, {5,26}, {19,25}, {3,11}, {4,25}, {14,30}, {12,33}, {11,19}, {8,33}, {1,8}, {4,12}, {17,34}, {21,35}, {28,33}, {28,36}, {11,31}, {20,33}, {14,24}, {19,35}, {3,15}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {26,32}, {1,34}, {22,27}, {13,35}, {21,27}, {12,34}, {17,21}, {19,36}, {28,35}, {23,30}, {6,28}, {16,23}, {4,35}, {13,33}, {1,15}, {14,25}, {20,34}, {7,26}, {7,18}, {23,33}, {11,28}, {7,16}, {5,18}, {16,35}, {10,24}, {11,20}, {10,27}, {5,17}, {7,17}, {8,35}, {13,23}, {17,27}, {4,26}, {15,20}, {1,28}, {26,34}, {16,24}, {9,27}, {12,32}, {15,36}, {22,35}, {21,36}, {15,31}, {1,27}, {5,13}, {5,25}, {10,23}, {15,26}, {22,36}, {26,33}, {14,22}, {22,32}, {29,35}, {3,12}, {9,14}, {16,19}, {5,36}, {10,14}, {24,33}, {10,32}, {7,36}, {6,35}, {17,32}, {12,19}, {21,26}, {22,28}, {8,25}, {2,9}, {16,32}, {2,32}, {12,21}, {6,7}, {2,14}, {18,34}, {15,25} }; // ET36.119 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[36][119]:={ {13,21}, {14,36}, {5,7}, {9,32}, {9,17}, {10,18}, {3,8}, {4,28}, {11,25}, {12,22}, {8,26}, {5,11}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {11,15}, {8,21}, {21,30}, {3,19}, {5,15}, {24,32}, {1,19}, {27,33}, {24,36}, {12,16}, {3,20}, {2,18}, {3,21}, {11,14}, {1,35}, {7,30}, {6,9}, {14,29}, {6,14}, {16,21}, {24,28}, {2,33}, {6,32}, {17,35}, {11,35}, {11,17}, {1,12}, {6,29}, {27,36}, {3,18}, {20,26}, {12,28}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,13}, {9,33}, {1,17}, {4,16}, {29,33}, {12,20}, {23,31}, {1,13}, {13,30}, {7,27}, {2,10}, {23,36}, {25,34}, {10,26}, {2,17}, {12,31}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {15,30}, {2,15}, {12,23}, {27,32}, {12,13}, {13,20}, {18,35}, {16,25}, {24,31}, {20,35}, {15,19}, {1,29}, {6,18}, {16,34}, {10,35}, {24,26}, {4,23}, {13,26}, {29,31}, {6,24}, {17,36}, {2,29}, {5,34}, {1,26}, {14,32}, {8,22}, {26,36}, {18,29}, {6,34}, {9,29}, {4,22}, {7,14}, {15,28}, {6,10}, {4,7}, {8,18}, {4,18}, {1,31}, {12,27}, {3,13}, {11,22}, {6,27}, {2,30}, {2,8}, {5,35}, {4,9}, {14,34}, {30,31}, {3,36}, {6,12}, {18,19}, {20,25}, {7,19}, {4,32}, {19,27}, {12,15}, {14,28}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {11,23}, {22,26}, {11,16}, {10,36}, {14,33}, {14,23}, {6,16}, {15,34}, {11,33}, {18,22}, {21,25}, {21,31}, {19,30}, {8,24}, {4,10}, {9,26}, {5,14}, {28,34}, {17,31}, {13,36}, {10,13}, {25,32}, {15,23}, {4,11}, {9,19}, {3,25}, {6,8}, {7,35}, {22,30}, {12,30}, {2,12}, {1,22}, {7,34}, {10,31}, {9,31}, {18,25}, {24,25}, {13,22}, {6,13}, {22,31}, {2,20}, {9,16}, {4,17}, {13,31}, {17,19}, {14,27}, {7,28}, {12,18}, {2,16}, {13,29}, {9,25}, {17,30}, {10,22}, {10,30}, {16,30}, {7,23}, {4,34}, {10,25}, {15,35}, {12,29}, {26,31}, {6,31}, {11,32}, {15,24}, {3,7}, {16,26}, {3,22}, {23,27}, {24,35}, {4,15}, {18,31}, {6,23}, {23,34}, {4,36}, {1,32}, {24,29}, {19,29}, {28,32}, {8,32}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {19,34}, {2,19}, {6,20}, {5,23}, {20,32}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {10,15}, {11,30}, {19,33}, {3,34}, {2,21}, {1,11}, {4,27}, {30,35}, {18,28}, {5,24}, {15,29}, {2,22}, {16,20}, {18,24}, {25,36}, {2,31}, {14,19}, {1,33}, {18,27}, {20,28}, {21,33}, {16,27}, {1,7}, {3,14}, {5,26}, {19,25}, {3,11}, {5,29}, {4,25}, {3,28}, {21,34}, {7,31}, {12,33}, {5,9}, {11,19}, {8,33}, {30,33}, {1,8}, {28,36}, {8,14}, {20,33}, {14,24}, {19,35}, {1,14}, {6,26}, {26,32}, {22,27}, {30,34}, {13,35}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {12,34}, {17,21}, {28,35}, {23,30}, {6,28}, {16,23}, {19,32}, {13,33}, {1,15}, {14,25}, {14,20}, {20,34}, {7,18}, {23,33}, {11,28}, {1,23}, {10,24}, {11,20}, {10,34}, {5,17}, {16,33}, {7,17}, {8,35}, {13,23}, {17,27}, {6,21}, {15,20}, {13,28}, {1,28}, {3,27}, {9,27}, {12,32}, {25,35}, {22,35}, {21,36}, {15,31}, {5,10}, {8,20}, {1,27}, {5,13}, {5,25}, {15,26}, {22,36}, {26,33}, {27,31}, {4,19}, {22,32}, {29,35}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {7,36}, {29,34}, {12,19}, {23,26}, {22,28}, {8,25}, {2,9}, {16,32}, {2,32}, {18,34}, {11,26}, {5,33}, {5,30} }; // ET36.120 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 51840 EdgePairs[36][120]:={ {13,21}, {24,34}, {15,33}, {19,28}, {5,7}, {6,25}, {23,29}, {10,18}, {19,26}, {3,8}, {4,28}, {11,25}, {9,10}, {12,22}, {3,26}, {5,11}, {1,3}, {17,33}, {4,31}, {6,15}, {11,15}, {10,33}, {21,30}, {3,19}, {14,31}, {15,27}, {5,15}, {27,33}, {3,23}, {12,16}, {3,20}, {2,18}, {3,21}, {16,28}, {21,28}, {11,14}, {5,32}, {2,7}, {6,9}, {8,31}, {21,22}, {6,14}, {19,20}, {2,33}, {6,32}, {11,35}, {11,29}, {1,12}, {11,27}, {1,20}, {8,16}, {9,18}, {20,26}, {12,28}, {19,31}, {4,24}, {2,6}, {32,33}, {4,30}, {8,13}, {8,12}, {1,17}, {29,33}, {28,31}, {1,10}, {12,20}, {31,36}, {1,13}, {13,30}, {12,26}, {7,27}, {8,9}, {3,9}, {23,36}, {25,34}, {10,26}, {17,20}, {33,35}, {23,28}, {10,20}, {1,24}, {13,24}, {24,30}, {2,15}, {12,23}, {18,35}, {16,25}, {20,35}, {9,35}, {15,19}, {1,29}, {10,35}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {17,36}, {30,36}, {13,16}, {2,29}, {14,32}, {2,36}, {7,15}, {8,22}, {26,36}, {22,34}, {27,30}, {18,29}, {6,34}, {9,20}, {18,33}, {18,36}, {29,32}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {32,35}, {4,7}, {8,18}, {12,24}, {25,26}, {3,13}, {11,22}, {9,13}, {5,35}, {4,9}, {14,34}, {30,31}, {3,36}, {25,29}, {4,21}, {17,29}, {4,32}, {16,18}, {1,2}, {2,13}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {16,17}, {3,16}, {2,24}, {22,26}, {14,15}, {14,33}, {14,23}, {6,16}, {18,22}, {13,25}, {21,25}, {19,30}, {8,24}, {4,10}, {5,14}, {28,34}, {3,29}, {29,36}, {10,13}, {20,22}, {10,19}, {15,23}, {9,22}, {9,19}, {20,31}, {19,24}, {11,34}, {17,28}, {34,36}, {7,35}, {22,30}, {27,34}, {12,30}, {6,30}, {1,22}, {10,31}, {5,19}, {1,6}, {7,8}, {10,29}, {13,22}, {6,13}, {1,25}, {22,31}, {23,35}, {2,20}, {9,16}, {4,17}, {13,31}, {17,19}, {9,30}, {3,32}, {14,27}, {25,31}, {6,11}, {8,34}, {13,29}, {17,30}, {16,30}, {7,23}, {10,25}, {15,35}, {12,29}, {26,31}, {11,32}, {21,32}, {3,7}, {12,25}, {1,16}, {4,14}, {24,35}, {31,32}, {18,31}, {16,31}, {6,23}, {15,17}, {4,29}, {1,5}, {2,3}, {26,27}, {19,29}, {8,32}, {7,24}, {10,28}, {5,31}, {29,30}, {17,22}, {19,34}, {2,19}, {6,20}, {5,23}, {20,32}, {12,14}, {9,21}, {26,30}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {2,11}, {16,36}, {13,32}, {14,26}, {23,32}, {11,30}, {3,5}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {15,29}, {16,20}, {18,24}, {25,36}, {2,31}, {18,27}, {21,33}, {16,27}, {1,7}, {3,14}, {4,8}, {4,25}, {21,34}, {7,31}, {12,33}, {11,19}, {4,12}, {17,34}, {20,27}, {21,35}, {28,33}, {28,36}, {8,14}, {27,29}, {22,33}, {11,31}, {20,33}, {14,24}, {19,35}, {7,25}, {7,22}, {6,26}, {1,34}, {14,18}, {22,23}, {5,21}, {21,27}, {9,15}, {17,24}, {2,4}, {19,36}, {23,30}, {18,23}, {13,33}, {13,15}, {11,12}, {7,26}, {7,18}, {1,23}, {5,16}, {16,35}, {10,24}, {11,20}, {35,36}, {10,27}, {10,34}, {5,17}, {16,33}, {7,17}, {8,35}, {17,27}, {32,36}, {15,22}, {1,28}, {26,34}, {3,27}, {7,20}, {9,27}, {25,35}, {21,36}, {5,10}, {4,20}, {5,13}, {25,27}, {32,34}, {10,23}, {15,26}, {26,33}, {4,6}, {22,32}, {3,12}, {25,28}, {9,34}, {24,33}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {21,24}, {12,19}, {23,26}, {22,28}, {8,25}, {2,9}, {12,21}, {2,14}, {18,34}, {33,36}, {15,25}, {5,30} }; // ET36.121 // Bipartite(8,28) Valencies [21,6] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 40320 EdgePairs[36][121]:={ {1,11}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {8,12}, {4,26}, {6,17}, {2,23}, {3,9}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {2,19}, {2,27}, {3,35}, {7,34}, {1,21}, {2,9}, {7,36}, {8,10}, {8,25}, {2,28}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {3,34}, {7,12}, {6,31}, {4,10}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {2,10}, {8,14}, {5,25}, {7,13}, {7,25}, {1,22}, {6,12}, {6,30}, {4,33}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {7,30}, {2,16}, {4,35}, {7,16}, {7,26}, {1,12}, {2,32}, {8,36}, {5,18}, {1,23}, {5,30}, {7,17}, {8,11}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {7,31}, {4,36}, {5,12}, {8,32}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {8,23}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {1,35}, {3,16}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {2,22}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {2,31}, {5,27}, {5,10}, {5,26}, {8,18}, {5,9}, {4,11}, {4,20}, {5,13}, {8,20}, {3,28}, {7,10}, {7,24}, {3,31}, {2,12}, {1,14}, {5,15}, {7,33}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {7,19}, {4,17}, {6,35}, {3,36}, {7,21}, {4,32}, {7,18} }; // ET36.122 // Bipartite(8,28) Valencies [21,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 247772652503040000 EdgePairs[36][122]:={ {5,17}, {1,20}, {2,33}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {3,22}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,9}, {8,28}, {4,29}, {1,32}, {8,33}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {8,25}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {6,29}, {8,16}, {6,21}, {3,34}, {7,12}, {2,25}, {6,31}, {2,34}, {1,17}, {5,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {2,10}, {5,29}, {5,25}, {7,32}, {3,12}, {2,35}, {1,22}, {6,30}, {4,33}, {4,21}, {3,20}, {2,13}, {6,18}, {1,29}, {7,30}, {8,17}, {3,32}, {4,35}, {7,16}, {7,26}, {1,12}, {6,33}, {8,36}, {5,18}, {5,30}, {8,11}, {5,24}, {8,13}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {6,23}, {3,10}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {6,27}, {6,26}, {3,23}, {8,23}, {5,36}, {1,25}, {6,19}, {6,9}, {6,14}, {2,11}, {7,28}, {3,16}, {7,23}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {8,24}, {6,25}, {2,31}, {6,34}, {6,10}, {5,10}, {5,26}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {7,10}, {7,24}, {3,31}, {1,14}, {7,35}, {5,21}, {2,30}, {6,13}, {2,18}, {1,34}, {7,19}, {4,17}, {6,35}, {3,36}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET36.123 // Bipartite(15,21) Valencies [21,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 66810315514914689431633920000000 EdgePairs[36][123]:={ {13,21}, {15,33}, {14,36}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {13,19}, {1,26}, {14,32}, {3,17}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,33}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {8,24}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {13,29}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,22}, {6,23}, {15,17}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {15,16}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30} }; // ET36.124 // Non-bipartite Valency 21 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 362880 EdgePairs[36][124]:={ {13,21}, {15,33}, {19,28}, {14,36}, {5,7}, {6,25}, {23,29}, {5,22}, {10,18}, {3,8}, {11,25}, {17,18}, {12,22}, {3,26}, {5,11}, {16,22}, {1,3}, {2,35}, {17,33}, {4,31}, {3,35}, {11,15}, {10,33}, {8,21}, {21,30}, {3,19}, {5,15}, {24,32}, {1,19}, {12,16}, {3,20}, {3,21}, {21,28}, {11,14}, {2,7}, {21,22}, {13,27}, {6,14}, {24,28}, {17,35}, {11,29}, {1,12}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {20,26}, {4,24}, {18,32}, {15,32}, {8,13}, {1,17}, {1,9}, {29,33}, {28,31}, {1,10}, {4,13}, {20,24}, {27,28}, {7,11}, {31,36}, {1,13}, {12,26}, {7,27}, {8,9}, {2,10}, {3,9}, {25,34}, {26,29}, {10,26}, {2,17}, {7,33}, {12,31}, {20,29}, {17,26}, {1,24}, {13,24}, {24,30}, {15,30}, {22,25}, {27,32}, {13,20}, {18,35}, {16,25}, {24,31}, {20,35}, {28,30}, {9,35}, {1,36}, {15,19}, {6,18}, {16,34}, {10,35}, {4,23}, {11,18}, {13,26}, {29,31}, {17,36}, {30,36}, {13,16}, {2,29}, {5,34}, {13,19}, {1,26}, {2,36}, {20,36}, {22,34}, {27,30}, {18,29}, {9,36}, {6,34}, {9,29}, {18,26}, {4,22}, {18,33}, {18,36}, {29,32}, {5,27}, {7,14}, {15,28}, {32,35}, {6,10}, {7,32}, {12,24}, {3,31}, {12,27}, {25,33}, {25,26}, {11,22}, {5,12}, {6,27}, {2,8}, {4,9}, {14,34}, {30,31}, {6,12}, {25,29}, {4,21}, {13,17}, {18,19}, {20,25}, {7,19}, {4,32}, {16,18}, {1,30}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {11,23}, {14,15}, {14,33}, {6,16}, {15,34}, {18,22}, {19,30}, {8,24}, {31,33}, {4,10}, {9,26}, {14,21}, {28,34}, {17,31}, {12,17}, {29,36}, {2,23}, {20,22}, {25,32}, {15,23}, {9,22}, {4,11}, {20,31}, {19,24}, {17,28}, {6,8}, {7,35}, {11,13}, {25,30}, {22,30}, {4,33}, {2,12}, {1,22}, {10,31}, {9,31}, {5,19}, {1,6}, {10,29}, {24,25}, {13,22}, {23,35}, {6,19}, {2,20}, {4,17}, {13,31}, {9,12}, {3,32}, {14,27}, {7,28}, {2,16}, {6,11}, {13,29}, {9,25}, {17,30}, {10,22}, {10,30}, {16,30}, {7,23}, {15,35}, {12,29}, {6,31}, {11,32}, {21,32}, {16,26}, {5,8}, {23,27}, {4,15}, {16,31}, {6,23}, {13,14}, {23,34}, {4,36}, {1,32}, {2,3}, {19,29}, {28,32}, {9,24}, {5,31}, {29,30}, {17,25}, {19,34}, {2,19}, {6,20}, {5,23}, {20,32}, {5,20}, {2,26}, {12,14}, {26,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {16,36}, {10,15}, {11,30}, {3,5}, {19,33}, {9,28}, {3,34}, {1,11}, {4,27}, {30,35}, {18,28}, {5,24}, {2,22}, {8,11}, {18,24}, {1,33}, {20,28}, {21,33}, {16,27}, {1,7}, {26,28}, {3,14}, {5,26}, {19,25}, {3,11}, {4,25}, {14,30}, {21,34}, {31,35}, {7,31}, {12,33}, {8,33}, {1,8}, {17,34}, {20,27}, {21,35}, {28,33}, {31,34}, {7,10}, {27,29}, {22,33}, {11,31}, {20,33}, {14,24}, {19,35}, {13,34}, {7,25}, {6,26}, {1,34}, {22,27}, {13,35}, {14,18}, {5,21}, {9,15}, {21,29}, {20,23}, {2,4}, {19,36}, {23,30}, {6,28}, {16,23}, {18,23}, {13,15}, {14,25}, {14,20}, {11,12}, {7,26}, {23,33}, {11,28}, {7,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {3,4}, {16,33}, {15,16}, {8,35}, {17,27}, {32,36}, {6,21}, {4,26}, {15,20}, {16,24}, {3,27}, {9,27}, {7,9}, {12,32}, {15,36}, {25,35}, {22,35}, {21,36}, {5,10}, {8,28}, {5,25}, {32,34}, {17,23}, {15,26}, {22,36}, {4,6}, {4,19}, {7,13}, {9,14}, {14,17}, {5,36}, {9,34}, {10,14}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {21,24}, {29,34}, {12,19}, {21,26}, {22,28}, {8,25}, {23,24}, {16,32}, {12,21}, {2,14}, {21,23} }; // ET36.125 // Non-bipartite Valency 21 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 12096 EdgePairs[36][125]:={ {13,21}, {24,34}, {15,33}, {19,28}, {14,36}, {5,7}, {6,25}, {23,29}, {5,22}, {9,17}, {19,26}, {11,25}, {4,28}, {9,10}, {17,18}, {8,26}, {5,11}, {16,22}, {2,35}, {6,15}, {3,35}, {8,21}, {21,30}, {33,34}, {5,6}, {3,19}, {14,31}, {15,27}, {5,15}, {1,19}, {27,33}, {24,36}, {3,23}, {3,20}, {1,21}, {3,21}, {21,28}, {11,14}, {1,35}, {7,30}, {2,7}, {8,31}, {21,22}, {13,27}, {14,29}, {6,14}, {16,21}, {24,28}, {19,20}, {10,11}, {19,21}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {9,11}, {1,20}, {27,36}, {8,16}, {10,17}, {2,34}, {20,26}, {19,31}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {8,12}, {1,17}, {29,33}, {4,13}, {27,28}, {7,11}, {12,20}, {31,36}, {23,31}, {3,10}, {8,9}, {2,10}, {23,36}, {25,34}, {17,20}, {33,35}, {12,31}, {10,20}, {1,24}, {15,30}, {2,15}, {12,23}, {13,20}, {26,35}, {16,25}, {28,30}, {9,35}, {1,36}, {15,19}, {1,29}, {24,26}, {4,23}, {11,18}, {13,26}, {29,31}, {6,24}, {30,36}, {13,16}, {2,29}, {5,34}, {1,26}, {14,32}, {2,36}, {20,36}, {7,15}, {8,22}, {26,36}, {22,34}, {18,29}, {9,29}, {9,20}, {4,22}, {18,36}, {29,32}, {8,19}, {1,18}, {15,28}, {6,17}, {32,35}, {6,10}, {8,18}, {4,18}, {14,35}, {10,12}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {25,26}, {3,13}, {11,22}, {9,13}, {6,27}, {2,30}, {2,8}, {4,9}, {30,31}, {3,36}, {25,29}, {4,21}, {17,29}, {13,17}, {18,19}, {7,19}, {1,30}, {16,18}, {2,13}, {12,15}, {8,10}, {11,21}, {16,29}, {10,16}, {16,17}, {11,16}, {10,36}, {3,24}, {14,15}, {6,16}, {15,34}, {11,33}, {13,25}, {7,12}, {8,24}, {31,33}, {14,21}, {9,26}, {18,20}, {5,14}, {28,34}, {12,17}, {13,36}, {10,13}, {22,29}, {25,32}, {9,22}, {20,31}, {19,24}, {11,34}, {17,28}, {34,36}, {6,8}, {22,30}, {27,34}, {2,27}, {2,12}, {1,22}, {7,34}, {11,24}, {10,31}, {7,8}, {18,25}, {24,25}, {6,13}, {1,25}, {22,31}, {23,35}, {6,19}, {20,30}, {4,17}, {9,16}, {9,30}, {17,19}, {9,12}, {3,32}, {7,28}, {12,18}, {4,5}, {10,22}, {7,23}, {6,22}, {10,25}, {12,29}, {26,31}, {6,31}, {11,32}, {21,32}, {16,26}, {1,16}, {3,22}, {4,14}, {24,35}, {4,15}, {31,32}, {6,23}, {16,31}, {15,17}, {13,14}, {4,36}, {4,29}, {1,32}, {30,32}, {28,32}, {24,27}, {7,24}, {29,30}, {17,25}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {26,30}, {18,30}, {2,28}, {9,23}, {14,16}, {8,36}, {8,27}, {3,33}, {2,11}, {14,26}, {23,32}, {3,5}, {19,33}, {9,28}, {3,34}, {4,27}, {5,24}, {15,29}, {16,20}, {8,11}, {18,24}, {25,36}, {2,31}, {14,19}, {1,33}, {18,27}, {12,36}, {16,27}, {26,28}, {3,14}, {5,26}, {3,11}, {4,8}, {5,29}, {14,30}, {21,34}, {12,33}, {5,9}, {11,19}, {4,12}, {21,35}, {28,33}, {8,14}, {7,10}, {27,29}, {3,6}, {22,33}, {20,33}, {19,35}, {3,15}, {13,34}, {7,25}, {6,26}, {1,34}, {22,27}, {30,34}, {13,35}, {14,18}, {22,23}, {20,23}, {17,21}, {28,35}, {23,30}, {6,28}, {4,35}, {19,32}, {13,33}, {13,15}, {14,25}, {11,12}, {20,34}, {7,26}, {7,18}, {5,18}, {5,16}, {1,23}, {22,24}, {35,36}, {15,18}, {10,34}, {10,27}, {3,4}, {16,33}, {7,17}, {17,27}, {15,20}, {13,28}, {1,28}, {23,25}, {7,20}, {7,9}, {25,35}, {21,36}, {15,31}, {8,28}, {1,27}, {5,13}, {5,25}, {25,27}, {32,34}, {17,23}, {10,23}, {26,33}, {4,6}, {27,31}, {22,32}, {29,35}, {3,12}, {16,19}, {24,33}, {10,32}, {12,35}, {17,32}, {12,19}, {23,26}, {20,21}, {22,28}, {23,24}, {2,9}, {2,32}, {6,7}, {2,14}, {18,34}, {5,33}, {5,30} }; // ET36.126 // Bipartite(3,33) Valencies [22,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 381608820557217792000000 EdgePairs[36][126]:={ {2,11}, {3,22}, {1,26}, {2,14}, {1,14}, {2,26}, {3,12}, {2,32}, {2,30}, {1,29}, {2,29}, {1,32}, {2,24}, {1,10}, {3,21}, {3,27}, {3,33}, {2,6}, {1,4}, {1,20}, {2,36}, {1,31}, {3,9}, {3,24}, {2,12}, {2,33}, {2,21}, {1,7}, {3,4}, {1,16}, {3,7}, {2,20}, {3,16}, {3,28}, {3,15}, {2,18}, {3,25}, {3,19}, {3,30}, {2,15}, {2,5}, {3,18}, {3,31}, {1,5}, {2,27}, {1,17}, {3,6}, {3,34}, {1,28}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {1,22}, {2,8}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {3,10}, {3,36} }; // ET36.127 // Bipartite(12,24) Valencies [22,11] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1961990553600 EdgePairs[36][127]:={ {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {8,31}, {6,14}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {12,20}, {1,13}, {12,26}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {2,15}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {6,24}, {2,29}, {5,34}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {8,18}, {4,18}, {7,32}, {12,24}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {6,27}, {2,30}, {5,35}, {3,36}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {6,16}, {11,33}, {8,24}, {9,26}, {5,14}, {3,29}, {12,17}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {11,13}, {7,35}, {2,27}, {12,30}, {6,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {4,17}, {9,16}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {4,34}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {1,15}, {7,26}, {11,28}, {7,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {7,13}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {6,35}, {12,19}, {8,25}, {6,33}, {12,21}, {2,14}, {5,33}, {5,30} }; // ET36.128 // Bipartite(14,22) Valencies [22,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 97988462755208211166396416000000 EdgePairs[36][128]:={ {13,21}, {14,36}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {13,27}, {14,29}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,15}, {14,33}, {14,23}, {6,16}, {11,33}, {13,25}, {8,24}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {3,15}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {13,15}, {1,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {12,19}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {5,30} }; // ET36.129 // Non-bipartite Valency 22 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 2874009600 EdgePairs[36][129]:={ {13,21}, {15,33}, {14,36}, {5,7}, {6,25}, {23,29}, {5,22}, {4,28}, {9,10}, {5,11}, {16,22}, {17,33}, {6,15}, {3,35}, {8,21}, {14,31}, {5,15}, {15,27}, {24,32}, {1,19}, {27,33}, {24,36}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {1,35}, {5,32}, {8,31}, {21,22}, {14,29}, {6,14}, {2,33}, {17,35}, {11,29}, {11,17}, {9,11}, {11,27}, {8,16}, {10,17}, {9,18}, {2,34}, {20,26}, {12,28}, {19,31}, {4,24}, {2,6}, {18,32}, {15,32}, {8,30}, {8,13}, {9,33}, {8,12}, {29,33}, {28,31}, {1,10}, {4,13}, {20,24}, {27,28}, {31,36}, {12,26}, {13,30}, {2,5}, {7,27}, {2,10}, {19,22}, {3,9}, {23,36}, {25,34}, {26,29}, {2,17}, {33,35}, {7,33}, {12,31}, {23,28}, {10,20}, {17,26}, {1,24}, {13,24}, {24,30}, {12,23}, {22,25}, {26,35}, {18,35}, {24,31}, {20,35}, {9,35}, {6,18}, {15,19}, {16,34}, {10,35}, {11,18}, {13,26}, {29,31}, {6,24}, {30,36}, {13,16}, {2,29}, {13,19}, {14,32}, {1,26}, {3,17}, {2,36}, {8,22}, {26,36}, {22,34}, {27,30}, {18,29}, {6,34}, {4,22}, {18,36}, {1,18}, {5,27}, {7,14}, {15,28}, {32,35}, {6,10}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {25,33}, {3,13}, {11,22}, {5,12}, {2,8}, {5,35}, {4,9}, {3,36}, {19,23}, {25,29}, {20,25}, {7,19}, {4,32}, {1,30}, {2,13}, {13,18}, {19,27}, {12,15}, {8,15}, {8,17}, {16,29}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {22,26}, {10,36}, {14,23}, {6,16}, {15,34}, {11,33}, {18,22}, {13,25}, {19,30}, {7,12}, {4,10}, {9,26}, {14,21}, {18,20}, {3,29}, {17,31}, {10,13}, {25,32}, {9,19}, {20,31}, {3,25}, {11,34}, {17,28}, {6,8}, {11,13}, {22,30}, {27,34}, {2,27}, {12,30}, {6,30}, {2,12}, {4,33}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {24,25}, {1,25}, {22,31}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {12,18}, {6,11}, {9,25}, {17,30}, {10,22}, {10,30}, {4,34}, {10,25}, {26,31}, {6,31}, {11,32}, {15,24}, {21,32}, {3,7}, {12,25}, {16,26}, {1,16}, {27,35}, {3,22}, {4,14}, {23,27}, {24,35}, {18,31}, {6,23}, {15,17}, {23,34}, {4,36}, {4,29}, {1,5}, {24,29}, {30,32}, {19,29}, {28,32}, {8,32}, {24,27}, {7,24}, {9,24}, {5,31}, {17,25}, {2,19}, {5,23}, {5,20}, {2,26}, {12,14}, {18,21}, {10,21}, {9,21}, {26,30}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {14,16}, {8,36}, {8,27}, {16,36}, {23,32}, {10,15}, {9,28}, {1,11}, {4,27}, {2,22}, {15,29}, {16,20}, {8,11}, {25,36}, {1,33}, {18,27}, {20,28}, {21,33}, {16,27}, {1,7}, {19,25}, {3,11}, {4,8}, {5,29}, {14,30}, {21,34}, {12,33}, {5,9}, {11,19}, {30,33}, {1,4}, {4,12}, {1,8}, {17,34}, {28,36}, {31,34}, {7,10}, {3,6}, {22,33}, {20,33}, {19,35}, {3,15}, {13,34}, {7,22}, {1,14}, {6,26}, {26,32}, {1,34}, {30,34}, {13,35}, {5,21}, {21,27}, {9,15}, {21,29}, {17,24}, {20,23}, {12,34}, {17,21}, {19,36}, {28,35}, {6,28}, {18,23}, {19,32}, {13,33}, {1,15}, {14,25}, {14,20}, {20,34}, {7,26}, {7,18}, {23,33}, {11,28}, {1,23}, {5,16}, {11,20}, {10,27}, {15,18}, {5,17}, {3,4}, {16,33}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {15,36}, {22,35}, {21,36}, {4,20}, {8,20}, {5,13}, {5,25}, {32,34}, {17,23}, {10,23}, {15,26}, {27,31}, {4,19}, {14,22}, {29,35}, {3,12}, {9,14}, {7,13}, {14,17}, {25,28}, {5,36}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {21,24}, {29,34}, {12,19}, {23,26}, {21,26}, {22,28}, {8,25}, {2,9}, {16,32}, {6,33}, {12,21}, {2,32}, {6,7}, {2,14}, {11,26}, {33,36}, {5,30} }; // ET36.130 // Bipartite(13,23) Valencies [23,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 160981045954984918344794112000000 EdgePairs[36][130]:={ {13,21}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {13,27}, {6,14}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,26}, {13,19}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {6,16}, {11,33}, {13,25}, {8,24}, {9,26}, {5,14}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {13,14}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {3,15}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {12,35}, {6,35}, {12,19}, {8,25}, {6,33}, {2,32}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30} }; // ET36.131 // Bipartite(4,32) Valencies [24,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 63429799040778240000 EdgePairs[36][131]:={ {4,35}, {3,15}, {2,22}, {4,8}, {4,27}, {3,7}, {2,11}, {1,25}, {4,16}, {3,32}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {3,10}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {1,17}, {1,22}, {1,16}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {4,29}, {3,22}, {3,23}, {4,31}, {3,27}, {2,34}, {4,21}, {4,36}, {4,17}, {2,35}, {4,15}, {2,9}, {4,25}, {1,26}, {4,11}, {2,27}, {3,35}, {2,21}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {1,14}, {4,32}, {1,20}, {3,16}, {1,13}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {4,9}, {2,7}, {4,23}, {1,8}, {1,30}, {4,13}, {1,21}, {2,30}, {1,6}, {1,18}, {4,19}, {4,24}, {2,5}, {1,24} }; // ET36.132 // Bipartite(9,27) Valencies [24,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3656994324480 EdgePairs[36][132]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {2,23}, {1,13}, {8,28}, {1,32}, {3,13}, {8,33}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {7,36}, {8,10}, {8,25}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {9,35}, {4,23}, {8,27}, {8,31}, {9,11}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {7,12}, {2,25}, {6,31}, {4,10}, {2,34}, {1,17}, {2,36}, {4,22}, {8,19}, {9,29}, {7,11}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {5,29}, {9,19}, {5,25}, {7,32}, {1,31}, {7,13}, {9,14}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {8,35}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {4,36}, {9,13}, {5,12}, {8,21}, {3,19}, {1,24}, {6,27}, {3,23}, {5,36}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {1,35}, {7,28}, {3,16}, {7,23}, {6,36}, {2,21}, {5,33}, {8,34}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,12}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {2,12}, {1,14}, {9,24}, {5,15}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {3,36}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET36.133 // Bipartite(12,24) Valencies [24,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 297195777147664464636542976000000 EdgePairs[36][133]:={ {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {6,14}, {2,33}, {6,32}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {12,20}, {1,13}, {12,26}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {2,15}, {12,23}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {6,24}, {2,29}, {5,34}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {6,16}, {11,33}, {8,24}, {9,26}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {11,13}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {7,13}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {12,35}, {6,35}, {12,19}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30} }; // ET36.134 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 659420041922872344576000000 EdgePairs[36][134]:={ {24,34}, {15,33}, {19,28}, {14,36}, {9,32}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {2,35}, {17,33}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {21,30}, {3,19}, {14,31}, {5,15}, {15,27}, {24,32}, {1,19}, {24,36}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {16,28}, {21,28}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {13,27}, {14,29}, {6,14}, {24,28}, {2,33}, {6,32}, {17,35}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {12,20}, {23,31}, {1,13}, {12,26}, {13,30}, {7,27}, {23,36}, {10,26}, {2,17}, {7,33}, {12,31}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {24,30}, {15,30}, {2,15}, {12,23}, {22,25}, {12,13}, {18,35}, {16,25}, {24,31}, {20,35}, {9,35}, {1,36}, {6,18}, {1,29}, {16,34}, {10,35}, {24,26}, {4,23}, {11,18}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,26}, {14,32}, {3,17}, {2,36}, {20,36}, {7,15}, {8,22}, {22,34}, {18,29}, {9,36}, {6,34}, {9,29}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {20,25}, {7,19}, {4,32}, {1,30}, {2,13}, {19,27}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {16,29}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {10,36}, {3,24}, {14,33}, {6,16}, {15,34}, {11,33}, {13,25}, {21,25}, {21,31}, {19,30}, {8,24}, {9,26}, {5,14}, {3,29}, {17,31}, {12,17}, {13,36}, {2,23}, {10,13}, {22,29}, {10,19}, {9,22}, {9,19}, {20,31}, {3,25}, {11,34}, {17,28}, {11,13}, {7,35}, {22,30}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {24,25}, {6,13}, {1,25}, {22,31}, {23,35}, {6,19}, {20,30}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {21,32}, {12,25}, {16,26}, {1,16}, {3,22}, {4,14}, {23,27}, {24,35}, {4,15}, {18,31}, {6,23}, {16,31}, {23,34}, {4,36}, {4,29}, {1,32}, {24,29}, {19,29}, {8,32}, {24,27}, {7,24}, {10,28}, {9,24}, {5,31}, {17,25}, {19,34}, {2,19}, {6,20}, {5,23}, {20,32}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {23,32}, {10,15}, {11,30}, {19,33}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {2,31}, {1,33}, {18,27}, {20,28}, {21,33}, {12,36}, {16,27}, {3,14}, {5,26}, {19,25}, {5,29}, {4,25}, {3,28}, {14,30}, {21,34}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {20,27}, {21,35}, {8,14}, {22,33}, {11,31}, {20,33}, {19,35}, {3,15}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {22,27}, {13,35}, {5,21}, {21,27}, {9,15}, {21,29}, {12,34}, {19,36}, {23,30}, {6,28}, {4,35}, {19,32}, {13,33}, {1,15}, {14,25}, {20,34}, {7,26}, {7,18}, {23,33}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {16,33}, {7,17}, {8,35}, {17,27}, {6,21}, {4,26}, {1,28}, {13,28}, {23,25}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {22,35}, {21,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {15,26}, {22,36}, {4,19}, {22,32}, {7,13}, {9,14}, {5,36}, {9,34}, {10,14}, {24,33}, {10,32}, {7,36}, {12,35}, {6,35}, {17,32}, {12,19}, {23,26}, {21,26}, {22,28}, {8,25}, {16,32}, {2,32}, {6,33}, {12,21}, {2,14}, {18,34}, {11,26}, {5,33}, {15,25}, {5,30} }; // ET36.135 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 8709120 EdgePairs[36][135]:={ {13,21}, {19,28}, {14,36}, {9,32}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {3,8}, {4,28}, {11,25}, {12,22}, {3,26}, {8,26}, {5,11}, {16,22}, {2,35}, {6,15}, {11,15}, {8,21}, {21,30}, {3,19}, {14,31}, {5,15}, {1,19}, {24,36}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {11,14}, {1,35}, {7,30}, {2,7}, {6,9}, {8,31}, {13,27}, {14,29}, {6,14}, {24,28}, {19,21}, {2,33}, {6,32}, {17,35}, {11,17}, {11,27}, {27,36}, {8,16}, {9,18}, {2,34}, {12,28}, {19,31}, {4,24}, {2,6}, {18,32}, {32,33}, {15,32}, {4,30}, {9,33}, {8,12}, {1,17}, {1,9}, {4,16}, {29,33}, {28,31}, {1,10}, {4,13}, {7,11}, {31,36}, {1,13}, {3,10}, {2,5}, {2,10}, {3,9}, {23,36}, {25,34}, {26,29}, {10,26}, {2,17}, {12,31}, {20,29}, {23,28}, {10,20}, {17,26}, {13,24}, {24,30}, {15,30}, {2,15}, {12,23}, {27,32}, {12,13}, {13,20}, {26,35}, {16,25}, {24,31}, {20,35}, {28,30}, {9,35}, {1,36}, {1,29}, {15,19}, {16,34}, {10,35}, {13,26}, {6,24}, {17,36}, {2,29}, {3,17}, {20,36}, {26,36}, {22,34}, {27,30}, {6,34}, {9,29}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {32,35}, {6,10}, {8,18}, {4,18}, {14,35}, {7,32}, {1,31}, {3,31}, {12,27}, {25,33}, {3,13}, {11,22}, {6,27}, {5,35}, {4,9}, {3,36}, {6,12}, {19,23}, {25,29}, {4,21}, {17,29}, {13,17}, {20,25}, {7,19}, {4,32}, {1,30}, {13,18}, {19,27}, {12,15}, {8,10}, {8,15}, {14,28}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {16,17}, {2,24}, {11,23}, {22,26}, {3,24}, {10,36}, {14,33}, {14,23}, {15,34}, {11,33}, {18,22}, {21,25}, {21,31}, {7,12}, {8,24}, {9,26}, {14,21}, {28,34}, {12,17}, {29,36}, {2,23}, {10,13}, {20,22}, {22,29}, {25,32}, {10,19}, {4,11}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {11,13}, {7,35}, {27,34}, {2,27}, {12,30}, {6,30}, {2,12}, {1,22}, {7,34}, {11,24}, {1,6}, {9,31}, {5,19}, {10,29}, {18,25}, {24,25}, {6,13}, {1,25}, {22,31}, {23,35}, {6,19}, {20,30}, {2,20}, {9,16}, {13,31}, {3,32}, {14,27}, {7,28}, {12,18}, {25,31}, {2,16}, {13,29}, {8,34}, {4,5}, {17,30}, {10,22}, {10,30}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {26,31}, {6,31}, {11,32}, {15,24}, {21,32}, {3,7}, {12,25}, {16,26}, {1,16}, {27,35}, {3,22}, {4,14}, {24,35}, {18,31}, {6,23}, {16,31}, {23,34}, {4,36}, {4,29}, {24,29}, {19,29}, {28,32}, {8,32}, {24,27}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {6,20}, {5,23}, {2,26}, {10,21}, {9,21}, {26,30}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,27}, {3,33}, {2,11}, {16,36}, {13,32}, {23,32}, {11,30}, {3,5}, {19,33}, {9,28}, {3,34}, {2,21}, {1,11}, {30,35}, {15,29}, {16,20}, {8,11}, {18,24}, {2,31}, {14,19}, {1,33}, {18,27}, {20,28}, {21,33}, {12,36}, {16,27}, {1,7}, {3,14}, {4,8}, {5,29}, {4,25}, {14,30}, {21,34}, {31,35}, {12,33}, {5,9}, {11,19}, {8,33}, {30,33}, {1,8}, {4,12}, {17,34}, {20,27}, {28,33}, {28,36}, {31,34}, {8,14}, {27,29}, {22,33}, {11,31}, {20,33}, {19,35}, {3,15}, {13,34}, {7,25}, {7,22}, {6,26}, {22,27}, {30,34}, {13,35}, {14,18}, {5,21}, {21,27}, {9,15}, {17,24}, {20,23}, {17,21}, {23,30}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {1,15}, {14,25}, {15,21}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,34}, {15,18}, {5,17}, {16,33}, {13,23}, {8,35}, {32,36}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {15,36}, {25,35}, {22,35}, {21,36}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {15,26}, {26,33}, {4,6}, {4,19}, {14,22}, {22,32}, {3,12}, {9,14}, {7,13}, {14,17}, {5,36}, {16,19}, {9,34}, {10,14}, {24,33}, {10,32}, {12,35}, {7,36}, {17,32}, {29,34}, {12,19}, {23,26}, {21,26}, {20,21}, {22,28}, {16,32}, {2,32}, {12,21}, {6,33}, {2,14}, {18,34}, {11,26}, {5,33}, {15,25}, {5,30} }; // ET36.136 // Bipartite(6,30) Valencies [25,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2149908480000000 EdgePairs[36][136]:={ {1,11}, {3,33}, {2,24}, {5,17}, {6,32}, {6,16}, {4,27}, {5,34}, {4,26}, {3,8}, {4,16}, {1,10}, {2,23}, {1,13}, {3,9}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {4,19}, {4,31}, {2,19}, {1,19}, {3,35}, {5,20}, {2,26}, {1,21}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {6,22}, {3,18}, {3,17}, {3,7}, {6,21}, {2,25}, {6,31}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,26}, {5,28}, {6,15}, {2,17}, {5,12}, {3,19}, {4,9}, {1,24}, {6,27}, {6,26}, {3,23}, {5,36}, {3,21}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {5,9}, {4,25}, {4,11}, {4,20}, {3,31}, {2,12}, {2,8}, {5,15}, {6,20}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {4,17}, {3,36}, {4,32}, {1,36}, {5,16} }; // ET36.137 // Bipartite(11,25) Valencies [25,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 619157869057634301326131200000000 EdgePairs[36][137]:={ {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {6,14}, {2,33}, {6,32}, {11,29}, {11,35}, {11,17}, {1,12}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {1,13}, {7,27}, {10,26}, {2,17}, {7,33}, {10,20}, {1,24}, {2,15}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {6,24}, {2,29}, {5,34}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {6,16}, {11,33}, {7,12}, {8,24}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {11,13}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {5,29}, {4,25}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {6,35}, {8,25}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30} }; // ET36.138 // Non-bipartite Valency 25 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1036800 EdgePairs[36][138]:={ {15,28}, {24,33}, {10,17}, {3,29}, {20,26}, {9,18}, {16,28}, {5,13}, {4,26}, {20,25}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {8,28}, {5,32}, {4,24}, {7,24}, {13,27}, {12,25}, {3,17}, {1,9}, {2,24}, {7,28}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {13,22}, {2,12}, {6,28}, {22,25}, {2,30}, {14,25}, {7,15}, {4,12}, {10,27}, {21,35}, {8,24}, {12,27}, {6,34}, {17,22}, {21,31}, {2,21}, {16,33}, {7,26}, {11,27}, {4,34}, {17,19}, {13,29}, {22,28}, {10,22}, {5,7}, {25,32}, {20,29}, {15,20}, {23,34}, {24,36}, {17,25}, {14,33}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {18,29}, {19,30}, {11,29}, {2,8}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {27,32}, {5,23}, {28,32}, {16,20}, {3,9}, {5,25}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {21,30}, {16,23}, {3,14}, {23,33}, {9,22}, {5,20}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {13,33}, {18,35}, {10,23}, {22,27}, {15,24}, {30,34}, {20,32}, {1,26}, {18,31}, {1,25}, {26,32}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {9,31}, {7,23}, {5,33}, {7,16}, {6,11}, {6,24}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {1,27}, {5,22}, {9,25}, {5,36}, {9,26}, {18,20}, {6,12}, {7,31}, {12,33}, {10,19}, {12,19}, {15,27}, {11,32}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {21,34}, {10,31}, {3,18}, {5,15}, {5,16}, {19,32}, {1,28}, {27,33}, {1,17}, {3,36}, {14,36}, {24,25}, {26,31}, {23,26}, {18,22}, {5,8}, {7,29}, {12,28}, {29,36}, {1,35}, {17,28}, {26,35}, {23,32}, {5,21}, {7,36}, {13,26}, {22,33}, {11,24}, {20,31}, {8,33}, {10,28}, {15,23}, {12,17}, {2,7}, {9,19}, {13,35}, {1,13}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {23,28}, {21,29}, {3,28}, {2,14}, {12,24}, {14,28}, {30,36}, {12,20}, {1,11}, {29,33}, {24,34}, {15,30}, {3,19}, {2,16}, {16,36}, {18,25}, {14,19}, {21,27}, {25,36}, {7,35}, {9,13}, {15,29}, {4,15}, {4,29}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {18,23}, {12,15}, {14,31}, {8,22}, {14,20}, {11,33}, {1,34}, {11,16}, {7,25}, {8,27}, {24,31}, {5,30}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {1,23}, {17,31}, {8,29}, {7,22}, {19,36}, {9,34}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {3,12}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {19,33}, {19,29}, {3,34}, {11,14}, {13,20}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {15,19}, {9,33}, {29,34}, {8,16}, {20,35}, {8,32}, {14,30}, {17,24}, {12,23}, {8,18}, {5,31}, {4,25}, {3,30}, {6,7}, {18,33}, {1,7}, {8,15}, {21,33}, {10,34}, {24,28}, {4,14}, {6,25}, {11,17}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {24,26}, {11,26}, {13,24}, {11,13}, {6,16}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {18,24}, {8,14}, {2,29}, {14,21}, {3,21}, {19,27}, {1,36}, {13,30}, {24,32}, {6,20}, {11,15}, {23,35}, {12,34}, {8,19}, {7,21}, {11,30}, {2,23}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {9,36}, {16,21}, {6,27}, {15,32}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {11,22}, {9,16}, {9,32}, {30,35}, {18,32}, {21,32}, {23,30}, {22,31}, {30,31}, {22,35}, {1,21}, {9,15}, {28,36}, {23,27}, {16,19}, {12,36}, {27,31}, {7,18}, {3,33}, {5,17}, {1,24}, {19,25}, {6,8}, {17,21}, {2,9}, {4,18}, {21,28}, {23,36}, {4,8}, {29,31}, {12,31}, {1,15}, {20,36}, {29,35}, {28,33}, {4,35}, {7,19}, {2,35}, {10,32}, {16,24}, {4,19}, {5,11}, {4,36}, {6,29}, {2,31} }; // ET36.139 // Bipartite(10,26) Valencies [26,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1463464054136226530407219200000000 EdgePairs[36][139]:={ {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {4,28}, {3,26}, {8,26}, {5,11}, {2,35}, {4,31}, {6,15}, {3,35}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {6,14}, {10,11}, {2,33}, {6,32}, {1,12}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {7,11}, {1,13}, {7,27}, {10,26}, {2,17}, {7,33}, {10,20}, {1,24}, {2,15}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {6,24}, {2,29}, {5,34}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {6,16}, {7,12}, {8,24}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {6,35}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30} }; // ET36.140 // Bipartite(9,27) Valencies [27,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3951352946167811632099491840000000 EdgePairs[36][140]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {7,36}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {9,35}, {4,23}, {8,27}, {8,31}, {9,11}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,11}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {9,19}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {9,34}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {8,35}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {4,36}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {1,35}, {7,28}, {3,16}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {8,34}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {6,35}, {3,36}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET36.141 // Non-bipartite Valency 27 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 416162911506546032640000 EdgePairs[36][141]:={ {15,28}, {6,36}, {24,33}, {15,17}, {10,17}, {3,29}, {20,26}, {9,18}, {5,13}, {4,26}, {20,25}, {14,29}, {2,4}, {26,33}, {2,20}, {3,7}, {19,22}, {8,28}, {5,32}, {4,24}, {1,5}, {7,24}, {15,16}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,11}, {8,36}, {1,18}, {3,10}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {14,16}, {12,32}, {22,25}, {2,30}, {5,9}, {20,22}, {7,15}, {4,12}, {10,27}, {7,10}, {21,35}, {8,24}, {8,11}, {12,27}, {6,34}, {17,22}, {2,21}, {16,33}, {7,26}, {31,36}, {11,27}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {25,29}, {5,7}, {25,32}, {20,29}, {15,20}, {9,10}, {14,33}, {17,25}, {3,32}, {11,31}, {7,13}, {10,13}, {25,28}, {19,30}, {22,29}, {11,29}, {2,8}, {20,28}, {10,25}, {13,17}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {21,30}, {16,23}, {23,33}, {9,22}, {31,35}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {13,33}, {18,35}, {22,27}, {15,24}, {30,34}, {18,31}, {9,27}, {26,32}, {10,16}, {6,14}, {15,34}, {24,30}, {8,35}, {5,27}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {6,24}, {29,32}, {19,35}, {10,14}, {16,34}, {18,26}, {14,23}, {3,16}, {18,21}, {22,26}, {2,28}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {18,20}, {6,12}, {21,36}, {12,33}, {13,18}, {1,29}, {21,22}, {2,34}, {10,19}, {12,19}, {14,35}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {16,35}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {10,18}, {9,17}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {21,34}, {18,34}, {10,31}, {3,18}, {13,23}, {5,15}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {14,36}, {24,25}, {26,31}, {23,26}, {18,22}, {5,8}, {7,29}, {12,28}, {29,36}, {1,35}, {26,35}, {23,32}, {5,21}, {7,36}, {22,33}, {4,7}, {10,28}, {15,23}, {12,17}, {2,7}, {13,35}, {13,32}, {17,36}, {17,23}, {23,28}, {21,29}, {3,28}, {9,35}, {18,19}, {3,4}, {14,28}, {30,36}, {15,36}, {12,20}, {1,11}, {29,33}, {33,34}, {15,30}, {3,19}, {2,16}, {16,36}, {18,25}, {14,19}, {21,27}, {25,36}, {7,35}, {9,13}, {21,23}, {15,29}, {30,33}, {4,15}, {8,25}, {5,34}, {26,34}, {1,30}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {8,27}, {24,31}, {15,22}, {16,27}, {9,30}, {16,31}, {22,30}, {27,34}, {4,13}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {19,36}, {9,34}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {17,35}, {6,32}, {15,31}, {4,27}, {18,36}, {3,12}, {14,24}, {3,24}, {7,27}, {7,11}, {4,32}, {15,35}, {1,19}, {2,10}, {32,35}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {13,21}, {3,11}, {4,10}, {14,34}, {3,5}, {15,19}, {29,34}, {8,16}, {20,35}, {14,30}, {17,24}, {13,31}, {8,18}, {5,31}, {4,25}, {3,30}, {6,7}, {24,27}, {18,33}, {1,7}, {8,15}, {24,28}, {4,14}, {11,28}, {6,25}, {28,34}, {11,17}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {12,26}, {6,9}, {10,30}, {5,12}, {11,20}, {4,9}, {5,10}, {24,26}, {11,26}, {13,24}, {11,13}, {26,36}, {20,34}, {25,34}, {4,31}, {30,32}, {10,33}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {20,30}, {2,29}, {14,21}, {3,21}, {19,27}, {1,36}, {26,30}, {2,6}, {13,30}, {24,32}, {9,24}, {6,20}, {11,15}, {6,26}, {4,20}, {23,31}, {12,16}, {11,30}, {2,23}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {27,30}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {15,32}, {11,25}, {25,35}, {17,27}, {2,17}, {33,35}, {25,31}, {5,14}, {5,35}, {9,16}, {16,32}, {27,28}, {30,35}, {18,32}, {23,30}, {21,26}, {22,31}, {30,31}, {26,29}, {1,21}, {19,34}, {6,21}, {9,15}, {28,36}, {8,12}, {23,27}, {16,19}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {27,35}, {1,24}, {19,25}, {6,8}, {17,21}, {2,9}, {2,18}, {21,28}, {26,28}, {4,8}, {29,31}, {1,16}, {2,19}, {5,24}, {6,15}, {12,31}, {20,36}, {29,35}, {27,29}, {28,33}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {4,36}, {2,31} }; // ET36.142 // Bipartite(8,28) Valencies [28,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12293098054744302855420641280000000 EdgePairs[36][142]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {3,17}, {6,29}, {8,16}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,11}, {7,20}, {5,11}, {2,10}, {5,29}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {7,28}, {3,16}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {7,19}, {4,17}, {6,35}, {3,36}, {7,21}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET36.143 // Bipartite(7,29) Valencies [29,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 44562480448448097850899824640000000 EdgePairs[36][143]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {7,28}, {3,16}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {7,19}, {4,17}, {6,35}, {3,36}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET36.144 // Bipartite(6,30) Valencies [30,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 190982059064777562218142105600000000 EdgePairs[36][144]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {1,21}, {2,9}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {6,21}, {3,34}, {2,25}, {6,31}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {6,8}, {5,25}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {5,36}, {3,21}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {3,16}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {4,17}, {6,35}, {3,36}, {4,32}, {1,36}, {5,16} }; // ET36.145 // Non-bipartite Valency 30 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 100306130042880000000 EdgePairs[36][145]:={ {13,25}, {15,28}, {6,36}, {24,33}, {10,17}, {3,29}, {9,18}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {8,28}, {5,32}, {4,24}, {8,31}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {12,32}, {22,25}, {2,30}, {14,25}, {5,9}, {7,15}, {3,25}, {4,12}, {10,27}, {4,30}, {21,35}, {8,24}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {10,22}, {5,7}, {25,32}, {20,29}, {12,22}, {15,20}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {2,8}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {13,33}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {5,27}, {9,31}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {6,24}, {29,32}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {27,33}, {1,17}, {3,36}, {9,14}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {15,23}, {12,17}, {2,7}, {9,19}, {13,35}, {1,13}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {18,19}, {14,28}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {2,16}, {16,36}, {14,19}, {18,25}, {21,27}, {25,36}, {7,35}, {9,13}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {11,16}, {7,25}, {24,35}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {19,33}, {19,29}, {3,34}, {11,14}, {13,20}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {15,19}, {9,33}, {29,34}, {8,16}, {20,35}, {8,32}, {14,30}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {23,25}, {18,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {1,36}, {13,30}, {9,24}, {24,32}, {6,20}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {9,36}, {8,13}, {16,21}, {6,27}, {15,32}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {7,20}, {16,19}, {23,27}, {12,36}, {27,31}, {7,18}, {10,21}, {3,33}, {27,35}, {5,17}, {1,24}, {6,8}, {19,25}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {4,8}, {29,31}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET36.146 // Bipartite(5,31) Valencies [31,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 986740638501350738127067545600000000 EdgePairs[36][146]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {3,18}, {3,17}, {3,7}, {3,34}, {2,25}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {5,25}, {1,31}, {3,12}, {2,35}, {1,22}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {3,26}, {5,28}, {2,17}, {4,36}, {4,6}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {3,23}, {3,21}, {5,36}, {2,7}, {1,25}, {1,15}, {2,11}, {1,35}, {3,16}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,31}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {5,6}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {5,21}, {2,30}, {5,35}, {2,18}, {1,34}, {4,17}, {3,36}, {4,32}, {1,36}, {5,16} }; // ET36.147 // Bipartite(4,32) Valencies [32,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6315140086408644724013232291840000000 EdgePairs[36][147]:={ {1,15}, {4,35}, {3,15}, {1,11}, {4,14}, {2,22}, {3,29}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {3,32}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,36}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {3,27}, {2,34}, {4,30}, {1,19}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,35}, {1,26}, {2,24}, {4,11}, {2,27}, {3,35}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {4,9}, {2,7}, {4,34}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET36.148 // Non-bipartite Valency 32 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 958659120196485120 EdgePairs[36][148]:={ {13,25}, {15,28}, {6,36}, {24,33}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {8,24}, {8,11}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {31,36}, {11,27}, {18,28}, {4,34}, {13,29}, {22,28}, {10,22}, {25,29}, {25,32}, {20,29}, {12,22}, {4,5}, {15,20}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {31,35}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {13,33}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {6,24}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {6,12}, {21,36}, {7,31}, {12,33}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {7,29}, {12,28}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {15,23}, {12,17}, {2,7}, {9,19}, {13,35}, {1,13}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {2,16}, {16,36}, {14,19}, {18,25}, {21,27}, {25,36}, {7,35}, {9,13}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {7,25}, {24,35}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {3,30}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {10,33}, {13,34}, {20,24}, {23,25}, {18,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {1,36}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {4,6}, {6,20}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {27,30}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {15,32}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {25,31}, {16,18}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {22,35}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {8,12}, {7,20}, {16,19}, {23,27}, {12,36}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {27,35}, {28,30}, {5,17}, {1,24}, {19,25}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {4,8}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET36.149 // Bipartite(3,33) Valencies [33,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 52099905712871318973109166407680000000 EdgePairs[36][149]:={ {1,15}, {3,15}, {1,11}, {2,22}, {3,29}, {1,31}, {3,7}, {2,11}, {2,20}, {1,25}, {3,32}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,36}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {2,34}, {3,27}, {1,19}, {2,35}, {2,9}, {3,5}, {1,4}, {1,35}, {1,26}, {2,4}, {2,24}, {2,27}, {3,4}, {3,35}, {1,23}, {2,21}, {1,7}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {2,7}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET36.150 // Non-bipartite Valency 33 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1042682221795737600 EdgePairs[36][150]:={ {13,25}, {15,28}, {6,36}, {24,33}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {8,28}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {15,16}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {8,24}, {8,11}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {15,20}, {9,10}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {31,35}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {13,33}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {6,24}, {29,32}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {13,18}, {1,29}, {2,34}, {21,22}, {10,19}, {12,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {15,23}, {12,17}, {2,7}, {9,19}, {13,35}, {1,13}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {3,4}, {18,19}, {14,28}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {1,11}, {29,33}, {33,34}, {15,30}, {24,34}, {3,19}, {2,16}, {16,36}, {14,19}, {18,25}, {21,27}, {25,36}, {7,35}, {9,13}, {21,23}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {24,35}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,35}, {8,32}, {14,30}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {1,36}, {26,30}, {2,6}, {13,30}, {9,24}, {24,32}, {6,20}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {27,30}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {15,32}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {33,35}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {8,12}, {7,20}, {16,19}, {23,27}, {12,36}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {27,35}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {26,28}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET36.151 // Bipartite(2,34) Valencies [34,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 590465598079208281695237219287040000000 EdgePairs[36][151]:={ {2,11}, {1,26}, {2,14}, {1,14}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,33}, {1,10}, {1,36}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {2,36}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET36.152 // Non-bipartite Valency 34 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1678343852714360832000 EdgePairs[36][152]:={ {13,25}, {15,28}, {6,36}, {24,33}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {8,24}, {8,11}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {4,5}, {15,20}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {31,35}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {34,36}, {13,33}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {22,24}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {13,35}, {10,11}, {1,13}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {18,19}, {14,28}, {2,3}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {2,16}, {16,36}, {14,19}, {18,25}, {21,27}, {25,36}, {7,35}, {9,13}, {21,23}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {24,35}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {1,36}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {4,6}, {6,20}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {27,30}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {15,32}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {33,35}, {25,31}, {16,18}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {8,12}, {7,20}, {16,19}, {23,27}, {34,35}, {12,36}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {27,35}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {26,28}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET36.153 // Bipartite(1,35) Valencies [35,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 10333147966386144929666651337523200000000 EdgePairs[36][153]:={ {1,4}, {1,20}, {1,3}, {1,34}, {1,30}, {1,14}, {1,23}, {1,33}, {1,24}, {1,7}, {1,27}, {1,29}, {1,35}, {1,5}, {1,15}, {1,22}, {1,28}, {1,16}, {1,10}, {1,12}, {1,13}, {1,17}, {1,2}, {1,11}, {1,36}, {1,19}, {1,18}, {1,25}, {1,32}, {1,21}, {1,9}, {1,26}, {1,31}, {1,6}, {1,8} }; // ET36.154 // Non-bipartite Valency 35 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 371993326789901217467999448150835200000000 EdgePairs[36][154]:={ {13,25}, {15,28}, {6,36}, {24,33}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {11,12}, {5,32}, {4,24}, {8,31}, {1,5}, {7,24}, {15,16}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {8,24}, {8,11}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {35,36}, {4,5}, {15,20}, {9,10}, {17,18}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {25,26}, {9,22}, {31,35}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {34,36}, {13,33}, {23,24}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {13,18}, {1,29}, {2,34}, {21,22}, {10,19}, {12,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {12,28}, {29,36}, {1,35}, {31,32}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {22,24}, {13,26}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {13,35}, {10,11}, {1,13}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {3,4}, {18,19}, {14,28}, {2,3}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {1,11}, {29,33}, {33,34}, {15,30}, {24,34}, {3,19}, {2,16}, {16,36}, {14,19}, {18,25}, {21,27}, {25,36}, {7,8}, {7,35}, {9,13}, {21,23}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {24,35}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {5,6}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {4,10}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {1,36}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {1,2}, {4,6}, {6,20}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {19,20}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {27,30}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {15,32}, {29,30}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {33,35}, {25,31}, {16,18}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {26,29}, {1,21}, {13,14}, {6,21}, {9,15}, {19,34}, {28,36}, {8,12}, {7,20}, {16,19}, {23,27}, {34,35}, {12,36}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {27,35}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {26,28}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // Total number of connected ET graphs of order 36 is 154 // ******************************************************************************************** // Order 37 // ET37.1 // Non-bipartite Valency 2 // Diameter 18 Girth 37 // Twin-free VT AT // Automorphism group of order 74 EdgePairs[37][1]:={ {15,35}, {18,35}, {17,37}, {15,32}, {4,24}, {8,28}, {10,27}, {14,31}, {17,34}, {6,26}, {11,28}, {8,25}, {12,32}, {10,30}, {14,34}, {3,23}, {16,33}, {3,20}, {16,36}, {7,27}, {9,29}, {5,25}, {20,37}, {13,33}, {1,21}, {4,21}, {1,18}, {12,29}, {2,19}, {9,26}, {13,30}, {11,31}, {5,22}, {6,23}, {2,22}, {7,24}, {19,36} }; // ET37.2 // Non-bipartite Valency 4 // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 148 EdgePairs[37][2]:={ {2,11}, {15,35}, {18,35}, {5,33}, {15,32}, {17,37}, {4,13}, {4,24}, {8,28}, {6,34}, {10,27}, {14,31}, {27,36}, {17,34}, {7,16}, {3,12}, {1,29}, {2,30}, {1,10}, {6,26}, {11,28}, {11,20}, {25,34}, {8,25}, {15,24}, {10,30}, {12,32}, {14,34}, {3,23}, {9,37}, {6,15}, {16,33}, {3,20}, {20,29}, {4,32}, {16,36}, {7,27}, {9,29}, {23,32}, {5,25}, {20,37}, {19,28}, {21,30}, {13,33}, {24,33}, {8,36}, {1,21}, {4,21}, {26,35}, {3,31}, {1,18}, {12,29}, {16,25}, {22,31}, {7,35}, {13,22}, {10,19}, {2,19}, {9,18}, {14,23}, {5,14}, {18,27}, {9,26}, {13,30}, {17,26}, {11,31}, {28,37}, {5,22}, {8,17}, {6,23}, {2,22}, {7,24}, {12,21}, {19,36} }; // ET37.3 // Non-bipartite Valency 6 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 222 EdgePairs[37][3]:={ {16,36}, {26,28}, {14,34}, {2,22}, {24,26}, {11,33}, {10,27}, {23,25}, {7,24}, {6,23}, {17,19}, {2,37}, {12,14}, {27,29}, {16,18}, {34,36}, {7,27}, {12,27}, {5,7}, {4,6}, {9,31}, {16,33}, {2,19}, {4,26}, {22,24}, {15,32}, {10,30}, {3,18}, {1,3}, {20,35}, {13,33}, {8,28}, {1,36}, {14,16}, {18,33}, {10,25}, {10,12}, {1,16}, {6,21}, {12,34}, {8,10}, {2,17}, {33,35}, {7,29}, {35,37}, {6,8}, {15,35}, {13,35}, {3,23}, {30,32}, {11,28}, {6,26}, {4,21}, {32,34}, {12,29}, {13,30}, {3,5}, {11,26}, {2,4}, {20,37}, {18,35}, {2,24}, {11,13}, {5,22}, {25,27}, {14,36}, {22,37}, {1,23}, {5,27}, {14,31}, {5,20}, {11,31}, {17,37}, {19,36}, {15,37}, {9,24}, {13,28}, {8,23}, {21,23}, {28,30}, {9,26}, {18,20}, {21,36}, {7,9}, {19,34}, {17,34}, {9,11}, {7,22}, {8,25}, {3,25}, {9,29}, {10,32}, {15,17}, {29,31}, {3,20}, {13,15}, {14,29}, {12,32}, {17,32}, {8,30}, {20,22}, {15,30}, {19,21}, {16,31}, {31,33}, {1,21}, {1,18}, {5,25}, {4,19}, {4,24}, {6,28} }; // ET37.4 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 444 EdgePairs[37][4]:={ {21,23}, {10,25}, {5,17}, {2,24}, {11,20}, {11,36}, {12,29}, {4,24}, {15,24}, {16,33}, {4,26}, {4,16}, {1,10}, {8,30}, {22,37}, {2,23}, {1,13}, {12,32}, {8,28}, {16,31}, {15,31}, {21,37}, {4,29}, {32,34}, {34,36}, {8,33}, {3,25}, {3,15}, {10,26}, {17,34}, {4,19}, {7,22}, {2,19}, {2,27}, {2,4}, {5,20}, {13,35}, {14,31}, {1,21}, {16,18}, {16,25}, {8,10}, {8,25}, {24,36}, {12,34}, {2,14}, {13,29}, {12,37}, {3,5}, {9,11}, {18,34}, {10,22}, {19,21}, {6,22}, {3,18}, {11,28}, {10,30}, {19,28}, {23,32}, {6,21}, {14,23}, {31,33}, {11,33}, {6,31}, {1,17}, {5,22}, {26,28}, {9,29}, {1,18}, {17,37}, {14,36}, {15,32}, {9,26}, {18,20}, {22,34}, {2,37}, {27,29}, {14,30}, {6,8}, {5,25}, {11,13}, {7,32}, {3,12}, {11,31}, {17,33}, {1,22}, {15,27}, {25,34}, {4,21}, {10,31}, {3,20}, {9,34}, {13,22}, {14,16}, {6,18}, {26,35}, {16,37}, {1,29}, {24,26}, {8,17}, {18,30}, {9,25}, {7,16}, {23,35}, {8,36}, {13,33}, {16,32}, {11,23}, {1,23}, {5,30}, {15,35}, {9,37}, {5,7}, {28,37}, {12,28}, {15,37}, {23,25}, {13,25}, {27,36}, {13,28}, {5,14}, {19,31}, {4,13}, {18,27}, {20,22}, {15,17}, {10,12}, {18,33}, {6,23}, {1,3}, {21,33}, {30,32}, {15,36}, {25,37}, {12,33}, {6,15}, {13,30}, {2,17}, {33,35}, {4,6}, {20,29}, {12,27}, {3,19}, {6,27}, {6,26}, {14,34}, {8,23}, {3,23}, {10,32}, {21,30}, {12,14}, {17,29}, {17,19}, {35,37}, {13,15}, {7,29}, {19,36}, {6,28}, {22,31}, {9,30}, {2,11}, {20,35}, {7,28}, {28,30}, {20,37}, {22,24}, {11,26}, {10,35}, {7,23}, {16,36}, {5,33}, {9,18}, {3,24}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {29,31}, {11,32}, {8,24}, {7,9}, {20,36}, {6,34}, {5,27}, {5,26}, {10,19}, {4,25}, {4,20}, {12,24}, {8,20}, {3,28}, {7,27}, {14,35}, {25,27}, {21,36}, {7,24}, {3,31}, {9,24}, {17,26}, {13,34}, {19,35}, {7,35}, {5,21}, {2,30}, {15,30}, {19,34}, {2,18}, {9,31}, {7,19}, {24,33}, {17,32}, {9,21}, {16,28}, {18,35}, {20,32}, {8,29}, {4,32}, {12,21}, {14,29}, {1,36}, {14,26} }; // ET37.5 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 666 EdgePairs[37][5]:={ {13,21}, {15,33}, {14,36}, {5,7}, {9,32}, {6,25}, {23,29}, {5,22}, {10,18}, {9,17}, {3,8}, {4,28}, {11,25}, {3,26}, {8,26}, {5,11}, {13,37}, {16,22}, {1,3}, {3,35}, {10,33}, {8,21}, {14,31}, {24,32}, {1,19}, {27,33}, {3,23}, {8,23}, {3,20}, {1,21}, {3,21}, {19,37}, {20,37}, {7,30}, {2,7}, {8,31}, {13,27}, {14,29}, {6,14}, {16,21}, {19,21}, {2,33}, {17,35}, {11,35}, {11,29}, {11,17}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {2,34}, {20,26}, {22,37}, {2,25}, {4,24}, {18,32}, {15,32}, {8,30}, {8,13}, {9,33}, {1,9}, {8,37}, {12,20}, {31,36}, {23,31}, {12,26}, {13,30}, {7,27}, {2,10}, {3,9}, {23,36}, {2,17}, {33,35}, {12,31}, {23,28}, {1,24}, {24,30}, {15,30}, {2,15}, {5,37}, {27,32}, {18,35}, {20,35}, {28,30}, {1,36}, {16,34}, {35,37}, {24,26}, {4,23}, {13,26}, {29,31}, {17,36}, {6,24}, {30,36}, {5,34}, {13,19}, {14,32}, {3,17}, {7,15}, {8,22}, {24,37}, {9,29}, {18,26}, {4,22}, {18,36}, {18,33}, {1,18}, {5,27}, {15,28}, {5,28}, {4,18}, {10,12}, {12,27}, {25,33}, {2,8}, {4,9}, {14,34}, {6,12}, {4,21}, {20,25}, {16,18}, {1,30}, {13,18}, {19,27}, {8,10}, {14,28}, {16,29}, {10,16}, {3,16}, {2,24}, {11,16}, {14,33}, {15,37}, {15,34}, {11,33}, {7,12}, {31,33}, {4,10}, {18,20}, {9,26}, {28,34}, {17,31}, {12,17}, {13,36}, {20,22}, {15,23}, {9,22}, {3,25}, {19,24}, {11,34}, {34,36}, {6,8}, {11,13}, {25,30}, {22,30}, {12,30}, {6,30}, {4,33}, {11,24}, {1,6}, {9,31}, {5,19}, {10,29}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {17,19}, {3,32}, {14,27}, {12,18}, {25,31}, {2,16}, {6,11}, {17,30}, {10,30}, {16,30}, {10,25}, {15,35}, {12,29}, {26,31}, {12,25}, {1,16}, {27,35}, {3,22}, {14,37}, {18,31}, {16,31}, {6,23}, {15,17}, {4,36}, {1,32}, {24,29}, {31,37}, {30,32}, {6,37}, {8,32}, {32,37}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {19,34}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {23,37}, {7,29}, {29,37}, {9,23}, {7,21}, {14,16}, {8,27}, {16,36}, {13,32}, {10,15}, {11,30}, {3,5}, {19,33}, {9,28}, {3,34}, {2,21}, {4,27}, {30,35}, {5,24}, {15,29}, {2,22}, {18,24}, {2,31}, {14,19}, {1,33}, {20,28}, {12,36}, {1,7}, {26,28}, {19,25}, {3,11}, {2,37}, {5,29}, {21,34}, {7,31}, {11,19}, {4,12}, {17,34}, {21,35}, {28,33}, {28,36}, {8,14}, {27,29}, {11,31}, {20,33}, {7,25}, {7,22}, {1,14}, {6,26}, {26,32}, {22,27}, {13,35}, {21,27}, {9,15}, {21,29}, {2,4}, {12,34}, {19,36}, {6,28}, {18,23}, {4,35}, {19,32}, {13,33}, {13,15}, {15,21}, {14,20}, {1,15}, {20,34}, {7,26}, {11,28}, {5,18}, {1,23}, {16,35}, {22,24}, {10,24}, {10,27}, {10,34}, {16,33}, {6,21}, {4,26}, {15,20}, {17,37}, {13,28}, {26,34}, {23,25}, {16,24}, {3,27}, {7,20}, {9,27}, {7,9}, {12,32}, {22,35}, {21,36}, {5,10}, {8,28}, {5,13}, {5,25}, {25,27}, {32,34}, {17,23}, {10,23}, {22,36}, {4,6}, {4,19}, {14,22}, {29,35}, {7,13}, {9,14}, {5,36}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {29,34}, {21,26}, {22,28}, {8,25}, {11,26}, {18,37}, {21,23} }; // ET37.6 // Bipartite(18,19) Valencies [19,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 778817392288148379660189696000000 EdgePairs[37][6]:={ {13,21}, {15,33}, {10,37}, {14,36}, {9,32}, {6,25}, {5,22}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {1,21}, {3,21}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {13,19}, {14,32}, {1,26}, {2,36}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {5,27}, {15,28}, {5,28}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {8,24}, {14,21}, {9,26}, {18,20}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {18,31}, {6,23}, {16,31}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {14,19}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {3,37}, {5,36}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {9,37} }; // ET37.7 // Bipartite(17,20) Valencies [20,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 865352658097942644066877440000000 EdgePairs[37][7]:={ {13,21}, {15,33}, {10,37}, {14,36}, {9,32}, {6,25}, {5,22}, {10,18}, {11,25}, {4,28}, {17,18}, {12,22}, {3,26}, {8,26}, {13,37}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {13,19}, {1,26}, {14,32}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {14,21}, {9,26}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {6,23}, {16,31}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {3,37}, {5,36}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {9,37} }; // ET37.8 // Bipartite(16,21) Valencies [21,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1068965048238635030906142720000000 EdgePairs[37][8]:={ {13,21}, {15,33}, {10,37}, {14,36}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {16,22}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {8,37}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {5,34}, {13,19}, {1,26}, {14,32}, {3,17}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {6,23}, {16,31}, {15,17}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {3,37}, {14,22}, {14,17}, {5,36}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {9,37} }; // ET37.9 // Bipartite(15,22) Valencies [22,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1469826941328123167495946240000000 EdgePairs[37][9]:={ {13,21}, {15,33}, {10,37}, {14,36}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {13,19}, {1,26}, {14,32}, {3,17}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,33}, {15,37}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {8,24}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,22}, {14,37}, {6,23}, {15,17}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {15,16}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {3,37}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {9,37} }; // ET37.10 // Bipartite(14,23) Valencies [23,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2253734643369788856827117568000000 EdgePairs[37][10]:={ {13,21}, {10,37}, {14,36}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,15}, {14,33}, {14,23}, {6,16}, {11,33}, {13,25}, {8,24}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {14,37}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {3,15}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {3,37}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {12,21}, {6,33}, {11,26}, {5,33}, {5,30}, {9,37} }; // ET37.11 // Bipartite(13,24) Valencies [24,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3863545102919638040275058688000000 EdgePairs[37][11]:={ {13,21}, {10,37}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {4,37}, {13,27}, {6,14}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,26}, {13,19}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {6,16}, {11,33}, {13,25}, {8,24}, {9,26}, {5,14}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {13,14}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {3,15}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {3,37}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {9,37} }; // ET37.12 // Bipartite(12,25) Valencies [25,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7429894428691611615913574400000000 EdgePairs[37][12]:={ {10,37}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {4,37}, {6,14}, {2,33}, {6,32}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {8,37}, {12,20}, {1,13}, {12,26}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {6,24}, {2,29}, {5,34}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {6,16}, {11,33}, {8,24}, {9,26}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {11,13}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {3,37}, {7,13}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {9,37} }; // ET37.13 // Bipartite(11,26) Valencies [26,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 16098104595498491834479411200000000 EdgePairs[37][13]:={ {10,37}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,37}, {6,14}, {2,33}, {6,32}, {11,29}, {11,35}, {1,12}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {1,13}, {7,27}, {10,26}, {2,17}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {6,24}, {2,29}, {5,34}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {6,16}, {11,33}, {7,12}, {8,24}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30}, {9,37} }; // ET37.14 // Bipartite(10,27) Valencies [27,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 39513529461678116320994918400000000 EdgePairs[37][14]:={ {10,37}, {9,32}, {6,25}, {5,22}, {10,18}, {9,17}, {4,28}, {3,26}, {8,26}, {5,11}, {2,35}, {4,31}, {6,15}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {1,12}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {7,11}, {1,13}, {7,27}, {10,26}, {2,17}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {6,24}, {2,29}, {5,34}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {6,16}, {7,12}, {8,24}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37} }; // ET37.15 // Bipartite(9,28) Valencies [28,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 110637882492698725698785771520000000 EdgePairs[37][15]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {7,36}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {9,35}, {4,23}, {8,27}, {8,31}, {9,11}, {6,22}, {3,18}, {3,17}, {6,29}, {8,16}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,11}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {9,19}, {2,37}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {9,34}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {9,37}, {8,13}, {8,22}, {8,35}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {8,37}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {4,36}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {1,35}, {1,37}, {7,28}, {3,16}, {4,37}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {8,34}, {9,18}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {9,31}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET37.16 // Bipartite(8,29) Valencies [29,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 356499843587584782807198597120000000 EdgePairs[37][16]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,9}, {3,9}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {3,17}, {6,29}, {8,16}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,11}, {7,20}, {5,11}, {2,10}, {5,29}, {2,37}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {8,37}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {7,28}, {3,16}, {4,37}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {7,21}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET37.17 // Bipartite(7,30) Valencies [30,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1336874413453442935526994739200000000 EdgePairs[37][17]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {2,37}, {6,8}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {7,28}, {3,16}, {4,37}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET37.18 // Bipartite(6,31) Valencies [31,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5920443831008104428762405273600000000 EdgePairs[37][18]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {6,21}, {3,34}, {2,25}, {6,31}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {2,37}, {6,8}, {5,25}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {5,36}, {3,21}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {3,16}, {4,37}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,37}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {5,37}, {4,17}, {6,35}, {3,36}, {4,32}, {1,36}, {5,16} }; // ET37.19 // Bipartite(5,32) Valencies [32,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31575700432043223620066161459200000000 EdgePairs[37][19]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {3,18}, {3,17}, {3,7}, {3,34}, {2,25}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {2,37}, {5,25}, {1,31}, {3,12}, {2,35}, {1,22}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {3,26}, {5,28}, {2,17}, {4,36}, {4,6}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {3,23}, {3,21}, {5,36}, {2,7}, {1,25}, {1,15}, {2,11}, {1,35}, {1,37}, {3,16}, {4,37}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,31}, {5,10}, {5,27}, {5,26}, {4,18}, {5,9}, {4,25}, {4,11}, {1,8}, {4,12}, {4,20}, {5,13}, {3,28}, {5,6}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {5,21}, {2,30}, {2,18}, {5,35}, {1,34}, {5,37}, {4,17}, {3,36}, {4,32}, {1,36}, {5,16} }; // ET37.20 // Bipartite(4,33) Valencies [33,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 208399622851485275892436665630720000000 EdgePairs[37][20]:={ {1,15}, {4,35}, {3,15}, {1,11}, {4,14}, {2,22}, {3,29}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {2,37}, {3,32}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {4,37}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,36}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {2,34}, {3,27}, {4,30}, {1,19}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,35}, {1,26}, {2,24}, {4,11}, {2,27}, {3,35}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {4,9}, {2,7}, {4,34}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET37.21 // Bipartite(3,34) Valencies [34,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1771396794237624845085711657861120000000 EdgePairs[37][21]:={ {1,15}, {3,15}, {1,11}, {2,22}, {3,29}, {1,31}, {3,7}, {2,11}, {2,20}, {1,25}, {2,37}, {3,32}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,36}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {2,34}, {3,27}, {1,19}, {2,35}, {2,9}, {3,5}, {1,4}, {1,35}, {1,26}, {2,4}, {2,24}, {2,27}, {3,4}, {3,35}, {1,23}, {2,21}, {1,7}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET37.22 // Bipartite(2,35) Valencies [35,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 20666295932772289859333302675046400000000 EdgePairs[37][22]:={ {2,11}, {1,26}, {2,14}, {1,14}, {2,37}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,37}, {1,33}, {1,10}, {1,36}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {2,36}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET37.23 // Bipartite(1,36) Valencies [36,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 371993326789901217467999448150835200000000 EdgePairs[37][23]:={ {1,4}, {1,20}, {1,3}, {1,34}, {1,37}, {1,30}, {1,14}, {1,23}, {1,33}, {1,24}, {1,7}, {1,27}, {1,29}, {1,35}, {1,5}, {1,15}, {1,22}, {1,28}, {1,16}, {1,10}, {1,12}, {1,13}, {1,17}, {1,2}, {1,11}, {1,36}, {1,19}, {1,18}, {1,25}, {1,32}, {1,21}, {1,9}, {1,26}, {1,31}, {1,6}, {1,8} }; // ET37.24 // Non-bipartite Valency 36 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 13763753091226345046315979581580902400000000 EdgePairs[37][24]:={ {13,25}, {15,28}, {6,36}, {24,33}, {30,37}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {22,37}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {36,37}, {11,12}, {5,32}, {4,24}, {8,37}, {8,31}, {1,5}, {7,24}, {15,16}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,24}, {8,11}, {31,37}, {12,27}, {6,34}, {17,22}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {35,36}, {4,5}, {15,20}, {9,10}, {17,18}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {25,26}, {9,22}, {31,35}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {34,36}, {13,33}, {23,24}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {1,37}, {13,18}, {21,37}, {1,29}, {26,37}, {2,34}, {21,22}, {10,19}, {12,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {6,37}, {12,28}, {3,37}, {29,36}, {1,35}, {31,32}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {22,24}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {9,19}, {13,35}, {10,11}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {3,4}, {18,19}, {14,28}, {2,3}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {1,11}, {29,33}, {33,34}, {15,30}, {24,34}, {3,19}, {2,16}, {16,36}, {17,37}, {14,19}, {18,25}, {21,27}, {10,37}, {25,36}, {7,8}, {15,37}, {7,35}, {9,13}, {21,23}, {15,29}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {5,6}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {4,10}, {33,37}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {5,37}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {1,36}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {1,2}, {4,6}, {6,20}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {19,20}, {15,21}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {27,30}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {29,37}, {15,32}, {29,30}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {33,35}, {25,31}, {5,14}, {16,18}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {26,29}, {1,21}, {13,14}, {6,21}, {9,15}, {19,34}, {28,36}, {23,37}, {8,12}, {7,20}, {16,19}, {23,27}, {34,35}, {12,36}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {27,35}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {26,28}, {12,37}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {25,37}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // Total number of connected ET graphs of order 37 is 24 // ******************************************************************************************** // Order 38 // ET38.1 // Bipartite(19,19) Valencies [2,2] // Diameter 19 Girth 38 // Twin-free VT AT // Automorphism group of order 76 EdgePairs[38][1]:={ {13,37}, {5,28}, {1,20}, {11,36}, {18,22}, {3,20}, {8,30}, {6,30}, {11,37}, {3,23}, {12,38}, {9,32}, {14,35}, {10,34}, {18,27}, {2,25}, {2,21}, {1,22}, {4,21}, {10,38}, {12,35}, {17,24}, {15,33}, {14,31}, {5,23}, {17,29}, {19,25}, {16,31}, {13,33}, {6,26}, {7,32}, {4,26}, {19,24}, {8,34}, {7,28}, {16,27}, {15,29}, {9,36} }; // ET38.2 // Bipartite(19,19) Valencies [3,3] // Diameter 5 Girth 6 // Twin-free VT AT // Automorphism group of order 114 EdgePairs[38][2]:={ {15,35}, {1,26}, {18,32}, {4,24}, {5,32}, {6,33}, {4,34}, {16,23}, {6,31}, {8,25}, {12,30}, {19,35}, {1,20}, {8,24}, {3,23}, {11,38}, {3,37}, {17,25}, {12,31}, {10,33}, {3,29}, {16,33}, {11,21}, {2,21}, {15,21}, {9,29}, {2,31}, {10,34}, {13,36}, {5,28}, {4,27}, {9,36}, {12,23}, {17,38}, {17,27}, {14,32}, {18,30}, {7,22}, {7,38}, {15,28}, {16,22}, {6,35}, {5,26}, {18,29}, {14,20}, {14,24}, {11,26}, {13,27}, {1,22}, {2,25}, {13,37}, {9,28}, {8,30}, {7,37}, {10,20}, {19,34}, {19,36} }; // ET38.3 // Non-bipartite Valency 4 // Diameter 9 Girth 4 // Has twins VT AT // Automorphism group of order 19922944 EdgePairs[38][3]:={ {3,22}, {11,30}, {15,35}, {18,35}, {17,37}, {4,24}, {19,37}, {8,28}, {4,23}, {10,27}, {14,31}, {5,24}, {15,36}, {13,31}, {16,34}, {20,38}, {13,34}, {6,26}, {3,21}, {11,29}, {8,25}, {10,30}, {12,30}, {12,32}, {1,20}, {14,34}, {3,23}, {3,24}, {12,31}, {16,33}, {17,35}, {2,21}, {8,27}, {5,23}, {13,32}, {16,36}, {7,27}, {9,29}, {5,25}, {20,37}, {2,20}, {13,33}, {1,21}, {11,32}, {9,27}, {4,21}, {19,38}, {17,36}, {17,38}, {14,32}, {7,25}, {10,29}, {12,29}, {16,35}, {4,22}, {14,33}, {18,37}, {2,19}, {8,26}, {15,34}, {7,28}, {6,25}, {15,33}, {5,26}, {18,38}, {10,28}, {9,30}, {1,19}, {1,22}, {9,28}, {11,31}, {6,23}, {2,22}, {18,36}, {6,24}, {7,26} }; // ET38.4 // Bipartite(19,19) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 228 EdgePairs[38][4]:={ {14,21}, {5,32}, {10,21}, {15,23}, {2,38}, {10,22}, {11,23}, {2,22}, {17,27}, {11,33}, {4,27}, {16,30}, {11,29}, {7,33}, {12,31}, {2,37}, {5,24}, {13,34}, {1,38}, {12,33}, {16,23}, {19,31}, {13,27}, {3,30}, {9,37}, {12,27}, {14,35}, {3,34}, {14,20}, {3,31}, {6,34}, {15,32}, {13,20}, {18,24}, {8,22}, {19,37}, {7,28}, {5,23}, {15,34}, {8,33}, {7,26}, {19,26}, {1,36}, {18,33}, {1,22}, {14,30}, {7,29}, {10,31}, {16,26}, {14,28}, {10,24}, {18,25}, {8,35}, {14,38}, {15,35}, {3,23}, {4,31}, {19,29}, {4,30}, {2,34}, {4,36}, {4,21}, {7,30}, {5,28}, {9,25}, {10,29}, {1,26}, {6,29}, {15,26}, {18,35}, {12,23}, {12,38}, {11,36}, {17,22}, {5,38}, {15,21}, {2,21}, {16,27}, {18,28}, {6,38}, {8,32}, {5,36}, {19,36}, {9,24}, {11,25}, {13,28}, {16,22}, {11,21}, {9,26}, {4,32}, {1,20}, {3,25}, {17,29}, {13,36}, {3,20}, {1,33}, {2,25}, {18,31}, {8,37}, {10,20}, {9,32}, {6,24}, {6,35}, {17,32}, {8,30}, {17,28}, {6,27}, {19,35}, {7,34}, {13,37}, {12,37}, {9,20}, {17,25}, {16,24} }; // ET38.5 // Bipartite(19,19) Valencies [9,9] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 342 EdgePairs[38][5]:={ {2,24}, {1,20}, {9,28}, {2,33}, {11,36}, {4,27}, {13,21}, {4,24}, {16,26}, {10,37}, {18,32}, {16,27}, {1,32}, {19,24}, {10,26}, {17,20}, {17,34}, {14,38}, {7,22}, {10,33}, {2,27}, {3,35}, {5,20}, {13,35}, {14,31}, {17,24}, {16,25}, {12,35}, {7,36}, {17,21}, {18,21}, {8,25}, {1,30}, {16,23}, {8,27}, {13,29}, {12,37}, {16,29}, {18,34}, {18,37}, {10,30}, {4,38}, {19,33}, {6,21}, {14,23}, {2,25}, {11,38}, {14,33}, {4,22}, {9,29}, {14,36}, {19,26}, {19,30}, {9,27}, {12,20}, {5,29}, {19,22}, {5,25}, {7,32}, {17,23}, {1,31}, {11,31}, {2,35}, {1,22}, {15,27}, {19,38}, {6,30}, {4,33}, {10,29}, {9,34}, {13,22}, {13,31}, {3,32}, {11,21}, {9,25}, {8,36}, {6,33}, {2,32}, {13,33}, {16,32}, {17,30}, {15,35}, {5,24}, {9,37}, {12,28}, {15,37}, {8,22}, {8,35}, {13,28}, {15,20}, {1,28}, {4,28}, {3,29}, {6,23}, {16,38}, {15,36}, {5,28}, {8,26}, {17,31}, {12,26}, {7,31}, {12,27}, {12,23}, {6,27}, {11,24}, {6,26}, {14,34}, {3,23}, {10,32}, {18,25}, {17,29}, {5,36}, {1,25}, {7,29}, {6,28}, {18,23}, {9,30}, {14,20}, {15,21}, {14,25}, {16,21}, {13,26}, {11,26}, {10,35}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {8,34}, {11,37}, {3,24}, {18,28}, {1,26}, {4,34}, {10,34}, {15,22}, {18,22}, {11,32}, {16,20}, {8,24}, {2,31}, {6,34}, {15,38}, {19,25}, {13,38}, {9,38}, {3,38}, {4,20}, {12,24}, {3,28}, {7,27}, {14,35}, {10,20}, {7,33}, {12,31}, {11,34}, {17,22}, {5,21}, {2,30}, {15,30}, {7,37}, {9,31}, {19,23}, {5,37}, {3,36}, {18,35}, {19,37}, {8,29}, {4,32}, {1,36} }; // ET38.6 // Bipartite(18,20) Valencies [10,9] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 232190115840000 EdgePairs[38][6]:={ {3,33}, {10,24}, {1,20}, {2,24}, {13,32}, {2,33}, {5,34}, {4,24}, {16,26}, {4,26}, {17,38}, {4,30}, {11,25}, {12,22}, {5,38}, {8,28}, {18,38}, {15,31}, {1,32}, {8,33}, {1,27}, {3,25}, {12,38}, {10,26}, {17,34}, {1,19}, {3,35}, {3,37}, {13,35}, {12,35}, {7,36}, {17,21}, {8,25}, {2,28}, {12,34}, {14,28}, {9,35}, {18,34}, {10,22}, {6,22}, {15,25}, {10,30}, {16,30}, {15,29}, {4,38}, {2,25}, {11,38}, {11,33}, {6,31}, {14,33}, {2,36}, {5,22}, {4,22}, {10,38}, {9,29}, {7,20}, {17,37}, {14,21}, {14,36}, {16,24}, {9,27}, {5,29}, {9,19}, {2,37}, {5,25}, {7,32}, {1,31}, {11,22}, {10,28}, {14,24}, {17,33}, {15,27}, {6,30}, {15,19}, {2,20}, {13,31}, {18,30}, {11,21}, {9,25}, {8,36}, {2,32}, {16,32}, {1,23}, {11,29}, {5,30}, {17,30}, {15,35}, {11,30}, {9,37}, {13,23}, {15,37}, {13,28}, {18,26}, {1,28}, {18,27}, {3,27}, {14,37}, {4,28}, {3,29}, {6,23}, {16,38}, {8,37}, {13,36}, {18,31}, {12,26}, {16,22}, {7,31}, {4,36}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {13,24}, {6,27}, {17,25}, {12,19}, {6,26}, {12,30}, {3,23}, {18,19}, {10,32}, {17,29}, {3,21}, {6,19}, {18,23}, {13,27}, {1,35}, {14,20}, {16,34}, {15,21}, {14,25}, {7,28}, {11,26}, {7,23}, {13,19}, {16,36}, {2,21}, {5,33}, {11,37}, {2,29}, {4,34}, {10,36}, {10,34}, {18,22}, {16,20}, {14,32}, {15,33}, {8,24}, {6,38}, {9,33}, {6,34}, {5,26}, {4,20}, {8,20}, {7,27}, {15,23}, {7,24}, {3,31}, {10,20}, {17,26}, {12,31}, {11,34}, {7,35}, {17,22}, {5,21}, {13,20}, {9,31}, {5,37}, {7,19}, {6,35}, {9,21}, {16,28}, {18,35}, {9,23}, {8,29}, {4,32}, {1,36}, {14,29} }; // ET38.7 // Bipartite(18,20) Valencies [10,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2866544640 EdgePairs[38][7]:={ {10,24}, {13,32}, {2,33}, {17,35}, {4,27}, {13,21}, {11,35}, {5,34}, {4,24}, {15,24}, {16,33}, {17,38}, {10,37}, {4,30}, {11,25}, {16,27}, {8,30}, {2,23}, {5,38}, {7,38}, {18,38}, {15,31}, {4,29}, {1,32}, {8,33}, {3,25}, {10,23}, {12,38}, {17,34}, {4,19}, {16,19}, {7,22}, {10,33}, {1,19}, {3,35}, {2,26}, {1,21}, {17,24}, {18,21}, {8,25}, {5,32}, {16,23}, {9,35}, {4,23}, {13,29}, {12,37}, {16,29}, {15,25}, {11,28}, {18,37}, {10,30}, {16,30}, {15,29}, {6,21}, {3,34}, {2,25}, {14,23}, {11,38}, {6,31}, {1,38}, {14,33}, {2,36}, {5,22}, {9,29}, {17,37}, {14,36}, {16,24}, {9,26}, {18,20}, {12,20}, {12,36}, {9,19}, {14,30}, {5,25}, {7,32}, {15,26}, {1,31}, {11,22}, {2,35}, {1,22}, {6,30}, {4,33}, {10,29}, {9,34}, {13,22}, {15,19}, {2,20}, {16,37}, {1,29}, {13,31}, {18,30}, {9,25}, {8,36}, {2,32}, {13,33}, {1,23}, {15,35}, {5,24}, {17,27}, {13,23}, {12,28}, {8,22}, {15,34}, {8,35}, {13,28}, {18,26}, {1,28}, {18,27}, {18,36}, {1,33}, {3,29}, {3,26}, {5,28}, {15,36}, {8,26}, {18,31}, {12,26}, {7,31}, {17,28}, {12,27}, {8,32}, {3,19}, {14,22}, {6,27}, {11,24}, {17,25}, {6,26}, {12,30}, {8,23}, {3,21}, {7,29}, {6,28}, {14,20}, {15,21}, {16,34}, {14,25}, {7,28}, {4,37}, {7,23}, {13,19}, {6,36}, {11,37}, {3,24}, {11,27}, {18,28}, {10,27}, {2,22}, {4,34}, {10,34}, {11,32}, {14,32}, {16,20}, {6,38}, {9,36}, {5,27}, {13,38}, {10,19}, {4,20}, {8,20}, {14,35}, {3,31}, {9,24}, {10,20}, {7,33}, {6,37}, {12,31}, {11,34}, {6,20}, {17,22}, {2,30}, {5,35}, {9,31}, {5,37}, {7,19}, {17,32}, {9,21}, {3,36}, {7,21}, {12,21}, {14,26} }; // ET38.8 // Bipartite(18,20) Valencies [10,9] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 33592320 EdgePairs[38][8]:={ {3,33}, {10,25}, {1,20}, {13,32}, {6,32}, {17,35}, {11,36}, {17,36}, {4,27}, {12,29}, {11,35}, {16,26}, {15,24}, {18,29}, {4,26}, {3,22}, {17,38}, {18,32}, {16,27}, {8,30}, {2,23}, {12,22}, {5,38}, {12,32}, {16,31}, {15,31}, {4,29}, {1,32}, {3,25}, {10,26}, {14,38}, {4,31}, {1,19}, {2,27}, {3,35}, {7,34}, {17,24}, {16,25}, {7,36}, {17,21}, {12,34}, {5,32}, {9,35}, {8,27}, {12,37}, {16,29}, {18,34}, {6,22}, {15,25}, {11,28}, {18,37}, {6,29}, {14,23}, {11,38}, {11,33}, {6,31}, {2,36}, {7,20}, {14,21}, {14,36}, {9,27}, {2,38}, {9,19}, {2,37}, {14,30}, {7,32}, {7,25}, {10,28}, {17,33}, {15,27}, {6,30}, {4,21}, {10,29}, {10,31}, {15,19}, {10,21}, {2,20}, {18,30}, {11,21}, {4,35}, {9,25}, {8,36}, {7,26}, {13,33}, {1,23}, {6,24}, {5,30}, {17,30}, {15,35}, {11,30}, {5,24}, {13,23}, {12,28}, {8,22}, {13,25}, {18,24}, {3,27}, {14,37}, {4,28}, {1,33}, {8,37}, {5,28}, {13,36}, {18,31}, {9,22}, {17,28}, {8,21}, {3,19}, {14,22}, {11,24}, {12,19}, {12,30}, {3,23}, {8,23}, {18,19}, {5,36}, {1,25}, {6,19}, {6,28}, {14,20}, {1,37}, {16,34}, {16,21}, {13,26}, {11,26}, {10,35}, {7,23}, {13,19}, {2,21}, {5,33}, {3,24}, {2,29}, {16,35}, {18,28}, {10,27}, {8,38}, {1,26}, {2,22}, {4,34}, {10,34}, {15,22}, {18,22}, {11,32}, {16,20}, {15,33}, {9,33}, {6,34}, {15,38}, {5,26}, {9,38}, {4,25}, {3,38}, {4,20}, {12,24}, {8,20}, {15,23}, {13,37}, {3,31}, {9,24}, {10,20}, {17,26}, {7,33}, {6,37}, {12,31}, {13,34}, {5,21}, {2,30}, {13,20}, {7,37}, {5,35}, {9,31}, {1,34}, {7,19}, {17,32}, {16,28}, {9,23}, {14,27}, {8,29}, {1,36}, {14,29} }; // ET38.9 // Bipartite(14,24) Valencies [12,7] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2257403904 EdgePairs[38][9]:={ {11,17}, {3,33}, {10,25}, {1,20}, {5,17}, {10,24}, {9,28}, {13,32}, {2,33}, {6,16}, {6,32}, {4,27}, {13,21}, {11,35}, {5,34}, {14,19}, {4,26}, {4,30}, {11,25}, {8,30}, {12,22}, {12,32}, {8,28}, {1,32}, {1,27}, {3,25}, {10,23}, {12,38}, {4,19}, {14,38}, {4,31}, {10,33}, {1,19}, {5,20}, {3,37}, {2,26}, {7,34}, {12,34}, {8,15}, {9,35}, {14,28}, {4,23}, {8,31}, {13,29}, {13,16}, {10,15}, {10,22}, {6,22}, {10,30}, {6,29}, {3,17}, {4,38}, {6,21}, {2,25}, {11,33}, {2,34}, {14,33}, {4,22}, {10,38}, {9,29}, {14,36}, {9,26}, {9,27}, {12,20}, {12,36}, {2,38}, {9,19}, {2,37}, {14,30}, {5,25}, {11,15}, {7,32}, {1,31}, {7,25}, {11,31}, {6,30}, {12,16}, {5,23}, {10,31}, {3,20}, {9,34}, {13,18}, {13,31}, {3,32}, {11,21}, {4,35}, {7,16}, {8,36}, {7,26}, {5,18}, {11,23}, {1,23}, {11,29}, {6,24}, {7,17}, {9,37}, {13,23}, {12,28}, {8,22}, {9,20}, {4,15}, {1,28}, {3,29}, {8,37}, {5,28}, {12,26}, {2,17}, {14,17}, {8,21}, {1,24}, {14,22}, {13,24}, {6,27}, {5,31}, {12,30}, {8,23}, {10,32}, {5,36}, {3,21}, {6,19}, {13,15}, {1,15}, {1,35}, {14,20}, {14,25}, {3,16}, {13,26}, {2,21}, {5,33}, {9,18}, {10,17}, {11,37}, {3,24}, {2,29}, {11,27}, {8,38}, {2,22}, {4,34}, {1,16}, {6,38}, {9,36}, {5,26}, {4,18}, {11,19}, {12,24}, {8,20}, {3,28}, {7,27}, {14,35}, {13,37}, {7,24}, {5,15}, {7,33}, {6,37}, {13,34}, {7,35}, {2,30}, {2,18}, {7,19}, {6,35}, {9,21}, {3,36}, {14,27}, {8,29}, {12,18}, {1,36}, {7,18}, {10,16} }; // ET38.10 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 59768832 EdgePairs[38][10]:={ {3,33}, {5,17}, {1,20}, {11,20}, {13,32}, {9,28}, {6,32}, {17,35}, {17,36}, {12,29}, {13,21}, {7,15}, {4,24}, {15,24}, {16,33}, {18,29}, {3,22}, {17,38}, {4,16}, {1,10}, {4,30}, {16,27}, {6,17}, {1,13}, {12,32}, {7,38}, {8,28}, {25,38}, {18,38}, {4,29}, {20,27}, {1,32}, {8,33}, {1,27}, {3,15}, {12,38}, {2,19}, {25,33}, {1,19}, {2,27}, {14,31}, {26,33}, {7,34}, {1,21}, {2,9}, {8,25}, {30,37}, {24,36}, {2,28}, {2,14}, {5,32}, {8,15}, {16,23}, {9,35}, {4,23}, {28,35}, {8,27}, {12,37}, {10,22}, {18,37}, {10,30}, {8,16}, {19,28}, {23,32}, {3,34}, {20,38}, {11,38}, {6,31}, {14,33}, {4,22}, {8,19}, {9,29}, {7,20}, {17,37}, {14,21}, {16,24}, {9,27}, {12,20}, {22,34}, {2,10}, {5,25}, {1,31}, {3,12}, {7,25}, {11,31}, {10,28}, {20,31}, {23,36}, {1,22}, {15,27}, {19,38}, {25,34}, {4,33}, {5,23}, {10,29}, {4,21}, {13,22}, {24,32}, {10,21}, {2,13}, {2,20}, {6,18}, {13,31}, {26,37}, {18,30}, {29,37}, {7,16}, {23,35}, {13,33}, {2,32}, {7,26}, {5,18}, {11,23}, {11,29}, {6,24}, {17,30}, {11,30}, {15,35}, {5,24}, {15,34}, {1,9}, {29,38}, {13,25}, {20,28}, {26,38}, {27,36}, {5,14}, {18,26}, {19,31}, {4,15}, {1,28}, {3,11}, {18,36}, {26,34}, {3,29}, {6,23}, {22,29}, {8,37}, {21,33}, {15,36}, {24,35}, {8,26}, {25,37}, {9,22}, {12,23}, {28,36}, {14,22}, {5,31}, {11,24}, {17,25}, {12,19}, {6,26}, {22,33}, {12,30}, {21,29}, {14,34}, {3,23}, {18,25}, {21,30}, {17,29}, {5,36}, {3,21}, {6,14}, {9,30}, {16,34}, {14,25}, {7,28}, {19,32}, {20,37}, {3,16}, {13,26}, {10,35}, {16,36}, {6,36}, {2,21}, {3,30}, {8,34}, {9,18}, {10,17}, {11,37}, {3,24}, {16,35}, {10,27}, {8,38}, {2,22}, {4,34}, {10,36}, {11,32}, {9,17}, {14,32}, {15,33}, {10,18}, {6,25}, {30,38}, {2,31}, {9,36}, {27,35}, {5,26}, {15,28}, {11,19}, {4,11}, {4,12}, {5,13}, {8,20}, {12,24}, {7,27}, {15,23}, {23,31}, {21,34}, {1,14}, {17,26}, {7,33}, {12,31}, {13,34}, {6,13}, {7,37}, {5,35}, {22,30}, {7,19}, {6,35}, {9,21}, {16,28}, {18,35}, {19,37}, {20,32}, {19,27}, {24,31}, {14,26} }; // ET38.11 // Bipartite(8,30) Valencies [15,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1146617856000000 EdgePairs[38][11]:={ {1,15}, {7,19}, {5,32}, {6,12}, {5,14}, {8,24}, {8,31}, {6,10}, {6,18}, {4,14}, {1,11}, {3,29}, {2,22}, {6,36}, {8,36}, {5,35}, {1,38}, {1,9}, {2,33}, {7,31}, {1,32}, {7,23}, {3,10}, {2,28}, {3,34}, {3,31}, {6,34}, {2,18}, {6,9}, {2,15}, {5,26}, {4,26}, {8,14}, {8,13}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {1,29}, {4,12}, {7,28}, {7,10}, {5,33}, {3,11}, {5,23}, {4,37}, {2,10}, {4,20}, {1,17}, {3,13}, {2,16}, {6,33}, {6,21}, {2,36}, {8,18}, {7,29}, {7,25}, {3,22}, {5,15}, {8,26}, {3,23}, {7,13}, {5,29}, {4,31}, {4,30}, {2,34}, {6,15}, {4,36}, {4,25}, {2,9}, {1,35}, {1,26}, {8,19}, {7,35}, {4,38}, {2,24}, {2,27}, {5,38}, {3,35}, {1,23}, {2,21}, {5,27}, {6,30}, {8,38}, {2,12}, {5,20}, {8,32}, {3,28}, {5,17}, {8,20}, {6,16}, {7,16}, {1,14}, {4,32}, {1,20}, {1,27}, {5,11}, {7,22}, {3,16}, {4,18}, {3,25}, {8,25}, {7,37}, {1,33}, {3,17}, {8,37}, {3,37}, {6,24}, {8,30}, {6,27}, {7,34}, {7,17}, {4,13}, {1,21}, {2,30}, {4,19}, {4,24}, {8,12}, {6,28} }; // ET38.12 // Bipartite(8,30) Valencies [15,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 143327232000000 EdgePairs[38][12]:={ {1,15}, {7,19}, {6,12}, {3,15}, {8,24}, {2,38}, {6,10}, {6,18}, {4,14}, {1,11}, {3,29}, {5,30}, {6,36}, {1,31}, {6,17}, {4,27}, {8,36}, {5,35}, {7,24}, {6,23}, {2,20}, {1,25}, {7,38}, {4,16}, {2,37}, {5,24}, {1,9}, {2,33}, {7,31}, {5,13}, {8,34}, {3,10}, {3,34}, {6,34}, {2,19}, {2,15}, {4,26}, {8,14}, {6,22}, {5,37}, {1,29}, {8,22}, {2,14}, {5,23}, {3,11}, {4,20}, {6,11}, {2,31}, {7,26}, {8,28}, {1,17}, {2,32}, {4,33}, {8,10}, {8,18}, {4,28}, {2,13}, {3,9}, {7,25}, {3,22}, {5,19}, {7,20}, {8,26}, {3,23}, {7,13}, {5,29}, {7,14}, {3,27}, {1,19}, {4,21}, {7,30}, {4,15}, {2,9}, {1,35}, {6,29}, {4,38}, {2,27}, {3,35}, {1,23}, {2,21}, {6,30}, {7,18}, {8,38}, {4,22}, {8,32}, {3,28}, {5,36}, {5,31}, {5,17}, {8,16}, {8,20}, {6,16}, {3,21}, {4,32}, {1,37}, {1,27}, {5,11}, {3,16}, {1,13}, {7,32}, {2,26}, {7,37}, {1,33}, {5,12}, {2,25}, {3,17}, {4,9}, {6,24}, {6,35}, {5,18}, {8,30}, {4,34}, {3,33}, {7,36}, {7,12}, {1,21}, {5,25}, {4,10}, {8,12}, {6,28} }; // ET38.13 // Bipartite(6,32) Valencies [16,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 63429799040778240000 EdgePairs[38][13]:={ {4,8}, {5,33}, {4,24}, {6,34}, {2,37}, {1,24}, {5,37}, {4,36}, {2,32}, {2,29}, {5,29}, {1,32}, {4,34}, {2,24}, {6,14}, {6,26}, {4,10}, {5,10}, {3,21}, {1,36}, {6,31}, {3,27}, {3,33}, {6,10}, {6,30}, {1,20}, {1,12}, {2,36}, {3,23}, {3,37}, {1,31}, {4,16}, {3,9}, {2,12}, {6,7}, {3,29}, {2,33}, {6,15}, {2,21}, {4,30}, {5,9}, {4,32}, {5,21}, {4,12}, {2,16}, {4,18}, {1,7}, {5,25}, {1,15}, {3,11}, {1,16}, {3,7}, {2,20}, {3,15}, {4,38}, {5,38}, {3,17}, {3,25}, {4,20}, {6,38}, {3,19}, {5,17}, {6,27}, {3,31}, {5,30}, {1,27}, {4,28}, {4,22}, {6,18}, {6,19}, {2,28}, {6,22}, {1,28}, {5,14}, {2,17}, {5,18}, {3,13}, {6,35}, {5,26}, {1,8}, {5,34}, {1,19}, {2,9}, {5,13}, {6,11}, {4,26}, {2,13}, {2,25}, {2,8}, {4,14}, {1,35}, {1,23}, {1,11}, {5,22}, {6,23}, {3,35} }; // ET38.14 // Bipartite(6,32) Valencies [16,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5283615080448 EdgePairs[38][14]:={ {1,15}, {4,35}, {5,32}, {3,15}, {2,38}, {6,10}, {6,18}, {4,14}, {2,22}, {6,14}, {1,31}, {4,27}, {3,7}, {5,35}, {2,20}, {1,25}, {6,13}, {5,24}, {1,9}, {2,33}, {6,32}, {1,32}, {5,7}, {5,13}, {2,28}, {3,31}, {6,34}, {2,18}, {6,22}, {5,21}, {3,19}, {5,37}, {4,12}, {1,34}, {2,14}, {5,23}, {3,11}, {4,37}, {2,10}, {4,20}, {1,10}, {1,17}, {1,16}, {6,21}, {2,36}, {2,17}, {4,28}, {3,9}, {4,29}, {5,19}, {5,15}, {6,8}, {3,23}, {6,37}, {5,29}, {3,27}, {2,34}, {4,30}, {6,26}, {4,36}, {4,21}, {2,9}, {1,26}, {6,29}, {4,38}, {4,11}, {3,35}, {1,23}, {5,27}, {1,7}, {6,30}, {5,8}, {6,38}, {2,12}, {4,22}, {3,28}, {5,31}, {3,12}, {6,16}, {5,11}, {3,25}, {2,26}, {3,20}, {1,33}, {2,25}, {3,36}, {3,17}, {6,24}, {3,33}, {1,8}, {5,16}, {4,13}, {2,30}, {1,18}, {4,19}, {1,24} }; // ET38.15 // Bipartite(19,19) Valencies [18,18] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 243290200817664000 EdgePairs[38][15]:={ {13,21}, {15,33}, {6,38}, {19,28}, {10,37}, {15,38}, {14,36}, {9,32}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {3,20}, {1,21}, {19,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {19,20}, {19,21}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {19,22}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,26}, {14,32}, {2,36}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,20}, {18,26}, {18,33}, {3,38}, {5,27}, {15,28}, {5,28}, {14,35}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {19,30}, {8,24}, {9,38}, {14,21}, {18,20}, {18,38}, {3,29}, {13,36}, {2,23}, {15,23}, {9,22}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {13,38}, {18,31}, {6,23}, {16,31}, {4,36}, {4,29}, {1,32}, {19,29}, {6,37}, {8,32}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {6,20}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {15,29}, {2,22}, {16,20}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {17,21}, {19,36}, {6,28}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {17,37}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {14,22}, {5,36}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {15,25}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37} }; // ET38.16 // Bipartite(19,19) Valencies [19,19] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 29595060906949638427087208448000000 EdgePairs[38][16]:={ {13,21}, {15,33}, {6,38}, {19,28}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {3,20}, {1,21}, {3,21}, {16,37}, {19,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {19,20}, {19,21}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {19,22}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {14,35}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {19,30}, {8,24}, {9,38}, {14,21}, {9,26}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {2,23}, {15,23}, {9,22}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {2,20}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {13,38}, {18,31}, {6,23}, {16,31}, {4,36}, {4,29}, {1,32}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {8,33}, {17,34}, {11,31}, {14,24}, {19,35}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {12,34}, {17,21}, {19,36}, {6,28}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {14,22}, {5,36}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37} }; // ET38.17 // Bipartite(18,20) Valencies [20,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 15576347845762967593203793920000000 EdgePairs[38][17]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {1,21}, {3,21}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {13,19}, {1,26}, {14,32}, {2,36}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {3,38}, {5,27}, {15,28}, {5,28}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {8,24}, {9,38}, {14,21}, {9,26}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {13,38}, {18,31}, {6,23}, {16,31}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {14,19}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {3,37}, {5,36}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37} }; // ET38.18 // Bipartite(17,21) Valencies [21,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 18172405820056795525404426240000000 EdgePairs[38][18]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {11,25}, {4,28}, {17,18}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {16,22}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {13,19}, {1,26}, {14,32}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {17,19}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {13,38}, {6,23}, {16,31}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {3,37}, {14,22}, {5,36}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37} }; // ET38.19 // Bipartite(16,22) Valencies [22,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23517231061249970679935139840000000 EdgePairs[38][19]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {16,22}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {13,19}, {1,26}, {14,32}, {3,17}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {13,38}, {6,23}, {16,31}, {15,17}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {3,37}, {14,22}, {14,17}, {5,36}, {16,19}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37} }; // ET38.20 // Bipartite(15,23) Valencies [23,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 33806019650546832852406763520000000 EdgePairs[38][20]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {2,33}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,33}, {15,37}, {10,38}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,22}, {14,37}, {13,38}, {6,23}, {15,17}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {15,16}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {3,37}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {12,35}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37} }; // ET38.21 // Bipartite(14,24) Valencies [24,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 54089631440874932563850821632000000 EdgePairs[38][21]:={ {13,21}, {6,38}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {14,38}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {2,33}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {6,17}, {5,28}, {8,18}, {4,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,15}, {14,33}, {10,38}, {14,23}, {6,16}, {11,33}, {13,25}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {14,37}, {13,38}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {11,31}, {14,24}, {3,15}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {3,37}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET38.22 // Bipartite(13,25) Valencies [25,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 96588627572990951006876467200000000 EdgePairs[38][22]:={ {13,21}, {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {4,37}, {13,27}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {10,38}, {6,16}, {11,33}, {13,25}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {13,38}, {4,15}, {6,23}, {13,14}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {3,15}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {3,37}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET38.23 // Bipartite(12,26) Valencies [26,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 193177255145981902013752934400000000 EdgePairs[38][23]:={ {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {3,20}, {2,18}, {1,21}, {3,21}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {8,37}, {12,20}, {12,38}, {1,13}, {12,26}, {7,27}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {10,38}, {6,16}, {11,33}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {11,13}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {3,37}, {7,13}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET38.24 // Bipartite(11,27) Valencies [27,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 434648824078459279530944102400000000 EdgePairs[38][24]:={ {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {1,13}, {7,27}, {10,26}, {2,17}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {7,12}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET38.25 // Bipartite(10,28) Valencies [28,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1106378824926987256987857715200000000 EdgePairs[38][25]:={ {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {3,26}, {8,26}, {5,11}, {2,35}, {4,31}, {6,15}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {1,12}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {7,11}, {1,13}, {7,27}, {10,26}, {2,17}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {8,18}, {4,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {7,12}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37} }; // ET38.26 // Bipartite(9,29) Valencies [29,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3208498592288263045264787374080000000 EdgePairs[38][26]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {5,38}, {7,38}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {7,36}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {9,35}, {4,23}, {8,27}, {8,31}, {9,11}, {6,22}, {3,18}, {3,17}, {6,29}, {8,16}, {4,38}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {7,11}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {2,38}, {9,19}, {2,37}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {9,14}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {9,34}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {9,37}, {8,13}, {8,22}, {8,35}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {8,37}, {5,28}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {4,36}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {1,35}, {1,37}, {7,28}, {3,16}, {4,37}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {8,34}, {9,18}, {3,24}, {2,29}, {8,38}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {9,17}, {8,24}, {6,25}, {6,38}, {2,31}, {9,33}, {9,36}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {9,38}, {4,25}, {3,38}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {5,15}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {9,31}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {9,16}, {9,21}, {9,23}, {7,21}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET38.27 // Bipartite(8,30) Valencies [30,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10694995307627543484215957913600000000 EdgePairs[38][27]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {5,38}, {8,9}, {3,9}, {7,38}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {3,17}, {6,29}, {8,16}, {4,38}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,11}, {7,20}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {8,14}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {8,37}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {7,28}, {3,16}, {4,37}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {8,38}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {6,38}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {3,38}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {7,21}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET38.28 // Bipartite(7,31) Valencies [31,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 41443106817056731001336836915200000000 EdgePairs[38][28]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {7,38}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {4,38}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {6,8}, {5,25}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {7,28}, {3,16}, {4,37}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {6,38}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET38.29 // Bipartite(6,32) Valencies [32,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 189454202592259341720396968755200000000 EdgePairs[38][29]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {4,38}, {6,21}, {3,34}, {2,25}, {6,31}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {6,8}, {5,25}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {3,21}, {5,36}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {3,16}, {4,37}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,38}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,37}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {5,37}, {4,17}, {6,35}, {3,36}, {4,32}, {1,36}, {5,16} }; // ET38.30 // Bipartite(5,33) Valencies [33,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1041998114257426379462183328153600000000 EdgePairs[38][30]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {3,18}, {3,17}, {3,7}, {4,38}, {3,34}, {2,25}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {5,25}, {1,31}, {3,12}, {2,35}, {1,22}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {3,26}, {5,28}, {2,17}, {4,36}, {4,6}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {3,23}, {3,21}, {5,36}, {2,7}, {1,25}, {1,15}, {2,11}, {1,35}, {1,37}, {3,16}, {4,37}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,31}, {5,10}, {5,27}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {5,6}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {5,21}, {2,30}, {2,18}, {5,35}, {1,34}, {5,37}, {4,17}, {3,36}, {4,32}, {1,36}, {5,16} }; // ET38.31 // Bipartite(4,34) Valencies [34,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7085587176950499380342846631444480000000 EdgePairs[38][31]:={ {1,15}, {4,35}, {3,15}, {2,38}, {1,11}, {4,14}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {4,37}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,36}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {2,34}, {3,27}, {4,30}, {1,19}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,35}, {1,26}, {4,38}, {2,24}, {4,11}, {2,27}, {3,35}, {1,23}, {2,21}, {1,7}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {4,9}, {2,7}, {4,34}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET38.32 // Bipartite(3,35) Valencies [35,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 61998887798316869577999908025139200000000 EdgePairs[38][32]:={ {1,15}, {3,15}, {2,38}, {1,11}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {2,11}, {2,20}, {1,25}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,36}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {2,34}, {3,27}, {1,19}, {2,35}, {2,9}, {3,5}, {1,4}, {1,35}, {1,26}, {2,4}, {2,24}, {2,27}, {3,4}, {3,35}, {1,23}, {2,21}, {1,7}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET38.33 // Bipartite(2,36) Valencies [36,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 743986653579802434935998896301670400000000 EdgePairs[38][33]:={ {2,11}, {1,26}, {2,14}, {1,14}, {2,37}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,37}, {1,33}, {1,10}, {1,36}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {2,36}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {1,38}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,38}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET38.34 // Non-bipartite Valency 36 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 63777066403145711616000 EdgePairs[38][34]:={ {13,25}, {15,28}, {6,36}, {24,33}, {30,37}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {22,37}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {36,37}, {5,32}, {4,24}, {8,37}, {8,31}, {1,5}, {7,24}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {4,5}, {15,20}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {25,28}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {36,38}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {31,35}, {5,20}, {29,38}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {34,36}, {13,33}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {11,38}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {35,38}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {27,38}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {22,24}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {30,38}, {9,19}, {13,35}, {10,11}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {18,19}, {14,28}, {2,3}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {23,38}, {2,16}, {16,36}, {17,37}, {14,19}, {18,25}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {9,13}, {21,23}, {15,29}, {20,38}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {7,38}, {14,30}, {8,32}, {15,38}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {10,38}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {33,38}, {28,38}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {20,24}, {23,25}, {26,38}, {18,24}, {21,24}, {8,14}, {1,38}, {5,37}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {1,36}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {4,6}, {6,20}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {27,30}, {24,38}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {29,37}, {15,32}, {14,38}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {33,35}, {25,31}, {5,14}, {16,18}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {8,12}, {7,20}, {16,19}, {23,27}, {34,35}, {12,36}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {32,38}, {27,35}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {26,28}, {16,38}, {12,37}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET38.35 // Bipartite(1,37) Valencies [37,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 13763753091226345046315979581580902400000000 EdgePairs[38][35]:={ {1,4}, {1,20}, {1,3}, {1,34}, {1,37}, {1,30}, {1,14}, {1,23}, {1,33}, {1,24}, {1,38}, {1,7}, {1,27}, {1,29}, {1,35}, {1,5}, {1,15}, {1,22}, {1,28}, {1,16}, {1,10}, {1,12}, {1,13}, {1,17}, {1,2}, {1,11}, {1,36}, {1,19}, {1,18}, {1,25}, {1,32}, {1,21}, {1,9}, {1,26}, {1,31}, {1,6}, {1,8} }; // ET38.36 // Non-bipartite Valency 37 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 523022617466601111760007224100074291200000000 EdgePairs[38][36]:={ {13,25}, {15,28}, {6,36}, {24,33}, {30,37}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {22,37}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {36,37}, {11,12}, {5,32}, {4,24}, {8,37}, {8,31}, {1,5}, {7,24}, {15,16}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,24}, {7,28}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {35,36}, {4,5}, {15,20}, {9,10}, {17,18}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {25,28}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {36,38}, {16,23}, {21,30}, {3,14}, {23,33}, {25,26}, {9,22}, {31,35}, {5,20}, {29,38}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {34,36}, {13,33}, {23,24}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {37,38}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {11,38}, {5,27}, {9,31}, {3,6}, {7,23}, {5,33}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {21,22}, {10,19}, {12,19}, {14,35}, {15,27}, {9,11}, {11,32}, {3,31}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {35,38}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {27,38}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {29,36}, {1,35}, {31,32}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {22,24}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {30,38}, {9,19}, {13,35}, {10,11}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {3,4}, {18,19}, {14,28}, {2,3}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {1,11}, {29,33}, {33,34}, {15,30}, {24,34}, {3,19}, {23,38}, {2,16}, {16,36}, {17,37}, {14,19}, {18,25}, {21,27}, {10,37}, {25,36}, {7,8}, {15,37}, {7,35}, {9,13}, {21,23}, {15,29}, {20,38}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {5,6}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {7,38}, {14,30}, {8,32}, {15,38}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {10,38}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {11,17}, {33,38}, {28,38}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {10,33}, {13,34}, {20,24}, {23,25}, {26,38}, {18,24}, {21,24}, {8,14}, {1,38}, {5,37}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {1,36}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {1,2}, {4,6}, {6,20}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {19,20}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {4,23}, {22,34}, {27,30}, {24,38}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {29,37}, {15,32}, {14,38}, {29,30}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {33,35}, {25,31}, {5,14}, {16,18}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {26,29}, {1,21}, {13,14}, {6,21}, {9,15}, {19,34}, {28,36}, {23,37}, {8,12}, {7,20}, {16,19}, {23,27}, {34,35}, {12,36}, {27,31}, {31,34}, {7,18}, {10,21}, {3,33}, {32,38}, {27,35}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {26,28}, {16,38}, {12,37}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // Total number of connected ET graphs of order 38 is 36 // ******************************************************************************************** // Order 39 // ET39.1 // Non-bipartite Valency 2 // Diameter 19 Girth 39 // Twin-free VT AT // Automorphism group of order 78 EdgePairs[39][1]:={ {23,31}, {6,13}, {30,39}, {9,38}, {3,10}, {9,16}, {20,30}, {13,24}, {1,33}, {19,29}, {27,36}, {7,17}, {8,18}, {2,31}, {4,14}, {15,23}, {5,15}, {22,33}, {3,32}, {25,34}, {10,19}, {12,21}, {17,25}, {1,11}, {11,20}, {21,28}, {28,37}, {8,37}, {24,32}, {4,35}, {29,38}, {18,26}, {5,36}, {2,12}, {16,27}, {14,22}, {6,34}, {7,39}, {26,35} }; // ET39.2 // Bipartite(13,26) Valencies [4,2] // Diameter 6 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 52 EdgePairs[39][2]:={ {5,33}, {9,19}, {1,14}, {4,36}, {8,31}, {2,29}, {4,34}, {7,34}, {8,38}, {8,16}, {1,36}, {3,27}, {11,23}, {7,33}, {9,37}, {9,32}, {13,18}, {2,21}, {5,16}, {5,21}, {2,20}, {3,17}, {11,32}, {4,20}, {11,22}, {6,38}, {3,30}, {6,27}, {12,37}, {2,15}, {12,14}, {3,26}, {12,29}, {8,35}, {10,24}, {13,23}, {1,17}, {13,15}, {4,25}, {6,19}, {6,25}, {7,39}, {5,26}, {10,28}, {12,28}, {1,22}, {9,39}, {13,30}, {11,31}, {10,35}, {10,18}, {7,24} }; // ET39.3 // Bipartite(13,26) Valencies [4,2] // Diameter 13 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 212992 EdgePairs[39][3]:={ {5,28}, {13,19}, {3,16}, {11,18}, {3,29}, {4,24}, {8,35}, {4,39}, {1,14}, {9,19}, {5,30}, {7,16}, {1,38}, {3,14}, {1,27}, {8,24}, {9,32}, {12,22}, {13,32}, {2,26}, {10,34}, {6,23}, {4,37}, {11,31}, {10,23}, {2,28}, {12,35}, {3,27}, {7,31}, {12,33}, {6,38}, {5,15}, {11,33}, {12,20}, {7,18}, {2,39}, {11,20}, {8,37}, {10,21}, {6,36}, {1,25}, {5,17}, {9,30}, {8,22}, {6,25}, {2,15}, {4,26}, {13,21}, {7,29}, {10,36}, {9,17}, {13,34} }; // ET39.4 // Non-bipartite Valency 4 // Diameter 6 Girth 4 // Twin-free VT AT // Automorphism group of order 156 EdgePairs[39][4]:={ {11,30}, {18,35}, {19,37}, {8,28}, {4,23}, {17,34}, {1,24}, {5,24}, {15,36}, {13,31}, {17,39}, {20,38}, {13,34}, {12,33}, {6,26}, {3,21}, {10,32}, {11,29}, {8,25}, {18,39}, {12,30}, {18,34}, {1,20}, {3,23}, {3,24}, {12,31}, {11,33}, {7,30}, {2,21}, {5,23}, {13,32}, {16,36}, {21,37}, {7,27}, {9,29}, {5,25}, {15,31}, {10,31}, {2,20}, {14,36}, {4,27}, {11,32}, {9,27}, {14,35}, {19,38}, {3,19}, {17,36}, {17,38}, {6,27}, {14,32}, {7,25}, {10,29}, {16,35}, {13,35}, {16,38}, {4,22}, {14,33}, {4,25}, {18,37}, {6,22}, {8,26}, {15,34}, {15,33}, {5,26}, {2,23}, {10,28}, {1,19}, {9,26}, {12,28}, {1,22}, {21,39}, {16,37}, {9,28}, {8,30}, {20,39}, {2,22}, {6,24}, {7,29} }; // ET39.5 // Non-bipartite Valency 4 // Diameter 4 Girth 3 // Twin-free VT Non-AT // Automorphism group of order 78 EdgePairs[39][5]:={ {5,12}, {26,31}, {17,37}, {18,32}, {13,19}, {27,33}, {18,22}, {14,31}, {24,29}, {2,26}, {4,37}, {20,38}, {7,23}, {15,20}, {12,16}, {14,39}, {4,10}, {8,15}, {7,13}, {10,32}, {11,29}, {8,25}, {10,30}, {15,38}, {28,35}, {3,8}, {17,35}, {22,28}, {4,30}, {5,23}, {13,32}, {16,36}, {21,37}, {9,29}, {7,32}, {1,7}, {5,25}, {24,38}, {9,24}, {2,20}, {12,36}, {19,27}, {3,17}, {13,36}, {2,18}, {3,25}, {1,21}, {15,30}, {9,27}, {9,33}, {4,21}, {14,35}, {33,37}, {6,27}, {5,39}, {21,34}, {16,38}, {12,25}, {6,19}, {11,34}, {6,22}, {20,26}, {17,33}, {11,26}, {6,28}, {1,34}, {23,39}, {1,23}, {14,28}, {31,39}, {8,30}, {16,24}, {29,34}, {11,31}, {2,22}, {10,18}, {19,36}, {3,35} }; // ET39.6 // Bipartite(13,26) Valencies [6,3] // Diameter 5 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 78 EdgePairs[39][6]:={ {12,38}, {5,33}, {12,20}, {10,15}, {6,37}, {13,19}, {1,14}, {4,37}, {5,24}, {2,30}, {9,25}, {11,17}, {11,25}, {1,32}, {7,34}, {9,31}, {12,33}, {6,26}, {2,39}, {12,16}, {13,26}, {10,36}, {2,36}, {4,31}, {11,37}, {4,16}, {8,29}, {10,33}, {3,29}, {6,32}, {7,30}, {8,32}, {5,21}, {1,38}, {7,27}, {10,16}, {3,28}, {6,20}, {3,17}, {5,19}, {8,36}, {11,35}, {5,28}, {3,25}, {13,39}, {9,27}, {4,20}, {5,17}, {12,23}, {2,15}, {3,14}, {3,18}, {1,18}, {10,29}, {7,38}, {9,34}, {7,21}, {13,35}, {4,15}, {2,27}, {4,22}, {9,22}, {8,26}, {9,14}, {13,24}, {6,35}, {8,18}, {10,28}, {1,34}, {1,23}, {13,30}, {11,19}, {11,31}, {6,23}, {2,22}, {7,24}, {8,39}, {12,21} }; // ET39.7 // Bipartite(13,26) Valencies [6,3] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 319488 EdgePairs[39][7]:={ {5,33}, {10,15}, {9,19}, {1,14}, {6,39}, {6,33}, {2,30}, {1,29}, {7,23}, {9,21}, {7,31}, {8,16}, {8,23}, {6,26}, {11,24}, {8,21}, {6,31}, {13,25}, {12,30}, {5,15}, {2,36}, {11,37}, {3,37}, {3,24}, {8,29}, {13,14}, {3,29}, {9,32}, {4,30}, {7,36}, {4,32}, {5,20}, {3,16}, {1,16}, {10,26}, {4,38}, {7,18}, {10,34}, {6,20}, {13,33}, {8,36}, {5,28}, {11,32}, {9,27}, {12,37}, {2,15}, {3,18}, {3,31}, {12,24}, {13,20}, {4,17}, {7,25}, {7,38}, {9,34}, {8,34}, {1,27}, {13,38}, {10,39}, {6,18}, {4,25}, {2,28}, {12,22}, {2,17}, {9,14}, {12,35}, {2,23}, {5,35}, {11,39}, {10,28}, {11,26}, {10,21}, {13,27}, {1,22}, {1,35}, {4,19}, {11,19}, {12,17}, {5,22} }; // ET39.8 // Non-bipartite Valency 6 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 234 EdgePairs[39][8]:={ {10,19}, {16,25}, {7,19}, {5,32}, {7,39}, {14,25}, {2,38}, {1,11}, {3,29}, {6,14}, {30,37}, {4,8}, {13,18}, {25,34}, {8,36}, {23,27}, {5,34}, {36,37}, {9,12}, {12,15}, {12,22}, {29,39}, {3,32}, {19,31}, {22,35}, {13,27}, {9,21}, {6,7}, {30,33}, {19,23}, {18,21}, {5,13}, {3,10}, {2,28}, {22,33}, {2,15}, {24,34}, {26,35}, {5,9}, {10,23}, {12,21}, {7,10}, {9,38}, {27,37}, {15,22}, {2,31}, {14,16}, {3,13}, {6,33}, {10,13}, {33,35}, {9,34}, {10,39}, {28,38}, {16,19}, {20,24}, {8,17}, {4,31}, {25,28}, {21,33}, {8,11}, {4,36}, {4,17}, {32,34}, {4,15}, {3,5}, {25,38}, {11,37}, {18,27}, {11,14}, {34,38}, {2,4}, {7,35}, {15,26}, {21,30}, {12,38}, {27,36}, {29,32}, {2,12}, {20,32}, {21,22}, {23,31}, {24,32}, {27,30}, {31,36}, {8,20}, {7,16}, {6,16}, {1,14}, {26,29}, {9,18}, {24,25}, {3,39}, {26,39}, {1,37}, {35,39}, {18,30}, {28,31}, {22,26}, {16,28}, {20,29}, {17,29}, {13,23}, {15,17}, {11,20}, {1,33}, {8,37}, {17,26}, {6,35}, {5,18}, {17,20}, {11,24}, {1,30}, {19,28}, {23,36}, {1,6}, {14,24} }; // ET39.9 // Non-bipartite Valency 6 // Diameter 6 Girth 4 // Has twins VT AT // Automorphism group of order 339578044416 EdgePairs[39][9]:={ {10,19}, {4,35}, {16,25}, {7,39}, {24,33}, {5,14}, {10,21}, {15,23}, {8,39}, {22,32}, {4,14}, {1,11}, {12,19}, {6,14}, {17,27}, {20,28}, {30,37}, {6,36}, {1,31}, {25,34}, {2,11}, {23,33}, {5,35}, {27,35}, {13,24}, {5,34}, {28,37}, {7,38}, {6,13}, {27,34}, {28,39}, {29,39}, {3,32}, {2,33}, {9,39}, {29,37}, {1,32}, {9,37}, {5,13}, {3,10}, {22,33}, {3,31}, {6,34}, {9,17}, {26,35}, {21,28}, {12,21}, {9,38}, {3,11}, {2,10}, {15,22}, {23,32}, {2,31}, {1,10}, {19,30}, {2,32}, {8,18}, {28,38}, {1,12}, {16,26}, {5,15}, {18,25}, {8,17}, {19,29}, {24,31}, {30,38}, {6,15}, {4,36}, {4,15}, {13,22}, {18,27}, {21,30}, {16,27}, {21,29}, {14,22}, {27,36}, {11,19}, {7,18}, {8,38}, {14,23}, {2,12}, {5,36}, {8,16}, {23,31}, {3,12}, {24,32}, {30,39}, {20,30}, {7,16}, {11,21}, {29,38}, {9,18}, {20,29}, {13,23}, {7,37}, {11,20}, {25,35}, {1,33}, {26,36}, {8,37}, {17,26}, {10,20}, {6,35}, {4,34}, {26,34}, {9,16}, {22,31}, {3,33}, {7,17}, {19,28}, {4,13}, {12,20}, {15,24}, {14,24}, {25,36}, {18,26}, {17,25} }; // ET39.10 // Bipartite(13,26) Valencies [8,4] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 425984 EdgePairs[39][10]:={ {10,19}, {13,14}, {11,15}, {8,39}, {8,24}, {12,26}, {6,18}, {12,39}, {3,29}, {2,22}, {5,30}, {12,16}, {1,31}, {7,24}, {10,38}, {5,34}, {1,25}, {7,33}, {12,22}, {5,24}, {13,34}, {1,38}, {7,31}, {12,33}, {7,27}, {13,27}, {11,38}, {2,28}, {9,31}, {2,19}, {2,15}, {4,26}, {6,22}, {5,21}, {10,23}, {5,37}, {11,34}, {1,34}, {9,38}, {10,36}, {8,33}, {4,39}, {10,25}, {2,32}, {3,14}, {10,16}, {5,15}, {7,20}, {8,26}, {6,37}, {8,17}, {3,23}, {7,14}, {11,28}, {3,27}, {4,30}, {6,15}, {4,36}, {4,17}, {2,35}, {5,28}, {12,29}, {12,35}, {13,30}, {9,25}, {10,29}, {6,31}, {9,35}, {11,19}, {7,18}, {2,39}, {5,17}, {11,25}, {8,20}, {11,21}, {1,14}, {9,18}, {4,32}, {13,21}, {1,27}, {11,32}, {3,16}, {9,29}, {13,23}, {2,26}, {10,32}, {13,36}, {7,37}, {13,17}, {3,20}, {3,36}, {8,37}, {6,35}, {6,24}, {8,30}, {9,16}, {3,33}, {4,23}, {1,21}, {12,20}, {1,18}, {4,19}, {9,22}, {6,28} }; // ET39.11 // Bipartite(13,26) Valencies [8,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 46006272 EdgePairs[39][11]:={ {4,35}, {13,25}, {5,14}, {10,21}, {13,29}, {8,39}, {10,22}, {9,30}, {6,36}, {12,16}, {1,31}, {11,29}, {6,23}, {7,38}, {12,15}, {12,31}, {5,24}, {3,32}, {7,31}, {11,16}, {12,18}, {11,22}, {7,23}, {8,34}, {13,38}, {6,34}, {2,19}, {2,18}, {9,17}, {10,30}, {3,19}, {5,37}, {8,15}, {13,16}, {2,14}, {5,33}, {10,34}, {4,20}, {9,27}, {2,31}, {8,28}, {1,17}, {2,32}, {6,33}, {6,21}, {8,21}, {4,33}, {4,28}, {7,25}, {10,37}, {9,23}, {10,24}, {8,26}, {3,23}, {11,39}, {2,34}, {12,28}, {12,29}, {13,30}, {4,15}, {9,15}, {1,26}, {11,26}, {11,14}, {6,29}, {7,35}, {12,24}, {2,27}, {5,38}, {2,21}, {5,27}, {1,39}, {7,18}, {8,38}, {13,32}, {5,20}, {9,28}, {4,22}, {3,26}, {3,24}, {6,16}, {6,20}, {10,17}, {11,27}, {4,32}, {3,39}, {1,20}, {7,22}, {8,25}, {13,17}, {1,33}, {9,14}, {3,36}, {3,37}, {9,36}, {10,35}, {13,19}, {7,36}, {1,30}, {12,37}, {11,35}, {1,18}, {5,25}, {4,19} }; // ET39.12 // Bipartite(15,24) Valencies [8,5] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 137594142720 EdgePairs[39][12]:={ {13,25}, {6,39}, {10,21}, {8,31}, {10,22}, {12,39}, {9,30}, {3,29}, {5,30}, {10,27}, {7,24}, {12,17}, {5,24}, {12,33}, {6,25}, {11,16}, {11,38}, {11,22}, {12,27}, {14,35}, {8,34}, {13,38}, {14,20}, {3,31}, {2,18}, {15,32}, {13,20}, {5,21}, {2,29}, {3,19}, {1,29}, {8,22}, {7,28}, {12,21}, {11,34}, {1,34}, {15,39}, {9,38}, {5,33}, {4,37}, {10,34}, {2,23}, {8,28}, {1,17}, {13,26}, {1,22}, {6,33}, {1,16}, {6,21}, {2,36}, {2,17}, {10,39}, {10,16}, {14,38}, {15,20}, {6,37}, {3,23}, {11,28}, {4,31}, {4,30}, {10,33}, {14,26}, {4,36}, {7,30}, {2,35}, {15,33}, {12,29}, {12,35}, {4,25}, {1,35}, {8,19}, {11,26}, {15,26}, {12,23}, {14,32}, {2,24}, {6,31}, {6,19}, {14,17}, {15,21}, {3,35}, {1,23}, {5,27}, {10,28}, {7,18}, {13,32}, {14,23}, {5,36}, {8,16}, {9,24}, {7,16}, {9,26}, {9,18}, {11,32}, {7,22}, {15,27}, {4,18}, {8,25}, {3,25}, {15,38}, {11,20}, {14,29}, {1,28}, {8,37}, {3,17}, {3,37}, {9,32}, {5,18}, {9,36}, {13,31}, {6,27}, {7,34}, {13,19}, {13,37}, {7,36}, {5,39}, {2,30}, {4,19}, {4,24}, {9,20} }; // ET39.13 // Bipartite(15,24) Valencies [8,5] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 491520 EdgePairs[39][13]:={ {10,19}, {14,39}, {5,32}, {13,29}, {8,31}, {6,18}, {3,29}, {3,38}, {6,36}, {6,17}, {5,35}, {13,24}, {14,19}, {14,18}, {4,16}, {12,22}, {5,24}, {12,33}, {9,39}, {13,27}, {12,18}, {11,22}, {7,23}, {13,38}, {2,28}, {3,34}, {2,19}, {4,26}, {15,32}, {14,27}, {5,37}, {1,29}, {7,28}, {12,21}, {12,30}, {1,34}, {11,34}, {15,39}, {5,23}, {4,37}, {9,27}, {2,31}, {2,23}, {8,33}, {1,17}, {10,25}, {13,26}, {2,16}, {1,22}, {14,30}, {1,16}, {12,34}, {2,36}, {8,21}, {4,33}, {9,34}, {7,29}, {4,28}, {10,31}, {10,16}, {3,22}, {10,37}, {9,23}, {8,26}, {14,38}, {15,20}, {11,39}, {14,26}, {7,30}, {4,21}, {2,35}, {15,33}, {12,35}, {4,25}, {8,19}, {11,37}, {6,29}, {7,35}, {4,38}, {12,23}, {2,24}, {6,31}, {11,36}, {6,19}, {15,21}, {6,30}, {10,28}, {9,35}, {15,18}, {7,18}, {14,31}, {8,38}, {8,32}, {5,20}, {5,36}, {3,26}, {11,25}, {8,20}, {7,16}, {11,27}, {15,27}, {3,25}, {10,32}, {13,36}, {13,17}, {1,33}, {1,28}, {3,17}, {10,20}, {3,37}, {6,24}, {9,32}, {15,30}, {7,17}, {11,24}, {1,21}, {5,25}, {9,20}, {9,22}, {13,39} }; // ET39.14 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 312 EdgePairs[39][14]:={ {1,15}, {27,39}, {13,25}, {16,34}, {5,32}, {16,36}, {17,39}, {21,31}, {12,39}, {21,39}, {3,29}, {2,22}, {11,33}, {4,27}, {6,17}, {16,30}, {18,39}, {10,38}, {6,23}, {2,20}, {12,31}, {12,22}, {5,24}, {13,34}, {18,37}, {17,35}, {12,33}, {19,31}, {7,27}, {9,19}, {11,38}, {3,30}, {11,22}, {27,38}, {14,35}, {22,36}, {8,34}, {19,38}, {2,28}, {2,19}, {2,15}, {5,26}, {6,22}, {15,32}, {10,23}, {2,29}, {10,30}, {14,27}, {19,37}, {14,33}, {5,33}, {17,30}, {15,34}, {20,33}, {20,38}, {9,27}, {2,23}, {13,33}, {8,28}, {3,13}, {13,26}, {15,25}, {1,22}, {6,33}, {26,38}, {8,21}, {7,29}, {15,36}, {3,14}, {2,13}, {10,31}, {7,25}, {10,37}, {10,24}, {7,20}, {8,35}, {8,26}, {13,35}, {3,23}, {11,39}, {16,29}, {11,28}, {4,31}, {6,26}, {14,26}, {21,33}, {1,19}, {12,28}, {7,30}, {4,17}, {26,37}, {12,29}, {4,25}, {10,29}, {8,19}, {18,35}, {12,23}, {25,37}, {6,31}, {5,22}, {14,36}, {15,31}, {25,39}, {9,35}, {18,28}, {14,31}, {13,32}, {9,28}, {20,32}, {3,24}, {22,34}, {24,35}, {6,16}, {9,26}, {3,21}, {1,14}, {18,29}, {11,30}, {4,32}, {21,37}, {17,34}, {11,32}, {15,27}, {4,18}, {8,25}, {9,29}, {10,32}, {17,38}, {3,20}, {7,21}, {1,28}, {18,36}, {20,39}, {16,38}, {5,18}, {8,30}, {16,37}, {17,28}, {9,36}, {19,32}, {23,34}, {6,27}, {7,34}, {23,35}, {7,36}, {4,23}, {11,24}, {1,30}, {12,37}, {5,16}, {1,21}, {5,25}, {4,24}, {9,20}, {1,24}, {24,36} }; // ET39.15 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT Non-AT // Automorphism group of order 156 EdgePairs[39][15]:={ {10,19}, {13,25}, {7,39}, {11,15}, {24,33}, {15,23}, {17,39}, {11,23}, {9,30}, {14,34}, {3,29}, {27,32}, {11,33}, {3,7}, {32,35}, {6,23}, {13,24}, {36,37}, {14,18}, {28,39}, {35,38}, {12,31}, {22,38}, {2,37}, {33,38}, {26,33}, {12,22}, {3,32}, {1,38}, {2,33}, {7,31}, {19,31}, {28,34}, {9,19}, {21,35}, {12,18}, {6,7}, {18,23}, {3,10}, {15,29}, {9,10}, {7,11}, {14,27}, {4,12}, {19,37}, {32,39}, {8,15}, {12,21}, {14,33}, {27,37}, {17,30}, {24,37}, {4,20}, {20,33}, {23,32}, {9,27}, {19,26}, {4,39}, {10,25}, {6,33}, {6,21}, {2,17}, {8,18}, {9,34}, {3,14}, {10,16}, {4,29}, {16,26}, {16,35}, {3,22}, {14,28}, {5,15}, {8,35}, {20,24}, {13,35}, {14,38}, {7,13}, {11,39}, {16,29}, {25,28}, {30,38}, {2,34}, {1,19}, {15,19}, {12,29}, {1,4}, {1,26}, {11,26}, {18,27}, {21,30}, {5,22}, {11,36}, {5,38}, {1,23}, {25,39}, {27,36}, {29,32}, {8,38}, {2,12}, {10,14}, {5,36}, {24,30}, {5,31}, {5,17}, {21,22}, {9,24}, {15,37}, {22,34}, {31,36}, {8,20}, {30,36}, {7,16}, {6,16}, {2,6}, {18,20}, {26,29}, {11,30}, {17,21}, {13,21}, {24,25}, {2,8}, {17,34}, {7,22}, {1,13}, {28,31}, {5,10}, {22,26}, {8,25}, {15,17}, {3,20}, {2,25}, {3,36}, {18,31}, {23,28}, {20,39}, {4,9}, {9,32}, {17,32}, {16,37}, {20,36}, {13,31}, {4,34}, {10,35}, {6,27}, {26,34}, {23,35}, {1,30}, {12,37}, {19,28}, {4,13}, {1,18}, {5,25}, {8,29}, {6,28}, {16,24}, {21,27} }; // ET39.16 // Bipartite(12,27) Valencies [9,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1296 EdgePairs[39][16]:={ {1,15}, {10,19}, {7,19}, {10,21}, {3,15}, {8,39}, {8,24}, {12,26}, {2,38}, {10,22}, {3,29}, {6,14}, {5,30}, {6,17}, {6,23}, {7,38}, {4,16}, {12,17}, {7,33}, {12,31}, {2,37}, {12,14}, {5,24}, {3,32}, {6,32}, {9,19}, {9,21}, {12,18}, {11,22}, {12,27}, {2,28}, {3,31}, {6,34}, {2,18}, {8,13}, {2,29}, {10,30}, {7,28}, {11,34}, {5,23}, {4,37}, {10,36}, {1,36}, {2,16}, {6,33}, {8,21}, {4,33}, {9,34}, {10,39}, {2,13}, {10,15}, {10,31}, {7,20}, {8,35}, {7,13}, {11,39}, {3,23}, {5,29}, {3,27}, {11,18}, {12,28}, {7,30}, {9,25}, {4,15}, {1,35}, {11,37}, {11,26}, {11,14}, {4,38}, {5,22}, {2,27}, {5,38}, {3,35}, {1,39}, {4,22}, {9,28}, {5,31}, {5,17}, {11,25}, {12,36}, {8,20}, {6,20}, {9,26}, {3,21}, {1,14}, {1,37}, {1,27}, {3,16}, {1,13}, {8,25}, {1,33}, {2,25}, {12,32}, {9,32}, {6,24}, {6,35}, {5,18}, {8,30}, {10,26}, {4,34}, {9,16}, {7,36}, {7,17}, {4,23}, {11,24}, {4,19}, {9,20}, {8,29} }; // ET39.17 // Bipartite(12,27) Valencies [9,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 46438023168 EdgePairs[39][17]:={ {1,15}, {4,35}, {8,39}, {11,17}, {8,24}, {2,38}, {10,22}, {6,18}, {12,19}, {3,29}, {6,14}, {3,38}, {5,30}, {6,36}, {1,31}, {5,35}, {7,24}, {6,23}, {2,20}, {4,16}, {7,33}, {12,14}, {2,33}, {6,32}, {7,31}, {12,18}, {1,32}, {12,27}, {7,23}, {7,15}, {3,34}, {2,15}, {5,26}, {4,26}, {5,21}, {2,29}, {5,37}, {3,18}, {8,15}, {9,38}, {10,34}, {9,27}, {8,33}, {10,25}, {1,22}, {10,13}, {8,21}, {9,34}, {10,31}, {10,16}, {5,19}, {6,37}, {7,13}, {11,39}, {7,14}, {4,31}, {11,28}, {3,27}, {12,28}, {4,17}, {5,28}, {9,25}, {4,25}, {11,26}, {11,37}, {12,23}, {2,24}, {6,19}, {1,23}, {2,21}, {11,19}, {8,38}, {2,39}, {4,22}, {5,17}, {12,36}, {8,20}, {11,21}, {1,14}, {11,30}, {9,18}, {10,17}, {7,22}, {3,16}, {1,13}, {9,29}, {3,25}, {7,32}, {3,20}, {1,33}, {12,32}, {3,36}, {8,30}, {10,26}, {9,36}, {4,34}, {10,35}, {6,27}, {9,16}, {5,39}, {11,35}, {12,37}, {4,13}, {2,30}, {9,20}, {1,24}, {8,29}, {6,28} }; // ET39.18 // Bipartite(12,27) Valencies [9,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4353564672 EdgePairs[39][18]:={ {9,13}, {10,19}, {5,32}, {11,15}, {5,14}, {3,15}, {11,17}, {8,31}, {2,38}, {9,30}, {12,19}, {2,22}, {6,14}, {11,33}, {6,17}, {6,23}, {2,20}, {5,34}, {4,16}, {2,33}, {6,32}, {7,31}, {9,39}, {7,27}, {9,21}, {11,16}, {12,18}, {3,30}, {12,27}, {8,34}, {9,31}, {2,15}, {8,13}, {10,23}, {2,29}, {3,18}, {8,22}, {11,34}, {5,23}, {4,20}, {2,31}, {7,26}, {8,28}, {4,39}, {1,17}, {2,13}, {10,15}, {4,29}, {10,37}, {9,23}, {10,24}, {7,13}, {3,27}, {4,30}, {6,26}, {10,33}, {1,19}, {12,28}, {4,21}, {12,29}, {4,25}, {1,35}, {1,26}, {8,19}, {11,26}, {6,29}, {7,35}, {4,38}, {2,24}, {12,38}, {5,27}, {10,28}, {1,39}, {6,38}, {7,18}, {10,14}, {5,36}, {8,16}, {3,24}, {11,25}, {12,36}, {6,20}, {3,21}, {3,39}, {1,37}, {7,22}, {8,25}, {10,32}, {9,14}, {1,28}, {3,36}, {8,37}, {9,32}, {6,35}, {5,18}, {4,34}, {3,33}, {7,36}, {7,17}, {11,24}, {1,30}, {5,16}, {11,35}, {12,37}, {1,21}, {12,20}, {5,25}, {9,22} }; // ET39.19 // Bipartite(9,30) Valencies [10,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 214990848000000 EdgePairs[39][19]:={ {3,22}, {4,13}, {4,24}, {5,32}, {9,23}, {4,37}, {5,37}, {6,39}, {4,36}, {6,33}, {9,20}, {2,10}, {1,37}, {8,23}, {1,10}, {8,11}, {2,39}, {6,12}, {9,38}, {6,30}, {4,31}, {8,24}, {3,23}, {9,11}, {1,31}, {7,33}, {6,36}, {8,29}, {3,29}, {2,33}, {6,15}, {9,32}, {4,30}, {2,21}, {4,12}, {5,20}, {7,27}, {9,29}, {4,18}, {2,16}, {7,32}, {5,25}, {5,31}, {3,11}, {3,16}, {3,28}, {1,16}, {5,38}, {3,17}, {5,19}, {8,36}, {7,15}, {6,27}, {2,15}, {8,12}, {6,21}, {7,38}, {7,21}, {9,35}, {8,35}, {7,20}, {2,27}, {6,18}, {4,25}, {2,28}, {3,34}, {1,28}, {5,14}, {9,14}, {7,39}, {5,26}, {1,13}, {8,18}, {5,13}, {1,19}, {2,34}, {9,26}, {1,22}, {1,34}, {4,19}, {7,14}, {8,30}, {1,25}, {8,17}, {2,22}, {9,17}, {6,24}, {3,10}, {3,35}, {7,26} }; // ET39.20 // Bipartite(13,26) Valencies [12,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 156 EdgePairs[39][20]:={ {4,35}, {7,19}, {13,25}, {7,39}, {11,15}, {10,21}, {13,29}, {8,39}, {11,17}, {8,24}, {8,31}, {12,26}, {10,22}, {12,39}, {4,14}, {9,30}, {12,19}, {3,29}, {3,38}, {5,30}, {6,17}, {13,18}, {10,27}, {8,36}, {5,35}, {2,20}, {13,24}, {12,17}, {2,37}, {12,14}, {6,32}, {12,33}, {7,27}, {9,19}, {9,21}, {11,16}, {1,32}, {11,22}, {7,23}, {8,34}, {13,38}, {2,28}, {3,34}, {9,31}, {12,25}, {3,31}, {6,34}, {2,15}, {5,26}, {4,26}, {10,18}, {13,20}, {2,29}, {3,19}, {1,29}, {8,22}, {12,21}, {11,34}, {12,30}, {9,38}, {5,33}, {5,23}, {4,37}, {4,20}, {10,34}, {9,27}, {2,31}, {13,33}, {7,26}, {8,33}, {8,28}, {1,17}, {10,25}, {2,16}, {1,22}, {6,33}, {6,21}, {2,36}, {8,18}, {4,28}, {10,39}, {3,14}, {10,15}, {7,25}, {5,15}, {7,20}, {3,23}, {3,27}, {10,33}, {4,36}, {13,30}, {4,15}, {10,29}, {1,35}, {8,19}, {11,26}, {11,37}, {6,29}, {7,35}, {12,24}, {4,38}, {5,22}, {2,27}, {6,19}, {5,38}, {1,23}, {2,21}, {5,27}, {1,39}, {6,38}, {7,18}, {2,39}, {13,32}, {9,28}, {10,14}, {11,31}, {5,36}, {8,16}, {5,17}, {11,25}, {12,36}, {8,23}, {7,16}, {6,20}, {6,16}, {9,26}, {11,21}, {1,14}, {9,18}, {1,37}, {11,32}, {4,18}, {7,32}, {3,25}, {13,23}, {7,37}, {13,15}, {9,14}, {1,28}, {3,36}, {3,17}, {3,37}, {6,35}, {9,32}, {13,31}, {4,34}, {10,35}, {11,24}, {1,30}, {5,16}, {2,30}, {12,20}, {4,24}, {1,24}, {6,28}, {9,22} }; // ET39.21 // Bipartite(13,26) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 638976 EdgePairs[39][21]:={ {13,14}, {7,19}, {13,25}, {5,32}, {8,39}, {11,17}, {8,24}, {12,26}, {10,22}, {6,18}, {11,23}, {12,39}, {4,14}, {12,19}, {3,29}, {3,38}, {5,30}, {4,27}, {6,17}, {11,29}, {1,25}, {4,16}, {2,37}, {12,14}, {12,22}, {3,32}, {13,34}, {1,38}, {6,25}, {9,39}, {12,33}, {7,27}, {9,19}, {13,27}, {9,21}, {11,16}, {12,27}, {7,15}, {8,34}, {13,38}, {2,28}, {9,31}, {3,31}, {2,18}, {2,15}, {5,26}, {4,26}, {10,18}, {6,22}, {13,20}, {10,23}, {3,19}, {1,29}, {3,18}, {8,22}, {8,15}, {7,28}, {11,34}, {9,38}, {5,33}, {4,20}, {2,31}, {2,23}, {10,36}, {13,33}, {8,28}, {4,39}, {1,36}, {1,17}, {1,22}, {6,33}, {1,16}, {2,36}, {8,21}, {2,17}, {4,33}, {9,34}, {3,14}, {10,15}, {10,31}, {4,29}, {10,16}, {5,19}, {9,23}, {5,15}, {8,35}, {8,26}, {6,37}, {7,14}, {4,31}, {3,27}, {10,33}, {7,30}, {4,21}, {5,28}, {12,35}, {9,25}, {10,29}, {1,35}, {11,37}, {7,35}, {12,24}, {2,24}, {6,31}, {11,36}, {5,38}, {1,23}, {6,30}, {10,28}, {11,19}, {6,38}, {2,39}, {5,20}, {8,16}, {5,17}, {3,24}, {13,28}, {6,20}, {9,26}, {11,21}, {1,14}, {11,30}, {9,18}, {13,21}, {1,27}, {7,22}, {11,32}, {3,16}, {4,18}, {7,32}, {3,25}, {13,23}, {2,26}, {13,36}, {7,21}, {13,15}, {12,32}, {8,37}, {10,20}, {3,37}, {6,24}, {6,35}, {9,32}, {9,36}, {4,34}, {10,35}, {7,34}, {7,17}, {11,24}, {1,30}, {5,39}, {12,37}, {2,30}, {12,20}, {5,25}, {8,29} }; // ET39.22 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 468 EdgePairs[39][22]:={ {1,11}, {3,33}, {5,17}, {2,33}, {6,16}, {6,32}, {36,38}, {8,12}, {15,24}, {18,29}, {23,27}, {4,16}, {10,37}, {16,27}, {32,35}, {1,13}, {12,22}, {30,33}, {25,38}, {3,6}, {1,32}, {3,15}, {12,38}, {10,23}, {17,20}, {16,19}, {12,39}, {25,29}, {7,34}, {22,32}, {16,25}, {11,14}, {7,36}, {21,22}, {17,21}, {18,21}, {8,10}, {30,37}, {24,36}, {2,28}, {2,14}, {1,30}, {9,35}, {29,39}, {9,11}, {16,29}, {10,15}, {10,22}, {15,16}, {32,36}, {8,16}, {16,30}, {19,28}, {14,23}, {7,12}, {11,38}, {6,31}, {36,37}, {8,19}, {27,28}, {7,11}, {7,20}, {3,14}, {19,30}, {12,20}, {22,34}, {27,30}, {1,5}, {31,35}, {2,5}, {2,10}, {34,38}, {2,38}, {9,19}, {2,37}, {26,29}, {19,22}, {22,35}, {7,39}, {6,8}, {11,13}, {15,26}, {1,31}, {25,28}, {22,27}, {23,36}, {24,25}, {15,27}, {25,34}, {20,33}, {4,33}, {13,22}, {24,32}, {10,21}, {2,13}, {14,16}, {6,18}, {13,18}, {26,35}, {24,26}, {8,17}, {3,39}, {29,37}, {11,21}, {4,35}, {7,16}, {23,35}, {2,32}, {3,4}, {1,12}, {5,18}, {11,23}, {2,6}, {17,30}, {5,7}, {23,25}, {13,25}, {20,28}, {26,38}, {27,36}, {9,10}, {8,35}, {5,14}, {9,20}, {18,26}, {19,31}, {1,28}, {4,13}, {18,27}, {24,34}, {3,11}, {4,7}, {26,36}, {15,17}, {21,31}, {10,13}, {3,29}, {3,10}, {8,37}, {21,33}, {30,32}, {25,37}, {29,32}, {31,34}, {6,15}, {25,35}, {17,28}, {20,29}, {33,34}, {8,21}, {4,9}, {14,18}, {14,22}, {13,24}, {17,25}, {11,24}, {5,31}, {12,19}, {22,33}, {28,33}, {20,23}, {21,29}, {18,19}, {1,39}, {21,30}, {12,14}, {5,36}, {34,39}, {6,9}, {35,37}, {1,15}, {12,15}, {13,27}, {10,39}, {33,36}, {1,37}, {14,25}, {19,32}, {22,26}, {28,39}, {6,36}, {3,30}, {5,33}, {8,34}, {9,18}, {11,37}, {2,29}, {18,28}, {8,38}, {23,33}, {4,34}, {4,14}, {5,8}, {29,31}, {16,20}, {9,17}, {30,38}, {20,24}, {9,36}, {6,34}, {28,38}, {9,39}, {9,38}, {11,19}, {27,37}, {1,4}, {3,38}, {26,39}, {12,24}, {28,31}, {15,23}, {27,39}, {23,31}, {3,31}, {2,12}, {10,20}, {17,26}, {5,15}, {35,39}, {21,24}, {13,17}, {6,13}, {7,37}, {5,35}, {27,34}, {19,23}, {4,17}, {20,32}, {7,21}, {4,32}, {24,31}, {14,26}, {26,30}, {7,18} }; // ET39.23 // Non-bipartite Valency 12 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 679156088832 EdgePairs[39][23]:={ {11,17}, {1,11}, {3,33}, {33,38}, {11,20}, {25,31}, {2,33}, {13,21}, {7,15}, {5,34}, {14,19}, {16,26}, {15,24}, {23,29}, {3,8}, {1,10}, {33,39}, {16,27}, {26,31}, {5,38}, {7,38}, {3,9}, {20,27}, {1,32}, {23,28}, {32,37}, {25,33}, {3,35}, {24,30}, {26,33}, {29,35}, {8,39}, {22,32}, {17,24}, {16,25}, {2,9}, {27,33}, {30,37}, {16,23}, {6,11}, {8,15}, {20,30}, {28,35}, {29,39}, {3,7}, {8,16}, {19,28}, {23,32}, {4,38}, {3,34}, {14,23}, {31,39}, {4,10}, {2,34}, {2,36}, {1,7}, {14,21}, {19,26}, {12,17}, {16,24}, {19,30}, {12,20}, {5,11}, {25,36}, {2,10}, {31,37}, {28,34}, {29,36}, {8,14}, {19,29}, {7,39}, {17,23}, {1,31}, {3,12}, {7,13}, {9,14}, {14,24}, {30,34}, {2,35}, {21,27}, {6,12}, {25,34}, {12,16}, {21,26}, {27,31}, {13,22}, {15,19}, {24,32}, {10,21}, {26,35}, {29,34}, {30,39}, {8,17}, {3,32}, {29,37}, {11,21}, {4,35}, {7,16}, {2,32}, {1,12}, {30,36}, {30,35}, {7,17}, {21,25}, {9,37}, {17,27}, {28,37}, {13,23}, {8,13}, {32,39}, {1,9}, {29,38}, {32,38}, {18,24}, {20,28}, {27,36}, {15,20}, {5,14}, {18,26}, {4,15}, {4,13}, {18,27}, {3,11}, {7,14}, {26,36}, {1,33}, {26,34}, {3,10}, {22,29}, {8,37}, {16,22}, {6,15}, {4,36}, {25,35}, {20,29}, {9,13}, {5,12}, {25,32}, {28,36}, {14,22}, {13,24}, {17,25}, {12,19}, {22,33}, {33,37}, {21,29}, {18,25}, {21,30}, {20,25}, {5,36}, {2,7}, {22,28}, {26,32}, {27,32}, {18,23}, {6,14}, {22,31}, {2,11}, {1,35}, {14,20}, {15,21}, {5,39}, {4,37}, {28,39}, {11,16}, {13,19}, {6,36}, {9,18}, {10,17}, {20,26}, {8,38}, {23,33}, {4,34}, {4,14}, {15,22}, {18,22}, {9,17}, {10,18}, {30,38}, {6,38}, {2,31}, {6,34}, {6,10}, {27,35}, {5,10}, {19,25}, {8,18}, {28,38}, {9,39}, {9,38}, {11,19}, {10,19}, {4,11}, {1,8}, {24,29}, {4,12}, {5,13}, {15,23}, {23,31}, {3,31}, {2,12}, {2,8}, {10,20}, {17,26}, {6,39}, {5,15}, {6,37}, {17,22}, {9,15}, {6,13}, {7,37}, {13,20}, {5,35}, {22,30}, {27,34}, {1,34}, {5,37}, {21,28}, {24,33}, {6,35}, {3,36}, {9,16}, {4,39}, {19,27}, {12,18}, {24,28}, {24,31}, {31,38}, {11,18}, {12,21}, {1,36}, {23,30}, {7,18}, {10,16} }; // ET39.24 // Bipartite(18,21) Valencies [14,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 286708355039232000000 EdgePairs[39][24]:={ {3,33}, {10,25}, {1,20}, {2,24}, {11,20}, {9,28}, {13,32}, {2,33}, {17,35}, {11,36}, {17,36}, {18,39}, {11,35}, {15,24}, {16,26}, {4,26}, {3,22}, {17,38}, {10,37}, {8,30}, {14,39}, {2,23}, {5,38}, {12,22}, {7,38}, {16,31}, {15,31}, {4,29}, {1,32}, {8,33}, {3,25}, {10,23}, {10,26}, {17,20}, {4,19}, {14,38}, {16,19}, {7,22}, {12,39}, {4,31}, {1,19}, {2,27}, {5,20}, {3,37}, {13,35}, {2,26}, {8,39}, {7,34}, {17,24}, {16,25}, {17,21}, {18,21}, {12,34}, {5,32}, {16,23}, {4,23}, {8,27}, {12,37}, {13,29}, {16,29}, {18,34}, {10,22}, {6,22}, {15,25}, {18,37}, {4,38}, {6,21}, {3,34}, {14,23}, {11,38}, {11,33}, {6,31}, {1,38}, {14,33}, {2,36}, {4,22}, {10,38}, {7,20}, {14,21}, {14,36}, {9,27}, {12,36}, {5,29}, {2,38}, {9,19}, {14,30}, {2,39}, {7,32}, {17,39}, {17,23}, {1,31}, {7,25}, {10,28}, {14,24}, {2,35}, {17,33}, {1,22}, {15,27}, {6,30}, {5,23}, {10,29}, {10,31}, {9,34}, {13,22}, {15,19}, {2,20}, {16,37}, {1,29}, {3,39}, {13,31}, {18,30}, {11,21}, {4,35}, {9,25}, {8,36}, {6,33}, {2,32}, {7,26}, {16,32}, {11,23}, {1,23}, {11,29}, {6,24}, {5,30}, {17,30}, {11,30}, {5,24}, {9,37}, {17,27}, {13,23}, {12,28}, {12,25}, {15,37}, {15,34}, {13,25}, {18,24}, {8,35}, {13,28}, {1,28}, {18,27}, {3,27}, {18,36}, {4,28}, {18,33}, {16,38}, {15,36}, {8,26}, {18,31}, {16,22}, {9,22}, {7,31}, {12,33}, {12,27}, {8,32}, {8,21}, {3,19}, {6,27}, {11,24}, {11,39}, {12,19}, {12,30}, {8,23}, {18,19}, {10,32}, {18,25}, {17,29}, {5,36}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {1,35}, {1,37}, {14,20}, {15,21}, {16,34}, {5,39}, {7,28}, {4,37}, {11,26}, {13,26}, {10,35}, {7,23}, {13,19}, {6,36}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {11,27}, {16,35}, {18,28}, {8,38}, {1,26}, {4,34}, {10,34}, {15,22}, {18,22}, {11,32}, {14,32}, {15,33}, {16,20}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {5,27}, {5,26}, {15,28}, {9,39}, {13,38}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {14,35}, {13,37}, {3,31}, {15,39}, {9,24}, {10,20}, {17,26}, {6,39}, {6,37}, {12,31}, {13,34}, {7,35}, {5,21}, {2,30}, {15,30}, {7,37}, {13,20}, {5,35}, {9,31}, {1,34}, {7,19}, {17,32}, {9,21}, {3,36}, {16,28}, {14,27}, {8,29}, {4,32}, {12,21}, {14,29}, {14,26} }; // ET39.25 // Bipartite(15,24) Valencies [16,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 679604989722624000000 EdgePairs[39][25]:={ {11,17}, {3,33}, {10,25}, {1,20}, {5,17}, {2,24}, {11,20}, {9,28}, {13,32}, {2,33}, {6,16}, {11,36}, {11,35}, {15,24}, {4,26}, {3,22}, {4,16}, {10,37}, {8,30}, {14,39}, {2,23}, {5,38}, {12,22}, {7,38}, {15,31}, {4,29}, {1,32}, {8,33}, {3,25}, {10,23}, {10,26}, {4,19}, {14,38}, {7,22}, {12,39}, {4,31}, {1,19}, {2,27}, {5,20}, {3,37}, {13,35}, {2,26}, {8,39}, {7,34}, {12,34}, {5,32}, {4,23}, {8,27}, {12,37}, {13,29}, {13,16}, {10,22}, {15,16}, {6,22}, {15,25}, {3,18}, {4,38}, {6,21}, {3,34}, {14,23}, {11,38}, {6,31}, {11,33}, {1,38}, {14,33}, {1,17}, {2,36}, {4,22}, {10,38}, {7,20}, {14,21}, {14,36}, {9,27}, {12,36}, {5,29}, {2,38}, {9,19}, {14,30}, {2,39}, {7,32}, {1,31}, {7,25}, {10,28}, {14,24}, {2,35}, {1,22}, {15,27}, {6,30}, {12,16}, {5,23}, {10,29}, {10,31}, {9,34}, {13,22}, {15,19}, {2,20}, {6,18}, {1,29}, {8,17}, {3,39}, {13,31}, {11,21}, {4,35}, {9,25}, {7,16}, {8,36}, {6,33}, {2,32}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {9,37}, {13,23}, {12,28}, {12,25}, {15,37}, {15,34}, {13,25}, {8,35}, {13,28}, {1,28}, {3,27}, {4,28}, {15,36}, {8,26}, {9,22}, {7,31}, {12,33}, {2,17}, {12,27}, {14,17}, {8,32}, {8,21}, {3,19}, {14,18}, {6,27}, {11,24}, {11,39}, {12,19}, {12,30}, {8,23}, {10,32}, {5,36}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {9,30}, {1,35}, {1,37}, {14,20}, {15,21}, {5,39}, {7,28}, {3,16}, {4,37}, {11,26}, {13,26}, {15,18}, {10,35}, {7,23}, {13,19}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {8,38}, {1,26}, {4,34}, {1,16}, {10,34}, {15,22}, {11,32}, {14,32}, {15,33}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {5,27}, {5,26}, {8,18}, {15,28}, {9,39}, {13,38}, {10,19}, {4,25}, {4,20}, {3,28}, {8,20}, {12,24}, {14,35}, {13,37}, {3,31}, {15,39}, {9,24}, {10,20}, {6,39}, {6,37}, {12,31}, {13,34}, {7,35}, {5,21}, {2,30}, {13,17}, {15,30}, {7,37}, {13,20}, {5,35}, {2,18}, {9,31}, {1,34}, {7,19}, {4,17}, {9,21}, {9,16}, {3,36}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {14,29}, {14,26}, {10,16} }; // ET39.26 // Bipartite(15,24) Valencies [16,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 137594142720 EdgePairs[39][26]:={ {11,17}, {5,17}, {10,24}, {10,25}, {11,20}, {9,28}, {13,32}, {2,33}, {6,32}, {11,36}, {4,27}, {12,29}, {11,35}, {5,34}, {4,24}, {14,19}, {15,24}, {4,16}, {10,37}, {4,30}, {14,39}, {2,23}, {5,38}, {12,22}, {12,32}, {8,28}, {4,29}, {1,27}, {3,25}, {10,23}, {12,38}, {14,38}, {7,22}, {12,39}, {2,19}, {1,19}, {2,27}, {10,33}, {3,35}, {5,20}, {3,37}, {14,31}, {7,34}, {1,21}, {12,35}, {7,36}, {8,25}, {2,28}, {12,34}, {1,30}, {5,32}, {4,23}, {8,31}, {13,16}, {15,16}, {3,18}, {10,30}, {3,17}, {8,16}, {6,21}, {2,25}, {14,23}, {11,38}, {6,31}, {11,33}, {2,34}, {14,33}, {5,22}, {4,22}, {8,19}, {1,18}, {9,32}, {14,21}, {12,17}, {15,32}, {9,26}, {9,27}, {12,20}, {5,29}, {9,19}, {2,37}, {2,39}, {15,26}, {1,31}, {7,25}, {2,35}, {1,22}, {15,27}, {6,30}, {4,33}, {12,16}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {9,34}, {13,22}, {10,21}, {6,18}, {13,18}, {7,30}, {8,17}, {2,16}, {13,31}, {3,32}, {11,21}, {4,35}, {9,25}, {7,16}, {6,33}, {5,18}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {9,37}, {12,28}, {8,22}, {15,34}, {13,25}, {8,35}, {13,28}, {15,20}, {9,20}, {1,28}, {14,37}, {4,28}, {1,33}, {3,29}, {3,26}, {8,37}, {5,28}, {13,36}, {15,36}, {8,26}, {12,26}, {9,22}, {7,31}, {12,33}, {13,30}, {2,17}, {4,36}, {12,27}, {14,17}, {8,32}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {13,24}, {11,39}, {6,26}, {3,23}, {8,23}, {1,39}, {5,36}, {1,25}, {6,19}, {7,29}, {10,39}, {1,37}, {14,20}, {15,21}, {14,25}, {7,28}, {11,26}, {13,26}, {15,18}, {10,35}, {7,23}, {13,19}, {6,36}, {2,21}, {3,30}, {8,34}, {10,17}, {3,24}, {2,29}, {11,27}, {8,38}, {10,27}, {2,22}, {4,34}, {1,16}, {10,36}, {15,22}, {11,32}, {10,18}, {14,32}, {15,33}, {6,25}, {6,38}, {2,31}, {9,33}, {15,38}, {5,26}, {4,18}, {15,28}, {9,39}, {13,38}, {9,38}, {10,19}, {3,38}, {8,20}, {14,35}, {13,37}, {7,24}, {3,31}, {15,39}, {6,39}, {6,37}, {13,34}, {6,20}, {7,35}, {15,30}, {7,37}, {13,20}, {5,35}, {9,31}, {1,34}, {7,19}, {4,17}, {9,21}, {9,16}, {3,36}, {4,39}, {14,27}, {8,29}, {11,18}, {1,36}, {12,21}, {14,29}, {14,26}, {7,18}, {5,16} }; // ET39.27 // Bipartite(12,27) Valencies [18,8] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1296 EdgePairs[39][27]:={ {11,17}, {5,17}, {10,24}, {10,25}, {9,28}, {11,36}, {7,15}, {11,35}, {5,34}, {4,24}, {4,26}, {3,22}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {5,38}, {12,22}, {12,32}, {8,28}, {4,29}, {1,32}, {8,33}, {1,27}, {3,25}, {3,15}, {10,26}, {4,19}, {1,19}, {10,33}, {5,20}, {8,39}, {11,14}, {12,35}, {8,25}, {12,34}, {2,14}, {1,30}, {9,35}, {4,23}, {8,31}, {8,27}, {12,37}, {10,15}, {10,22}, {6,22}, {3,18}, {8,16}, {4,38}, {6,21}, {3,34}, {2,25}, {11,38}, {11,33}, {1,38}, {2,34}, {2,36}, {5,22}, {4,22}, {9,29}, {10,38}, {1,18}, {3,14}, {7,20}, {9,32}, {12,17}, {9,26}, {9,27}, {12,20}, {12,36}, {5,29}, {9,19}, {2,37}, {8,14}, {7,39}, {2,39}, {7,32}, {11,13}, {1,31}, {11,22}, {7,13}, {10,28}, {2,35}, {6,30}, {12,16}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {2,20}, {7,30}, {8,17}, {2,16}, {3,39}, {11,21}, {4,35}, {9,25}, {7,26}, {6,33}, {2,32}, {1,23}, {11,23}, {6,24}, {7,17}, {12,28}, {8,13}, {5,14}, {9,20}, {4,15}, {4,13}, {3,27}, {1,33}, {10,13}, {3,29}, {6,23}, {5,28}, {8,26}, {9,22}, {7,31}, {12,33}, {6,15}, {2,17}, {4,36}, {12,27}, {8,32}, {8,21}, {1,24}, {5,31}, {6,27}, {6,26}, {12,19}, {12,30}, {8,23}, {1,39}, {10,32}, {12,14}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {11,26}, {10,35}, {7,23}, {11,16}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {3,24}, {11,37}, {2,29}, {11,27}, {8,38}, {10,27}, {4,34}, {10,34}, {11,32}, {9,17}, {10,18}, {8,24}, {6,38}, {2,31}, {9,36}, {5,26}, {4,18}, {11,19}, {4,25}, {10,19}, {3,38}, {4,20}, {5,13}, {3,28}, {7,24}, {3,31}, {9,24}, {1,14}, {6,39}, {5,15}, {7,33}, {6,37}, {12,31}, {11,34}, {6,20}, {7,35}, {5,21}, {2,30}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {7,19}, {9,21}, {9,16}, {3,36}, {4,39}, {9,23}, {8,29}, {12,18}, {1,36}, {7,18}, {10,16}, {5,16} }; // ET39.28 // Bipartite(12,27) Valencies [18,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3963456300062343168000 EdgePairs[39][28]:={ {11,17}, {3,33}, {2,24}, {1,20}, {5,17}, {10,25}, {11,20}, {9,28}, {2,33}, {6,16}, {11,36}, {11,35}, {4,26}, {3,22}, {4,16}, {10,37}, {8,30}, {2,23}, {1,13}, {5,38}, {12,22}, {7,38}, {4,29}, {1,32}, {3,13}, {8,33}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {12,39}, {4,31}, {1,19}, {2,27}, {5,20}, {3,37}, {2,26}, {8,39}, {7,34}, {11,14}, {12,34}, {2,14}, {5,32}, {8,15}, {4,23}, {8,27}, {12,37}, {10,22}, {6,22}, {3,18}, {4,38}, {6,21}, {3,34}, {11,38}, {6,31}, {11,33}, {1,38}, {1,17}, {2,36}, {4,22}, {10,38}, {7,20}, {9,27}, {12,36}, {5,29}, {2,38}, {9,19}, {8,14}, {2,39}, {7,32}, {11,15}, {1,31}, {7,13}, {7,25}, {10,28}, {2,35}, {1,22}, {12,13}, {6,30}, {12,16}, {5,23}, {10,29}, {10,31}, {9,34}, {2,20}, {6,18}, {1,29}, {8,17}, {3,39}, {11,21}, {4,35}, {9,25}, {7,16}, {8,36}, {6,33}, {2,32}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {9,37}, {12,28}, {12,25}, {8,35}, {5,14}, {1,28}, {4,13}, {7,14}, {3,27}, {4,28}, {10,13}, {8,26}, {9,22}, {7,31}, {12,33}, {6,15}, {2,17}, {9,13}, {12,27}, {8,32}, {8,21}, {3,19}, {6,27}, {11,24}, {11,39}, {12,19}, {12,30}, {8,23}, {10,32}, {5,36}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {12,15}, {9,30}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {11,26}, {10,35}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {8,38}, {1,26}, {4,34}, {1,16}, {4,14}, {10,34}, {11,32}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {5,27}, {5,26}, {8,18}, {9,39}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {3,31}, {1,14}, {9,24}, {10,20}, {6,39}, {5,15}, {6,37}, {12,31}, {10,14}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {9,21}, {9,16}, {3,36}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {10,16} }; // ET39.29 // Bipartite(12,27) Valencies [18,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 46438023168 EdgePairs[39][29]:={ {11,17}, {2,24}, {1,20}, {5,17}, {10,25}, {9,28}, {2,33}, {6,32}, {4,27}, {12,29}, {7,15}, {11,35}, {4,26}, {4,16}, {10,37}, {8,30}, {1,13}, {12,32}, {7,38}, {1,32}, {8,33}, {1,27}, {3,25}, {10,23}, {12,38}, {10,26}, {2,15}, {4,19}, {7,22}, {12,39}, {4,31}, {3,35}, {3,37}, {2,26}, {8,39}, {7,34}, {11,14}, {7,36}, {8,25}, {5,32}, {8,15}, {9,35}, {4,23}, {8,31}, {12,37}, {10,22}, {3,18}, {11,28}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {2,25}, {11,33}, {1,38}, {2,34}, {5,22}, {4,22}, {9,29}, {1,18}, {7,20}, {9,26}, {9,27}, {12,20}, {12,36}, {2,38}, {9,19}, {2,39}, {7,32}, {11,13}, {11,15}, {1,31}, {11,22}, {7,13}, {7,25}, {10,28}, {11,31}, {2,35}, {1,22}, {6,30}, {5,23}, {3,20}, {10,31}, {9,34}, {2,13}, {2,20}, {6,18}, {1,29}, {8,17}, {2,16}, {3,39}, {11,21}, {4,35}, {9,25}, {7,16}, {6,33}, {1,23}, {11,23}, {6,24}, {5,30}, {11,30}, {5,24}, {9,37}, {12,28}, {8,13}, {8,22}, {8,35}, {5,14}, {9,20}, {4,13}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {7,31}, {12,33}, {6,15}, {2,17}, {4,36}, {12,27}, {8,21}, {3,19}, {1,24}, {12,23}, {5,31}, {6,27}, {11,24}, {11,39}, {12,19}, {12,30}, {10,32}, {12,14}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {6,14}, {9,30}, {5,39}, {3,16}, {4,37}, {11,26}, {10,35}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {8,34}, {9,18}, {10,17}, {11,37}, {2,29}, {8,38}, {10,27}, {2,22}, {4,34}, {1,16}, {10,36}, {4,14}, {10,34}, {11,32}, {9,17}, {10,18}, {8,24}, {6,38}, {2,31}, {9,36}, {5,26}, {4,18}, {9,39}, {9,38}, {11,19}, {4,25}, {10,19}, {3,38}, {5,13}, {8,20}, {3,28}, {12,24}, {7,27}, {7,24}, {1,14}, {6,39}, {5,15}, {7,33}, {6,37}, {10,14}, {5,19}, {6,20}, {5,21}, {2,30}, {5,35}, {1,34}, {5,37}, {4,17}, {9,21}, {9,16}, {3,36}, {8,29}, {4,32}, {12,18}, {1,36}, {12,21}, {7,18}, {10,16} }; // ET39.30 // Bipartite(12,27) Valencies [18,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4353564672 EdgePairs[39][30]:={ {5,17}, {1,20}, {10,25}, {11,20}, {9,28}, {6,16}, {11,36}, {4,27}, {7,15}, {4,24}, {4,26}, {3,22}, {8,30}, {2,23}, {1,13}, {5,38}, {12,22}, {12,32}, {7,38}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {10,26}, {4,19}, {12,39}, {4,31}, {2,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {8,39}, {7,34}, {11,14}, {12,35}, {2,28}, {12,34}, {2,14}, {8,15}, {9,35}, {4,23}, {8,27}, {10,22}, {6,22}, {11,28}, {10,30}, {3,17}, {6,21}, {3,34}, {2,25}, {11,38}, {6,31}, {1,38}, {2,34}, {2,36}, {5,22}, {4,22}, {9,29}, {10,38}, {1,18}, {3,14}, {7,20}, {12,17}, {9,26}, {9,27}, {5,29}, {9,19}, {2,37}, {8,14}, {7,39}, {2,39}, {7,32}, {11,13}, {1,31}, {11,22}, {7,25}, {11,31}, {2,35}, {1,22}, {12,13}, {6,30}, {4,33}, {12,16}, {10,29}, {3,20}, {10,31}, {9,34}, {10,21}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,32}, {11,21}, {4,35}, {9,25}, {7,16}, {8,36}, {6,33}, {2,32}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {11,30}, {5,24}, {9,37}, {12,25}, {8,35}, {9,20}, {4,15}, {4,13}, {7,14}, {4,28}, {1,33}, {10,13}, {3,29}, {3,26}, {5,28}, {8,26}, {12,26}, {12,33}, {6,15}, {2,17}, {4,36}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {5,31}, {6,27}, {11,39}, {12,30}, {3,23}, {8,23}, {12,14}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {12,15}, {10,39}, {5,39}, {7,28}, {3,16}, {4,37}, {10,35}, {7,23}, {6,36}, {2,21}, {5,33}, {9,18}, {10,17}, {11,37}, {11,27}, {8,38}, {10,27}, {1,16}, {10,36}, {4,14}, {10,34}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {5,26}, {8,18}, {4,18}, {9,38}, {11,19}, {3,38}, {5,13}, {8,20}, {3,28}, {12,24}, {7,24}, {3,31}, {9,24}, {1,14}, {10,20}, {6,39}, {5,15}, {7,33}, {6,37}, {12,31}, {5,19}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {9,16}, {7,21}, {8,29}, {4,32}, {11,18}, {1,36}, {12,21}, {10,16} }; // ET39.31 // Bipartite(13,26) Valencies [18,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 46006272 EdgePairs[39][31]:={ {11,17}, {3,33}, {2,24}, {5,17}, {10,25}, {11,20}, {2,33}, {6,32}, {11,36}, {4,27}, {13,21}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {4,16}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {12,32}, {4,29}, {1,32}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {12,38}, {10,26}, {2,15}, {12,39}, {4,31}, {1,19}, {10,33}, {3,35}, {13,35}, {2,26}, {7,34}, {1,21}, {12,35}, {2,28}, {12,34}, {5,32}, {9,35}, {4,23}, {8,31}, {8,27}, {10,15}, {6,22}, {3,18}, {11,28}, {3,17}, {8,16}, {4,38}, {3,34}, {2,25}, {11,38}, {6,31}, {11,33}, {1,38}, {2,36}, {5,22}, {8,19}, {9,29}, {10,38}, {3,14}, {7,20}, {9,32}, {12,17}, {9,26}, {12,20}, {12,36}, {5,29}, {2,38}, {9,19}, {2,37}, {8,14}, {7,39}, {2,39}, {7,32}, {11,15}, {10,28}, {11,31}, {2,35}, {1,22}, {6,30}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {9,34}, {13,22}, {2,20}, {6,18}, {13,18}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {11,21}, {9,25}, {7,16}, {8,36}, {7,26}, {13,33}, {5,18}, {1,23}, {11,23}, {6,24}, {5,30}, {7,17}, {11,30}, {9,37}, {13,23}, {12,25}, {8,22}, {8,35}, {13,28}, {9,20}, {1,28}, {7,14}, {3,27}, {3,29}, {8,37}, {5,28}, {13,36}, {12,26}, {9,22}, {12,33}, {6,15}, {2,17}, {4,36}, {12,27}, {8,32}, {1,24}, {12,23}, {5,31}, {6,27}, {11,24}, {13,24}, {6,26}, {12,19}, {12,30}, {8,23}, {10,32}, {12,14}, {5,36}, {3,21}, {1,25}, {6,19}, {13,15}, {7,29}, {1,15}, {6,28}, {6,14}, {10,39}, {13,27}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {13,26}, {3,30}, {9,18}, {11,37}, {2,29}, {10,27}, {2,22}, {4,34}, {1,16}, {10,36}, {4,14}, {11,32}, {10,18}, {8,24}, {6,25}, {6,38}, {9,33}, {13,14}, {5,26}, {8,18}, {4,18}, {9,39}, {9,38}, {11,19}, {4,25}, {10,19}, {3,38}, {3,28}, {8,20}, {7,27}, {13,37}, {7,24}, {3,31}, {9,24}, {1,14}, {10,20}, {6,39}, {5,15}, {7,33}, {6,37}, {10,14}, {11,34}, {13,34}, {5,19}, {13,39}, {5,21}, {2,30}, {7,37}, {13,20}, {5,35}, {9,31}, {1,34}, {7,19}, {4,17}, {6,35}, {9,21}, {9,16}, {4,39}, {7,21}, {8,29}, {11,18}, {1,36}, {12,21}, {10,16}, {5,16} }; // ET39.32 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1018734133248 EdgePairs[39][32]:={ {24,34}, {19,28}, {10,37}, {5,7}, {35,38}, {9,17}, {25,37}, {9,10}, {12,22}, {4,31}, {6,15}, {11,15}, {8,21}, {21,30}, {33,34}, {15,27}, {5,15}, {24,32}, {24,36}, {10,39}, {26,37}, {36,39}, {3,39}, {16,28}, {21,28}, {11,14}, {5,32}, {29,39}, {6,9}, {21,22}, {13,27}, {6,14}, {16,21}, {2,33}, {6,32}, {1,12}, {9,11}, {27,36}, {8,16}, {9,18}, {19,31}, {26,38}, {2,6}, {8,12}, {4,16}, {29,33}, {28,31}, {1,10}, {8,37}, {4,13}, {20,24}, {26,39}, {27,28}, {7,11}, {12,20}, {31,36}, {12,38}, {23,31}, {1,13}, {3,10}, {2,5}, {2,10}, {19,22}, {23,36}, {25,34}, {11,39}, {26,29}, {17,20}, {33,35}, {20,29}, {10,20}, {17,26}, {13,24}, {2,15}, {12,23}, {22,25}, {12,13}, {26,35}, {16,25}, {24,31}, {9,35}, {6,18}, {1,29}, {12,37}, {35,37}, {24,26}, {8,38}, {34,37}, {13,26}, {29,31}, {13,16}, {2,29}, {5,34}, {1,38}, {36,38}, {26,36}, {22,34}, {27,30}, {18,29}, {9,36}, {6,34}, {9,39}, {9,20}, {18,26}, {30,38}, {29,32}, {8,19}, {3,38}, {6,17}, {32,35}, {4,7}, {2,39}, {4,18}, {8,18}, {27,39}, {12,24}, {1,31}, {3,31}, {3,13}, {11,22}, {35,39}, {1,39}, {7,37}, {2,30}, {5,35}, {4,9}, {30,31}, {19,23}, {25,29}, {17,29}, {13,17}, {18,19}, {7,19}, {4,32}, {1,30}, {2,13}, {13,18}, {12,15}, {8,10}, {11,21}, {6,36}, {8,17}, {16,29}, {3,30}, {11,23}, {22,26}, {14,23}, {10,38}, {6,16}, {13,25}, {21,31}, {19,30}, {7,12}, {9,38}, {27,37}, {18,20}, {5,14}, {3,29}, {20,22}, {10,13}, {10,19}, {15,23}, {9,19}, {20,31}, {19,24}, {17,28}, {6,8}, {7,35}, {11,13}, {25,30}, {27,34}, {4,33}, {2,12}, {7,34}, {11,24}, {1,6}, {18,25}, {24,25}, {13,22}, {6,13}, {22,31}, {23,35}, {20,30}, {4,17}, {9,16}, {17,19}, {9,12}, {3,32}, {14,27}, {8,34}, {17,30}, {10,22}, {28,37}, {16,30}, {4,34}, {29,38}, {6,31}, {15,24}, {21,32}, {16,26}, {27,35}, {4,14}, {5,8}, {23,27}, {24,35}, {36,37}, {4,15}, {25,38}, {15,17}, {7,39}, {23,34}, {34,38}, {4,36}, {1,32}, {1,5}, {30,32}, {19,29}, {28,32}, {24,27}, {5,31}, {17,25}, {20,32}, {34,39}, {12,14}, {18,21}, {10,21}, {9,21}, {26,30}, {18,30}, {29,37}, {2,28}, {7,21}, {14,16}, {28,39}, {8,36}, {3,33}, {2,11}, {14,26}, {23,32}, {10,15}, {3,5}, {19,33}, {1,11}, {18,28}, {16,20}, {8,11}, {25,36}, {25,39}, {2,31}, {20,28}, {1,33}, {18,27}, {21,33}, {16,27}, {26,28}, {3,14}, {3,11}, {2,37}, {4,8}, {3,28}, {31,35}, {5,9}, {11,19}, {12,39}, {30,33}, {1,4}, {28,33}, {31,34}, {7,10}, {27,29}, {3,6}, {22,33}, {20,33}, {14,24}, {3,15}, {1,14}, {22,27}, {14,18}, {21,29}, {20,23}, {2,4}, {17,21}, {4,35}, {19,32}, {1,15}, {14,25}, {7,18}, {11,37}, {23,33}, {7,16}, {5,16}, {5,18}, {10,24}, {11,20}, {15,18}, {5,17}, {3,4}, {15,16}, {7,17}, {8,35}, {13,23}, {17,27}, {32,36}, {15,22}, {1,28}, {26,34}, {23,25}, {28,38}, {7,20}, {7,38}, {2,38}, {25,35}, {22,35}, {8,20}, {5,13}, {32,34}, {10,23}, {15,26}, {22,36}, {3,37}, {14,22}, {8,39}, {22,32}, {3,12}, {14,17}, {25,28}, {16,19}, {5,36}, {9,34}, {10,14}, {24,33}, {7,36}, {6,35}, {21,24}, {12,19}, {23,26}, {1,37}, {30,39}, {30,37}, {6,33}, {12,21}, {2,32}, {6,7}, {2,14}, {33,36}, {15,25}, {5,33}, {11,38}, {9,37}, {27,38}, {21,23} }; // ET39.33 // Bipartite(9,30) Valencies [20,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 61929004688474112000000 EdgePairs[39][33]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {8,30}, {2,23}, {1,13}, {5,38}, {7,38}, {4,29}, {1,32}, {3,13}, {8,33}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {5,20}, {3,37}, {2,26}, {7,34}, {8,39}, {2,14}, {5,32}, {8,15}, {4,23}, {8,27}, {6,22}, {3,18}, {4,38}, {6,21}, {3,34}, {6,31}, {1,38}, {4,10}, {1,17}, {2,36}, {4,22}, {7,11}, {7,20}, {9,27}, {5,11}, {5,29}, {2,38}, {9,19}, {8,14}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {5,23}, {9,34}, {2,20}, {6,18}, {1,29}, {8,17}, {3,39}, {4,35}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {9,37}, {8,35}, {9,10}, {5,14}, {1,28}, {4,13}, {7,14}, {3,27}, {4,28}, {3,10}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {9,13}, {5,12}, {8,32}, {8,21}, {3,19}, {6,27}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {6,28}, {2,11}, {9,30}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {3,24}, {2,29}, {8,38}, {1,26}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {6,10}, {5,27}, {5,26}, {8,18}, {9,39}, {4,25}, {4,11}, {4,20}, {3,28}, {8,20}, {7,10}, {3,31}, {2,12}, {1,14}, {9,24}, {6,39}, {5,15}, {6,37}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {3,36}, {9,16}, {9,21}, {8,29}, {4,32} }; // ET39.34 // Bipartite(9,30) Valencies [20,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 214990848000000 EdgePairs[39][34]:={ {1,11}, {3,33}, {5,17}, {1,20}, {2,33}, {6,16}, {7,15}, {4,24}, {8,12}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {1,13}, {5,38}, {7,38}, {8,28}, {4,29}, {1,32}, {8,33}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {8,39}, {7,36}, {8,10}, {2,28}, {2,14}, {5,32}, {8,15}, {9,35}, {4,23}, {8,27}, {9,11}, {6,22}, {3,17}, {8,16}, {6,21}, {3,34}, {7,12}, {2,25}, {6,31}, {1,38}, {4,10}, {2,34}, {1,17}, {4,22}, {9,29}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {7,13}, {9,14}, {7,25}, {1,22}, {6,12}, {6,30}, {5,23}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,39}, {3,32}, {4,35}, {7,26}, {6,33}, {2,32}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {8,11}, {5,24}, {8,22}, {8,35}, {5,14}, {9,20}, {1,28}, {4,13}, {3,11}, {7,14}, {3,27}, {4,28}, {3,29}, {3,10}, {3,26}, {7,31}, {6,15}, {4,36}, {5,12}, {8,21}, {5,31}, {6,27}, {3,23}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {6,28}, {9,30}, {1,35}, {1,37}, {3,16}, {4,37}, {6,36}, {2,21}, {8,34}, {9,18}, {1,26}, {2,22}, {4,34}, {1,16}, {9,17}, {8,24}, {6,25}, {2,31}, {9,33}, {9,36}, {6,34}, {6,10}, {5,26}, {8,18}, {4,18}, {9,39}, {9,38}, {4,25}, {3,38}, {4,11}, {4,12}, {5,13}, {3,28}, {7,27}, {7,24}, {1,14}, {9,24}, {6,39}, {7,33}, {6,37}, {5,19}, {9,15}, {6,13}, {7,37}, {5,35}, {1,34}, {5,37}, {7,19}, {4,17}, {9,21}, {9,23}, {7,21}, {8,29}, {7,18} }; // ET39.35 // Bipartite(19,20) Valencies [20,19] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 295950609069496384270872084480000000 EdgePairs[39][35]:={ {13,21}, {15,33}, {6,38}, {19,28}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {19,20}, {19,21}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {17,39}, {12,38}, {12,26}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {9,38}, {14,21}, {9,26}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {2,23}, {15,23}, {9,22}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {2,20}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {13,38}, {18,31}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {19,35}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {12,34}, {17,21}, {19,36}, {6,28}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {14,22}, {8,39}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37} }; // ET39.36 // Bipartite(18,21) Valencies [21,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 327103304761022319457279672320000000 EdgePairs[39][36]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {17,39}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {13,19}, {1,26}, {14,32}, {2,36}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {14,21}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {13,38}, {18,31}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {14,19}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37} }; // ET39.37 // Bipartite(6,33) Valencies [22,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3052870564457742336000000 EdgePairs[39][37]:={ {4,35}, {5,32}, {6,39}, {6,12}, {5,14}, {3,15}, {2,38}, {6,10}, {6,18}, {4,14}, {1,11}, {5,30}, {6,36}, {4,8}, {3,7}, {1,31}, {2,11}, {5,35}, {2,20}, {1,25}, {4,16}, {6,13}, {5,24}, {1,38}, {2,33}, {6,25}, {6,7}, {3,30}, {1,32}, {3,10}, {3,34}, {3,31}, {6,34}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {3,18}, {1,34}, {2,14}, {5,23}, {5,33}, {4,37}, {4,20}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {1,22}, {2,32}, {6,33}, {1,16}, {6,21}, {2,36}, {2,17}, {4,28}, {3,9}, {4,29}, {3,22}, {5,15}, {6,37}, {5,29}, {4,31}, {3,27}, {6,15}, {1,19}, {4,17}, {2,35}, {4,25}, {2,9}, {1,35}, {1,26}, {4,38}, {2,24}, {6,31}, {4,11}, {2,27}, {6,19}, {5,38}, {1,23}, {2,21}, {5,27}, {1,7}, {6,30}, {5,8}, {2,39}, {2,12}, {4,22}, {5,20}, {3,28}, {5,36}, {3,24}, {5,17}, {3,12}, {6,16}, {3,21}, {1,14}, {4,32}, {3,39}, {2,8}, {1,37}, {1,20}, {5,11}, {3,16}, {1,13}, {3,25}, {2,26}, {5,12}, {1,28}, {3,36}, {3,37}, {6,24}, {5,18}, {4,34}, {6,27}, {3,33}, {4,23}, {1,8}, {5,39}, {4,13}, {2,30}, {4,19}, {4,10}, {6,28} }; // ET39.38 // Bipartite(17,22) Valencies [22,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 399792928041249501558897377280000000 EdgePairs[39][38]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {11,25}, {4,28}, {17,18}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {17,39}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {13,19}, {1,26}, {14,32}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {13,38}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {16,33}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {4,26}, {15,20}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37} }; // ET39.39 // Bipartite(16,23) Valencies [23,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 540896314408749325638508216320000000 EdgePairs[39][39]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {16,22}, {13,39}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {2,33}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {13,19}, {1,26}, {14,32}, {3,17}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {13,38}, {6,23}, {16,31}, {15,17}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {16,39}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {14,17}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37} }; // ET39.40 // Bipartite(3,36) Valencies [24,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 659420041922872344576000000 EdgePairs[39][40]:={ {2,11}, {3,22}, {1,26}, {2,14}, {1,14}, {2,26}, {3,12}, {2,32}, {2,30}, {1,29}, {2,29}, {1,32}, {2,24}, {1,37}, {1,10}, {2,39}, {3,21}, {3,27}, {3,33}, {2,6}, {1,4}, {1,20}, {2,36}, {3,37}, {1,31}, {3,9}, {3,24}, {2,12}, {2,33}, {2,21}, {1,38}, {1,7}, {3,4}, {1,16}, {2,20}, {3,7}, {3,16}, {3,28}, {3,15}, {2,38}, {2,18}, {3,25}, {3,19}, {3,30}, {2,15}, {2,5}, {3,18}, {3,31}, {1,5}, {2,27}, {1,17}, {3,6}, {3,39}, {3,34}, {1,28}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {1,22}, {2,8}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {3,10}, {3,36} }; // ET39.41 // Bipartite(13,26) Valencies [24,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 51011754393600 EdgePairs[39][41]:={ {13,21}, {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {8,26}, {13,39}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {4,37}, {13,27}, {6,14}, {2,33}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {1,17}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {13,19}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {11,16}, {10,36}, {3,24}, {6,16}, {11,33}, {13,25}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {13,38}, {4,15}, {6,23}, {7,39}, {13,14}, {4,36}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {12,21}, {6,33}, {11,26}, {5,33}, {11,38}, {9,37} }; // ET39.42 // Bipartite(15,24) Valencies [24,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 811344471613123988457762324480000000 EdgePairs[39][42]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {13,39}, {2,35}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {2,33}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,33}, {15,37}, {10,38}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,22}, {14,37}, {13,38}, {6,23}, {15,17}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {15,16}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {12,21}, {6,33}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37} }; // ET39.43 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 37362124800 EdgePairs[39][43]:={ {15,28}, {24,33}, {30,37}, {15,17}, {10,17}, {20,26}, {9,18}, {20,33}, {4,26}, {22,37}, {14,29}, {2,4}, {2,20}, {36,37}, {4,24}, {8,31}, {7,24}, {15,16}, {11,34}, {13,27}, {3,17}, {1,9}, {2,39}, {7,28}, {18,38}, {2,24}, {20,27}, {4,28}, {4,11}, {8,36}, {1,18}, {19,37}, {5,18}, {17,29}, {23,29}, {8,26}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {22,25}, {14,25}, {5,9}, {20,22}, {3,25}, {4,12}, {4,30}, {21,35}, {8,11}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {16,33}, {19,38}, {7,26}, {31,36}, {11,27}, {18,28}, {17,19}, {13,29}, {22,28}, {9,12}, {31,38}, {18,37}, {25,29}, {5,7}, {20,29}, {12,22}, {15,20}, {9,10}, {23,34}, {24,36}, {17,25}, {11,35}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {8,38}, {19,30}, {11,29}, {14,27}, {2,8}, {10,25}, {13,17}, {14,22}, {16,26}, {6,19}, {1,10}, {27,32}, {5,23}, {2,37}, {7,30}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {3,14}, {9,22}, {31,35}, {29,38}, {8,39}, {22,32}, {7,14}, {12,38}, {13,33}, {18,35}, {10,23}, {30,34}, {15,24}, {1,26}, {9,27}, {26,32}, {10,16}, {24,30}, {16,30}, {5,27}, {9,31}, {3,6}, {20,39}, {7,23}, {5,33}, {7,16}, {1,22}, {6,24}, {29,32}, {6,39}, {35,39}, {19,35}, {10,14}, {16,34}, {8,21}, {9,20}, {18,26}, {28,39}, {3,16}, {18,21}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {5,36}, {18,20}, {12,39}, {6,12}, {12,33}, {5,38}, {13,18}, {21,37}, {25,38}, {26,37}, {1,29}, {21,22}, {2,34}, {12,19}, {14,35}, {11,32}, {23,39}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {35,38}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {36,39}, {9,37}, {27,38}, {2,5}, {12,21}, {1,14}, {10,20}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {21,34}, {22,38}, {13,23}, {5,15}, {19,32}, {6,10}, {7,37}, {27,33}, {14,18}, {1,17}, {3,36}, {20,23}, {26,31}, {34,38}, {6,37}, {29,36}, {3,37}, {17,28}, {26,35}, {23,32}, {5,21}, {7,36}, {9,39}, {13,26}, {22,33}, {14,37}, {11,24}, {20,31}, {8,33}, {10,28}, {15,23}, {12,17}, {2,7}, {9,19}, {10,24}, {2,25}, {26,39}, {23,28}, {21,29}, {3,28}, {9,35}, {14,28}, {15,36}, {10,36}, {16,29}, {1,11}, {29,33}, {33,34}, {24,34}, {15,30}, {2,16}, {16,36}, {1,39}, {17,37}, {18,25}, {14,19}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {9,13}, {20,38}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {3,8}, {16,22}, {3,35}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {32,39}, {14,20}, {19,28}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {8,27}, {24,31}, {5,30}, {16,27}, {2,13}, {16,31}, {22,36}, {22,30}, {4,13}, {18,30}, {8,17}, {28,31}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {19,36}, {9,34}, {15,25}, {6,22}, {5,19}, {6,32}, {17,35}, {10,35}, {18,36}, {3,12}, {14,24}, {4,17}, {3,24}, {7,11}, {4,32}, {2,27}, {15,35}, {1,19}, {2,10}, {19,33}, {7,12}, {13,21}, {3,11}, {3,38}, {33,37}, {14,34}, {3,5}, {15,38}, {7,38}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {6,7}, {24,27}, {18,33}, {1,7}, {8,15}, {25,39}, {4,14}, {11,28}, {6,25}, {28,34}, {13,39}, {28,38}, {32,34}, {24,29}, {17,34}, {4,16}, {12,26}, {10,30}, {6,18}, {17,39}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {24,26}, {6,16}, {11,13}, {20,34}, {25,34}, {2,15}, {30,32}, {10,33}, {13,34}, {23,25}, {18,24}, {21,24}, {8,14}, {16,39}, {1,38}, {8,23}, {20,30}, {2,29}, {3,21}, {33,39}, {1,36}, {13,30}, {9,24}, {14,39}, {6,20}, {11,15}, {23,35}, {12,34}, {8,19}, {4,20}, {7,21}, {23,31}, {34,37}, {15,21}, {27,37}, {1,33}, {12,30}, {2,32}, {19,26}, {12,14}, {4,23}, {27,30}, {24,38}, {32,36}, {16,21}, {6,27}, {29,37}, {15,32}, {11,25}, {17,27}, {33,35}, {25,31}, {5,14}, {11,22}, {9,16}, {9,32}, {27,28}, {30,35}, {18,32}, {21,32}, {30,31}, {22,35}, {5,39}, {26,29}, {1,21}, {28,36}, {9,15}, {23,37}, {7,20}, {23,27}, {16,19}, {12,36}, {21,39}, {10,21}, {3,33}, {32,38}, {27,35}, {5,17}, {6,8}, {19,25}, {15,26}, {2,18}, {21,28}, {26,28}, {16,38}, {4,8}, {2,19}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {30,39}, {4,37}, {28,33}, {12,29}, {4,35}, {2,35}, {10,32}, {5,11}, {4,36}, {6,29}, {2,31} }; // ET39.44 // Bipartite(14,25) Valencies [25,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1352240786021873314096270540800000000 EdgePairs[39][44]:={ {13,21}, {6,38}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {14,38}, {13,39}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,15}, {14,33}, {10,38}, {14,23}, {6,16}, {11,33}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {14,37}, {13,38}, {4,15}, {6,23}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {3,15}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET39.45 // Bipartite(13,26) Valencies [26,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2511304316897764726178788147200000000 EdgePairs[39][45]:={ {13,21}, {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {13,39}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {4,37}, {13,27}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {10,38}, {6,16}, {11,33}, {13,25}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {13,38}, {4,15}, {6,23}, {7,39}, {13,14}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {13,23}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET39.46 // Non-bipartite Valency 26 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1448745832104550541033472000000 EdgePairs[39][46]:={ {13,25}, {15,28}, {6,36}, {24,33}, {10,17}, {3,29}, {9,18}, {16,28}, {20,33}, {4,26}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {7,24}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {19,37}, {5,18}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {12,32}, {2,30}, {7,15}, {3,25}, {10,27}, {4,30}, {21,35}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {24,39}, {21,31}, {2,21}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {4,34}, {13,29}, {22,28}, {10,22}, {18,37}, {25,29}, {25,32}, {20,29}, {12,22}, {23,34}, {14,33}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {25,28}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {13,15}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {11,21}, {3,22}, {6,19}, {5,23}, {2,37}, {7,30}, {5,25}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {21,30}, {3,14}, {23,33}, {9,22}, {5,20}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {13,33}, {18,35}, {10,23}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {26,32}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {11,38}, {5,27}, {9,31}, {20,39}, {7,23}, {5,33}, {4,39}, {7,16}, {1,22}, {25,27}, {6,24}, {6,39}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {3,16}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {21,34}, {18,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {7,37}, {1,28}, {1,17}, {3,36}, {9,14}, {14,36}, {26,31}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {22,33}, {11,24}, {20,31}, {8,33}, {10,28}, {12,17}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {26,39}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {15,36}, {10,36}, {12,20}, {16,29}, {15,30}, {24,34}, {3,19}, {23,38}, {2,16}, {16,36}, {1,39}, {17,37}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {15,29}, {20,38}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,35}, {12,15}, {25,30}, {14,31}, {8,22}, {19,28}, {20,37}, {11,33}, {1,34}, {11,16}, {7,25}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {16,27}, {9,30}, {16,31}, {22,36}, {22,30}, {18,30}, {8,17}, {4,22}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {19,36}, {9,34}, {6,22}, {5,19}, {13,28}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {4,17}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {6,17}, {19,33}, {19,29}, {3,34}, {18,39}, {11,14}, {13,20}, {13,21}, {3,38}, {14,34}, {11,23}, {9,33}, {8,16}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {24,27}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {11,28}, {6,25}, {13,39}, {11,17}, {24,29}, {17,34}, {4,16}, {12,26}, {10,30}, {6,18}, {17,39}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {15,39}, {10,33}, {10,39}, {13,34}, {26,38}, {8,14}, {16,39}, {1,38}, {5,37}, {8,23}, {20,30}, {2,29}, {3,21}, {19,27}, {1,36}, {26,30}, {13,30}, {9,24}, {24,32}, {14,39}, {6,20}, {3,39}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {2,23}, {7,39}, {9,38}, {1,33}, {12,30}, {2,32}, {6,33}, {12,14}, {4,23}, {22,34}, {24,38}, {9,36}, {6,27}, {15,32}, {14,38}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {18,32}, {21,32}, {23,30}, {22,31}, {22,35}, {5,39}, {26,29}, {1,21}, {13,14}, {6,21}, {9,15}, {19,34}, {23,37}, {7,20}, {23,27}, {12,36}, {7,18}, {21,39}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {2,18}, {21,28}, {23,36}, {26,28}, {16,38}, {12,37}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {4,19}, {21,38}, {25,37}, {13,16}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET39.47 // Bipartite(12,27) Valencies [27,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5215785888941511354371329228800000000 EdgePairs[39][47]:={ {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {8,37}, {12,20}, {12,38}, {1,13}, {12,26}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {7,13}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET39.48 // Bipartite(11,28) Valencies [28,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12170167074196859826866434867200000000 EdgePairs[39][48]:={ {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {8,26}, {2,35}, {4,31}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {1,13}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {7,12}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET39.49 // Bipartite(10,29) Valencies [29,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 32084985922882630452647873740800000000 EdgePairs[39][49]:={ {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {3,26}, {8,26}, {5,11}, {2,35}, {4,31}, {6,15}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {1,12}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {7,11}, {1,13}, {7,27}, {6,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {7,12}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37} }; // ET39.50 // Bipartite(9,30) Valencies [30,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 96254957768647891357943621222400000000 EdgePairs[39][50]:={ {6,38}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {4,28}, {9,10}, {3,26}, {8,26}, {5,11}, {2,35}, {4,31}, {6,15}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {1,10}, {8,37}, {4,13}, {7,11}, {1,13}, {3,10}, {7,27}, {2,10}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {9,38}, {4,10}, {9,26}, {5,14}, {3,29}, {2,23}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {5,31}, {2,19}, {6,20}, {5,23}, {5,20}, {2,26}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37} }; // ET39.51 // Bipartite(8,31) Valencies [31,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 331544854536453848010694695321600000000 EdgePairs[39][51]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {5,38}, {8,9}, {3,9}, {7,38}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {8,39}, {1,21}, {2,9}, {7,36}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {3,17}, {6,29}, {8,16}, {4,38}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,11}, {7,20}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {8,14}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {8,37}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {1,39}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {8,38}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {6,38}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {3,38}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {6,39}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {4,39}, {7,21}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET39.52 // Bipartite(7,32) Valencies [32,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1326179418145815392042778781286400000000 EdgePairs[39][52]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {7,38}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {4,38}, {6,21}, {3,34}, {2,25}, {7,12}, {6,31}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {6,8}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {6,38}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {4,39}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET39.53 // Bipartite(6,33) Valencies [33,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6251988685544558276773099968921600000000 EdgePairs[39][53]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {4,38}, {6,21}, {3,34}, {2,25}, {6,31}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {6,8}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,38}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {5,35}, {1,34}, {5,37}, {4,17}, {6,35}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET39.54 // Bipartite(5,34) Valencies [34,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 35427935884752496901714233157222400000000 EdgePairs[39][54]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {3,18}, {3,17}, {3,7}, {4,38}, {3,34}, {2,25}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {3,26}, {5,28}, {2,17}, {4,36}, {4,6}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {1,15}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,31}, {5,10}, {5,27}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {5,6}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {5,21}, {2,30}, {2,18}, {5,35}, {1,34}, {5,37}, {4,17}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET39.55 // Bipartite(4,35) Valencies [35,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 247995551193267478311999632100556800000000 EdgePairs[39][55]:={ {1,15}, {4,35}, {3,15}, {2,38}, {1,11}, {4,14}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {2,20}, {1,25}, {4,16}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {4,37}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {4,39}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,36}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {2,34}, {3,27}, {4,30}, {1,19}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,35}, {1,26}, {4,38}, {2,24}, {4,11}, {2,27}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {4,9}, {2,7}, {4,34}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET39.56 // Bipartite(3,36) Valencies [36,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2231959960739407304807996688905011200000000 EdgePairs[39][56]:={ {1,15}, {3,15}, {2,38}, {1,11}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {2,11}, {2,20}, {1,25}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {2,36}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {2,34}, {3,27}, {1,19}, {2,35}, {2,9}, {3,5}, {1,4}, {1,35}, {1,26}, {2,4}, {2,24}, {2,27}, {3,4}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET39.57 // Non-bipartite Valency 36 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 81329213300067532800 EdgePairs[39][57]:={ {13,25}, {15,28}, {6,36}, {24,33}, {30,37}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {22,37}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {8,28}, {36,37}, {5,32}, {4,24}, {8,37}, {8,31}, {1,5}, {7,24}, {15,16}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {15,20}, {9,10}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {25,28}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {34,39}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {36,38}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {31,35}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {13,33}, {10,23}, {15,24}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {11,38}, {5,27}, {9,31}, {3,6}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {6,11}, {1,22}, {6,24}, {29,32}, {6,39}, {35,39}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {18,21}, {31,39}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {21,22}, {10,19}, {12,19}, {14,35}, {15,27}, {9,11}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {35,38}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {36,39}, {9,37}, {27,38}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {15,23}, {12,17}, {2,7}, {30,38}, {9,19}, {13,35}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {26,39}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {3,4}, {18,19}, {14,28}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {1,11}, {29,33}, {33,34}, {15,30}, {24,34}, {3,19}, {23,38}, {2,16}, {16,36}, {1,39}, {17,37}, {14,19}, {18,25}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {9,13}, {21,23}, {15,29}, {20,38}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {18,39}, {11,14}, {7,12}, {13,20}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,35}, {8,32}, {7,38}, {14,30}, {15,38}, {22,39}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {33,38}, {28,38}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {6,18}, {5,12}, {17,39}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {23,25}, {26,38}, {18,24}, {21,24}, {8,14}, {16,39}, {1,38}, {5,37}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {33,39}, {1,36}, {26,30}, {2,6}, {13,30}, {9,24}, {24,32}, {14,39}, {6,20}, {3,39}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {7,39}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {4,23}, {22,34}, {27,30}, {24,38}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {29,37}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {33,35}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {5,39}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {8,12}, {7,20}, {16,19}, {23,27}, {12,36}, {27,31}, {31,34}, {7,18}, {21,39}, {10,21}, {3,33}, {32,38}, {27,35}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {26,28}, {16,38}, {12,37}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {30,39}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET39.58 // Bipartite(2,37) Valencies [37,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 27527506182452690092631959163161804800000000 EdgePairs[39][58]:={ {2,11}, {1,26}, {2,14}, {1,14}, {2,37}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,37}, {1,33}, {1,10}, {2,39}, {1,39}, {1,36}, {1,6}, {2,6}, {1,4}, {1,20}, {1,12}, {2,36}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {1,38}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,38}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET39.59 // Bipartite(1,38) Valencies [38,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 523022617466601111760007224100074291200000000 EdgePairs[39][59]:={ {1,4}, {1,20}, {1,3}, {1,34}, {1,37}, {1,30}, {1,14}, {1,23}, {1,39}, {1,33}, {1,24}, {1,38}, {1,7}, {1,27}, {1,29}, {1,35}, {1,5}, {1,15}, {1,22}, {1,28}, {1,16}, {1,10}, {1,12}, {1,13}, {1,17}, {1,2}, {1,11}, {1,36}, {1,19}, {1,18}, {1,25}, {1,32}, {1,21}, {1,9}, {1,26}, {1,31}, {1,6}, {1,8} }; // ET39.60 // Non-bipartite Valency 38 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 20397882081197443358640281739902897356800000000 EdgePairs[39][60]:={ {13,25}, {15,28}, {6,36}, {24,33}, {30,37}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {22,37}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {36,37}, {11,12}, {5,32}, {4,24}, {8,37}, {8,31}, {1,5}, {7,24}, {15,16}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {35,36}, {4,5}, {15,20}, {9,10}, {17,18}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {25,28}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {34,39}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {38,39}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {36,38}, {16,23}, {21,30}, {3,14}, {23,33}, {25,26}, {9,22}, {31,35}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {34,36}, {13,33}, {23,24}, {10,23}, {15,24}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {37,38}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {11,38}, {5,27}, {9,31}, {3,6}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {6,39}, {35,39}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {18,21}, {31,39}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {21,22}, {10,19}, {12,19}, {14,35}, {15,27}, {9,11}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {35,38}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {36,39}, {9,37}, {27,38}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {37,39}, {4,33}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {29,36}, {1,35}, {31,32}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {22,24}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {30,38}, {9,19}, {13,35}, {10,11}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {26,39}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {3,4}, {18,19}, {14,28}, {2,3}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {1,11}, {29,33}, {33,34}, {15,30}, {24,34}, {3,19}, {23,38}, {2,16}, {16,36}, {1,39}, {17,37}, {14,19}, {18,25}, {21,27}, {10,37}, {25,36}, {7,8}, {15,37}, {7,35}, {9,13}, {21,23}, {15,29}, {20,38}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {14,31}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {5,6}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {18,39}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {7,38}, {14,30}, {8,32}, {15,38}, {22,39}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {22,23}, {4,25}, {10,38}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {33,38}, {28,38}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {17,39}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {23,25}, {26,38}, {18,24}, {21,24}, {8,14}, {16,39}, {1,38}, {5,37}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {33,39}, {1,36}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {14,39}, {1,2}, {4,6}, {6,20}, {3,39}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {19,20}, {7,39}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {4,23}, {22,34}, {27,30}, {24,38}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {29,37}, {15,32}, {14,38}, {29,30}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {33,35}, {25,31}, {5,14}, {16,18}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {27,28}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {5,39}, {26,29}, {1,21}, {13,14}, {6,21}, {9,15}, {19,34}, {28,36}, {23,37}, {8,12}, {7,20}, {16,19}, {23,27}, {34,35}, {12,36}, {27,31}, {31,34}, {7,18}, {21,39}, {10,21}, {3,33}, {32,38}, {27,35}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {26,28}, {16,38}, {12,37}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {30,39}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // Total number of connected ET graphs of order 39 is 60 // ******************************************************************************************** // Order 40 // ET40.1 // Bipartite(20,20) Valencies [2,2] // Diameter 20 Girth 40 // Twin-free VT AT // Automorphism group of order 80 EdgePairs[40][1]:={ {12,32}, {8,33}, {19,21}, {4,24}, {20,23}, {18,23}, {4,39}, {5,24}, {14,27}, {20,40}, {17,38}, {1,39}, {10,31}, {3,37}, {12,31}, {2,40}, {10,28}, {11,29}, {2,22}, {15,36}, {13,29}, {16,34}, {5,35}, {7,35}, {3,22}, {17,25}, {6,37}, {19,38}, {8,26}, {9,30}, {14,32}, {6,26}, {18,36}, {1,21}, {9,33}, {16,25}, {7,28}, {11,30}, {15,27}, {13,34} }; // ET40.2 // Bipartite(16,24) Valencies [3,2] // Diameter 8 Girth 12 // Twin-free Non-VT Non-AT // Automorphism group of order 96 EdgePairs[40][2]:={ {4,38}, {14,18}, {11,36}, {4,30}, {9,19}, {14,38}, {5,29}, {1,24}, {7,27}, {2,19}, {8,24}, {1,35}, {3,33}, {13,32}, {14,28}, {5,20}, {2,40}, {6,18}, {3,21}, {3,31}, {10,25}, {2,28}, {12,30}, {16,39}, {7,31}, {15,23}, {10,35}, {1,17}, {11,33}, {10,22}, {9,29}, {12,20}, {9,34}, {8,37}, {6,36}, {15,37}, {8,26}, {11,23}, {15,34}, {5,32}, {6,25}, {4,26}, {7,40}, {16,22}, {13,21}, {16,27}, {12,39}, {13,17} }; // ET40.3 // Bipartite(20,20) Valencies [3,3] // Diameter 6 Girth 8 // Twin-free VT AT // Automorphism group of order 480 EdgePairs[40][3]:={ {15,35}, {1,26}, {15,32}, {6,34}, {2,37}, {15,36}, {20,38}, {13,34}, {11,24}, {2,39}, {5,40}, {16,31}, {8,25}, {11,27}, {18,33}, {12,32}, {13,26}, {12,30}, {3,38}, {6,30}, {3,23}, {8,29}, {16,27}, {9,29}, {4,33}, {5,25}, {19,28}, {10,23}, {19,21}, {5,28}, {3,25}, {1,21}, {2,38}, {4,21}, {9,33}, {11,40}, {14,32}, {7,22}, {12,29}, {10,24}, {20,34}, {4,22}, {17,31}, {6,22}, {8,26}, {17,30}, {14,37}, {16,39}, {19,31}, {13,27}, {1,35}, {14,28}, {9,39}, {7,37}, {20,36}, {10,35}, {7,24}, {18,36}, {17,23}, {18,40} }; // ET40.4 // Bipartite(20,20) Valencies [4,4] // Diameter 4 Girth 6 // Twin-free VT AT // Automorphism group of order 160 EdgePairs[40][4]:={ {1,26}, {15,35}, {5,33}, {6,37}, {18,22}, {17,34}, {13,31}, {19,26}, {9,25}, {2,29}, {16,34}, {14,26}, {7,23}, {20,23}, {11,24}, {11,28}, {8,21}, {4,40}, {3,27}, {13,25}, {16,31}, {8,25}, {18,39}, {12,30}, {11,37}, {2,36}, {12,40}, {6,40}, {6,36}, {3,29}, {17,35}, {5,23}, {9,29}, {4,33}, {20,27}, {9,24}, {2,31}, {3,28}, {12,39}, {9,40}, {8,36}, {5,28}, {1,21}, {13,39}, {11,32}, {4,21}, {6,27}, {14,32}, {20,31}, {5,30}, {15,25}, {7,38}, {16,38}, {4,22}, {19,33}, {3,34}, {14,38}, {18,27}, {12,35}, {17,32}, {17,33}, {10,28}, {18,24}, {10,38}, {10,21}, {15,26}, {20,32}, {1,34}, {13,37}, {1,23}, {8,30}, {16,24}, {7,37}, {2,22}, {10,35}, {19,39}, {14,30}, {15,22}, {19,36}, {7,29} }; // ET40.5 // Bipartite(20,20) Valencies [4,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 80 EdgePairs[40][5]:={ {1,26}, {17,37}, {3,40}, {6,37}, {18,22}, {19,24}, {10,27}, {2,32}, {13,31}, {16,34}, {2,24}, {8,23}, {11,24}, {6,26}, {3,21}, {1,36}, {9,38}, {10,30}, {3,38}, {11,23}, {17,35}, {4,30}, {4,32}, {20,30}, {7,27}, {8,37}, {8,40}, {5,31}, {15,31}, {8,33}, {12,36}, {19,27}, {1,21}, {11,32}, {9,36}, {9,33}, {19,38}, {12,34}, {14,32}, {3,31}, {14,40}, {15,25}, {7,22}, {7,35}, {10,24}, {4,28}, {5,39}, {13,21}, {20,25}, {14,38}, {18,27}, {18,23}, {12,35}, {16,28}, {6,25}, {5,34}, {13,29}, {2,35}, {17,33}, {2,34}, {16,39}, {11,26}, {15,26}, {6,28}, {16,37}, {10,25}, {1,23}, {9,39}, {13,30}, {14,28}, {20,33}, {17,29}, {5,22}, {20,36}, {19,39}, {12,21}, {15,22}, {4,29}, {7,29}, {18,40} }; // ET40.6 // Bipartite(20,20) Valencies [4,4] // Diameter 6 Girth 4 // Twin-free VT AT // Automorphism group of order 160 EdgePairs[40][6]:={ {3,22}, {12,38}, {15,35}, {5,36}, {19,23}, {19,37}, {13,28}, {18,22}, {10,27}, {2,37}, {2,26}, {6,33}, {2,30}, {1,29}, {11,25}, {7,34}, {13,34}, {9,21}, {20,35}, {11,24}, {8,21}, {3,21}, {16,31}, {8,25}, {15,24}, {9,38}, {11,27}, {12,32}, {4,31}, {11,23}, {8,29}, {7,30}, {20,29}, {13,32}, {4,33}, {8,40}, {16,40}, {2,31}, {12,39}, {9,40}, {10,26}, {4,27}, {1,21}, {12,34}, {17,38}, {6,27}, {14,40}, {5,30}, {13,35}, {15,28}, {10,24}, {5,39}, {16,38}, {3,39}, {17,31}, {14,23}, {7,28}, {18,23}, {19,30}, {6,25}, {17,32}, {5,34}, {14,37}, {17,33}, {10,28}, {18,24}, {4,26}, {1,22}, {16,37}, {20,32}, {1,35}, {9,39}, {20,33}, {14,25}, {6,29}, {18,36}, {3,36}, {15,22}, {19,36}, {7,26} }; // ET40.7 // Bipartite(20,20) Valencies [4,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 80 EdgePairs[40][7]:={ {1,26}, {15,35}, {18,32}, {12,27}, {4,23}, {13,28}, {19,24}, {6,34}, {2,32}, {5,29}, {16,34}, {13,34}, {9,31}, {7,31}, {8,23}, {2,39}, {3,33}, {12,32}, {19,35}, {8,24}, {2,36}, {3,37}, {11,38}, {7,33}, {6,40}, {20,29}, {8,32}, {1,38}, {16,40}, {20,37}, {19,28}, {7,40}, {5,38}, {19,21}, {14,22}, {13,36}, {4,27}, {1,21}, {15,30}, {20,31}, {5,30}, {15,25}, {18,31}, {10,29}, {9,35}, {11,36}, {10,24}, {1,27}, {4,28}, {13,23}, {16,38}, {10,37}, {12,25}, {4,22}, {14,33}, {3,34}, {14,27}, {18,23}, {6,25}, {6,35}, {17,30}, {11,39}, {14,37}, {17,33}, {11,26}, {10,21}, {2,25}, {9,28}, {9,39}, {8,30}, {17,26}, {20,39}, {5,22}, {16,29}, {17,24}, {3,36}, {12,21}, {15,22}, {7,26}, {18,40} }; // ET40.8 // Bipartite(20,20) Valencies [4,4] // Diameter 4 Girth 6 // Twin-free VT AT // Automorphism group of order 160 EdgePairs[40][8]:={ {18,32}, {5,36}, {4,23}, {6,34}, {2,26}, {4,36}, {2,30}, {19,26}, {8,38}, {11,28}, {16,23}, {1,39}, {6,31}, {11,29}, {18,39}, {10,30}, {15,29}, {11,38}, {12,40}, {15,37}, {2,33}, {8,27}, {16,27}, {9,29}, {13,40}, {5,38}, {19,21}, {1,21}, {11,32}, {9,27}, {3,30}, {14,32}, {3,31}, {12,24}, {16,21}, {7,25}, {7,22}, {9,35}, {8,34}, {10,24}, {20,34}, {13,38}, {4,28}, {13,21}, {10,37}, {4,22}, {12,25}, {14,33}, {9,22}, {3,39}, {17,31}, {14,27}, {19,32}, {17,40}, {12,35}, {6,25}, {15,33}, {15,39}, {5,26}, {2,23}, {5,35}, {10,28}, {19,31}, {18,24}, {1,22}, {6,28}, {1,34}, {13,37}, {20,40}, {8,30}, {16,24}, {20,33}, {7,37}, {17,29}, {14,25}, {20,36}, {18,36}, {17,23}, {7,26}, {3,35} }; // ET40.9 // Bipartite(20,20) Valencies [4,4] // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 160 EdgePairs[40][9]:={ {15,35}, {19,23}, {3,40}, {18,22}, {10,40}, {2,26}, {5,37}, {1,30}, {9,25}, {20,38}, {4,34}, {13,34}, {7,31}, {6,26}, {8,21}, {3,27}, {10,32}, {11,27}, {12,30}, {19,35}, {18,34}, {17,25}, {3,24}, {12,31}, {7,33}, {9,37}, {2,33}, {6,32}, {16,33}, {11,33}, {11,21}, {8,27}, {1,38}, {13,40}, {15,31}, {20,37}, {2,31}, {19,28}, {10,23}, {5,38}, {12,36}, {8,36}, {5,28}, {1,21}, {13,39}, {15,30}, {11,22}, {17,36}, {14,32}, {16,21}, {7,22}, {12,29}, {9,34}, {15,28}, {10,24}, {5,39}, {13,23}, {16,38}, {4,22}, {4,25}, {1,28}, {20,26}, {18,27}, {6,35}, {14,37}, {2,35}, {14,24}, {20,32}, {9,39}, {8,30}, {17,29}, {14,25}, {6,23}, {17,24}, {19,39}, {3,36}, {16,26}, {4,29}, {7,29}, {18,40} }; // ET40.10 // Bipartite(20,20) Valencies [4,4] // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 160 EdgePairs[40][10]:={ {1,26}, {18,35}, {5,33}, {17,37}, {9,23}, {6,34}, {14,31}, {10,40}, {4,36}, {2,30}, {19,26}, {2,29}, {9,31}, {20,23}, {6,26}, {1,39}, {6,31}, {5,40}, {10,32}, {3,27}, {11,29}, {11,27}, {12,30}, {15,29}, {17,22}, {3,37}, {3,24}, {8,29}, {10,33}, {9,37}, {11,21}, {4,32}, {13,32}, {15,21}, {7,27}, {16,30}, {13,40}, {9,24}, {12,39}, {5,38}, {12,36}, {8,36}, {18,25}, {5,28}, {1,21}, {2,38}, {20,28}, {11,22}, {19,38}, {17,27}, {7,21}, {7,35}, {15,28}, {8,22}, {20,34}, {13,23}, {16,38}, {4,22}, {14,33}, {4,25}, {19,33}, {2,28}, {15,34}, {12,35}, {7,39}, {17,32}, {14,24}, {16,39}, {19,31}, {18,24}, {1,34}, {10,25}, {13,37}, {20,40}, {8,30}, {14,25}, {6,23}, {18,36}, {16,26}, {3,35} }; // ET40.11 // Bipartite(20,20) Valencies [4,4] // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 20480 EdgePairs[40][11]:={ {15,32}, {17,37}, {17,34}, {4,37}, {6,39}, {19,26}, {9,25}, {20,22}, {7,34}, {2,24}, {14,26}, {1,40}, {5,27}, {11,24}, {16,31}, {9,38}, {11,27}, {10,30}, {3,38}, {15,27}, {14,34}, {15,23}, {12,40}, {8,29}, {2,33}, {6,32}, {11,33}, {9,32}, {5,23}, {20,30}, {8,40}, {5,25}, {5,31}, {10,31}, {8,33}, {14,36}, {14,22}, {8,36}, {11,35}, {1,21}, {19,38}, {3,30}, {12,23}, {16,25}, {16,35}, {7,21}, {1,27}, {13,38}, {10,39}, {18,21}, {20,25}, {4,22}, {2,28}, {3,34}, {17,40}, {16,28}, {6,35}, {15,39}, {2,23}, {18,29}, {13,29}, {17,33}, {19,31}, {10,22}, {18,24}, {9,26}, {12,28}, {4,26}, {6,28}, {20,32}, {1,35}, {13,37}, {13,30}, {7,37}, {7,24}, {18,36}, {19,39}, {3,36}, {12,21}, {4,29} }; // ET40.12 // Bipartite(20,20) Valencies [4,4] // Diameter 10 Girth 4 // Has twins VT AT // Automorphism group of order 41943040 EdgePairs[40][12]:={ {16,25}, {14,34}, {2,22}, {1,31}, {4,27}, {8,36}, {19,39}, {1,40}, {13,24}, {12,31}, {7,33}, {12,22}, {3,32}, {13,34}, {10,40}, {17,35}, {6,25}, {9,39}, {18,23}, {7,23}, {3,34}, {20,40}, {15,28}, {10,30}, {14,27}, {5,37}, {12,21}, {17,23}, {4,37}, {2,31}, {8,33}, {19,26}, {18,33}, {2,32}, {10,39}, {16,35}, {7,25}, {3,22}, {8,26}, {19,29}, {17,33}, {5,28}, {10,29}, {13,22}, {7,35}, {5,38}, {2,21}, {5,27}, {6,38}, {13,32}, {14,37}, {11,40}, {11,31}, {3,24}, {19,36}, {15,37}, {8,23}, {20,30}, {11,21}, {9,26}, {11,30}, {15,27}, {16,28}, {20,29}, {9,29}, {15,38}, {12,32}, {18,36}, {20,39}, {16,38}, {6,35}, {9,36}, {4,34}, {1,30}, {1,21}, {14,24}, {4,24}, {18,26}, {17,25}, {6,28} }; // ET40.13 // Bipartite(20,20) Valencies [4,4] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 245760 EdgePairs[40][13]:={ {15,35}, {15,32}, {5,36}, {19,37}, {5,32}, {17,34}, {15,36}, {2,32}, {5,29}, {18,26}, {7,34}, {7,23}, {9,31}, {12,33}, {1,33}, {11,28}, {2,39}, {16,23}, {8,21}, {6,31}, {4,40}, {13,25}, {16,31}, {11,27}, {12,32}, {15,29}, {3,38}, {19,22}, {3,24}, {9,37}, {2,33}, {20,24}, {11,33}, {11,21}, {20,37}, {7,40}, {12,39}, {10,34}, {8,36}, {4,27}, {13,39}, {3,25}, {1,21}, {20,28}, {6,38}, {18,30}, {14,40}, {16,35}, {10,24}, {20,34}, {13,38}, {1,27}, {16,38}, {10,37}, {18,21}, {9,22}, {3,39}, {4,25}, {12,22}, {8,26}, {1,28}, {14,27}, {17,40}, {13,24}, {19,30}, {6,35}, {5,35}, {10,28}, {9,30}, {19,31}, {14,29}, {8,30}, {17,26}, {14,25}, {6,23}, {2,22}, {18,36}, {17,23}, {7,26}, {4,29} }; // ET40.14 // Bipartite(20,20) Valencies [4,4] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 327680 EdgePairs[40][14]:={ {11,30}, {12,38}, {18,35}, {19,37}, {19,24}, {6,34}, {6,39}, {5,24}, {4,36}, {6,33}, {2,30}, {13,31}, {19,26}, {1,30}, {16,34}, {20,22}, {7,23}, {9,31}, {4,40}, {10,32}, {13,25}, {15,24}, {11,27}, {12,30}, {3,23}, {7,33}, {8,29}, {9,37}, {16,33}, {11,21}, {4,32}, {5,21}, {15,21}, {7,27}, {8,37}, {8,40}, {9,24}, {10,26}, {14,36}, {13,36}, {5,28}, {3,25}, {1,21}, {2,38}, {11,22}, {6,38}, {17,27}, {14,32}, {3,31}, {14,40}, {15,28}, {8,35}, {1,27}, {13,23}, {4,28}, {16,38}, {10,39}, {12,25}, {18,37}, {15,34}, {20,26}, {12,35}, {18,29}, {5,34}, {2,35}, {17,33}, {16,39}, {19,31}, {10,22}, {9,26}, {1,22}, {2,25}, {20,32}, {14,28}, {17,29}, {20,39}, {3,36}, {17,23}, {7,29}, {18,40} }; // ET40.15 // Non-bipartite Valency 4 // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 320 EdgePairs[40][15]:={ {2,11}, {8,19}, {5,36}, {13,28}, {27,36}, {7,16}, {3,12}, {6,39}, {1,30}, {29,37}, {4,34}, {9,21}, {8,38}, {2,10}, {21,35}, {24,30}, {11,20}, {9,38}, {27,37}, {2,36}, {12,40}, {11,23}, {1,31}, {3,9}, {6,15}, {4,32}, {20,30}, {18,28}, {20,27}, {1,15}, {22,29}, {10,23}, {8,33}, {5,38}, {24,33}, {5,19}, {18,25}, {12,37}, {18,30}, {26,35}, {16,25}, {29,40}, {23,35}, {15,28}, {8,35}, {32,39}, {4,15}, {16,22}, {26,33}, {14,21}, {17,31}, {10,19}, {10,17}, {14,23}, {20,26}, {22,33}, {3,13}, {6,17}, {7,39}, {5,34}, {28,40}, {7,17}, {19,31}, {26,37}, {24,31}, {2,13}, {1,34}, {25,40}, {9,39}, {7,14}, {16,24}, {11,18}, {27,34}, {14,25}, {32,38}, {6,13}, {3,36}, {12,21}, {22,32}, {4,29} }; // ET40.16 // Bipartite(15,25) Valencies [5,3] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 600 EdgePairs[40][16]:={ {3,22}, {12,27}, {4,24}, {11,16}, {5,32}, {13,28}, {9,23}, {2,37}, {4,37}, {11,25}, {14,26}, {12,33}, {5,27}, {8,23}, {2,40}, {11,29}, {12,30}, {15,38}, {10,36}, {8,24}, {1,31}, {9,32}, {11,21}, {7,30}, {6,16}, {4,32}, {5,20}, {15,21}, {9,29}, {15,31}, {2,31}, {1,16}, {7,40}, {3,28}, {9,40}, {8,33}, {5,38}, {10,34}, {14,36}, {6,20}, {13,33}, {14,22}, {2,18}, {9,36}, {3,19}, {12,37}, {7,21}, {7,35}, {8,35}, {1,27}, {13,38}, {7,20}, {10,39}, {6,18}, {12,25}, {2,28}, {3,34}, {6,17}, {15,39}, {5,34}, {13,29}, {4,26}, {15,26}, {1,22}, {10,25}, {1,23}, {4,19}, {11,19}, {14,17}, {13,17}, {10,18}, {6,24}, {8,39}, {14,30}, {3,35} }; // ET40.17 // Bipartite(10,30) Valencies [6,2] // Diameter 5 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[40][17]:={ {3,22}, {5,33}, {8,19}, {9,23}, {3,12}, {2,32}, {1,29}, {7,34}, {2,24}, {9,21}, {7,12}, {5,27}, {2,39}, {4,40}, {10,32}, {8,25}, {5,11}, {10,36}, {4,31}, {3,24}, {8,29}, {9,37}, {6,15}, {3,20}, {4,30}, {2,21}, {10,13}, {8,37}, {2,16}, {2,31}, {1,16}, {7,40}, {8,33}, {10,34}, {4,20}, {6,38}, {6,27}, {5,30}, {1,18}, {7,38}, {4,15}, {9,13}, {5,39}, {4,28}, {1,17}, {6,19}, {9,22}, {1,28}, {8,26}, {5,14}, {9,14}, {6,35}, {7,17}, {10,25}, {1,11}, {6,23}, {10,18}, {3,36}, {7,26}, {3,35} }; // ET40.18 // Bipartite(10,30) Valencies [6,2] // Diameter 10 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1209323520 EdgePairs[40][18]:={ {4,13}, {4,24}, {5,36}, {4,23}, {9,19}, {10,40}, {5,37}, {6,39}, {2,32}, {9,20}, {4,34}, {7,34}, {1,32}, {5,27}, {8,16}, {8,15}, {3,27}, {8,25}, {10,30}, {3,38}, {1,12}, {3,37}, {1,31}, {2,12}, {2,33}, {5,16}, {9,29}, {4,33}, {10,31}, {3,28}, {9,40}, {3,17}, {8,36}, {1,21}, {10,11}, {6,38}, {7,15}, {5,17}, {3,18}, {7,25}, {7,35}, {8,35}, {6,18}, {6,19}, {8,26}, {5,26}, {2,23}, {9,30}, {10,21}, {1,22}, {2,13}, {6,28}, {4,14}, {9,39}, {7,14}, {10,20}, {1,11}, {6,29}, {2,22}, {7,24} }; // ET40.19 // Bipartite(10,30) Valencies [6,2] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3932160 EdgePairs[40][19]:={ {1,26}, {10,40}, {2,37}, {3,12}, {5,24}, {2,32}, {6,33}, {5,29}, {9,20}, {7,23}, {9,31}, {9,16}, {6,26}, {8,15}, {4,40}, {7,13}, {3,27}, {2,36}, {1,31}, {3,24}, {6,36}, {10,33}, {4,30}, {2,21}, {8,27}, {5,23}, {8,37}, {7,32}, {1,16}, {5,38}, {4,20}, {3,19}, {10,14}, {8,12}, {6,21}, {10,29}, {7,38}, {9,35}, {8,22}, {4,15}, {9,13}, {5,39}, {6,18}, {4,25}, {3,39}, {3,34}, {5,14}, {2,17}, {7,28}, {7,17}, {1,19}, {6,11}, {4,35}, {1,34}, {10,25}, {9,28}, {8,30}, {1,11}, {2,22}, {10,18} }; // ET40.20 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 192 EdgePairs[40][20]:={ {10,19}, {15,23}, {14,25}, {8,39}, {10,22}, {6,18}, {9,30}, {6,36}, {4,27}, {1,25}, {12,40}, {13,34}, {1,38}, {6,32}, {12,33}, {13,27}, {12,18}, {16,20}, {7,23}, {15,29}, {13,38}, {3,34}, {9,31}, {9,17}, {10,18}, {3,18}, {14,33}, {11,34}, {16,21}, {4,37}, {2,23}, {7,26}, {4,39}, {13,26}, {1,17}, {15,25}, {1,22}, {3,40}, {4,33}, {4,28}, {7,29}, {16,26}, {5,19}, {10,24}, {15,35}, {11,39}, {4,31}, {2,34}, {2,40}, {12,28}, {15,19}, {5,28}, {13,30}, {12,35}, {10,29}, {8,19}, {6,29}, {7,35}, {2,24}, {5,22}, {11,36}, {3,35}, {14,22}, {6,30}, {10,28}, {8,38}, {14,23}, {5,20}, {11,31}, {5,31}, {5,17}, {15,37}, {8,20}, {11,21}, {3,21}, {11,27}, {1,27}, {8,25}, {7,32}, {2,26}, {13,17}, {7,21}, {1,33}, {14,40}, {3,36}, {8,37}, {9,32}, {6,24}, {16,38}, {9,36}, {16,32}, {12,37}, {16,39}, {2,30}, {14,24}, {9,20} }; // ET40.21 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 192 EdgePairs[40][21]:={ {10,19}, {16,25}, {6,39}, {10,21}, {8,39}, {9,30}, {3,38}, {6,36}, {13,18}, {7,40}, {10,27}, {5,35}, {11,29}, {1,40}, {5,34}, {12,31}, {2,33}, {6,32}, {7,31}, {9,39}, {16,23}, {12,33}, {16,40}, {13,27}, {12,18}, {11,38}, {16,20}, {14,35}, {2,28}, {3,34}, {2,19}, {4,26}, {5,21}, {15,28}, {2,29}, {3,18}, {15,39}, {15,22}, {13,33}, {2,23}, {7,26}, {8,28}, {1,17}, {10,25}, {14,30}, {12,34}, {4,33}, {9,34}, {4,29}, {7,25}, {10,37}, {5,19}, {6,37}, {4,31}, {4,36}, {2,35}, {11,26}, {15,26}, {5,22}, {6,30}, {9,35}, {8,38}, {14,23}, {3,24}, {12,36}, {13,28}, {8,20}, {8,23}, {11,21}, {3,21}, {4,32}, {1,27}, {11,32}, {7,22}, {10,32}, {15,17}, {13,17}, {15,38}, {3,20}, {14,29}, {14,40}, {8,37}, {16,37}, {9,36}, {6,27}, {13,19}, {7,17}, {11,24}, {1,30}, {16,31}, {12,20}, {1,18}, {5,25}, {14,24}, {1,24}, {9,22} }; // ET40.22 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1152 EdgePairs[40][22]:={ {10,19}, {16,25}, {14,21}, {5,32}, {7,39}, {16,36}, {8,24}, {6,18}, {3,38}, {13,18}, {4,27}, {16,30}, {10,27}, {10,38}, {6,23}, {5,34}, {12,17}, {2,37}, {13,34}, {10,40}, {1,38}, {7,31}, {16,23}, {7,27}, {13,27}, {12,18}, {11,22}, {9,37}, {15,29}, {9,31}, {14,20}, {9,17}, {15,32}, {5,21}, {15,28}, {2,29}, {3,19}, {12,30}, {16,21}, {5,33}, {13,33}, {1,17}, {10,25}, {2,32}, {12,34}, {2,36}, {8,18}, {4,28}, {10,39}, {4,29}, {15,35}, {11,39}, {4,31}, {6,26}, {2,40}, {15,33}, {4,25}, {1,35}, {1,26}, {11,26}, {8,19}, {8,40}, {15,26}, {5,22}, {3,35}, {14,22}, {6,30}, {9,35}, {14,31}, {1,39}, {14,23}, {11,40}, {5,36}, {12,36}, {13,28}, {8,20}, {3,21}, {11,32}, {7,22}, {9,29}, {3,20}, {2,25}, {8,37}, {6,24}, {16,38}, {13,19}, {3,33}, {7,34}, {7,17}, {4,23}, {11,24}, {1,30}, {12,37}, {14,24}, {9,20}, {6,28} }; // ET40.23 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 192 EdgePairs[40][23]:={ {10,19}, {14,21}, {16,34}, {9,40}, {10,21}, {14,25}, {8,39}, {8,24}, {11,23}, {9,30}, {3,38}, {8,36}, {12,17}, {2,37}, {6,32}, {6,25}, {9,39}, {16,40}, {7,27}, {13,27}, {12,18}, {11,22}, {7,23}, {13,38}, {15,29}, {2,28}, {14,20}, {16,33}, {6,34}, {2,19}, {5,26}, {4,26}, {10,18}, {3,19}, {1,29}, {7,28}, {11,34}, {2,23}, {13,26}, {1,17}, {15,25}, {1,22}, {3,40}, {4,33}, {8,18}, {4,29}, {16,26}, {9,23}, {10,24}, {13,35}, {6,37}, {11,39}, {4,31}, {4,30}, {2,34}, {2,40}, {12,28}, {15,19}, {13,30}, {10,29}, {7,35}, {14,32}, {9,33}, {5,22}, {11,36}, {3,35}, {15,31}, {9,35}, {10,28}, {14,31}, {6,38}, {1,39}, {5,20}, {5,36}, {5,31}, {5,17}, {15,37}, {8,20}, {16,22}, {3,21}, {11,27}, {7,32}, {3,25}, {13,36}, {15,17}, {7,21}, {1,33}, {12,32}, {16,38}, {8,30}, {6,27}, {12,37}, {12,20}, {1,18}, {14,24}, {4,24} }; // ET40.24 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 6144 EdgePairs[40][24]:={ {11,17}, {8,39}, {6,18}, {10,27}, {10,38}, {14,19}, {7,38}, {1,25}, {12,31}, {2,37}, {13,34}, {10,40}, {2,33}, {6,32}, {6,25}, {13,27}, {9,21}, {12,27}, {14,35}, {7,23}, {15,29}, {9,31}, {3,31}, {2,18}, {4,26}, {6,22}, {3,19}, {12,21}, {12,30}, {11,34}, {14,33}, {9,38}, {5,23}, {15,34}, {15,22}, {2,31}, {2,23}, {13,33}, {1,36}, {1,17}, {3,40}, {8,18}, {9,34}, {16,26}, {16,35}, {5,29}, {2,40}, {7,30}, {4,21}, {4,17}, {5,28}, {12,35}, {15,26}, {14,22}, {10,28}, {8,38}, {13,32}, {5,20}, {9,28}, {11,40}, {5,36}, {3,26}, {9,24}, {15,37}, {6,20}, {11,30}, {10,17}, {1,37}, {7,22}, {15,27}, {4,18}, {8,25}, {3,25}, {7,32}, {11,20}, {1,33}, {14,29}, {3,36}, {8,30}, {16,37}, {10,35}, {13,19}, {16,32}, {7,36}, {4,23}, {11,24}, {5,39}, {16,39}, {1,21}, {12,20}, {14,24}, {4,19}, {8,29}, {13,39}, {6,28}, {16,24} }; // ET40.25 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 192 EdgePairs[40][25]:={ {7,19}, {16,34}, {9,40}, {14,25}, {15,23}, {16,36}, {8,31}, {8,24}, {2,38}, {10,22}, {12,39}, {9,30}, {5,30}, {6,36}, {11,33}, {6,17}, {5,35}, {1,40}, {13,24}, {14,18}, {7,33}, {12,31}, {6,25}, {9,19}, {12,18}, {11,38}, {6,40}, {7,23}, {15,29}, {2,28}, {3,31}, {6,34}, {2,18}, {5,21}, {10,23}, {3,19}, {12,21}, {16,21}, {4,37}, {10,34}, {13,33}, {2,23}, {4,39}, {1,17}, {14,30}, {2,36}, {8,18}, {7,29}, {4,29}, {16,26}, {3,22}, {10,37}, {8,26}, {15,20}, {15,35}, {3,27}, {5,28}, {12,29}, {1,26}, {3,35}, {15,31}, {16,27}, {14,22}, {8,27}, {10,28}, {9,35}, {6,38}, {14,37}, {5,20}, {9,24}, {11,25}, {12,36}, {13,28}, {9,26}, {10,17}, {11,27}, {4,32}, {1,20}, {11,32}, {7,22}, {7,32}, {3,25}, {13,17}, {15,38}, {11,20}, {1,33}, {14,40}, {8,37}, {4,34}, {13,19}, {16,32}, {5,39}, {2,30}, {1,21}, {4,24}, {13,39} }; // ET40.26 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 96 EdgePairs[40][26]:={ {13,25}, {6,39}, {7,39}, {9,40}, {10,21}, {13,29}, {8,24}, {12,26}, {10,22}, {6,18}, {3,29}, {2,22}, {1,31}, {1,40}, {4,40}, {5,34}, {5,24}, {6,32}, {2,33}, {12,33}, {9,39}, {9,19}, {13,27}, {11,22}, {16,20}, {8,34}, {3,34}, {14,20}, {5,21}, {3,19}, {9,38}, {10,34}, {4,20}, {13,33}, {8,28}, {4,39}, {15,25}, {2,36}, {8,18}, {14,28}, {9,23}, {14,38}, {6,37}, {3,23}, {16,29}, {14,26}, {11,18}, {7,30}, {4,21}, {2,35}, {15,33}, {5,28}, {12,35}, {9,25}, {10,29}, {1,26}, {8,19}, {12,24}, {15,26}, {4,38}, {12,23}, {2,27}, {6,19}, {14,17}, {3,35}, {1,23}, {16,27}, {6,30}, {14,31}, {13,32}, {8,32}, {4,22}, {11,40}, {11,31}, {5,36}, {5,17}, {15,37}, {12,36}, {11,30}, {11,27}, {16,28}, {3,25}, {7,37}, {15,17}, {15,38}, {7,21}, {10,20}, {10,35}, {13,37}, {16,32}, {7,36}, {7,17}, {16,31}, {2,30}, {1,18}, {1,24} }; // ET40.27 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 384 EdgePairs[40][27]:={ {3,22}, {11,30}, {1,26}, {12,27}, {8,19}, {4,23}, {9,23}, {14,31}, {15,40}, {2,37}, {5,24}, {2,32}, {6,33}, {11,17}, {16,34}, {13,34}, {9,21}, {7,31}, {8,38}, {8,23}, {6,26}, {14,39}, {1,39}, {2,40}, {11,20}, {13,25}, {11,29}, {12,32}, {15,29}, {6,30}, {1,20}, {6,36}, {3,29}, {3,20}, {11,33}, {9,32}, {13,18}, {8,27}, {4,32}, {16,27}, {16,36}, {1,38}, {15,21}, {5,31}, {15,31}, {7,40}, {9,40}, {4,38}, {10,34}, {8,36}, {13,36}, {5,28}, {3,25}, {2,18}, {4,27}, {4,21}, {9,33}, {3,30}, {12,37}, {12,24}, {15,17}, {7,25}, {7,22}, {7,35}, {10,24}, {4,28}, {5,39}, {16,19}, {10,39}, {1,17}, {6,18}, {14,21}, {3,34}, {10,19}, {14,38}, {8,26}, {9,18}, {12,35}, {15,33}, {5,35}, {2,35}, {1,19}, {10,22}, {11,26}, {12,28}, {2,25}, {16,37}, {13,37}, {13,30}, {14,28}, {16,24}, {10,20}, {14,17}, {5,22}, {6,23}, {7,29} }; // ET40.28 // Bipartite(16,24) Valencies [6,4] // Diameter 8 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6879707136 EdgePairs[40][28]:={ {14,39}, {4,35}, {10,19}, {16,25}, {6,39}, {7,39}, {15,23}, {13,29}, {8,24}, {12,19}, {3,29}, {3,38}, {7,40}, {4,27}, {10,27}, {7,24}, {11,29}, {6,23}, {1,25}, {7,31}, {16,40}, {15,40}, {11,38}, {3,30}, {11,22}, {12,27}, {7,23}, {16,33}, {2,19}, {2,18}, {9,17}, {10,18}, {15,32}, {6,22}, {13,20}, {5,21}, {5,37}, {1,34}, {15,39}, {10,34}, {4,20}, {8,33}, {1,17}, {14,30}, {16,17}, {9,34}, {4,28}, {3,22}, {14,38}, {8,17}, {5,29}, {2,34}, {12,28}, {4,36}, {2,35}, {5,28}, {12,35}, {9,25}, {1,26}, {11,37}, {8,40}, {6,31}, {9,33}, {2,27}, {15,31}, {14,22}, {6,30}, {14,31}, {6,38}, {14,23}, {8,32}, {5,20}, {5,36}, {12,36}, {13,28}, {11,21}, {9,26}, {3,21}, {11,30}, {9,18}, {13,21}, {8,25}, {7,32}, {2,26}, {13,36}, {1,33}, {3,37}, {10,26}, {10,35}, {13,37}, {16,32}, {12,20}, {1,18}, {15,24}, {4,19}, {16,24} }; // ET40.29 // Bipartite(16,24) Valencies [6,4] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 50331648 EdgePairs[40][29]:={ {7,19}, {14,21}, {16,34}, {9,40}, {7,39}, {10,21}, {15,23}, {14,25}, {13,29}, {14,34}, {16,30}, {10,27}, {1,40}, {2,20}, {4,40}, {13,24}, {12,40}, {5,24}, {16,18}, {2,33}, {7,31}, {6,25}, {7,27}, {12,18}, {7,23}, {8,34}, {13,38}, {3,31}, {6,34}, {5,26}, {9,17}, {6,22}, {3,19}, {1,29}, {8,22}, {12,30}, {14,33}, {15,39}, {4,20}, {13,26}, {1,17}, {2,32}, {6,33}, {6,21}, {8,18}, {4,28}, {10,39}, {16,26}, {9,23}, {15,35}, {8,26}, {6,37}, {5,29}, {4,30}, {10,33}, {15,19}, {12,28}, {1,35}, {11,37}, {7,35}, {11,36}, {2,27}, {5,38}, {15,31}, {1,23}, {2,21}, {14,22}, {9,35}, {11,19}, {8,38}, {14,37}, {2,39}, {9,28}, {11,31}, {5,36}, {3,24}, {5,17}, {11,25}, {16,22}, {4,32}, {15,27}, {4,18}, {9,29}, {3,25}, {10,32}, {13,36}, {13,17}, {12,32}, {1,28}, {3,36}, {10,20}, {3,37}, {16,38}, {8,30}, {11,24}, {12,20} }; // ET40.30 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1934917632 EdgePairs[40][30]:={ {4,35}, {7,19}, {16,25}, {15,23}, {13,29}, {8,39}, {8,31}, {12,26}, {10,22}, {12,39}, {9,30}, {3,29}, {4,27}, {8,36}, {10,38}, {14,19}, {13,24}, {5,34}, {1,25}, {12,31}, {2,37}, {9,39}, {16,40}, {15,40}, {7,27}, {12,18}, {14,35}, {9,31}, {16,33}, {2,18}, {5,26}, {15,32}, {6,22}, {2,29}, {14,27}, {10,30}, {15,39}, {9,38}, {5,33}, {7,26}, {8,28}, {1,36}, {1,17}, {10,25}, {12,34}, {6,21}, {16,17}, {9,23}, {6,37}, {11,28}, {4,30}, {2,34}, {10,33}, {13,40}, {6,29}, {7,35}, {4,38}, {12,23}, {14,32}, {11,36}, {15,31}, {2,21}, {6,30}, {11,19}, {7,18}, {6,38}, {13,32}, {4,22}, {3,28}, {5,17}, {8,20}, {8,23}, {3,21}, {10,17}, {11,27}, {13,21}, {1,20}, {2,26}, {11,20}, {3,20}, {1,33}, {14,40}, {1,28}, {3,36}, {3,37}, {5,18}, {7,34}, {13,37}, {16,32}, {11,35}, {15,24}, {5,25}, {4,19}, {14,24}, {9,22}, {16,24} }; // ET40.31 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 98304 EdgePairs[40][31]:={ {14,39}, {13,25}, {6,39}, {10,21}, {13,29}, {8,39}, {8,31}, {8,24}, {11,23}, {14,34}, {6,36}, {7,40}, {4,27}, {5,35}, {2,20}, {5,34}, {7,38}, {7,33}, {3,32}, {13,34}, {2,33}, {6,32}, {7,31}, {15,40}, {9,19}, {6,40}, {11,22}, {9,37}, {12,27}, {6,34}, {2,18}, {5,26}, {9,17}, {10,18}, {3,19}, {8,22}, {12,21}, {12,30}, {9,27}, {1,36}, {13,26}, {1,17}, {14,30}, {16,17}, {4,28}, {3,22}, {10,24}, {15,35}, {13,35}, {3,23}, {8,17}, {5,29}, {16,29}, {4,30}, {10,33}, {1,19}, {12,28}, {4,21}, {15,33}, {5,28}, {7,35}, {4,38}, {12,23}, {14,32}, {2,24}, {12,38}, {14,36}, {15,31}, {2,21}, {6,30}, {11,19}, {15,37}, {11,25}, {13,28}, {16,22}, {9,18}, {1,37}, {1,27}, {11,32}, {3,25}, {2,26}, {7,37}, {15,38}, {11,20}, {3,20}, {14,40}, {10,20}, {10,26}, {9,36}, {4,23}, {16,31}, {16,39}, {1,18}, {5,25}, {8,29}, {16,24} }; // ET40.32 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2359296 EdgePairs[40][32]:={ {14,39}, {16,25}, {9,40}, {8,39}, {11,23}, {6,18}, {14,34}, {5,30}, {11,33}, {6,17}, {16,30}, {10,27}, {7,24}, {5,34}, {7,38}, {1,25}, {12,22}, {16,18}, {12,33}, {16,23}, {6,40}, {15,29}, {13,38}, {3,34}, {2,19}, {5,26}, {14,27}, {1,29}, {12,21}, {4,20}, {2,31}, {2,23}, {13,33}, {7,26}, {8,28}, {13,26}, {10,25}, {1,17}, {12,34}, {15,36}, {10,39}, {16,35}, {7,25}, {3,22}, {10,37}, {8,26}, {3,23}, {11,28}, {4,31}, {4,30}, {15,19}, {2,35}, {8,40}, {6,29}, {5,22}, {2,27}, {5,38}, {14,17}, {15,31}, {3,35}, {14,22}, {6,30}, {8,27}, {8,38}, {2,39}, {11,40}, {9,28}, {3,24}, {9,24}, {11,21}, {4,32}, {13,21}, {1,37}, {4,18}, {10,32}, {15,17}, {7,37}, {1,33}, {14,29}, {12,32}, {3,36}, {10,20}, {9,32}, {5,18}, {16,37}, {13,31}, {9,36}, {13,19}, {7,36}, {11,35}, {1,21}, {12,20}, {15,24}, {4,19}, {9,20}, {6,28} }; // ET40.33 // Bipartite(16,24) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 786432 EdgePairs[40][33]:={ {12,38}, {5,33}, {6,37}, {5,32}, {13,28}, {10,27}, {14,19}, {14,31}, {10,40}, {2,26}, {4,37}, {6,39}, {12,18}, {1,29}, {9,25}, {11,17}, {16,34}, {1,37}, {1,33}, {16,23}, {3,21}, {2,40}, {10,32}, {3,33}, {11,29}, {9,38}, {11,27}, {12,30}, {15,38}, {15,27}, {8,24}, {3,23}, {12,31}, {8,29}, {9,37}, {2,33}, {7,30}, {2,21}, {4,30}, {4,32}, {5,21}, {5,20}, {4,18}, {16,30}, {13,40}, {9,24}, {7,40}, {16,18}, {7,18}, {14,36}, {8,36}, {13,36}, {2,38}, {1,21}, {9,36}, {4,20}, {3,19}, {6,27}, {14,32}, {3,31}, {12,19}, {16,35}, {13,35}, {8,34}, {8,22}, {12,26}, {16,22}, {13,23}, {10,39}, {1,17}, {4,25}, {2,28}, {15,34}, {7,28}, {13,24}, {6,25}, {6,35}, {15,39}, {5,34}, {14,20}, {11,39}, {14,24}, {7,17}, {10,28}, {9,26}, {15,26}, {11,19}, {10,20}, {11,31}, {5,22}, {1,25}, {8,17}, {6,23}, {15,22}, {3,35}, {7,29} }; // ET40.34 // Bipartite(20,20) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 240 EdgePairs[40][34]:={ {13,25}, {7,39}, {15,23}, {8,24}, {11,23}, {14,34}, {1,31}, {16,30}, {18,39}, {12,40}, {20,21}, {20,23}, {3,32}, {19,40}, {2,33}, {7,31}, {9,21}, {19,24}, {1,32}, {12,27}, {14,35}, {7,23}, {9,31}, {5,26}, {4,26}, {15,32}, {6,22}, {15,28}, {2,29}, {14,27}, {19,37}, {14,33}, {11,34}, {16,21}, {9,38}, {5,33}, {5,23}, {17,30}, {4,37}, {9,27}, {20,35}, {10,36}, {2,23}, {4,39}, {1,36}, {13,26}, {10,25}, {15,25}, {1,22}, {3,40}, {6,21}, {9,34}, {7,25}, {10,37}, {18,25}, {15,35}, {14,38}, {11,39}, {5,29}, {19,29}, {3,27}, {2,34}, {4,30}, {12,28}, {4,21}, {15,33}, {17,33}, {5,28}, {10,29}, {11,26}, {8,40}, {13,22}, {7,35}, {12,24}, {6,31}, {18,32}, {3,35}, {9,35}, {10,28}, {6,38}, {8,38}, {4,22}, {3,28}, {19,36}, {12,36}, {16,22}, {11,21}, {11,30}, {17,34}, {1,27}, {7,32}, {17,29}, {2,26}, {13,36}, {20,34}, {17,38}, {12,32}, {14,40}, {18,31}, {8,37}, {18,36}, {20,31}, {20,39}, {6,24}, {16,38}, {18,22}, {8,30}, {16,37}, {10,26}, {6,27}, {3,33}, {13,37}, {17,40}, {19,28}, {2,30}, {5,25}, {1,24}, {8,29}, {13,39}, {16,24} }; // ET40.35 // Bipartite(20,20) Valencies [6,6] // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 480 EdgePairs[40][35]:={ {14,39}, {16,25}, {13,25}, {20,27}, {10,21}, {16,36}, {12,26}, {2,38}, {11,23}, {17,27}, {3,38}, {20,28}, {6,36}, {1,31}, {16,30}, {8,36}, {5,35}, {10,38}, {1,40}, {4,40}, {1,38}, {19,27}, {16,40}, {7,27}, {15,40}, {9,21}, {11,38}, {3,30}, {19,23}, {14,35}, {18,23}, {3,34}, {6,22}, {10,23}, {5,37}, {7,28}, {12,21}, {11,34}, {15,39}, {9,38}, {17,23}, {5,33}, {10,34}, {20,33}, {2,31}, {8,33}, {8,28}, {19,26}, {18,33}, {15,25}, {14,30}, {6,33}, {3,40}, {12,34}, {15,36}, {16,35}, {7,25}, {9,23}, {8,35}, {13,35}, {6,37}, {4,31}, {4,30}, {2,34}, {4,21}, {17,33}, {12,29}, {10,29}, {11,26}, {13,40}, {12,24}, {5,22}, {17,22}, {18,32}, {14,36}, {2,21}, {5,27}, {8,27}, {18,28}, {14,31}, {1,39}, {2,39}, {14,37}, {20,32}, {3,24}, {9,24}, {15,37}, {9,26}, {18,29}, {19,22}, {20,26}, {3,39}, {11,32}, {7,22}, {8,25}, {9,29}, {17,29}, {20,29}, {10,32}, {7,37}, {12,32}, {17,26}, {6,35}, {18,22}, {13,31}, {19,32}, {4,34}, {13,37}, {15,30}, {7,36}, {11,24}, {16,31}, {19,28}, {2,30}, {1,21}, {5,25}, {4,24}, {1,24}, {13,39}, {6,28} }; // ET40.36 // Bipartite(20,20) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 480 EdgePairs[40][36]:={ {15,23}, {14,25}, {8,39}, {12,26}, {18,40}, {9,30}, {17,27}, {20,28}, {7,40}, {10,27}, {5,35}, {11,29}, {13,24}, {7,38}, {7,33}, {2,37}, {13,34}, {10,40}, {2,33}, {6,32}, {12,33}, {9,39}, {19,31}, {11,38}, {19,23}, {7,23}, {18,21}, {19,38}, {13,38}, {15,29}, {9,31}, {12,25}, {16,33}, {5,26}, {4,26}, {6,22}, {20,40}, {5,21}, {10,23}, {14,27}, {1,29}, {8,22}, {20,25}, {7,28}, {1,34}, {16,21}, {4,37}, {10,34}, {2,31}, {4,39}, {1,22}, {12,34}, {15,36}, {4,29}, {10,24}, {18,25}, {8,35}, {15,35}, {6,37}, {3,23}, {11,28}, {14,26}, {2,40}, {7,30}, {2,35}, {17,33}, {12,35}, {13,30}, {1,26}, {4,38}, {2,24}, {11,36}, {17,22}, {16,27}, {5,27}, {6,30}, {8,27}, {14,31}, {14,23}, {14,37}, {11,31}, {5,36}, {3,24}, {17,37}, {15,37}, {9,26}, {3,21}, {18,29}, {19,22}, {4,32}, {13,21}, {17,34}, {18,30}, {16,28}, {8,25}, {3,25}, {10,32}, {20,34}, {17,38}, {12,32}, {1,28}, {3,36}, {18,31}, {20,39}, {6,24}, {20,36}, {9,36}, {19,32}, {19,35}, {3,33}, {15,30}, {16,32}, {11,24}, {16,39}, {1,21}, {5,40}, {8,29}, {13,39}, {6,28}, {9,22} }; // ET40.37 // Bipartite(20,20) Valencies [6,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 122880 EdgePairs[40][37]:={ {16,36}, {10,22}, {12,39}, {9,30}, {5,30}, {6,36}, {11,33}, {16,30}, {5,35}, {11,29}, {10,38}, {4,40}, {1,25}, {12,40}, {7,33}, {20,23}, {3,32}, {18,37}, {1,38}, {19,27}, {7,31}, {15,40}, {13,27}, {11,38}, {9,37}, {19,23}, {12,27}, {18,21}, {15,29}, {12,25}, {3,31}, {4,26}, {5,21}, {10,23}, {1,29}, {8,22}, {19,37}, {7,28}, {11,34}, {1,34}, {17,31}, {16,21}, {10,34}, {20,38}, {9,27}, {2,23}, {8,33}, {19,30}, {18,33}, {13,26}, {15,25}, {18,38}, {6,21}, {8,21}, {4,28}, {10,39}, {16,26}, {4,29}, {14,28}, {9,23}, {8,35}, {15,35}, {6,37}, {5,29}, {3,27}, {14,26}, {6,26}, {2,40}, {4,36}, {17,33}, {17,36}, {12,24}, {18,35}, {12,23}, {2,24}, {6,31}, {2,27}, {17,22}, {14,36}, {15,21}, {6,30}, {9,35}, {8,38}, {13,32}, {2,39}, {3,28}, {20,32}, {3,26}, {11,25}, {13,28}, {3,39}, {17,34}, {7,22}, {10,32}, {20,34}, {1,33}, {14,29}, {14,40}, {2,25}, {8,37}, {20,39}, {9,32}, {18,22}, {16,37}, {17,28}, {13,31}, {19,32}, {19,35}, {20,22}, {7,34}, {15,30}, {7,36}, {11,24}, {16,31}, {5,25}, {14,24}, {4,24}, {5,40}, {1,24}, {13,39} }; // ET40.38 // Bipartite(20,20) Valencies [6,6] // Diameter 5 Girth 4 // Has twins VT AT // Automorphism group of order 251658240 EdgePairs[40][38]:={ {14,39}, {14,21}, {9,40}, {13,29}, {8,24}, {12,26}, {12,39}, {9,30}, {3,29}, {16,30}, {5,35}, {7,38}, {7,33}, {20,23}, {19,40}, {18,37}, {1,38}, {6,32}, {16,40}, {19,24}, {11,38}, {3,30}, {6,40}, {7,23}, {8,34}, {12,25}, {6,22}, {5,21}, {10,23}, {2,29}, {5,37}, {18,24}, {8,22}, {7,28}, {16,21}, {17,23}, {10,34}, {20,33}, {10,36}, {13,33}, {19,30}, {4,39}, {1,36}, {15,25}, {3,40}, {6,21}, {2,36}, {9,34}, {4,28}, {4,29}, {14,28}, {10,24}, {20,24}, {14,38}, {15,35}, {3,23}, {11,28}, {4,31}, {18,34}, {10,33}, {4,21}, {2,35}, {17,33}, {12,29}, {13,30}, {12,35}, {9,25}, {1,26}, {11,26}, {11,37}, {13,40}, {18,27}, {4,38}, {6,31}, {11,36}, {17,22}, {18,32}, {15,21}, {15,31}, {5,27}, {6,30}, {9,35}, {8,27}, {14,31}, {2,39}, {8,32}, {5,31}, {9,24}, {15,37}, {12,36}, {16,22}, {20,26}, {11,27}, {19,34}, {3,39}, {1,37}, {1,27}, {15,27}, {7,22}, {7,32}, {13,23}, {2,26}, {20,34}, {17,38}, {14,29}, {2,25}, {1,28}, {8,37}, {17,32}, {18,22}, {17,28}, {20,36}, {10,26}, {19,25}, {19,35}, {3,33}, {16,32}, {16,31}, {5,25}, {13,39} }; // ET40.39 // Non-bipartite Valency 6 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 240 EdgePairs[40][39]:={ {14,39}, {16,34}, {13,25}, {16,36}, {17,39}, {12,26}, {18,40}, {6,18}, {14,34}, {2,22}, {11,33}, {1,31}, {16,30}, {19,39}, {23,33}, {10,38}, {2,20}, {12,40}, {10,40}, {6,32}, {6,25}, {9,39}, {22,35}, {13,27}, {11,38}, {3,30}, {9,37}, {14,35}, {19,38}, {19,33}, {15,29}, {2,28}, {9,31}, {3,31}, {24,34}, {5,26}, {4,26}, {20,40}, {15,28}, {10,30}, {1,29}, {3,18}, {8,22}, {7,28}, {5,23}, {9,27}, {13,33}, {15,25}, {18,38}, {2,32}, {12,34}, {24,38}, {7,29}, {16,26}, {4,29}, {7,25}, {3,22}, {14,28}, {7,20}, {15,35}, {8,26}, {3,23}, {8,17}, {11,39}, {14,26}, {21,33}, {1,19}, {4,21}, {4,17}, {15,33}, {5,28}, {12,29}, {8,19}, {13,40}, {17,36}, {20,37}, {18,35}, {2,24}, {6,19}, {1,23}, {16,27}, {8,27}, {10,28}, {14,31}, {7,18}, {13,32}, {5,20}, {22,39}, {23,37}, {11,31}, {17,37}, {5,17}, {5,31}, {15,37}, {11,25}, {22,34}, {11,30}, {21,36}, {4,32}, {1,27}, {9,29}, {3,25}, {10,32}, {13,36}, {20,34}, {7,21}, {21,40}, {12,32}, {16,38}, {6,24}, {8,30}, {9,36}, {6,27}, {10,35}, {23,35}, {12,37}, {2,30}, {1,21}, {4,24}, {24,36} }; // ET40.40 // Non-bipartite Valency 6 // Diameter 5 Girth 4 // Has twins VT AT // Automorphism group of order 125829120 EdgePairs[40][40]:={ {10,19}, {24,39}, {20,27}, {28,33}, {16,36}, {11,17}, {8,31}, {17,39}, {18,40}, {9,30}, {14,34}, {2,22}, {5,30}, {20,28}, {16,30}, {18,39}, {6,23}, {12,17}, {23,39}, {27,34}, {12,31}, {22,38}, {5,24}, {13,34}, {19,27}, {1,9}, {7,31}, {16,40}, {23,40}, {28,34}, {15,40}, {9,19}, {12,18}, {19,38}, {15,29}, {13,38}, {3,34}, {26,35}, {10,30}, {4,12}, {8,22}, {19,37}, {24,40}, {14,33}, {15,39}, {27,33}, {5,23}, {3,11}, {2,10}, {20,38}, {13,33}, {1,10}, {7,26}, {21,38}, {1,36}, {1,22}, {2,36}, {8,21}, {4,33}, {15,36}, {16,35}, {7,25}, {18,25}, {15,35}, {8,26}, {14,38}, {3,23}, {5,29}, {16,29}, {11,18}, {2,35}, {5,28}, {2,9}, {10,29}, {1,35}, {6,29}, {20,37}, {14,32}, {4,11}, {22,37}, {2,21}, {5,27}, {6,30}, {14,31}, {13,32}, {14,37}, {8,32}, {11,31}, {3,24}, {3,12}, {21,37}, {11,32}, {7,22}, {8,25}, {7,32}, {9,29}, {7,21}, {25,35}, {12,32}, {26,36}, {10,20}, {17,26}, {6,24}, {13,31}, {4,34}, {6,27}, {3,33}, {13,37}, {15,30}, {17,40}, {4,23}, {16,39}, {19,28}, {1,21}, {4,24}, {25,36}, {9,20}, {17,25}, {18,26}, {6,28} }; // ET40.41 // Non-bipartite Valency 6 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 480 EdgePairs[40][41]:={ {1,15}, {6,39}, {24,33}, {10,21}, {15,23}, {2,38}, {36,39}, {11,23}, {4,14}, {35,40}, {8,36}, {2,20}, {14,19}, {5,34}, {28,37}, {1,25}, {12,40}, {12,14}, {25,32}, {20,21}, {17,35}, {12,33}, {22,35}, {13,27}, {21,25}, {27,38}, {18,23}, {4,6}, {25,40}, {12,25}, {3,31}, {6,9}, {8,14}, {7,11}, {13,20}, {2,29}, {3,18}, {11,34}, {9,38}, {20,33}, {9,27}, {10,36}, {17,24}, {19,30}, {4,39}, {3,13}, {2,16}, {15,25}, {6,33}, {3,40}, {16,17}, {29,40}, {28,29}, {8,18}, {4,28}, {10,16}, {16,26}, {10,37}, {14,28}, {5,19}, {7,13}, {11,39}, {32,38}, {26,31}, {3,27}, {6,15}, {1,19}, {4,17}, {32,34}, {3,5}, {9,15}, {11,26}, {23,29}, {34,38}, {7,35}, {12,24}, {11,13}, {29,35}, {14,22}, {1,7}, {15,18}, {10,28}, {9,35}, {8,38}, {24,30}, {31,37}, {27,30}, {30,39}, {30,36}, {6,20}, {21,32}, {19,22}, {21,36}, {19,34}, {4,32}, {13,21}, {2,8}, {26,39}, {1,37}, {5,10}, {22,26}, {20,29}, {2,26}, {33,37}, {7,37}, {24,27}, {18,31}, {23,28}, {18,36}, {17,32}, {23,34}, {22,31}, {7,17}, {1,30}, {5,16}, {31,33}, {5,40}, {8,12}, {9,22}, {16,24} }; // ET40.42 // Non-bipartite Valency 6 // Diameter 3 Girth 5 // Twin-free VT AT // Automorphism group of order 480 EdgePairs[40][42]:={ {16,25}, {14,21}, {22,32}, {12,26}, {10,22}, {21,31}, {6,10}, {12,39}, {11,33}, {4,27}, {10,27}, {23,33}, {10,38}, {23,27}, {4,40}, {7,38}, {2,37}, {33,38}, {27,29}, {29,39}, {16,18}, {24,29}, {3,32}, {1,38}, {16,23}, {4,5}, {21,26}, {9,21}, {21,35}, {6,40}, {9,37}, {22,36}, {19,33}, {14,20}, {6,34}, {2,19}, {2,15}, {24,34}, {8,13}, {23,30}, {5,9}, {14,27}, {1,29}, {18,24}, {22,25}, {17,31}, {26,40}, {17,23}, {27,37}, {5,33}, {1,16}, {12,34}, {3,14}, {10,15}, {28,38}, {26,32}, {30,40}, {5,15}, {8,35}, {32,37}, {8,17}, {7,14}, {19,29}, {4,31}, {8,11}, {1,26}, {13,22}, {11,14}, {17,36}, {18,35}, {15,26}, {12,23}, {30,35}, {6,19}, {18,32}, {31,38}, {25,31}, {25,39}, {7,18}, {5,20}, {9,28}, {11,40}, {3,28}, {11,25}, {13,28}, {20,30}, {28,30}, {6,16}, {32,33}, {34,37}, {3,39}, {1,20}, {35,39}, {31,34}, {4,18}, {29,36}, {20,34}, {15,17}, {3,6}, {2,25}, {8,37}, {3,17}, {2,7}, {9,36}, {10,35}, {20,22}, {9,16}, {13,19}, {7,36}, {19,21}, {36,40}, {11,24}, {1,8}, {7,12}, {5,39}, {4,13}, {2,30}, {15,24}, {12,13}, {24,28} }; // ET40.43 // Non-bipartite Valency 6 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 7680 EdgePairs[40][43]:={ {24,39}, {20,27}, {16,36}, {8,24}, {9,30}, {1,11}, {14,34}, {12,19}, {2,22}, {5,30}, {20,28}, {16,30}, {18,39}, {25,34}, {7,24}, {6,23}, {27,35}, {23,39}, {22,38}, {26,33}, {13,34}, {19,40}, {19,27}, {6,32}, {7,31}, {16,40}, {23,40}, {28,34}, {7,27}, {12,18}, {14,35}, {3,10}, {15,29}, {9,31}, {16,33}, {9,17}, {26,35}, {5,21}, {4,12}, {8,22}, {19,37}, {24,40}, {1,34}, {15,39}, {27,33}, {5,23}, {3,11}, {20,38}, {2,23}, {1,10}, {8,28}, {21,38}, {18,38}, {1,22}, {6,21}, {2,36}, {4,33}, {15,36}, {7,25}, {18,25}, {13,35}, {8,26}, {14,38}, {5,29}, {28,36}, {6,26}, {11,18}, {4,21}, {15,33}, {2,35}, {12,29}, {13,30}, {2,9}, {10,29}, {6,31}, {15,31}, {3,35}, {22,37}, {1,23}, {5,27}, {11,19}, {14,31}, {13,32}, {2,12}, {11,31}, {3,24}, {17,37}, {15,37}, {3,21}, {11,30}, {10,17}, {21,37}, {7,22}, {7,32}, {10,32}, {1,33}, {14,29}, {12,32}, {14,40}, {3,36}, {10,20}, {17,26}, {20,39}, {4,9}, {16,38}, {8,30}, {4,34}, {16,32}, {13,37}, {17,40}, {19,28}, {5,25}, {4,24}, {25,36}, {9,20}, {17,25}, {18,26}, {8,29}, {13,39}, {6,28} }; // ET40.44 // Non-bipartite Valency 6 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 7680 EdgePairs[40][44]:={ {14,39}, {4,35}, {10,19}, {16,34}, {5,32}, {28,33}, {13,29}, {11,17}, {8,31}, {17,39}, {18,40}, {21,39}, {17,27}, {23,38}, {2,11}, {19,39}, {11,29}, {12,17}, {27,34}, {12,31}, {5,24}, {18,37}, {1,9}, {2,33}, {6,25}, {15,40}, {9,19}, {7,23}, {19,38}, {13,38}, {3,34}, {5,26}, {10,18}, {15,32}, {6,22}, {20,40}, {10,30}, {20,25}, {7,28}, {12,30}, {14,33}, {24,37}, {2,10}, {15,34}, {13,33}, {7,26}, {19,26}, {1,36}, {14,30}, {24,38}, {8,21}, {7,29}, {10,31}, {1,12}, {16,35}, {3,9}, {25,33}, {3,22}, {15,35}, {3,23}, {16,29}, {2,34}, {4,36}, {7,30}, {5,28}, {1,35}, {28,35}, {13,40}, {6,29}, {18,27}, {20,37}, {14,32}, {2,24}, {4,11}, {5,22}, {14,36}, {2,21}, {27,36}, {6,30}, {8,27}, {18,28}, {14,37}, {8,32}, {4,22}, {22,39}, {23,37}, {5,31}, {3,12}, {8,23}, {9,18}, {20,26}, {11,32}, {8,25}, {9,29}, {13,36}, {15,38}, {17,38}, {11,20}, {7,21}, {25,35}, {21,40}, {26,36}, {9,32}, {6,24}, {16,37}, {17,28}, {13,31}, {6,27}, {19,25}, {26,34}, {22,40}, {3,33}, {15,30}, {4,23}, {16,31}, {16,39}, {1,21}, {12,20}, {4,10}, {1,24} }; // ET40.45 // Bipartite(8,32) Valencies [8,2] // Diameter 8 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1761205026816 EdgePairs[40][45]:={ {2,11}, {3,22}, {5,12}, {1,26}, {5,36}, {7,16}, {2,26}, {5,37}, {6,39}, {4,36}, {5,29}, {7,23}, {2,10}, {7,31}, {8,9}, {1,33}, {8,16}, {1,10}, {6,14}, {4,11}, {3,21}, {6,31}, {8,25}, {3,38}, {6,30}, {8,24}, {3,37}, {3,29}, {6,15}, {8,32}, {5,21}, {5,20}, {4,12}, {7,32}, {8,40}, {7,40}, {8,33}, {5,28}, {2,18}, {4,27}, {4,20}, {6,38}, {3,30}, {7,15}, {3,14}, {1,18}, {4,28}, {2,27}, {1,17}, {6,22}, {2,19}, {3,13}, {7,39}, {2,35}, {5,13}, {2,34}, {1,9}, {4,35}, {1,34}, {4,19}, {1,25}, {8,17}, {6,23}, {7,24} }; // ET40.46 // Bipartite(8,32) Valencies [8,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 75497472 EdgePairs[40][46]:={ {3,22}, {4,9}, {6,34}, {7,16}, {1,24}, {3,12}, {5,37}, {2,26}, {1,29}, {6,33}, {2,29}, {7,23}, {2,10}, {8,38}, {1,40}, {5,27}, {8,23}, {6,14}, {4,11}, {5,10}, {8,21}, {6,12}, {5,11}, {3,38}, {6,30}, {2,36}, {8,24}, {4,16}, {7,33}, {7,36}, {4,32}, {5,21}, {7,32}, {8,37}, {8,40}, {2,31}, {2,20}, {3,28}, {3,15}, {4,27}, {3,19}, {2,15}, {3,31}, {5,30}, {1,18}, {8,22}, {7,20}, {6,18}, {4,25}, {5,14}, {6,17}, {7,39}, {5,26}, {1,13}, {7,17}, {1,9}, {2,13}, {6,28}, {4,35}, {1,34}, {4,19}, {1,25}, {8,39}, {3,35} }; // ET40.47 // Bipartite(20,20) Valencies [8,8] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 320 EdgePairs[40][47]:={ {10,24}, {13,32}, {4,27}, {12,29}, {5,34}, {13,40}, {16,33}, {16,26}, {18,29}, {10,37}, {18,32}, {16,40}, {14,39}, {12,22}, {12,32}, {7,38}, {8,28}, {16,31}, {18,38}, {4,29}, {10,23}, {1,40}, {10,26}, {17,34}, {14,38}, {7,22}, {3,37}, {2,26}, {1,21}, {12,35}, {17,21}, {8,25}, {5,32}, {4,23}, {8,27}, {16,29}, {19,21}, {15,25}, {10,30}, {4,38}, {6,21}, {14,23}, {5,40}, {11,38}, {6,31}, {2,34}, {4,22}, {19,40}, {17,37}, {14,36}, {9,32}, {19,26}, {16,24}, {19,30}, {5,29}, {2,38}, {2,37}, {14,30}, {7,39}, {5,25}, {17,39}, {7,32}, {17,23}, {1,31}, {10,28}, {14,24}, {20,31}, {2,35}, {17,33}, {20,33}, {4,33}, {13,22}, {16,37}, {3,39}, {18,30}, {3,32}, {11,21}, {9,25}, {13,33}, {6,33}, {7,26}, {11,23}, {5,30}, {15,35}, {12,28}, {12,25}, {15,34}, {18,24}, {13,28}, {18,27}, {1,28}, {18,36}, {1,33}, {6,23}, {16,38}, {15,36}, {18,31}, {9,22}, {7,31}, {4,36}, {17,28}, {20,29}, {12,27}, {9,40}, {1,24}, {6,27}, {11,24}, {11,39}, {6,26}, {8,40}, {20,23}, {20,39}, {8,23}, {20,25}, {3,21}, {1,25}, {19,36}, {13,27}, {15,21}, {14,25}, {5,39}, {20,35}, {19,32}, {20,37}, {13,26}, {11,26}, {10,35}, {6,36}, {3,30}, {8,34}, {3,24}, {2,29}, {10,27}, {2,22}, {4,34}, {15,22}, {8,24}, {11,40}, {9,33}, {9,36}, {15,28}, {9,39}, {9,38}, {3,28}, {14,35}, {13,37}, {3,31}, {12,31}, {11,34}, {7,35}, {17,22}, {2,30}, {15,30}, {19,34}, {5,37}, {6,35}, {7,21}, {8,29}, {19,27}, {1,36} }; // ET40.48 // Bipartite(20,20) Valencies [8,8] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 1920 EdgePairs[40][48]:={ {10,25}, {10,24}, {9,28}, {6,32}, {18,39}, {17,36}, {4,24}, {15,24}, {18,29}, {3,22}, {17,38}, {10,37}, {16,40}, {12,22}, {5,38}, {12,32}, {7,38}, {8,28}, {15,31}, {10,23}, {12,38}, {1,40}, {17,34}, {14,38}, {4,31}, {10,33}, {2,27}, {13,35}, {1,21}, {16,25}, {17,21}, {2,28}, {12,34}, {17,40}, {4,23}, {8,27}, {19,21}, {11,28}, {6,29}, {16,30}, {15,29}, {4,38}, {3,34}, {11,33}, {2,34}, {10,38}, {17,37}, {14,36}, {9,32}, {9,26}, {19,30}, {9,27}, {12,36}, {14,30}, {14,40}, {5,25}, {2,39}, {1,31}, {7,25}, {11,31}, {20,31}, {15,27}, {19,38}, {20,33}, {6,30}, {5,23}, {4,21}, {16,37}, {10,40}, {3,39}, {4,35}, {8,36}, {2,32}, {13,33}, {16,32}, {11,23}, {11,29}, {17,30}, {15,35}, {13,23}, {12,25}, {8,22}, {18,24}, {20,28}, {13,28}, {18,26}, {18,27}, {3,27}, {14,37}, {1,33}, {3,29}, {3,26}, {8,26}, {18,31}, {16,22}, {9,22}, {7,31}, {20,29}, {8,32}, {1,24}, {14,22}, {13,24}, {11,24}, {5,31}, {6,26}, {20,23}, {12,40}, {20,39}, {1,25}, {19,36}, {18,23}, {6,28}, {9,30}, {13,27}, {1,35}, {1,37}, {16,34}, {14,25}, {16,21}, {20,35}, {19,32}, {4,37}, {11,26}, {13,26}, {4,40}, {10,35}, {7,23}, {6,36}, {3,30}, {5,33}, {8,34}, {20,26}, {2,29}, {11,27}, {2,22}, {15,33}, {14,32}, {9,36}, {6,34}, {19,25}, {15,28}, {9,39}, {7,24}, {15,39}, {6,39}, {7,33}, {17,22}, {13,39}, {5,21}, {2,30}, {19,34}, {5,35}, {5,37}, {3,36}, {18,35}, {7,40}, {19,37}, {7,21}, {8,29}, {12,21} }; // ET40.49 // Bipartite(20,20) Valencies [8,8] // Diameter 5 Girth 4 // Has twins VT AT // Automorphism group of order 1268067619307520 EdgePairs[40][49]:={ {3,33}, {10,24}, {17,35}, {18,39}, {11,36}, {5,34}, {16,33}, {15,24}, {16,26}, {18,29}, {4,26}, {10,37}, {4,30}, {12,22}, {12,32}, {8,28}, {18,38}, {16,31}, {20,27}, {8,33}, {7,22}, {4,31}, {2,27}, {14,31}, {8,39}, {1,21}, {12,35}, {5,32}, {17,40}, {16,23}, {9,35}, {13,29}, {12,37}, {18,34}, {10,22}, {19,21}, {11,28}, {15,29}, {6,21}, {3,34}, {2,25}, {11,38}, {11,33}, {6,31}, {1,38}, {5,22}, {19,40}, {17,37}, {14,21}, {14,36}, {19,26}, {15,32}, {9,26}, {19,30}, {5,29}, {2,37}, {14,30}, {14,40}, {7,32}, {1,31}, {7,25}, {11,31}, {2,35}, {15,27}, {4,21}, {10,29}, {7,30}, {3,39}, {11,21}, {4,35}, {9,25}, {13,33}, {6,33}, {2,32}, {11,23}, {1,23}, {17,30}, {5,24}, {17,27}, {13,23}, {12,25}, {15,37}, {15,34}, {18,24}, {13,28}, {19,31}, {1,28}, {20,22}, {1,33}, {18,33}, {3,29}, {6,23}, {16,38}, {4,36}, {20,29}, {12,27}, {9,40}, {13,24}, {17,25}, {6,26}, {12,40}, {20,39}, {12,30}, {3,23}, {8,23}, {10,32}, {19,36}, {18,23}, {6,28}, {9,30}, {10,39}, {14,25}, {5,39}, {16,21}, {20,37}, {11,26}, {4,40}, {16,36}, {6,36}, {8,34}, {3,24}, {18,28}, {10,27}, {20,34}, {8,38}, {1,26}, {2,22}, {10,34}, {15,22}, {8,24}, {20,24}, {6,38}, {2,40}, {9,36}, {5,27}, {19,25}, {13,38}, {4,25}, {3,38}, {3,28}, {7,27}, {14,35}, {15,39}, {13,34}, {19,35}, {7,35}, {13,39}, {17,22}, {2,30}, {7,37}, {9,31}, {5,37}, {17,32}, {9,21}, {16,28}, {7,40}, {20,32}, {8,29}, {1,36}, {14,26} }; // ET40.50 // Bipartite(20,20) Valencies [8,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 978447237120 EdgePairs[40][50]:={ {4,35}, {14,21}, {16,34}, {5,32}, {6,39}, {14,25}, {8,24}, {2,38}, {10,22}, {18,40}, {2,22}, {17,27}, {5,30}, {1,31}, {4,27}, {8,36}, {5,35}, {11,29}, {13,24}, {7,38}, {7,33}, {2,37}, {12,22}, {13,34}, {10,40}, {1,38}, {19,27}, {2,33}, {12,33}, {19,31}, {7,27}, {15,40}, {9,21}, {11,38}, {3,30}, {9,37}, {12,27}, {14,35}, {18,23}, {7,23}, {8,34}, {15,29}, {2,28}, {3,34}, {9,31}, {6,34}, {4,26}, {15,32}, {20,40}, {10,30}, {14,27}, {1,29}, {18,24}, {19,37}, {20,25}, {7,28}, {11,34}, {1,34}, {15,39}, {16,21}, {17,23}, {4,37}, {15,22}, {9,27}, {20,35}, {2,23}, {13,33}, {8,33}, {19,26}, {18,33}, {10,25}, {13,26}, {15,25}, {2,32}, {3,40}, {6,21}, {10,39}, {8,26}, {15,35}, {3,23}, {11,39}, {5,29}, {16,29}, {11,28}, {4,31}, {18,34}, {14,26}, {12,28}, {4,36}, {4,21}, {17,33}, {13,30}, {9,25}, {4,25}, {10,29}, {13,40}, {8,40}, {6,29}, {12,23}, {6,31}, {12,38}, {5,22}, {2,27}, {17,22}, {14,36}, {9,35}, {1,39}, {6,38}, {14,31}, {14,37}, {11,31}, {20,32}, {3,26}, {3,24}, {17,37}, {19,36}, {8,23}, {20,30}, {11,21}, {9,26}, {7,22}, {18,30}, {16,28}, {7,32}, {20,29}, {13,23}, {10,32}, {13,36}, {7,37}, {17,38}, {12,32}, {1,28}, {3,36}, {18,36}, {20,39}, {6,24}, {16,38}, {17,32}, {8,30}, {17,28}, {9,36}, {10,35}, {19,25}, {19,35}, {20,22}, {3,33}, {15,30}, {19,21}, {11,24}, {12,37}, {5,39}, {16,31}, {16,39}, {1,21}, {5,25}, {5,40}, {18,26}, {1,24}, {6,28}, {16,24} }; // ET40.51 // Bipartite(20,20) Valencies [8,8] // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 83886080 EdgePairs[40][51]:={ {4,35}, {16,25}, {13,25}, {6,39}, {10,21}, {14,25}, {8,39}, {8,31}, {2,38}, {2,22}, {17,27}, {5,30}, {1,31}, {4,27}, {16,30}, {18,39}, {19,39}, {6,23}, {13,24}, {12,40}, {7,33}, {12,22}, {20,21}, {20,23}, {13,34}, {18,37}, {1,38}, {17,35}, {7,31}, {9,39}, {6,25}, {16,23}, {16,40}, {7,27}, {15,40}, {19,24}, {11,38}, {3,30}, {1,32}, {11,22}, {6,40}, {19,23}, {14,35}, {7,23}, {18,21}, {19,33}, {15,29}, {2,28}, {3,34}, {16,33}, {4,26}, {10,23}, {15,28}, {14,27}, {5,37}, {8,22}, {12,30}, {15,39}, {17,31}, {17,23}, {4,37}, {10,34}, {20,33}, {10,36}, {1,36}, {13,26}, {1,22}, {2,32}, {6,33}, {3,40}, {12,34}, {8,21}, {9,34}, {4,28}, {10,31}, {16,35}, {7,25}, {14,28}, {9,23}, {10,24}, {20,24}, {13,35}, {14,38}, {5,29}, {16,29}, {11,28}, {19,29}, {2,34}, {10,33}, {14,26}, {2,40}, {12,28}, {4,36}, {17,33}, {5,28}, {13,30}, {4,25}, {1,26}, {11,26}, {13,40}, {6,29}, {18,27}, {7,35}, {12,24}, {4,38}, {2,24}, {9,33}, {12,38}, {11,36}, {18,32}, {14,36}, {5,38}, {3,35}, {5,27}, {6,30}, {8,27}, {14,37}, {8,32}, {11,31}, {3,26}, {3,24}, {17,37}, {9,24}, {15,37}, {11,21}, {18,29}, {19,22}, {17,21}, {20,26}, {19,34}, {11,32}, {15,27}, {9,29}, {3,25}, {13,36}, {20,34}, {7,37}, {15,38}, {7,21}, {12,32}, {1,28}, {3,36}, {18,31}, {8,37}, {20,31}, {9,32}, {6,35}, {18,22}, {20,36}, {10,26}, {19,32}, {15,30}, {5,39}, {16,39}, {2,30}, {1,21}, {5,40}, {17,25}, {8,29}, {9,22} }; // ET40.52 // Bipartite(20,20) Valencies [8,8] // Diameter 4 Girth 4 // Twin-free VT Non-AT // Automorphism group of order 640 EdgePairs[40][52]:={ {3,33}, {2,24}, {13,32}, {9,28}, {2,33}, {6,32}, {11,36}, {11,35}, {13,40}, {4,24}, {16,33}, {16,26}, {18,29}, {4,26}, {3,40}, {17,38}, {11,25}, {8,30}, {14,39}, {2,23}, {12,32}, {16,31}, {4,29}, {20,27}, {1,32}, {8,33}, {1,27}, {10,23}, {1,40}, {17,34}, {12,39}, {7,22}, {14,31}, {7,34}, {1,21}, {16,25}, {18,21}, {2,28}, {12,34}, {17,40}, {9,35}, {20,30}, {8,27}, {13,29}, {12,37}, {10,22}, {10,30}, {19,28}, {6,21}, {3,34}, {2,25}, {11,33}, {6,40}, {2,34}, {5,22}, {4,22}, {9,29}, {17,37}, {14,21}, {9,32}, {14,36}, {19,26}, {15,32}, {16,24}, {9,26}, {15,40}, {2,37}, {5,25}, {17,23}, {11,31}, {14,24}, {17,33}, {15,27}, {19,38}, {5,23}, {4,21}, {10,31}, {1,29}, {3,39}, {9,25}, {8,36}, {7,26}, {13,33}, {11,29}, {5,30}, {17,30}, {5,24}, {9,37}, {12,28}, {13,25}, {18,24}, {8,35}, {18,26}, {19,31}, {18,27}, {20,22}, {18,36}, {16,38}, {13,30}, {17,28}, {20,29}, {12,23}, {14,22}, {5,31}, {11,24}, {6,26}, {8,40}, {20,23}, {12,40}, {14,34}, {1,39}, {20,25}, {19,36}, {6,28}, {10,39}, {1,35}, {15,21}, {7,28}, {20,37}, {4,37}, {7,23}, {3,30}, {5,33}, {16,35}, {11,27}, {10,27}, {8,38}, {10,36}, {10,34}, {15,22}, {18,22}, {19,39}, {6,38}, {2,31}, {5,27}, {13,38}, {9,38}, {4,25}, {3,38}, {15,23}, {13,37}, {7,24}, {15,39}, {3,31}, {6,39}, {19,35}, {15,30}, {19,34}, {7,37}, {6,35}, {3,36}, {18,35}, {16,28}, {20,32}, {7,21}, {8,29}, {4,32}, {12,21}, {1,36}, {14,26} }; // ET40.53 // Bipartite(20,20) Valencies [8,8] // Diameter 3 Girth 4 // Twin-free VT Non-AT // Automorphism group of order 320 EdgePairs[40][53]:={ {10,25}, {9,28}, {4,27}, {12,29}, {16,26}, {4,26}, {3,40}, {18,32}, {8,30}, {16,40}, {14,39}, {7,38}, {16,31}, {18,38}, {15,31}, {4,29}, {20,40}, {7,22}, {3,35}, {14,31}, {2,26}, {8,39}, {7,34}, {1,21}, {16,25}, {7,36}, {17,21}, {2,28}, {12,34}, {16,23}, {9,35}, {20,30}, {12,37}, {18,34}, {10,22}, {11,28}, {18,37}, {19,33}, {6,21}, {3,34}, {2,25}, {11,33}, {6,40}, {1,38}, {14,33}, {4,22}, {10,38}, {9,29}, {9,32}, {15,32}, {19,30}, {12,36}, {2,38}, {2,37}, {19,22}, {2,39}, {17,39}, {17,23}, {15,26}, {1,31}, {10,28}, {14,24}, {11,31}, {2,35}, {6,30}, {5,23}, {10,29}, {4,21}, {13,22}, {10,40}, {7,30}, {13,31}, {3,32}, {11,21}, {4,35}, {8,36}, {13,33}, {16,32}, {1,23}, {11,29}, {6,24}, {15,35}, {11,30}, {5,24}, {17,27}, {8,22}, {13,25}, {18,26}, {18,27}, {14,37}, {3,26}, {8,37}, {8,26}, {17,31}, {12,26}, {16,22}, {7,31}, {12,33}, {17,28}, {12,23}, {6,27}, {20,23}, {12,40}, {20,39}, {1,39}, {17,29}, {20,25}, {5,36}, {3,21}, {1,25}, {6,28}, {18,23}, {13,27}, {1,35}, {14,25}, {4,40}, {16,36}, {5,33}, {3,24}, {18,28}, {10,27}, {20,34}, {10,36}, {15,22}, {15,33}, {14,32}, {8,24}, {19,39}, {6,25}, {20,24}, {11,40}, {9,33}, {9,36}, {5,27}, {15,28}, {13,38}, {9,38}, {3,38}, {13,37}, {7,24}, {9,24}, {6,37}, {13,34}, {11,34}, {19,35}, {5,21}, {2,30}, {15,30}, {19,34}, {5,35}, {19,23}, {5,37}, {17,32}, {4,39}, {20,32}, {7,21}, {8,29}, {19,27}, {1,36}, {14,29} }; // ET40.54 // Bipartite(20,20) Valencies [8,8] // Diameter 4 Girth 4 // Twin-free VT Non-AT // Automorphism group of order 640 EdgePairs[40][54]:={ {3,33}, {10,25}, {2,24}, {13,32}, {9,28}, {2,33}, {17,35}, {6,32}, {17,36}, {4,27}, {11,35}, {13,40}, {16,33}, {15,24}, {4,26}, {3,40}, {17,38}, {10,37}, {8,30}, {16,40}, {12,22}, {7,38}, {15,31}, {4,29}, {1,27}, {19,24}, {12,38}, {10,23}, {1,40}, {10,33}, {3,35}, {20,21}, {14,31}, {2,26}, {8,39}, {17,24}, {1,21}, {16,25}, {18,21}, {8,25}, {2,28}, {12,34}, {1,30}, {20,30}, {16,29}, {10,22}, {11,28}, {19,28}, {4,38}, {6,21}, {5,40}, {11,33}, {2,36}, {5,22}, {10,38}, {9,29}, {19,40}, {14,36}, {9,32}, {15,32}, {9,26}, {12,36}, {5,29}, {2,38}, {2,37}, {14,30}, {5,25}, {17,39}, {7,32}, {1,22}, {15,27}, {19,38}, {20,33}, {9,34}, {10,21}, {18,30}, {3,32}, {8,36}, {13,33}, {11,30}, {5,24}, {13,23}, {15,37}, {8,22}, {15,34}, {18,26}, {18,27}, {14,37}, {20,22}, {6,23}, {8,26}, {18,31}, {12,26}, {7,31}, {20,29}, {9,40}, {5,31}, {11,24}, {11,39}, {12,40}, {14,34}, {8,23}, {3,23}, {18,25}, {1,39}, {17,29}, {7,29}, {18,23}, {6,28}, {9,30}, {13,27}, {1,35}, {14,25}, {16,21}, {7,28}, {20,37}, {4,37}, {13,26}, {10,35}, {16,36}, {6,36}, {3,30}, {5,33}, {20,26}, {11,37}, {18,28}, {11,27}, {4,34}, {15,22}, {8,24}, {2,31}, {6,34}, {5,27}, {19,25}, {16,39}, {13,38}, {4,25}, {7,27}, {15,23}, {14,35}, {3,31}, {9,24}, {6,39}, {12,31}, {6,37}, {19,35}, {7,35}, {13,39}, {17,22}, {19,34}, {19,23}, {1,34}, {17,32}, {3,36}, {4,39}, {16,28}, {20,32}, {7,21}, {12,21}, {14,29} }; // ET40.55 // Non-bipartite Valency 8 // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 335544320 EdgePairs[40][55]:={ {11,17}, {1,11}, {3,33}, {5,17}, {2,33}, {13,21}, {7,15}, {29,40}, {15,24}, {23,29}, {4,16}, {10,37}, {18,32}, {25,39}, {21,32}, {3,9}, {20,27}, {4,29}, {3,13}, {8,33}, {3,15}, {12,38}, {10,23}, {2,15}, {12,39}, {25,33}, {5,20}, {24,30}, {7,34}, {16,25}, {7,36}, {24,36}, {1,30}, {16,23}, {20,30}, {28,35}, {8,16}, {23,32}, {19,28}, {14,23}, {6,40}, {4,10}, {2,36}, {8,19}, {7,20}, {19,26}, {22,34}, {12,20}, {2,10}, {31,37}, {19,29}, {22,35}, {7,39}, {26,40}, {15,26}, {1,31}, {23,34}, {11,22}, {15,27}, {10,21}, {2,13}, {6,18}, {30,39}, {10,40}, {18,30}, {29,37}, {4,35}, {23,35}, {2,32}, {7,17}, {17,27}, {8,13}, {32,39}, {1,9}, {32,38}, {13,25}, {27,36}, {26,38}, {8,35}, {13,28}, {19,31}, {18,26}, {9,20}, {3,11}, {7,14}, {26,36}, {26,34}, {21,33}, {17,31}, {25,37}, {16,22}, {9,22}, {6,15}, {25,35}, {28,40}, {12,23}, {14,22}, {13,24}, {17,25}, {11,24}, {28,33}, {8,40}, {21,29}, {20,25}, {17,29}, {6,19}, {6,14}, {22,31}, {1,35}, {15,21}, {5,39}, {6,36}, {3,30}, {5,33}, {9,18}, {10,17}, {11,37}, {2,29}, {18,28}, {8,38}, {4,34}, {1,16}, {4,14}, {30,38}, {6,38}, {11,40}, {6,34}, {31,40}, {8,18}, {28,38}, {9,39}, {9,38}, {11,19}, {27,37}, {10,19}, {4,12}, {5,13}, {27,39}, {21,36}, {3,31}, {2,12}, {1,14}, {9,24}, {7,37}, {5,35}, {27,34}, {22,30}, {1,34}, {5,37}, {24,33}, {3,36}, {16,28}, {20,32}, {14,27}, {4,32}, {12,18}, {24,31}, {12,21}, {14,26}, {5,16} }; // ET40.56 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 1920 EdgePairs[40][56]:={ {3,33}, {36,38}, {13,40}, {23,29}, {3,40}, {4,16}, {1,10}, {18,32}, {32,40}, {11,25}, {26,31}, {22,37}, {1,13}, {8,9}, {3,9}, {1,27}, {23,28}, {3,25}, {10,23}, {10,26}, {2,15}, {14,38}, {16,19}, {35,40}, {4,31}, {10,33}, {25,29}, {20,21}, {29,35}, {2,26}, {17,24}, {16,25}, {12,35}, {7,36}, {6,11}, {20,30}, {29,39}, {3,5}, {12,37}, {6,22}, {6,29}, {4,38}, {7,12}, {2,36}, {1,7}, {10,38}, {1,18}, {3,14}, {14,21}, {4,8}, {9,27}, {25,36}, {31,37}, {8,14}, {22,35}, {2,39}, {11,15}, {26,40}, {30,34}, {17,33}, {24,25}, {23,36}, {15,27}, {21,27}, {24,32}, {2,20}, {1,29}, {7,30}, {13,31}, {11,21}, {4,35}, {7,16}, {2,32}, {6,33}, {5,18}, {16,32}, {2,6}, {7,17}, {32,33}, {5,24}, {27,38}, {12,28}, {15,37}, {13,28}, {19,31}, {24,34}, {18,36}, {21,31}, {15,17}, {4,28}, {26,34}, {31,36}, {21,33}, {8,37}, {25,37}, {16,22}, {9,22}, {21,39}, {9,13}, {8,32}, {3,19}, {14,18}, {13,24}, {5,31}, {28,33}, {12,19}, {33,37}, {8,23}, {12,14}, {17,29}, {20,25}, {34,39}, {6,19}, {27,32}, {24,38}, {1,37}, {20,35}, {5,39}, {28,30}, {23,40}, {28,39}, {22,26}, {3,30}, {8,34}, {18,28}, {18,22}, {9,17}, {30,38}, {6,38}, {11,40}, {9,36}, {27,35}, {5,10}, {16,39}, {9,39}, {4,11}, {12,24}, {8,20}, {15,23}, {2,12}, {10,20}, {17,26}, {5,15}, {11,34}, {19,34}, {15,30}, {6,13}, {13,20}, {5,35}, {22,30}, {19,23}, {1,34}, {4,17}, {7,40}, {7,21}, {19,27}, {11,18}, {14,29}, {14,26}, {10,16} }; // ET40.57 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1920 EdgePairs[40][57]:={ {3,33}, {11,20}, {9,28}, {6,32}, {17,36}, {36,38}, {14,19}, {15,24}, {4,16}, {25,39}, {22,37}, {8,9}, {30,33}, {7,38}, {3,13}, {32,34}, {1,27}, {32,37}, {10,26}, {2,15}, {35,40}, {4,31}, {1,19}, {21,35}, {25,30}, {8,39}, {16,25}, {7,36}, {27,33}, {24,36}, {28,35}, {8,31}, {3,5}, {19,21}, {3,18}, {16,30}, {23,32}, {6,21}, {14,23}, {5,40}, {2,25}, {11,33}, {2,36}, {10,38}, {7,11}, {7,20}, {12,17}, {15,32}, {25,36}, {31,35}, {12,36}, {2,37}, {29,36}, {27,29}, {19,29}, {14,40}, {23,34}, {11,22}, {22,27}, {23,26}, {5,23}, {9,34}, {13,22}, {10,21}, {30,39}, {1,29}, {8,17}, {13,31}, {18,30}, {4,35}, {7,16}, {2,32}, {5,18}, {5,30}, {2,6}, {21,25}, {12,25}, {15,37}, {8,13}, {8,22}, {1,9}, {29,38}, {18,24}, {26,38}, {5,14}, {4,7}, {4,28}, {10,13}, {26,34}, {18,33}, {3,10}, {3,26}, {17,31}, {6,15}, {2,17}, {21,39}, {28,40}, {5,12}, {12,23}, {17,25}, {22,33}, {20,23}, {33,37}, {12,40}, {21,30}, {1,39}, {12,14}, {34,39}, {6,19}, {26,32}, {7,29}, {22,31}, {24,38}, {16,21}, {23,40}, {13,26}, {15,18}, {4,40}, {10,35}, {11,16}, {3,30}, {5,33}, {8,34}, {9,18}, {20,26}, {11,37}, {18,28}, {11,27}, {20,34}, {16,20}, {6,10}, {31,40}, {15,28}, {16,39}, {9,39}, {13,38}, {27,37}, {10,19}, {3,38}, {1,8}, {4,11}, {24,29}, {4,20}, {28,31}, {7,24}, {2,12}, {1,14}, {9,24}, {6,37}, {19,35}, {17,22}, {9,15}, {13,17}, {1,34}, {6,35}, {20,32}, {14,27}, {19,27}, {24,28}, {14,29} }; // ET40.58 // Non-bipartite Valency 8 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 10240 EdgePairs[40][58]:={ {11,17}, {1,11}, {11,20}, {6,32}, {6,16}, {17,35}, {13,21}, {7,15}, {29,40}, {8,12}, {15,24}, {4,26}, {21,40}, {4,16}, {32,40}, {4,30}, {22,37}, {12,22}, {30,33}, {8,28}, {18,38}, {3,13}, {32,34}, {1,27}, {32,37}, {3,25}, {3,15}, {10,23}, {20,40}, {17,34}, {2,15}, {16,19}, {25,33}, {21,35}, {2,26}, {16,18}, {8,10}, {2,28}, {16,23}, {28,35}, {8,31}, {23,39}, {32,36}, {8,16}, {20,38}, {31,33}, {31,39}, {7,11}, {17,37}, {31,35}, {5,11}, {2,10}, {5,29}, {9,19}, {29,36}, {8,14}, {17,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {14,24}, {23,36}, {6,12}, {20,33}, {6,30}, {10,21}, {2,13}, {13,18}, {30,39}, {29,34}, {1,29}, {7,30}, {29,37}, {11,21}, {23,37}, {2,32}, {11,23}, {30,35}, {27,38}, {28,37}, {13,23}, {1,9}, {26,38}, {27,36}, {15,20}, {24,34}, {3,27}, {26,36}, {18,36}, {4,28}, {15,17}, {26,34}, {18,33}, {3,29}, {3,10}, {5,28}, {21,38}, {24,35}, {8,26}, {25,37}, {9,22}, {25,40}, {24,40}, {25,35}, {28,40}, {14,17}, {22,39}, {4,9}, {14,22}, {5,31}, {6,27}, {28,33}, {22,33}, {12,19}, {1,25}, {6,14}, {24,38}, {14,20}, {16,21}, {13,19}, {9,18}, {10,17}, {23,33}, {1,16}, {4,14}, {15,22}, {19,39}, {6,25}, {30,38}, {7,9}, {20,36}, {6,10}, {5,26}, {5,9}, {4,11}, {26,39}, {5,13}, {12,24}, {7,27}, {27,39}, {3,31}, {21,34}, {18,40}, {1,14}, {9,24}, {2,12}, {10,20}, {5,15}, {19,35}, {2,30}, {19,34}, {27,34}, {22,36}, {19,37}, {8,29}, {4,32}, {12,18}, {31,38} }; // ET40.59 // Bipartite(10,30) Valencies [9,3] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7255941120 EdgePairs[40][59]:={ {1,15}, {10,19}, {9,13}, {5,32}, {6,12}, {8,31}, {8,24}, {2,38}, {5,35}, {4,40}, {7,38}, {1,25}, {9,12}, {2,37}, {6,32}, {7,31}, {3,30}, {6,40}, {7,15}, {8,34}, {2,28}, {2,18}, {8,14}, {7,11}, {6,22}, {10,23}, {7,28}, {1,34}, {4,20}, {6,11}, {10,36}, {4,39}, {1,36}, {3,13}, {2,16}, {3,40}, {6,21}, {1,16}, {2,36}, {10,13}, {8,21}, {2,17}, {9,34}, {4,28}, {10,39}, {10,16}, {4,29}, {7,25}, {9,23}, {5,19}, {5,15}, {3,23}, {8,17}, {5,29}, {3,27}, {4,30}, {10,33}, {8,11}, {10,29}, {1,35}, {1,26}, {7,35}, {4,38}, {6,31}, {9,33}, {5,22}, {2,27}, {6,30}, {8,27}, {7,18}, {9,24}, {6,20}, {1,14}, {4,18}, {2,26}, {3,20}, {7,21}, {5,12}, {9,14}, {8,37}, {3,17}, {3,37}, {9,32}, {10,26}, {3,33}, {5,39}, {5,25}, {4,19}, {1,24}, {9,22} }; // ET40.60 // Bipartite(16,24) Valencies [9,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 576 EdgePairs[40][60]:={ {11,17}, {10,25}, {11,20}, {13,32}, {9,28}, {6,32}, {4,27}, {14,19}, {16,33}, {15,24}, {4,30}, {16,40}, {5,38}, {4,29}, {1,32}, {8,33}, {12,38}, {2,19}, {1,19}, {2,27}, {14,31}, {7,34}, {16,18}, {16,25}, {7,36}, {12,34}, {5,32}, {16,23}, {9,35}, {4,23}, {8,27}, {12,37}, {16,29}, {3,18}, {11,28}, {6,29}, {3,17}, {16,30}, {6,21}, {3,34}, {2,25}, {11,33}, {6,31}, {6,40}, {1,17}, {2,36}, {5,22}, {4,22}, {14,21}, {14,36}, {9,26}, {9,19}, {14,40}, {7,39}, {2,39}, {2,35}, {1,22}, {10,31}, {3,20}, {13,22}, {10,21}, {2,20}, {10,40}, {3,39}, {13,31}, {11,21}, {7,26}, {2,32}, {1,23}, {11,30}, {5,24}, {9,37}, {13,23}, {12,25}, {8,22}, {15,20}, {13,28}, {15,17}, {3,26}, {16,38}, {8,37}, {15,36}, {5,28}, {16,22}, {12,33}, {12,27}, {1,24}, {12,23}, {13,24}, {6,27}, {5,31}, {11,39}, {8,40}, {12,40}, {12,30}, {10,39}, {1,35}, {14,20}, {1,37}, {15,21}, {14,25}, {7,28}, {4,37}, {11,26}, {15,18}, {10,35}, {13,19}, {6,36}, {3,30}, {8,34}, {3,24}, {2,29}, {10,27}, {8,38}, {1,26}, {4,34}, {9,17}, {14,32}, {15,33}, {5,26}, {8,18}, {15,28}, {4,18}, {13,38}, {9,38}, {10,19}, {4,25}, {7,24}, {10,20}, {6,39}, {7,33}, {11,34}, {13,17}, {15,30}, {5,35}, {9,31}, {5,37}, {6,35}, {3,36}, {9,23}, {7,21}, {8,29}, {14,29}, {7,18} }; // ET40.61 // Bipartite(16,24) Valencies [9,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 20639121408 EdgePairs[40][61]:={ {10,19}, {7,19}, {13,25}, {9,40}, {10,21}, {14,25}, {8,24}, {12,26}, {6,18}, {11,23}, {12,39}, {14,34}, {3,29}, {5,30}, {6,36}, {6,17}, {16,30}, {10,27}, {11,29}, {1,40}, {4,40}, {7,38}, {1,25}, {14,18}, {12,40}, {12,31}, {2,37}, {6,25}, {16,40}, {7,27}, {9,19}, {12,18}, {1,32}, {13,38}, {14,20}, {3,31}, {6,34}, {2,19}, {2,18}, {4,26}, {9,17}, {10,18}, {15,28}, {2,29}, {8,22}, {7,28}, {14,33}, {16,21}, {5,33}, {5,23}, {10,34}, {15,22}, {9,27}, {13,33}, {4,39}, {1,17}, {6,33}, {12,34}, {8,21}, {15,36}, {10,37}, {14,28}, {7,20}, {15,20}, {15,35}, {3,23}, {11,39}, {16,29}, {4,31}, {11,28}, {2,34}, {6,26}, {14,26}, {1,19}, {15,19}, {7,30}, {2,35}, {13,30}, {9,25}, {10,29}, {1,35}, {11,37}, {8,40}, {13,22}, {7,35}, {12,24}, {12,23}, {9,33}, {5,22}, {2,27}, {11,36}, {14,36}, {5,38}, {14,17}, {2,21}, {9,35}, {8,38}, {8,32}, {3,28}, {11,31}, {5,31}, {5,17}, {9,24}, {16,22}, {6,20}, {11,21}, {3,21}, {4,32}, {3,39}, {1,27}, {7,22}, {15,27}, {4,18}, {13,23}, {2,26}, {13,17}, {15,38}, {11,20}, {3,20}, {1,33}, {12,32}, {3,36}, {8,37}, {3,37}, {9,32}, {16,38}, {8,30}, {16,37}, {10,26}, {13,31}, {4,34}, {10,35}, {15,30}, {16,32}, {7,36}, {4,23}, {5,39}, {5,25}, {4,24}, {1,24}, {8,29}, {6,28}, {13,39}, {16,24} }; // ET40.62 // Bipartite(20,20) Valencies [9,9] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 5760 EdgePairs[40][62]:={ {10,25}, {13,32}, {2,33}, {6,32}, {17,36}, {4,27}, {13,21}, {5,34}, {13,40}, {4,24}, {15,24}, {18,29}, {4,26}, {3,22}, {3,40}, {17,38}, {16,27}, {16,40}, {14,39}, {2,23}, {8,28}, {16,31}, {20,27}, {1,32}, {8,33}, {10,23}, {12,38}, {19,24}, {1,40}, {10,26}, {14,38}, {12,39}, {7,22}, {2,27}, {3,35}, {2,26}, {8,39}, {7,34}, {17,24}, {1,21}, {12,35}, {7,36}, {18,21}, {8,25}, {2,28}, {1,30}, {17,40}, {9,35}, {20,30}, {8,27}, {16,29}, {10,22}, {15,25}, {11,28}, {18,37}, {19,28}, {6,21}, {5,40}, {11,33}, {6,31}, {14,33}, {2,34}, {10,38}, {19,40}, {14,36}, {9,27}, {12,36}, {5,29}, {2,38}, {19,22}, {5,25}, {17,23}, {15,26}, {11,22}, {11,31}, {20,31}, {2,35}, {17,33}, {1,22}, {19,38}, {4,33}, {5,23}, {10,29}, {10,21}, {16,37}, {7,30}, {3,39}, {18,30}, {7,26}, {11,29}, {6,24}, {5,30}, {11,30}, {9,37}, {13,23}, {12,25}, {13,28}, {18,26}, {18,27}, {14,37}, {3,29}, {16,38}, {17,31}, {7,31}, {13,30}, {4,36}, {20,29}, {12,27}, {9,40}, {8,32}, {12,23}, {14,22}, {13,24}, {6,26}, {8,40}, {20,23}, {20,39}, {3,23}, {18,25}, {10,32}, {1,39}, {5,36}, {3,21}, {1,25}, {6,28}, {9,30}, {13,27}, {1,37}, {16,34}, {16,21}, {4,37}, {16,36}, {5,33}, {20,26}, {11,37}, {18,28}, {8,38}, {4,34}, {10,34}, {15,22}, {11,32}, {15,33}, {6,38}, {2,31}, {9,33}, {20,36}, {19,25}, {15,28}, {9,39}, {4,25}, {12,24}, {3,28}, {15,23}, {14,35}, {7,24}, {15,39}, {3,31}, {9,24}, {6,39}, {6,37}, {13,34}, {11,34}, {19,35}, {7,35}, {17,22}, {15,30}, {19,34}, {5,35}, {9,31}, {17,32}, {18,35}, {19,37}, {20,32}, {7,21}, {8,29}, {4,32}, {12,21}, {14,29}, {1,36}, {14,26} }; // ET40.63 // Non-bipartite Valency 9 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[40][63]:={ {1,11}, {10,24}, {11,20}, {6,32}, {4,27}, {13,21}, {36,38}, {16,33}, {15,24}, {3,40}, {4,16}, {8,30}, {2,23}, {1,13}, {5,38}, {3,9}, {25,38}, {29,33}, {3,15}, {12,38}, {17,34}, {10,26}, {14,38}, {4,19}, {20,21}, {13,35}, {2,26}, {25,30}, {16,25}, {11,14}, {8,10}, {27,33}, {12,34}, {2,14}, {16,23}, {6,11}, {14,28}, {20,30}, {9,35}, {29,39}, {3,5}, {11,28}, {32,36}, {16,30}, {23,32}, {15,29}, {11,33}, {1,38}, {4,10}, {2,34}, {1,17}, {4,22}, {19,26}, {9,32}, {14,36}, {31,35}, {15,40}, {31,37}, {28,34}, {2,37}, {26,29}, {19,29}, {22,35}, {19,22}, {7,39}, {17,39}, {17,23}, {15,26}, {11,22}, {27,40}, {7,25}, {30,34}, {24,25}, {21,27}, {19,38}, {12,13}, {23,26}, {5,23}, {10,31}, {3,20}, {15,19}, {1,29}, {8,17}, {13,31}, {26,37}, {4,35}, {23,37}, {9,25}, {8,36}, {11,29}, {6,24}, {8,13}, {15,34}, {8,22}, {33,40}, {32,38}, {18,24}, {18,27}, {24,34}, {7,14}, {26,36}, {1,33}, {18,33}, {5,28}, {8,26}, {18,31}, {6,15}, {25,35}, {4,6}, {21,39}, {17,28}, {12,27}, {9,40}, {5,12}, {14,18}, {1,24}, {14,22}, {5,31}, {6,27}, {30,40}, {12,19}, {8,40}, {12,30}, {21,29}, {20,25}, {3,21}, {2,7}, {34,39}, {1,25}, {22,28}, {35,37}, {7,29}, {27,32}, {13,27}, {10,39}, {24,38}, {20,37}, {28,39}, {5,33}, {11,37}, {23,33}, {10,36}, {16,20}, {14,32}, {10,18}, {9,17}, {7,9}, {20,36}, {6,34}, {16,39}, {1,8}, {3,28}, {28,31}, {22,40}, {13,37}, {21,36}, {3,31}, {18,40}, {2,12}, {6,37}, {19,35}, {5,19}, {6,20}, {7,35}, {9,15}, {2,30}, {13,17}, {22,30}, {2,18}, {17,32}, {3,36}, {4,39}, {9,23}, {7,21}, {4,32}, {24,31}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET40.64 // Non-bipartite Valency 9 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 2880 EdgePairs[40][64]:={ {11,17}, {1,11}, {3,33}, {2,24}, {11,20}, {13,32}, {2,33}, {6,32}, {18,39}, {13,40}, {4,24}, {16,33}, {21,40}, {17,38}, {8,30}, {22,37}, {12,32}, {18,38}, {15,31}, {21,37}, {20,40}, {14,38}, {7,22}, {3,35}, {14,31}, {26,33}, {1,21}, {2,9}, {8,25}, {27,33}, {5,32}, {4,23}, {28,35}, {8,31}, {8,27}, {16,29}, {6,22}, {16,30}, {15,29}, {6,31}, {4,10}, {14,33}, {2,34}, {4,22}, {9,29}, {19,40}, {17,37}, {9,32}, {19,26}, {12,17}, {15,32}, {25,36}, {15,40}, {2,10}, {5,29}, {9,19}, {28,34}, {14,30}, {14,40}, {5,25}, {17,39}, {7,32}, {24,39}, {3,12}, {11,31}, {2,35}, {1,22}, {19,38}, {25,34}, {6,30}, {4,33}, {5,23}, {10,29}, {10,31}, {26,35}, {16,37}, {13,31}, {23,37}, {13,33}, {1,12}, {7,26}, {16,32}, {1,23}, {11,29}, {6,24}, {5,30}, {15,35}, {11,30}, {5,24}, {17,27}, {8,22}, {15,34}, {1,9}, {20,28}, {27,36}, {9,20}, {18,26}, {18,27}, {3,11}, {14,37}, {23,38}, {26,36}, {6,23}, {3,10}, {16,38}, {15,36}, {13,36}, {5,28}, {8,26}, {7,31}, {24,40}, {13,30}, {4,36}, {25,35}, {21,39}, {17,28}, {22,39}, {8,21}, {4,9}, {17,25}, {12,19}, {6,26}, {28,33}, {20,39}, {12,30}, {14,34}, {3,23}, {10,32}, {20,25}, {3,21}, {7,29}, {6,28}, {9,30}, {1,35}, {24,38}, {7,28}, {20,37}, {23,40}, {16,36}, {7,23}, {2,21}, {9,18}, {10,17}, {20,26}, {3,24}, {16,35}, {18,28}, {2,22}, {4,34}, {8,24}, {6,25}, {5,27}, {15,38}, {19,25}, {16,39}, {10,19}, {4,11}, {7,27}, {14,35}, {13,37}, {15,39}, {2,12}, {18,40}, {10,20}, {12,31}, {13,34}, {13,39}, {5,21}, {27,34}, {1,34}, {3,36}, {19,37}, {7,21}, {8,29}, {12,18}, {19,27}, {11,18}, {1,36}, {14,29}, {22,38} }; // ET40.65 // Bipartite(15,25) Valencies [10,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 300 EdgePairs[40][65]:={ {7,19}, {13,25}, {5,32}, {10,21}, {13,29}, {14,25}, {8,39}, {8,24}, {12,26}, {2,38}, {10,22}, {6,18}, {9,30}, {3,29}, {6,36}, {4,27}, {6,17}, {13,18}, {8,36}, {5,35}, {6,23}, {1,40}, {14,19}, {7,38}, {1,25}, {4,16}, {7,33}, {12,31}, {2,37}, {3,32}, {13,34}, {7,31}, {12,33}, {7,27}, {15,40}, {9,21}, {11,16}, {1,32}, {11,22}, {9,37}, {8,34}, {12,25}, {2,18}, {9,17}, {10,18}, {15,32}, {5,21}, {15,28}, {2,29}, {3,19}, {10,30}, {14,27}, {5,37}, {1,29}, {1,34}, {11,34}, {12,30}, {15,39}, {5,33}, {15,34}, {4,20}, {15,22}, {2,31}, {2,23}, {10,36}, {8,33}, {8,28}, {14,16}, {1,17}, {13,26}, {14,30}, {2,32}, {3,40}, {6,21}, {1,16}, {12,34}, {8,21}, {2,17}, {4,33}, {4,28}, {10,39}, {10,31}, {3,22}, {10,37}, {7,20}, {8,35}, {13,35}, {3,23}, {11,39}, {5,29}, {3,27}, {14,26}, {12,28}, {5,28}, {13,30}, {9,25}, {11,26}, {13,40}, {8,40}, {6,29}, {12,24}, {15,26}, {4,38}, {9,33}, {12,38}, {2,27}, {6,19}, {11,36}, {5,38}, {14,17}, {3,35}, {15,31}, {1,23}, {14,22}, {11,19}, {14,31}, {14,23}, {9,24}, {11,25}, {8,20}, {6,16}, {6,20}, {9,18}, {4,32}, {3,39}, {7,22}, {15,27}, {7,37}, {13,17}, {15,38}, {7,21}, {11,20}, {1,28}, {3,36}, {6,35}, {5,18}, {10,26}, {10,35}, {9,16}, {7,36}, {4,23}, {11,24}, {12,37}, {2,30}, {4,19}, {4,24}, {5,40}, {9,20}, {1,24}, {13,39} }; // ET40.66 // Bipartite(15,25) Valencies [10,6] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1934917632000000 EdgePairs[40][66]:={ {4,35}, {10,19}, {5,32}, {6,39}, {9,40}, {14,25}, {8,31}, {10,22}, {9,30}, {2,22}, {3,38}, {6,36}, {1,31}, {7,40}, {13,18}, {10,27}, {8,36}, {11,29}, {2,20}, {4,40}, {5,34}, {14,18}, {12,17}, {12,40}, {2,37}, {12,22}, {5,24}, {7,27}, {11,16}, {12,27}, {14,35}, {13,38}, {15,29}, {14,20}, {12,25}, {3,31}, {6,34}, {15,32}, {5,37}, {1,29}, {3,18}, {1,34}, {11,34}, {12,30}, {13,16}, {14,33}, {15,39}, {9,38}, {15,34}, {4,20}, {10,34}, {15,22}, {13,33}, {8,33}, {8,28}, {1,36}, {13,26}, {14,30}, {2,32}, {1,16}, {6,21}, {8,21}, {8,18}, {2,17}, {4,33}, {4,28}, {10,39}, {7,25}, {10,37}, {14,28}, {5,19}, {9,23}, {10,24}, {7,20}, {8,26}, {14,38}, {3,23}, {11,39}, {5,29}, {4,30}, {6,26}, {1,19}, {2,40}, {15,19}, {7,30}, {2,35}, {12,35}, {9,25}, {4,25}, {10,29}, {1,26}, {11,26}, {6,29}, {7,35}, {4,38}, {6,31}, {9,33}, {5,22}, {2,27}, {6,19}, {11,36}, {5,27}, {9,35}, {11,19}, {1,39}, {8,38}, {14,23}, {9,28}, {3,28}, {11,31}, {3,26}, {8,16}, {5,17}, {15,37}, {13,28}, {8,23}, {6,16}, {11,21}, {3,21}, {9,18}, {10,17}, {13,21}, {7,22}, {15,27}, {3,16}, {4,18}, {7,32}, {13,23}, {10,32}, {13,36}, {7,37}, {15,17}, {2,25}, {12,32}, {14,40}, {3,36}, {6,24}, {13,31}, {3,33}, {7,17}, {4,23}, {11,24}, {5,39}, {12,37}, {2,30}, {1,21}, {12,20}, {15,24}, {9,20}, {1,24} }; // ET40.67 // Bipartite(20,20) Valencies [10,10] // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 687970713600000000 EdgePairs[40][67]:={ {10,24}, {2,24}, {6,32}, {11,36}, {4,27}, {12,29}, {13,21}, {11,35}, {5,34}, {16,33}, {15,24}, {3,40}, {17,38}, {18,32}, {16,27}, {5,38}, {16,31}, {18,38}, {15,31}, {4,29}, {20,27}, {8,33}, {19,24}, {10,26}, {17,34}, {14,38}, {12,39}, {4,31}, {3,35}, {20,21}, {2,26}, {8,39}, {1,21}, {16,25}, {12,35}, {7,36}, {17,21}, {8,25}, {2,28}, {1,30}, {16,23}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {12,37}, {16,29}, {18,34}, {10,22}, {6,22}, {11,28}, {10,30}, {19,28}, {6,40}, {1,38}, {2,34}, {2,36}, {5,22}, {10,38}, {9,29}, {19,40}, {17,37}, {14,36}, {15,32}, {9,26}, {15,40}, {5,29}, {2,38}, {14,30}, {14,40}, {7,39}, {5,25}, {7,32}, {10,28}, {14,24}, {11,31}, {20,31}, {17,33}, {1,22}, {15,27}, {20,33}, {6,30}, {4,33}, {4,21}, {9,34}, {13,22}, {16,37}, {10,40}, {1,29}, {3,39}, {18,30}, {3,32}, {4,35}, {9,25}, {13,33}, {2,32}, {11,23}, {6,24}, {5,30}, {17,30}, {15,35}, {9,37}, {12,25}, {13,25}, {18,24}, {8,35}, {18,26}, {19,31}, {3,27}, {18,36}, {1,33}, {8,37}, {15,36}, {9,22}, {7,31}, {12,33}, {13,30}, {20,29}, {12,27}, {8,21}, {12,23}, {14,22}, {11,24}, {17,25}, {11,39}, {6,26}, {20,23}, {20,39}, {14,34}, {8,23}, {3,23}, {10,32}, {17,29}, {20,25}, {1,25}, {19,36}, {6,28}, {9,30}, {1,37}, {16,21}, {20,35}, {7,28}, {19,32}, {20,37}, {4,37}, {13,26}, {7,23}, {6,36}, {5,33}, {3,24}, {16,35}, {11,27}, {18,28}, {1,26}, {2,22}, {10,36}, {10,34}, {18,22}, {11,32}, {14,32}, {19,39}, {6,38}, {2,40}, {11,40}, {9,33}, {6,34}, {5,26}, {15,28}, {16,39}, {13,38}, {9,38}, {4,25}, {3,28}, {7,27}, {15,23}, {13,37}, {7,24}, {15,39}, {3,31}, {18,40}, {17,26}, {12,31}, {13,34}, {19,35}, {7,35}, {17,22}, {5,21}, {2,30}, {1,34}, {19,23}, {5,37}, {9,21}, {3,36}, {4,39}, {7,40}, {8,29}, {19,27}, {12,21}, {14,26} }; // ET40.68 // Bipartite(8,32) Valencies [12,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 384 EdgePairs[40][68]:={ {7,19}, {5,32}, {7,39}, {6,12}, {8,24}, {2,38}, {1,11}, {2,22}, {8,36}, {5,35}, {6,23}, {1,40}, {4,40}, {7,38}, {4,16}, {1,9}, {6,32}, {7,15}, {5,13}, {3,10}, {3,34}, {3,31}, {2,19}, {8,14}, {6,22}, {5,21}, {1,29}, {7,28}, {1,34}, {2,14}, {5,23}, {3,11}, {4,37}, {2,10}, {8,33}, {6,33}, {8,10}, {8,18}, {8,21}, {7,29}, {3,9}, {7,25}, {7,20}, {5,29}, {4,30}, {6,26}, {6,15}, {8,11}, {2,40}, {4,17}, {5,28}, {4,15}, {2,9}, {1,35}, {4,38}, {6,31}, {2,27}, {6,19}, {3,35}, {8,27}, {1,39}, {2,39}, {4,22}, {8,32}, {3,28}, {5,36}, {3,26}, {8,16}, {5,17}, {5,31}, {6,20}, {1,14}, {1,37}, {1,13}, {4,18}, {3,25}, {2,26}, {7,37}, {3,20}, {5,12}, {2,25}, {3,36}, {6,24}, {8,30}, {6,27}, {7,34}, {3,33}, {7,17}, {4,23}, {7,12}, {5,16}, {4,13}, {1,21}, {2,30}, {1,18}, {4,24} }; // ET40.69 // Bipartite(8,32) Valencies [12,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5283615080448 EdgePairs[40][69]:={ {7,19}, {6,12}, {5,14}, {3,15}, {8,24}, {6,10}, {6,18}, {1,11}, {3,29}, {5,30}, {6,36}, {6,17}, {2,11}, {1,40}, {4,40}, {7,38}, {1,25}, {4,16}, {2,37}, {1,9}, {6,25}, {7,27}, {1,32}, {3,31}, {6,34}, {2,19}, {2,18}, {6,9}, {8,14}, {4,26}, {8,13}, {7,11}, {5,9}, {2,29}, {8,22}, {7,28}, {5,33}, {5,23}, {2,10}, {4,39}, {1,17}, {3,13}, {6,33}, {1,16}, {8,21}, {2,13}, {5,15}, {7,20}, {3,23}, {7,14}, {4,31}, {2,34}, {6,26}, {1,19}, {7,30}, {2,35}, {4,15}, {1,35}, {8,40}, {7,35}, {5,22}, {2,27}, {5,38}, {2,21}, {8,38}, {8,32}, {3,28}, {8,16}, {5,17}, {5,31}, {3,12}, {6,20}, {3,21}, {4,32}, {3,39}, {1,27}, {7,22}, {4,18}, {2,26}, {3,20}, {1,33}, {3,36}, {8,37}, {3,37}, {8,30}, {4,34}, {7,36}, {4,23}, {7,12}, {5,39}, {5,25}, {4,10}, {4,24}, {1,24}, {8,29}, {6,28} }; // ET40.70 // Bipartite(10,30) Valencies [12,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 240 EdgePairs[40][70]:={ {10,19}, {7,19}, {5,32}, {7,39}, {9,40}, {5,14}, {3,15}, {8,31}, {10,22}, {6,18}, {4,14}, {1,11}, {9,30}, {3,29}, {6,14}, {5,30}, {6,17}, {10,27}, {2,11}, {5,34}, {7,38}, {1,25}, {4,16}, {5,24}, {10,40}, {1,38}, {2,33}, {7,31}, {5,13}, {8,34}, {2,28}, {9,31}, {5,26}, {9,17}, {6,22}, {5,21}, {10,23}, {2,29}, {5,37}, {4,12}, {3,18}, {5,33}, {4,37}, {9,27}, {8,33}, {8,28}, {4,39}, {10,25}, {2,32}, {3,40}, {6,21}, {1,16}, {2,36}, {8,21}, {10,39}, {2,13}, {10,31}, {1,12}, {10,16}, {3,22}, {9,23}, {5,15}, {7,20}, {8,35}, {8,26}, {8,17}, {7,14}, {3,27}, {6,26}, {6,15}, {1,19}, {2,40}, {4,36}, {4,15}, {1,35}, {6,29}, {7,35}, {4,38}, {2,24}, {1,23}, {6,30}, {7,18}, {8,38}, {2,12}, {8,32}, {9,28}, {5,36}, {3,24}, {3,12}, {8,23}, {6,20}, {9,26}, {3,39}, {1,37}, {9,11}, {7,22}, {3,16}, {1,13}, {4,18}, {3,25}, {9,29}, {7,21}, {1,33}, {2,25}, {1,28}, {3,36}, {8,37}, {10,20}, {6,24}, {9,32}, {4,34}, {6,27}, {10,35}, {7,34}, {7,17}, {4,13}, {2,30}, {10,11}, {4,19}, {9,20} }; // ET40.71 // Bipartite(10,30) Valencies [12,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1440 EdgePairs[40][71]:={ {1,15}, {9,13}, {10,19}, {7,19}, {5,32}, {10,21}, {8,39}, {8,24}, {8,31}, {6,18}, {4,14}, {3,29}, {3,38}, {5,30}, {1,31}, {7,40}, {10,27}, {2,11}, {5,35}, {6,23}, {2,20}, {4,40}, {5,34}, {7,38}, {9,12}, {7,33}, {2,37}, {7,31}, {6,25}, {7,27}, {1,32}, {5,13}, {6,34}, {2,18}, {5,26}, {9,17}, {7,11}, {6,22}, {10,23}, {2,29}, {3,19}, {4,12}, {8,22}, {3,11}, {4,20}, {10,34}, {2,31}, {2,23}, {8,28}, {4,39}, {1,36}, {3,13}, {10,25}, {2,16}, {10,12}, {1,16}, {4,33}, {4,28}, {3,14}, {10,16}, {5,15}, {8,35}, {8,26}, {6,37}, {5,29}, {6,15}, {7,30}, {4,21}, {9,25}, {9,15}, {10,29}, {8,19}, {8,40}, {4,38}, {9,33}, {3,35}, {2,21}, {6,30}, {6,38}, {2,39}, {5,20}, {8,32}, {10,14}, {5,36}, {3,24}, {5,17}, {9,24}, {8,23}, {9,26}, {1,14}, {9,18}, {10,17}, {3,39}, {1,37}, {1,20}, {1,27}, {9,11}, {7,22}, {4,18}, {3,25}, {2,26}, {10,32}, {7,21}, {1,33}, {1,28}, {3,36}, {3,37}, {6,35}, {4,34}, {6,27}, {9,16}, {7,36}, {7,17}, {4,13}, {2,30}, {5,40}, {8,12}, {1,24}, {6,28}, {9,22} }; // ET40.72 // Bipartite(10,30) Valencies [12,4] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 61917364224000000 EdgePairs[40][72]:={ {4,35}, {9,13}, {10,19}, {5,32}, {6,39}, {9,40}, {5,14}, {8,31}, {10,22}, {1,11}, {9,30}, {2,22}, {6,14}, {3,38}, {6,36}, {1,31}, {7,40}, {10,27}, {8,36}, {2,20}, {4,40}, {5,34}, {2,37}, {5,24}, {7,27}, {7,15}, {3,31}, {6,34}, {2,15}, {8,13}, {5,37}, {1,29}, {3,18}, {1,34}, {9,38}, {3,11}, {4,20}, {10,34}, {6,11}, {8,33}, {8,28}, {1,36}, {3,13}, {10,12}, {2,32}, {1,16}, {6,21}, {4,33}, {2,17}, {8,18}, {8,21}, {4,28}, {10,39}, {7,25}, {10,37}, {5,19}, {9,23}, {10,24}, {7,20}, {8,26}, {3,23}, {5,29}, {4,30}, {6,26}, {1,19}, {8,11}, {2,40}, {7,30}, {2,35}, {9,25}, {4,15}, {4,25}, {9,15}, {10,29}, {1,26}, {6,29}, {7,35}, {4,38}, {6,31}, {9,33}, {5,22}, {2,27}, {6,19}, {5,27}, {9,35}, {1,39}, {8,38}, {2,12}, {9,28}, {10,14}, {3,28}, {3,26}, {8,16}, {5,17}, {8,23}, {6,16}, {3,21}, {1,14}, {9,18}, {10,17}, {7,22}, {3,16}, {4,18}, {7,32}, {10,32}, {7,37}, {5,12}, {2,25}, {3,36}, {6,24}, {3,33}, {7,17}, {4,23}, {7,12}, {5,39}, {4,13}, {1,21}, {2,30}, {9,20}, {1,24} }; // ET40.73 // Bipartite(10,30) Valencies [12,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23219011584000000 EdgePairs[40][73]:={ {7,19}, {6,39}, {7,39}, {9,40}, {5,14}, {8,31}, {6,18}, {1,11}, {9,30}, {2,22}, {6,14}, {3,38}, {5,30}, {1,31}, {8,36}, {5,35}, {7,24}, {6,23}, {10,38}, {2,20}, {5,34}, {4,16}, {6,13}, {2,37}, {5,24}, {3,32}, {10,40}, {7,27}, {9,21}, {9,31}, {6,34}, {2,15}, {4,26}, {10,18}, {10,23}, {10,30}, {1,29}, {3,18}, {8,22}, {1,34}, {1,36}, {3,13}, {10,25}, {2,32}, {6,33}, {1,16}, {10,13}, {8,21}, {2,17}, {4,33}, {4,28}, {7,29}, {10,15}, {3,22}, {5,19}, {5,15}, {8,26}, {3,23}, {8,17}, {5,29}, {7,14}, {4,31}, {3,27}, {10,33}, {1,19}, {8,11}, {2,40}, {4,36}, {4,21}, {2,35}, {9,25}, {9,15}, {1,26}, {6,29}, {4,38}, {4,11}, {2,27}, {6,19}, {8,27}, {9,35}, {10,28}, {1,39}, {6,38}, {2,12}, {5,20}, {8,32}, {3,28}, {8,16}, {3,12}, {9,26}, {1,14}, {9,11}, {7,22}, {4,18}, {7,32}, {7,37}, {2,25}, {3,17}, {8,37}, {10,20}, {3,37}, {6,24}, {9,36}, {10,35}, {9,16}, {7,34}, {3,33}, {7,17}, {4,23}, {7,12}, {5,39}, {4,13}, {1,21}, {2,30}, {5,25}, {5,40}, {8,12}, {9,20}, {1,24}, {6,28} }; // ET40.74 // Bipartite(10,30) Valencies [12,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 232190115840 EdgePairs[40][74]:={ {4,35}, {10,19}, {5,32}, {6,39}, {8,24}, {2,38}, {10,22}, {6,18}, {1,11}, {2,22}, {6,14}, {5,30}, {1,31}, {4,27}, {8,36}, {5,35}, {7,38}, {4,16}, {7,33}, {2,37}, {10,40}, {1,38}, {2,33}, {7,27}, {9,21}, {3,30}, {9,37}, {7,23}, {8,34}, {2,28}, {3,34}, {9,31}, {6,34}, {2,18}, {8,14}, {4,26}, {8,13}, {9,17}, {10,30}, {1,29}, {7,28}, {1,34}, {4,37}, {6,11}, {9,27}, {2,23}, {8,33}, {3,13}, {10,25}, {10,12}, {2,32}, {3,40}, {6,21}, {2,17}, {10,39}, {3,14}, {2,13}, {10,15}, {5,19}, {5,15}, {8,26}, {7,13}, {3,23}, {5,29}, {4,31}, {1,19}, {4,36}, {4,21}, {4,17}, {9,25}, {4,15}, {4,25}, {9,15}, {10,29}, {8,40}, {6,29}, {6,31}, {4,11}, {5,22}, {2,27}, {6,19}, {9,35}, {1,39}, {6,38}, {7,18}, {2,12}, {5,20}, {3,26}, {8,16}, {3,24}, {8,20}, {8,23}, {9,26}, {1,14}, {9,11}, {7,22}, {3,16}, {7,32}, {10,32}, {7,37}, {3,20}, {5,12}, {1,28}, {3,36}, {10,20}, {6,24}, {8,30}, {9,36}, {10,35}, {9,16}, {3,33}, {7,17}, {7,12}, {5,39}, {1,21}, {1,18}, {5,25}, {5,40}, {1,24}, {6,28} }; // ET40.75 // Bipartite(10,30) Valencies [12,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2418647040 EdgePairs[40][75]:={ {5,14}, {8,31}, {8,24}, {2,38}, {10,22}, {1,11}, {3,29}, {2,22}, {6,14}, {1,31}, {2,11}, {7,24}, {6,23}, {1,40}, {4,40}, {5,34}, {7,38}, {6,13}, {5,24}, {1,38}, {9,39}, {7,27}, {9,19}, {3,30}, {6,40}, {7,15}, {8,34}, {5,13}, {2,28}, {6,34}, {2,19}, {2,18}, {5,26}, {8,14}, {10,23}, {2,29}, {3,19}, {5,37}, {4,12}, {8,22}, {8,15}, {7,28}, {9,38}, {5,33}, {5,23}, {4,20}, {6,11}, {2,31}, {10,36}, {4,39}, {1,17}, {10,25}, {10,12}, {2,32}, {6,33}, {3,40}, {6,21}, {10,13}, {8,21}, {4,33}, {10,15}, {4,29}, {10,16}, {7,25}, {8,35}, {7,14}, {3,27}, {4,30}, {10,33}, {8,11}, {9,25}, {9,15}, {7,35}, {6,31}, {2,21}, {5,27}, {6,30}, {9,35}, {7,18}, {2,39}, {2,12}, {4,22}, {8,32}, {9,28}, {5,36}, {3,26}, {5,17}, {6,20}, {9,26}, {9,18}, {4,32}, {3,39}, {1,37}, {1,20}, {1,27}, {3,16}, {8,25}, {9,29}, {10,32}, {7,37}, {3,20}, {1,28}, {3,36}, {3,17}, {3,37}, {6,24}, {9,36}, {10,26}, {10,35}, {9,16}, {7,34}, {7,17}, {4,23}, {1,30}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {8,12} }; // ET40.76 // Bipartite(10,30) Valencies [12,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23592960 EdgePairs[40][76]:={ {4,35}, {5,32}, {5,14}, {2,38}, {10,22}, {6,18}, {1,11}, {5,30}, {1,31}, {8,36}, {6,23}, {1,40}, {2,20}, {4,40}, {5,34}, {1,25}, {6,13}, {9,12}, {7,33}, {7,31}, {6,25}, {7,27}, {9,19}, {9,21}, {6,40}, {7,15}, {5,13}, {2,28}, {3,34}, {3,31}, {5,26}, {10,18}, {7,11}, {6,22}, {3,19}, {1,29}, {8,22}, {8,15}, {9,38}, {4,20}, {6,11}, {9,27}, {2,31}, {2,23}, {7,26}, {4,39}, {1,36}, {3,13}, {2,16}, {2,32}, {6,33}, {1,16}, {2,36}, {2,17}, {8,21}, {9,34}, {10,39}, {2,13}, {3,22}, {10,37}, {5,19}, {9,23}, {10,24}, {5,15}, {7,20}, {6,37}, {8,17}, {5,29}, {3,27}, {4,30}, {6,26}, {10,33}, {7,30}, {2,35}, {5,28}, {4,15}, {4,25}, {10,29}, {1,26}, {8,40}, {7,35}, {4,38}, {9,33}, {2,21}, {8,27}, {1,39}, {6,38}, {7,18}, {8,32}, {10,14}, {3,28}, {3,24}, {5,17}, {3,12}, {7,16}, {1,14}, {9,18}, {10,17}, {3,39}, {5,11}, {3,16}, {8,25}, {9,29}, {10,32}, {9,14}, {8,37}, {10,20}, {3,37}, {8,30}, {9,36}, {4,34}, {10,35}, {4,23}, {7,12}, {1,21}, {4,19}, {4,24}, {8,12}, {1,24}, {6,28} }; // ET40.77 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 9216 EdgePairs[40][77]:={ {10,24}, {11,20}, {9,28}, {12,29}, {13,21}, {13,40}, {15,24}, {16,26}, {16,33}, {3,40}, {11,25}, {16,27}, {14,39}, {2,23}, {12,22}, {5,38}, {16,31}, {4,29}, {1,32}, {1,27}, {3,25}, {10,23}, {12,38}, {10,26}, {14,38}, {16,19}, {4,31}, {2,19}, {2,27}, {3,35}, {5,20}, {13,35}, {2,26}, {8,39}, {8,25}, {12,34}, {1,30}, {5,32}, {16,23}, {9,35}, {4,23}, {8,31}, {8,27}, {12,37}, {16,29}, {6,22}, {11,28}, {3,17}, {15,29}, {14,23}, {11,33}, {6,31}, {6,40}, {1,38}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {7,20}, {9,32}, {14,36}, {12,17}, {15,32}, {9,27}, {12,20}, {5,29}, {2,37}, {14,30}, {14,40}, {7,39}, {5,25}, {7,32}, {15,26}, {1,31}, {2,35}, {15,27}, {6,30}, {4,33}, {5,23}, {10,29}, {4,21}, {10,31}, {3,20}, {13,22}, {10,21}, {2,20}, {13,18}, {16,37}, {10,40}, {7,30}, {8,17}, {3,39}, {13,31}, {11,21}, {9,25}, {8,36}, {7,26}, {13,33}, {5,18}, {11,23}, {6,24}, {7,17}, {11,30}, {5,24}, {9,37}, {15,34}, {13,25}, {15,20}, {14,37}, {4,28}, {1,33}, {15,17}, {3,29}, {6,23}, {16,38}, {8,37}, {15,36}, {12,26}, {9,22}, {12,33}, {13,30}, {8,21}, {3,19}, {1,24}, {14,18}, {11,24}, {13,24}, {11,39}, {12,19}, {6,26}, {12,40}, {14,34}, {1,39}, {10,32}, {6,19}, {6,28}, {9,30}, {10,39}, {14,20}, {15,21}, {14,25}, {7,28}, {4,37}, {4,40}, {10,35}, {13,19}, {6,36}, {2,21}, {8,34}, {5,33}, {3,24}, {11,27}, {16,35}, {1,26}, {2,22}, {4,34}, {10,36}, {15,22}, {9,17}, {10,18}, {14,32}, {6,38}, {9,36}, {6,34}, {5,27}, {8,18}, {15,28}, {16,39}, {9,38}, {11,19}, {4,25}, {3,38}, {3,28}, {7,33}, {11,34}, {7,35}, {2,30}, {13,17}, {7,37}, {5,35}, {2,18}, {9,31}, {1,34}, {3,36}, {16,28}, {7,40}, {7,21}, {8,29}, {4,32}, {12,18} }; // ET40.78 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 9216 EdgePairs[40][78]:={ {11,17}, {3,33}, {10,25}, {2,24}, {6,32}, {11,36}, {13,21}, {11,35}, {4,24}, {14,19}, {15,24}, {16,33}, {4,26}, {3,22}, {3,40}, {10,37}, {11,25}, {8,30}, {16,40}, {14,39}, {2,23}, {12,22}, {5,38}, {12,32}, {7,38}, {8,33}, {1,27}, {10,23}, {1,40}, {10,26}, {12,39}, {4,31}, {2,19}, {1,19}, {13,35}, {2,26}, {14,31}, {7,34}, {16,25}, {12,35}, {7,36}, {8,25}, {1,30}, {14,28}, {13,29}, {6,22}, {3,18}, {11,28}, {10,30}, {3,17}, {16,30}, {4,38}, {2,25}, {14,23}, {11,33}, {6,31}, {1,38}, {2,34}, {1,17}, {10,38}, {9,29}, {14,36}, {15,32}, {9,27}, {12,36}, {5,29}, {14,40}, {2,39}, {7,32}, {15,26}, {11,22}, {7,25}, {11,31}, {10,28}, {15,27}, {4,33}, {5,23}, {3,20}, {9,34}, {2,20}, {13,18}, {1,29}, {8,17}, {13,31}, {3,32}, {11,21}, {4,35}, {5,18}, {16,32}, {11,29}, {5,30}, {7,17}, {9,37}, {15,37}, {8,22}, {15,34}, {8,35}, {9,20}, {1,28}, {3,27}, {14,37}, {15,17}, {16,38}, {8,37}, {5,28}, {15,36}, {7,31}, {4,36}, {12,27}, {9,40}, {14,18}, {14,22}, {13,24}, {6,27}, {12,19}, {8,40}, {6,26}, {12,40}, {12,30}, {3,23}, {10,32}, {5,36}, {3,21}, {6,19}, {6,28}, {13,27}, {1,35}, {1,37}, {16,34}, {5,39}, {14,25}, {16,21}, {4,37}, {11,26}, {13,26}, {7,23}, {13,19}, {2,21}, {5,33}, {10,17}, {2,29}, {16,35}, {2,22}, {15,22}, {10,18}, {15,33}, {16,20}, {8,24}, {9,33}, {6,34}, {5,27}, {5,26}, {8,18}, {4,18}, {16,39}, {9,39}, {13,38}, {9,38}, {10,19}, {4,25}, {12,24}, {8,20}, {3,28}, {15,23}, {7,24}, {3,31}, {9,24}, {10,20}, {6,39}, {6,37}, {11,34}, {6,20}, {5,21}, {2,30}, {13,17}, {15,30}, {13,20}, {9,31}, {1,34}, {7,19}, {6,35}, {4,39}, {16,28}, {7,40}, {9,23}, {7,21}, {8,29}, {4,32}, {12,18}, {12,21}, {1,36}, {14,29} }; // ET40.79 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 768 EdgePairs[40][79]:={ {11,17}, {10,25}, {1,20}, {5,17}, {2,24}, {11,35}, {13,40}, {4,24}, {15,24}, {16,33}, {3,22}, {3,40}, {4,30}, {16,40}, {14,39}, {2,23}, {5,38}, {8,28}, {16,31}, {4,29}, {1,27}, {3,25}, {10,23}, {12,38}, {1,40}, {4,19}, {14,38}, {16,19}, {12,39}, {10,33}, {1,19}, {3,37}, {13,35}, {1,21}, {2,28}, {1,30}, {5,32}, {16,23}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {15,25}, {3,17}, {15,29}, {6,21}, {14,23}, {5,40}, {2,34}, {14,33}, {1,17}, {2,36}, {5,22}, {9,29}, {14,21}, {9,32}, {9,26}, {9,27}, {12,20}, {12,36}, {5,29}, {2,38}, {7,39}, {5,25}, {7,32}, {15,26}, {11,22}, {7,25}, {11,31}, {10,28}, {14,24}, {2,35}, {15,27}, {6,30}, {4,33}, {5,23}, {10,31}, {3,20}, {9,34}, {13,22}, {10,21}, {13,18}, {16,37}, {10,40}, {7,30}, {13,31}, {4,35}, {8,36}, {6,33}, {2,32}, {7,26}, {5,18}, {16,32}, {11,29}, {6,24}, {7,17}, {11,30}, {9,37}, {12,28}, {12,25}, {8,22}, {13,25}, {8,35}, {15,20}, {3,27}, {14,37}, {1,33}, {3,26}, {8,37}, {5,28}, {13,36}, {15,36}, {12,26}, {9,22}, {12,33}, {13,30}, {4,36}, {14,17}, {8,21}, {12,23}, {5,31}, {6,27}, {14,34}, {1,39}, {3,21}, {1,25}, {6,19}, {7,29}, {9,30}, {13,27}, {1,37}, {16,34}, {16,17}, {16,21}, {15,18}, {10,35}, {7,23}, {13,19}, {6,36}, {8,34}, {11,37}, {2,29}, {11,27}, {16,35}, {8,38}, {1,26}, {2,22}, {4,34}, {10,36}, {15,22}, {11,32}, {9,17}, {10,18}, {14,32}, {8,24}, {2,31}, {11,40}, {6,34}, {15,38}, {5,26}, {4,18}, {9,39}, {9,38}, {11,19}, {10,19}, {3,38}, {12,24}, {8,20}, {3,28}, {3,31}, {15,39}, {9,24}, {10,20}, {6,39}, {7,33}, {6,37}, {11,34}, {6,20}, {15,30}, {13,20}, {2,18}, {7,19}, {6,35}, {4,39}, {16,28}, {7,40}, {4,32}, {12,18}, {12,21}, {14,26}, {7,18} }; // ET40.80 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 713288035860480000 EdgePairs[40][80]:={ {10,25}, {1,20}, {5,17}, {11,20}, {13,32}, {9,28}, {2,33}, {11,36}, {4,27}, {13,21}, {11,35}, {13,40}, {15,24}, {16,26}, {4,26}, {3,40}, {10,37}, {4,30}, {16,27}, {8,30}, {6,17}, {12,22}, {16,31}, {15,31}, {1,32}, {12,38}, {1,40}, {10,26}, {4,19}, {14,38}, {16,19}, {12,39}, {4,31}, {10,33}, {3,35}, {5,20}, {2,26}, {8,39}, {1,21}, {16,18}, {12,35}, {7,36}, {12,34}, {5,32}, {16,23}, {4,23}, {8,31}, {8,27}, {13,29}, {10,22}, {6,22}, {11,28}, {10,30}, {6,29}, {16,30}, {4,38}, {6,21}, {2,25}, {5,40}, {2,34}, {14,33}, {1,17}, {4,22}, {10,38}, {9,29}, {8,19}, {7,20}, {14,21}, {9,32}, {15,32}, {15,40}, {5,29}, {2,38}, {2,37}, {14,30}, {7,39}, {5,25}, {7,32}, {11,31}, {15,27}, {6,30}, {10,29}, {3,20}, {15,19}, {10,21}, {6,18}, {1,29}, {3,39}, {3,32}, {4,35}, {9,25}, {13,33}, {6,33}, {11,23}, {15,35}, {5,24}, {9,37}, {8,22}, {13,25}, {8,35}, {13,28}, {15,20}, {9,20}, {1,28}, {3,27}, {14,37}, {1,33}, {16,38}, {5,28}, {13,36}, {15,36}, {8,26}, {12,26}, {16,22}, {7,31}, {2,17}, {12,27}, {9,40}, {14,17}, {3,19}, {14,18}, {1,24}, {12,23}, {14,22}, {13,24}, {11,24}, {11,39}, {12,19}, {6,26}, {12,30}, {3,23}, {8,23}, {14,34}, {5,36}, {1,25}, {1,37}, {16,34}, {14,25}, {7,28}, {7,23}, {2,21}, {8,34}, {5,33}, {10,17}, {3,24}, {2,29}, {11,27}, {16,35}, {8,38}, {2,22}, {4,34}, {10,34}, {11,32}, {9,17}, {10,18}, {6,25}, {6,38}, {11,40}, {9,33}, {9,36}, {6,34}, {8,18}, {4,18}, {15,28}, {16,39}, {11,19}, {3,28}, {7,27}, {15,23}, {13,37}, {7,24}, {3,31}, {15,39}, {9,24}, {12,31}, {6,37}, {7,35}, {5,21}, {2,30}, {13,17}, {13,20}, {2,18}, {5,37}, {7,19}, {9,21}, {3,36}, {4,39}, {7,40}, {12,18}, {1,36}, {14,29}, {14,26} }; // ET40.81 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1521681143169024 EdgePairs[40][81]:={ {3,33}, {10,24}, {5,17}, {2,24}, {9,28}, {6,32}, {11,36}, {4,27}, {5,34}, {13,40}, {15,24}, {16,26}, {16,33}, {4,26}, {11,25}, {16,27}, {16,40}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {15,31}, {8,33}, {3,25}, {10,23}, {12,38}, {1,40}, {10,26}, {14,38}, {12,39}, {1,19}, {3,37}, {13,35}, {2,26}, {8,39}, {7,36}, {12,34}, {9,35}, {8,27}, {13,29}, {15,25}, {3,18}, {10,30}, {6,29}, {4,38}, {5,40}, {14,23}, {11,33}, {1,17}, {2,36}, {5,22}, {4,22}, {10,38}, {9,29}, {14,36}, {12,20}, {5,29}, {2,38}, {9,19}, {14,30}, {7,39}, {5,25}, {1,31}, {7,25}, {11,31}, {14,24}, {2,35}, {1,22}, {15,27}, {6,30}, {4,33}, {5,23}, {10,29}, {4,21}, {9,34}, {13,22}, {15,19}, {2,20}, {6,18}, {1,29}, {7,30}, {3,39}, {13,31}, {11,21}, {9,25}, {2,32}, {16,32}, {1,23}, {6,24}, {11,30}, {9,37}, {13,23}, {12,28}, {15,37}, {8,22}, {13,25}, {13,28}, {1,28}, {3,27}, {4,28}, {6,23}, {16,38}, {5,28}, {15,36}, {8,26}, {12,26}, {16,22}, {9,22}, {7,31}, {12,33}, {2,17}, {12,27}, {9,40}, {14,17}, {8,32}, {8,21}, {3,19}, {14,18}, {5,31}, {11,24}, {11,39}, {6,26}, {8,40}, {12,40}, {10,32}, {3,21}, {1,25}, {1,35}, {1,37}, {14,20}, {15,21}, {16,34}, {16,21}, {15,18}, {4,40}, {10,35}, {13,19}, {6,36}, {3,30}, {8,34}, {10,17}, {11,37}, {3,24}, {2,29}, {11,27}, {8,38}, {4,34}, {10,36}, {9,17}, {10,18}, {14,32}, {15,33}, {16,20}, {6,38}, {16,39}, {11,19}, {4,20}, {8,20}, {7,27}, {14,35}, {13,37}, {7,24}, {3,31}, {15,39}, {10,20}, {7,33}, {13,34}, {5,19}, {6,20}, {2,30}, {13,17}, {15,30}, {7,37}, {5,35}, {2,18}, {9,31}, {1,34}, {5,37}, {7,19}, {6,35}, {3,36}, {4,39}, {16,28}, {9,23}, {7,21}, {4,32}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18} }; // ET40.82 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2348273369088 EdgePairs[40][82]:={ {11,17}, {13,32}, {2,33}, {6,32}, {11,36}, {12,29}, {13,21}, {11,35}, {4,24}, {14,19}, {16,26}, {4,30}, {11,25}, {8,30}, {16,40}, {2,23}, {12,22}, {5,38}, {7,38}, {8,28}, {4,29}, {1,27}, {3,25}, {10,23}, {14,38}, {7,22}, {10,33}, {2,27}, {1,19}, {3,35}, {5,20}, {3,37}, {14,31}, {7,34}, {1,21}, {16,18}, {12,35}, {2,28}, {12,34}, {5,32}, {9,35}, {4,23}, {10,22}, {3,18}, {3,17}, {16,30}, {6,31}, {2,34}, {1,17}, {4,22}, {9,29}, {7,20}, {14,36}, {12,17}, {15,32}, {16,24}, {9,27}, {12,36}, {15,40}, {9,19}, {14,30}, {7,39}, {5,25}, {2,39}, {7,32}, {15,26}, {1,31}, {10,28}, {11,31}, {14,24}, {2,35}, {15,27}, {6,30}, {10,29}, {10,21}, {6,18}, {10,40}, {1,29}, {13,31}, {4,35}, {9,25}, {8,36}, {7,26}, {13,33}, {16,32}, {11,23}, {1,23}, {11,29}, {6,24}, {11,30}, {9,37}, {12,28}, {8,22}, {15,34}, {13,25}, {15,20}, {14,37}, {4,28}, {1,33}, {3,29}, {16,38}, {8,26}, {16,22}, {2,17}, {4,36}, {8,32}, {3,19}, {14,18}, {12,23}, {5,31}, {11,24}, {6,26}, {8,40}, {12,40}, {12,30}, {3,23}, {1,39}, {1,25}, {6,19}, {13,27}, {10,39}, {1,35}, {1,37}, {14,20}, {15,21}, {16,34}, {5,39}, {14,25}, {7,28}, {13,26}, {4,40}, {10,35}, {13,19}, {16,36}, {6,36}, {2,21}, {3,30}, {5,33}, {8,34}, {10,17}, {11,37}, {3,24}, {2,29}, {10,27}, {8,38}, {2,22}, {4,34}, {10,34}, {15,22}, {9,17}, {14,32}, {15,33}, {16,20}, {8,24}, {6,25}, {6,38}, {2,40}, {9,33}, {5,27}, {15,38}, {5,26}, {8,18}, {4,18}, {15,28}, {9,39}, {13,38}, {11,19}, {12,24}, {8,20}, {7,27}, {13,37}, {3,31}, {15,39}, {7,33}, {6,37}, {5,19}, {6,20}, {13,39}, {5,21}, {13,20}, {9,31}, {5,37}, {4,17}, {9,21}, {3,36}, {16,28}, {7,40}, {9,23}, {7,21}, {12,18}, {11,18}, {14,26} }; // ET40.83 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 82556485632 EdgePairs[40][83]:={ {10,25}, {1,20}, {2,24}, {10,24}, {9,28}, {2,33}, {4,27}, {12,29}, {11,35}, {5,34}, {4,24}, {15,24}, {16,26}, {16,33}, {3,22}, {10,37}, {8,30}, {6,17}, {12,32}, {7,38}, {16,31}, {15,31}, {4,29}, {1,32}, {8,33}, {1,40}, {4,19}, {7,22}, {10,33}, {3,35}, {5,20}, {3,37}, {13,35}, {8,39}, {16,18}, {16,25}, {12,35}, {8,25}, {16,23}, {14,28}, {8,31}, {12,37}, {10,22}, {3,18}, {10,30}, {6,29}, {16,30}, {6,21}, {3,34}, {2,25}, {11,38}, {14,33}, {1,17}, {10,38}, {9,32}, {14,21}, {14,36}, {15,32}, {12,20}, {12,36}, {15,40}, {2,38}, {2,37}, {7,39}, {7,32}, {1,31}, {11,22}, {15,27}, {5,23}, {10,29}, {4,21}, {15,19}, {10,21}, {6,18}, {13,18}, {10,40}, {7,30}, {8,17}, {13,31}, {11,21}, {4,35}, {9,25}, {2,32}, {6,33}, {5,18}, {1,23}, {11,29}, {11,30}, {15,35}, {13,23}, {12,28}, {8,22}, {13,28}, {9,20}, {1,28}, {3,27}, {14,37}, {4,28}, {1,33}, {3,29}, {3,26}, {16,38}, {5,28}, {13,36}, {8,26}, {16,22}, {7,31}, {2,17}, {4,36}, {12,27}, {9,40}, {14,17}, {3,19}, {1,24}, {14,18}, {5,31}, {12,19}, {6,26}, {12,40}, {8,23}, {14,34}, {1,39}, {10,32}, {5,36}, {3,21}, {1,25}, {6,28}, {13,27}, {14,20}, {16,34}, {5,39}, {14,25}, {16,17}, {4,37}, {11,26}, {13,26}, {4,40}, {7,23}, {13,19}, {6,36}, {2,21}, {3,30}, {8,34}, {10,17}, {11,37}, {2,29}, {11,27}, {8,38}, {2,22}, {15,22}, {9,17}, {6,25}, {2,40}, {9,33}, {9,36}, {6,34}, {5,27}, {15,38}, {5,26}, {8,18}, {16,39}, {9,39}, {11,19}, {3,38}, {4,20}, {12,24}, {7,27}, {15,23}, {7,24}, {15,39}, {9,24}, {6,37}, {13,34}, {11,34}, {5,19}, {6,20}, {7,35}, {13,39}, {2,30}, {15,30}, {13,20}, {5,35}, {9,31}, {7,19}, {7,40}, {9,23}, {4,32}, {11,18}, {12,21}, {1,36}, {14,29}, {14,26} }; // ET40.84 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 644972544 EdgePairs[40][84]:={ {11,17}, {10,25}, {10,24}, {11,20}, {2,33}, {6,32}, {11,36}, {13,21}, {11,35}, {5,34}, {14,19}, {16,33}, {3,22}, {4,30}, {11,25}, {8,30}, {2,23}, {16,31}, {15,31}, {4,29}, {1,32}, {1,27}, {10,23}, {1,40}, {4,31}, {10,33}, {1,19}, {3,35}, {3,37}, {13,35}, {2,26}, {7,34}, {16,25}, {12,35}, {2,28}, {12,34}, {1,30}, {5,32}, {16,23}, {4,23}, {8,27}, {13,29}, {10,22}, {11,28}, {10,30}, {6,29}, {16,30}, {4,38}, {15,29}, {6,21}, {2,25}, {5,40}, {11,38}, {11,33}, {6,31}, {6,40}, {1,38}, {2,34}, {14,33}, {1,17}, {2,36}, {4,22}, {10,38}, {9,29}, {8,19}, {9,32}, {12,17}, {12,20}, {12,36}, {5,29}, {14,40}, {7,39}, {2,39}, {7,32}, {15,26}, {11,22}, {7,25}, {14,24}, {1,22}, {4,21}, {10,31}, {3,20}, {2,20}, {6,18}, {13,18}, {10,40}, {7,26}, {5,18}, {6,24}, {7,17}, {11,30}, {5,24}, {9,37}, {12,28}, {12,25}, {15,37}, {8,22}, {15,34}, {8,35}, {13,28}, {15,20}, {3,27}, {4,28}, {1,33}, {3,29}, {6,23}, {16,38}, {8,37}, {13,36}, {15,36}, {12,26}, {16,22}, {9,22}, {7,31}, {12,33}, {2,17}, {4,36}, {12,27}, {9,40}, {14,17}, {8,32}, {8,21}, {3,19}, {1,24}, {14,18}, {12,19}, {8,40}, {6,26}, {14,34}, {10,32}, {3,21}, {1,25}, {9,30}, {10,39}, {13,27}, {1,35}, {15,21}, {14,25}, {16,17}, {4,37}, {13,26}, {15,18}, {7,23}, {13,19}, {16,36}, {3,30}, {10,17}, {11,27}, {8,38}, {14,32}, {16,20}, {8,24}, {2,31}, {6,34}, {5,27}, {5,26}, {15,28}, {16,39}, {9,39}, {9,38}, {11,19}, {3,38}, {4,20}, {3,28}, {14,35}, {15,23}, {13,37}, {7,24}, {15,39}, {9,24}, {6,39}, {7,33}, {6,37}, {13,34}, {5,19}, {5,21}, {13,20}, {5,35}, {2,18}, {9,31}, {5,37}, {9,21}, {3,36}, {4,39}, {16,28}, {7,40}, {9,23}, {14,27}, {8,29}, {12,18}, {14,26}, {7,18} }; // ET40.85 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 201326592 EdgePairs[40][85]:={ {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {11,36}, {11,35}, {5,34}, {15,24}, {16,26}, {16,33}, {4,26}, {3,22}, {10,37}, {4,30}, {8,30}, {16,40}, {6,17}, {5,38}, {12,32}, {8,28}, {1,32}, {8,33}, {1,27}, {12,38}, {4,19}, {4,31}, {2,19}, {3,35}, {1,21}, {16,18}, {16,25}, {12,35}, {7,36}, {8,25}, {2,28}, {9,35}, {14,28}, {4,23}, {13,29}, {6,22}, {15,25}, {3,18}, {6,29}, {16,30}, {4,38}, {6,21}, {3,34}, {2,25}, {14,23}, {6,40}, {1,38}, {14,33}, {1,17}, {2,36}, {5,22}, {9,29}, {7,20}, {9,32}, {14,21}, {14,36}, {15,32}, {9,26}, {9,27}, {12,20}, {5,29}, {2,37}, {14,40}, {7,39}, {5,25}, {7,32}, {11,22}, {7,25}, {11,31}, {10,28}, {14,24}, {15,27}, {10,29}, {10,31}, {13,22}, {2,20}, {16,37}, {10,40}, {1,29}, {7,30}, {3,39}, {13,31}, {4,35}, {2,32}, {6,33}, {11,23}, {1,23}, {6,24}, {11,30}, {12,28}, {15,37}, {8,22}, {13,25}, {15,20}, {9,20}, {3,27}, {4,28}, {1,33}, {6,23}, {16,38}, {8,37}, {15,36}, {8,26}, {12,26}, {16,22}, {2,17}, {14,17}, {8,21}, {3,19}, {12,23}, {14,22}, {5,31}, {11,24}, {11,39}, {12,19}, {8,40}, {12,40}, {12,30}, {3,23}, {14,34}, {1,39}, {10,32}, {6,28}, {13,27}, {1,35}, {15,21}, {16,34}, {5,39}, {16,21}, {13,26}, {15,18}, {4,40}, {13,19}, {6,36}, {3,30}, {8,34}, {10,17}, {3,24}, {2,29}, {11,27}, {8,38}, {1,26}, {10,36}, {9,17}, {15,33}, {2,40}, {2,31}, {9,33}, {6,34}, {5,27}, {5,26}, {8,18}, {4,18}, {9,39}, {13,38}, {9,38}, {11,19}, {10,19}, {4,20}, {7,27}, {14,35}, {13,37}, {7,24}, {3,31}, {15,39}, {10,20}, {7,33}, {12,31}, {13,34}, {11,34}, {5,19}, {13,39}, {13,17}, {15,30}, {7,37}, {5,37}, {6,35}, {9,21}, {3,36}, {16,28}, {9,23}, {7,21}, {4,32}, {12,18}, {11,18}, {14,29}, {7,18} }; // ET40.86 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 49152 EdgePairs[40][86]:={ {11,20}, {9,28}, {2,33}, {6,32}, {12,29}, {13,21}, {13,40}, {15,24}, {16,26}, {16,33}, {4,26}, {3,22}, {10,37}, {16,27}, {6,17}, {14,39}, {2,23}, {12,22}, {5,38}, {12,32}, {7,38}, {15,31}, {4,29}, {1,32}, {8,33}, {1,27}, {10,23}, {1,40}, {4,19}, {16,19}, {7,22}, {4,31}, {10,33}, {5,20}, {16,18}, {16,25}, {8,25}, {12,34}, {1,30}, {4,23}, {8,27}, {10,22}, {15,25}, {3,18}, {11,28}, {6,29}, {3,34}, {5,40}, {11,38}, {1,17}, {2,36}, {4,22}, {8,19}, {9,32}, {16,24}, {9,26}, {9,27}, {12,36}, {15,40}, {2,37}, {14,30}, {1,31}, {11,22}, {7,25}, {11,31}, {2,35}, {6,30}, {4,33}, {5,23}, {10,29}, {3,20}, {10,21}, {2,20}, {6,18}, {16,37}, {10,40}, {7,30}, {3,39}, {11,21}, {9,25}, {8,36}, {2,32}, {1,23}, {11,29}, {7,17}, {11,30}, {15,35}, {5,24}, {13,23}, {12,28}, {12,25}, {8,35}, {13,28}, {1,28}, {14,37}, {4,28}, {15,17}, {3,29}, {16,38}, {8,37}, {5,28}, {13,36}, {8,26}, {12,26}, {7,31}, {12,33}, {2,17}, {4,36}, {9,40}, {14,17}, {3,19}, {1,24}, {14,18}, {12,23}, {13,24}, {6,27}, {11,39}, {12,19}, {6,26}, {14,34}, {1,39}, {10,32}, {5,36}, {3,21}, {1,25}, {9,30}, {13,27}, {14,20}, {15,21}, {16,34}, {5,39}, {15,18}, {10,35}, {13,19}, {16,36}, {2,21}, {3,30}, {8,34}, {10,17}, {2,29}, {16,35}, {8,38}, {1,26}, {2,22}, {4,34}, {10,36}, {15,22}, {9,17}, {14,32}, {15,33}, {8,24}, {2,40}, {6,34}, {5,27}, {15,38}, {8,18}, {9,39}, {13,38}, {11,19}, {4,25}, {3,38}, {3,28}, {14,35}, {13,37}, {7,24}, {3,31}, {9,24}, {10,20}, {6,39}, {7,33}, {6,37}, {12,31}, {11,34}, {5,19}, {6,20}, {7,35}, {13,39}, {5,21}, {15,30}, {13,20}, {9,31}, {5,37}, {6,35}, {7,40}, {9,23}, {7,21}, {14,27}, {4,32}, {11,18}, {14,29}, {14,26}, {7,18} }; // ET40.87 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3145728 EdgePairs[40][87]:={ {10,25}, {1,20}, {9,28}, {6,32}, {4,27}, {12,29}, {11,35}, {13,40}, {4,24}, {14,19}, {16,26}, {3,22}, {10,37}, {11,25}, {16,27}, {2,23}, {5,38}, {7,38}, {16,31}, {1,32}, {1,27}, {12,38}, {4,19}, {16,19}, {7,22}, {12,39}, {4,31}, {2,19}, {10,33}, {13,35}, {2,26}, {14,31}, {8,39}, {7,34}, {1,21}, {16,18}, {16,25}, {12,35}, {2,28}, {1,30}, {14,28}, {4,23}, {8,31}, {8,27}, {13,29}, {10,22}, {3,18}, {10,30}, {3,17}, {16,30}, {15,29}, {6,21}, {3,34}, {5,40}, {2,25}, {11,38}, {11,33}, {6,40}, {2,34}, {1,17}, {8,19}, {1,18}, {9,32}, {14,36}, {12,17}, {15,32}, {16,24}, {12,36}, {15,40}, {2,38}, {9,19}, {2,37}, {14,30}, {14,40}, {5,25}, {11,22}, {14,24}, {2,35}, {9,34}, {10,21}, {16,37}, {1,29}, {7,30}, {8,17}, {3,39}, {13,31}, {11,21}, {4,35}, {9,25}, {7,26}, {6,33}, {5,18}, {11,23}, {6,24}, {5,30}, {7,17}, {15,35}, {5,24}, {9,37}, {13,23}, {8,22}, {15,34}, {8,35}, {13,28}, {15,20}, {9,20}, {3,27}, {1,33}, {15,17}, {3,29}, {6,23}, {3,26}, {16,38}, {5,28}, {13,36}, {12,26}, {9,22}, {12,33}, {4,36}, {12,27}, {9,40}, {14,17}, {8,32}, {3,19}, {1,24}, {14,18}, {12,23}, {13,24}, {11,39}, {8,23}, {1,39}, {10,32}, {5,36}, {7,29}, {6,28}, {9,30}, {10,39}, {14,20}, {15,21}, {7,28}, {4,37}, {11,26}, {13,26}, {13,19}, {16,36}, {6,36}, {3,30}, {5,33}, {8,34}, {9,18}, {11,37}, {11,27}, {10,27}, {2,22}, {10,34}, {15,22}, {10,18}, {14,32}, {15,33}, {6,25}, {2,40}, {2,31}, {5,26}, {15,28}, {16,39}, {13,38}, {4,25}, {3,38}, {4,20}, {12,24}, {8,20}, {15,23}, {3,31}, {10,20}, {7,33}, {6,37}, {11,34}, {6,20}, {5,21}, {13,17}, {9,31}, {5,37}, {6,35}, {4,39}, {7,40}, {7,21}, {8,29}, {4,32}, {12,21}, {1,36}, {14,29}, {7,18} }; // ET40.88 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4718592 EdgePairs[40][88]:={ {3,33}, {10,25}, {5,17}, {9,28}, {11,36}, {4,27}, {13,21}, {11,35}, {5,34}, {13,40}, {4,24}, {15,24}, {16,26}, {3,40}, {10,37}, {8,30}, {6,17}, {14,39}, {2,23}, {12,22}, {12,32}, {7,38}, {8,28}, {16,31}, {4,29}, {1,27}, {10,23}, {12,38}, {10,26}, {4,19}, {16,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {8,39}, {7,34}, {1,21}, {8,25}, {2,28}, {12,34}, {4,23}, {8,27}, {12,37}, {16,29}, {11,28}, {10,30}, {6,29}, {15,29}, {6,21}, {2,25}, {11,38}, {11,33}, {1,17}, {5,22}, {10,38}, {14,36}, {15,32}, {16,24}, {9,27}, {12,20}, {5,29}, {2,37}, {14,30}, {5,25}, {2,39}, {15,26}, {1,31}, {7,25}, {10,28}, {14,24}, {2,35}, {6,30}, {9,34}, {13,22}, {2,20}, {6,18}, {10,40}, {1,29}, {3,39}, {13,31}, {11,21}, {4,35}, {7,26}, {6,33}, {2,32}, {13,33}, {5,18}, {16,32}, {11,23}, {1,23}, {5,30}, {7,17}, {11,30}, {15,35}, {12,28}, {12,25}, {8,22}, {13,28}, {15,20}, {3,27}, {1,33}, {15,17}, {6,23}, {16,38}, {8,37}, {13,36}, {15,36}, {12,26}, {16,22}, {9,22}, {7,31}, {4,36}, {9,40}, {14,17}, {8,32}, {3,19}, {14,18}, {14,22}, {13,24}, {11,24}, {12,19}, {8,40}, {6,26}, {12,40}, {3,23}, {14,34}, {1,39}, {10,32}, {3,21}, {1,25}, {7,29}, {9,30}, {1,35}, {1,37}, {14,20}, {16,34}, {5,39}, {16,17}, {11,26}, {13,26}, {15,18}, {10,35}, {13,19}, {16,36}, {8,34}, {5,33}, {9,18}, {3,24}, {10,18}, {14,32}, {16,20}, {6,25}, {6,38}, {2,40}, {2,31}, {11,40}, {9,33}, {9,36}, {5,27}, {15,38}, {8,18}, {9,39}, {13,38}, {4,20}, {3,28}, {8,20}, {15,23}, {3,31}, {9,24}, {10,20}, {7,33}, {6,37}, {12,31}, {13,34}, {5,21}, {15,30}, {7,37}, {5,37}, {7,19}, {4,17}, {6,35}, {9,21}, {3,36}, {4,39}, {7,21}, {14,27}, {4,32}, {11,18}, {14,29} }; // ET40.89 // Bipartite(16,24) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 786432 EdgePairs[40][89]:={ {3,33}, {10,25}, {2,24}, {13,32}, {2,33}, {12,29}, {11,35}, {13,40}, {4,24}, {14,19}, {15,24}, {4,26}, {3,22}, {10,37}, {4,30}, {11,25}, {16,27}, {8,30}, {16,40}, {6,17}, {14,39}, {12,22}, {12,32}, {7,38}, {4,29}, {1,27}, {10,26}, {12,39}, {7,22}, {10,33}, {2,27}, {1,19}, {13,35}, {14,31}, {7,34}, {1,21}, {16,18}, {8,25}, {2,28}, {12,34}, {16,23}, {9,35}, {14,28}, {4,23}, {12,37}, {10,22}, {11,28}, {10,30}, {6,29}, {3,17}, {16,30}, {4,38}, {15,29}, {6,21}, {3,34}, {5,40}, {11,38}, {11,33}, {6,31}, {2,34}, {1,17}, {2,36}, {10,38}, {9,29}, {7,20}, {9,32}, {14,36}, {12,17}, {16,24}, {9,27}, {12,20}, {14,40}, {5,25}, {2,39}, {7,32}, {15,26}, {1,31}, {7,25}, {11,31}, {10,28}, {14,24}, {5,23}, {10,21}, {10,40}, {1,29}, {8,17}, {3,39}, {13,31}, {11,21}, {4,35}, {9,25}, {7,26}, {6,33}, {5,18}, {16,32}, {11,23}, {1,23}, {6,24}, {5,30}, {9,37}, {13,23}, {12,25}, {8,22}, {15,34}, {13,28}, {9,20}, {3,27}, {1,33}, {15,17}, {3,29}, {6,23}, {8,37}, {5,28}, {13,36}, {15,36}, {8,26}, {7,31}, {4,36}, {12,27}, {8,32}, {3,19}, {14,22}, {13,24}, {12,19}, {6,26}, {14,34}, {1,39}, {3,21}, {1,25}, {6,19}, {9,30}, {1,35}, {1,37}, {14,20}, {15,21}, {5,39}, {7,28}, {13,26}, {11,26}, {15,18}, {13,19}, {16,36}, {6,36}, {2,21}, {8,34}, {5,33}, {9,18}, {11,37}, {3,24}, {16,35}, {8,38}, {2,22}, {10,34}, {15,22}, {9,17}, {10,18}, {14,32}, {15,33}, {16,20}, {6,38}, {2,40}, {11,40}, {5,27}, {15,38}, {8,18}, {4,18}, {16,39}, {9,39}, {13,38}, {11,19}, {4,20}, {8,20}, {3,31}, {12,31}, {5,21}, {2,30}, {15,30}, {13,20}, {7,37}, {5,35}, {2,18}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {16,28}, {7,40}, {9,23}, {14,27}, {8,29}, {4,32} }; // ET40.90 // Bipartite(20,20) Valencies [12,12] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 5760 EdgePairs[40][90]:={ {10,25}, {2,24}, {10,24}, {6,32}, {17,36}, {18,39}, {4,27}, {13,21}, {11,35}, {5,34}, {4,24}, {15,24}, {16,26}, {16,33}, {3,22}, {3,40}, {10,37}, {18,32}, {4,30}, {11,25}, {16,27}, {8,30}, {14,39}, {2,23}, {12,32}, {7,38}, {8,28}, {16,31}, {15,31}, {4,29}, {1,32}, {8,33}, {1,27}, {3,25}, {10,23}, {12,38}, {19,24}, {20,40}, {1,40}, {17,34}, {14,38}, {7,22}, {4,31}, {10,33}, {20,21}, {7,34}, {1,21}, {12,35}, {17,21}, {18,21}, {8,25}, {2,28}, {1,30}, {5,32}, {17,40}, {14,28}, {8,27}, {13,29}, {16,29}, {18,34}, {10,22}, {6,22}, {18,37}, {10,30}, {16,30}, {19,28}, {4,38}, {15,29}, {6,21}, {3,34}, {5,40}, {2,25}, {14,23}, {11,38}, {2,34}, {14,33}, {2,36}, {5,22}, {10,38}, {19,40}, {17,37}, {9,32}, {14,21}, {14,36}, {19,26}, {16,24}, {9,26}, {9,27}, {12,36}, {5,29}, {2,38}, {19,29}, {14,30}, {7,39}, {2,39}, {17,39}, {15,26}, {17,23}, {1,31}, {11,22}, {7,25}, {11,31}, {14,24}, {20,31}, {17,33}, {1,22}, {15,27}, {20,33}, {6,30}, {4,21}, {9,34}, {13,22}, {1,29}, {3,39}, {13,31}, {7,26}, {6,33}, {2,32}, {13,33}, {11,23}, {1,23}, {5,30}, {15,35}, {9,37}, {13,23}, {12,25}, {15,37}, {18,24}, {20,28}, {8,35}, {19,31}, {3,27}, {14,37}, {18,36}, {4,28}, {18,33}, {3,29}, {16,38}, {13,36}, {8,26}, {17,31}, {12,26}, {9,22}, {12,33}, {13,30}, {4,36}, {20,29}, {12,27}, {9,40}, {8,32}, {8,21}, {14,22}, {11,24}, {8,40}, {12,40}, {12,30}, {3,23}, {1,39}, {10,32}, {18,25}, {17,29}, {20,25}, {7,29}, {6,28}, {18,23}, {9,30}, {13,27}, {5,39}, {16,21}, {20,35}, {7,28}, {11,26}, {13,26}, {4,40}, {10,35}, {16,36}, {2,21}, {5,33}, {20,26}, {11,37}, {3,24}, {11,27}, {16,35}, {18,28}, {8,38}, {2,22}, {10,36}, {10,34}, {15,22}, {19,39}, {6,25}, {6,38}, {20,24}, {11,40}, {9,33}, {9,36}, {20,36}, {6,34}, {5,27}, {15,38}, {19,25}, {5,26}, {15,28}, {4,25}, {3,38}, {12,24}, {3,28}, {7,27}, {14,35}, {15,23}, {13,37}, {3,31}, {15,39}, {17,26}, {6,39}, {12,31}, {6,37}, {11,34}, {19,35}, {7,35}, {13,39}, {5,21}, {2,30}, {19,34}, {7,37}, {9,31}, {1,34}, {19,23}, {5,37}, {6,35}, {17,32}, {16,28}, {18,35}, {7,40}, {9,23}, {19,37}, {20,32}, {8,29}, {4,32}, {1,36} }; // ET40.91 // Bipartite(20,20) Valencies [12,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 978447237120 EdgePairs[40][91]:={ {3,33}, {10,24}, {2,24}, {9,28}, {6,32}, {11,36}, {17,36}, {18,39}, {12,29}, {13,21}, {11,35}, {5,34}, {13,40}, {4,24}, {15,24}, {16,26}, {16,33}, {18,29}, {3,40}, {17,38}, {10,37}, {4,30}, {11,25}, {8,30}, {7,38}, {15,31}, {20,27}, {1,32}, {8,33}, {3,25}, {10,23}, {12,38}, {19,24}, {10,26}, {17,34}, {14,38}, {12,39}, {4,31}, {10,33}, {2,27}, {3,35}, {3,37}, {20,21}, {13,35}, {2,26}, {14,31}, {8,39}, {7,34}, {17,24}, {16,25}, {7,36}, {18,21}, {8,25}, {2,28}, {12,34}, {5,32}, {16,23}, {17,40}, {9,35}, {14,28}, {8,31}, {8,27}, {13,29}, {12,37}, {16,29}, {10,22}, {19,21}, {6,22}, {11,28}, {18,37}, {6,29}, {19,28}, {4,38}, {11,38}, {11,33}, {1,38}, {2,34}, {2,36}, {5,22}, {4,22}, {19,40}, {17,37}, {9,32}, {14,21}, {15,32}, {19,30}, {12,36}, {2,38}, {2,37}, {14,30}, {14,40}, {19,22}, {7,39}, {2,39}, {17,39}, {15,26}, {11,22}, {14,24}, {20,31}, {1,22}, {15,27}, {19,38}, {20,33}, {5,23}, {4,21}, {10,31}, {9,34}, {10,21}, {1,29}, {7,30}, {3,39}, {13,31}, {18,30}, {4,35}, {9,25}, {13,33}, {6,33}, {7,26}, {16,32}, {11,23}, {1,23}, {11,29}, {17,30}, {5,24}, {17,27}, {13,23}, {12,28}, {15,37}, {15,34}, {13,25}, {8,35}, {19,31}, {1,28}, {18,27}, {3,27}, {20,22}, {4,28}, {1,33}, {18,33}, {3,29}, {6,23}, {16,38}, {8,37}, {15,36}, {18,31}, {12,26}, {16,22}, {9,22}, {13,30}, {17,28}, {12,27}, {9,40}, {8,21}, {14,22}, {5,31}, {11,39}, {6,26}, {8,40}, {20,23}, {12,40}, {12,30}, {3,23}, {8,23}, {14,34}, {1,39}, {10,32}, {18,25}, {17,29}, {5,36}, {3,21}, {1,25}, {7,29}, {6,28}, {18,23}, {9,30}, {13,27}, {1,35}, {15,21}, {14,25}, {7,28}, {19,32}, {20,37}, {11,26}, {4,40}, {16,36}, {6,36}, {3,30}, {5,33}, {20,26}, {2,29}, {16,35}, {10,27}, {20,34}, {1,26}, {4,34}, {10,36}, {10,34}, {15,22}, {11,32}, {14,32}, {15,33}, {6,25}, {6,38}, {20,24}, {2,40}, {20,36}, {5,27}, {19,25}, {5,26}, {16,39}, {9,38}, {4,25}, {12,24}, {7,27}, {14,35}, {15,23}, {13,37}, {7,24}, {3,31}, {9,24}, {18,40}, {17,26}, {6,39}, {19,35}, {13,39}, {5,21}, {2,30}, {19,34}, {7,37}, {9,31}, {5,37}, {6,35}, {9,21}, {16,28}, {18,35}, {7,40}, {20,32}, {8,29}, {4,32}, {1,36} }; // ET40.92 // Bipartite(20,20) Valencies [12,12] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 251658240 EdgePairs[40][92]:={ {10,25}, {2,24}, {13,32}, {2,33}, {17,36}, {4,27}, {13,21}, {11,35}, {5,34}, {15,24}, {16,33}, {4,26}, {3,22}, {10,37}, {4,30}, {11,25}, {16,27}, {8,30}, {2,23}, {5,38}, {8,28}, {18,38}, {20,27}, {1,32}, {8,33}, {3,25}, {12,38}, {20,40}, {17,34}, {2,27}, {3,35}, {13,35}, {7,34}, {1,21}, {17,24}, {16,25}, {7,36}, {17,21}, {18,21}, {8,25}, {2,28}, {12,34}, {5,32}, {16,23}, {17,40}, {20,30}, {4,23}, {8,31}, {12,37}, {16,29}, {10,22}, {19,21}, {10,30}, {6,29}, {15,29}, {19,33}, {3,34}, {5,40}, {14,23}, {20,38}, {11,33}, {2,34}, {14,33}, {5,22}, {4,22}, {10,38}, {9,29}, {17,37}, {9,32}, {14,36}, {19,26}, {15,32}, {16,24}, {9,26}, {9,27}, {15,40}, {5,29}, {2,38}, {2,37}, {19,29}, {14,30}, {14,40}, {19,22}, {7,39}, {17,39}, {15,26}, {1,31}, {11,22}, {10,28}, {11,31}, {1,22}, {4,33}, {10,29}, {13,22}, {16,37}, {10,40}, {1,29}, {7,30}, {13,31}, {18,30}, {3,32}, {11,21}, {4,35}, {8,36}, {6,33}, {7,26}, {11,23}, {1,23}, {11,29}, {6,24}, {5,30}, {17,30}, {5,24}, {9,37}, {17,27}, {12,28}, {15,34}, {13,25}, {20,28}, {8,35}, {13,28}, {18,26}, {19,31}, {14,37}, {20,22}, {18,36}, {1,33}, {18,33}, {6,23}, {3,26}, {16,38}, {5,28}, {13,36}, {15,36}, {8,26}, {17,31}, {18,31}, {9,22}, {7,31}, {12,33}, {4,36}, {20,29}, {12,27}, {8,21}, {1,24}, {12,23}, {14,22}, {13,24}, {11,24}, {6,27}, {11,39}, {8,40}, {12,40}, {20,39}, {12,30}, {8,23}, {1,39}, {10,32}, {18,25}, {17,29}, {20,25}, {5,36}, {3,21}, {1,25}, {7,29}, {19,36}, {6,28}, {18,23}, {10,39}, {1,35}, {16,34}, {5,39}, {14,25}, {20,35}, {19,32}, {20,37}, {4,37}, {13,26}, {4,40}, {10,35}, {2,21}, {3,24}, {16,35}, {18,28}, {10,27}, {8,38}, {15,22}, {11,32}, {14,32}, {19,39}, {6,25}, {6,38}, {2,40}, {2,31}, {9,33}, {9,36}, {6,34}, {15,38}, {5,26}, {15,28}, {16,39}, {9,39}, {13,38}, {4,25}, {3,38}, {12,24}, {3,28}, {7,27}, {14,35}, {7,24}, {3,31}, {15,39}, {18,40}, {17,26}, {6,39}, {12,31}, {6,37}, {11,34}, {13,34}, {2,30}, {15,30}, {7,37}, {9,31}, {1,34}, {19,23}, {6,35}, {9,21}, {3,36}, {16,28}, {18,35}, {7,40}, {9,23}, {19,37}, {20,32}, {7,21}, {14,27}, {4,32}, {19,27}, {12,21}, {14,26} }; // ET40.93 // Non-bipartite Valency 12 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 7608405715845120 EdgePairs[40][93]:={ {11,17}, {1,11}, {3,33}, {2,24}, {11,20}, {13,32}, {2,33}, {6,32}, {18,39}, {12,29}, {13,40}, {4,24}, {16,33}, {3,22}, {21,40}, {17,38}, {1,10}, {8,30}, {16,40}, {22,37}, {14,39}, {2,23}, {12,32}, {3,9}, {8,28}, {16,31}, {18,38}, {15,31}, {21,37}, {20,27}, {20,40}, {14,38}, {7,22}, {25,33}, {3,35}, {13,35}, {14,31}, {26,33}, {1,21}, {2,9}, {8,25}, {27,33}, {5,32}, {17,40}, {4,23}, {28,35}, {8,31}, {8,27}, {13,29}, {16,29}, {23,39}, {6,22}, {18,37}, {10,30}, {6,29}, {16,30}, {19,28}, {15,29}, {6,21}, {3,34}, {20,38}, {6,31}, {4,10}, {14,33}, {2,34}, {2,36}, {5,22}, {4,22}, {9,29}, {19,40}, {17,37}, {14,36}, {9,32}, {19,26}, {12,17}, {15,32}, {24,37}, {12,20}, {25,36}, {15,40}, {2,10}, {5,29}, {9,19}, {28,34}, {14,30}, {14,40}, {5,25}, {7,32}, {17,39}, {24,39}, {3,12}, {7,25}, {11,31}, {2,35}, {1,22}, {19,38}, {25,34}, {6,30}, {4,33}, {5,23}, {10,29}, {4,21}, {10,31}, {26,35}, {16,37}, {7,30}, {13,31}, {4,35}, {23,37}, {13,33}, {1,12}, {7,26}, {16,32}, {1,23}, {11,29}, {6,24}, {5,30}, {11,30}, {15,35}, {5,24}, {17,27}, {15,37}, {8,22}, {15,34}, {1,9}, {20,28}, {27,36}, {9,20}, {18,26}, {18,27}, {3,11}, {14,37}, {23,38}, {26,36}, {1,33}, {26,34}, {6,23}, {3,10}, {16,38}, {5,28}, {13,36}, {15,36}, {21,38}, {8,26}, {7,31}, {24,40}, {13,30}, {4,36}, {25,35}, {21,39}, {17,28}, {8,32}, {22,39}, {8,21}, {4,9}, {1,24}, {28,36}, {5,31}, {6,27}, {17,25}, {12,19}, {6,26}, {28,33}, {20,39}, {12,30}, {14,34}, {8,23}, {3,23}, {10,32}, {18,25}, {20,25}, {3,21}, {7,29}, {6,28}, {9,30}, {2,11}, {1,35}, {24,38}, {16,34}, {7,28}, {20,37}, {23,40}, {7,23}, {16,36}, {2,21}, {9,18}, {10,17}, {20,26}, {3,24}, {16,35}, {18,28}, {2,22}, {4,34}, {11,32}, {9,17}, {14,32}, {10,18}, {15,33}, {8,24}, {19,39}, {6,25}, {27,35}, {5,27}, {15,38}, {19,25}, {5,26}, {16,39}, {13,38}, {11,19}, {10,19}, {4,11}, {4,12}, {7,27}, {14,35}, {22,40}, {13,37}, {7,24}, {15,39}, {2,12}, {18,40}, {10,20}, {17,26}, {12,31}, {13,34}, {13,39}, {5,21}, {15,30}, {27,34}, {9,31}, {1,34}, {3,36}, {19,37}, {7,21}, {8,29}, {12,18}, {19,27}, {11,18}, {1,36}, {14,29}, {22,38} }; // ET40.94 // Non-bipartite Valency 12 // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 251658240 EdgePairs[40][94]:={ {2,24}, {1,20}, {5,17}, {13,32}, {9,28}, {6,32}, {17,35}, {17,36}, {18,39}, {12,29}, {13,40}, {4,24}, {16,26}, {16,33}, {4,26}, {3,22}, {21,40}, {17,38}, {10,37}, {4,30}, {11,25}, {16,27}, {8,30}, {6,17}, {14,39}, {2,23}, {12,32}, {8,28}, {18,38}, {4,29}, {1,32}, {1,27}, {3,25}, {12,38}, {20,40}, {12,39}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {21,35}, {5,20}, {13,35}, {14,31}, {1,21}, {16,25}, {8,25}, {24,36}, {2,28}, {12,34}, {1,30}, {5,32}, {17,40}, {9,35}, {14,28}, {4,23}, {8,27}, {12,37}, {16,29}, {15,25}, {3,18}, {18,37}, {10,30}, {3,17}, {16,30}, {15,29}, {19,33}, {20,38}, {11,38}, {11,33}, {6,31}, {14,33}, {4,22}, {10,38}, {9,29}, {8,19}, {19,40}, {7,20}, {17,37}, {9,32}, {14,36}, {9,27}, {24,37}, {22,34}, {14,40}, {22,35}, {5,25}, {17,39}, {15,26}, {1,31}, {23,34}, {7,25}, {11,31}, {10,28}, {23,36}, {1,22}, {15,27}, {19,38}, {20,33}, {5,23}, {10,29}, {4,21}, {10,31}, {2,20}, {6,18}, {16,37}, {10,40}, {1,29}, {7,30}, {8,17}, {13,31}, {3,32}, {23,37}, {23,35}, {7,26}, {2,32}, {13,33}, {5,18}, {1,23}, {11,29}, {6,24}, {7,17}, {11,30}, {15,35}, {5,24}, {9,37}, {12,25}, {15,37}, {8,22}, {15,34}, {13,25}, {13,28}, {1,28}, {24,34}, {23,38}, {18,36}, {3,29}, {6,23}, {3,26}, {16,38}, {21,33}, {5,28}, {13,36}, {15,36}, {24,35}, {8,26}, {12,26}, {12,33}, {21,39}, {9,40}, {22,39}, {8,21}, {1,24}, {5,31}, {6,27}, {11,39}, {6,26}, {22,33}, {12,40}, {20,39}, {12,30}, {3,23}, {14,34}, {10,32}, {3,21}, {6,19}, {7,29}, {6,28}, {9,30}, {10,39}, {13,27}, {24,38}, {16,34}, {14,25}, {7,28}, {20,37}, {13,26}, {11,26}, {10,35}, {16,36}, {2,21}, {3,30}, {11,37}, {3,24}, {2,29}, {16,35}, {10,27}, {20,34}, {2,22}, {23,33}, {10,36}, {11,32}, {14,32}, {15,33}, {19,39}, {6,25}, {2,31}, {11,40}, {9,36}, {5,27}, {15,38}, {5,26}, {8,18}, {4,18}, {15,28}, {9,39}, {9,38}, {4,25}, {8,20}, {7,27}, {14,35}, {22,40}, {21,36}, {3,31}, {21,34}, {18,40}, {12,31}, {11,34}, {13,34}, {5,19}, {6,20}, {13,39}, {2,30}, {15,30}, {19,34}, {22,36}, {9,31}, {7,19}, {24,33}, {4,17}, {16,28}, {18,35}, {19,37}, {7,21}, {14,27}, {8,29}, {4,32}, {14,26}, {7,18} }; // ET40.95 // Non-bipartite Valency 12 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 251658240 EdgePairs[40][95]:={ {33,38}, {10,24}, {9,28}, {25,31}, {17,35}, {17,36}, {4,27}, {13,21}, {7,15}, {14,19}, {8,12}, {15,24}, {18,29}, {23,27}, {32,40}, {4,30}, {11,25}, {16,27}, {25,39}, {26,31}, {12,22}, {7,38}, {3,6}, {4,29}, {1,32}, {3,13}, {32,34}, {8,33}, {24,27}, {23,28}, {10,23}, {12,38}, {19,24}, {1,40}, {2,15}, {4,19}, {35,40}, {21,35}, {5,20}, {3,37}, {2,26}, {29,35}, {7,34}, {16,18}, {11,14}, {17,21}, {18,21}, {30,37}, {12,34}, {8,15}, {16,23}, {9,35}, {3,5}, {12,37}, {10,15}, {8,16}, {23,32}, {4,38}, {19,33}, {2,25}, {5,40}, {7,12}, {31,33}, {11,38}, {31,39}, {11,33}, {6,40}, {1,17}, {1,7}, {1,18}, {7,11}, {3,14}, {14,21}, {16,24}, {9,27}, {27,30}, {34,38}, {27,29}, {29,36}, {22,35}, {2,39}, {11,13}, {26,40}, {1,31}, {23,34}, {11,22}, {10,28}, {20,31}, {15,27}, {12,13}, {20,33}, {21,26}, {3,20}, {13,22}, {24,32}, {10,40}, {28,29}, {8,17}, {2,16}, {18,30}, {29,37}, {11,21}, {7,16}, {2,32}, {30,36}, {30,35}, {7,17}, {17,30}, {32,33}, {8,11}, {21,25}, {27,38}, {28,37}, {12,25}, {32,39}, {36,40}, {29,38}, {13,25}, {5,14}, {19,31}, {4,13}, {24,34}, {3,27}, {18,36}, {4,28}, {15,17}, {3,29}, {22,29}, {8,37}, {12,26}, {31,34}, {12,33}, {25,40}, {2,17}, {4,6}, {9,40}, {22,25}, {25,32}, {3,19}, {14,22}, {20,23}, {33,37}, {21,29}, {1,39}, {21,30}, {12,14}, {17,29}, {5,36}, {2,7}, {1,25}, {6,19}, {6,9}, {26,32}, {36,39}, {1,15}, {6,14}, {10,39}, {4,5}, {14,20}, {14,25}, {5,39}, {16,17}, {19,32}, {28,30}, {4,37}, {11,26}, {13,26}, {15,18}, {22,26}, {10,35}, {13,19}, {6,36}, {3,30}, {8,34}, {11,37}, {10,27}, {8,38}, {20,34}, {1,26}, {23,33}, {10,36}, {1,16}, {4,14}, {18,22}, {30,38}, {20,24}, {2,40}, {2,31}, {9,36}, {6,10}, {5,10}, {31,40}, {8,18}, {15,28}, {28,38}, {9,39}, {5,9}, {27,37}, {3,38}, {1,8}, {26,39}, {4,20}, {5,13}, {3,28}, {15,23}, {21,36}, {23,31}, {9,24}, {2,8}, {6,39}, {35,39}, {7,33}, {11,34}, {5,19}, {6,20}, {17,22}, {9,15}, {19,34}, {6,13}, {7,37}, {13,20}, {5,35}, {2,18}, {22,30}, {22,36}, {19,23}, {24,33}, {6,35}, {9,16}, {16,28}, {18,35}, {9,23}, {20,32}, {24,28}, {24,31}, {34,37}, {12,21}, {14,26}, {7,18}, {10,16} }; // ET40.96 // Non-bipartite Valency 12 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 251658240 EdgePairs[40][96]:={ {33,38}, {1,20}, {9,28}, {25,31}, {17,35}, {6,16}, {17,36}, {4,27}, {13,21}, {29,40}, {5,34}, {14,19}, {8,12}, {16,26}, {15,24}, {23,29}, {3,40}, {23,27}, {10,37}, {18,32}, {11,25}, {25,39}, {26,31}, {21,32}, {7,38}, {3,6}, {3,13}, {32,34}, {24,27}, {23,28}, {32,37}, {2,15}, {12,39}, {35,40}, {4,31}, {2,19}, {1,19}, {21,35}, {5,20}, {20,21}, {2,26}, {24,30}, {29,35}, {22,32}, {17,24}, {16,18}, {16,25}, {11,14}, {7,36}, {12,34}, {1,30}, {16,23}, {14,28}, {9,35}, {20,30}, {29,39}, {3,5}, {10,15}, {10,22}, {19,21}, {15,25}, {3,18}, {3,17}, {19,33}, {2,25}, {5,40}, {7,12}, {31,33}, {11,33}, {6,40}, {1,38}, {1,7}, {10,38}, {7,11}, {3,14}, {14,21}, {16,24}, {19,30}, {9,27}, {27,30}, {34,38}, {2,38}, {31,37}, {2,37}, {27,29}, {29,36}, {8,14}, {19,29}, {19,22}, {22,35}, {11,13}, {17,23}, {15,26}, {26,40}, {23,34}, {7,13}, {10,28}, {12,13}, {20,33}, {21,26}, {13,22}, {10,21}, {2,20}, {30,39}, {28,29}, {1,29}, {8,17}, {2,16}, {3,39}, {3,32}, {8,36}, {6,33}, {30,36}, {11,23}, {30,35}, {7,17}, {32,33}, {8,11}, {21,25}, {9,37}, {27,38}, {28,37}, {12,25}, {8,13}, {36,40}, {32,38}, {18,24}, {8,35}, {13,28}, {4,13}, {24,34}, {7,14}, {3,27}, {20,22}, {18,36}, {4,28}, {15,17}, {21,31}, {8,37}, {17,31}, {18,31}, {12,26}, {9,22}, {31,34}, {12,33}, {25,40}, {6,15}, {4,6}, {20,29}, {22,25}, {25,32}, {12,23}, {14,22}, {11,24}, {11,39}, {30,40}, {33,37}, {12,40}, {12,14}, {2,7}, {1,25}, {6,19}, {6,9}, {26,32}, {36,39}, {1,15}, {18,23}, {22,31}, {13,27}, {4,5}, {14,20}, {1,37}, {16,17}, {5,39}, {28,30}, {11,26}, {15,18}, {22,26}, {4,40}, {10,35}, {13,19}, {5,33}, {2,29}, {10,27}, {8,38}, {20,34}, {1,26}, {23,33}, {10,36}, {1,16}, {4,14}, {11,40}, {9,36}, {6,34}, {6,10}, {5,10}, {8,18}, {4,18}, {28,38}, {5,9}, {9,38}, {27,37}, {1,8}, {24,29}, {26,39}, {12,24}, {3,28}, {15,23}, {21,36}, {3,31}, {2,8}, {6,39}, {5,15}, {35,39}, {11,34}, {5,19}, {6,20}, {7,35}, {9,15}, {2,30}, {19,34}, {13,20}, {7,37}, {22,36}, {24,33}, {4,17}, {17,32}, {9,21}, {9,16}, {4,39}, {18,35}, {14,27}, {4,32}, {24,28}, {31,38}, {34,37}, {23,30}, {7,18}, {10,16}, {5,16} }; // ET40.97 // Non-bipartite Valency 12 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 3840 EdgePairs[40][97]:={ {11,17}, {1,20}, {25,31}, {6,16}, {18,39}, {13,21}, {11,35}, {36,38}, {5,34}, {13,40}, {14,19}, {8,12}, {16,26}, {4,26}, {3,8}, {21,40}, {17,38}, {4,16}, {1,10}, {32,40}, {25,39}, {16,40}, {22,37}, {32,35}, {14,39}, {12,22}, {8,9}, {30,33}, {25,38}, {4,29}, {3,13}, {8,33}, {32,37}, {3,25}, {3,15}, {10,23}, {20,40}, {2,15}, {4,19}, {35,40}, {2,19}, {2,27}, {21,35}, {25,29}, {20,21}, {26,33}, {7,34}, {17,24}, {2,9}, {17,21}, {8,25}, {27,33}, {30,37}, {24,36}, {1,30}, {8,15}, {17,40}, {14,28}, {20,30}, {29,39}, {8,27}, {3,5}, {23,39}, {6,22}, {15,25}, {3,18}, {18,37}, {10,30}, {14,23}, {2,25}, {20,38}, {31,39}, {1,7}, {9,29}, {1,18}, {7,11}, {9,32}, {16,24}, {12,20}, {27,30}, {5,11}, {25,36}, {2,5}, {12,36}, {34,38}, {9,19}, {28,34}, {29,36}, {19,29}, {19,22}, {5,25}, {26,40}, {1,31}, {3,12}, {23,34}, {27,40}, {20,31}, {15,27}, {6,12}, {25,34}, {5,23}, {10,31}, {3,20}, {15,19}, {10,21}, {2,13}, {26,35}, {29,34}, {28,29}, {26,37}, {18,30}, {11,21}, {23,37}, {7,16}, {23,35}, {8,36}, {1,12}, {6,33}, {2,32}, {7,26}, {11,23}, {30,35}, {11,29}, {6,24}, {32,33}, {15,37}, {8,13}, {8,22}, {33,40}, {29,38}, {13,25}, {1,28}, {7,14}, {3,27}, {14,37}, {4,7}, {4,28}, {31,36}, {3,10}, {16,38}, {21,38}, {18,31}, {9,22}, {31,34}, {12,33}, {24,40}, {2,17}, {4,6}, {22,39}, {4,9}, {14,18}, {28,36}, {14,22}, {13,24}, {30,40}, {6,26}, {22,33}, {33,37}, {12,30}, {17,29}, {34,39}, {6,9}, {35,37}, {26,32}, {36,39}, {27,32}, {6,28}, {18,23}, {6,14}, {2,11}, {13,27}, {24,38}, {16,21}, {16,17}, {7,28}, {19,32}, {15,18}, {28,39}, {10,35}, {7,23}, {6,36}, {3,30}, {2,29}, {1,26}, {1,16}, {4,14}, {15,22}, {10,34}, {18,22}, {11,32}, {16,20}, {10,18}, {9,17}, {8,24}, {19,39}, {20,24}, {9,33}, {9,36}, {27,35}, {5,27}, {5,10}, {28,38}, {13,38}, {11,19}, {27,37}, {4,11}, {5,13}, {12,24}, {7,10}, {28,31}, {15,23}, {3,31}, {15,39}, {21,34}, {9,24}, {1,14}, {2,8}, {10,20}, {1,6}, {5,15}, {12,31}, {11,34}, {7,35}, {5,21}, {13,17}, {13,20}, {5,35}, {22,36}, {19,23}, {24,33}, {4,17}, {17,32}, {16,28}, {19,37}, {7,21}, {4,32}, {12,18}, {31,38}, {14,26}, {26,30} }; // ET40.98 // Non-bipartite Valency 12 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 3840 EdgePairs[40][98]:={ {1,11}, {33,38}, {10,24}, {11,20}, {11,36}, {4,27}, {12,29}, {7,15}, {29,40}, {15,24}, {18,29}, {18,32}, {33,39}, {4,30}, {16,27}, {26,31}, {1,13}, {12,32}, {3,9}, {8,28}, {29,33}, {18,38}, {3,6}, {21,37}, {1,32}, {32,34}, {1,27}, {19,24}, {16,19}, {14,38}, {7,22}, {4,31}, {25,33}, {10,33}, {1,19}, {28,32}, {2,26}, {25,30}, {29,35}, {34,40}, {16,18}, {16,25}, {12,35}, {7,36}, {18,21}, {8,10}, {2,28}, {12,34}, {2,14}, {16,23}, {6,11}, {9,35}, {28,35}, {10,22}, {19,21}, {32,36}, {3,17}, {3,7}, {8,16}, {6,21}, {7,12}, {31,33}, {11,33}, {36,37}, {4,10}, {1,17}, {5,22}, {19,40}, {35,38}, {3,14}, {17,37}, {14,21}, {12,17}, {4,8}, {19,30}, {24,37}, {22,34}, {1,5}, {31,35}, {15,40}, {2,10}, {31,37}, {27,29}, {26,29}, {8,14}, {14,40}, {22,35}, {17,39}, {17,23}, {15,26}, {24,39}, {11,22}, {7,13}, {7,25}, {14,24}, {11,31}, {30,34}, {23,36}, {19,38}, {10,29}, {27,31}, {9,34}, {13,22}, {2,20}, {13,18}, {30,39}, {16,37}, {1,29}, {2,16}, {3,32}, {29,37}, {30,36}, {2,6}, {17,30}, {8,11}, {11,30}, {5,24}, {27,38}, {28,37}, {13,23}, {32,39}, {36,40}, {1,9}, {32,38}, {18,24}, {26,38}, {27,36}, {8,35}, {13,28}, {15,20}, {5,14}, {9,20}, {19,31}, {4,15}, {4,13}, {24,34}, {3,11}, {20,22}, {23,38}, {26,36}, {15,17}, {26,34}, {3,29}, {6,23}, {3,26}, {21,33}, {5,28}, {24,35}, {8,26}, {17,31}, {25,37}, {16,22}, {25,40}, {6,15}, {25,35}, {21,39}, {20,29}, {28,40}, {5,12}, {25,32}, {14,17}, {8,21}, {3,19}, {12,23}, {6,27}, {11,24}, {12,19}, {28,33}, {20,23}, {20,39}, {8,23}, {10,32}, {5,36}, {2,7}, {1,25}, {1,15}, {9,30}, {4,5}, {14,20}, {15,21}, {14,25}, {28,30}, {20,37}, {3,16}, {13,26}, {23,40}, {13,19}, {8,34}, {5,33}, {9,18}, {10,17}, {23,33}, {10,36}, {6,25}, {30,38}, {7,9}, {2,31}, {6,34}, {6,10}, {15,38}, {31,40}, {5,26}, {15,28}, {16,39}, {4,18}, {5,9}, {10,19}, {4,25}, {1,8}, {26,39}, {4,12}, {4,20}, {3,28}, {7,27}, {22,40}, {13,37}, {27,39}, {21,36}, {7,24}, {2,12}, {18,40}, {35,39}, {7,33}, {17,22}, {13,39}, {2,30}, {6,13}, {2,18}, {27,34}, {9,31}, {6,35}, {9,21}, {9,23}, {20,32}, {14,27}, {11,18}, {34,37}, {12,21}, {22,38}, {5,16} }; // ET40.99 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 51840 EdgePairs[40][99]:={ {33,38}, {10,25}, {10,24}, {11,36}, {17,36}, {4,27}, {11,35}, {8,12}, {15,24}, {18,29}, {23,29}, {3,8}, {3,40}, {23,27}, {10,37}, {32,40}, {33,39}, {4,30}, {11,25}, {16,27}, {25,39}, {6,17}, {32,35}, {12,22}, {5,38}, {30,33}, {4,29}, {1,32}, {3,13}, {8,33}, {24,27}, {1,27}, {23,28}, {32,37}, {1,40}, {16,19}, {4,19}, {12,39}, {10,33}, {25,29}, {5,20}, {20,21}, {2,26}, {34,40}, {8,39}, {7,34}, {17,24}, {16,18}, {16,25}, {11,14}, {17,21}, {30,37}, {24,36}, {2,28}, {12,34}, {8,15}, {6,11}, {14,28}, {9,35}, {29,39}, {10,15}, {18,34}, {10,22}, {11,28}, {3,7}, {23,32}, {19,33}, {14,23}, {5,40}, {11,38}, {31,39}, {6,40}, {36,37}, {1,38}, {1,17}, {1,7}, {10,38}, {1,18}, {35,38}, {16,24}, {9,26}, {9,27}, {27,30}, {2,5}, {2,37}, {29,36}, {26,29}, {19,22}, {22,35}, {7,39}, {2,39}, {15,26}, {1,31}, {23,34}, {10,28}, {20,31}, {17,33}, {6,12}, {12,16}, {21,26}, {3,20}, {27,31}, {13,22}, {15,19}, {24,32}, {2,13}, {29,34}, {2,16}, {26,37}, {18,30}, {11,21}, {7,16}, {8,36}, {2,32}, {5,18}, {11,23}, {30,35}, {17,30}, {7,17}, {2,6}, {32,33}, {8,11}, {21,25}, {27,38}, {13,23}, {8,13}, {36,40}, {29,38}, {13,25}, {26,38}, {5,14}, {19,31}, {4,15}, {7,14}, {21,31}, {10,13}, {31,36}, {3,29}, {3,26}, {8,37}, {21,33}, {24,35}, {12,26}, {31,34}, {12,33}, {25,40}, {6,15}, {2,17}, {4,6}, {28,40}, {9,13}, {12,27}, {9,40}, {22,25}, {25,32}, {14,17}, {3,19}, {14,22}, {30,40}, {12,40}, {21,30}, {12,14}, {17,29}, {5,36}, {1,25}, {6,19}, {26,32}, {19,36}, {1,15}, {18,23}, {22,31}, {13,27}, {4,5}, {14,20}, {15,21}, {16,21}, {20,35}, {19,32}, {28,30}, {3,16}, {4,37}, {15,18}, {22,26}, {28,39}, {11,16}, {3,30}, {5,33}, {11,37}, {20,34}, {23,33}, {4,14}, {10,34}, {18,22}, {7,9}, {6,38}, {20,24}, {2,31}, {9,36}, {6,34}, {5,10}, {8,18}, {15,28}, {9,39}, {5,9}, {27,37}, {4,25}, {3,38}, {1,8}, {24,29}, {4,20}, {12,24}, {8,20}, {3,28}, {7,10}, {28,31}, {21,34}, {1,14}, {35,39}, {7,35}, {9,15}, {13,17}, {6,13}, {7,37}, {13,20}, {2,18}, {22,30}, {22,36}, {19,23}, {7,19}, {6,35}, {9,21}, {4,39}, {18,35}, {9,23}, {20,32}, {24,28}, {31,38}, {34,37}, {14,26}, {5,16} }; // ET40.100 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1920 EdgePairs[40][100]:={ {5,17}, {1,20}, {9,28}, {25,31}, {6,16}, {17,35}, {13,21}, {7,15}, {29,40}, {36,38}, {5,34}, {14,19}, {16,26}, {4,26}, {4,16}, {18,32}, {26,31}, {21,32}, {1,13}, {8,9}, {7,38}, {25,38}, {29,33}, {3,6}, {32,34}, {3,25}, {3,15}, {12,38}, {10,23}, {19,24}, {10,26}, {17,34}, {2,15}, {35,40}, {4,31}, {2,19}, {1,19}, {2,27}, {28,32}, {21,35}, {3,37}, {24,30}, {25,30}, {29,35}, {22,32}, {12,35}, {7,36}, {18,21}, {8,10}, {2,14}, {1,30}, {16,23}, {20,30}, {3,5}, {12,37}, {19,21}, {15,25}, {3,18}, {32,36}, {3,17}, {8,16}, {4,38}, {2,25}, {7,12}, {31,33}, {11,33}, {8,19}, {7,11}, {7,20}, {3,14}, {14,21}, {4,8}, {19,30}, {22,34}, {1,5}, {5,11}, {31,35}, {12,36}, {34,38}, {2,38}, {31,37}, {27,29}, {8,14}, {19,29}, {11,15}, {11,13}, {17,23}, {26,40}, {11,22}, {27,40}, {7,13}, {9,14}, {14,24}, {22,27}, {30,34}, {23,36}, {24,25}, {15,27}, {21,27}, {12,13}, {20,33}, {23,26}, {9,34}, {10,21}, {2,20}, {6,18}, {13,18}, {30,39}, {10,40}, {28,29}, {1,29}, {24,26}, {8,17}, {3,39}, {3,32}, {29,37}, {9,25}, {23,35}, {6,33}, {30,36}, {9,37}, {28,37}, {12,28}, {12,25}, {23,25}, {32,39}, {33,40}, {32,38}, {18,24}, {8,35}, {13,28}, {15,20}, {1,28}, {4,13}, {24,34}, {3,27}, {20,22}, {4,7}, {18,36}, {4,28}, {15,17}, {18,33}, {22,29}, {17,31}, {18,31}, {25,37}, {16,22}, {9,22}, {20,29}, {5,12}, {14,18}, {12,23}, {13,24}, {11,24}, {11,39}, {8,40}, {22,33}, {20,23}, {33,37}, {21,29}, {1,39}, {2,7}, {34,39}, {22,28}, {6,9}, {35,37}, {36,39}, {27,32}, {12,15}, {6,14}, {10,39}, {1,37}, {14,25}, {5,39}, {16,17}, {13,26}, {11,26}, {4,40}, {10,35}, {13,19}, {6,36}, {8,34}, {2,29}, {11,27}, {10,27}, {8,38}, {1,26}, {10,36}, {1,16}, {15,22}, {16,20}, {30,38}, {2,40}, {11,40}, {9,33}, {20,36}, {6,10}, {31,40}, {4,18}, {28,38}, {9,38}, {26,39}, {5,13}, {15,23}, {27,39}, {21,36}, {23,31}, {3,31}, {9,24}, {2,8}, {1,6}, {6,39}, {5,15}, {7,33}, {6,37}, {11,34}, {10,14}, {19,35}, {5,19}, {6,20}, {17,22}, {2,30}, {19,34}, {5,35}, {5,37}, {21,28}, {24,33}, {4,17}, {17,32}, {9,16}, {16,28}, {7,40}, {14,27}, {4,32}, {24,31}, {12,21}, {23,30}, {26,30}, {7,18}, {10,16} }; // ET40.101 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 51840 EdgePairs[40][101]:={ {11,17}, {19,20}, {9,28}, {18,39}, {5,34}, {14,19}, {8,12}, {16,33}, {4,26}, {23,29}, {3,40}, {23,27}, {18,32}, {33,39}, {11,25}, {25,39}, {16,40}, {2,23}, {1,13}, {5,38}, {30,33}, {7,38}, {3,9}, {8,28}, {25,38}, {21,37}, {4,29}, {20,27}, {1,32}, {3,13}, {32,34}, {34,36}, {24,27}, {1,27}, {32,37}, {3,15}, {10,23}, {17,34}, {35,40}, {4,31}, {7,8}, {20,21}, {8,39}, {17,24}, {2,9}, {11,14}, {18,21}, {6,7}, {24,36}, {2,14}, {1,30}, {8,15}, {9,35}, {20,30}, {28,35}, {13,29}, {10,22}, {19,21}, {15,16}, {23,39}, {6,22}, {3,18}, {32,36}, {39,40}, {3,7}, {16,30}, {4,38}, {19,33}, {6,21}, {2,25}, {6,40}, {1,38}, {14,33}, {2,34}, {10,38}, {8,19}, {27,28}, {35,38}, {7,20}, {9,32}, {9,26}, {9,27}, {24,37}, {5,11}, {31,35}, {12,36}, {15,40}, {5,29}, {34,38}, {31,37}, {2,37}, {29,36}, {19,29}, {19,22}, {7,39}, {15,26}, {10,28}, {20,31}, {15,27}, {12,13}, {21,26}, {10,31}, {37,40}, {10,21}, {6,18}, {28,29}, {7,30}, {24,26}, {8,17}, {2,16}, {13,31}, {26,37}, {3,32}, {29,37}, {23,37}, {9,25}, {14,15}, {5,18}, {11,29}, {5,30}, {2,6}, {11,30}, {21,25}, {17,27}, {12,25}, {8,22}, {36,40}, {15,20}, {17,18}, {4,15}, {7,14}, {23,38}, {4,28}, {1,33}, {10,13}, {26,34}, {10,12}, {18,33}, {3,29}, {8,37}, {17,31}, {18,31}, {9,22}, {7,31}, {12,33}, {25,40}, {2,17}, {4,36}, {33,35}, {5,12}, {8,32}, {3,19}, {22,23}, {28,36}, {6,27}, {11,24}, {11,39}, {20,23}, {10,32}, {20,25}, {17,19}, {2,7}, {29,30}, {34,39}, {1,25}, {9,12}, {35,37}, {12,15}, {18,23}, {6,14}, {9,30}, {10,11}, {13,27}, {24,38}, {33,36}, {1,37}, {16,34}, {16,17}, {16,21}, {7,28}, {3,16}, {13,26}, {22,26}, {28,39}, {13,19}, {6,36}, {9,18}, {3,24}, {2,29}, {11,27}, {20,34}, {23,33}, {1,16}, {4,14}, {5,8}, {11,32}, {14,32}, {11,40}, {20,36}, {27,35}, {31,40}, {19,25}, {4,18}, {4,25}, {1,4}, {3,38}, {1,8}, {26,39}, {12,24}, {15,23}, {14,35}, {22,40}, {5,6}, {7,24}, {2,12}, {1,6}, {30,31}, {5,15}, {12,31}, {13,34}, {10,14}, {19,35}, {13,39}, {17,22}, {21,24}, {5,21}, {6,13}, {5,35}, {22,30}, {22,36}, {21,28}, {24,33}, {4,17}, {16,28}, {20,32}, {34,35}, {22,38}, {14,26}, {26,30}, {10,16} }; // ET40.102 // Bipartite(5,35) Valencies [14,2] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 32520160641024000000 EdgePairs[40][102]:={ {5,12}, {1,26}, {4,8}, {4,13}, {4,23}, {5,32}, {1,14}, {2,37}, {1,24}, {5,37}, {5,24}, {2,32}, {2,30}, {1,29}, {5,29}, {2,10}, {5,27}, {1,39}, {4,10}, {3,21}, {2,40}, {1,6}, {1,36}, {4,40}, {3,33}, {3,38}, {3,8}, {3,23}, {1,31}, {2,12}, {4,30}, {5,9}, {5,7}, {4,18}, {4,33}, {2,7}, {3,11}, {3,16}, {3,28}, {2,20}, {1,16}, {4,38}, {5,19}, {1,21}, {4,20}, {5,17}, {2,15}, {3,18}, {3,31}, {3,26}, {4,15}, {4,28}, {5,39}, {2,27}, {3,6}, {4,25}, {5,14}, {2,17}, {3,13}, {5,34}, {2,35}, {1,19}, {1,9}, {2,25}, {4,35}, {1,34}, {1,11}, {5,22}, {2,22}, {3,36} }; // ET40.103 // Bipartite(12,28) Valencies [14,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6689861617582080000 EdgePairs[40][103]:={ {10,25}, {1,20}, {5,17}, {11,20}, {9,28}, {2,33}, {11,36}, {4,27}, {7,15}, {11,35}, {4,26}, {3,40}, {10,37}, {4,30}, {8,30}, {6,17}, {1,13}, {12,22}, {1,32}, {3,15}, {12,38}, {1,40}, {10,26}, {4,19}, {12,39}, {4,31}, {10,33}, {3,35}, {5,20}, {2,26}, {8,39}, {1,21}, {12,35}, {7,36}, {12,34}, {2,14}, {5,32}, {8,15}, {4,23}, {8,31}, {8,27}, {10,22}, {6,22}, {11,28}, {10,30}, {6,29}, {4,38}, {6,21}, {2,25}, {5,40}, {2,34}, {1,17}, {4,22}, {10,38}, {9,29}, {8,19}, {7,20}, {9,32}, {5,29}, {2,38}, {2,37}, {8,14}, {7,39}, {5,25}, {11,15}, {7,32}, {11,31}, {6,30}, {10,29}, {3,20}, {10,21}, {2,13}, {6,18}, {1,29}, {3,39}, {3,32}, {4,35}, {9,25}, {7,16}, {6,33}, {11,23}, {5,24}, {9,37}, {8,22}, {8,35}, {9,20}, {4,15}, {1,28}, {3,27}, {1,33}, {10,13}, {5,28}, {8,26}, {12,26}, {7,31}, {2,17}, {9,13}, {12,27}, {9,40}, {3,19}, {1,24}, {12,23}, {11,24}, {11,39}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {12,14}, {5,36}, {1,25}, {12,15}, {6,14}, {1,37}, {7,28}, {3,16}, {11,16}, {7,23}, {2,21}, {8,34}, {5,33}, {10,17}, {3,24}, {2,29}, {11,27}, {8,38}, {2,22}, {4,34}, {1,16}, {4,14}, {10,34}, {11,32}, {9,17}, {10,18}, {6,25}, {6,38}, {11,40}, {9,33}, {9,36}, {6,34}, {8,18}, {4,18}, {11,19}, {5,13}, {3,28}, {7,27}, {7,24}, {3,31}, {9,24}, {6,37}, {12,31}, {10,14}, {7,35}, {5,21}, {2,30}, {6,13}, {2,18}, {5,37}, {7,19}, {9,21}, {9,16}, {3,36}, {4,39}, {7,40}, {12,18}, {1,36}, {5,16} }; // ET40.104 // Bipartite(12,28) Valencies [14,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 991090610012160000 EdgePairs[40][104]:={ {3,33}, {10,24}, {11,20}, {6,32}, {6,16}, {11,36}, {12,29}, {11,35}, {4,24}, {4,26}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {12,32}, {7,38}, {3,13}, {3,25}, {3,15}, {10,26}, {2,15}, {7,22}, {2,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {8,39}, {7,34}, {1,21}, {2,14}, {1,30}, {5,32}, {8,15}, {9,35}, {8,31}, {8,27}, {12,37}, {10,22}, {11,28}, {10,30}, {6,29}, {3,17}, {4,38}, {6,21}, {5,40}, {6,40}, {1,38}, {2,34}, {1,17}, {4,22}, {10,38}, {9,29}, {8,19}, {1,18}, {12,17}, {9,27}, {12,20}, {12,36}, {2,38}, {9,19}, {8,14}, {2,39}, {11,15}, {7,13}, {7,25}, {11,31}, {10,28}, {2,35}, {1,22}, {12,13}, {12,16}, {5,23}, {10,40}, {1,29}, {7,30}, {3,39}, {9,25}, {7,26}, {6,33}, {11,23}, {6,24}, {7,17}, {5,24}, {9,37}, {12,28}, {12,25}, {8,22}, {8,35}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {5,28}, {8,26}, {12,33}, {4,36}, {9,13}, {3,19}, {5,31}, {11,24}, {11,39}, {12,40}, {3,23}, {8,23}, {10,32}, {5,36}, {3,21}, {1,25}, {7,29}, {6,28}, {1,37}, {5,39}, {4,40}, {11,16}, {6,36}, {8,34}, {11,27}, {8,38}, {1,26}, {2,22}, {4,34}, {10,36}, {4,14}, {10,34}, {11,32}, {9,17}, {10,18}, {6,25}, {2,31}, {11,40}, {9,33}, {5,27}, {8,18}, {4,18}, {9,39}, {11,19}, {4,20}, {12,24}, {3,31}, {1,14}, {10,20}, {5,15}, {7,33}, {6,37}, {10,14}, {5,19}, {6,20}, {9,15}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {9,31}, {1,34}, {9,21}, {9,23}, {7,21}, {4,32}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET40.105 // Non-bipartite Valency 14 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 403200 EdgePairs[40][105]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {31,39}, {14,36}, {5,7}, {9,32}, {35,38}, {5,38}, {5,22}, {10,18}, {9,17}, {19,26}, {25,37}, {3,26}, {8,26}, {22,40}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {24,32}, {1,19}, {24,36}, {3,20}, {3,21}, {19,37}, {20,37}, {21,28}, {16,28}, {5,32}, {7,30}, {8,31}, {4,37}, {6,14}, {19,21}, {13,40}, {17,35}, {11,29}, {9,11}, {6,29}, {20,38}, {8,16}, {10,17}, {2,34}, {26,38}, {19,31}, {2,25}, {15,32}, {8,30}, {1,9}, {4,16}, {28,31}, {26,39}, {12,20}, {17,39}, {21,38}, {23,31}, {1,13}, {13,30}, {3,10}, {2,10}, {19,22}, {23,36}, {6,39}, {11,39}, {12,40}, {1,24}, {2,15}, {5,37}, {13,20}, {18,35}, {24,31}, {6,18}, {1,29}, {16,34}, {35,37}, {24,26}, {31,38}, {11,18}, {34,37}, {13,26}, {29,31}, {6,24}, {13,16}, {2,29}, {1,38}, {14,32}, {7,15}, {32,39}, {24,37}, {22,34}, {9,36}, {6,34}, {18,26}, {4,22}, {30,38}, {18,36}, {29,32}, {1,18}, {5,27}, {7,14}, {15,28}, {5,28}, {4,7}, {2,39}, {27,39}, {10,12}, {28,40}, {27,40}, {12,24}, {3,31}, {25,33}, {1,39}, {5,12}, {2,30}, {3,36}, {4,21}, {17,29}, {7,19}, {4,32}, {19,27}, {8,15}, {23,40}, {16,29}, {3,30}, {3,16}, {2,24}, {11,23}, {15,37}, {10,38}, {11,33}, {13,25}, {14,21}, {9,26}, {32,40}, {29,36}, {13,36}, {20,22}, {10,13}, {22,29}, {25,32}, {15,23}, {9,22}, {4,11}, {3,25}, {11,34}, {34,36}, {7,35}, {22,30}, {27,34}, {12,30}, {7,34}, {11,24}, {9,31}, {18,25}, {6,13}, {23,35}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,12}, {14,27}, {17,30}, {10,22}, {12,29}, {12,25}, {33,40}, {27,35}, {14,37}, {5,8}, {18,31}, {25,38}, {6,23}, {15,17}, {7,39}, {4,36}, {21,39}, {30,32}, {24,27}, {22,39}, {7,24}, {10,28}, {17,25}, {2,19}, {7,40}, {5,23}, {20,32}, {18,21}, {9,21}, {7,29}, {18,30}, {29,37}, {14,16}, {8,36}, {14,26}, {4,27}, {8,11}, {16,38}, {20,28}, {21,33}, {1,33}, {3,11}, {21,34}, {11,19}, {12,39}, {30,33}, {1,8}, {4,12}, {20,27}, {28,36}, {17,34}, {3,6}, {20,33}, {3,15}, {7,25}, {1,14}, {1,34}, {13,35}, {21,29}, {17,24}, {20,23}, {17,40}, {12,34}, {19,36}, {28,35}, {23,30}, {6,28}, {16,23}, {19,32}, {11,28}, {5,18}, {1,23}, {15,18}, {10,27}, {5,17}, {16,33}, {3,40}, {8,35}, {2,40}, {15,22}, {4,26}, {16,39}, {1,28}, {26,34}, {16,24}, {7,20}, {9,27}, {22,35}, {18,40}, {8,20}, {5,13}, {25,27}, {10,23}, {26,33}, {4,6}, {14,22}, {14,17}, {25,28}, {10,32}, {12,35}, {12,19}, {23,26}, {8,25}, {2,9}, {30,37}, {6,33}, {2,14}, {33,36}, {5,33}, {11,38}, {9,37} }; // ET40.106 // Bipartite(10,30) Valencies [15,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 179159040000000 EdgePairs[40][106]:={ {1,11}, {2,24}, {1,20}, {5,17}, {9,28}, {6,32}, {4,27}, {7,15}, {4,24}, {8,12}, {3,22}, {3,40}, {4,30}, {8,30}, {1,13}, {5,38}, {8,28}, {4,29}, {1,32}, {3,13}, {3,25}, {10,23}, {10,33}, {1,19}, {3,35}, {5,20}, {3,37}, {2,26}, {7,36}, {8,25}, {2,28}, {2,14}, {5,32}, {4,23}, {8,31}, {10,15}, {10,22}, {3,17}, {8,16}, {6,21}, {3,34}, {7,12}, {6,31}, {1,38}, {2,34}, {1,17}, {2,36}, {8,19}, {9,32}, {9,26}, {9,27}, {5,11}, {5,29}, {2,38}, {7,39}, {1,31}, {7,13}, {9,14}, {7,25}, {10,28}, {4,33}, {5,23}, {10,29}, {4,21}, {9,34}, {10,21}, {2,20}, {10,40}, {1,29}, {7,30}, {2,16}, {4,35}, {8,36}, {6,33}, {2,32}, {5,18}, {1,23}, {5,30}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {3,11}, {3,29}, {8,37}, {9,22}, {7,31}, {6,15}, {4,36}, {9,40}, {5,12}, {3,19}, {6,27}, {6,26}, {8,40}, {3,23}, {5,36}, {1,25}, {6,19}, {6,14}, {10,11}, {10,39}, {1,35}, {1,37}, {3,16}, {10,35}, {8,34}, {10,17}, {10,27}, {1,26}, {2,22}, {10,34}, {8,24}, {6,25}, {6,38}, {2,40}, {9,33}, {5,26}, {8,18}, {4,18}, {9,39}, {9,38}, {4,11}, {4,12}, {3,28}, {7,27}, {7,24}, {3,31}, {2,12}, {1,14}, {6,39}, {7,33}, {6,37}, {6,20}, {9,15}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {7,19}, {4,17}, {9,21}, {9,16}, {4,39}, {7,21}, {7,18}, {10,16} }; // ET40.107 // Bipartite(20,20) Valencies [15,15] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 2063912140800000000 EdgePairs[40][107]:={ {13,21}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {4,28}, {3,26}, {13,37}, {1,40}, {14,38}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {1,21}, {16,37}, {3,39}, {20,37}, {16,28}, {5,32}, {7,30}, {8,31}, {4,40}, {4,37}, {14,29}, {16,21}, {13,40}, {2,33}, {11,35}, {6,29}, {11,27}, {19,40}, {2,34}, {12,28}, {19,31}, {2,25}, {4,24}, {15,32}, {9,33}, {8,37}, {20,24}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {20,35}, {1,36}, {1,29}, {12,37}, {10,35}, {18,39}, {4,23}, {13,26}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {20,36}, {16,40}, {18,29}, {9,36}, {6,34}, {9,29}, {18,26}, {18,33}, {3,38}, {15,28}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {19,38}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {16,29}, {11,36}, {3,30}, {11,23}, {3,24}, {14,33}, {14,23}, {10,38}, {15,34}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {9,38}, {14,21}, {9,26}, {18,38}, {13,36}, {2,23}, {15,23}, {9,22}, {20,31}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {10,29}, {18,25}, {13,22}, {1,25}, {9,30}, {3,32}, {14,27}, {7,28}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {16,31}, {6,23}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {17,22}, {17,25}, {19,34}, {7,40}, {20,32}, {2,26}, {18,21}, {10,21}, {9,21}, {18,30}, {8,29}, {8,36}, {8,27}, {16,36}, {13,32}, {14,26}, {11,30}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {18,27}, {1,33}, {20,28}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {19,35}, {13,34}, {7,22}, {6,26}, {1,34}, {5,21}, {17,24}, {17,40}, {20,23}, {17,21}, {19,36}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,25}, {7,26}, {11,28}, {16,35}, {10,27}, {10,34}, {16,33}, {3,40}, {8,35}, {6,21}, {15,22}, {17,37}, {16,39}, {13,28}, {1,28}, {16,24}, {3,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {20,40}, {5,25}, {10,23}, {15,26}, {8,39}, {14,22}, {5,36}, {9,34}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {20,21}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {18,34}, {11,26}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37} }; // ET40.108 // Bipartite(8,32) Valencies [16,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 338292261550817280000 EdgePairs[40][108]:={ {4,35}, {7,19}, {5,32}, {7,39}, {3,15}, {8,39}, {8,31}, {2,38}, {6,10}, {6,18}, {4,14}, {2,22}, {6,14}, {4,27}, {6,17}, {7,40}, {7,24}, {1,40}, {1,25}, {6,13}, {2,37}, {5,24}, {3,32}, {1,9}, {2,33}, {6,25}, {7,31}, {7,27}, {1,32}, {7,15}, {7,23}, {5,13}, {8,34}, {3,31}, {6,34}, {2,18}, {6,9}, {4,26}, {8,14}, {5,9}, {6,22}, {7,11}, {5,21}, {2,29}, {3,19}, {5,37}, {1,29}, {8,22}, {7,28}, {8,15}, {2,14}, {5,33}, {3,11}, {2,10}, {4,39}, {1,36}, {1,17}, {6,33}, {3,40}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {2,13}, {1,12}, {7,20}, {8,35}, {8,26}, {3,23}, {6,37}, {5,29}, {4,31}, {3,27}, {2,34}, {4,30}, {6,26}, {8,11}, {5,28}, {4,15}, {2,9}, {8,19}, {6,29}, {7,35}, {4,38}, {4,11}, {3,35}, {2,21}, {6,30}, {8,27}, {6,38}, {8,38}, {5,20}, {4,22}, {3,28}, {5,36}, {3,24}, {5,17}, {3,12}, {8,23}, {7,16}, {3,39}, {1,37}, {1,20}, {3,16}, {1,13}, {4,18}, {7,32}, {2,26}, {3,20}, {1,33}, {5,12}, {2,25}, {1,28}, {3,36}, {8,30}, {4,34}, {7,36}, {4,23}, {5,16}, {7,12}, {2,30}, {1,21}, {5,25}, {4,19}, {4,10}, {5,40}, {1,24} }; // ET40.109 // Bipartite(8,32) Valencies [16,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 21134460321792 EdgePairs[40][109]:={ {1,15}, {4,35}, {7,19}, {7,39}, {6,12}, {8,39}, {8,31}, {2,38}, {6,10}, {6,18}, {3,29}, {2,22}, {3,38}, {6,36}, {1,31}, {6,17}, {4,27}, {7,40}, {5,35}, {7,24}, {1,40}, {4,40}, {5,34}, {1,25}, {7,38}, {4,16}, {6,13}, {2,37}, {1,9}, {2,33}, {6,25}, {7,31}, {7,27}, {3,30}, {1,32}, {7,15}, {7,23}, {8,34}, {3,10}, {3,34}, {6,34}, {6,9}, {5,26}, {8,14}, {7,11}, {2,29}, {3,19}, {4,12}, {3,18}, {8,22}, {8,15}, {2,14}, {5,23}, {3,11}, {4,37}, {4,20}, {8,33}, {1,36}, {1,17}, {3,13}, {2,16}, {2,32}, {6,33}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {4,28}, {3,14}, {2,13}, {1,12}, {4,29}, {3,22}, {5,19}, {5,15}, {8,26}, {6,37}, {8,17}, {7,14}, {3,27}, {6,26}, {2,40}, {4,36}, {4,21}, {7,30}, {5,28}, {2,9}, {6,29}, {7,35}, {2,24}, {4,11}, {3,35}, {1,23}, {2,21}, {5,27}, {1,39}, {8,9}, {8,38}, {5,20}, {5,36}, {3,26}, {5,31}, {8,23}, {6,20}, {7,16}, {3,21}, {4,32}, {1,20}, {5,11}, {7,22}, {5,10}, {7,32}, {8,25}, {1,33}, {5,12}, {2,25}, {1,28}, {3,37}, {5,18}, {8,30}, {5,39}, {4,13}, {2,30}, {4,19}, {4,24}, {1,24}, {6,28} }; // ET40.110 // Bipartite(8,32) Valencies [16,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 25165824 EdgePairs[40][110]:={ {1,15}, {4,35}, {5,32}, {7,39}, {6,12}, {5,14}, {8,31}, {2,38}, {6,18}, {3,29}, {2,22}, {3,38}, {5,30}, {1,31}, {6,17}, {4,27}, {7,40}, {7,24}, {1,40}, {2,20}, {4,40}, {1,25}, {7,33}, {2,37}, {3,32}, {1,38}, {1,9}, {6,32}, {6,25}, {7,31}, {6,40}, {7,15}, {7,23}, {5,13}, {8,34}, {6,34}, {2,15}, {6,9}, {4,26}, {8,14}, {8,13}, {5,21}, {2,29}, {3,19}, {5,37}, {4,12}, {8,22}, {7,28}, {8,15}, {1,34}, {7,10}, {2,14}, {5,33}, {3,11}, {5,23}, {4,37}, {2,10}, {4,20}, {6,11}, {2,31}, {2,23}, {1,10}, {7,26}, {8,33}, {4,39}, {1,36}, {3,13}, {1,22}, {6,33}, {2,36}, {8,18}, {4,28}, {2,13}, {3,9}, {3,22}, {8,17}, {5,29}, {7,14}, {3,27}, {1,19}, {4,36}, {4,21}, {7,30}, {5,28}, {1,35}, {1,26}, {4,11}, {6,19}, {3,35}, {2,21}, {5,27}, {7,18}, {2,39}, {8,9}, {8,38}, {8,32}, {5,17}, {8,16}, {6,16}, {3,21}, {1,20}, {5,11}, {3,16}, {3,25}, {8,25}, {2,26}, {3,20}, {5,12}, {3,36}, {3,37}, {6,24}, {6,35}, {8,30}, {6,27}, {7,34}, {7,17}, {4,23}, {5,16}, {5,39}, {7,12}, {2,30}, {1,18}, {4,19}, {4,10}, {4,24}, {1,24}, {8,29}, {6,28} }; // ET40.111 // Bipartite(20,20) Valencies [16,16] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 15216811431690240 EdgePairs[40][111]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {1,21}, {3,21}, {19,37}, {20,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {19,21}, {13,40}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {20,38}, {2,34}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {8,30}, {9,33}, {8,37}, {20,24}, {17,39}, {12,26}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {15,30}, {20,39}, {5,37}, {18,35}, {16,25}, {20,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {16,40}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {1,39}, {7,37}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {9,38}, {14,21}, {9,26}, {18,38}, {17,31}, {13,36}, {20,22}, {15,23}, {9,22}, {3,25}, {19,24}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {7,34}, {11,24}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {5,39}, {3,32}, {14,27}, {17,30}, {10,22}, {5,40}, {10,30}, {16,30}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {15,24}, {16,26}, {12,25}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {16,31}, {6,23}, {7,39}, {4,36}, {15,39}, {4,29}, {19,29}, {8,32}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {19,34}, {7,40}, {5,23}, {20,32}, {2,26}, {10,40}, {18,21}, {9,21}, {7,29}, {18,30}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {2,21}, {4,27}, {18,28}, {5,24}, {15,29}, {2,22}, {2,31}, {16,38}, {1,33}, {18,27}, {20,28}, {12,36}, {2,37}, {5,29}, {3,28}, {7,31}, {8,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {14,24}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {17,24}, {17,40}, {20,23}, {12,34}, {17,21}, {19,36}, {6,28}, {16,23}, {18,23}, {19,32}, {13,33}, {20,34}, {7,26}, {11,28}, {1,23}, {16,35}, {10,24}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {9,27}, {12,32}, {8,28}, {18,40}, {20,40}, {5,25}, {10,23}, {3,37}, {14,22}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {8,25}, {6,33}, {12,21}, {2,32}, {11,26}, {15,25}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.112 // Non-bipartite Valency 16 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 1065620623885074432000000 EdgePairs[40][112]:={ {13,21}, {24,34}, {19,28}, {6,38}, {11,40}, {10,37}, {31,39}, {5,38}, {23,29}, {9,17}, {10,18}, {19,26}, {25,37}, {31,40}, {12,22}, {25,40}, {16,22}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {21,30}, {30,40}, {15,27}, {5,15}, {24,32}, {27,33}, {24,36}, {10,39}, {26,37}, {16,28}, {1,35}, {29,39}, {13,27}, {6,14}, {16,21}, {2,33}, {11,17}, {1,12}, {27,36}, {8,16}, {20,26}, {10,17}, {9,18}, {2,34}, {19,31}, {26,38}, {18,32}, {4,30}, {8,13}, {1,9}, {4,16}, {1,10}, {8,37}, {4,13}, {26,39}, {12,20}, {12,38}, {23,31}, {1,13}, {3,10}, {2,10}, {3,9}, {6,39}, {23,36}, {25,34}, {11,39}, {7,33}, {20,29}, {12,40}, {10,20}, {17,26}, {13,24}, {24,30}, {2,15}, {12,23}, {5,37}, {26,35}, {16,25}, {24,31}, {1,36}, {6,18}, {1,29}, {12,37}, {31,38}, {11,18}, {8,38}, {13,26}, {2,29}, {5,34}, {2,36}, {7,15}, {26,36}, {32,39}, {22,34}, {18,29}, {6,34}, {9,39}, {9,20}, {18,26}, {30,38}, {8,19}, {7,14}, {15,28}, {6,17}, {8,18}, {27,39}, {28,40}, {12,24}, {27,40}, {1,31}, {3,31}, {25,33}, {3,13}, {11,22}, {7,37}, {2,30}, {5,35}, {4,9}, {3,36}, {17,29}, {20,25}, {7,19}, {4,32}, {1,30}, {2,13}, {19,27}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {3,30}, {3,16}, {11,23}, {14,23}, {10,38}, {6,16}, {13,25}, {21,31}, {32,38}, {19,30}, {9,38}, {27,37}, {4,10}, {14,21}, {5,14}, {32,40}, {28,34}, {3,29}, {17,31}, {12,17}, {22,29}, {10,19}, {15,23}, {9,22}, {4,11}, {9,19}, {20,31}, {17,28}, {7,35}, {22,30}, {27,34}, {4,33}, {2,12}, {7,34}, {11,24}, {5,19}, {18,25}, {13,22}, {6,13}, {22,31}, {23,35}, {20,30}, {6,19}, {5,39}, {3,32}, {14,27}, {12,18}, {2,16}, {8,34}, {17,30}, {10,22}, {5,40}, {28,37}, {4,34}, {29,38}, {15,24}, {21,32}, {16,26}, {1,16}, {27,35}, {4,14}, {24,35}, {4,15}, {18,31}, {25,38}, {7,39}, {23,34}, {4,36}, {4,29}, {1,32}, {24,29}, {31,37}, {19,29}, {6,37}, {32,37}, {9,24}, {17,25}, {6,20}, {7,40}, {20,32}, {5,20}, {10,40}, {10,21}, {9,21}, {18,30}, {29,37}, {9,23}, {28,39}, {8,36}, {3,33}, {2,11}, {14,26}, {23,32}, {3,34}, {1,11}, {18,28}, {25,36}, {25,39}, {2,31}, {20,28}, {21,33}, {1,33}, {18,27}, {16,27}, {3,14}, {19,25}, {3,11}, {21,34}, {11,19}, {8,33}, {12,39}, {4,12}, {20,27}, {21,35}, {28,33}, {28,36}, {8,14}, {22,33}, {14,24}, {3,15}, {1,14}, {1,34}, {21,29}, {28,35}, {23,30}, {16,23}, {4,35}, {19,32}, {1,15}, {14,25}, {15,21}, {7,18}, {11,37}, {23,33}, {7,16}, {5,16}, {5,18}, {10,24}, {11,20}, {5,17}, {7,17}, {8,35}, {13,23}, {17,27}, {15,22}, {13,28}, {26,34}, {16,24}, {28,38}, {7,20}, {7,38}, {25,35}, {22,35}, {21,36}, {9,40}, {8,20}, {26,40}, {5,13}, {10,23}, {15,26}, {22,36}, {26,33}, {8,39}, {14,22}, {22,32}, {3,12}, {7,13}, {5,36}, {24,33}, {7,36}, {6,35}, {17,32}, {12,19}, {30,39}, {2,9}, {30,37}, {6,33}, {12,21}, {2,32}, {2,14}, {15,25}, {5,33}, {11,38}, {9,37}, {27,38}, {6,40}, {29,40} }; // ET40.113 // Non-bipartite Valency 16 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 7680 EdgePairs[40][113]:={ {13,21}, {19,28}, {10,37}, {15,38}, {35,38}, {5,38}, {5,22}, {3,8}, {31,40}, {3,26}, {25,40}, {5,11}, {13,39}, {2,35}, {6,15}, {8,40}, {3,35}, {8,21}, {21,30}, {14,31}, {27,33}, {24,36}, {10,39}, {3,20}, {2,18}, {26,37}, {16,37}, {3,39}, {21,28}, {11,14}, {5,32}, {2,7}, {8,31}, {4,40}, {4,37}, {13,27}, {6,14}, {16,21}, {24,28}, {19,21}, {11,35}, {11,17}, {1,12}, {1,20}, {27,36}, {8,16}, {20,26}, {10,17}, {9,18}, {2,34}, {2,25}, {21,40}, {15,32}, {4,30}, {23,38}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {1,9}, {33,39}, {26,39}, {7,11}, {12,20}, {12,38}, {3,10}, {2,5}, {2,10}, {6,39}, {25,34}, {11,39}, {26,29}, {20,29}, {12,40}, {22,25}, {12,23}, {12,13}, {18,35}, {24,31}, {9,35}, {1,36}, {15,19}, {6,18}, {24,26}, {31,38}, {8,38}, {34,37}, {13,26}, {17,36}, {6,24}, {2,29}, {1,38}, {13,19}, {1,26}, {3,17}, {20,36}, {16,40}, {7,15}, {26,36}, {32,39}, {24,37}, {27,30}, {18,29}, {6,34}, {9,20}, {18,26}, {18,33}, {8,19}, {3,38}, {7,14}, {15,28}, {6,10}, {4,7}, {4,18}, {24,40}, {27,39}, {28,40}, {7,32}, {3,31}, {12,27}, {3,13}, {11,22}, {35,39}, {1,39}, {7,37}, {4,9}, {34,40}, {6,12}, {4,32}, {1,30}, {2,13}, {13,18}, {12,15}, {8,10}, {14,28}, {23,39}, {8,17}, {16,17}, {3,16}, {11,16}, {10,36}, {11,33}, {19,30}, {8,24}, {31,33}, {9,38}, {27,37}, {9,26}, {21,37}, {28,34}, {3,29}, {29,36}, {20,22}, {10,13}, {22,29}, {10,19}, {20,31}, {19,24}, {17,28}, {7,35}, {25,30}, {2,27}, {6,30}, {4,33}, {7,34}, {11,24}, {1,6}, {5,19}, {22,31}, {23,35}, {9,16}, {12,18}, {25,31}, {2,16}, {13,29}, {4,5}, {17,30}, {10,22}, {5,40}, {33,38}, {16,30}, {7,23}, {10,25}, {29,38}, {6,31}, {15,24}, {21,32}, {16,26}, {12,25}, {14,37}, {4,14}, {13,38}, {23,27}, {36,37}, {4,15}, {18,31}, {14,40}, {16,31}, {25,38}, {7,39}, {23,34}, {4,36}, {15,39}, {1,32}, {24,29}, {28,32}, {6,37}, {22,39}, {32,37}, {17,22}, {17,25}, {2,19}, {6,20}, {5,23}, {18,21}, {9,21}, {7,29}, {9,23}, {22,38}, {8,36}, {28,29}, {2,11}, {13,32}, {23,32}, {10,15}, {19,33}, {9,28}, {3,34}, {4,27}, {30,35}, {15,29}, {36,40}, {16,20}, {18,24}, {2,31}, {18,27}, {1,33}, {12,36}, {16,27}, {19,25}, {3,11}, {2,37}, {5,29}, {4,25}, {14,30}, {21,34}, {3,28}, {31,35}, {5,9}, {11,19}, {8,33}, {30,33}, {1,8}, {4,12}, {20,27}, {21,35}, {17,34}, {3,6}, {22,33}, {14,24}, {19,35}, {7,22}, {1,14}, {26,32}, {22,27}, {20,23}, {12,34}, {28,35}, {23,30}, {16,23}, {19,32}, {1,15}, {14,25}, {14,20}, {20,34}, {7,18}, {11,37}, {11,28}, {5,16}, {10,24}, {15,18}, {10,34}, {10,27}, {5,17}, {13,23}, {2,40}, {32,36}, {6,21}, {15,22}, {1,28}, {23,25}, {28,38}, {7,20}, {7,9}, {25,35}, {9,40}, {5,13}, {32,34}, {17,23}, {22,36}, {26,33}, {27,31}, {4,19}, {14,22}, {9,14}, {14,17}, {5,36}, {24,33}, {6,35}, {17,32}, {29,34}, {21,26}, {30,39}, {30,37}, {12,21}, {11,26}, {15,25}, {5,33}, {29,40} }; // ET40.114 // Non-bipartite Valency 16 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 7680 EdgePairs[40][114]:={ {13,21}, {24,34}, {19,28}, {6,38}, {11,40}, {10,37}, {15,38}, {31,39}, {35,38}, {23,29}, {9,17}, {10,18}, {19,26}, {11,25}, {12,22}, {25,40}, {5,11}, {13,37}, {1,40}, {16,22}, {14,38}, {2,35}, {17,33}, {8,40}, {3,35}, {11,15}, {8,21}, {14,31}, {30,40}, {15,27}, {5,15}, {24,32}, {12,16}, {10,39}, {3,20}, {2,18}, {26,37}, {16,37}, {16,28}, {11,14}, {5,32}, {7,30}, {29,39}, {6,9}, {13,27}, {6,14}, {13,40}, {17,35}, {4,38}, {11,17}, {1,12}, {1,20}, {8,16}, {2,34}, {21,40}, {32,33}, {4,30}, {23,38}, {9,33}, {1,17}, {33,39}, {29,33}, {1,10}, {4,13}, {20,24}, {26,39}, {12,20}, {31,36}, {23,31}, {1,13}, {12,26}, {2,5}, {19,22}, {3,9}, {23,36}, {25,34}, {23,28}, {20,29}, {10,20}, {17,26}, {24,30}, {15,30}, {22,25}, {5,37}, {12,13}, {20,35}, {9,35}, {1,36}, {6,18}, {12,37}, {24,26}, {8,38}, {34,37}, {30,36}, {2,29}, {5,34}, {13,19}, {3,17}, {16,40}, {7,15}, {26,36}, {22,34}, {24,37}, {27,30}, {18,29}, {30,38}, {18,36}, {32,35}, {2,39}, {4,18}, {8,18}, {24,40}, {12,24}, {27,40}, {3,31}, {12,27}, {9,13}, {35,39}, {7,37}, {2,8}, {5,35}, {34,40}, {6,12}, {19,23}, {25,29}, {20,25}, {7,19}, {4,32}, {16,18}, {1,30}, {13,18}, {8,10}, {14,28}, {11,21}, {6,36}, {23,39}, {16,29}, {11,36}, {3,16}, {11,23}, {10,36}, {6,16}, {18,22}, {13,25}, {14,39}, {21,31}, {32,38}, {19,30}, {7,12}, {8,24}, {9,38}, {4,10}, {9,26}, {21,37}, {32,40}, {3,29}, {25,32}, {15,23}, {9,19}, {20,31}, {3,25}, {11,34}, {17,28}, {7,35}, {22,30}, {27,34}, {2,27}, {6,30}, {4,33}, {7,34}, {1,6}, {5,19}, {18,25}, {1,25}, {9,16}, {5,39}, {12,18}, {2,16}, {13,29}, {4,5}, {17,30}, {10,22}, {28,37}, {33,38}, {7,23}, {6,22}, {10,25}, {26,31}, {6,31}, {3,7}, {16,26}, {27,35}, {24,35}, {36,37}, {4,15}, {18,31}, {6,23}, {25,38}, {15,17}, {7,39}, {4,36}, {15,39}, {1,32}, {31,37}, {28,32}, {8,32}, {22,39}, {24,27}, {10,28}, {19,34}, {2,19}, {6,20}, {2,26}, {9,21}, {26,30}, {29,37}, {8,29}, {9,23}, {22,38}, {28,39}, {8,36}, {28,29}, {2,11}, {13,32}, {14,26}, {10,15}, {3,34}, {4,27}, {5,24}, {36,40}, {8,11}, {2,31}, {18,27}, {21,33}, {1,33}, {1,7}, {3,14}, {3,11}, {4,8}, {5,29}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {4,12}, {20,27}, {28,33}, {28,36}, {31,34}, {8,14}, {3,6}, {20,33}, {14,24}, {7,22}, {30,34}, {21,27}, {5,21}, {21,29}, {17,24}, {17,21}, {19,36}, {18,23}, {19,32}, {1,15}, {15,21}, {14,20}, {23,33}, {11,28}, {10,24}, {10,34}, {5,17}, {3,40}, {7,17}, {13,23}, {4,26}, {15,20}, {1,28}, {23,25}, {16,24}, {9,27}, {2,38}, {7,9}, {25,35}, {22,35}, {21,36}, {15,31}, {5,10}, {9,40}, {8,20}, {5,13}, {26,33}, {27,31}, {4,19}, {14,22}, {22,32}, {3,37}, {29,35}, {7,13}, {14,17}, {16,19}, {10,14}, {4,39}, {12,35}, {17,32}, {21,26}, {20,21}, {22,28}, {1,37}, {2,9}, {16,32}, {6,33}, {2,14}, {18,34}, {15,25}, {11,38}, {27,38}, {6,40} }; // ET40.115 // Bipartite(4,36) Valencies [18,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 138720970502182010880000 EdgePairs[40][115]:={ {3,32}, {2,14}, {3,40}, {4,23}, {4,39}, {2,37}, {1,24}, {3,12}, {2,26}, {1,29}, {2,30}, {2,29}, {1,32}, {4,34}, {2,10}, {1,37}, {1,33}, {1,40}, {4,11}, {4,10}, {1,36}, {3,27}, {2,6}, {4,7}, {1,20}, {1,12}, {4,31}, {3,8}, {3,23}, {3,24}, {2,33}, {3,20}, {2,21}, {4,6}, {4,30}, {4,18}, {3,11}, {3,16}, {3,7}, {1,16}, {3,28}, {3,15}, {4,38}, {2,38}, {1,21}, {2,18}, {4,27}, {3,19}, {2,5}, {3,31}, {1,5}, {4,15}, {1,17}, {4,22}, {3,39}, {1,28}, {2,17}, {1,8}, {1,13}, {2,34}, {2,9}, {1,9}, {4,26}, {2,13}, {2,25}, {4,14}, {4,35}, {4,19}, {1,25}, {2,22}, {3,36}, {3,35} }; // ET40.116 // Bipartite(4,36) Valencies [18,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3343537668096000000 EdgePairs[40][116]:={ {2,11}, {2,14}, {4,8}, {4,9}, {4,39}, {2,26}, {3,12}, {2,32}, {2,30}, {1,29}, {2,29}, {4,34}, {2,24}, {1,37}, {1,40}, {1,10}, {4,10}, {3,21}, {3,27}, {4,40}, {3,33}, {2,6}, {2,36}, {3,37}, {1,31}, {4,16}, {3,24}, {3,9}, {2,12}, {4,32}, {4,33}, {1,7}, {1,16}, {3,7}, {2,20}, {3,15}, {4,38}, {2,38}, {3,25}, {2,18}, {4,27}, {4,21}, {4,20}, {3,19}, {3,30}, {3,18}, {2,5}, {3,31}, {1,5}, {4,15}, {4,28}, {1,17}, {4,22}, {3,6}, {3,39}, {1,28}, {2,17}, {3,13}, {2,23}, {1,13}, {2,35}, {1,19}, {4,26}, {1,22}, {2,8}, {4,14}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {3,36} }; // ET40.117 // Bipartite(10,30) Valencies [18,6] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1440 EdgePairs[40][117]:={ {1,11}, {3,33}, {2,24}, {10,24}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {4,24}, {4,26}, {3,22}, {3,40}, {4,16}, {10,37}, {4,30}, {8,30}, {6,17}, {1,13}, {5,38}, {4,29}, {8,33}, {3,15}, {1,40}, {10,26}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {7,34}, {1,21}, {8,25}, {2,28}, {2,14}, {1,30}, {8,15}, {6,11}, {9,35}, {4,23}, {8,27}, {10,15}, {10,22}, {3,18}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {7,12}, {2,25}, {6,40}, {6,31}, {1,38}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {9,29}, {10,38}, {1,18}, {7,20}, {9,32}, {9,27}, {5,11}, {2,38}, {9,19}, {8,14}, {7,39}, {5,25}, {7,32}, {3,12}, {7,13}, {9,14}, {7,25}, {10,28}, {2,35}, {1,22}, {6,12}, {5,23}, {3,20}, {10,31}, {9,34}, {2,13}, {10,40}, {1,29}, {8,17}, {3,32}, {4,35}, {7,16}, {8,36}, {1,12}, {6,33}, {2,32}, {7,26}, {5,18}, {1,23}, {6,24}, {8,11}, {5,24}, {9,37}, {8,13}, {5,14}, {9,20}, {4,15}, {7,14}, {3,27}, {10,13}, {3,26}, {8,37}, {5,28}, {2,17}, {4,36}, {5,12}, {9,40}, {8,21}, {5,31}, {6,26}, {3,23}, {1,39}, {3,21}, {1,25}, {6,19}, {7,29}, {6,14}, {9,30}, {10,11}, {10,39}, {1,35}, {5,39}, {7,28}, {3,16}, {4,37}, {10,35}, {7,23}, {6,36}, {3,30}, {5,33}, {8,34}, {8,38}, {1,26}, {2,22}, {10,36}, {10,18}, {2,40}, {9,36}, {5,27}, {8,18}, {9,39}, {9,38}, {4,25}, {4,11}, {3,28}, {8,20}, {7,24}, {3,31}, {2,12}, {10,20}, {6,39}, {5,19}, {6,20}, {7,35}, {5,21}, {6,13}, {7,37}, {1,34}, {9,31}, {5,37}, {4,17}, {9,21}, {9,23}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET40.118 // Bipartite(10,30) Valencies [18,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23219011584000000 EdgePairs[40][118]:={ {3,33}, {2,24}, {1,20}, {10,24}, {9,28}, {6,32}, {6,16}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {3,40}, {10,37}, {4,30}, {6,17}, {1,13}, {5,38}, {7,38}, {4,29}, {3,13}, {3,25}, {3,15}, {10,23}, {1,40}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {10,33}, {3,35}, {2,26}, {8,39}, {2,14}, {1,30}, {6,11}, {8,31}, {8,27}, {9,11}, {10,22}, {6,22}, {3,18}, {8,16}, {6,21}, {2,25}, {7,12}, {6,40}, {6,31}, {1,38}, {2,34}, {2,36}, {4,22}, {8,19}, {10,38}, {1,18}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {5,29}, {8,14}, {2,39}, {7,32}, {7,13}, {7,25}, {10,28}, {2,35}, {6,12}, {6,30}, {5,23}, {10,29}, {3,20}, {2,20}, {1,29}, {7,30}, {8,17}, {2,16}, {4,35}, {8,36}, {5,18}, {1,23}, {7,17}, {8,11}, {5,24}, {9,37}, {8,22}, {5,14}, {4,15}, {1,28}, {3,11}, {1,33}, {10,13}, {10,12}, {3,26}, {8,37}, {5,28}, {8,26}, {9,22}, {6,15}, {9,13}, {8,32}, {8,21}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {10,32}, {5,36}, {3,21}, {1,25}, {9,12}, {1,15}, {2,11}, {10,39}, {1,35}, {5,39}, {7,28}, {3,16}, {4,37}, {4,40}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {8,34}, {9,18}, {10,17}, {2,29}, {10,27}, {4,34}, {4,14}, {10,34}, {9,17}, {10,18}, {8,24}, {6,25}, {2,40}, {2,31}, {9,33}, {9,36}, {5,26}, {9,38}, {4,25}, {10,19}, {3,38}, {4,12}, {4,20}, {5,13}, {3,28}, {7,27}, {3,31}, {1,14}, {7,33}, {6,37}, {10,14}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {7,37}, {1,34}, {9,31}, {4,17}, {6,35}, {9,21}, {9,16}, {3,36}, {4,39}, {7,40}, {9,23}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET40.119 // Bipartite(10,30) Valencies [18,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 232190115840 EdgePairs[40][119]:={ {3,33}, {2,24}, {5,17}, {10,24}, {9,28}, {6,32}, {6,16}, {5,34}, {4,24}, {3,40}, {10,37}, {4,30}, {8,30}, {1,13}, {7,38}, {1,32}, {3,13}, {8,33}, {3,25}, {3,15}, {10,23}, {10,26}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {3,35}, {3,37}, {2,26}, {8,39}, {7,34}, {7,36}, {8,25}, {2,28}, {2,14}, {5,32}, {8,15}, {9,35}, {8,31}, {8,27}, {9,11}, {10,22}, {6,22}, {6,29}, {3,17}, {4,38}, {1,38}, {2,34}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {7,20}, {9,32}, {5,11}, {2,38}, {2,37}, {7,39}, {2,39}, {9,14}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {10,31}, {9,34}, {10,21}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,39}, {4,35}, {9,25}, {7,16}, {7,26}, {1,12}, {6,33}, {1,23}, {7,17}, {8,11}, {5,24}, {8,13}, {8,35}, {5,14}, {9,20}, {4,15}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {10,12}, {3,29}, {6,23}, {8,37}, {9,22}, {6,15}, {2,17}, {9,40}, {5,12}, {8,21}, {3,19}, {5,31}, {6,26}, {8,40}, {3,23}, {8,23}, {1,39}, {10,32}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {1,15}, {6,28}, {9,30}, {10,11}, {1,35}, {7,28}, {4,40}, {6,36}, {3,30}, {5,33}, {9,18}, {10,17}, {2,29}, {10,27}, {1,26}, {4,34}, {1,16}, {10,36}, {4,14}, {10,34}, {6,25}, {6,38}, {2,40}, {5,27}, {5,26}, {4,18}, {9,38}, {4,25}, {4,11}, {4,12}, {4,20}, {5,13}, {8,20}, {7,27}, {7,24}, {3,31}, {9,24}, {6,39}, {10,14}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {2,18}, {9,31}, {5,37}, {7,19}, {6,35}, {9,21}, {7,40}, {8,29}, {4,32}, {1,36}, {7,18}, {10,16}, {5,16} }; // ET40.120 // Bipartite(10,30) Valencies [18,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7255941120 EdgePairs[40][120]:={ {1,11}, {2,24}, {10,24}, {10,25}, {2,33}, {4,27}, {5,34}, {8,12}, {4,26}, {3,22}, {4,16}, {10,37}, {8,30}, {6,17}, {2,23}, {1,13}, {5,38}, {8,28}, {1,32}, {8,33}, {1,27}, {2,15}, {7,22}, {4,31}, {2,19}, {1,19}, {5,20}, {7,34}, {1,21}, {7,36}, {8,25}, {2,14}, {8,15}, {9,35}, {4,23}, {9,11}, {10,15}, {10,22}, {3,18}, {10,30}, {6,29}, {8,16}, {3,34}, {5,40}, {7,12}, {2,25}, {1,38}, {2,34}, {1,17}, {4,22}, {9,29}, {10,38}, {1,18}, {3,14}, {7,20}, {9,26}, {9,27}, {5,11}, {9,19}, {7,39}, {2,39}, {7,32}, {1,31}, {3,12}, {10,28}, {2,35}, {1,22}, {4,33}, {5,23}, {4,21}, {2,13}, {2,20}, {6,18}, {10,40}, {1,29}, {7,30}, {3,39}, {3,32}, {4,35}, {9,25}, {7,16}, {8,36}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {9,37}, {8,13}, {8,22}, {8,35}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {1,33}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {6,15}, {4,36}, {9,40}, {8,32}, {3,19}, {5,31}, {6,27}, {8,40}, {8,23}, {1,39}, {10,32}, {5,36}, {3,21}, {6,19}, {7,29}, {6,28}, {6,14}, {2,11}, {9,30}, {1,37}, {3,16}, {4,37}, {10,35}, {2,21}, {5,33}, {10,17}, {3,24}, {2,29}, {8,38}, {10,27}, {10,34}, {9,17}, {10,18}, {6,25}, {6,38}, {2,40}, {2,31}, {9,36}, {6,34}, {5,26}, {8,18}, {9,39}, {4,25}, {3,38}, {4,11}, {4,12}, {5,13}, {8,20}, {3,28}, {7,27}, {7,24}, {3,31}, {10,20}, {6,39}, {6,37}, {10,14}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {9,31}, {7,19}, {4,17}, {6,35}, {9,21}, {9,16}, {3,36}, {7,40}, {4,32}, {5,16} }; // ET40.121 // Bipartite(10,30) Valencies [18,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23592960 EdgePairs[40][121]:={ {1,11}, {1,20}, {10,24}, {10,25}, {6,16}, {4,27}, {5,34}, {8,12}, {4,26}, {3,40}, {4,16}, {10,37}, {8,30}, {2,23}, {1,13}, {5,38}, {7,38}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {1,40}, {10,26}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {1,21}, {8,25}, {2,28}, {2,14}, {8,15}, {6,11}, {8,31}, {8,27}, {10,15}, {10,22}, {6,22}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {7,12}, {6,31}, {2,34}, {1,17}, {4,22}, {9,29}, {10,38}, {7,11}, {7,20}, {3,14}, {9,32}, {2,38}, {9,19}, {2,37}, {7,39}, {7,32}, {9,14}, {10,28}, {2,35}, {6,30}, {4,33}, {5,23}, {9,34}, {2,13}, {2,20}, {10,40}, {8,17}, {3,32}, {9,25}, {7,16}, {8,36}, {1,12}, {2,32}, {7,26}, {5,18}, {6,24}, {5,30}, {7,17}, {5,24}, {9,37}, {8,22}, {8,35}, {1,28}, {4,13}, {3,11}, {7,14}, {4,28}, {10,13}, {3,29}, {3,26}, {8,37}, {5,28}, {9,22}, {7,31}, {6,15}, {2,17}, {5,12}, {9,40}, {8,32}, {8,21}, {1,24}, {5,31}, {6,26}, {8,40}, {3,23}, {1,39}, {5,36}, {3,21}, {1,25}, {6,19}, {7,29}, {6,14}, {10,11}, {10,39}, {1,35}, {5,39}, {3,16}, {4,37}, {4,40}, {10,35}, {7,23}, {6,36}, {3,30}, {5,33}, {9,18}, {2,29}, {1,26}, {2,22}, {4,34}, {4,14}, {9,17}, {10,18}, {9,33}, {9,36}, {6,34}, {5,27}, {8,18}, {4,18}, {9,39}, {9,38}, {4,25}, {3,38}, {4,11}, {4,12}, {5,13}, {8,20}, {3,28}, {7,27}, {7,24}, {3,31}, {2,12}, {9,24}, {10,20}, {6,39}, {5,15}, {7,33}, {6,37}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {1,34}, {6,35}, {3,36}, {9,21}, {9,23}, {1,36}, {7,18}, {5,16} }; // ET40.122 // Bipartite(16,24) Valencies [18,12] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1152 EdgePairs[40][122]:={ {13,21}, {6,38}, {11,40}, {10,37}, {15,38}, {9,32}, {5,38}, {5,22}, {9,17}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {16,22}, {2,35}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {10,39}, {3,20}, {2,18}, {1,21}, {16,37}, {16,28}, {1,35}, {8,31}, {4,40}, {14,29}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {3,18}, {2,34}, {10,17}, {9,18}, {2,25}, {15,32}, {4,30}, {8,30}, {8,37}, {12,20}, {12,38}, {12,26}, {7,27}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {1,24}, {15,30}, {12,23}, {13,20}, {15,19}, {1,29}, {6,18}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {1,38}, {13,19}, {14,32}, {1,26}, {3,17}, {2,36}, {16,40}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {8,19}, {5,27}, {2,39}, {4,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {1,39}, {7,37}, {6,27}, {5,35}, {3,36}, {4,21}, {13,17}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {3,30}, {16,17}, {2,24}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {14,21}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {3,25}, {11,34}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {13,38}, {14,40}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {10,28}, {9,24}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,21}, {7,29}, {8,29}, {9,23}, {7,21}, {8,36}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {2,21}, {4,27}, {5,24}, {15,29}, {2,22}, {2,31}, {14,19}, {16,38}, {1,33}, {16,27}, {5,26}, {2,37}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {1,34}, {13,35}, {14,18}, {5,21}, {6,28}, {16,23}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,28}, {5,18}, {16,35}, {11,20}, {10,27}, {10,34}, {5,17}, {16,33}, {7,17}, {8,35}, {13,23}, {2,40}, {15,22}, {15,20}, {16,39}, {13,28}, {1,28}, {16,24}, {3,27}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {14,22}, {8,39}, {3,37}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {6,33}, {12,21}, {11,26}, {15,25}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.123 // Bipartite(16,24) Valencies [18,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2139864107581440000 EdgePairs[40][123]:={ {13,21}, {6,38}, {11,40}, {10,37}, {15,38}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {3,26}, {13,37}, {1,40}, {14,38}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,39}, {16,37}, {16,28}, {5,32}, {7,30}, {8,31}, {4,40}, {4,37}, {14,29}, {16,21}, {13,40}, {2,33}, {11,35}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {9,33}, {1,17}, {8,37}, {12,20}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {12,31}, {12,40}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {1,36}, {15,19}, {1,29}, {6,18}, {12,37}, {10,35}, {4,23}, {11,18}, {13,26}, {2,29}, {5,34}, {1,38}, {1,26}, {16,40}, {9,36}, {6,34}, {9,29}, {9,20}, {8,19}, {3,38}, {1,18}, {15,28}, {6,17}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {11,23}, {3,24}, {14,33}, {14,23}, {10,38}, {15,34}, {13,25}, {14,39}, {8,24}, {9,38}, {14,21}, {9,26}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {11,34}, {7,35}, {2,27}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {10,29}, {13,22}, {1,25}, {6,19}, {4,17}, {9,30}, {3,32}, {14,27}, {7,28}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {15,40}, {3,22}, {14,37}, {13,38}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {2,19}, {7,40}, {5,20}, {2,26}, {10,21}, {9,21}, {8,29}, {8,36}, {8,27}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {16,20}, {2,31}, {14,19}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {13,34}, {7,22}, {6,26}, {1,34}, {14,18}, {5,21}, {16,23}, {4,35}, {13,33}, {14,25}, {7,26}, {7,18}, {11,28}, {5,18}, {16,35}, {11,20}, {15,18}, {10,34}, {10,27}, {5,17}, {16,33}, {3,40}, {8,35}, {6,21}, {15,22}, {15,20}, {16,39}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {8,39}, {14,17}, {5,36}, {16,19}, {9,34}, {4,39}, {12,35}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET40.124 // Bipartite(16,24) Valencies [18,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1934917632 EdgePairs[40][124]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {8,26}, {13,37}, {14,38}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {2,34}, {10,17}, {9,18}, {15,32}, {8,30}, {9,33}, {1,17}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {10,26}, {12,31}, {12,40}, {10,20}, {15,30}, {12,23}, {5,37}, {13,20}, {9,35}, {15,19}, {1,29}, {12,37}, {16,34}, {4,23}, {8,38}, {13,26}, {6,24}, {5,34}, {1,38}, {13,19}, {14,32}, {1,26}, {3,17}, {2,36}, {16,40}, {8,22}, {9,36}, {9,39}, {9,20}, {1,18}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {16,18}, {1,30}, {13,18}, {11,21}, {8,17}, {16,29}, {11,36}, {2,24}, {3,24}, {10,36}, {14,33}, {14,23}, {11,33}, {13,25}, {14,39}, {8,24}, {9,38}, {14,21}, {9,26}, {3,29}, {13,36}, {2,23}, {15,23}, {9,22}, {9,19}, {3,25}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {9,30}, {3,32}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {5,40}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {16,26}, {15,40}, {14,37}, {13,38}, {14,40}, {6,23}, {16,31}, {15,17}, {4,36}, {15,39}, {4,29}, {6,37}, {8,32}, {7,24}, {10,28}, {2,19}, {7,40}, {5,20}, {2,26}, {10,40}, {10,21}, {7,29}, {2,28}, {9,23}, {7,21}, {8,36}, {3,33}, {16,36}, {14,26}, {11,30}, {9,28}, {4,27}, {5,24}, {2,22}, {16,20}, {2,31}, {1,33}, {16,27}, {5,26}, {5,29}, {4,25}, {14,30}, {3,28}, {11,19}, {8,33}, {12,39}, {14,24}, {13,34}, {7,22}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {16,23}, {4,35}, {13,33}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,34}, {5,17}, {3,40}, {2,40}, {6,21}, {15,22}, {4,26}, {15,20}, {16,39}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {14,22}, {8,39}, {3,37}, {14,17}, {16,19}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {15,25}, {5,33}, {5,30}, {11,38}, {6,40} }; // ET40.125 // Bipartite(16,24) Valencies [18,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2359296 EdgePairs[40][125]:={ {15,33}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {11,25}, {12,22}, {8,26}, {13,37}, {14,38}, {16,22}, {13,39}, {4,31}, {3,35}, {10,33}, {3,19}, {14,31}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {3,18}, {2,34}, {10,17}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {8,37}, {12,38}, {12,26}, {13,30}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {13,24}, {15,30}, {12,23}, {13,20}, {9,35}, {15,19}, {1,29}, {16,34}, {10,35}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {13,19}, {14,32}, {1,26}, {3,17}, {16,40}, {8,22}, {9,36}, {6,34}, {9,39}, {9,20}, {4,22}, {8,19}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {4,21}, {13,17}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {6,36}, {16,29}, {11,36}, {3,30}, {16,17}, {11,23}, {10,36}, {14,33}, {15,37}, {10,38}, {13,25}, {14,39}, {8,24}, {9,38}, {14,21}, {9,26}, {3,29}, {12,17}, {13,36}, {10,19}, {15,23}, {9,22}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {5,19}, {10,29}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {5,40}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {15,40}, {13,38}, {14,40}, {6,23}, {16,31}, {4,36}, {4,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {2,21}, {2,22}, {16,20}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {4,25}, {3,28}, {12,39}, {14,24}, {7,25}, {7,22}, {1,34}, {5,21}, {12,34}, {16,23}, {14,20}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {15,18}, {10,27}, {16,33}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {15,20}, {13,28}, {16,24}, {3,27}, {9,27}, {7,38}, {2,38}, {15,36}, {15,31}, {9,40}, {4,20}, {8,20}, {1,27}, {10,23}, {15,26}, {4,19}, {14,22}, {8,39}, {3,37}, {14,17}, {16,19}, {9,34}, {12,35}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {2,32}, {15,25}, {5,33}, {5,30}, {9,37} }; // ET40.126 // Bipartite(20,20) Valencies [18,18] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 7610145177600 EdgePairs[40][126]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {16,21}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {20,24}, {17,39}, {12,38}, {12,26}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {7,33}, {12,40}, {20,29}, {13,24}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {20,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {20,36}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {19,30}, {8,24}, {9,38}, {14,21}, {9,26}, {3,29}, {17,31}, {13,36}, {2,23}, {15,23}, {9,22}, {20,31}, {3,25}, {19,24}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {17,30}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {16,31}, {7,39}, {4,36}, {15,39}, {1,32}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {7,40}, {5,23}, {2,26}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {4,27}, {5,24}, {15,29}, {2,22}, {18,24}, {16,38}, {1,33}, {18,27}, {20,28}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {13,35}, {5,21}, {17,24}, {17,40}, {20,23}, {12,34}, {17,21}, {19,36}, {6,28}, {18,23}, {4,35}, {19,32}, {13,33}, {15,21}, {14,25}, {20,34}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {10,27}, {10,34}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {18,40}, {9,40}, {20,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {8,39}, {14,22}, {5,36}, {9,34}, {12,35}, {6,35}, {17,32}, {20,21}, {1,37}, {8,25}, {16,32}, {2,32}, {18,34}, {11,26}, {15,25}, {5,33}, {18,37}, {11,38}, {9,37}, {6,40} }; // ET40.127 // Non-bipartite Valency 18 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 1509949440 EdgePairs[40][127]:={ {13,21}, {24,34}, {15,33}, {6,38}, {14,36}, {9,32}, {35,38}, {5,38}, {9,17}, {10,18}, {19,26}, {4,28}, {25,37}, {12,22}, {8,26}, {22,40}, {5,11}, {13,37}, {14,38}, {17,33}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {21,30}, {3,19}, {14,31}, {30,40}, {5,15}, {24,32}, {27,33}, {10,39}, {3,20}, {2,18}, {26,37}, {3,21}, {3,39}, {19,37}, {20,37}, {21,28}, {11,14}, {5,32}, {7,30}, {2,7}, {29,39}, {4,40}, {13,27}, {19,21}, {2,33}, {6,32}, {11,29}, {1,12}, {11,27}, {20,38}, {2,34}, {10,17}, {9,18}, {20,26}, {12,28}, {26,38}, {2,25}, {21,40}, {18,32}, {8,30}, {8,13}, {23,38}, {1,17}, {33,39}, {4,16}, {29,33}, {28,31}, {12,20}, {17,39}, {31,36}, {12,38}, {23,31}, {1,13}, {3,10}, {8,9}, {19,22}, {3,9}, {26,29}, {10,26}, {2,17}, {20,29}, {1,24}, {15,30}, {5,37}, {27,32}, {12,13}, {26,35}, {16,25}, {24,31}, {20,35}, {9,35}, {15,19}, {1,29}, {12,37}, {16,34}, {35,37}, {10,35}, {18,39}, {24,26}, {31,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {36,38}, {20,36}, {16,40}, {8,22}, {26,36}, {24,37}, {9,36}, {6,34}, {9,39}, {4,22}, {18,33}, {1,18}, {5,27}, {7,14}, {5,28}, {32,35}, {8,18}, {14,35}, {27,39}, {28,40}, {27,40}, {19,38}, {3,31}, {12,27}, {11,22}, {5,12}, {6,27}, {2,30}, {2,8}, {4,9}, {3,36}, {34,40}, {6,12}, {25,29}, {4,21}, {13,17}, {20,25}, {4,32}, {1,30}, {2,13}, {13,18}, {8,10}, {14,28}, {11,21}, {8,17}, {16,29}, {10,16}, {3,16}, {2,24}, {10,36}, {6,16}, {15,34}, {11,33}, {32,38}, {19,30}, {4,10}, {9,26}, {14,21}, {28,34}, {17,31}, {13,36}, {2,23}, {20,22}, {22,29}, {15,23}, {11,34}, {17,28}, {11,13}, {7,35}, {25,30}, {22,30}, {27,34}, {12,30}, {2,12}, {10,31}, {9,31}, {5,19}, {24,25}, {13,22}, {1,25}, {6,19}, {20,30}, {13,31}, {9,16}, {24,38}, {3,32}, {14,27}, {6,11}, {9,25}, {4,5}, {16,30}, {10,25}, {12,29}, {6,31}, {15,24}, {16,26}, {33,40}, {15,40}, {3,22}, {14,37}, {13,38}, {36,37}, {4,15}, {18,31}, {6,23}, {25,38}, {7,39}, {23,34}, {4,36}, {15,39}, {31,37}, {21,39}, {19,29}, {28,32}, {6,37}, {22,39}, {32,37}, {9,24}, {5,31}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {34,39}, {10,40}, {12,14}, {23,37}, {26,30}, {7,29}, {8,29}, {9,23}, {7,21}, {28,39}, {8,36}, {2,11}, {13,32}, {23,32}, {10,15}, {11,30}, {3,5}, {1,11}, {4,27}, {18,28}, {5,24}, {15,29}, {16,20}, {18,24}, {25,36}, {1,33}, {18,27}, {1,7}, {19,25}, {2,37}, {3,28}, {31,35}, {12,33}, {11,19}, {30,33}, {1,8}, {17,34}, {21,35}, {28,33}, {8,14}, {7,10}, {3,6}, {19,35}, {3,15}, {7,25}, {7,22}, {1,14}, {1,34}, {22,27}, {30,34}, {13,35}, {14,18}, {21,27}, {9,15}, {21,29}, {17,24}, {17,40}, {12,34}, {19,36}, {6,28}, {16,23}, {18,23}, {4,35}, {7,26}, {7,18}, {11,37}, {23,33}, {11,28}, {1,23}, {5,16}, {10,24}, {11,20}, {16,33}, {3,40}, {7,17}, {8,35}, {17,27}, {32,36}, {15,20}, {16,39}, {13,28}, {23,25}, {16,24}, {3,27}, {2,38}, {7,9}, {25,35}, {22,35}, {21,36}, {18,40}, {9,40}, {4,20}, {17,23}, {10,23}, {15,26}, {22,36}, {4,6}, {27,31}, {4,19}, {14,22}, {8,39}, {7,13}, {14,17}, {16,19}, {24,33}, {10,32}, {4,39}, {7,36}, {17,32}, {29,34}, {12,19}, {23,26}, {20,21}, {22,28}, {1,37}, {8,25}, {30,39}, {6,33}, {12,21}, {2,14}, {18,34}, {15,25}, {5,33}, {11,38}, {29,40} }; // ET40.128 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 2880 EdgePairs[40][128]:={ {24,34}, {11,40}, {31,39}, {5,38}, {23,29}, {3,8}, {4,28}, {11,25}, {12,22}, {25,40}, {5,11}, {1,40}, {17,33}, {4,31}, {8,40}, {6,15}, {11,15}, {21,30}, {3,19}, {30,40}, {15,27}, {5,15}, {24,32}, {1,19}, {24,36}, {12,16}, {10,39}, {3,20}, {2,18}, {26,37}, {3,39}, {21,28}, {16,28}, {2,7}, {29,39}, {6,9}, {4,37}, {4,40}, {6,14}, {16,21}, {24,28}, {19,21}, {17,35}, {11,35}, {11,27}, {1,20}, {3,18}, {8,16}, {12,28}, {19,31}, {26,38}, {2,25}, {18,32}, {2,6}, {32,33}, {4,30}, {8,13}, {9,33}, {8,12}, {1,17}, {33,39}, {4,16}, {29,33}, {28,31}, {8,37}, {20,24}, {26,39}, {7,11}, {31,36}, {23,31}, {1,13}, {12,26}, {2,5}, {8,9}, {19,22}, {6,39}, {26,29}, {10,26}, {2,17}, {12,40}, {13,24}, {2,15}, {12,23}, {22,25}, {5,37}, {27,32}, {18,35}, {16,25}, {24,31}, {28,30}, {9,35}, {15,19}, {1,29}, {6,18}, {12,37}, {35,37}, {10,35}, {24,26}, {31,38}, {8,38}, {34,37}, {13,26}, {17,36}, {30,36}, {2,29}, {1,38}, {13,19}, {1,26}, {36,38}, {20,36}, {27,30}, {18,29}, {9,36}, {6,34}, {9,39}, {30,38}, {18,36}, {3,38}, {7,14}, {15,28}, {6,17}, {32,35}, {6,10}, {4,7}, {8,18}, {4,18}, {27,39}, {28,40}, {12,24}, {27,40}, {1,31}, {3,13}, {11,22}, {9,13}, {35,39}, {1,39}, {5,12}, {2,30}, {5,35}, {25,29}, {17,29}, {13,17}, {7,19}, {4,32}, {16,18}, {2,13}, {13,18}, {12,15}, {8,10}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {3,30}, {11,16}, {10,36}, {10,38}, {6,16}, {11,33}, {18,22}, {21,25}, {13,25}, {21,31}, {32,38}, {19,30}, {7,12}, {31,33}, {9,38}, {27,37}, {14,21}, {5,14}, {32,40}, {3,29}, {29,36}, {20,22}, {10,13}, {22,29}, {25,32}, {15,23}, {20,31}, {3,25}, {19,24}, {11,34}, {11,13}, {7,35}, {22,30}, {2,27}, {7,34}, {11,24}, {1,6}, {5,19}, {13,22}, {23,35}, {20,30}, {6,19}, {2,20}, {4,17}, {5,39}, {3,32}, {14,27}, {25,31}, {2,16}, {6,11}, {8,34}, {9,25}, {4,5}, {17,30}, {10,22}, {28,37}, {33,38}, {21,32}, {3,7}, {12,25}, {33,40}, {1,16}, {4,14}, {23,27}, {24,35}, {36,37}, {4,15}, {18,31}, {25,38}, {15,17}, {7,39}, {23,34}, {34,38}, {1,32}, {1,5}, {24,29}, {31,37}, {19,29}, {6,37}, {24,27}, {32,37}, {10,28}, {9,24}, {19,34}, {7,40}, {20,32}, {5,20}, {2,26}, {34,39}, {10,40}, {12,14}, {18,21}, {10,21}, {9,21}, {26,30}, {29,37}, {9,23}, {28,29}, {14,26}, {19,33}, {9,28}, {30,35}, {36,40}, {16,20}, {25,39}, {2,31}, {21,33}, {12,36}, {16,27}, {3,14}, {2,37}, {4,8}, {4,25}, {3,28}, {21,34}, {31,35}, {12,33}, {8,33}, {12,39}, {1,8}, {3,6}, {22,33}, {20,33}, {35,40}, {14,24}, {19,35}, {3,15}, {1,14}, {26,32}, {22,27}, {30,34}, {14,18}, {9,15}, {17,24}, {20,23}, {12,34}, {17,21}, {23,30}, {16,23}, {18,23}, {14,20}, {14,25}, {15,21}, {20,34}, {11,37}, {23,33}, {7,16}, {5,18}, {10,27}, {10,34}, {7,17}, {8,35}, {13,23}, {2,40}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {23,25}, {16,24}, {28,38}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {7,9}, {22,35}, {21,36}, {5,10}, {8,20}, {1,27}, {5,13}, {32,34}, {17,23}, {10,23}, {15,26}, {22,36}, {27,31}, {4,19}, {14,22}, {3,37}, {22,32}, {7,13}, {9,14}, {14,17}, {16,19}, {5,36}, {10,14}, {4,39}, {7,36}, {17,32}, {29,34}, {23,26}, {21,26}, {22,28}, {30,39}, {6,33}, {18,34}, {11,26}, {5,33}, {11,38}, {9,37}, {6,40}, {29,40} }; // ET40.129 // Non-bipartite Valency 18 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[40][129]:={ {15,33}, {10,37}, {31,39}, {14,36}, {6,25}, {35,38}, {5,38}, {19,26}, {3,26}, {16,22}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {5,15}, {27,33}, {24,36}, {3,23}, {8,23}, {3,20}, {2,18}, {26,37}, {1,21}, {3,21}, {36,39}, {3,39}, {20,37}, {5,32}, {1,35}, {7,30}, {2,7}, {4,37}, {4,40}, {6,14}, {13,40}, {2,33}, {11,29}, {1,12}, {6,29}, {1,20}, {3,18}, {19,40}, {8,16}, {10,17}, {9,18}, {2,25}, {4,24}, {21,40}, {2,6}, {32,33}, {8,13}, {23,38}, {1,17}, {1,9}, {33,39}, {29,33}, {28,31}, {4,13}, {8,37}, {17,39}, {12,38}, {1,13}, {7,27}, {8,9}, {2,10}, {19,22}, {3,9}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {23,28}, {10,20}, {1,24}, {13,24}, {15,30}, {2,15}, {12,23}, {20,39}, {27,32}, {13,20}, {26,35}, {18,35}, {24,31}, {20,35}, {28,30}, {6,18}, {16,34}, {10,35}, {24,26}, {31,38}, {11,18}, {34,37}, {13,26}, {17,36}, {30,36}, {2,29}, {1,26}, {14,32}, {2,36}, {7,15}, {22,34}, {24,37}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {18,26}, {4,22}, {3,38}, {7,14}, {15,28}, {5,28}, {6,10}, {27,39}, {28,40}, {19,38}, {1,31}, {12,27}, {25,33}, {11,22}, {1,39}, {5,12}, {6,27}, {14,34}, {34,40}, {25,29}, {13,17}, {20,25}, {7,19}, {1,30}, {19,27}, {12,15}, {23,40}, {8,17}, {16,29}, {11,36}, {16,17}, {3,30}, {3,16}, {22,26}, {11,16}, {15,37}, {14,23}, {6,16}, {11,33}, {21,25}, {14,39}, {7,12}, {9,38}, {27,37}, {4,10}, {14,21}, {21,37}, {32,40}, {28,34}, {12,17}, {2,23}, {10,13}, {9,19}, {20,31}, {24,39}, {19,24}, {11,13}, {7,35}, {22,30}, {12,30}, {11,24}, {5,19}, {9,31}, {13,22}, {22,31}, {23,35}, {20,30}, {13,31}, {9,16}, {4,17}, {3,32}, {14,27}, {25,31}, {6,11}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {33,38}, {6,22}, {4,34}, {17,38}, {29,38}, {6,31}, {11,32}, {15,24}, {21,32}, {3,7}, {16,26}, {12,25}, {15,40}, {1,16}, {27,35}, {14,37}, {13,38}, {36,37}, {4,15}, {18,31}, {6,23}, {25,38}, {7,39}, {23,34}, {4,36}, {4,29}, {1,5}, {24,29}, {19,29}, {6,37}, {8,32}, {22,39}, {24,27}, {32,37}, {7,24}, {9,24}, {17,22}, {17,25}, {19,34}, {2,19}, {6,20}, {10,40}, {12,14}, {18,21}, {9,21}, {26,30}, {2,28}, {8,29}, {22,38}, {8,36}, {3,33}, {2,11}, {23,32}, {10,15}, {3,5}, {9,28}, {4,27}, {18,28}, {5,24}, {2,22}, {8,11}, {18,24}, {25,36}, {25,39}, {14,19}, {16,38}, {20,28}, {21,33}, {16,27}, {3,14}, {5,26}, {3,11}, {4,8}, {4,25}, {14,30}, {3,28}, {31,35}, {7,31}, {5,9}, {1,8}, {4,12}, {21,35}, {28,36}, {31,34}, {7,10}, {27,29}, {20,33}, {35,40}, {7,22}, {26,32}, {1,34}, {30,34}, {13,35}, {14,18}, {5,21}, {21,27}, {21,29}, {20,23}, {12,34}, {19,36}, {23,30}, {16,23}, {19,32}, {13,33}, {15,21}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {16,35}, {11,20}, {15,18}, {10,27}, {5,17}, {17,27}, {2,40}, {32,36}, {15,20}, {16,39}, {13,28}, {26,34}, {23,25}, {28,38}, {7,38}, {2,38}, {15,36}, {15,31}, {8,28}, {18,40}, {8,20}, {26,40}, {1,27}, {5,13}, {17,23}, {10,23}, {22,36}, {4,6}, {4,19}, {29,35}, {9,14}, {16,19}, {5,36}, {9,34}, {24,33}, {10,32}, {12,35}, {6,35}, {17,32}, {12,19}, {20,21}, {22,28}, {1,37}, {8,25}, {30,39}, {30,37}, {16,32}, {2,32}, {12,21}, {2,14}, {18,34}, {11,26}, {15,25}, {5,33}, {18,37}, {5,30}, {29,40} }; // ET40.130 // Bipartite(20,20) Valencies [19,19] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 4865804016353280000 EdgePairs[40][130]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {8,23}, {10,39}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {5,32}, {1,35}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {8,37}, {20,24}, {17,39}, {12,38}, {12,26}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {20,36}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {14,35}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {9,38}, {14,21}, {9,26}, {18,38}, {3,29}, {17,31}, {13,36}, {2,23}, {20,22}, {15,23}, {9,22}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {16,26}, {15,40}, {3,22}, {13,38}, {18,31}, {14,40}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {19,34}, {7,40}, {5,23}, {20,32}, {2,26}, {10,40}, {18,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {2,31}, {1,33}, {18,27}, {20,28}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {5,29}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {14,24}, {19,35}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {20,23}, {12,34}, {17,21}, {19,36}, {6,28}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,25}, {15,21}, {20,34}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {6,21}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {20,40}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {14,22}, {8,39}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {20,21}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.131 // Bipartite(15,25) Valencies [20,12] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 600 EdgePairs[40][131]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {2,35}, {4,31}, {8,40}, {3,35}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {6,29}, {1,20}, {8,16}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {1,17}, {4,16}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {10,26}, {2,17}, {7,33}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {5,34}, {1,38}, {13,19}, {14,32}, {3,17}, {2,36}, {9,36}, {9,29}, {9,39}, {9,20}, {4,22}, {1,18}, {3,38}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {14,34}, {13,17}, {4,32}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,33}, {15,37}, {14,23}, {10,38}, {6,16}, {15,34}, {13,25}, {14,39}, {8,24}, {14,21}, {3,29}, {12,17}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {4,33}, {1,22}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {10,30}, {5,40}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {15,40}, {3,22}, {13,38}, {6,23}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {2,31}, {14,19}, {1,33}, {12,36}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {12,33}, {11,19}, {8,33}, {12,39}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {13,33}, {14,20}, {15,21}, {7,26}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {10,27}, {10,34}, {15,18}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {15,22}, {4,26}, {1,28}, {7,20}, {9,27}, {7,38}, {12,32}, {15,36}, {15,31}, {8,20}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {8,39}, {3,37}, {14,17}, {5,36}, {9,34}, {4,39}, {12,35}, {7,36}, {12,19}, {1,37}, {8,25}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.132 // Bipartite(15,25) Valencies [20,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23219011584000000 EdgePairs[40][132]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {5,38}, {5,22}, {10,18}, {9,17}, {12,22}, {3,26}, {8,26}, {13,39}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {7,30}, {8,31}, {4,40}, {4,37}, {14,29}, {13,40}, {2,33}, {6,32}, {11,29}, {11,17}, {6,29}, {11,27}, {3,18}, {8,16}, {10,17}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {1,17}, {4,16}, {12,20}, {12,38}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {11,18}, {8,38}, {13,26}, {6,24}, {13,16}, {2,29}, {1,38}, {13,19}, {1,26}, {14,32}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {7,19}, {4,32}, {13,18}, {11,21}, {6,36}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {15,37}, {10,38}, {6,16}, {11,33}, {13,25}, {14,39}, {8,24}, {14,21}, {9,26}, {3,29}, {12,17}, {13,36}, {2,23}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {15,40}, {14,37}, {13,38}, {14,40}, {6,23}, {15,17}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {7,40}, {5,23}, {5,20}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {14,16}, {8,36}, {3,33}, {14,26}, {3,34}, {4,27}, {2,22}, {14,19}, {1,33}, {5,26}, {2,37}, {4,25}, {3,28}, {14,30}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {12,34}, {6,28}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,18}, {11,37}, {11,28}, {5,18}, {5,16}, {1,23}, {10,27}, {15,18}, {5,17}, {3,40}, {15,16}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {4,26}, {15,20}, {13,28}, {1,28}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {8,39}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37} }; // ET40.133 // Bipartite(20,20) Valencies [20,20] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 11838024362779855370834883379200000000 EdgePairs[40][133]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {20,24}, {17,39}, {12,38}, {12,26}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {20,35}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {20,36}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {9,38}, {14,21}, {9,26}, {18,38}, {3,29}, {17,31}, {13,36}, {2,23}, {20,22}, {15,23}, {9,22}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {7,40}, {5,23}, {20,32}, {2,26}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {20,28}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {14,24}, {19,35}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {17,40}, {20,23}, {12,34}, {17,21}, {19,36}, {6,28}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,25}, {15,21}, {20,34}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {20,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {14,22}, {8,39}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {20,21}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.134 // Bipartite(12,28) Valencies [21,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 20069584852746240000 EdgePairs[40][134]:={ {5,17}, {1,20}, {10,25}, {11,20}, {9,28}, {2,33}, {11,36}, {4,27}, {12,29}, {7,15}, {11,35}, {5,34}, {4,24}, {3,22}, {3,40}, {4,16}, {10,37}, {6,17}, {2,23}, {1,13}, {5,38}, {12,32}, {7,38}, {8,28}, {4,29}, {1,32}, {8,33}, {3,15}, {10,23}, {1,40}, {10,26}, {2,15}, {4,19}, {7,22}, {12,39}, {4,31}, {2,19}, {2,27}, {10,33}, {3,35}, {5,20}, {2,26}, {7,34}, {8,39}, {1,21}, {11,14}, {12,35}, {7,36}, {8,25}, {2,14}, {1,30}, {5,32}, {8,15}, {4,23}, {8,27}, {8,31}, {12,37}, {10,15}, {10,22}, {6,22}, {3,18}, {11,28}, {10,30}, {6,29}, {8,16}, {6,21}, {3,34}, {5,40}, {2,25}, {11,38}, {6,31}, {1,38}, {2,34}, {1,17}, {5,22}, {8,19}, {9,29}, {10,38}, {1,18}, {3,14}, {7,20}, {9,32}, {12,17}, {9,26}, {12,20}, {12,36}, {5,29}, {2,38}, {2,37}, {7,39}, {5,25}, {2,39}, {7,32}, {11,15}, {11,22}, {9,14}, {11,31}, {2,35}, {1,22}, {12,13}, {6,30}, {4,33}, {12,16}, {4,21}, {10,29}, {3,20}, {10,31}, {9,34}, {2,13}, {10,21}, {6,18}, {1,29}, {7,30}, {8,17}, {3,39}, {3,32}, {4,35}, {9,25}, {7,16}, {7,26}, {6,33}, {8,36}, {5,18}, {11,23}, {5,30}, {11,30}, {5,24}, {9,37}, {12,28}, {12,25}, {8,13}, {8,35}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {6,23}, {3,26}, {8,37}, {5,28}, {9,22}, {7,31}, {12,33}, {6,15}, {2,17}, {4,36}, {9,13}, {12,27}, {9,40}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {11,39}, {6,26}, {8,40}, {12,19}, {12,40}, {3,23}, {8,23}, {5,36}, {1,25}, {6,19}, {12,15}, {6,14}, {9,30}, {10,39}, {1,37}, {7,28}, {3,16}, {4,37}, {11,26}, {4,40}, {10,35}, {7,23}, {11,16}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {1,16}, {10,34}, {11,32}, {9,17}, {10,18}, {8,24}, {6,25}, {6,38}, {2,31}, {11,40}, {9,33}, {9,36}, {6,34}, {5,26}, {9,38}, {11,19}, {4,25}, {10,19}, {3,38}, {4,20}, {5,13}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {3,31}, {1,14}, {9,24}, {6,39}, {6,37}, {12,31}, {10,14}, {11,34}, {7,35}, {5,21}, {2,30}, {6,13}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {9,16}, {9,21}, {4,39}, {7,40}, {8,29}, {4,32}, {11,18}, {1,36}, {12,21}, {7,18}, {5,16} }; // ET40.135 // Bipartite(16,24) Valencies [21,14] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 17336861982720 EdgePairs[40][135]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {14,36}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {12,22}, {8,26}, {13,37}, {14,38}, {16,22}, {13,39}, {2,35}, {4,31}, {8,40}, {3,35}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {4,37}, {4,40}, {16,21}, {13,40}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {11,27}, {1,20}, {2,34}, {9,18}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {8,37}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {13,24}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {8,38}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {3,17}, {2,36}, {16,40}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {13,29}, {8,34}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {13,38}, {14,40}, {6,23}, {15,17}, {7,39}, {15,39}, {4,29}, {8,32}, {7,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {7,25}, {6,26}, {1,34}, {14,18}, {5,21}, {12,34}, {6,28}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {4,26}, {15,20}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {3,37}, {14,17}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.136 // Bipartite(19,21) Valencies [21,19] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6214962790459424069688313774080000000 EdgePairs[40][136]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {19,20}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {19,40}, {2,34}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {17,39}, {12,38}, {12,26}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {9,38}, {9,26}, {14,21}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {2,23}, {15,23}, {9,22}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {2,20}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {19,35}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {17,40}, {12,34}, {17,21}, {19,36}, {6,28}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {4,26}, {15,20}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {8,39}, {14,22}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.137 // Bipartite(18,22) Valencies [22,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7196272704742491028060152791040000000 EdgePairs[40][137]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {17,39}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {13,19}, {1,26}, {14,32}, {2,36}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {14,21}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {7,28}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {14,19}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {17,24}, {17,40}, {12,34}, {17,21}, {6,28}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.138 // Bipartite(17,23) Valencies [23,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 9195237344948738535854639677440000000 EdgePairs[40][138]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {11,25}, {4,28}, {17,18}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {17,39}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {13,19}, {1,26}, {14,32}, {2,36}, {16,40}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {17,31}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {17,24}, {17,40}, {12,34}, {17,21}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {16,33}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.139 // Bipartite(8,32) Valencies [24,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1014876784652451840000 EdgePairs[40][139]:={ {5,17}, {1,20}, {2,33}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {3,22}, {3,40}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {5,38}, {8,9}, {7,38}, {8,28}, {4,29}, {1,32}, {8,33}, {3,15}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {8,39}, {1,21}, {2,9}, {7,36}, {8,25}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {6,29}, {8,16}, {6,21}, {3,34}, {5,40}, {2,25}, {7,12}, {6,31}, {1,38}, {2,34}, {1,17}, {5,22}, {8,19}, {1,18}, {7,11}, {3,14}, {7,20}, {2,10}, {5,29}, {2,38}, {2,37}, {7,39}, {5,25}, {2,39}, {7,32}, {3,12}, {2,35}, {1,22}, {6,30}, {4,33}, {4,21}, {3,20}, {2,13}, {6,18}, {1,29}, {7,30}, {8,17}, {3,39}, {3,32}, {4,35}, {7,16}, {6,33}, {1,12}, {7,26}, {8,36}, {5,18}, {5,30}, {8,11}, {5,24}, {8,13}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {6,23}, {3,10}, {3,26}, {8,37}, {5,28}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {6,27}, {6,26}, {8,40}, {3,23}, {8,23}, {5,36}, {1,25}, {6,19}, {6,9}, {6,14}, {2,11}, {1,37}, {7,28}, {3,16}, {4,37}, {4,40}, {7,23}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {8,24}, {6,25}, {6,38}, {2,31}, {6,34}, {6,10}, {5,10}, {5,26}, {5,9}, {4,25}, {3,38}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {1,14}, {6,39}, {6,37}, {7,35}, {5,21}, {2,30}, {6,13}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET40.140 // Bipartite(8,32) Valencies [24,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 75497472 EdgePairs[40][140]:={ {1,11}, {3,33}, {2,24}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,40}, {4,16}, {8,30}, {6,17}, {1,13}, {5,38}, {3,9}, {7,38}, {4,29}, {1,32}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {7,22}, {4,31}, {1,19}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {8,39}, {1,21}, {2,9}, {7,36}, {8,10}, {2,28}, {1,30}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {6,29}, {3,17}, {8,16}, {6,21}, {2,25}, {5,40}, {7,12}, {6,31}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {8,19}, {1,18}, {7,11}, {7,20}, {3,14}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {8,14}, {7,39}, {5,25}, {7,32}, {3,12}, {7,25}, {1,22}, {6,30}, {4,33}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {7,30}, {2,16}, {3,39}, {4,35}, {7,16}, {7,26}, {1,12}, {6,33}, {2,32}, {8,36}, {5,18}, {1,23}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {6,23}, {3,10}, {3,26}, {5,28}, {8,26}, {6,15}, {2,17}, {5,12}, {8,32}, {3,19}, {5,31}, {6,26}, {8,40}, {3,23}, {8,23}, {1,39}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {6,14}, {1,35}, {1,37}, {7,28}, {4,37}, {4,40}, {7,23}, {6,36}, {2,21}, {3,30}, {8,34}, {3,24}, {2,29}, {8,38}, {2,22}, {4,34}, {1,16}, {8,24}, {6,25}, {7,9}, {6,38}, {2,40}, {2,31}, {6,10}, {5,27}, {8,18}, {4,18}, {5,9}, {4,11}, {4,12}, {5,13}, {3,28}, {8,20}, {7,27}, {7,10}, {7,24}, {3,31}, {2,12}, {1,14}, {6,39}, {5,15}, {6,37}, {7,33}, {5,19}, {6,20}, {5,21}, {6,13}, {5,35}, {2,18}, {1,34}, {5,37}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {8,29}, {4,32}, {7,18} }; // ET40.141 // Bipartite(10,30) Valencies [24,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 743008370688000000 EdgePairs[40][141]:={ {1,11}, {3,33}, {2,24}, {5,17}, {10,25}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {4,24}, {4,26}, {3,40}, {4,16}, {10,37}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {5,38}, {7,38}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {10,26}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {10,33}, {3,35}, {5,20}, {7,34}, {8,39}, {1,21}, {8,25}, {2,28}, {2,14}, {5,32}, {6,11}, {8,15}, {9,35}, {8,31}, {9,11}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {8,16}, {6,21}, {3,34}, {5,40}, {2,25}, {7,12}, {6,31}, {1,38}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {10,38}, {1,18}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {2,38}, {9,19}, {2,37}, {8,14}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {7,13}, {9,14}, {7,25}, {10,28}, {2,35}, {1,22}, {6,12}, {5,23}, {4,21}, {3,20}, {10,31}, {9,34}, {2,13}, {10,21}, {2,20}, {6,18}, {10,40}, {1,29}, {7,30}, {3,39}, {4,35}, {9,25}, {2,32}, {1,12}, {6,33}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {9,37}, {8,13}, {8,35}, {9,20}, {4,15}, {1,28}, {3,11}, {7,14}, {1,33}, {10,13}, {10,12}, {3,29}, {6,23}, {3,26}, {5,28}, {8,26}, {9,22}, {2,17}, {4,36}, {5,12}, {9,40}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {8,40}, {3,23}, {8,23}, {1,39}, {10,32}, {5,36}, {3,21}, {6,19}, {9,12}, {7,29}, {6,28}, {6,14}, {9,30}, {10,11}, {1,37}, {7,28}, {3,16}, {4,37}, {4,40}, {10,35}, {7,23}, {6,36}, {3,30}, {5,33}, {8,34}, {10,17}, {3,24}, {2,29}, {8,38}, {10,27}, {1,26}, {2,22}, {4,34}, {1,16}, {10,36}, {4,14}, {9,17}, {10,18}, {8,24}, {6,38}, {2,40}, {9,36}, {6,34}, {5,27}, {5,26}, {8,18}, {9,39}, {4,25}, {3,38}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {9,24}, {10,20}, {5,15}, {6,39}, {6,37}, {7,33}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {9,31}, {5,37}, {7,19}, {4,17}, {3,36}, {9,16}, {9,21}, {4,39}, {7,40}, {8,29}, {4,32}, {1,36}, {7,18}, {10,16}, {5,16} }; // ET40.142 // Bipartite(16,24) Valencies [24,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12981511545809983815324197191680000000 EdgePairs[40][142]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {16,40}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {6,23}, {16,31}, {15,17}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {4,26}, {15,20}, {16,39}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {14,17}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {16,32}, {2,32}, {12,21}, {6,33}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.143 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 3019898880 EdgePairs[40][143]:={ {13,25}, {15,28}, {13,40}, {24,33}, {6,36}, {15,17}, {20,26}, {3,29}, {16,28}, {20,33}, {4,26}, {20,25}, {2,20}, {16,17}, {8,28}, {5,32}, {4,24}, {8,37}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {14,17}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {8,36}, {9,21}, {3,15}, {8,20}, {19,37}, {5,18}, {17,29}, {3,10}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {2,12}, {6,28}, {12,32}, {22,25}, {2,30}, {14,25}, {5,9}, {3,25}, {10,27}, {7,10}, {4,30}, {21,35}, {8,11}, {2,38}, {31,37}, {6,34}, {4,38}, {11,39}, {21,31}, {3,13}, {2,21}, {16,33}, {19,38}, {7,26}, {31,36}, {18,28}, {4,34}, {22,28}, {31,38}, {10,22}, {18,37}, {20,29}, {12,22}, {14,40}, {15,20}, {23,34}, {24,36}, {14,33}, {3,32}, {11,31}, {7,13}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {13,17}, {11,21}, {19,40}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {3,14}, {23,33}, {9,22}, {31,35}, {5,20}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {13,33}, {18,35}, {10,23}, {22,27}, {30,34}, {20,32}, {18,31}, {9,27}, {24,30}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {20,39}, {5,33}, {4,39}, {6,11}, {1,22}, {6,24}, {6,39}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {28,39}, {3,16}, {22,26}, {30,40}, {2,28}, {1,27}, {3,23}, {1,12}, {5,36}, {12,39}, {6,12}, {21,36}, {12,33}, {1,37}, {13,18}, {25,38}, {26,37}, {1,29}, {10,19}, {15,27}, {14,35}, {11,32}, {3,31}, {11,18}, {21,25}, {9,28}, {8,10}, {20,40}, {16,35}, {21,40}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {27,38}, {12,21}, {1,14}, {10,20}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {21,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {27,33}, {14,18}, {32,37}, {14,36}, {24,25}, {23,26}, {7,29}, {28,40}, {3,37}, {29,36}, {1,35}, {17,28}, {26,35}, {7,36}, {9,39}, {13,26}, {22,33}, {11,24}, {20,31}, {8,33}, {10,28}, {12,17}, {9,19}, {13,35}, {1,13}, {16,37}, {13,32}, {10,24}, {17,36}, {26,39}, {23,28}, {2,14}, {9,35}, {12,24}, {14,28}, {30,36}, {15,36}, {10,36}, {16,29}, {28,37}, {2,40}, {1,11}, {29,33}, {24,34}, {15,30}, {4,40}, {23,38}, {2,16}, {16,36}, {29,40}, {1,39}, {17,37}, {14,19}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {15,29}, {20,38}, {30,33}, {4,15}, {27,40}, {4,29}, {8,25}, {5,34}, {1,30}, {3,26}, {13,36}, {9,23}, {16,22}, {14,26}, {9,40}, {14,31}, {8,22}, {14,20}, {20,37}, {11,33}, {7,25}, {22,40}, {24,35}, {24,37}, {8,27}, {15,22}, {16,27}, {9,30}, {2,13}, {5,40}, {22,36}, {27,34}, {26,40}, {4,13}, {18,30}, {8,17}, {4,22}, {1,40}, {6,23}, {1,23}, {17,31}, {8,29}, {7,22}, {25,40}, {15,25}, {5,19}, {13,28}, {16,25}, {6,32}, {17,35}, {10,35}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {18,39}, {13,20}, {7,12}, {31,33}, {3,38}, {4,10}, {14,34}, {11,23}, {15,19}, {29,34}, {15,38}, {7,38}, {22,39}, {8,9}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {24,27}, {21,33}, {17,38}, {25,39}, {24,28}, {4,14}, {6,25}, {28,34}, {13,39}, {11,17}, {28,38}, {15,18}, {32,34}, {24,29}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {17,39}, {4,9}, {5,10}, {24,26}, {11,26}, {13,24}, {6,16}, {26,36}, {20,34}, {4,31}, {2,15}, {10,39}, {13,34}, {23,25}, {26,38}, {8,14}, {1,38}, {2,29}, {20,30}, {3,21}, {1,36}, {18,40}, {32,33}, {9,24}, {14,39}, {6,20}, {3,39}, {6,26}, {23,35}, {12,34}, {8,19}, {7,21}, {11,30}, {2,23}, {15,21}, {9,38}, {27,37}, {12,30}, {2,32}, {6,33}, {19,26}, {29,39}, {4,23}, {22,34}, {24,38}, {9,36}, {32,36}, {8,13}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {27,39}, {11,25}, {25,35}, {17,27}, {11,40}, {16,18}, {5,35}, {11,22}, {9,32}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {22,35}, {5,39}, {1,21}, {19,34}, {23,37}, {8,12}, {7,20}, {3,40}, {23,27}, {16,19}, {31,34}, {21,39}, {7,18}, {10,21}, {3,33}, {32,38}, {5,17}, {1,24}, {19,25}, {4,18}, {15,26}, {21,28}, {23,36}, {16,38}, {12,37}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {29,35}, {30,39}, {4,37}, {28,33}, {12,29}, {7,19}, {2,35}, {10,32}, {25,37}, {5,11}, {2,31} }; // ET40.144 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 7608405715845120 EdgePairs[40][144]:={ {13,25}, {15,28}, {6,36}, {24,33}, {30,37}, {15,17}, {3,29}, {16,28}, {5,13}, {20,33}, {4,26}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {36,37}, {8,37}, {1,5}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {17,29}, {5,18}, {23,29}, {7,17}, {13,22}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,11}, {2,38}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {21,31}, {3,13}, {31,36}, {11,27}, {22,28}, {31,38}, {10,22}, {25,29}, {25,32}, {20,29}, {12,22}, {4,5}, {15,20}, {23,34}, {24,36}, {11,35}, {3,27}, {3,32}, {7,13}, {10,13}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {14,27}, {34,39}, {2,8}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {35,40}, {6,19}, {27,32}, {28,32}, {16,20}, {2,37}, {8,40}, {1,31}, {6,35}, {17,32}, {36,38}, {21,30}, {16,23}, {3,14}, {23,33}, {9,22}, {31,35}, {29,38}, {5,20}, {8,39}, {22,32}, {7,34}, {1,20}, {7,14}, {12,38}, {18,35}, {10,23}, {30,34}, {22,27}, {15,24}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {24,30}, {34,40}, {8,35}, {11,38}, {6,40}, {3,6}, {5,33}, {4,39}, {7,16}, {6,11}, {6,39}, {35,39}, {19,35}, {10,14}, {19,31}, {14,23}, {28,39}, {3,16}, {18,21}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {9,25}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {12,33}, {5,38}, {1,37}, {33,40}, {13,18}, {25,38}, {26,37}, {1,29}, {15,27}, {3,31}, {3,20}, {21,25}, {9,28}, {6,13}, {8,10}, {19,24}, {35,38}, {36,39}, {9,37}, {27,38}, {2,5}, {12,21}, {1,14}, {8,34}, {13,19}, {21,34}, {18,34}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {1,17}, {20,23}, {9,14}, {32,37}, {24,25}, {26,31}, {23,26}, {18,22}, {34,38}, {6,37}, {12,28}, {3,37}, {29,36}, {28,40}, {23,32}, {7,36}, {9,39}, {13,26}, {22,33}, {11,24}, {20,31}, {8,33}, {4,7}, {10,28}, {15,23}, {2,7}, {30,38}, {1,13}, {10,24}, {2,25}, {17,36}, {17,23}, {26,39}, {23,28}, {21,29}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {30,36}, {10,36}, {28,37}, {2,40}, {36,40}, {29,33}, {24,34}, {3,19}, {4,40}, {2,16}, {29,40}, {1,39}, {7,40}, {14,19}, {21,27}, {10,37}, {7,35}, {9,13}, {30,33}, {4,15}, {27,40}, {4,29}, {5,34}, {1,30}, {3,26}, {9,23}, {3,8}, {16,22}, {32,40}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {9,40}, {32,39}, {14,20}, {11,33}, {19,23}, {11,16}, {24,35}, {24,31}, {15,22}, {16,27}, {2,13}, {5,40}, {22,36}, {22,30}, {26,40}, {4,13}, {18,30}, {8,17}, {28,31}, {1,40}, {10,26}, {17,31}, {25,40}, {19,36}, {9,34}, {15,25}, {5,19}, {13,28}, {16,25}, {17,35}, {10,35}, {4,27}, {18,36}, {14,24}, {4,17}, {7,11}, {4,32}, {2,27}, {1,19}, {6,17}, {32,35}, {19,33}, {19,29}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,38}, {33,37}, {11,23}, {3,5}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {7,38}, {17,24}, {12,23}, {8,18}, {4,25}, {10,38}, {3,30}, {24,27}, {18,33}, {1,7}, {8,15}, {21,33}, {10,34}, {25,39}, {24,28}, {4,14}, {11,28}, {33,38}, {28,38}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {7,9}, {6,18}, {5,12}, {5,10}, {24,26}, {11,26}, {13,24}, {11,13}, {6,16}, {20,34}, {4,31}, {2,15}, {10,33}, {10,39}, {20,24}, {23,25}, {26,38}, {18,24}, {8,14}, {1,38}, {5,37}, {2,29}, {20,30}, {14,21}, {33,39}, {26,30}, {2,6}, {32,33}, {24,32}, {9,24}, {4,6}, {6,20}, {3,39}, {11,15}, {23,35}, {12,34}, {8,19}, {4,20}, {23,31}, {12,16}, {34,37}, {7,39}, {15,21}, {9,38}, {27,37}, {1,8}, {2,32}, {6,33}, {29,39}, {12,14}, {22,34}, {27,30}, {9,36}, {32,36}, {8,13}, {10,40}, {16,21}, {29,37}, {12,40}, {27,39}, {11,25}, {6,38}, {2,17}, {11,40}, {25,31}, {16,18}, {5,14}, {5,35}, {11,22}, {9,16}, {30,35}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {22,35}, {5,39}, {26,29}, {19,34}, {9,15}, {8,12}, {7,20}, {3,40}, {23,27}, {16,19}, {12,36}, {27,31}, {31,34}, {7,18}, {10,21}, {32,38}, {28,30}, {5,17}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {12,37}, {4,8}, {17,30}, {2,19}, {1,16}, {6,15}, {7,33}, {1,15}, {20,36}, {29,35}, {27,29}, {30,39}, {31,40}, {4,37}, {7,19}, {17,33}, {16,24}, {25,37}, {4,19}, {5,11}, {10,15}, {2,31} }; // ET40.145 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1920 EdgePairs[40][145]:={ {13,25}, {15,28}, {13,40}, {24,33}, {15,17}, {10,17}, {3,29}, {20,26}, {9,18}, {16,28}, {5,13}, {20,33}, {4,26}, {20,25}, {22,37}, {14,29}, {2,20}, {2,26}, {3,7}, {19,22}, {36,37}, {8,37}, {1,5}, {7,24}, {11,34}, {13,27}, {12,25}, {2,11}, {1,9}, {14,17}, {2,39}, {1,32}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {17,29}, {23,29}, {7,17}, {2,12}, {22,25}, {2,30}, {14,25}, {5,9}, {20,22}, {7,15}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {12,27}, {6,34}, {24,39}, {21,31}, {3,13}, {31,36}, {4,34}, {31,38}, {10,22}, {25,29}, {25,32}, {4,5}, {15,20}, {23,34}, {11,35}, {3,27}, {3,32}, {10,13}, {11,37}, {8,38}, {18,29}, {19,30}, {34,39}, {20,28}, {10,25}, {13,17}, {11,36}, {14,22}, {16,26}, {35,40}, {6,19}, {1,10}, {28,32}, {5,23}, {16,20}, {2,37}, {3,9}, {6,31}, {1,31}, {6,35}, {17,32}, {36,38}, {3,14}, {9,22}, {31,35}, {5,20}, {29,38}, {8,39}, {22,32}, {18,27}, {2,36}, {7,14}, {12,38}, {18,35}, {22,27}, {20,32}, {18,31}, {9,27}, {1,25}, {26,32}, {19,21}, {6,14}, {24,30}, {34,40}, {11,38}, {6,40}, {3,6}, {7,23}, {4,39}, {7,16}, {6,11}, {6,24}, {6,39}, {35,39}, {19,35}, {10,14}, {8,21}, {9,20}, {14,23}, {18,26}, {18,21}, {31,39}, {22,26}, {30,40}, {1,27}, {5,22}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {33,40}, {13,18}, {25,38}, {10,19}, {12,19}, {15,27}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {21,40}, {25,33}, {12,18}, {8,30}, {14,32}, {36,39}, {9,37}, {2,5}, {12,21}, {9,17}, {1,14}, {10,20}, {17,26}, {8,34}, {4,33}, {15,40}, {22,38}, {3,18}, {13,23}, {5,16}, {19,32}, {1,28}, {27,33}, {14,18}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {18,22}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {28,40}, {1,35}, {17,28}, {26,35}, {23,32}, {5,21}, {7,36}, {9,39}, {13,26}, {22,33}, {14,37}, {11,24}, {20,31}, 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{8,9}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {4,25}, {24,27}, {18,33}, {1,7}, {8,15}, {21,33}, {25,39}, {24,28}, {4,14}, {11,28}, {11,17}, {33,38}, {28,38}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {6,9}, {6,18}, {5,12}, {7,32}, {5,10}, {13,38}, {24,26}, {11,26}, {13,24}, {11,13}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {15,39}, {10,33}, {10,39}, {20,24}, {23,25}, {26,38}, {16,39}, {1,38}, {5,37}, {8,23}, {20,30}, {2,29}, {19,27}, {26,30}, {2,6}, {13,30}, {32,33}, {14,39}, {4,6}, {11,15}, {23,35}, {12,34}, {8,19}, {4,20}, {12,16}, {7,39}, {15,21}, {9,38}, {27,37}, {1,33}, {1,8}, {2,32}, {6,33}, {12,14}, {22,34}, {27,30}, {24,38}, {32,36}, {8,13}, {10,40}, {16,21}, {29,37}, {12,40}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {2,17}, {11,40}, {25,31}, {16,18}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {30,35}, {21,32}, {23,30}, {21,26}, {22,31}, {26,29}, {19,34}, {6,21}, {9,15}, {28,36}, {23,37}, {7,20}, {3,40}, {23,27}, {16,19}, {12,36}, {27,31}, {31,34}, {21,39}, {7,18}, {10,21}, {28,30}, {5,17}, {19,25}, {17,21}, {2,9}, {4,18}, {21,28}, {23,36}, {4,8}, {1,16}, {2,19}, {6,15}, {7,33}, {29,35}, {27,29}, {30,39}, {4,37}, {28,33}, {2,35}, {17,33}, {16,24}, {25,37}, {21,38}, {10,15}, {4,36} }; // ET40.146 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1920 EdgePairs[40][146]:={ {13,25}, {15,28}, {13,40}, {24,33}, {6,36}, {30,37}, {15,17}, {9,18}, {20,26}, {20,33}, {20,25}, {22,37}, {26,33}, {2,26}, {3,7}, {19,22}, {16,17}, {5,32}, {7,24}, {11,34}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {7,17}, {2,12}, {22,25}, {28,29}, {5,9}, {7,15}, {3,25}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {12,27}, {6,34}, {17,22}, {11,39}, {21,31}, {31,36}, {18,28}, {4,34}, {13,29}, {22,28}, {31,38}, {10,22}, {25,29}, {25,32}, {20,29}, {12,22}, {14,40}, {4,5}, {15,20}, {23,34}, {11,35}, {3,27}, {3,32}, {7,13}, {10,13}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {14,27}, {34,39}, {10,25}, {14,22}, {11,21}, {16,26}, {35,40}, {6,19}, {1,10}, {5,23}, {28,32}, {16,20}, {2,37}, {6,31}, {8,40}, {17,32}, {36,38}, {3,14}, {23,33}, {9,22}, {31,35}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {7,14}, {12,38}, {18,35}, {10,23}, {22,27}, {30,34}, {1,26}, {18,31}, {9,27}, {26,32}, {6,14}, {24,30}, {16,30}, {34,40}, {8,35}, {7,23}, {4,39}, {6,24}, {6,39}, {19,35}, {10,14}, {19,31}, {8,21}, {14,23}, {28,39}, {3,16}, {18,21}, {30,40}, {2,28}, {1,27}, {5,22}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {7,31}, {12,33}, {13,18}, {25,38}, {1,29}, {2,34}, {10,19}, {15,27}, {3,31}, {23,39}, {3,20}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {19,24}, {35,38}, {21,40}, {25,33}, {12,18}, {8,30}, {14,32}, {36,39}, {27,38}, {2,5}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {13,19}, {15,40}, {21,34}, {18,34}, {22,38}, {13,23}, {5,15}, {5,16}, 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{2,33}, {17,35}, {10,35}, {4,27}, {18,36}, {3,12}, {14,24}, {7,11}, {32,35}, {19,33}, {13,20}, {7,12}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {11,23}, {3,5}, {29,34}, {8,16}, {20,21}, {8,9}, {7,38}, {14,30}, {22,39}, {8,32}, {17,24}, {12,23}, {13,31}, {23,40}, {5,31}, {4,25}, {10,38}, {3,30}, {24,27}, {1,7}, {8,15}, {25,39}, {24,28}, {11,28}, {28,34}, {13,39}, {11,17}, {33,38}, {15,18}, {24,29}, {17,34}, {4,16}, {12,26}, {6,9}, {6,18}, {5,12}, {11,20}, {7,32}, {13,38}, {4,9}, {24,26}, {11,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {4,31}, {15,39}, {10,33}, {20,24}, {23,25}, {26,38}, {16,39}, {1,38}, {5,37}, {2,29}, {20,30}, {33,39}, {1,36}, {26,30}, {2,6}, {32,33}, {9,24}, {4,6}, {6,20}, {11,15}, {12,34}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {34,37}, {15,21}, {9,38}, {27,37}, {1,33}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {27,30}, {24,38}, {9,36}, {32,36}, {8,13}, {10,40}, {16,21}, {29,37}, {15,32}, {14,38}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {11,40}, {25,31}, {5,14}, {5,35}, {9,16}, {18,32}, {24,40}, {21,32}, {23,30}, {21,26}, {22,35}, {5,39}, {23,37}, {7,20}, {3,40}, {16,19}, {12,36}, {27,31}, {31,34}, {21,39}, {7,18}, {3,33}, {32,38}, {27,35}, {28,30}, {5,17}, {19,25}, {17,21}, {2,9}, {4,18}, {2,18}, {23,36}, {16,38}, {12,37}, {4,8}, {17,30}, {2,19}, {7,33}, {1,15}, {20,36}, {29,35}, {27,29}, {30,39}, {31,40}, {4,37}, {28,33}, {4,35}, {2,35}, {17,33}, {16,24}, {25,37}, {4,19}, {21,38}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET40.147 // Bipartite(15,25) Valencies [25,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 20283611790328099711444058112000000000 EdgePairs[40][147]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,33}, {15,37}, {10,38}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {15,23}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {6,23}, {15,17}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {3,40}, {15,16}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {4,26}, {15,20}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.148 // Bipartite(14,26) Valencies [26,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 35158260436568706166503034060800000000 EdgePairs[40][148]:={ {13,21}, {6,38}, {11,40}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,15}, {14,33}, {10,38}, {14,23}, {6,16}, {11,33}, {13,25}, {14,39}, {8,24}, {9,38}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {14,37}, {13,38}, {4,15}, {14,40}, {6,23}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {3,15}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.149 // Bipartite(4,36) Valencies [27,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 416162911506546032640000 EdgePairs[40][149]:={ {4,35}, {3,15}, {2,38}, {2,22}, {3,38}, {4,8}, {3,7}, {4,27}, {2,11}, {1,40}, {4,40}, {1,25}, {4,16}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {3,10}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {4,37}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {4,39}, {1,17}, {1,22}, {3,40}, {1,16}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {4,29}, {3,22}, {3,23}, {4,31}, {3,27}, {2,34}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {1,26}, {4,11}, {2,27}, {3,35}, {2,21}, {2,39}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {1,14}, {4,32}, {3,39}, {1,37}, {1,20}, {3,16}, {1,13}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {4,9}, {2,7}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {2,5}, {4,24}, {1,24} }; // ET40.150 // Bipartite(10,30) Valencies [27,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 219419659468800 EdgePairs[40][150]:={ {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {8,26}, {5,11}, {1,40}, {2,35}, {6,15}, {8,40}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {7,11}, {1,13}, {7,27}, {6,39}, {10,26}, {2,17}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {4,23}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {5,28}, {2,39}, {4,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {5,35}, {6,12}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {7,12}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {7,34}, {10,31}, {9,31}, {10,29}, {6,13}, {1,25}, {6,19}, {4,17}, {9,16}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {10,22}, {5,40}, {10,30}, {6,22}, {4,34}, {6,31}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {4,36}, {4,29}, {8,32}, {7,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {3,12}, {5,36}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET40.151 // Bipartite(13,27) Valencies [27,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 67805216556239647606827279974400000000 EdgePairs[40][151]:={ {13,21}, {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {13,39}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {6,14}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {13,25}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {12,17}, {13,36}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {13,38}, {4,15}, {6,23}, {7,39}, {13,14}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {13,34}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.152 // Non-bipartite Valency 27 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 87091200 EdgePairs[40][152]:={ {13,25}, {15,28}, {13,40}, {6,36}, {24,33}, {30,37}, {15,17}, {10,17}, {9,18}, {16,28}, {5,13}, {20,33}, {4,26}, {20,25}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {19,22}, {16,17}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {1,5}, {7,24}, {11,34}, {3,17}, {2,11}, {1,9}, {14,17}, {18,38}, {7,28}, {20,27}, {8,36}, {9,21}, {1,18}, {8,20}, {3,10}, {17,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {12,32}, {22,25}, {14,25}, {28,29}, {5,9}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,11}, {2,38}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {3,13}, {2,21}, {16,33}, {19,38}, {7,26}, {31,36}, {11,27}, {4,34}, {13,29}, {22,28}, {31,38}, {18,37}, {25,32}, {20,29}, {12,22}, {15,20}, {23,34}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {7,13}, {10,13}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {19,40}, {3,22}, {35,40}, {6,19}, {5,23}, {27,32}, {28,32}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {8,40}, {1,31}, {17,32}, {36,38}, {21,30}, {16,23}, {3,14}, {23,33}, {9,22}, {31,35}, {5,20}, {29,38}, {7,34}, {18,27}, {2,36}, {7,14}, {12,38}, {13,33}, {18,35}, {10,23}, {22,27}, {15,24}, {1,25}, {19,21}, {6,14}, {15,34}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {3,6}, {20,39}, {4,39}, {7,16}, {6,11}, {6,24}, {6,39}, {35,39}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {31,39}, {30,40}, {2,28}, {1,27}, {5,22}, {9,25}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {10,19}, {15,27}, {14,35}, {11,32}, {3,31}, {23,39}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {20,40}, {19,24}, {25,33}, {12,18}, {14,32}, {36,39}, {9,37}, {27,38}, {2,5}, {12,21}, {10,18}, {1,14}, {17,26}, {13,19}, {9,29}, {2,22}, {15,40}, {21,34}, {18,34}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {1,28}, {27,33}, {1,17}, {20,23}, {9,14}, {32,37}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {34,38}, {6,37}, {12,28}, {17,28}, {23,32}, {13,26}, {22,33}, {14,37}, {11,24}, {20,31}, {8,33}, {4,7}, {10,28}, {12,17}, {2,7}, {30,38}, {9,19}, {13,35}, {1,13}, {16,37}, {13,32}, {10,24}, 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{15,38}, {7,38}, {14,30}, {22,39}, {8,32}, {23,40}, {13,31}, {8,18}, {4,25}, {3,30}, {1,7}, {8,15}, {17,38}, {10,34}, {25,39}, {24,28}, {6,25}, {28,34}, {11,17}, {33,38}, {28,38}, {15,18}, {32,34}, {24,29}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {11,13}, {26,36}, {20,34}, {25,34}, {2,15}, {15,39}, {10,33}, {10,39}, {20,24}, {18,24}, {8,14}, {16,39}, {5,37}, {8,23}, {20,30}, {2,29}, {3,21}, {19,27}, {33,39}, {1,36}, {26,30}, {2,6}, {32,33}, {24,32}, {14,39}, {4,6}, {3,39}, {11,15}, {23,35}, {12,34}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {7,39}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {4,23}, {22,34}, {24,38}, {9,36}, {32,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {15,32}, {14,38}, {6,30}, {11,25}, {25,35}, {25,31}, {16,18}, {5,35}, {11,22}, {9,16}, {9,32}, {30,35}, {18,32}, {21,32}, {24,40}, {23,30}, {21,26}, {22,31}, {5,39}, {26,29}, {1,21}, {19,34}, {6,21}, {9,15}, {28,36}, {8,12}, {7,20}, {3,40}, {23,27}, {16,19}, {27,31}, {31,34}, {21,39}, {7,18}, {10,21}, {3,33}, {27,35}, {28,30}, {5,17}, {1,24}, {17,21}, {15,26}, {2,18}, {4,8}, {2,19}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {4,37}, {4,35}, {2,35}, {17,33}, {16,24}, {21,38}, {4,19}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET40.153 // Non-bipartite Valency 27 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 51840 EdgePairs[40][153]:={ {13,25}, {15,28}, {13,40}, {30,37}, {15,17}, {10,17}, {20,26}, {5,13}, {20,33}, {22,37}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {36,37}, {11,12}, {5,32}, {4,24}, {8,31}, {1,5}, {26,27}, {11,34}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {18,38}, {2,24}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {19,37}, {17,29}, {3,10}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {8,24}, {2,38}, {8,11}, {12,27}, {6,34}, {24,39}, {21,31}, {2,21}, {19,38}, {7,26}, {31,36}, {18,28}, {4,34}, {22,28}, {31,38}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {14,40}, {35,36}, {4,5}, {9,10}, {23,34}, {17,25}, {11,35}, {3,27}, {11,31}, {7,13}, {11,37}, {25,28}, {8,38}, {18,29}, {19,30}, {22,29}, {14,27}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {19,40}, {38,39}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {5,25}, {5,26}, {6,31}, {8,40}, {1,31}, {6,35}, {17,32}, {36,38}, {21,30}, {16,23}, {3,14}, {25,26}, {5,20}, {29,38}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {12,38}, {13,33}, {23,24}, {18,35}, {22,27}, {15,24}, {30,34}, {1,26}, {37,38}, {26,32}, {15,34}, {24,30}, {34,40}, {8,35}, {11,38}, {5,27}, {9,31}, {3,6}, {20,39}, {7,23}, {5,33}, {4,39}, {7,16}, {6,11}, {1,22}, {38,40}, {25,27}, {6,24}, {29,32}, {6,39}, {35,39}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {31,39}, {30,40}, {2,28}, {5,22}, {3,23}, {1,12}, {5,36}, {18,20}, {12,39}, {6,12}, {21,36}, {33,40}, {13,18}, {1,29}, {21,22}, {10,19}, {12,19}, {9,11}, {3,31}, {11,18}, {3,20}, {27,36}, {11,19}, {8,10}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {36,39}, {9,37}, {27,38}, {2,5}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {8,34}, {9,29}, {2,22}, {37,39}, {4,33}, {21,34}, {18,34}, {13,23}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {28,40}, {1,35}, {31,32}, {17,28}, {23,32}, {26,35}, {7,36}, {9,39}, {22,24}, {14,37}, {22,33}, {8,33}, {4,7}, {12,17}, {30,38}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {17,36}, {17,23}, {23,28}, {21,29}, {3,28}, {18,19}, {3,4}, {14,28}, {2,3}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {2,40}, {1,11}, {29,33}, {33,34}, {15,30}, {24,34}, {4,40}, {16,36}, {29,40}, {1,39}, {7,40}, 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{4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {17,39}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {13,24}, {11,13}, {6,16}, {26,36}, {25,34}, {2,15}, {30,32}, {15,39}, {10,33}, {10,39}, {20,24}, {23,25}, {26,38}, {18,24}, {8,14}, {16,39}, {5,37}, {8,23}, {14,21}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {32,33}, {9,24}, {24,32}, {14,39}, {1,2}, {4,6}, {6,20}, {3,39}, {11,15}, {6,26}, {23,35}, {12,34}, {4,20}, {7,21}, {23,31}, {12,16}, {34,37}, {15,21}, {9,38}, {27,37}, {12,30}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {4,23}, {22,34}, {27,30}, {9,36}, {8,13}, {10,40}, {12,40}, {17,40}, {15,32}, {14,38}, {27,39}, {6,30}, {25,35}, {6,38}, {25,31}, {16,18}, {5,14}, {11,22}, {9,16}, {16,32}, {30,35}, {21,32}, {24,40}, {23,30}, {22,31}, {22,35}, {5,39}, {26,29}, {1,21}, {13,14}, {9,15}, {19,34}, {16,19}, {27,31}, {31,34}, {21,39}, {7,18}, {3,33}, {32,38}, {28,30}, {5,17}, {1,24}, {6,8}, {17,21}, {2,18}, {23,36}, {26,28}, {16,38}, {12,37}, {4,8}, {29,31}, {17,30}, {2,19}, {5,24}, {6,15}, {7,33}, {1,15}, {29,35}, {27,29}, {30,39}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {16,24}, {21,38}, {4,19}, {25,37}, {13,16}, {10,15}, {6,29}, {2,31} }; // ET40.154 // Non-bipartite Valency 27 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 51840 EdgePairs[40][154]:={ {13,25}, {15,28}, {13,40}, {6,36}, {30,37}, {15,17}, {9,18}, {3,29}, {20,26}, {16,28}, {20,33}, {4,26}, {22,37}, {2,4}, {2,20}, {3,7}, {19,22}, {16,17}, {36,37}, {11,12}, {5,32}, {4,24}, {8,37}, {8,31}, {7,24}, {15,16}, {26,27}, {11,34}, {13,27}, {12,25}, {14,17}, {2,39}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {9,21}, {1,18}, {3,15}, {19,37}, {5,18}, {17,29}, {14,15}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {37,40}, {14,16}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {7,10}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {6,34}, {17,22}, {4,38}, {24,39}, {21,31}, {2,21}, {16,33}, {19,38}, {7,26}, {31,36}, {11,27}, {18,28}, {4,34}, {22,28}, {9,12}, {31,38}, {10,22}, {25,29}, {5,7}, {20,29}, {12,22}, {4,5}, {15,20}, {9,10}, {17,18}, {23,34}, {14,33}, {11,35}, {3,27}, {3,32}, {7,13}, {10,13}, {25,28}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {34,39}, {1,3}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {14,22}, {19,40}, {3,22}, {35,40}, {6,19}, {1,10}, {5,23}, {28,32}, {16,20}, {7,30}, {5,25}, {8,40}, {6,35}, {17,32}, {36,38}, {21,30}, {16,23}, {23,33}, {25,26}, {31,35}, {29,38}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {13,33}, {23,24}, {18,35}, {22,27}, {30,34}, {1,26}, {18,31}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {34,40}, {11,38}, {6,40}, {9,31}, {20,39}, {5,33}, {4,39}, {1,22}, {38,40}, {25,27}, {29,32}, {6,39}, {35,39}, {10,14}, {16,34}, {14,23}, {28,39}, {18,21}, {31,39}, {22,26}, {30,40}, {1,27}, {5,22}, {9,25}, {1,12}, {9,26}, {12,39}, {18,20}, {21,36}, {12,33}, {5,38}, {1,37}, {33,40}, {21,37}, {25,38}, {26,37}, {21,22}, {2,34}, {10,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {23,39}, {11,18}, {21,25}, {9,28}, {6,13}, {11,19}, {8,10}, {20,40}, {16,35}, {5,28}, {25,33}, {12,18}, {14,32}, {9,37}, {27,38}, {9,17}, {1,14}, {10,20}, {17,26}, {8,34}, {9,29}, {37,39}, {18,34}, {22,38}, {3,18}, {13,23}, {5,15}, {19,32}, {6,10}, {7,37}, {1,28}, {3,36}, {20,23}, {24,25}, {6,37}, {12,28}, {3,37}, {29,36}, {31,32}, {17,28}, {7,36}, {9,39}, {22,24}, {13,26}, {22,33}, {14,37}, {11,24}, {4,7}, {10,28}, {10,12}, {15,23}, {2,7}, {30,38}, {9,19}, {13,35}, {10,11}, {16,37}, {10,24}, {2,25}, {17,36}, {26,39}, {23,28}, {21,29}, {2,14}, {12,24}, {3,4}, {14,28}, {2,3}, {30,36}, {15,36}, {12,20}, {16,29}, {2,40}, {36,40}, {24,34}, {3,19}, {4,40}, {23,38}, {16,36}, {29,40}, {1,39}, {17,37}, {18,25}, {14,19}, {21,27}, {7,8}, {15,37}, {7,35}, {9,13}, {15,29}, {20,38}, {30,33}, {4,15}, {4,29}, {8,25}, {5,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {32,40}, {3,35}, {18,23}, {12,15}, {9,40}, {14,31}, {19,28}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {22,40}, {13,37}, {8,27}, {5,30}, {24,31}, {16,27}, {9,30}, {2,13}, {5,40}, {16,31}, {22,30}, {27,34}, {18,30}, {4,22}, {28,31}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {5,6}, {9,34}, {15,25}, {5,19}, {33,36}, {2,33}, {17,35}, {10,35}, {18,36}, {3,12}, {14,24}, {4,17}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {19,33}, {19,29}, {18,39}, {13,20}, {7,12}, {13,21}, {3,11}, {3,38}, {4,10}, {14,34}, {3,5}, {16,40}, {15,19}, {29,34}, {8,16}, {20,35}, {15,38}, {22,39}, {8,32}, {8,9}, {17,24}, {12,23}, {13,31}, {23,40}, {5,31}, {3,30}, {6,7}, {24,27}, {18,33}, {1,7}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {6,25}, {11,17}, {33,38}, {28,38}, {15,18}, {32,34}, {17,34}, {12,13}, {12,26}, {6,9}, {7,9}, {5,12}, {11,20}, {7,32}, {13,38}, {11,26}, {24,26}, {13,24}, {11,13}, {26,36}, {20,34}, {4,31}, {30,32}, {10,33}, {10,39}, {20,24}, {23,25}, {26,38}, {18,24}, {8,14}, {5,37}, {8,23}, {20,30}, {2,29}, {14,21}, {3,21}, {19,27}, {1,36}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {1,2}, {4,6}, {6,20}, {3,39}, {11,15}, {6,26}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {27,37}, {1,33}, {1,8}, {2,32}, {6,33}, {19,26}, {29,39}, {27,30}, {24,38}, {9,36}, {32,36}, {8,13}, {10,40}, {16,21}, {12,40}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {33,35}, {11,40}, {25,31}, {16,18}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {39,40}, {22,35}, {5,39}, {26,29}, {1,21}, {13,14}, {6,21}, {19,34}, {28,36}, {23,37}, {8,12}, {3,40}, {23,27}, {16,19}, {34,35}, {12,36}, {27,31}, {21,39}, {7,18}, {10,21}, {3,33}, {32,38}, {27,35}, {5,17}, {1,24}, {19,25}, {17,21}, {15,26}, {2,18}, {21,28}, {23,36}, {26,28}, {12,37}, {4,8}, {29,31}, {17,30}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {30,39}, {31,40}, {4,37}, {28,33}, {4,35}, {2,35}, {10,32}, {13,16}, {5,11}, {4,36}, {6,29}, {2,31} }; // ET40.155 // Bipartite(5,35) Valencies [28,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 390241927692288000000 EdgePairs[40][155]:={ {4,35}, {5,32}, {3,15}, {2,38}, {1,11}, {4,14}, {3,29}, {2,22}, {3,38}, {5,30}, {1,31}, {4,27}, {5,35}, {2,20}, {4,40}, {4,16}, {2,37}, {1,38}, {1,9}, {2,33}, {3,30}, {1,32}, {5,7}, {4,6}, {5,13}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {5,26}, {5,21}, {2,29}, {3,19}, {1,29}, {4,12}, {5,6}, {5,37}, {3,18}, {1,34}, {2,14}, {3,11}, {5,23}, {5,33}, {2,10}, {4,37}, {4,20}, {2,23}, {4,7}, {1,36}, {4,39}, {1,17}, {3,13}, {1,22}, {2,32}, {3,40}, {1,16}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {5,15}, {3,23}, {4,31}, {2,34}, {4,30}, {1,19}, {2,40}, {4,21}, {4,36}, {2,35}, {4,17}, {5,28}, {2,9}, {4,15}, {4,25}, {1,26}, {2,24}, {4,11}, {5,22}, {2,27}, {5,38}, {3,35}, {1,23}, {5,27}, {1,7}, {5,8}, {1,39}, {2,39}, {2,12}, {4,22}, {5,20}, {3,28}, {3,26}, {5,36}, {3,24}, {5,17}, {5,31}, {3,21}, {1,14}, {4,32}, {3,39}, {2,8}, {1,37}, {1,27}, {5,11}, {3,16}, {1,13}, {5,10}, {3,25}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {5,12}, {1,28}, {3,36}, {4,9}, {2,7}, {5,18}, {4,34}, {3,33}, {1,8}, {5,16}, {2,30}, {1,21}, {1,6}, {1,18}, {4,19}, {5,25}, {4,10}, {4,24}, {5,40}, {1,24} }; // ET40.156 // Bipartite(8,32) Valencies [28,7] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4438236667576320 EdgePairs[40][156]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {3,40}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {5,38}, {8,9}, {3,9}, {8,28}, {4,29}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {7,36}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {8,27}, {6,22}, {3,17}, {8,16}, {4,38}, {5,40}, {7,12}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,11}, {7,20}, {2,10}, {5,29}, {2,38}, {2,37}, {8,14}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {8,17}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {1,33}, {3,29}, {6,23}, {8,37}, {5,28}, {8,26}, {7,31}, {6,15}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {5,31}, {6,27}, {6,26}, {8,40}, {3,23}, {1,39}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {4,40}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {8,38}, {1,26}, {2,22}, {4,34}, {4,14}, {8,24}, {6,25}, {7,9}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {3,38}, {4,11}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {6,39}, {7,33}, {6,20}, {7,35}, {5,21}, {2,30}, {7,37}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {7,21}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET40.157 // Bipartite(12,28) Valencies [28,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 146042004890362317922397218406400000000 EdgePairs[40][157]:={ {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {8,37}, {12,20}, {12,38}, {1,13}, {12,26}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {12,17}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {12,34}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {7,13}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.158 // Non-bipartite Valency 28 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 4838400 EdgePairs[40][158]:={ {13,25}, {15,28}, {13,40}, {24,33}, {30,37}, {15,17}, {10,17}, {3,29}, {20,26}, {9,18}, {16,28}, {5,13}, {20,33}, {4,26}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {5,32}, {8,37}, {8,31}, {7,24}, {15,16}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {19,37}, {5,18}, {17,29}, {3,10}, {23,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {14,16}, {2,30}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {4,30}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {6,34}, {4,38}, {11,39}, {2,21}, {16,33}, {19,38}, {7,26}, {11,27}, {13,29}, {22,28}, {9,12}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {14,40}, {35,36}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {7,13}, {10,13}, {11,37}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {2,8}, {20,28}, {12,35}, {13,17}, {14,22}, {19,40}, {3,22}, {6,19}, {1,10}, {5,23}, {28,32}, {7,30}, {3,9}, {5,26}, {8,40}, {6,35}, {21,30}, {16,23}, {3,14}, {25,26}, {9,22}, {29,38}, {8,39}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {34,36}, {18,35}, {10,23}, {15,24}, {30,34}, {20,32}, {18,31}, {9,27}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {3,6}, {20,39}, {7,23}, {5,33}, {7,16}, {1,22}, {25,27}, {6,24}, {29,32}, {6,39}, {35,39}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {18,21}, {31,39}, {22,26}, {2,28}, {1,27}, {5,22}, {9,25}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {7,31}, {12,33}, {5,38}, {1,37}, {33,40}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {27,36}, {9,28}, {6,13}, {11,19}, {35,38}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {27,38}, {12,21}, {10,18}, {9,17}, {1,14}, {17,26}, {8,34}, {13,19}, {4,33}, {21,34}, {18,34}, {10,31}, {22,38}, {5,16}, {19,32}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {20,23}, {14,36}, {23,26}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {13,26}, {22,33}, {14,37}, {11,24}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {30,38}, {13,35}, {10,11}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {26,39}, {21,29}, {2,14}, {9,35}, {12,24}, {14,28}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {2,40}, {29,33}, {3,19}, {4,40}, {2,16}, {29,40}, {1,39}, {7,40}, {18,25}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {9,13}, {15,29}, {20,38}, {30,33}, {4,15}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {16,22}, {32,40}, {3,35}, {14,26}, {9,40}, {14,31}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {22,36}, {22,30}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {1,40}, {6,23}, {28,35}, {10,26}, {1,23}, {17,31}, {8,29}, {5,6}, {19,36}, {6,22}, {5,19}, {33,36}, {16,25}, {2,33}, {17,35}, {6,32}, {15,31}, {4,27}, {18,36}, {3,12}, {4,17}, {3,24}, {7,11}, {4,32}, {1,19}, {2,10}, {6,17}, {19,33}, {3,34}, {18,39}, {13,20}, {13,21}, {3,11}, {4,10}, {33,37}, {11,23}, {16,40}, {15,19}, {9,33}, {8,16}, {20,21}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {5,31}, {4,25}, {10,38}, {3,30}, {24,27}, {1,7}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {24,28}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {15,18}, {17,34}, {4,16}, {12,26}, {6,18}, {5,12}, {17,39}, {11,20}, {24,26}, {13,24}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {26,38}, {18,24}, {8,14}, {16,39}, {1,38}, {5,37}, {2,29}, {14,21}, {3,21}, {19,27}, {33,39}, {18,40}, {2,6}, {13,30}, {24,32}, {4,6}, {6,20}, {3,39}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {7,39}, {15,21}, {9,38}, {1,33}, {12,30}, {1,8}, {6,33}, {19,26}, {4,23}, {22,34}, {24,38}, {9,36}, {32,36}, {6,27}, {29,37}, {12,40}, {17,40}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {6,38}, {11,40}, {25,31}, {5,14}, {11,22}, {9,16}, {16,32}, {9,32}, {18,32}, {21,32}, {24,40}, {23,30}, {22,31}, {30,31}, {22,35}, {5,39}, {9,15}, {28,36}, {23,37}, {8,12}, {7,20}, {3,40}, {23,27}, {12,36}, {27,31}, {21,39}, {7,18}, {10,21}, {32,38}, {27,35}, {5,17}, {1,24}, {19,25}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {16,38}, {4,8}, {29,31}, {17,30}, {2,19}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {30,39}, {31,40}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {25,37}, {13,16}, {5,11}, {4,36}, {6,29}, {2,31} }; // ET40.159 // Bipartite(11,29) Valencies [29,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 352934845151708934979126611148800000000 EdgePairs[40][159]:={ {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {8,26}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {1,13}, {7,27}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {7,12}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET40.160 // Bipartite(10,30) Valencies [30,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 962549577686478913579436212224000000000 EdgePairs[40][160]:={ {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {1,12}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {7,11}, {1,13}, {7,27}, {6,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {7,12}, {8,24}, {9,38}, {9,26}, {5,14}, {3,29}, {2,23}, {10,13}, {10,19}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET40.161 // Non-bipartite Valency 30 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 4161629115065460326400000000 EdgePairs[40][161]:={ {13,25}, {15,28}, {13,40}, {6,36}, {24,33}, {30,37}, {9,18}, {3,29}, {10,17}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {17,29}, {5,18}, {19,37}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {12,32}, {2,30}, {14,25}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {4,30}, {21,35}, {8,24}, {2,38}, {8,11}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {18,28}, {4,34}, {13,29}, {9,12}, {10,22}, {18,37}, {25,32}, {20,29}, {12,22}, {14,40}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {6,19}, {5,23}, {27,32}, {28,32}, {2,37}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {1,31}, {6,35}, {17,32}, {16,23}, {3,14}, {23,33}, {9,22}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {13,33}, {15,24}, {10,23}, {18,35}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {6,11}, {1,22}, {6,24}, {29,32}, {6,39}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {18,21}, {30,40}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {23,39}, {3,20}, {5,29}, {27,36}, {9,28}, {6,13}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {25,33}, {8,30}, {4,21}, {14,32}, {9,37}, {27,38}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {7,37}, {1,28}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {14,36}, {26,31}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {10,28}, {10,12}, {15,23}, {30,38}, {9,19}, {13,35}, {10,11}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {26,39}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {30,36}, {15,36}, {10,36}, {16,29}, {28,37}, {2,40}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {4,40}, {23,38}, {2,16}, {16,36}, {29,40}, {1,39}, {7,40}, {17,37}, {18,25}, {10,37}, {25,36}, {15,37}, {7,35}, {9,13}, {15,29}, {20,38}, {30,33}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,22}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {5,40}, {16,31}, {22,36}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {1,40}, {6,23}, {28,35}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {25,40}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {6,17}, {19,33}, {19,29}, {3,34}, {18,39}, {7,12}, {13,21}, {3,11}, {3,38}, {14,34}, {11,23}, {16,40}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {11,28}, {6,25}, {28,34}, {13,39}, {28,38}, {17,34}, {4,16}, {12,26}, {10,30}, {6,18}, {5,12}, {17,39}, {7,32}, {13,38}, {11,26}, {13,24}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {26,38}, {18,24}, {8,14}, {16,39}, {1,38}, {5,37}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {24,32}, {14,39}, {6,20}, {3,39}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {11,30}, {2,23}, {7,39}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {29,39}, {4,23}, {22,34}, {24,38}, {9,36}, {8,13}, {10,40}, {16,21}, {6,27}, {29,37}, {12,40}, {17,40}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {11,40}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {30,35}, {18,32}, {21,32}, {24,40}, {22,31}, {30,31}, {22,35}, {5,39}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {8,12}, {7,20}, {3,40}, {12,36}, {27,31}, {7,18}, {21,39}, {10,21}, {3,33}, {27,35}, {5,17}, {1,24}, {19,25}, {17,21}, {4,18}, {15,26}, {2,18}, {23,36}, {16,38}, {12,37}, {29,31}, {17,30}, {2,19}, {1,16}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {30,39}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET40.162 // Bipartite(9,31) Valencies [31,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2983903690828084632096252257894400000000 EdgePairs[40][162]:={ {6,38}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {4,28}, {9,10}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {1,10}, {8,37}, {4,13}, {7,11}, {1,13}, {3,10}, {7,27}, {2,10}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {9,38}, {4,10}, {9,26}, {5,14}, {3,29}, {2,23}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {5,23}, {5,20}, {2,26}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {5,10}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET40.163 // Bipartite(8,32) Valencies [32,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10609435345166523136342230250291200000000 EdgePairs[40][163]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {3,40}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {5,38}, {8,9}, {3,9}, {7,38}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {8,39}, {1,21}, {2,9}, {7,36}, {8,10}, {8,25}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {3,17}, {6,29}, {8,16}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {7,12}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,11}, {7,20}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {8,14}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {8,37}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {8,40}, {3,23}, {8,23}, {1,39}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {4,40}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {8,38}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {3,38}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {6,39}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {7,21}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET40.164 // Non-bipartite Valency 32 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 12787447486620893184000000 EdgePairs[40][164]:={ {13,25}, {15,28}, {13,40}, {6,36}, {24,33}, {30,37}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {16,17}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {12,32}, {22,25}, {2,30}, {14,25}, {5,9}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {8,24}, {2,38}, {8,11}, {31,37}, {12,27}, {6,34}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {18,28}, {4,34}, {13,29}, {22,28}, {31,38}, {10,22}, {18,37}, {20,29}, {12,22}, {14,40}, {15,20}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {6,19}, {1,10}, {5,23}, {16,20}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {8,40}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {31,35}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {13,33}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {6,14}, {15,34}, {24,30}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {6,11}, {1,22}, {6,24}, {6,39}, {19,35}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {20,40}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {27,38}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {32,37}, {14,36}, {24,25}, {23,26}, {7,29}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {10,28}, {15,23}, {12,17}, {30,38}, {9,19}, {13,35}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {26,39}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {2,40}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {4,40}, {23,38}, {2,16}, {16,36}, {29,40}, {1,39}, {7,40}, {17,37}, {14,19}, {18,25}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {15,29}, {20,38}, {30,33}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {16,22}, {32,40}, {3,35}, {14,26}, {9,40}, {14,31}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {5,40}, {16,31}, {22,36}, {22,30}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {1,40}, {6,23}, {28,35}, {10,26}, {1,23}, {8,29}, {17,31}, {7,22}, {25,40}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {18,39}, {13,20}, {7,12}, {31,33}, {13,21}, {3,11}, {3,38}, {4,10}, {14,34}, {11,23}, {16,40}, {15,19}, {9,33}, {29,34}, {8,16}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {8,9}, {22,39}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {24,27}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {28,38}, {15,18}, {32,34}, {24,29}, {17,34}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {17,39}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {13,24}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {15,39}, {10,33}, {10,39}, {13,34}, {23,25}, {26,38}, {8,14}, {16,39}, {1,38}, {5,37}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {32,33}, {9,24}, {24,32}, {14,39}, {6,20}, {3,39}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {11,30}, {2,23}, {7,39}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {29,39}, {4,23}, {22,34}, {24,38}, {9,36}, {32,36}, {8,13}, {10,40}, {16,21}, {6,27}, {29,37}, {12,40}, {17,40}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {11,40}, {16,18}, {5,14}, {5,35}, {11,22}, {16,32}, {9,32}, {30,35}, {18,32}, {21,32}, {24,40}, {23,30}, {21,26}, {22,31}, {22,35}, {5,39}, {1,21}, {6,21}, {19,34}, {28,36}, {23,37}, {8,12}, {7,20}, {3,40}, {16,19}, {23,27}, {12,36}, {31,34}, {7,18}, {21,39}, {10,21}, {3,33}, {32,38}, {27,35}, {5,17}, {1,24}, {19,25}, {2,9}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {16,38}, {12,37}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {30,39}, {31,40}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {5,11}, {4,36}, {6,29}, {2,31} }; // ET40.165 // Bipartite(7,33) Valencies [33,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 43763920798811907937411699782451200000000 EdgePairs[40][165]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {7,38}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {7,12}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {6,8}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {1,25}, {6,19}, {6,9}, {7,29}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {4,40}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {2,18}, {5,35}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET40.166 // Bipartite(6,34) Valencies [34,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 212567615308514981410285398943334400000000 EdgePairs[40][166]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {6,8}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {4,40}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {5,35}, {1,34}, {5,37}, {4,17}, {6,35}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET40.167 // Bipartite(5,35) Valencies [35,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1239977755966337391559998160502784000000000 EdgePairs[40][167]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {3,18}, {3,17}, {3,7}, {4,38}, {3,34}, {2,25}, {5,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {5,29}, {2,38}, {2,37}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {3,26}, {5,28}, {2,17}, {4,36}, {4,6}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {1,15}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,40}, {2,31}, {5,10}, {5,27}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {5,6}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {2,30}, {5,21}, {2,18}, {5,35}, {1,34}, {5,37}, {4,17}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET40.168 // Non-bipartite Valency 35 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1733686198272000000000 EdgePairs[40][168]:={ {13,25}, {15,28}, {13,40}, {6,36}, {24,33}, {30,37}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {7,24}, {15,16}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {2,30}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {4,30}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {18,28}, {4,34}, {13,29}, {22,28}, {9,12}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {14,40}, {35,36}, {15,20}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {25,28}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {34,39}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {35,40}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {8,40}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {25,26}, {9,22}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {34,36}, {13,33}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {3,6}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {6,11}, {1,22}, {25,27}, {6,24}, {29,32}, {6,39}, {35,39}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {18,21}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {33,40}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {9,11}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {27,36}, {9,28}, {6,13}, {11,19}, {20,40}, {19,24}, {35,38}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {27,38}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {30,38}, {9,19}, {13,35}, {10,11}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {26,39}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {2,40}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {4,40}, {23,38}, {2,16}, {16,36}, {29,40}, {1,39}, {7,40}, {17,37}, {14,19}, {18,25}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {9,13}, {15,29}, {20,38}, {30,33}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {32,40}, {3,35}, {14,26}, {18,23}, {1,6}, {9,40}, {25,30}, {14,31}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {11,16}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {5,40}, {16,31}, {22,36}, {22,30}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {1,40}, {6,23}, {28,35}, {10,26}, {1,23}, {8,29}, {17,31}, {7,22}, {5,6}, {25,40}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {19,33}, {19,29}, {3,34}, {18,39}, {13,20}, {7,12}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {16,40}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,32}, {7,38}, {14,30}, {15,38}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {33,38}, {28,38}, {15,18}, {24,29}, {17,34}, {4,16}, {12,26}, {10,30}, {6,18}, {5,12}, {17,39}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {13,24}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {26,38}, {18,24}, {8,14}, {16,39}, {1,38}, {5,37}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {33,39}, {1,36}, {18,40}, {2,6}, {13,30}, {9,24}, {24,32}, {14,39}, {4,6}, {6,20}, {3,39}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {7,39}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {29,39}, {4,23}, {22,34}, {24,38}, {9,36}, {32,36}, {8,13}, {10,40}, {16,21}, {6,27}, {29,37}, {12,40}, {17,40}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {11,40}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {30,35}, {18,32}, {21,32}, {24,40}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {5,39}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {8,12}, {7,20}, {3,40}, {23,27}, {12,36}, {27,31}, {7,18}, {21,39}, {10,21}, {3,33}, {32,38}, {27,35}, {5,17}, {1,24}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {16,38}, {12,37}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {30,39}, {31,40}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET40.169 // Bipartite(4,36) Valencies [36,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8927839842957629219231986755620044800000000 EdgePairs[40][169]:={ {1,15}, {4,35}, {3,15}, {2,38}, {1,11}, {4,14}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {1,40}, {2,20}, {4,40}, {1,25}, {4,16}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {4,37}, {4,20}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {4,39}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {2,34}, {3,27}, {4,30}, {1,19}, {2,40}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,35}, {1,26}, {4,38}, {2,24}, {4,11}, {2,27}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {4,32}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {4,9}, {2,7}, {4,34}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET40.170 // Non-bipartite Valency 36 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 230078188847156428800 EdgePairs[40][170]:={ {13,25}, {15,28}, {13,40}, {6,36}, {24,33}, {30,37}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {36,37}, {5,32}, {4,24}, {8,37}, {8,31}, {1,5}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {18,28}, {4,34}, {13,29}, {22,28}, {31,38}, {10,22}, {18,37}, {25,29}, {25,32}, {20,29}, {12,22}, {14,40}, {4,5}, {15,20}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {34,39}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {35,40}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {8,40}, {1,31}, {6,35}, {17,32}, {36,38}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {31,35}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {13,33}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {3,6}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {6,11}, {1,22}, {6,24}, {6,39}, {35,39}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {18,21}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {33,40}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {12,19}, {14,35}, {15,27}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {20,40}, {19,24}, {35,38}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {36,39}, {9,37}, {27,38}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {15,23}, {12,17}, {2,7}, {30,38}, {9,19}, {13,35}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {26,39}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {2,40}, {36,40}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {4,40}, {23,38}, {2,16}, {16,36}, {29,40}, {1,39}, {7,40}, {17,37}, {14,19}, {18,25}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {9,13}, {15,29}, {20,38}, {30,33}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {32,40}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {9,40}, {25,30}, {14,31}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {11,16}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {5,40}, {16,31}, {22,36}, {22,30}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {1,40}, {6,23}, {28,35}, {10,26}, {1,23}, {8,29}, {17,31}, {7,22}, {25,40}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {18,39}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {3,5}, {16,40}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {7,38}, {14,30}, {8,32}, {15,38}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {33,38}, {28,38}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {17,39}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {23,25}, {26,38}, {18,24}, {8,14}, {16,39}, {1,38}, {5,37}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {33,39}, {1,36}, {18,40}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {14,39}, {4,6}, {6,20}, {3,39}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {7,39}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {4,23}, {22,34}, {27,30}, {24,38}, {9,36}, {32,36}, {8,13}, {10,40}, {16,21}, {6,27}, {29,37}, {12,40}, {17,40}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {11,40}, {25,31}, {5,14}, {16,18}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {30,35}, {18,32}, {21,32}, {24,40}, {23,30}, {21,26}, {22,31}, {22,35}, {5,39}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {8,12}, {7,20}, {3,40}, {16,19}, {23,27}, {12,36}, {27,31}, {31,34}, {7,18}, {21,39}, {10,21}, {3,33}, {32,38}, {27,35}, {28,30}, {5,17}, {1,24}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {16,38}, {12,37}, {4,8}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {30,39}, {31,40}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET40.171 // Bipartite(3,37) Valencies [37,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 82582518547358070277895877489485414400000000 EdgePairs[40][171]:={ {1,15}, {3,15}, {2,38}, {1,11}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {2,11}, {1,40}, {2,20}, {1,25}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {2,34}, {3,27}, {1,19}, {2,40}, {2,35}, {2,9}, {3,5}, {1,4}, {1,35}, {1,26}, {2,4}, {2,24}, {2,27}, {3,4}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET40.172 // Bipartite(2,38) Valencies [38,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1046045234933202223520014448200148582400000000 EdgePairs[40][172]:={ {2,11}, {1,26}, {2,14}, {1,14}, {2,37}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,37}, {1,33}, {1,40}, {1,10}, {2,39}, {1,39}, {1,36}, {1,6}, {2,40}, {2,6}, {1,4}, {1,20}, {1,12}, {2,36}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {1,38}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,38}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET40.173 // Non-bipartite Valency 38 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 2551082656125828464640000 EdgePairs[40][173]:={ {13,25}, {15,28}, {13,40}, {6,36}, {24,33}, {30,37}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {22,37}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {36,37}, {5,32}, {4,24}, {8,37}, {8,31}, {1,5}, {7,24}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {37,40}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {10,27}, {7,10}, {4,30}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {12,22}, {14,40}, {4,5}, {15,20}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {25,28}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {34,39}, {1,3}, {13,15}, {2,8}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {19,40}, {38,39}, {16,26}, {3,22}, {35,40}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {8,40}, {1,31}, {6,35}, {17,32}, {36,38}, {16,23}, {21,30}, {3,14}, {23,33}, {9,22}, {31,35}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {34,36}, {13,33}, {10,23}, {15,24}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {19,21}, {10,16}, {6,14}, {15,34}, {24,30}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {3,6}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {6,11}, {1,22}, {38,40}, {25,27}, {6,24}, {29,32}, {6,39}, {35,39}, {19,35}, {10,14}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {18,21}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {33,40}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {12,19}, {14,35}, {15,27}, {9,11}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {11,19}, {8,10}, {20,40}, {19,24}, {35,38}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {36,39}, {9,37}, {27,38}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {8,34}, {13,19}, {9,29}, {2,22}, {37,39}, {4,33}, {15,40}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {22,24}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {12,17}, {2,7}, {30,38}, {9,19}, {13,35}, {10,11}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {26,39}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {18,19}, {14,28}, {2,3}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {28,37}, {2,40}, {36,40}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {4,40}, {23,38}, {2,16}, {16,36}, {29,40}, {1,39}, {7,40}, {17,37}, {14,19}, {18,25}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {9,13}, {21,23}, {15,29}, {20,38}, {30,33}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {16,22}, {32,40}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {9,40}, {25,30}, {14,31}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {11,16}, {1,4}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {5,40}, {16,31}, {22,36}, {22,30}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {1,40}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {25,40}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {18,39}, {11,14}, {7,12}, {13,20}, {31,33}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {3,5}, {16,40}, {15,19}, {9,33}, {29,34}, {8,16}, {20,21}, {20,35}, {8,9}, {7,38}, {14,30}, {8,32}, {15,38}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {22,23}, {4,25}, {10,38}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {33,38}, {28,38}, {15,18}, {32,34}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {6,18}, {5,12}, {17,39}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {23,25}, {26,38}, {18,24}, {21,24}, {8,14}, {16,39}, {1,38}, {5,37}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {33,39}, {1,36}, {18,40}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {14,39}, {4,6}, {6,20}, {3,39}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {11,30}, {34,37}, {2,23}, {7,39}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {4,23}, {22,34}, {27,30}, {24,38}, {9,36}, {32,36}, {8,13}, {10,40}, {16,21}, {6,27}, {29,37}, {12,40}, {17,40}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {33,35}, {11,40}, {25,31}, {5,14}, {16,18}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {30,35}, {18,32}, {21,32}, {24,40}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {5,39}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {8,12}, {7,20}, {3,40}, {16,19}, {23,27}, {34,35}, {12,36}, {27,31}, {31,34}, {7,18}, {21,39}, {10,21}, {3,33}, {32,38}, {27,35}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {21,28}, {23,36}, {26,28}, {16,38}, {12,37}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {30,39}, {31,40}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET40.174 // Bipartite(1,39) Valencies [39,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 20397882081197443358640281739902897356800000000 EdgePairs[40][174]:={ {1,4}, {1,20}, {1,3}, {1,34}, {1,37}, {1,30}, {1,14}, {1,23}, {1,40}, {1,39}, {1,33}, {1,24}, {1,38}, {1,7}, {1,27}, {1,29}, {1,35}, {1,5}, {1,15}, {1,22}, {1,28}, {1,16}, {1,10}, {1,12}, {1,13}, {1,17}, {1,2}, {1,11}, {1,36}, {1,19}, {1,18}, {1,25}, {1,32}, {1,21}, {1,9}, {1,26}, {1,31}, {1,6}, {1,8} }; // ET40.175 // Non-bipartite Valency 39 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 815915283247897734345611269596115894272000000000 EdgePairs[40][175]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {13,18}, {32,33}, {2,6}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {15,21}, {24,40}, {5,40}, {4,35}, {6,39}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {19,27}, {32,34}, {7,12}, {31,33}, {21,34}, {4,10}, {33,34}, {3,19}, {1,15}, {5,8}, {10,30}, {31,32}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {30,31}, {21,31}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {34,35}, {3,27}, {29,39}, {25,32}, {5,13}, {15,33}, {21,33}, {30,34}, {22,27}, {17,36}, {10,35}, {13,40}, {11,15}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {22,37}, {12,26}, {15,34}, {7,16}, {12,16}, {14,19}, {3,38}, {13,24}, {11,30}, {30,32}, {4,21}, {29,36}, {30,33}, {20,34}, {23,29}, {1,33}, {4,25}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, {1,30}, {14,27}, {11,35}, {2,29}, {16,39}, {15,31}, {10,21}, {17,23}, {12,19}, {3,7}, {10,25}, {6,17}, {32,35}, {20,33}, {2,17}, {33,35}, {36,37}, {20,32}, {18,40}, {11,33}, {19,22}, {16,26}, {3,22}, {5,24}, {11,32}, {1,5}, {28,37}, {26,27}, {11,20}, {17,28}, {1,8}, {11,24}, {1,35}, {9,17}, {10,18}, {19,38}, {8,15}, {5,20}, 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{19,39}, {3,39}, {5,29}, {8,35}, {6,24}, {24,31}, {9,32}, {39,40}, {2,5}, {2,24}, {4,19}, {5,6}, {9,33}, {9,20}, {18,26}, {8,29}, {4,14}, {30,37}, {8,23}, {3,21}, {5,36}, {23,37}, {4,27}, {2,8}, {6,8}, {24,29}, {13,17}, {3,25}, {1,37}, {13,23}, {12,40}, {1,28}, {16,38}, {25,27}, {9,31}, {21,27}, {4,38}, {8,9}, {28,32}, {24,34}, {10,14}, {13,29}, {4,22}, {4,7}, {10,22}, {10,12}, {26,40}, {17,24}, {28,33}, {21,38}, {15,37}, {8,36}, {9,34}, {15,17}, {10,38}, {34,36}, {11,28}, {13,36}, {18,19}, {28,34}, {19,25}, {25,38}, {19,21}, {20,37}, {6,11}, {38,40}, {5,23}, {11,23}, {31,36}, {2,11}, {9,30}, {7,40}, {20,29}, {33,36}, {32,36}, {28,31}, {18,27}, {1,6}, {11,37}, {1,2}, {5,9}, {4,26}, {4,12}, {2,30}, {3,18}, {7,10}, {1,29}, {6,30}, {9,35}, {1,17}, {8,28}, {18,39}, {21,26}, {35,36}, {5,28}, {25,26}, {17,33}, {2,35}, {10,26}, {17,20}, {16,40}, {6,35}, {15,29}, {17,32}, {28,35}, {24,28}, {27,40}, {16,25}, {11,17}, {25,39}, {16,21}, {5,37}, {24,36}, {9,24}, {21,39}, {30,36}, {6,20}, {2,20}, {1,36}, {14,18}, {10,16}, {4,16}, {20,23}, {7,25}, {15,36}, {17,34}, {28,30}, {6,15}, {7,21}, {3,5}, {19,40}, {18,22}, {29,31}, {8,37}, {12,25}, {22,24}, {2,15}, {13,14}, {20,36}, {6,31}, {9,13}, {1,7}, {1,23}, {12,21}, {23,30}, {29,34}, {15,23}, {17,31}, {2,31}, {13,28}, {9,18}, {20,26}, {10,17}, {11,29}, {12,15}, {3,40}, {11,16}, {2,34}, {8,19}, {22,40}, {13,37}, {6,34}, {2,21}, {23,35}, {18,28}, {29,33}, {29,35}, {21,23}, {23,25}, {29,32}, {23,32}, {6,21}, {1,12}, {2,32}, {6,33}, {5,19}, {18,38}, {23,33}, {7,20}, {4,29}, {3,8}, {10,39}, {6,25}, {4,17}, {7,31}, {12,33}, {2,25}, {17,35}, {6,32}, {2,33}, {4,6}, {7,15}, {12,32}, {2,4}, {1,26}, {15,26}, {12,20}, {11,12}, {11,36}, {5,14}, {29,30}, {5,27}, {8,27}, {15,16}, {3,13}, {17,30}, {30,39}, {24,37}, {4,39}, {23,31}, {25,29}, {28,40}, {35,39}, {16,35}, {24,27}, {18,37}, {13,19}, {4,36}, {10,29}, {13,22}, {14,40}, {37,40}, {7,11}, {26,34}, {7,34}, {23,34}, {10,23}, {33,39}, {14,24}, {21,29}, {8,22}, {32,39}, {2,10}, {5,38}, {6,10}, {9,40}, {1,16}, {10,36}, {16,30}, {12,34}, {7,33}, {12,31}, {15,19}, {7,32}, {13,27}, {11,39}, {19,24}, {5,7}, {7,30}, {26,31}, {9,10}, {17,18}, {31,39}, {8,14}, {4,23}, {8,12}, {5,22}, {7,35}, {17,25}, {1,3}, {34,39}, {3,24}, {8,38}, {17,21}, {15,27}, {3,20}, {5,12}, {26,32}, {4,9}, {26,33}, {11,22}, {16,20}, {20,39}, {11,26}, {34,38}, {7,8}, {5,26}, {16,32}, {31,38}, {13,16}, {16,33}, {13,38}, {16,31}, {20,27}, {16,24}, {3,15}, {26,35}, {10,28}, {16,34}, {25,36}, {12,30}, {20,38}, {15,39}, {18,29}, {24,38}, {33,38}, {32,38}, {21,36}, {1,19}, {26,30}, {11,14}, {12,35}, {14,35}, {19,32}, {36,40}, {19,33}, {3,34}, {3,31}, {11,19}, {24,39}, {19,20}, {8,16}, {13,26}, {1,39}, {4,37}, {1,14}, {14,15}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {25,28}, {8,26}, {30,38}, {3,32}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {24,26}, {8,10}, {1,22}, {27,33}, {14,34}, {17,19}, {7,24}, {9,12}, {29,40}, {11,27}, {27,32}, {35,38}, {22,23}, {4,5}, {10,37}, {22,30}, {27,34}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {22,35}, {32,40}, {33,40}, {15,18}, {2,14}, {3,35}, {27,31}, {26,28}, {13,39}, {6,14}, {14,31}, {4,8}, {17,27}, {24,25}, {7,9}, {13,21}, {27,29}, {5,10}, {3,17}, {12,28}, {36,38}, {19,35}, {21,24}, {1,18}, {6,22}, {22,31}, {14,32}, {22,33}, {5,39}, {25,37}, {13,25}, {14,33}, {2,22}, {2,3}, {3,29}, {22,32}, {8,39}, {19,30}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {7,37}, {9,16}, {3,36}, {2,40}, {11,38}, {4,13}, {6,40}, {31,40}, {14,17}, {5,25}, {5,21}, {20,40}, {18,32}, {7,28}, {14,23}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {1,4}, {14,29}, {18,34}, {19,23}, {18,31}, {26,37}, {15,40}, {2,19}, {6,19}, {4,24}, {12,37}, {17,22}, {27,28}, {14,36}, {27,36}, {26,29}, {8,18}, {8,21}, {10,15}, {12,17}, {30,40}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {17,38}, {6,27}, {16,37}, {37,39}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {2,16}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {20,21}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {5,18}, {9,39}, {7,17}, {10,11}, {20,25}, {3,28}, {9,27}, {37,38}, {11,25}, {16,17}, {11,21}, {23,39}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // Total number of connected ET graphs of order 40 is 175 // ******************************************************************************************** // Order 41 // ET41.1 // Non-bipartite Valency 2 // Diameter 20 Girth 41 // Twin-free VT AT // Automorphism group of order 82 EdgePairs[41][1]:={ {30,39}, {6,15}, {5,14}, {24,33}, {19,28}, {2,34}, {1,33}, {20,29}, {7,16}, {4,36}, {2,11}, {27,36}, {18,27}, {1,10}, {3,35}, {5,37}, {13,22}, {17,26}, {15,24}, {6,38}, {14,23}, {23,32}, {25,34}, {22,31}, {10,19}, {12,21}, {11,20}, {28,37}, {8,17}, {32,41}, {29,38}, {3,12}, {9,41}, {8,40}, {4,13}, {9,18}, {16,25}, {21,30}, {31,40}, {7,39}, {26,35} }; // ET41.2 // Non-bipartite Valency 4 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 164 EdgePairs[41][2]:={ {2,11}, {28,29}, {4,13}, {25,26}, {27,36}, {7,16}, {5,37}, {3,12}, {30,39}, {4,36}, {8,9}, {1,33}, {21,22}, {1,10}, {1,2}, {7,8}, {11,20}, {25,34}, {29,30}, {15,24}, {20,21}, {32,33}, {13,14}, {6,7}, {6,15}, {30,31}, {32,41}, {20,29}, {31,32}, {23,32}, {8,40}, {3,4}, {23,24}, {31,40}, {19,28}, {29,38}, {11,12}, {21,30}, {9,10}, {17,18}, {24,33}, {40,41}, {2,3}, {36,37}, {37,38}, {10,11}, {33,34}, {6,38}, {34,35}, {5,6}, {26,35}, {18,19}, {15,16}, {12,13}, {4,5}, {19,20}, {9,41}, {16,25}, {27,28}, {22,31}, {13,22}, {26,27}, {39,40}, {22,23}, {10,19}, {14,23}, {9,18}, {5,14}, {18,27}, {7,39}, {35,36}, {2,34}, {16,17}, {38,39}, {1,41}, {14,15}, {17,26}, {28,37}, {8,17}, {24,25}, {12,21}, {3,35} }; // ET41.3 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 328 EdgePairs[41][3]:={ {35,36}, {19,20}, {10,24}, {11,20}, {13,40}, {15,24}, {1,10}, {10,37}, {18,32}, {25,39}, {11,25}, {38,41}, {32,41}, {32,35}, {8,9}, {30,33}, {3,6}, {24,27}, {17,20}, {16,19}, {12,39}, {4,31}, {7,8}, {3,35}, {21,35}, {20,21}, {7,34}, {16,25}, {11,14}, {21,22}, {18,21}, {6,7}, {11,12}, {5,32}, {14,28}, {13,16}, {15,16}, {39,40}, {3,17}, {16,30}, {19,28}, {23,32}, {19,33}, {15,29}, {14,23}, {11,38}, {36,37}, {40,41}, {2,34}, {27,28}, {35,38}, {37,38}, {27,30}, {2,5}, {26,27}, {26,29}, {19,22}, {7,39}, {9,41}, {26,40}, {3,12}, {25,28}, {24,25}, {12,13}, {25,34}, {23,26}, {1,2}, {13,22}, {37,40}, {26,35}, {30,39}, {28,29}, {8,17}, {2,16}, {23,37}, {7,16}, {6,33}, {3,4}, {14,15}, {32,33}, {8,11}, {28,37}, {8,22}, {29,38}, {27,36}, {9,10}, {8,35}, {17,18}, {5,14}, {18,27}, {4,13}, {1,28}, {14,41}, {4,7}, {1,33}, {10,13}, {2,3}, {17,31}, {29,32}, {12,26}, {31,34}, {6,15}, {4,36}, {20,29}, {22,25}, {14,17}, {33,34}, {22,23}, {8,40}, {20,23}, {18,19}, {21,30}, {27,41}, {1,39}, {29,30}, {9,12}, {6,9}, {36,39}, {1,15}, {12,15}, {22,31}, {2,11}, {10,11}, {13,27}, {4,5}, {24,38}, {33,36}, {16,17}, {15,18}, {38,39}, {3,30}, {9,18}, {2,29}, {20,34}, {5,8}, {31,32}, {6,38}, {2,40}, {9,36}, {13,14}, {31,40}, {4,18}, {10,19}, {1,4}, {7,10}, {28,31}, {25,26}, {1,41}, {5,6}, {3,41}, {30,31}, {17,26}, {5,19}, {6,20}, {21,24}, {22,36}, {5,37}, {24,33}, {23,24}, {9,23}, {7,21}, {34,35}, {34,37}, {12,21} }; // ET41.4 // Non-bipartite Valency 10 // Diameter 2 Girth 4 // Twin-free VT AT // Automorphism group of order 410 EdgePairs[41][4]:={ {21,23}, {33,38}, {11,20}, {18,39}, {13,21}, {7,15}, {36,38}, {14,19}, {4,24}, {15,24}, {3,8}, {17,38}, {1,10}, {32,40}, {26,31}, {32,41}, {2,23}, {5,38}, {12,32}, {39,41}, {8,28}, {18,38}, {32,34}, {34,36}, {23,28}, {32,37}, {19,24}, {20,40}, {1,40}, {35,40}, {25,33}, {3,35}, {2,4}, {25,30}, {1,21}, {16,18}, {16,25}, {8,10}, {2,41}, {6,11}, {38,40}, {3,5}, {9,11}, {10,15}, {19,21}, {10,30}, {8,16}, {19,28}, {23,32}, {14,23}, {7,12}, {31,33}, {31,39}, {2,34}, {26,28}, {9,29}, {19,40}, {17,37}, {12,17}, {16,24}, {18,20}, {12,20}, {2,10}, {8,41}, {2,38}, {27,29}, {7,39}, {6,8}, {9,41}, {5,25}, {11,13}, {3,12}, {9,14}, {11,31}, {22,27}, {2,35}, {1,22}, {25,34}, {21,26}, {10,31}, {13,22}, {24,32}, {14,16}, {13,18}, {26,35}, {29,34}, {30,39}, {16,37}, {24,26}, {8,17}, {3,39}, {29,37}, {7,16}, {13,33}, {30,35}, {15,35}, {5,7}, {28,37}, {23,25}, {8,13}, {1,9}, {29,38}, {20,28}, {27,36}, {15,20}, {5,14}, {18,26}, {18,27}, {4,13}, {3,11}, {20,22}, {15,17}, {1,33}, {33,41}, {26,34}, {31,36}, {10,12}, {1,3}, {30,32}, {15,36}, {37,39}, {12,33}, {6,15}, {5,41}, {4,36}, {33,35}, {4,6}, {20,29}, {4,9}, {28,36}, {14,22}, {6,27}, {17,25}, {6,26}, {8,40}, {28,33}, {21,29}, {14,34}, {3,23}, {21,30}, {12,14}, {20,25}, {36,41}, {17,19}, {2,7}, {34,39}, {35,37}, {13,15}, {27,32}, {18,23}, {6,14}, {22,31}, {9,30}, {2,11}, {1,37}, {16,21}, {7,28}, {28,30}, {22,24}, {4,37}, {4,40}, {16,36}, {11,16}, {9,18}, {3,24}, {2,22}, {29,31}, {11,32}, {10,18}, {9,17}, {19,39}, {30,38}, {7,9}, {6,38}, {27,35}, {5,10}, {31,40}, {5,26}, {11,19}, {10,19}, {4,25}, {24,29}, {4,12}, {5,13}, {7,27}, {20,41}, {15,23}, {14,35}, {25,27}, {23,31}, {17,26}, {1,6}, {6,39}, {13,34}, {17,22}, {22,30}, {1,34}, {5,37}, {21,41}, {24,33}, {3,36}, {7,40}, {8,29}, {19,27}, {12,21} }; // ET41.5 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 820 EdgePairs[41][5]:={ {13,21}, {24,34}, {15,33}, {6,38}, {19,28}, {15,38}, {31,39}, {5,7}, {9,32}, {5,38}, {9,17}, {10,18}, {3,8}, {9,10}, {17,18}, {31,40}, {12,22}, {3,26}, {8,26}, {22,40}, {1,40}, {1,3}, {2,35}, {17,33}, {6,15}, {8,40}, {3,35}, {11,15}, {10,33}, {21,30}, {33,34}, {5,6}, {3,19}, {30,40}, {5,15}, {24,32}, {1,19}, {21,41}, {3,23}, {12,16}, {2,18}, {1,21}, {3,21}, {16,37}, {3,39}, {19,37}, {7,30}, {2,7}, {29,39}, {8,31}, {4,40}, {4,37}, {21,22}, {6,14}, {16,21}, {24,28}, {19,20}, {10,11}, {19,21}, {2,33}, {17,35}, {11,29}, {9,11}, {11,27}, {6,29}, {27,36}, {19,40}, {20,38}, {8,16}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {2,6}, {32,33}, {8,13}, {8,12}, {1,17}, {1,9}, {29,33}, {1,10}, {4,13}, {20,24}, {27,28}, {7,11}, {12,20}, {5,41}, {31,36}, {23,31}, {7,27}, {8,9}, {2,10}, {6,39}, {25,34}, {10,26}, {33,35}, {20,29}, {23,28}, {10,20}, {17,26}, {1,24}, {5,37}, {27,32}, {12,13}, {26,35}, {16,25}, {28,30}, {15,19}, {12,37}, {16,34}, {35,37}, {10,35}, {18,39}, {24,26}, {29,31}, {6,24}, {1,38}, {1,26}, {14,32}, {36,38}, {20,36}, {7,15}, {26,36}, {9,29}, {18,26}, {4,22}, {30,38}, {18,36}, {5,28}, {6,10}, {20,41}, {2,39}, {8,18}, {24,40}, {14,35}, {10,12}, {7,32}, {25,33}, {25,26}, {3,13}, {9,13}, {35,39}, {6,27}, {4,9}, {14,34}, {30,31}, {3,36}, {19,23}, {25,29}, {36,41}, {13,17}, {18,19}, {20,25}, {16,18}, {1,2}, {13,18}, {19,27}, {8,10}, {11,21}, {34,35}, {23,39}, {8,17}, {11,36}, {16,17}, {22,26}, {11,16}, {3,24}, {14,15}, {14,23}, {6,16}, {18,22}, {39,40}, {21,25}, {14,39}, {21,31}, {7,12}, {8,24}, {31,33}, {31,41}, {4,41}, {8,41}, {27,37}, {18,20}, {5,14}, {18,38}, {21,37}, {32,40}, {12,17}, {13,36}, {1,41}, {2,23}, {20,22}, {10,19}, {15,23}, {9,19}, {19,24}, {11,34}, {34,36}, {6,8}, {11,13}, {25,30}, {22,30}, {2,27}, {12,30}, {2,12}, {1,22}, {10,31}, {1,6}, {25,41}, {7,8}, {24,25}, {33,37}, {13,22}, {22,31}, {20,30}, {2,20}, {13,31}, {17,19}, {9,30}, {16,41}, {7,28}, {6,11}, {13,29}, {9,25}, {4,5}, {38,40}, {10,30}, {28,37}, {33,38}, {7,23}, {6,22}, {15,35}, {17,38}, {29,38}, {26,31}, {6,31}, {11,32}, {15,24}, {3,7}, {16,26}, {15,40}, {27,35}, {14,37}, {4,14}, {13,38}, {23,27}, {36,37}, {32,41}, {31,32}, {9,41}, {15,17}, {37,39}, {7,39}, {13,14}, {34,38}, {4,36}, {4,29}, {1,32}, {1,5}, {2,3}, {24,29}, {21,39}, {30,32}, {26,27}, {19,29}, {28,32}, {6,37}, {32,37}, {10,28}, {29,30}, {17,22}, {17,25}, {7,40}, {2,41}, {5,23}, {18,41}, {34,39}, {12,14}, {26,30}, {29,37}, {8,29}, {14,16}, {22,38}, {28,29}, {2,11}, {16,36}, {23,32}, {10,15}, {3,5}, {19,39}, {3,34}, {1,11}, {4,27}, {30,35}, {18,28}, {2,22}, {36,40}, {16,20}, {14,19}, {1,33}, {18,27}, {20,28}, {33,41}, {26,28}, {5,26}, {3,11}, {4,8}, {10,41}, {4,25}, {14,30}, {3,28}, {31,35}, {12,33}, {5,9}, {11,19}, {8,33}, {39,41}, {4,12}, {28,33}, {28,36}, {27,29}, {11,31}, {35,40}, {14,24}, {19,35}, {13,34}, {7,25}, {6,26}, {1,34}, {22,27}, {30,34}, {14,18}, {22,23}, {5,21}, {21,29}, {17,40}, {2,4}, {17,21}, {18,23}, {4,35}, {13,33}, {13,15}, {11,12}, {23,33}, {7,16}, {22,24}, {11,20}, {35,36}, {3,4}, {3,40}, {15,16}, {38,39}, {7,17}, {13,23}, {17,27}, {32,36}, {15,20}, {17,37}, {16,39}, {40,41}, {26,34}, {23,25}, {16,24}, {28,38}, {9,27}, {37,38}, {7,38}, {2,38}, {7,9}, {12,32}, {15,36}, {25,35}, {15,31}, {5,10}, {8,28}, {9,40}, {4,20}, {20,40}, {5,13}, {5,25}, {25,27}, {32,34}, {4,6}, {27,31}, {8,39}, {14,22}, {22,32}, {3,12}, {9,14}, {23,41}, {5,36}, {9,34}, {10,14}, {24,33}, {12,35}, {29,34}, {37,41}, {21,26}, {20,21}, {1,37}, {23,24}, {30,39}, {16,32}, {12,21}, {6,7}, {18,34}, {15,25}, {5,30}, {21,23} }; // ET41.6 // Bipartite(20,21) Valencies [21,20] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 124299255809188481393766275481600000000 EdgePairs[41][6]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {20,24}, {5,41}, {17,39}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {20,35}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {20,36}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {18,38}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {20,22}, {15,23}, {12,41}, {9,22}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {19,41}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {7,40}, {2,41}, {17,41}, {5,23}, {20,32}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {20,28}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {6,41}, {17,24}, {17,40}, {20,23}, {12,34}, {17,21}, {19,36}, {6,28}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,25}, {15,21}, {20,34}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {20,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {8,39}, {14,22}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {20,21}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET41.7 // Bipartite(19,22) Valencies [22,19] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 136729181390107329533142903029760000000 EdgePairs[41][7]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {19,20}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {19,40}, {2,34}, {12,28}, {19,31}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {15,23}, {12,41}, {9,22}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {2,20}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {19,41}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {5,20}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {6,41}, {17,24}, {17,40}, {12,34}, {17,21}, {19,36}, {6,28}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {8,39}, {14,22}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET41.8 // Bipartite(18,23) Valencies [23,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 165514272209077293645383514193920000000 EdgePairs[41][8]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {9,35}, {1,36}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {13,19}, {1,26}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {12,41}, {9,22}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {16,41}, {7,28}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {5,20}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {14,19}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {6,41}, {17,24}, {17,40}, {12,34}, {17,21}, {6,28}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {16,33}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET41.9 // Bipartite(17,24) Valencies [24,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 220685696278769724860511352258560000000 EdgePairs[41][9]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {11,25}, {4,28}, {17,18}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {16,41}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {6,41}, {17,24}, {17,40}, {12,34}, {17,21}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {16,33}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET41.10 // Bipartite(16,25) Valencies [25,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 324537788645249595383104929792000000000 EdgePairs[41][10]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {16,40}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {9,41}, {6,23}, {16,31}, {15,17}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {6,41}, {12,34}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {14,17}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {16,32}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET41.11 // Bipartite(15,26) Valencies [26,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 527373906548530592497545510912000000000 EdgePairs[41][11]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,33}, {15,37}, {10,38}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {9,41}, {6,23}, {15,17}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {6,41}, {12,34}, {6,28}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {15,18}, {5,17}, {3,40}, {15,16}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET41.12 // Bipartite(14,27) Valencies [27,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 949273031787355066495581919641600000000 EdgePairs[41][12]:={ {13,21}, {6,38}, {11,40}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,15}, {14,33}, {10,38}, {14,23}, {6,16}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {14,37}, {13,38}, {4,15}, {14,40}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {6,41}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {14,41}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {14,22}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET41.13 // Bipartite(13,28) Valencies [28,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1898546063574710132991163839283200000000 EdgePairs[41][13]:={ {13,21}, {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {13,39}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {6,14}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {13,25}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {13,38}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {13,14}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {6,41}, {9,15}, {12,34}, {6,28}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET41.14 // Bipartite(12,29) Valencies [29,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4235218141820507219749519333785600000000 EdgePairs[41][14]:={ {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {1,13}, {12,26}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {3,29}, {12,17}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {6,41}, {9,15}, {12,34}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {7,13}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET41.15 // Bipartite(11,30) Valencies [30,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10588045354551268049373798334464000000000 EdgePairs[41][15]:={ {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {8,26}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {7,12}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {2,37}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {6,41}, {9,15}, {6,28}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET41.16 // Bipartite(10,31) Valencies [31,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 29839036908280846320962522578944000000000 EdgePairs[41][16]:={ {6,38}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {1,12}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {7,12}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {6,41}, {9,15}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET41.17 // Bipartite(9,32) Valencies [32,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 95484918106498708227080072252620800000000 EdgePairs[41][17]:={ {6,38}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {4,28}, {9,10}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {1,10}, {8,37}, {4,13}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {2,10}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {4,10}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {9,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {3,33}, {2,11}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {6,41}, {9,15}, {6,28}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {5,10}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {5,36}, {9,34}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET41.18 // Bipartite(8,33) Valencies [33,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 350111366390495263499293598259609600000000 EdgePairs[41][18]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {3,40}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {5,38}, {8,9}, {3,9}, {7,38}, {8,28}, {4,29}, {1,32}, {3,13}, {8,33}, {1,27}, {3,25}, {3,15}, {7,41}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {8,39}, {1,21}, {2,9}, {7,36}, {8,10}, {8,25}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,27}, {8,31}, {6,22}, {3,18}, {3,17}, {6,29}, {8,16}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {7,12}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {3,14}, {7,11}, {7,20}, {5,11}, {2,10}, {4,41}, {5,29}, {8,41}, {2,38}, {2,37}, {8,14}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {8,13}, {8,22}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {8,37}, {5,28}, {8,26}, {7,31}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {8,32}, {8,21}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {8,40}, {3,23}, {8,23}, {1,39}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {4,40}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {8,34}, {3,24}, {2,29}, {8,38}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {7,9}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {8,18}, {4,18}, {5,9}, {4,25}, {3,38}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {1,41}, {3,41}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {6,39}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {7,21}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET41.19 // Bipartite(7,34) Valencies [34,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1487973307159604869871997792603340800000000 EdgePairs[41][19]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {7,38}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {7,41}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {7,12}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {6,8}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {7,31}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {1,25}, {6,19}, {6,9}, {7,29}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {4,40}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {1,41}, {3,41}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {2,18}, {5,35}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET41.20 // Bipartite(6,35) Valencies [35,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7439866535798024349359988963016704000000000 EdgePairs[41][20]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {6,8}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {6,19}, {6,9}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {4,40}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {1,41}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {5,35}, {1,34}, {5,37}, {4,17}, {6,35}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET41.21 // Bipartite(5,36) Valencies [36,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 44639199214788146096159933778100224000000000 EdgePairs[41][21]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {3,18}, {3,17}, {3,7}, {4,38}, {3,34}, {2,25}, {5,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {3,26}, {5,28}, {2,17}, {4,36}, {5,41}, {4,6}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {1,15}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,40}, {2,31}, {5,10}, {5,27}, {5,26}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {1,41}, {5,6}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {2,30}, {5,21}, {2,18}, {5,35}, {1,34}, {5,37}, {4,17}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET41.22 // Bipartite(4,37) Valencies [37,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 330330074189432281111583509957941657600000000 EdgePairs[41][22]:={ {1,15}, {4,35}, {3,15}, {2,38}, {1,11}, {4,14}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {1,40}, {2,20}, {4,40}, {1,25}, {4,16}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {4,37}, {4,20}, {2,41}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {4,39}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {2,34}, {3,27}, {4,30}, {1,19}, {2,40}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,35}, {1,26}, {4,38}, {2,24}, {4,11}, {2,27}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {1,41}, {4,32}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {4,9}, {2,7}, {4,34}, {4,41}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET41.23 // Bipartite(3,38) Valencies [38,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3138135704799606670560043344600445747200000000 EdgePairs[41][23]:={ {1,15}, {3,15}, {2,38}, {1,11}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {2,11}, {1,40}, {2,20}, {1,25}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {2,41}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {2,34}, {3,27}, {1,19}, {2,40}, {2,35}, {2,9}, {3,5}, {1,4}, {1,35}, {1,26}, {2,4}, {2,24}, {2,27}, {3,4}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {2,6}, {3,21}, {1,14}, {1,41}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET41.24 // Bipartite(2,39) Valencies [39,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 40795764162394886717280563479805794713600000000 EdgePairs[41][24]:={ {2,11}, {1,26}, {2,14}, {1,14}, {2,37}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,37}, {1,33}, {1,40}, {1,10}, {2,39}, {1,39}, {1,36}, {1,6}, {2,40}, {2,6}, {1,4}, {1,20}, {1,12}, {2,36}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {1,38}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,38}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {1,28}, {2,19}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {2,41}, {1,41}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET41.25 // Bipartite(1,40) Valencies [40,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 815915283247897734345611269596115894272000000000 EdgePairs[41][25]:={ {1,4}, {1,20}, {1,3}, {1,34}, {1,37}, {1,30}, {1,14}, {1,23}, {1,40}, {1,39}, {1,33}, {1,41}, {1,24}, {1,38}, {1,7}, {1,27}, {1,29}, {1,35}, {1,5}, {1,15}, {1,22}, {1,28}, {1,16}, {1,10}, {1,12}, {1,13}, {1,17}, {1,2}, {1,11}, {1,36}, {1,19}, {1,18}, {1,25}, {1,32}, {1,21}, {1,9}, {1,26}, {1,31}, {1,6}, {1,8} }; // ET41.26 // Non-bipartite Valency 40 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 33452526613163807108170062053440751665152000000000 EdgePairs[41][26]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {13,18}, {32,33}, {2,6}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {15,21}, {24,40}, {5,40}, {4,35}, {6,39}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {19,27}, {32,34}, {7,12}, {31,33}, {21,34}, {4,10}, {33,34}, {3,19}, {1,15}, {5,8}, {10,30}, {31,32}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {30,31}, {21,31}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {34,35}, {3,27}, {29,39}, {25,32}, {5,13}, {15,33}, {21,33}, {30,34}, {22,27}, {17,36}, {10,35}, {13,40}, {11,15}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {13,41}, {22,37}, {12,26}, {15,34}, {18,41}, {7,16}, {12,16}, {14,19}, {3,38}, {13,24}, {11,30}, {30,32}, {4,21}, {29,36}, {30,33}, {20,34}, {23,29}, {1,33}, {4,25}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, {1,30}, {14,27}, {11,35}, {2,29}, {16,39}, {15,31}, {10,21}, {17,23}, {12,19}, {3,7}, {10,25}, {6,17}, {32,35}, {20,33}, {2,17}, {33,35}, {36,37}, {20,32}, {18,40}, {11,33}, {19,22}, {16,26}, {3,22}, {5,24}, {11,32}, {1,5}, {28,37}, {26,27}, {11,20}, {24,41}, {17,28}, {1,8}, {11,24}, {1,35}, {9,17}, {10,18}, {19,38}, {8,15}, {5,20}, {14,16}, {3,12}, {3,26}, {28,29}, {11,31}, {16,22}, {12,39}, {6,36}, {5,15}, {20,30}, {2,36}, {4,18}, {35,41}, {22,38}, {26,39}, {8,11}, {15,35}, {30,41}, {14,38}, {5,41}, {12,27}, {11,13}, {15,30}, {7,19}, {11,34}, {8,32}, {7,39}, {22,39}, {19,26}, {8,33}, {8,20}, {5,31}, {20,35}, {16,19}, {1,13}, {26,38}, {9,23}, {7,14}, {34,41}, {13,15}, {5,34}, {9,29}, {13,35}, {14,26}, {23,28}, {7,27}, {2,9}, {10,40}, {29,37}, {38,39}, {13,30}, {6,9}, {13,20}, {16,27}, {23,36}, {8,41}, {5,32}, {5,33}, {8,31}, {17,37}, {5,11}, {3,16}, {20,24}, {7,22}, {22,26}, {12,14}, {12,22}, {7,38}, {13,34}, {28,36}, {23,24}, {9,36}, {3,4}, {31,41}, {8,34}, {15,24}, {10,19}, {1,24}, {20,41}, {12,38}, {27,39}, {32,41}, {31,37}, {14,39}, {34,37}, {2,13}, {5,30}, {33,41}, {24,30}, {6,13}, {5,35}, {24,35}, {8,17}, {1,9}, {18,25}, {4,40}, {2,37}, {12,18}, {6,37}, {9,15}, {3,10}, {21,40}, {18,21}, {8,30}, {13,31}, {2,28}, {25,40}, {22,25}, {15,28}, {6,28}, {14,21}, {7,18}, {11,41}, {21,22}, {14,25}, {5,17}, {24,33}, {20,28}, {13,32}, {13,33}, {35,37}, {10,27}, {9,11}, {24,32}, {16,18}, {32,37}, {33,37}, {19,39}, {1,41}, {3,39}, {5,29}, {8,35}, {15,41}, {6,24}, {24,31}, {9,32}, {39,40}, {2,5}, {2,24}, {4,19}, {5,6}, {9,33}, {9,20}, {18,26}, {8,29}, {4,14}, {30,37}, {8,23}, {3,21}, {5,36}, {23,37}, {4,27}, {2,8}, {6,8}, {24,29}, {13,17}, {3,25}, {1,37}, {13,23}, {12,40}, {36,41}, {1,28}, {16,38}, {25,27}, {9,31}, {21,27}, {4,38}, {8,9}, {28,32}, {24,34}, {10,14}, {13,29}, {4,22}, {4,7}, {10,22}, {10,12}, {26,40}, {17,24}, {28,33}, {21,38}, {15,37}, {2,41}, {8,36}, {23,41}, {9,34}, {15,17}, {10,38}, {6,41}, {34,36}, {11,28}, {13,36}, {18,19}, {28,34}, {19,25}, {25,38}, {19,21}, {20,37}, {6,11}, {38,40}, {5,23}, {11,23}, {31,36}, {2,11}, {9,30}, {29,41}, {7,40}, {20,29}, {33,36}, {32,36}, {28,31}, {18,27}, {1,6}, {11,37}, {1,2}, {5,9}, {4,26}, {4,12}, {2,30}, {3,18}, {7,10}, {1,29}, {6,30}, {9,35}, {1,17}, {8,28}, {18,39}, {21,26}, {17,41}, {35,36}, {5,28}, {25,26}, {17,33}, {2,35}, {10,26}, {17,20}, {16,40}, {6,35}, {15,29}, {17,32}, {28,35}, {24,28}, {27,40}, {16,25}, {11,17}, {25,39}, {16,21}, {5,37}, {24,36}, {9,24}, {21,39}, {30,36}, {6,20}, {2,20}, {1,36}, {14,18}, {10,16}, {4,16}, {20,23}, {7,25}, {15,36}, {17,34}, {28,30}, {6,15}, {7,21}, {3,5}, {19,40}, {18,22}, {29,31}, {8,37}, {37,41}, {12,25}, {22,24}, {2,15}, {13,14}, {20,36}, {6,31}, {9,13}, {1,7}, {1,23}, {12,21}, {23,30}, {29,34}, {15,23}, {17,31}, {2,31}, {13,28}, {9,18}, {20,26}, {10,17}, {11,29}, {12,15}, {3,40}, {11,16}, {2,34}, {8,19}, {22,40}, {13,37}, {6,34}, {2,21}, {23,35}, {18,28}, {29,33}, {28,41}, {29,35}, {21,23}, {23,25}, {29,32}, {23,32}, {6,21}, {1,12}, {2,32}, {6,33}, {5,19}, {18,38}, {23,33}, {7,20}, {4,29}, {3,8}, {10,39}, {6,25}, {4,17}, {7,31}, {12,33}, {2,25}, {17,35}, {6,32}, {2,33}, {4,6}, {7,15}, {12,32}, {2,4}, {1,26}, {15,26}, {12,20}, {11,12}, {38,41}, {11,36}, {5,14}, {29,30}, {5,27}, {8,27}, {15,16}, {3,13}, {17,30}, {30,39}, {24,37}, {4,39}, {23,31}, {25,29}, {28,40}, {35,39}, {16,35}, {24,27}, {18,37}, {13,19}, {4,36}, {10,29}, {14,41}, {13,22}, {14,40}, {37,40}, {9,41}, {7,11}, {26,34}, {7,34}, {23,34}, {10,23}, {33,39}, {14,24}, {21,29}, {8,22}, {32,39}, {2,10}, {5,38}, {6,10}, {9,40}, {1,16}, {10,36}, {16,30}, {12,34}, {7,33}, {12,31}, {15,19}, {7,32}, {13,27}, {11,39}, {19,24}, {5,7}, {7,30}, {26,31}, {9,10}, {17,18}, {31,39}, {8,14}, {4,23}, {8,12}, {5,22}, {22,41}, {7,35}, {17,25}, {1,3}, {34,39}, {3,24}, {8,38}, {17,21}, {15,27}, {3,20}, {5,12}, {26,32}, {4,9}, {26,33}, {11,22}, {16,20}, {20,39}, {27,41}, {11,26}, {34,38}, {7,8}, {5,26}, {16,32}, {39,41}, {31,38}, {13,16}, {16,33}, {13,38}, {16,31}, {20,27}, {16,24}, {3,15}, {26,35}, {10,28}, {16,34}, {25,36}, {12,30}, {20,38}, {3,41}, {15,39}, {18,29}, {24,38}, {33,38}, {32,38}, {21,36}, {1,19}, {26,30}, {19,41}, {11,14}, {12,35}, {14,35}, {19,32}, {36,40}, {19,33}, {3,34}, {3,31}, {11,19}, {24,39}, {19,20}, {8,16}, {13,26}, {1,39}, {4,37}, {1,14}, {14,15}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {25,28}, {8,26}, {30,38}, {3,32}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {24,26}, {8,10}, {1,22}, {27,33}, {14,34}, {17,19}, {7,24}, {9,12}, {29,40}, {11,27}, {26,41}, {27,32}, {35,38}, {22,23}, {4,5}, {10,37}, {22,30}, {27,34}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {22,35}, {32,40}, {16,41}, {33,40}, {15,18}, {2,14}, {3,35}, {27,31}, {26,28}, {13,39}, {6,14}, {14,31}, {4,8}, {17,27}, {24,25}, {7,9}, {13,21}, {27,29}, {5,10}, {3,17}, {12,28}, {36,38}, {19,35}, {21,24}, {1,18}, {6,22}, {22,31}, {14,32}, {22,33}, {5,39}, {25,37}, {13,25}, {14,33}, {2,22}, {2,3}, {3,29}, {22,32}, {8,39}, {19,30}, {7,41}, {21,41}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {7,37}, {9,16}, {3,36}, {2,40}, {11,38}, {12,41}, {4,13}, {6,40}, {31,40}, {14,17}, {5,25}, {25,41}, {5,21}, {20,40}, {18,32}, {7,28}, {14,23}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {1,4}, {14,29}, {18,34}, {19,23}, {18,31}, {26,37}, {15,40}, {2,19}, {6,19}, {4,24}, {12,37}, {17,22}, {27,28}, {14,36}, {27,36}, {26,29}, {8,18}, {8,21}, {10,15}, {12,17}, {30,40}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {17,38}, {6,27}, {16,37}, {37,39}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {2,16}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {20,21}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {5,18}, {9,39}, {7,17}, {10,11}, {20,25}, {4,41}, {3,28}, {9,27}, {37,38}, {11,25}, {16,17}, {11,21}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // Total number of connected ET graphs of order 41 is 26 // ******************************************************************************************** // Order 42 // ET42.1 // Bipartite(21,21) Valencies [2,2] // Diameter 21 Girth 42 // Twin-free VT AT // Automorphism group of order 84 EdgePairs[42][1]:={ {4,40}, {19,32}, {13,24}, {18,37}, {8,30}, {5,25}, {7,36}, {3,28}, {20,25}, {16,34}, {7,41}, {18,29}, {5,26}, {17,28}, {11,40}, {8,22}, {6,31}, {21,38}, {14,33}, {1,22}, {14,41}, {10,31}, {9,35}, {13,27}, {2,42}, {2,35}, {20,33}, {15,38}, {9,27}, {6,39}, {11,37}, {21,39}, {15,30}, {12,26}, {19,24}, {1,29}, {10,23}, {16,42}, {3,36}, {17,23}, {4,32}, {12,34} }; // ET42.2 // Bipartite(21,21) Valencies [3,3] // Diameter 6 Girth 6 // Twin-free VT AT // Automorphism group of order 126 EdgePairs[42][2]:={ {12,38}, {18,35}, {3,40}, {10,40}, {17,34}, {2,26}, {21,36}, {4,36}, {13,31}, {2,30}, {11,25}, {7,34}, {21,33}, {9,31}, {20,23}, {1,33}, {16,23}, {5,40}, {10,32}, {15,24}, {9,38}, {11,27}, {18,39}, {15,29}, {19,35}, {3,37}, {8,29}, {20,24}, {18,41}, {13,32}, {5,31}, {20,37}, {19,28}, {8,33}, {10,34}, {19,27}, {17,36}, {6,42}, {12,24}, {13,22}, {12,26}, {8,41}, {16,22}, {16,38}, {3,39}, {14,42}, {2,28}, {14,27}, {6,25}, {11,41}, {17,30}, {15,39}, {5,35}, {4,26}, {1,22}, {7,42}, {9,28}, {21,32}, {7,37}, {1,25}, {6,23}, {14,30}, {4,29} }; // ET42.3 // Bipartite(14,28) Valencies [4,2] // Diameter 6 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 336 EdgePairs[42][3]:={ {5,32}, {13,28}, {4,36}, {2,32}, {6,33}, {14,18}, {11,25}, {8,38}, {1,33}, {8,16}, {6,26}, {2,39}, {8,21}, {1,39}, {9,38}, {10,30}, {13,26}, {14,34}, {11,37}, {6,40}, {3,29}, {6,15}, {3,20}, {13,18}, {5,16}, {5,23}, {8,37}, {10,31}, {2,20}, {4,27}, {9,36}, {12,41}, {3,19}, {7,15}, {11,40}, {9,41}, {10,24}, {1,27}, {4,28}, {13,21}, {14,42}, {10,19}, {3,34}, {12,22}, {14,23}, {12,35}, {5,35}, {7,17}, {9,30}, {1,22}, {7,42}, {2,25}, {12,17}, {11,31}, {7,24}, {4,29} }; // ET42.4 // Bipartite(14,28) Valencies [4,2] // Diameter 7 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 1792 EdgePairs[42][4]:={ {11,30}, {4,24}, {4,41}, {14,18}, {5,29}, {7,34}, {13,16}, {5,27}, {11,28}, {2,39}, {3,21}, {4,40}, {13,25}, {10,30}, {1,20}, {3,23}, {12,40}, {3,24}, {10,33}, {6,36}, {6,32}, {11,21}, {8,37}, {7,32}, {5,31}, {14,36}, {2,38}, {4,27}, {9,33}, {10,41}, {7,15}, {6,42}, {1,18}, {3,26}, {9,35}, {8,34}, {8,35}, {13,22}, {7,20}, {1,17}, {12,25}, {13,15}, {2,19}, {12,42}, {2,23}, {14,37}, {1,19}, {10,38}, {9,26}, {12,28}, {11,31}, {6,29}, {5,22}, {14,16}, {9,17}, {8,39} }; // ET42.5 // Bipartite(14,28) Valencies [4,2] // Diameter 14 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 458752 EdgePairs[42][5]:={ {12,20}, {8,19}, {1,29}, {2,30}, {9,25}, {2,29}, {5,27}, {11,24}, {3,42}, {6,31}, {5,40}, {3,27}, {9,38}, {11,37}, {4,31}, {11,23}, {11,38}, {4,16}, {10,33}, {6,32}, {4,30}, {8,32}, {2,16}, {1,15}, {9,24}, {3,28}, {7,40}, {8,33}, {10,34}, {14,36}, {14,22}, {13,36}, {14,35}, {12,34}, {2,15}, {4,17}, {7,25}, {13,22}, {13,23}, {6,18}, {14,21}, {10,19}, {1,28}, {1,42}, {3,41}, {12,35}, {6,17}, {7,39}, {5,26}, {8,18}, {5,41}, {13,37}, {9,39}, {10,20}, {12,21}, {7,26} }; // ET42.6 // Bipartite(18,24) Valencies [4,3] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 1152 EdgePairs[42][6]:={ {3,32}, {1,26}, {4,24}, {8,19}, {5,42}, {6,34}, {14,31}, {4,37}, {8,31}, {2,30}, {11,25}, {13,34}, {7,23}, {2,40}, {11,20}, {10,32}, {3,33}, {18,39}, {11,37}, {2,36}, {17,35}, {3,20}, {11,42}, {2,21}, {7,36}, {5,23}, {13,32}, {1,38}, {8,40}, {5,31}, {12,39}, {17,20}, {4,27}, {15,30}, {9,27}, {9,33}, {10,41}, {17,38}, {18,19}, {16,21}, {15,25}, {12,29}, {7,38}, {8,34}, {10,24}, {13,23}, {14,33}, {3,39}, {18,37}, {12,22}, {7,28}, {15,41}, {17,40}, {12,35}, {6,25}, {14,24}, {1,19}, {9,30}, {16,42}, {10,21}, {9,26}, {13,27}, {1,41}, {6,28}, {4,35}, {14,28}, {6,29}, {5,22}, {16,29}, {18,36}, {15,22}, {16,26} }; // ET42.7 // Bipartite(18,24) Valencies [4,3] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 1152 EdgePairs[42][7]:={ {3,22}, {15,35}, {15,32}, {17,41}, {12,27}, {5,36}, {8,28}, {10,40}, {6,39}, {5,24}, {9,21}, {7,31}, {12,33}, {1,37}, {8,23}, {16,23}, {11,20}, {4,40}, {13,25}, {16,31}, {15,24}, {18,39}, {18,34}, {6,30}, {11,37}, {4,31}, {3,23}, {2,33}, {6,32}, {5,21}, {16,27}, {16,36}, {9,29}, {2,20}, {10,26}, {13,42}, {14,22}, {17,19}, {2,38}, {3,25}, {11,32}, {6,27}, {12,24}, {13,20}, {14,40}, {7,38}, {7,35}, {8,34}, {15,28}, {11,36}, {8,41}, {4,28}, {10,39}, {7,19}, {18,21}, {14,33}, {9,22}, {1,42}, {12,42}, {17,30}, {5,26}, {13,29}, {18,38}, {14,37}, {1,19}, {9,30}, {2,41}, {1,34}, {10,25}, {17,26}, {3,35}, {4,29} }; // ET42.8 // Bipartite(21,21) Valencies [4,4] // Diameter 7 Girth 4 // Twin-free VT AT // Automorphism group of order 168 EdgePairs[42][8]:={ {4,35}, {9,40}, {7,39}, {13,29}, {8,31}, {4,42}, {10,22}, {14,34}, {3,29}, {6,36}, {16,30}, {18,39}, {5,35}, {12,22}, {5,24}, {19,27}, {9,39}, {7,27}, {11,38}, {1,32}, {13,42}, {14,35}, {15,29}, {3,34}, {9,31}, {12,25}, {16,33}, {21,28}, {20,40}, {1,29}, {18,24}, {19,37}, {17,31}, {5,33}, {15,34}, {20,38}, {9,27}, {2,23}, {17,24}, {7,26}, {21,38}, {1,22}, {2,32}, {4,33}, {10,41}, {15,36}, {16,26}, {3,22}, {13,35}, {8,26}, {4,30}, {2,34}, {12,28}, {17,33}, {8,40}, {20,37}, {11,41}, {12,38}, {14,36}, {1,23}, {15,42}, {6,30}, {10,28}, {14,23}, {5,36}, {11,25}, {6,42}, {11,32}, {18,30}, {3,25}, {13,23}, {10,32}, {7,37}, {19,41}, {21,40}, {2,25}, {18,31}, {8,37}, {17,26}, {6,24}, {19,28}, {16,39}, {20,41}, {21,27} }; // ET42.9 // Bipartite(21,21) Valencies [4,4] // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[42][9]:={ {12,38}, {15,32}, {5,36}, {8,28}, {6,37}, {17,34}, {2,37}, {5,37}, {21,36}, {4,36}, {19,26}, {5,29}, {13,41}, {21,33}, {8,38}, {1,33}, {14,39}, {18,42}, {4,40}, {3,27}, {3,33}, {11,29}, {14,41}, {18,34}, {14,34}, {15,23}, {8,24}, {3,37}, {6,40}, {12,31}, {17,35}, {9,32}, {17,42}, {8,27}, {13,32}, {7,32}, {16,30}, {5,25}, {2,31}, {7,40}, {9,40}, {21,30}, {10,26}, {18,25}, {13,39}, {20,28}, {9,27}, {10,41}, {21,28}, {18,30}, {3,31}, {12,29}, {16,25}, {16,35}, {7,38}, {13,22}, {1,27}, {4,22}, {4,25}, {2,42}, {6,22}, {14,23}, {15,34}, {20,26}, {1,42}, {12,35}, {19,30}, {11,41}, {2,23}, {11,26}, {10,38}, {9,28}, {1,23}, {16,24}, {20,33}, {20,39}, {11,31}, {6,29}, {10,35}, {7,24}, {17,24}, {19,39}, {15,22}, {19,36} }; // ET42.10 // Bipartite(21,21) Valencies [4,4] // Diameter 4 Girth 6 // Twin-free VT AT // Automorphism group of order 672 EdgePairs[42][10]:={ {20,42}, {6,41}, {3,40}, {6,37}, {5,32}, {18,22}, {14,31}, {9,25}, {17,39}, {4,34}, {7,23}, {16,41}, {20,23}, {20,35}, {11,28}, {2,39}, {16,23}, {18,42}, {13,25}, {11,29}, {18,33}, {12,32}, {10,30}, {12,30}, {15,38}, {3,38}, {2,36}, {4,31}, {7,33}, {6,36}, {9,37}, {3,29}, {17,35}, {4,30}, {8,27}, {5,23}, {1,38}, {21,27}, {4,33}, {8,40}, {5,25}, {21,30}, {14,22}, {8,36}, {18,25}, {11,32}, {10,41}, {19,38}, {21,28}, {12,37}, {14,40}, {3,26}, {10,29}, {8,34}, {16,22}, {1,27}, {19,33}, {2,28}, {2,42}, {17,31}, {10,42}, {15,34}, {19,32}, {15,41}, {21,26}, {12,35}, {13,24}, {16,28}, {15,39}, {5,34}, {13,29}, {14,37}, {9,26}, {13,27}, {1,22}, {1,35}, {9,39}, {20,40}, {11,31}, {7,24}, {17,24}, {6,24}, {19,36}, {7,26} }; // ET42.11 // Non-bipartite Valency 4 // Diameter 10 Girth 4 // Has twins VT AT // Automorphism group of order 88080384 EdgePairs[42][11]:={ {1,26}, {18,35}, {20,42}, {17,37}, {12,27}, {4,24}, {19,41}, {22,38}, {4,23}, {14,31}, {2,26}, {8,31}, {13,31}, {9,25}, {5,29}, {16,34}, {7,31}, {16,41}, {11,28}, {21,38}, {14,39}, {19,42}, {3,27}, {11,27}, {6,30}, {3,23}, {3,24}, {8,29}, {10,33}, {16,33}, {17,35}, {7,30}, {2,21}, {8,32}, {13,32}, {5,20}, {21,37}, {7,32}, {13,40}, {3,28}, {10,26}, {10,34}, {12,36}, {6,20}, {5,19}, {11,35}, {23,40}, {4,27}, {1,21}, {13,39}, {9,33}, {22,37}, {17,36}, {17,38}, {14,32}, {14,40}, {5,30}, {9,34}, {20,41}, {11,36}, {24,40}, {4,28}, {6,19}, {24,39}, {18,37}, {15,34}, {15,41}, {12,35}, {15,33}, {18,38}, {16,42}, {9,26}, {12,28}, {1,22}, {15,42}, {2,25}, {10,25}, {23,39}, {8,30}, {6,29}, {1,25}, {2,22}, {18,36}, {7,29} }; // ET42.12 // Non-bipartite Valency 4 // Diameter 5 Girth 3 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[42][12]:={ {6,41}, {4,9}, {27,36}, {27,40}, {2,29}, {11,25}, {16,34}, {4,34}, {14,26}, {9,21}, {7,31}, {16,41}, {1,33}, {11,24}, {2,39}, {5,10}, {18,42}, {35,38}, {6,12}, {3,27}, {5,40}, {15,24}, {19,25}, {26,39}, {3,24}, {9,32}, {22,28}, {7,30}, {4,30}, {6,16}, {5,23}, {13,32}, {20,27}, {15,31}, {3,11}, {29,35}, {10,23}, {8,36}, {18,25}, {4,21}, {36,41}, {19,38}, {5,17}, {22,37}, {2,15}, {23,33}, {9,42}, {12,13}, {13,20}, {1,18}, {12,29}, {8,41}, {25,38}, {16,19}, {14,33}, {6,22}, {12,22}, {8,26}, {1,28}, {14,23}, {1,42}, {17,40}, {21,26}, {32,42}, {15,39}, {17,30}, {30,34}, {13,29}, {8,14}, {2,35}, {7,17}, {10,38}, {24,31}, {21,39}, {20,32}, {28,33}, {20,40}, {31,37}, {7,37}, {11,18}, {28,37}, {10,35}, {3,36}, {19,34} }; // ET42.13 // Bipartite(12,30) Valencies [5,2] // Diameter 6 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[42][13]:={ {8,19}, {11,15}, {8,20}, {4,37}, {4,41}, {2,32}, {1,29}, {6,33}, {9,25}, {2,29}, {11,17}, {4,34}, {7,34}, {7,23}, {9,21}, {8,38}, {5,27}, {6,30}, {1,20}, {5,15}, {2,36}, {3,23}, {12,40}, {6,40}, {10,33}, {6,32}, {11,21}, {5,16}, {6,16}, {9,24}, {10,31}, {2,31}, {4,38}, {8,36}, {3,25}, {12,41}, {3,14}, {12,24}, {1,18}, {3,26}, {12,26}, {11,13}, {10,39}, {2,27}, {7,19}, {10,37}, {9,22}, {10,42}, {1,28}, {7,28}, {5,18}, {12,42}, {1,13}, {7,17}, {9,30}, {4,35}, {11,14}, {5,22}, {8,39}, {3,35} }; // ET42.14 // Bipartite(12,30) Valencies [5,2] // Diameter 6 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 1440 EdgePairs[42][14]:={ {2,14}, {12,20}, {5,36}, {6,34}, {9,23}, {2,37}, {4,41}, {9,20}, {11,25}, {1,32}, {2,24}, {8,23}, {11,24}, {4,40}, {9,38}, {6,30}, {4,16}, {7,33}, {10,33}, {3,29}, {6,15}, {11,42}, {5,16}, {4,32}, {10,13}, {5,31}, {1,15}, {10,31}, {3,28}, {8,36}, {2,38}, {1,21}, {3,30}, {11,40}, {3,14}, {6,42}, {1,18}, {3,26}, {9,41}, {12,29}, {1,27}, {4,28}, {11,13}, {2,27}, {7,19}, {12,25}, {6,19}, {9,22}, {8,26}, {12,35}, {7,39}, {5,34}, {5,35}, {8,18}, {7,17}, {10,22}, {10,21}, {7,37}, {12,17}, {8,39} }; // ET42.15 // Bipartite(21,21) Valencies [5,5] // Diameter 3 Girth 6 // Twin-free VT AT // Automorphism group of order 241920 EdgePairs[42][15]:={ {14,39}, {16,34}, {13,41}, {14,25}, {21,39}, {3,29}, {17,27}, {3,38}, {9,42}, {6,36}, {7,40}, {10,27}, {6,41}, {11,29}, {10,38}, {13,24}, {11,42}, {12,40}, {12,31}, {20,23}, {19,40}, {5,41}, {6,32}, {17,35}, {2,33}, {21,26}, {7,27}, {21,35}, {7,23}, {8,34}, {19,33}, {2,28}, {12,25}, {5,26}, {6,22}, {14,27}, {1,29}, {8,22}, {1,34}, {15,39}, {5,23}, {15,34}, {10,36}, {2,23}, {8,33}, {19,26}, {1,36}, {3,40}, {2,36}, {4,33}, {16,35}, {3,22}, {10,37}, {9,23}, {11,28}, {4,31}, {4,30}, {7,30}, {17,33}, {12,35}, {1,26}, {13,40}, {18,27}, {20,37}, {4,38}, {14,32}, {21,30}, {5,38}, {15,31}, {15,42}, {6,30}, {9,35}, {18,28}, {2,39}, {20,32}, {9,24}, {11,25}, {12,36}, {19,42}, {13,28}, {11,30}, {21,37}, {3,39}, {10,42}, {17,41}, {15,41}, {16,28}, {8,25}, {17,29}, {20,29}, {18,31}, {8,37}, {20,31}, {18,22}, {16,38}, {19,32}, {7,34}, {13,37}, {16,32}, {5,25}, {14,24}, {4,24}, {18,26}, {1,24}, {9,22} }; // ET42.16 // Bipartite(14,28) Valencies [6,3] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 1344 EdgePairs[42][16]:={ {3,22}, {12,38}, {6,41}, {12,20}, {5,42}, {8,19}, {9,19}, {10,27}, {8,20}, {4,37}, {4,41}, {6,39}, {5,24}, {4,36}, {1,29}, {5,29}, {1,32}, {7,23}, {9,21}, {9,16}, {11,28}, {2,39}, {14,39}, {4,40}, {10,32}, {13,25}, {9,38}, {11,27}, {10,30}, {3,38}, {2,36}, {8,24}, {3,37}, {11,23}, {12,40}, {4,16}, {12,31}, {11,42}, {7,32}, {2,31}, {10,31}, {1,16}, {10,26}, {6,20}, {13,33}, {8,36}, {9,33}, {10,41}, {14,35}, {7,15}, {5,17}, {12,23}, {2,15}, {6,21}, {3,18}, {4,17}, {14,40}, {7,22}, {7,21}, {8,22}, {6,18}, {12,25}, {14,33}, {13,15}, {2,28}, {14,42}, {3,34}, {1,28}, {13,24}, {5,26}, {5,34}, {2,34}, {7,17}, {9,26}, {13,27}, {1,35}, {13,37}, {8,30}, {11,19}, {11,18}, {6,29}, {1,25}, {14,30}, {3,35} }; // ET42.17 // Bipartite(21,21) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 252 EdgePairs[42][17]:={ {14,39}, {13,25}, {7,42}, {5,32}, {6,39}, {13,29}, {12,26}, {4,42}, {18,40}, {21,31}, {11,23}, {21,39}, {14,34}, {3,29}, {11,33}, {4,27}, {16,30}, {10,27}, {6,41}, {7,24}, {10,38}, {6,23}, {1,40}, {1,25}, {2,37}, {18,37}, {1,38}, {2,33}, {7,31}, {9,39}, {6,25}, {15,40}, {21,25}, {11,22}, {19,23}, {14,35}, {13,38}, {2,28}, {3,34}, {16,41}, {4,26}, {8,41}, {21,28}, {20,40}, {5,37}, {3,41}, {9,38}, {17,23}, {10,34}, {20,35}, {17,24}, {19,30}, {1,22}, {14,30}, {2,32}, {4,33}, {15,36}, {10,31}, {16,35}, {7,25}, {18,25}, {20,24}, {11,39}, {5,29}, {19,29}, {3,27}, {4,30}, {14,26}, {21,33}, {12,28}, {15,33}, {17,33}, {12,29}, {1,35}, {11,37}, {8,40}, {18,27}, {17,36}, {12,24}, {4,38}, {2,24}, {5,22}, {15,31}, {15,42}, {8,27}, {13,32}, {14,37}, {8,32}, {9,28}, {11,40}, {20,32}, {5,36}, {5,31}, {19,42}, {13,28}, {8,23}, {16,22}, {1,42}, {9,26}, {18,29}, {19,22}, {20,26}, {19,34}, {3,39}, {17,34}, {12,42}, {15,41}, {16,28}, {13,23}, {10,32}, {7,37}, {17,38}, {12,41}, {3,36}, {6,35}, {6,24}, {8,30}, {20,36}, {9,36}, {10,35}, {7,34}, {16,31}, {2,30}, {18,26}, {9,22}, {21,27} }; // ET42.18 // Bipartite(21,21) Valencies [6,6] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 252 EdgePairs[42][18]:={ {16,25}, {13,41}, {7,42}, {7,39}, {18,41}, {13,29}, {8,31}, {17,39}, {10,22}, {21,31}, {21,39}, {9,30}, {3,38}, {5,30}, {6,36}, {1,31}, {6,41}, {5,35}, {11,42}, {20,23}, {10,40}, {18,37}, {12,33}, {1,32}, {6,40}, {9,37}, {8,34}, {6,34}, {5,26}, {18,24}, {20,25}, {12,30}, {1,34}, {17,23}, {15,22}, {2,41}, {10,36}, {19,30}, {21,38}, {10,25}, {1,22}, {14,30}, {6,33}, {12,34}, {15,36}, {7,29}, {4,29}, {16,26}, {16,35}, {10,37}, {13,35}, {8,26}, {14,38}, {3,23}, {11,39}, {4,31}, {19,29}, {2,42}, {18,34}, {14,26}, {21,33}, {2,40}, {15,33}, {17,33}, {12,35}, {9,25}, {4,25}, {10,29}, {1,35}, {11,26}, {8,40}, {18,27}, {7,35}, {4,38}, {12,23}, {14,32}, {9,33}, {11,41}, {12,38}, {5,22}, {2,27}, {17,22}, {15,42}, {5,27}, {8,27}, {14,37}, {9,28}, {3,28}, {11,31}, {20,32}, {3,24}, {9,24}, {19,42}, {13,28}, {8,23}, {18,29}, {19,22}, {20,26}, {19,34}, {4,32}, {21,37}, {3,39}, {1,37}, {15,27}, {16,28}, {7,32}, {13,23}, {16,42}, {14,40}, {2,25}, {3,36}, {16,38}, {17,32}, {20,36}, {13,31}, {7,36}, {17,40}, {11,24}, {5,39}, {19,28}, {2,30}, {15,24}, {4,24}, {20,41}, {6,28}, {21,27} }; // ET42.19 // Bipartite(21,21) Valencies [6,6] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 2016 EdgePairs[42][19]:={ {9,40}, {13,29}, {16,36}, {8,31}, {12,26}, {17,39}, {2,38}, {11,23}, {14,34}, {7,40}, {19,39}, {6,41}, {5,35}, {1,40}, {13,24}, {5,34}, {12,40}, {5,24}, {10,40}, {1,38}, {19,27}, {17,35}, {7,31}, {12,33}, {21,26}, {13,27}, {14,42}, {1,32}, {9,37}, {19,33}, {20,42}, {16,33}, {6,34}, {6,22}, {15,28}, {2,29}, {10,30}, {5,37}, {1,29}, {20,25}, {12,30}, {11,34}, {17,31}, {15,34}, {2,23}, {7,41}, {8,28}, {18,33}, {1,22}, {2,32}, {21,41}, {3,40}, {12,34}, {10,39}, {15,36}, {7,25}, {3,22}, {14,28}, {9,23}, {10,24}, {6,37}, {11,39}, {3,23}, {19,29}, {2,42}, {3,27}, {4,30}, {10,33}, {21,33}, {2,35}, {13,30}, {4,25}, {11,26}, {20,37}, {18,35}, {4,38}, {12,23}, {3,42}, {5,38}, {3,35}, {15,42}, {6,30}, {18,28}, {14,31}, {8,32}, {9,28}, {4,22}, {8,23}, {16,22}, {20,26}, {21,37}, {1,27}, {15,27}, {11,32}, {8,25}, {7,32}, {20,29}, {10,32}, {13,36}, {17,38}, {19,41}, {14,29}, {21,42}, {8,37}, {9,41}, {17,26}, {18,36}, {20,39}, {6,35}, {16,38}, {18,22}, {17,28}, {13,31}, {9,36}, {19,25}, {4,41}, {15,30}, {7,36}, {11,24}, {16,31}, {16,39}, {5,25}, {14,24}, {4,24}, {18,26}, {21,27} }; // ET42.20 // Bipartite(21,21) Valencies [6,6] // Diameter 7 Girth 4 // Has twins VT AT // Automorphism group of order 2194196594688 EdgePairs[42][20]:={ {14,39}, {13,41}, {20,27}, {5,32}, {7,39}, {9,40}, {18,41}, {13,29}, {14,25}, {8,31}, {8,24}, {18,40}, {12,39}, {21,39}, {9,30}, {5,42}, {3,38}, {6,36}, {11,33}, {1,31}, {4,27}, {16,30}, {8,36}, {19,39}, {6,41}, {5,35}, {10,38}, {4,40}, {2,37}, {13,34}, {1,38}, {2,33}, {17,35}, {16,23}, {16,40}, {13,27}, {21,25}, {9,37}, {17,42}, {7,23}, {15,29}, {12,25}, {3,31}, {16,33}, {6,34}, {4,26}, {6,22}, {1,29}, {8,22}, {11,34}, {17,31}, {15,22}, {2,23}, {17,24}, {1,36}, {18,33}, {1,22}, {14,30}, {4,33}, {15,36}, {10,31}, {16,26}, {7,25}, {9,23}, {10,24}, {18,34}, {2,40}, {12,28}, {7,30}, {5,28}, {12,35}, {11,26}, {13,22}, {6,29}, {18,27}, {14,32}, {9,33}, {21,30}, {11,41}, {3,42}, {15,31}, {3,35}, {10,28}, {8,38}, {14,37}, {14,23}, {11,40}, {3,28}, {3,24}, {19,42}, {21,23}, {9,26}, {21,32}, {11,27}, {21,37}, {10,42}, {12,42}, {7,32}, {20,29}, {2,26}, {13,36}, {20,34}, {7,37}, {15,38}, {17,38}, {12,32}, {16,37}, {17,28}, {20,36}, {19,32}, {4,34}, {10,35}, {6,27}, {19,25}, {19,35}, {20,22}, {4,41}, {5,39}, {19,28}, {2,30}, {15,24}, {5,25}, {18,26}, {20,41}, {1,24}, {8,29} }; // ET42.21 // Bipartite(21,21) Valencies [6,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1410877440 EdgePairs[42][21]:={ {14,39}, {7,39}, {18,41}, {8,31}, {17,39}, {2,38}, {4,42}, {21,31}, {21,39}, {9,30}, {1,31}, {4,27}, {7,40}, {16,30}, {11,29}, {11,42}, {5,34}, {1,25}, {12,40}, {2,37}, {18,42}, {19,40}, {1,38}, {19,27}, {17,35}, {7,31}, {12,33}, {16,23}, {21,26}, {3,30}, {9,37}, {12,27}, {13,42}, {7,23}, {8,34}, {19,33}, {20,42}, {2,28}, {8,41}, {6,22}, {2,29}, {10,30}, {18,24}, {8,22}, {1,34}, {9,38}, {5,33}, {17,30}, {15,34}, {20,33}, {15,22}, {20,35}, {10,36}, {2,23}, {13,33}, {17,24}, {7,26}, {13,26}, {10,25}, {15,25}, {1,22}, {6,33}, {12,34}, {10,39}, {4,29}, {9,23}, {10,24}, {13,35}, {6,37}, {16,29}, {14,26}, {6,26}, {12,28}, {5,28}, {13,22}, {18,27}, {17,36}, {20,37}, {14,32}, {11,41}, {18,32}, {15,31}, {3,35}, {5,27}, {14,31}, {8,38}, {14,23}, {9,28}, {5,36}, {3,24}, {19,36}, {12,36}, {21,23}, {21,32}, {18,29}, {1,41}, {20,26}, {11,27}, {19,34}, {4,32}, {6,42}, {3,39}, {11,32}, {15,41}, {16,28}, {8,25}, {3,25}, {7,32}, {9,29}, {15,38}, {21,40}, {14,40}, {3,36}, {6,35}, {16,38}, {16,37}, {10,35}, {20,22}, {4,41}, {13,37}, {11,24}, {19,28}, {2,30}, {4,24}, {5,40}, {17,25} }; // ET42.22 // Non-bipartite Valency 6 // Diameter 3 Girth 5 // Twin-free VT AT // Automorphism group of order 5040 EdgePairs[42][22]:={ {1,15}, {10,19}, {9,13}, {5,32}, {28,33}, {15,23}, {13,29}, {11,17}, {6,14}, {27,32}, {6,36}, {4,27}, {23,38}, {18,39}, {1,40}, {17,19}, {12,15}, {28,39}, {7,33}, {13,42}, {22,36}, {5,7}, {36,38}, {20,42}, {16,33}, {23,30}, {26,35}, {15,32}, {15,28}, {19,37}, {24,40}, {1,34}, {32,42}, {16,21}, {9,38}, {27,37}, {3,11}, {17,30}, {4,20}, {20,33}, {7,41}, {1,10}, {3,13}, {10,25}, {2,16}, {1,22}, {21,41}, {6,21}, {29,40}, {26,38}, {8,18}, {9,34}, {10,31}, {10,16}, {5,19}, {18,25}, {6,8}, {8,35}, {13,35}, {3,23}, {11,39}, {5,29}, {7,14}, {4,31}, {18,34}, {14,26}, {7,30}, {4,17}, {2,35}, {12,29}, {1,26}, {11,26}, {8,40}, {13,22}, {25,41}, {17,36}, {22,27}, {30,34}, {31,39}, {2,24}, {5,38}, {33,40}, {16,27}, {21,29}, {8,27}, {14,31}, {2,39}, {14,37}, {2,12}, {9,28}, {22,39}, {23,31}, {9,24}, {12,36}, {24,32}, {8,23}, {11,21}, {18,20}, {20,26}, {34,37}, {6,42}, {24,25}, {10,42}, {11,32}, {7,22}, {15,41}, {35,41}, {3,25}, {29,31}, {30,42}, {21,34}, {4,9}, {16,38}, {3,37}, {5,18}, {19,35}, {4,41}, {3,33}, {17,40}, {19,28}, {12,37}, {2,30}, {12,20}, {14,24}, {25,36}, {6,28} }; // ET42.23 // Bipartite(14,28) Valencies [8,4] // Diameter 7 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8218956791808 EdgePairs[42][23]:={ {1,15}, {4,35}, {7,19}, {13,25}, {13,41}, {5,32}, {6,39}, {3,15}, {4,42}, {10,22}, {12,39}, {6,18}, {9,30}, {3,29}, {3,38}, {5,30}, {9,42}, {11,33}, {12,16}, {7,40}, {13,18}, {8,36}, {6,41}, {7,24}, {10,38}, {4,40}, {14,19}, {11,42}, {7,38}, {7,33}, {2,37}, {13,34}, {6,32}, {7,31}, {6,25}, {13,27}, {9,21}, {12,18}, {9,37}, {8,34}, {2,28}, {12,25}, {3,31}, {6,34}, {4,26}, {8,41}, {13,20}, {5,37}, {1,29}, {8,22}, {8,15}, {12,30}, {1,34}, {14,33}, {5,23}, {10,36}, {2,23}, {7,26}, {1,36}, {2,16}, {1,22}, {4,33}, {4,28}, {10,15}, {10,31}, {3,22}, {9,23}, {10,24}, {14,38}, {11,28}, {2,42}, {14,26}, {4,21}, {2,35}, {10,29}, {11,26}, {12,23}, {14,17}, {2,21}, {8,27}, {9,35}, {11,19}, {14,31}, {13,32}, {11,40}, {9,28}, {3,24}, {8,20}, {11,21}, {6,20}, {10,17}, {1,41}, {1,20}, {1,27}, {12,32}, {14,40}, {3,36}, {3,17}, {5,18}, {6,27}, {9,16}, {7,17}, {5,16}, {5,39}, {12,37}, {11,35}, {2,30}, {5,25}, {4,19}, {14,24}, {8,29}, {13,39} }; // ET42.24 // Bipartite(14,28) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5505024 EdgePairs[42][24]:={ {1,15}, {7,19}, {6,39}, {7,39}, {9,40}, {10,21}, {13,29}, {3,15}, {8,31}, {12,26}, {3,29}, {3,38}, {5,30}, {1,31}, {12,16}, {13,18}, {8,36}, {5,35}, {1,40}, {1,25}, {12,40}, {7,33}, {13,34}, {2,33}, {6,25}, {9,21}, {12,18}, {14,42}, {11,22}, {12,27}, {13,42}, {7,23}, {8,34}, {2,28}, {2,19}, {10,18}, {13,20}, {5,21}, {10,23}, {1,29}, {8,22}, {3,41}, {12,30}, {9,38}, {5,33}, {2,41}, {2,31}, {1,17}, {4,33}, {2,17}, {9,34}, {10,31}, {7,25}, {10,37}, {14,28}, {5,19}, {5,15}, {7,20}, {3,23}, {8,17}, {11,39}, {5,29}, {2,42}, {3,27}, {14,26}, {4,36}, {1,26}, {4,38}, {11,41}, {11,36}, {2,27}, {14,36}, {14,22}, {6,30}, {9,35}, {1,39}, {6,38}, {13,32}, {14,23}, {14,37}, {4,22}, {8,16}, {3,24}, {9,24}, {11,25}, {13,28}, {8,20}, {11,21}, {9,26}, {6,16}, {10,17}, {11,27}, {4,32}, {6,42}, {4,18}, {10,32}, {7,37}, {13,15}, {12,41}, {12,32}, {14,40}, {3,37}, {6,24}, {8,30}, {10,35}, {7,34}, {5,16}, {11,35}, {4,19}, {4,24}, {9,20}, {6,28} }; // ET42.25 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 864 EdgePairs[42][25]:={ {16,41}, {2,24}, {1,20}, {2,33}, {17,35}, {12,29}, {11,35}, {5,34}, {14,19}, {16,33}, {3,22}, {17,38}, {10,37}, {16,40}, {5,38}, {7,38}, {4,29}, {8,33}, {1,27}, {12,38}, {7,41}, {14,38}, {4,31}, {12,41}, {1,19}, {7,34}, {1,21}, {8,25}, {1,30}, {5,32}, {16,23}, {8,27}, {2,42}, {18,34}, {10,22}, {11,28}, {18,37}, {10,30}, {6,29}, {15,29}, {14,23}, {11,33}, {6,31}, {5,22}, {14,36}, {15,32}, {16,24}, {9,26}, {2,38}, {14,40}, {4,42}, {9,41}, {2,39}, {17,39}, {17,23}, {15,26}, {1,31}, {10,28}, {17,33}, {3,20}, {9,42}, {16,37}, {10,40}, {7,30}, {18,30}, {11,21}, {4,35}, {9,25}, {15,35}, {12,25}, {8,22}, {15,34}, {18,24}, {15,20}, {13,28}, {9,20}, {18,27}, {18,36}, {6,23}, {3,26}, {17,31}, {5,42}, {12,26}, {7,31}, {17,28}, {8,32}, {3,19}, {13,24}, {6,27}, {12,19}, {12,30}, {3,23}, {8,23}, {18,25}, {10,32}, {5,36}, {3,21}, {6,19}, {6,41}, {13,27}, {10,39}, {1,35}, {13,42}, {14,25}, {16,21}, {7,28}, {4,37}, {4,40}, {16,36}, {11,37}, {3,24}, {2,29}, {11,27}, {2,22}, {4,34}, {18,22}, {11,32}, {14,32}, {13,41}, {2,40}, {9,33}, {9,36}, {5,26}, {10,19}, {4,25}, {12,24}, {8,20}, {3,28}, {14,35}, {15,39}, {17,26}, {6,39}, {6,37}, {13,34}, {13,39}, {5,21}, {15,30}, {13,20}, {9,31}, {11,42}, {7,40}, {7,21}, {8,29}, {1,36} }; // ET42.26 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 288 EdgePairs[42][26]:={ {3,33}, {16,41}, {10,25}, {9,28}, {5,34}, {13,40}, {11,25}, {8,30}, {7,38}, {8,42}, {16,31}, {18,38}, {8,33}, {3,25}, {10,23}, {12,38}, {17,34}, {16,19}, {4,19}, {12,39}, {1,19}, {14,31}, {2,26}, {7,34}, {17,24}, {12,35}, {7,36}, {2,41}, {12,34}, {1,30}, {9,35}, {4,23}, {8,31}, {12,37}, {16,29}, {15,25}, {18,42}, {10,30}, {6,21}, {2,25}, {11,33}, {6,40}, {5,22}, {4,22}, {9,29}, {7,20}, {17,37}, {14,21}, {9,26}, {15,40}, {12,36}, {5,29}, {8,41}, {4,42}, {2,39}, {17,39}, {15,26}, {1,31}, {10,41}, {11,22}, {14,24}, {10,31}, {2,20}, {16,37}, {10,40}, {1,29}, {3,39}, {3,32}, {4,35}, {13,33}, {6,33}, {2,32}, {16,32}, {11,23}, {1,23}, {6,24}, {5,30}, {15,35}, {9,37}, {17,27}, {8,22}, {15,20}, {13,28}, {9,20}, {18,26}, {1,28}, {14,41}, {3,27}, {18,36}, {18,33}, {3,26}, {5,28}, {13,36}, {5,42}, {12,26}, {13,30}, {4,36}, {12,27}, {14,22}, {5,31}, {11,24}, {6,27}, {8,40}, {14,34}, {10,32}, {18,25}, {17,19}, {5,36}, {7,29}, {6,41}, {18,23}, {1,35}, {13,42}, {1,37}, {16,21}, {7,28}, {4,37}, {2,21}, {3,24}, {4,34}, {11,32}, {8,24}, {6,38}, {2,40}, {15,28}, {16,39}, {9,39}, {13,38}, {11,19}, {10,19}, {3,38}, {7,27}, {15,23}, {6,20}, {17,22}, {15,30}, {13,20}, {17,32}, {11,42}, {9,21}, {18,35}, {14,27}, {7,21}, {14,29} }; // ET42.27 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 288 EdgePairs[42][27]:={ {10,19}, {7,19}, {5,32}, {7,39}, {9,40}, {14,25}, {16,36}, {8,24}, {2,38}, {4,42}, {11,23}, {3,29}, {2,22}, {5,30}, {1,31}, {10,27}, {11,29}, {6,23}, {1,40}, {5,34}, {12,31}, {18,42}, {3,32}, {13,34}, {12,33}, {16,40}, {7,27}, {9,21}, {3,30}, {14,42}, {6,40}, {11,22}, {8,42}, {18,23}, {7,23}, {18,21}, {13,38}, {3,34}, {3,31}, {5,26}, {13,20}, {15,28}, {14,27}, {12,30}, {11,34}, {16,21}, {9,38}, {17,30}, {4,37}, {4,20}, {15,22}, {2,41}, {10,36}, {10,25}, {15,25}, {2,36}, {10,41}, {10,39}, {7,29}, {10,31}, {16,35}, {7,25}, {16,19}, {7,20}, {8,26}, {6,37}, {5,29}, {11,28}, {10,33}, {14,26}, {1,19}, {4,36}, {4,21}, {15,33}, {17,33}, {13,30}, {1,35}, {13,40}, {8,40}, {15,26}, {18,35}, {14,32}, {6,19}, {17,22}, {18,32}, {5,38}, {3,35}, {2,21}, {9,35}, {8,38}, {2,39}, {14,23}, {8,32}, {9,28}, {4,22}, {3,28}, {17,37}, {9,24}, {12,36}, {11,21}, {9,26}, {6,20}, {18,29}, {6,42}, {17,34}, {1,27}, {12,42}, {15,27}, {17,41}, {15,41}, {2,26}, {11,20}, {12,41}, {1,33}, {14,29}, {12,32}, {2,25}, {1,28}, {18,31}, {8,37}, {18,36}, {6,24}, {16,38}, {8,30}, {17,28}, {17,20}, {6,27}, {4,41}, {13,19}, {3,33}, {7,34}, {13,37}, {4,23}, {11,35}, {5,39}, {12,37}, {16,31}, {16,39}, {15,24}, {5,25}, {14,24}, {1,24}, {9,22}, {13,39} }; // ET42.28 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[42][28]:={ {7,42}, {16,34}, {5,32}, {9,40}, {18,41}, {15,23}, {16,36}, {8,39}, {17,39}, {10,22}, {12,19}, {3,29}, {1,31}, {7,40}, {6,41}, {5,35}, {14,19}, {11,42}, {7,38}, {13,34}, {1,38}, {2,33}, {17,35}, {7,31}, {12,33}, {16,40}, {9,19}, {13,27}, {9,21}, {3,30}, {14,42}, {6,40}, {12,27}, {14,35}, {18,21}, {13,38}, {2,28}, {3,34}, {14,20}, {16,33}, {6,34}, {8,41}, {6,22}, {5,21}, {2,29}, {10,30}, {8,22}, {17,31}, {9,38}, {4,37}, {4,20}, {15,22}, {9,27}, {10,36}, {13,33}, {17,24}, {8,33}, {8,28}, {4,39}, {13,26}, {15,25}, {18,38}, {14,30}, {2,32}, {3,40}, {12,34}, {9,34}, {7,29}, {10,39}, {7,25}, {3,22}, {5,19}, {10,24}, {18,25}, {8,26}, {2,42}, {12,28}, {15,19}, {4,36}, {4,21}, {2,35}, {5,28}, {12,35}, {11,37}, {18,27}, {4,38}, {12,23}, {6,31}, {3,42}, {11,36}, {18,32}, {15,21}, {1,23}, {15,42}, {6,30}, {9,35}, {13,32}, {14,23}, {11,31}, {5,36}, {3,26}, {11,25}, {8,20}, {8,23}, {11,30}, {1,41}, {1,37}, {1,20}, {1,27}, {11,32}, {15,41}, {16,28}, {9,29}, {17,29}, {2,26}, {13,36}, {10,32}, {7,37}, {7,21}, {12,41}, {14,29}, {2,25}, {10,20}, {6,24}, {18,22}, {16,37}, {17,28}, {10,26}, {17,20}, {6,27}, {3,33}, {13,37}, {15,30}, {17,40}, {4,23}, {11,24}, {5,39}, {16,31}, {16,39}, {5,25}, {4,19}, {14,24}, {18,26}, {1,24} }; // ET42.29 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[42][29]:={ {10,19}, {7,19}, {5,32}, {6,39}, {13,29}, {14,25}, {15,23}, {8,24}, {4,42}, {18,40}, {12,39}, {9,30}, {9,42}, {5,30}, {1,31}, {10,27}, {6,23}, {5,34}, {7,33}, {12,31}, {2,37}, {3,32}, {12,33}, {6,25}, {16,40}, {9,21}, {11,38}, {6,40}, {9,37}, {17,42}, {8,42}, {12,27}, {14,35}, {7,23}, {8,34}, {16,41}, {12,25}, {16,33}, {4,26}, {15,32}, {13,20}, {15,28}, {2,29}, {14,27}, {18,24}, {8,22}, {7,28}, {11,34}, {1,34}, {15,39}, {17,31}, {9,38}, {17,23}, {5,33}, {15,34}, {2,41}, {10,36}, {2,23}, {7,41}, {4,39}, {1,36}, {18,33}, {13,26}, {10,25}, {14,30}, {8,21}, {10,39}, {7,29}, {10,31}, {4,29}, {16,35}, {16,19}, {3,22}, {7,20}, {18,25}, {8,35}, {8,26}, {14,38}, {15,20}, {6,37}, {3,27}, {2,40}, {5,28}, {10,29}, {18,19}, {1,35}, {11,37}, {11,26}, {8,40}, {15,26}, {4,38}, {12,23}, {2,24}, {5,22}, {6,19}, {14,36}, {3,35}, {15,42}, {16,27}, {5,27}, {10,28}, {6,38}, {13,32}, {11,40}, {3,28}, {5,31}, {17,37}, {9,24}, {16,22}, {3,21}, {11,30}, {17,21}, {6,42}, {13,21}, {17,34}, {1,20}, {11,32}, {18,30}, {17,29}, {2,26}, {3,20}, {12,41}, {1,33}, {2,25}, {3,36}, {14,41}, {18,36}, {9,32}, {16,38}, {18,22}, {17,28}, {13,31}, {4,41}, {13,37}, {7,36}, {1,30}, {11,35}, {1,21}, {12,20}, {4,19}, {14,24}, {4,24}, {9,22}, {13,39} }; // ET42.30 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[42][30]:={ {7,42}, {14,21}, {16,36}, {8,39}, {2,38}, {11,23}, {12,19}, {3,29}, {9,42}, {4,27}, {18,39}, {8,36}, {6,23}, {2,20}, {13,24}, {14,19}, {17,19}, {7,38}, {7,33}, {12,31}, {5,24}, {3,32}, {13,34}, {10,40}, {5,41}, {6,32}, {16,40}, {7,27}, {9,19}, {9,21}, {11,38}, {14,42}, {6,40}, {17,42}, {18,23}, {15,29}, {9,31}, {14,20}, {16,41}, {16,33}, {4,26}, {8,41}, {6,22}, {5,21}, {10,23}, {15,28}, {2,29}, {14,27}, {12,21}, {1,34}, {12,30}, {5,33}, {15,22}, {2,41}, {2,31}, {1,36}, {10,25}, {15,25}, {18,38}, {3,40}, {4,33}, {9,34}, {10,39}, {16,35}, {3,22}, {14,28}, {10,24}, {18,25}, {8,26}, {13,35}, {6,37}, {11,28}, {2,42}, {18,34}, {14,26}, {1,19}, {4,36}, {4,21}, {2,35}, {17,33}, {12,29}, {4,25}, {1,26}, {11,37}, {8,40}, {7,35}, {9,33}, {3,42}, {6,19}, {5,38}, {15,21}, {3,35}, {1,23}, {6,30}, {10,28}, {2,39}, {13,32}, {5,20}, {3,28}, {5,31}, {17,37}, {12,36}, {11,27}, {3,39}, {1,37}, {1,27}, {7,22}, {15,27}, {17,41}, {18,30}, {8,25}, {13,23}, {13,36}, {7,37}, {15,38}, {11,20}, {12,41}, {14,29}, {12,32}, {18,31}, {10,20}, {17,26}, {9,32}, {18,22}, {8,30}, {16,37}, {10,26}, {13,31}, {17,20}, {4,34}, {7,34}, {15,30}, {16,32}, {17,40}, {11,24}, {1,30}, {11,35}, {5,25}, {4,24}, {8,29}, {9,22}, {6,28}, {13,39}, {16,24} }; // ET42.31 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[42][31]:={ {4,35}, {13,25}, {14,21}, {18,41}, {13,29}, {8,39}, {17,39}, {10,22}, {14,34}, {3,29}, {17,27}, {6,36}, {11,33}, {7,40}, {7,24}, {10,38}, {6,23}, {1,40}, {11,42}, {12,40}, {12,31}, {2,37}, {5,24}, {1,38}, {5,41}, {2,33}, {6,32}, {6,25}, {9,39}, {16,40}, {9,19}, {9,21}, {16,20}, {8,42}, {13,42}, {8,34}, {2,28}, {16,41}, {12,25}, {3,31}, {16,33}, {5,26}, {10,23}, {15,28}, {10,30}, {3,19}, {1,29}, {18,24}, {7,28}, {14,33}, {15,39}, {16,21}, {17,23}, {17,30}, {4,37}, {4,20}, {2,23}, {7,41}, {8,33}, {10,25}, {13,26}, {15,25}, {18,38}, {1,22}, {2,32}, {3,40}, {6,21}, {2,36}, {4,33}, {9,34}, {10,31}, {3,22}, {10,37}, {5,19}, {10,24}, {13,35}, {14,38}, {15,35}, {4,30}, {2,34}, {18,34}, {12,28}, {15,19}, {7,30}, {4,21}, {2,35}, {12,35}, {4,25}, {1,26}, {11,26}, {7,35}, {12,23}, {12,38}, {3,42}, {11,36}, {18,32}, {14,36}, {5,38}, {15,42}, {14,22}, {5,27}, {6,30}, {8,27}, {11,19}, {14,31}, {8,32}, {3,24}, {5,31}, {17,37}, {8,20}, {1,42}, {11,21}, {9,26}, {6,20}, {18,20}, {1,41}, {11,27}, {3,39}, {1,27}, {11,32}, {7,22}, {15,27}, {9,29}, {17,29}, {13,23}, {7,37}, {12,41}, {14,40}, {17,26}, {18,36}, {18,22}, {17,28}, {9,36}, {4,34}, {13,19}, {13,37}, {15,30}, {16,32}, {5,39}, {16,31}, {9,20}, {8,29}, {6,28}, {16,24} }; // ET42.32 // Bipartite(18,24) Valencies [8,6] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 106993205379072 EdgePairs[42][32]:={ {4,35}, {14,39}, {7,19}, {13,25}, {14,21}, {16,34}, {9,40}, {8,39}, {2,38}, {10,22}, {11,23}, {12,19}, {5,42}, {5,30}, {6,36}, {1,31}, {5,35}, {11,29}, {2,20}, {4,40}, {11,42}, {7,38}, {1,25}, {12,31}, {18,42}, {5,24}, {10,40}, {18,37}, {1,38}, {5,41}, {2,33}, {17,35}, {7,31}, {9,39}, {6,25}, {16,23}, {16,40}, {15,40}, {9,21}, {1,32}, {17,42}, {13,38}, {3,34}, {14,20}, {16,41}, {12,25}, {13,20}, {10,23}, {15,28}, {14,27}, {18,24}, {12,30}, {14,33}, {15,39}, {17,23}, {5,23}, {17,30}, {15,34}, {10,34}, {15,22}, {9,27}, {17,24}, {8,33}, {7,26}, {13,26}, {2,32}, {3,40}, {8,21}, {10,41}, {9,34}, {4,28}, {4,29}, {16,35}, {7,25}, {3,22}, {7,20}, {18,25}, {8,26}, {14,38}, {6,37}, {5,29}, {16,29}, {3,27}, {14,26}, {1,19}, {15,33}, {10,29}, {18,19}, {1,26}, {17,36}, {12,24}, {14,32}, {6,31}, {9,33}, {11,41}, {11,36}, {6,19}, {2,27}, {15,21}, {2,21}, {6,30}, {10,28}, {8,27}, {8,38}, {2,39}, {13,32}, {8,32}, {9,28}, {4,22}, {3,28}, {5,36}, {12,36}, {8,20}, {16,22}, {3,21}, {11,30}, {6,42}, {3,39}, {1,37}, {1,20}, {12,42}, {15,27}, {17,41}, {18,30}, {16,28}, {7,32}, {17,29}, {2,26}, {7,37}, {18,31}, {18,36}, {6,24}, {13,31}, {4,34}, {10,35}, {4,41}, {13,19}, {3,33}, {13,37}, {4,23}, {11,24}, {11,35}, {12,37}, {9,22} }; // ET42.33 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7044820107264 EdgePairs[42][33]:={ {10,19}, {7,42}, {6,39}, {18,41}, {16,36}, {8,39}, {12,26}, {17,39}, {10,22}, {12,19}, {14,34}, {17,27}, {3,38}, {6,36}, {1,31}, {4,27}, {16,30}, {5,35}, {7,24}, {1,40}, {4,40}, {11,42}, {5,34}, {1,25}, {12,31}, {2,37}, {3,32}, {13,34}, {10,40}, {5,41}, {16,23}, {13,27}, {14,35}, {18,23}, {7,23}, {16,41}, {12,25}, {3,31}, {2,19}, {3,19}, {1,34}, {15,39}, {9,38}, {5,23}, {10,34}, {2,31}, {13,33}, {7,41}, {8,33}, {4,39}, {10,25}, {18,38}, {1,22}, {6,33}, {6,21}, {2,36}, {8,21}, {4,33}, {4,28}, {7,29}, {15,36}, {10,31}, {16,35}, {10,37}, {14,28}, {9,23}, {8,26}, {5,29}, {16,29}, {2,42}, {1,19}, {7,30}, {4,21}, {15,33}, {17,33}, {5,28}, {11,37}, {13,40}, {13,22}, {7,35}, {18,35}, {2,24}, {5,22}, {12,38}, {11,36}, {18,32}, {15,21}, {15,42}, {14,22}, {6,30}, {10,28}, {9,35}, {8,27}, {11,19}, {8,38}, {14,23}, {8,32}, {4,22}, {11,31}, {3,26}, {11,25}, {13,28}, {8,20}, {9,26}, {18,20}, {18,29}, {11,30}, {17,21}, {6,42}, {13,21}, {1,37}, {15,27}, {9,29}, {3,25}, {17,38}, {3,20}, {16,42}, {14,29}, {12,32}, {2,25}, {14,40}, {1,28}, {9,41}, {14,41}, {17,26}, {3,37}, {6,24}, {9,32}, {17,32}, {17,20}, {4,34}, {6,27}, {15,30}, {7,36}, {11,24}, {12,37}, {2,30}, {12,20}, {15,24}, {5,40}, {9,20}, {18,26}, {13,39}, {16,24} }; // ET42.34 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 9172942848 EdgePairs[42][34]:={ {4,35}, {7,19}, {13,25}, {13,41}, {16,34}, {6,39}, {9,40}, {13,29}, {15,23}, {12,26}, {17,39}, {2,38}, {4,42}, {10,22}, {12,39}, {17,27}, {5,42}, {5,30}, {1,31}, {16,30}, {18,39}, {2,20}, {11,42}, {17,19}, {1,25}, {7,33}, {12,22}, {5,24}, {18,37}, {7,31}, {6,25}, {16,23}, {15,40}, {9,21}, {16,20}, {17,42}, {12,27}, {2,28}, {14,20}, {12,25}, {6,34}, {8,41}, {6,22}, {10,23}, {15,28}, {2,29}, {10,30}, {1,29}, {17,31}, {17,30}, {10,34}, {4,20}, {2,41}, {13,33}, {17,24}, {7,41}, {8,28}, {18,38}, {2,32}, {3,40}, {12,34}, {7,29}, {15,36}, {16,35}, {7,25}, {14,28}, {9,23}, {5,19}, {18,25}, {8,26}, {14,38}, {15,35}, {6,37}, {11,39}, {3,23}, {4,30}, {18,34}, {6,26}, {14,26}, {1,19}, {2,40}, {15,33}, {8,40}, {18,27}, {17,36}, {14,32}, {9,33}, {12,38}, {11,36}, {15,21}, {3,35}, {5,27}, {9,35}, {11,19}, {6,38}, {8,38}, {8,32}, {9,28}, {4,22}, {3,28}, {11,31}, {5,36}, {3,24}, {5,31}, {9,24}, {8,20}, {16,22}, {3,21}, {11,30}, {1,41}, {11,27}, {4,32}, {13,21}, {1,37}, {10,42}, {2,26}, {10,32}, {7,37}, {7,21}, {16,42}, {1,33}, {14,29}, {14,40}, {3,36}, {10,20}, {14,41}, {18,22}, {13,31}, {9,36}, {4,34}, {10,35}, {6,27}, {13,19}, {13,37}, {3,33}, {16,32}, {4,23}, {11,24}, {12,37}, {5,39}, {1,21}, {15,24}, {18,26}, {8,29} }; // ET42.35 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 905969664 EdgePairs[42][35]:={ {4,35}, {7,19}, {7,42}, {13,41}, {13,29}, {14,25}, {15,23}, {8,24}, {11,23}, {3,29}, {7,40}, {16,30}, {10,27}, {18,39}, {8,36}, {10,38}, {6,23}, {14,19}, {7,38}, {1,25}, {12,40}, {5,24}, {3,32}, {13,34}, {1,38}, {5,41}, {7,31}, {9,39}, {6,25}, {12,33}, {16,40}, {9,19}, {9,21}, {1,32}, {17,42}, {8,42}, {18,21}, {8,34}, {13,38}, {2,28}, {9,31}, {4,26}, {5,37}, {8,22}, {7,28}, {12,21}, {3,41}, {17,30}, {9,27}, {2,23}, {17,24}, {7,26}, {18,33}, {13,26}, {10,25}, {15,25}, {6,33}, {3,40}, {6,21}, {2,36}, {9,34}, {10,39}, {4,29}, {16,26}, {16,19}, {10,37}, {5,19}, {13,35}, {15,35}, {6,37}, {11,39}, {5,29}, {11,28}, {18,34}, {2,40}, {12,28}, {7,30}, {2,35}, {15,33}, {12,29}, {18,19}, {1,26}, {13,22}, {18,27}, {17,36}, {4,38}, {2,24}, {9,33}, {11,36}, {2,27}, {17,22}, {14,36}, {15,21}, {15,42}, {6,30}, {1,39}, {14,31}, {2,39}, {14,37}, {8,32}, {4,22}, {11,40}, {3,28}, {5,36}, {5,31}, {15,37}, {8,20}, {3,21}, {11,27}, {6,42}, {17,34}, {1,37}, {1,20}, {1,27}, {16,28}, {13,23}, {10,32}, {3,20}, {12,41}, {16,42}, {14,29}, {12,32}, {18,31}, {10,20}, {14,41}, {6,35}, {16,38}, {17,32}, {18,22}, {8,30}, {10,26}, {17,20}, {4,34}, {4,41}, {3,33}, {15,30}, {4,23}, {11,24}, {11,35}, {16,31}, {12,20}, {5,25}, {14,24}, {9,22} }; // ET42.36 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 589824 EdgePairs[42][36]:={ {4,35}, {14,39}, {5,32}, {10,21}, {15,23}, {16,36}, {8,31}, {2,38}, {4,42}, {12,19}, {14,34}, {5,42}, {5,30}, {1,31}, {16,30}, {10,38}, {6,23}, {4,40}, {7,38}, {12,31}, {12,22}, {13,34}, {18,37}, {1,38}, {5,41}, {2,33}, {6,32}, {17,35}, {6,25}, {9,39}, {12,33}, {15,40}, {13,27}, {3,30}, {11,22}, {9,37}, {17,42}, {7,23}, {8,34}, {2,28}, {16,33}, {2,19}, {8,41}, {10,23}, {15,28}, {14,27}, {1,29}, {8,22}, {12,21}, {11,34}, {16,21}, {17,23}, {17,30}, {9,27}, {10,36}, {2,31}, {13,33}, {17,24}, {7,41}, {7,26}, {1,36}, {15,25}, {18,38}, {3,40}, {12,34}, {4,33}, {9,34}, {7,29}, {4,28}, {10,24}, {7,20}, {18,25}, {15,35}, {6,37}, {5,29}, {11,28}, {3,27}, {4,30}, {10,33}, {1,19}, {2,40}, {4,21}, {9,25}, {18,19}, {1,26}, {11,37}, {8,19}, {13,40}, {13,22}, {7,35}, {17,36}, {12,24}, {15,26}, {3,42}, {18,32}, {14,36}, {2,21}, {16,27}, {14,22}, {5,27}, {6,30}, {11,19}, {8,32}, {11,40}, {5,20}, {3,28}, {11,31}, {15,37}, {11,25}, {12,36}, {13,28}, {8,20}, {6,20}, {18,20}, {1,41}, {6,42}, {13,21}, {3,39}, {17,41}, {7,32}, {3,25}, {17,29}, {2,26}, {15,38}, {16,42}, {14,29}, {18,31}, {14,41}, {3,37}, {6,35}, {9,32}, {10,26}, {10,35}, {4,23}, {5,39}, {16,39}, {14,24}, {9,20}, {18,26}, {1,24}, {8,29}, {9,22}, {13,39}, {16,24} }; // ET42.37 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 589824 EdgePairs[42][37]:={ {10,25}, {1,20}, {13,32}, {11,36}, {18,39}, {12,29}, {13,21}, {4,24}, {16,33}, {15,24}, {16,26}, {4,26}, {3,22}, {10,37}, {16,27}, {14,39}, {5,38}, {12,32}, {8,28}, {15,31}, {1,32}, {3,25}, {7,41}, {12,39}, {2,19}, {12,41}, {1,19}, {12,42}, {3,35}, {3,37}, {13,35}, {2,26}, {7,36}, {17,21}, {17,40}, {14,28}, {4,23}, {18,34}, {15,25}, {18,37}, {10,30}, {6,29}, {4,38}, {3,34}, {5,40}, {2,25}, {11,33}, {6,31}, {6,40}, {14,33}, {9,29}, {14,21}, {9,26}, {9,27}, {12,20}, {8,41}, {2,38}, {2,37}, {14,40}, {9,41}, {5,25}, {1,31}, {11,22}, {10,28}, {11,31}, {17,33}, {1,22}, {4,33}, {5,23}, {4,21}, {3,20}, {15,19}, {15,42}, {2,20}, {10,40}, {1,29}, {7,30}, {3,32}, {11,21}, {4,35}, {13,33}, {2,32}, {16,32}, {17,30}, {13,23}, {15,37}, {8,22}, {18,24}, {8,35}, {10,42}, {18,27}, {18,36}, {16,38}, {15,36}, {5,28}, {17,31}, {13,30}, {4,36}, {17,28}, {12,27}, {14,22}, {11,24}, {6,26}, {8,40}, {12,30}, {14,34}, {8,23}, {3,23}, {18,25}, {17,19}, {6,19}, {7,29}, {6,41}, {6,28}, {10,39}, {13,42}, {16,21}, {7,23}, {8,34}, {10,27}, {18,22}, {16,20}, {6,38}, {2,31}, {9,36}, {5,26}, {16,39}, {9,39}, {9,38}, {11,19}, {1,41}, {7,24}, {9,24}, {17,42}, {11,34}, {7,35}, {15,30}, {13,20}, {5,35}, {1,34}, {5,37}, {7,42}, {14,27}, {8,29} }; // ET42.38 // Bipartite(18,24) Valencies [8,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 589824 EdgePairs[42][38]:={ {10,19}, {4,35}, {13,25}, {5,32}, {7,39}, {16,36}, {4,42}, {10,22}, {18,40}, {11,23}, {9,30}, {3,29}, {3,38}, {9,42}, {1,31}, {4,27}, {10,27}, {6,41}, {5,35}, {7,33}, {2,37}, {18,42}, {1,38}, {6,32}, {6,25}, {12,33}, {16,40}, {7,27}, {13,27}, {9,21}, {14,42}, {6,40}, {7,23}, {8,34}, {3,34}, {14,20}, {2,19}, {4,26}, {2,29}, {10,30}, {18,24}, {8,22}, {3,41}, {12,21}, {1,34}, {9,38}, {5,23}, {15,34}, {10,34}, {15,22}, {2,41}, {2,31}, {2,23}, {13,33}, {17,24}, {7,41}, {8,28}, {4,39}, {15,25}, {1,22}, {14,30}, {10,39}, {7,29}, {10,31}, {16,19}, {3,22}, {5,19}, {8,26}, {14,38}, {6,37}, {11,39}, {4,30}, {18,34}, {14,26}, {1,19}, {2,35}, {15,33}, {17,33}, {5,28}, {12,29}, {1,35}, {1,26}, {8,40}, {6,29}, {7,35}, {17,36}, {12,24}, {4,38}, {14,32}, {9,33}, {11,36}, {14,36}, {15,21}, {1,23}, {15,42}, {16,27}, {18,28}, {8,38}, {8,32}, {5,20}, {3,26}, {5,31}, {17,37}, {15,37}, {12,36}, {8,20}, {6,20}, {9,26}, {17,21}, {11,27}, {13,21}, {10,42}, {11,32}, {18,30}, {16,28}, {9,29}, {3,25}, {11,20}, {7,21}, {12,41}, {2,25}, {12,32}, {9,41}, {18,36}, {3,37}, {18,22}, {17,28}, {13,31}, {13,19}, {13,37}, {15,30}, {17,40}, {4,23}, {11,24}, {11,35}, {16,31}, {16,39}, {12,20}, {14,24}, {5,40}, {17,25}, {6,28}, {13,39}, {16,24} }; // ET42.39 // Bipartite(21,21) Valencies [8,8] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 672 EdgePairs[42][39]:={ {21,23}, {16,41}, {10,25}, {2,24}, {4,27}, {5,34}, {16,33}, {18,29}, {4,26}, {3,22}, {18,32}, {16,27}, {11,25}, {21,32}, {12,22}, {5,38}, {12,32}, {16,31}, {15,31}, {3,25}, {19,24}, {10,23}, {20,40}, {1,40}, {14,38}, {10,33}, {3,35}, {21,35}, {13,35}, {2,26}, {8,39}, {7,36}, {21,22}, {8,25}, {12,34}, {18,41}, {17,40}, {14,28}, {4,23}, {10,22}, {11,28}, {15,29}, {4,38}, {1,38}, {2,36}, {9,29}, {19,40}, {17,37}, {14,36}, {9,26}, {12,36}, {4,41}, {8,41}, {2,38}, {7,39}, {4,42}, {9,41}, {2,39}, {17,39}, {14,24}, {17,33}, {1,22}, {19,38}, {4,33}, {5,23}, {9,34}, {9,42}, {16,37}, {10,40}, {7,30}, {3,39}, {13,31}, {3,32}, {4,35}, {9,25}, {8,36}, {19,42}, {6,33}, {2,32}, {7,26}, {13,33}, {16,32}, {6,24}, {15,35}, {11,30}, {5,24}, {12,28}, {13,25}, {10,42}, {19,31}, {18,26}, {18,27}, {14,37}, {20,22}, {21,31}, {8,37}, {15,36}, {5,28}, {21,38}, {18,31}, {16,22}, {7,31}, {12,33}, {13,30}, {5,41}, {20,29}, {17,28}, {12,23}, {13,24}, {6,26}, {12,30}, {21,29}, {8,23}, {17,29}, {1,25}, {6,28}, {9,30}, {13,27}, {1,35}, {14,25}, {5,39}, {20,35}, {19,32}, {20,37}, {6,42}, {7,23}, {3,30}, {8,34}, {3,24}, {18,28}, {11,27}, {10,27}, {20,34}, {1,26}, {10,36}, {11,32}, {15,33}, {20,42}, {20,24}, {2,40}, {11,40}, {6,34}, {5,27}, {15,38}, {15,28}, {16,39}, {1,41}, {13,37}, {3,41}, {21,34}, {18,40}, {17,26}, {6,39}, {11,34}, {17,22}, {2,30}, {15,30}, {7,37}, {19,23}, {9,31}, {6,35}, {11,42}, {7,42}, {19,37}, {14,27}, {8,29}, {1,36}, {14,29} }; // ET42.40 // Bipartite(21,21) Valencies [8,8] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 672 EdgePairs[42][40]:={ {2,24}, {17,36}, {12,29}, {11,35}, {13,40}, {16,33}, {15,24}, {3,22}, {21,40}, {18,32}, {16,40}, {21,32}, {14,39}, {2,23}, {12,22}, {5,38}, {4,29}, {20,27}, {8,33}, {3,25}, {10,23}, {10,26}, {14,38}, {12,39}, {7,22}, {21,42}, {3,35}, {8,39}, {7,34}, {11,41}, {16,25}, {12,34}, {18,41}, {17,40}, {9,35}, {4,23}, {16,29}, {18,34}, {10,22}, {16,30}, {4,38}, {3,34}, {14,23}, {20,38}, {11,33}, {6,31}, {2,34}, {5,22}, {9,29}, {19,40}, {15,32}, {19,30}, {9,27}, {15,40}, {8,41}, {2,38}, {2,37}, {14,30}, {7,39}, {9,41}, {7,32}, {1,31}, {14,24}, {20,31}, {15,27}, {20,33}, {10,31}, {15,42}, {1,29}, {4,35}, {13,33}, {1,23}, {5,30}, {17,30}, {19,41}, {21,25}, {5,24}, {13,23}, {12,28}, {15,37}, {14,42}, {8,22}, {18,24}, {20,28}, {8,35}, {13,28}, {19,31}, {18,26}, {4,28}, {21,31}, {21,38}, {8,26}, {5,42}, {12,33}, {13,30}, {4,36}, {8,32}, {1,42}, {5,31}, {17,25}, {6,26}, {12,40}, {10,32}, {20,25}, {5,36}, {17,41}, {7,29}, {6,28}, {10,39}, {1,37}, {20,37}, {4,37}, {6,42}, {11,26}, {16,36}, {3,30}, {11,37}, {3,24}, {2,29}, {11,27}, {18,28}, {16,35}, {10,27}, {1,26}, {2,22}, {10,36}, {15,33}, {14,32}, {19,39}, {6,25}, {6,38}, {9,33}, {9,36}, {6,34}, {19,25}, {5,26}, {15,28}, {16,39}, {13,38}, {4,25}, {12,24}, {3,28}, {7,27}, {20,41}, {13,37}, {18,40}, {17,26}, {11,34}, {17,22}, {13,39}, {21,24}, {2,30}, {7,37}, {19,23}, {1,34}, {9,31}, {21,41}, {6,35}, {17,32}, {11,42}, {3,36}, {18,35}, {7,42}, {9,23}, {14,27}, {8,29}, {19,27}, {1,36} }; // ET42.41 // Bipartite(21,21) Valencies [8,8] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 2016 EdgePairs[42][41]:={ {4,35}, {14,39}, {16,25}, {13,25}, {13,41}, {9,40}, {7,39}, {8,39}, {8,24}, {17,39}, {10,22}, {11,23}, {9,30}, {14,34}, {3,29}, {5,30}, {20,28}, {6,36}, {7,40}, {10,27}, {19,39}, {6,41}, {5,35}, {11,29}, {1,40}, {11,42}, {5,34}, {12,40}, {7,33}, {12,22}, {18,42}, {20,23}, {10,40}, {6,32}, {17,35}, {16,23}, {21,26}, {7,27}, {15,40}, {13,27}, {11,38}, {21,25}, {3,30}, {17,42}, {19,23}, {20,42}, {15,29}, {2,28}, {16,33}, {6,34}, {5,26}, {15,32}, {10,23}, {2,29}, {14,27}, {5,37}, {18,24}, {19,37}, {3,41}, {11,34}, {17,31}, {9,38}, {17,23}, {17,30}, {4,37}, {15,34}, {20,38}, {10,36}, {2,23}, {17,24}, {21,38}, {18,33}, {15,25}, {1,22}, {6,33}, {21,41}, {3,40}, {12,34}, {4,33}, {4,28}, {10,31}, {16,35}, {7,25}, {3,22}, {10,37}, {14,28}, {18,25}, {8,35}, {20,24}, {4,31}, {2,42}, {18,34}, {6,26}, {14,26}, {4,36}, {2,35}, {5,28}, {12,29}, {9,25}, {1,35}, {11,37}, {13,40}, {7,35}, {20,37}, {15,26}, {9,33}, {12,38}, {3,42}, {2,27}, {18,32}, {5,38}, {1,23}, {6,30}, {8,27}, {6,38}, {14,31}, {8,38}, {13,32}, {11,31}, {3,26}, {5,31}, {19,36}, {21,22}, {9,24}, {12,36}, {13,28}, {16,22}, {19,22}, {21,36}, {1,41}, {20,26}, {11,27}, {4,32}, {17,34}, {1,27}, {12,42}, {18,30}, {15,41}, {9,29}, {2,26}, {10,32}, {7,37}, {19,41}, {1,33}, {14,29}, {12,32}, {1,28}, {21,42}, {8,37}, {20,39}, {18,22}, {8,30}, {9,36}, {13,31}, {19,25}, {4,41}, {3,33}, {16,32}, {7,36}, {16,31}, {16,39}, {19,28}, {2,30}, {15,24}, {14,24}, {21,24}, {8,29}, {13,39} }; // ET42.42 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 176160768 EdgePairs[42][42]:={ {3,33}, {10,24}, {5,17}, {11,20}, {29,40}, {5,34}, {18,29}, {4,16}, {16,27}, {6,17}, {1,13}, {7,38}, {25,38}, {1,32}, {3,15}, {12,38}, {10,23}, {2,15}, {7,22}, {4,31}, {12,41}, {12,42}, {21,35}, {8,39}, {11,41}, {29,41}, {24,36}, {2,14}, {29,42}, {14,28}, {29,39}, {12,37}, {16,29}, {10,22}, {3,18}, {3,17}, {16,30}, {23,32}, {19,33}, {15,29}, {3,34}, {11,38}, {2,36}, {8,19}, {7,20}, {22,34}, {12,20}, {22,35}, {7,39}, {9,41}, {1,31}, {10,41}, {27,40}, {20,31}, {2,35}, {23,36}, {15,27}, {20,33}, {4,33}, {25,41}, {24,32}, {10,21}, {2,13}, {9,42}, {6,18}, {30,39}, {10,40}, {30,42}, {2,16}, {26,37}, {18,30}, {3,32}, {23,35}, {2,32}, {6,33}, {5,18}, {11,23}, {17,30}, {27,38}, {28,37}, {8,22}, {13,25}, {26,38}, {13,28}, {10,42}, {5,14}, {18,26}, {19,31}, {4,15}, {21,33}, {8,37}, {24,35}, {25,37}, {9,22}, {26,42}, {28,40}, {9,40}, {8,21}, {12,23}, {11,24}, {17,25}, {30,40}, {12,19}, {8,40}, {22,33}, {30,41}, {18,25}, {17,29}, {5,36}, {26,41}, {25,42}, {1,15}, {6,14}, {13,27}, {10,39}, {1,35}, {14,25}, {19,32}, {3,16}, {13,26}, {28,39}, {6,36}, {5,33}, {11,37}, {8,38}, {20,34}, {4,34}, {1,16}, {2,31}, {6,34}, {15,28}, {4,18}, {28,38}, {9,39}, {27,37}, {11,19}, {5,13}, {8,20}, {12,24}, {27,39}, {21,36}, {23,31}, {3,31}, {21,34}, {9,24}, {1,14}, {17,26}, {19,34}, {15,30}, {6,13}, {7,37}, {5,35}, {22,36}, {7,19}, {4,17}, {6,35}, {11,42}, {9,21}, {16,28}, {7,40}, {9,23}, {20,32}, {14,27}, {7,21}, {4,32}, {24,31}, {1,36}, {14,26} }; // ET42.43 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 704643072 EdgePairs[42][43]:={ {1,11}, {33,38}, {10,25}, {10,24}, {18,39}, {29,40}, {4,26}, {35,42}, {4,16}, {10,37}, {18,32}, {16,27}, {1,13}, {5,38}, {12,32}, {30,33}, {29,33}, {1,32}, {3,25}, {3,15}, {10,23}, {20,40}, {10,26}, {16,19}, {4,19}, {7,22}, {22,42}, {10,33}, {21,42}, {3,35}, {21,35}, {8,39}, {17,24}, {6,7}, {2,41}, {2,14}, {17,40}, {20,30}, {29,39}, {13,29}, {35,41}, {2,42}, {6,22}, {11,28}, {23,32}, {6,21}, {14,33}, {5,22}, {10,38}, {19,40}, {9,26}, {19,30}, {25,36}, {34,38}, {19,29}, {22,35}, {14,30}, {7,39}, {6,8}, {22,41}, {11,15}, {17,39}, {17,23}, {1,31}, {11,31}, {30,34}, {24,25}, {15,27}, {23,26}, {12,16}, {3,20}, {9,34}, {15,19}, {24,32}, {2,13}, {26,35}, {29,34}, {30,39}, {24,26}, {8,17}, {4,35}, {9,25}, {13,33}, {1,12}, {2,32}, {7,17}, {9,37}, {27,38}, {28,37}, {5,7}, {12,28}, {23,25}, {14,42}, {8,22}, {18,24}, {15,20}, {4,15}, {14,41}, {26,36}, {3,26}, {5,28}, {17,31}, {18,31}, {13,30}, {4,36}, {25,35}, {20,29}, {12,27}, {8,21}, {1,42}, {3,19}, {6,27}, {30,40}, {8,40}, {33,37}, {20,39}, {14,34}, {36,41}, {12,15}, {6,28}, {18,23}, {2,11}, {13,42}, {3,16}, {11,16}, {11,27}, {10,34}, {5,8}, {11,32}, {16,20}, {19,39}, {13,41}, {6,38}, {2,31}, {9,33}, {5,27}, {8,18}, {15,28}, {28,38}, {9,38}, {27,37}, {4,25}, {4,20}, {1,41}, {21,36}, {23,31}, {36,42}, {18,40}, {1,14}, {9,24}, {2,12}, {12,31}, {6,37}, {13,34}, {5,21}, {22,36}, {5,37}, {21,41}, {17,32}, {3,36}, {16,28}, {7,40}, {9,23}, {7,21}, {24,31}, {34,37}, {14,29}, {7,18} }; // ET42.44 // Non-bipartite Valency 8 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 672 EdgePairs[42][44]:={ {33,38}, {11,20}, {13,21}, {11,35}, {29,40}, {5,34}, {16,26}, {23,27}, {17,38}, {1,10}, {2,23}, {1,13}, {8,28}, {12,38}, {10,26}, {35,40}, {4,31}, {22,42}, {25,33}, {12,42}, {28,32}, {22,32}, {17,24}, {1,21}, {11,41}, {2,9}, {6,7}, {2,14}, {8,15}, {20,30}, {16,29}, {18,34}, {23,39}, {15,25}, {11,28}, {18,37}, {10,30}, {3,17}, {3,7}, {2,25}, {1,38}, {9,29}, {4,8}, {18,20}, {22,34}, {25,36}, {12,36}, {5,29}, {4,41}, {9,19}, {2,37}, {19,29}, {14,40}, {7,39}, {1,31}, {9,14}, {17,33}, {23,36}, {6,30}, {27,31}, {25,41}, {28,41}, {26,35}, {30,39}, {16,37}, {24,26}, {3,39}, {3,32}, {29,37}, {23,37}, {9,25}, {7,16}, {2,32}, {19,42}, {1,12}, {6,33}, {23,25}, {14,42}, {8,22}, {32,39}, {13,28}, {4,15}, {18,27}, {21,31}, {10,13}, {33,41}, {26,34}, {3,26}, {21,33}, {30,32}, {15,36}, {13,36}, {5,28}, {24,35}, {18,31}, {27,42}, {24,40}, {26,42}, {17,28}, {12,27}, {9,40}, {3,19}, {1,24}, {14,22}, {6,27}, {12,19}, {8,40}, {21,29}, {17,19}, {5,36}, {36,39}, {19,36}, {12,15}, {18,23}, {6,14}, {2,11}, {10,39}, {24,38}, {16,21}, {20,35}, {3,16}, {4,40}, {11,16}, {7,23}, {8,34}, {11,37}, {16,35}, {1,26}, {2,22}, {10,34}, {15,22}, {5,8}, {29,31}, {11,32}, {9,17}, {10,18}, {8,24}, {13,41}, {30,38}, {6,38}, {9,33}, {15,38}, {31,40}, {3,42}, {4,18}, {4,25}, {4,20}, {5,13}, {7,27}, {20,41}, {14,35}, {10,20}, {7,33}, {12,31}, {5,19}, {6,20}, {13,39}, {15,30}, {34,42}, {22,30}, {5,37}, {21,41}, {6,35}, {17,32}, {14,27}, {7,21}, {24,28}, {34,37} }; // ET42.45 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 672 EdgePairs[42][45]:={ {11,17}, {10,24}, {2,33}, {4,27}, {36,38}, {4,24}, {16,33}, {21,40}, {10,37}, {25,39}, {8,30}, {32,41}, {6,17}, {30,33}, {7,38}, {3,9}, {8,42}, {16,31}, {21,37}, {4,29}, {1,27}, {32,37}, {7,41}, {3,35}, {7,36}, {8,25}, {27,33}, {2,28}, {18,41}, {6,11}, {9,35}, {8,31}, {35,41}, {2,42}, {19,33}, {6,21}, {3,34}, {20,38}, {6,40}, {4,10}, {1,17}, {2,36}, {5,22}, {4,22}, {19,40}, {19,26}, {15,32}, {16,24}, {15,40}, {31,42}, {28,34}, {29,36}, {9,41}, {17,39}, {7,32}, {11,13}, {26,40}, {3,12}, {23,34}, {11,22}, {20,31}, {14,24}, {22,27}, {4,33}, {15,19}, {24,32}, {10,21}, {29,34}, {1,29}, {8,17}, {2,16}, {13,31}, {18,30}, {15,41}, {13,33}, {7,26}, {5,18}, {11,23}, {30,35}, {11,29}, {21,25}, {5,24}, {13,23}, {12,25}, {8,13}, {15,34}, {20,28}, {26,38}, {8,35}, {10,42}, {18,26}, {7,14}, {6,23}, {8,37}, {25,37}, {9,22}, {6,15}, {13,30}, {5,41}, {4,36}, {28,40}, {5,12}, {22,39}, {28,36}, {17,25}, {20,39}, {12,30}, {14,34}, {3,23}, {1,39}, {10,32}, {12,14}, {17,29}, {20,25}, {3,21}, {35,37}, {7,29}, {1,15}, {1,35}, {14,20}, {14,25}, {5,39}, {19,32}, {13,26}, {6,42}, {11,26}, {22,26}, {13,19}, {3,30}, {20,34}, {10,36}, {16,20}, {14,32}, {2,40}, {16,42}, {6,10}, {27,35}, {16,39}, {28,38}, {5,9}, {9,38}, {27,37}, {4,11}, {12,24}, {3,28}, {15,23}, {1,41}, {27,39}, {23,31}, {36,42}, {18,40}, {17,42}, {2,30}, {2,18}, {9,31}, {1,34}, {24,33}, {21,28}, {19,37}, {9,23}, {19,27}, {12,18}, {31,38}, {12,21}, {14,29}, {22,38}, {7,18}, {5,16} }; // ET42.46 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 672 EdgePairs[42][46]:={ {1,11}, {10,25}, {2,24}, {11,36}, {7,15}, {13,40}, {4,26}, {3,8}, {3,40}, {4,16}, {18,32}, {32,40}, {21,32}, {14,39}, {5,38}, {12,32}, {18,38}, {1,32}, {8,33}, {24,27}, {23,28}, {3,25}, {3,15}, {17,34}, {17,20}, {4,19}, {7,22}, {12,41}, {10,33}, {21,42}, {5,20}, {13,35}, {26,33}, {2,26}, {8,39}, {7,34}, {16,25}, {12,35}, {30,37}, {24,36}, {14,28}, {29,39}, {8,27}, {12,37}, {3,18}, {6,29}, {8,16}, {16,30}, {15,29}, {11,38}, {31,39}, {17,37}, {14,21}, {14,36}, {9,26}, {19,30}, {24,37}, {12,20}, {2,10}, {34,38}, {2,38}, {4,42}, {6,8}, {22,41}, {11,15}, {24,39}, {15,26}, {17,23}, {11,31}, {24,25}, {1,22}, {25,34}, {23,26}, {12,16}, {10,29}, {3,20}, {9,34}, {13,22}, {2,13}, {10,40}, {23,35}, {1,23}, {5,30}, {19,41}, {15,35}, {17,27}, {5,7}, {12,28}, {15,37}, {33,42}, {36,40}, {1,9}, {29,38}, {18,24}, {5,14}, {9,20}, {14,41}, {23,38}, {4,7}, {26,36}, {18,33}, {22,29}, {16,38}, {17,31}, {29,32}, {16,22}, {25,35}, {20,29}, {9,13}, {8,21}, {30,40}, {22,33}, {33,37}, {18,19}, {8,23}, {21,30}, {27,41}, {28,42}, {1,25}, {6,19}, {26,41}, {25,42}, {27,32}, {6,28}, {22,31}, {9,30}, {13,27}, {13,42}, {1,37}, {15,21}, {7,28}, {23,40}, {16,36}, {6,36}, {2,21}, {5,33}, {9,18}, {10,17}, {18,28}, {11,27}, {20,42}, {2,31}, {20,36}, {6,34}, {5,27}, {9,39}, {11,19}, {10,19}, {28,31}, {3,41}, {7,24}, {21,34}, {3,31}, {2,12}, {1,14}, {30,31}, {35,39}, {6,37}, {10,14}, {19,35}, {6,13}, {5,35}, {4,17}, {11,42}, {4,39}, {7,40}, {4,32}, {34,41} }; // ET42.47 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[42][47]:={ {1,11}, {10,25}, {2,24}, {11,36}, {7,15}, {11,35}, {29,40}, {16,26}, {3,8}, {3,40}, {17,38}, {4,16}, {1,10}, {32,40}, {21,32}, {14,39}, {2,23}, {1,13}, {18,38}, {8,33}, {24,27}, {3,25}, {12,38}, {17,34}, {10,26}, {7,22}, {35,40}, {4,31}, {12,41}, {10,33}, {12,42}, {28,32}, {5,20}, {26,33}, {8,39}, {16,25}, {8,15}, {14,28}, {20,30}, {29,39}, {8,27}, {12,37}, {16,29}, {23,39}, {10,30}, {16,30}, {2,25}, {14,36}, {4,8}, {18,20}, {19,30}, {5,29}, {34,38}, {9,19}, {2,37}, {14,40}, {7,39}, {6,8}, {22,41}, {11,15}, {1,31}, {9,14}, {11,31}, {17,33}, {24,25}, {10,29}, {3,20}, {13,22}, {2,13}, {26,35}, {24,26}, {3,39}, {29,37}, {23,37}, {23,35}, {6,33}, {1,12}, {5,30}, {19,41}, {14,42}, {36,40}, {1,9}, {29,38}, {18,24}, {13,28}, {4,15}, {14,41}, {23,38}, {26,36}, {21,31}, {26,34}, {16,38}, {21,33}, {30,32}, {15,36}, {13,36}, {5,28}, {24,35}, {17,31}, {29,32}, {16,22}, {27,42}, {26,42}, {17,28}, {9,13}, {12,27}, {14,22}, {12,19}, {18,19}, {21,30}, {28,42}, {1,25}, {25,42}, {27,32}, {12,15}, {18,23}, {10,39}, {1,37}, {20,35}, {23,40}, {16,36}, {7,23}, {6,36}, {2,21}, {9,18}, {18,28}, {11,27}, {2,22}, {15,22}, {5,8}, {11,32}, {9,17}, {2,31}, {9,33}, {6,34}, {5,27}, {15,38}, {31,40}, {3,42}, {4,18}, {9,39}, {11,19}, {10,19}, {4,25}, {4,20}, {5,13}, {7,27}, {20,41}, {3,41}, {7,24}, {21,34}, {3,31}, {7,33}, {6,37}, {19,35}, {6,20}, {34,42}, {6,13}, {22,30}, {5,37}, {21,41}, {4,17}, {17,32}, {6,35}, {7,21}, {34,41}, {24,28}, {34,37} }; // ET42.48 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 672 EdgePairs[42][48]:={ {11,17}, {3,33}, {10,24}, {5,17}, {2,33}, {12,29}, {14,19}, {15,24}, {3,22}, {35,42}, {4,30}, {25,39}, {8,30}, {16,40}, {32,41}, {12,22}, {3,9}, {25,38}, {29,33}, {15,31}, {21,37}, {1,27}, {32,37}, {3,35}, {2,41}, {2,28}, {16,23}, {6,11}, {4,23}, {8,31}, {18,42}, {23,32}, {19,33}, {6,21}, {6,40}, {36,37}, {4,10}, {5,22}, {10,38}, {19,40}, {1,18}, {35,38}, {31,42}, {8,41}, {29,36}, {8,14}, {17,39}, {7,32}, {11,13}, {26,40}, {10,41}, {27,40}, {7,13}, {7,25}, {14,24}, {20,31}, {30,34}, {2,35}, {21,27}, {19,38}, {4,21}, {15,19}, {10,21}, {9,42}, {6,18}, {1,29}, {2,16}, {13,31}, {26,37}, {18,30}, {11,21}, {15,41}, {8,36}, {13,33}, {16,32}, {30,35}, {7,17}, {21,25}, {11,30}, {5,24}, {9,37}, {13,23}, {12,25}, {13,25}, {20,28}, {24,34}, {3,11}, {3,27}, {4,28}, {3,29}, {6,23}, {8,26}, {5,42}, {9,22}, {6,15}, {13,30}, {2,17}, {4,36}, {21,39}, {5,12}, {1,42}, {12,23}, {28,36}, {11,24}, {28,33}, {20,39}, {14,34}, {18,25}, {10,32}, {1,39}, {12,14}, {17,29}, {36,41}, {22,28}, {6,9}, {17,41}, {7,29}, {6,41}, {1,15}, {16,34}, {5,39}, {19,32}, {20,37}, {11,26}, {22,26}, {28,39}, {10,35}, {20,26}, {3,24}, {8,38}, {20,34}, {23,33}, {4,34}, {16,20}, {14,32}, {15,33}, {2,40}, {16,42}, {9,36}, {27,35}, {5,10}, {19,25}, {8,18}, {28,38}, {27,37}, {4,12}, {22,40}, {15,39}, {18,40}, {17,26}, {7,35}, {2,30}, {13,20}, {7,37}, {27,34}, {9,31}, {1,34}, {7,42}, {9,23}, {19,27}, {12,18}, {24,31}, {31,38}, {1,36}, {14,29}, {22,38}, {14,26}, {5,16} }; // ET42.49 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 336 EdgePairs[42][49]:={ {11,17}, {3,33}, {16,41}, {13,32}, {2,33}, {4,27}, {16,33}, {15,24}, {18,29}, {32,42}, {3,22}, {21,40}, {10,37}, {25,39}, {11,25}, {8,30}, {22,37}, {6,17}, {30,33}, {7,38}, {25,38}, {16,31}, {4,29}, {32,37}, {20,40}, {10,23}, {1,40}, {16,19}, {2,27}, {14,31}, {7,36}, {27,33}, {1,30}, {16,23}, {6,11}, {9,35}, {4,23}, {13,29}, {35,41}, {2,42}, {10,22}, {18,42}, {6,22}, {19,33}, {20,38}, {5,40}, {36,37}, {14,33}, {1,17}, {2,36}, {35,38}, {19,26}, {9,32}, {15,32}, {15,40}, {8,41}, {28,34}, {29,36}, {14,30}, {2,39}, {17,39}, {11,13}, {26,40}, {10,41}, {23,34}, {3,12}, {11,22}, {7,25}, {14,24}, {20,31}, {21,27}, {5,23}, {4,21}, {21,26}, {10,31}, {15,42}, {24,32}, {9,42}, {29,34}, {8,17}, {2,16}, {26,37}, {4,35}, {5,18}, {11,23}, {30,35}, {11,29}, {6,24}, {17,30}, {27,38}, {28,37}, {13,23}, {8,13}, {15,34}, {20,28}, {8,35}, {15,20}, {18,26}, {1,28}, {31,41}, {7,14}, {3,10}, {8,37}, {21,38}, {8,26}, {12,26}, {7,31}, {6,15}, {5,41}, {28,40}, {22,25}, {5,12}, {8,32}, {22,39}, {4,9}, {28,36}, {17,25}, {12,30}, {12,14}, {20,25}, {22,28}, {6,9}, {17,41}, {7,29}, {1,15}, {1,35}, {14,20}, {14,25}, {19,32}, {13,26}, {6,42}, {13,19}, {3,30}, {3,24}, {2,29}, {20,34}, {4,34}, {10,36}, {19,39}, {27,35}, {5,10}, {16,39}, {9,38}, {4,11}, {12,24}, {3,28}, {27,39}, {1,41}, {23,31}, {36,42}, {18,40}, {9,24}, {6,39}, {13,34}, {5,21}, {2,18}, {1,34}, {24,33}, {9,21}, {3,36}, {7,42}, {19,37}, {19,27}, {12,18}, {31,38}, {12,21}, {7,18}, {5,16} }; // ET42.50 // Bipartite(21,21) Valencies [9,9] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 26330359136256 EdgePairs[42][50]:={ {10,24}, {9,28}, {11,36}, {18,39}, {13,40}, {4,24}, {18,29}, {17,38}, {10,37}, {18,32}, {11,25}, {21,32}, {14,39}, {2,23}, {12,32}, {18,38}, {4,29}, {8,33}, {1,27}, {10,23}, {20,40}, {7,41}, {1,40}, {17,34}, {12,39}, {4,31}, {21,42}, {21,35}, {3,37}, {13,35}, {7,34}, {17,24}, {2,28}, {5,32}, {16,23}, {14,28}, {9,35}, {8,27}, {12,37}, {16,29}, {2,42}, {10,30}, {16,30}, {15,29}, {4,38}, {19,33}, {3,34}, {5,40}, {20,38}, {11,38}, {6,40}, {6,31}, {2,36}, {4,22}, {10,38}, {9,29}, {19,40}, {17,37}, {19,26}, {19,30}, {15,40}, {8,41}, {2,37}, {7,39}, {5,25}, {7,32}, {17,23}, {15,26}, {10,41}, {11,22}, {7,25}, {11,31}, {20,31}, {2,35}, {1,22}, {15,27}, {21,27}, {20,33}, {5,23}, {10,31}, {9,42}, {16,37}, {1,29}, {13,31}, {15,41}, {8,36}, {6,33}, {13,33}, {11,29}, {6,24}, {5,30}, {17,30}, {21,25}, {9,37}, {17,27}, {12,25}, {14,42}, {15,34}, {8,22}, {18,24}, {20,28}, {13,28}, {14,41}, {3,27}, {18,36}, {1,33}, {15,36}, {17,31}, {8,26}, {18,31}, {12,26}, {16,22}, {9,22}, {12,33}, {4,36}, {21,39}, {12,23}, {13,24}, {11,24}, {11,39}, {6,26}, {8,40}, {12,40}, {12,30}, {14,34}, {3,23}, {18,25}, {17,41}, {6,28}, {9,30}, {13,42}, {14,25}, {5,39}, {20,35}, {7,28}, {19,32}, {13,26}, {6,42}, {16,36}, {3,30}, {5,33}, {8,34}, {20,26}, {3,24}, {2,29}, {16,35}, {10,27}, {1,26}, {2,22}, {10,34}, {15,22}, {18,22}, {11,32}, {15,33}, {14,32}, {19,39}, {20,42}, {6,38}, {20,24}, {16,42}, {9,36}, {19,25}, {5,26}, {13,38}, {4,25}, {3,38}, {7,27}, {14,35}, {1,41}, {3,41}, {3,31}, {21,34}, {7,35}, {2,30}, {1,34}, {19,23}, {5,37}, {21,41}, {21,28}, {6,35}, {4,39}, {16,28}, {7,42}, {9,23}, {19,37}, {14,27}, {8,29}, {4,32}, {1,36} }; // ET42.51 // Bipartite(7,35) Valencies [10,2] // Diameter 7 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5016453120000000 EdgePairs[42][51]:={ {3,22}, {2,14}, {6,41}, {5,32}, {6,34}, {2,37}, {5,37}, {6,39}, {1,29}, {2,30}, {7,31}, {7,12}, {1,36}, {4,40}, {5,11}, {3,38}, {1,20}, {3,8}, {3,24}, {7,33}, {3,29}, {6,32}, {2,21}, {5,9}, {5,16}, {5,23}, {4,12}, {4,33}, {2,16}, {5,25}, {1,15}, {7,10}, {7,40}, {3,15}, {6,20}, {3,17}, {4,21}, {6,27}, {3,31}, {5,30}, {7,38}, {1,27}, {4,28}, {5,39}, {7,19}, {6,18}, {2,28}, {2,42}, {5,18}, {6,25}, {2,23}, {1,8}, {1,13}, {2,35}, {2,9}, {7,17}, {6,11}, {4,26}, {1,41}, {1,22}, {4,14}, {4,35}, {1,34}, {4,42}, {4,19}, {6,13}, {7,24}, {3,10}, {3,36}, {7,26} }; // ET42.52 // Bipartite(12,30) Valencies [10,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 240 EdgePairs[42][52]:={ {1,15}, {10,19}, {9,40}, {3,15}, {8,39}, {11,17}, {8,24}, {6,18}, {12,39}, {9,30}, {4,14}, {2,22}, {6,36}, {4,27}, {6,17}, {8,36}, {5,35}, {7,24}, {11,29}, {1,40}, {4,40}, {4,16}, {6,13}, {12,17}, {7,33}, {12,31}, {2,37}, {3,32}, {10,40}, {1,38}, {6,32}, {7,31}, {12,33}, {7,27}, {9,19}, {9,21}, {3,30}, {11,22}, {9,37}, {7,23}, {5,13}, {9,31}, {2,18}, {5,26}, {8,14}, {9,17}, {5,21}, {10,23}, {10,30}, {1,29}, {8,22}, {8,15}, {12,21}, {11,34}, {12,30}, {5,33}, {2,41}, {7,41}, {1,22}, {9,34}, {4,28}, {2,13}, {4,29}, {10,16}, {7,25}, {10,37}, {5,19}, {8,26}, {11,39}, {7,14}, {4,31}, {11,28}, {2,34}, {10,33}, {12,28}, {2,35}, {4,15}, {1,35}, {6,29}, {11,14}, {12,24}, {11,13}, {11,41}, {3,42}, {2,27}, {6,19}, {11,36}, {5,38}, {1,23}, {2,21}, {6,38}, {8,38}, {5,20}, {3,28}, {3,26}, {3,24}, {8,23}, {1,42}, {7,16}, {6,20}, {9,18}, {4,32}, {6,42}, {1,27}, {10,42}, {3,16}, {8,25}, {7,37}, {3,20}, {12,41}, {2,25}, {3,36}, {9,32}, {10,26}, {4,34}, {10,35}, {5,39}, {1,18}, {12,20}, {5,25} }; // ET42.53 // Bipartite(12,30) Valencies [10,4] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2293235712000000 EdgePairs[42][53]:={ {4,35}, {7,19}, {9,40}, {3,15}, {8,39}, {11,17}, {2,38}, {10,22}, {6,18}, {11,23}, {12,19}, {5,42}, {5,30}, {6,36}, {1,31}, {5,35}, {11,29}, {2,20}, {4,40}, {11,42}, {7,38}, {1,25}, {4,16}, {6,13}, {12,31}, {5,24}, {10,40}, {1,38}, {5,41}, {2,33}, {7,31}, {9,39}, {6,25}, {9,21}, {12,18}, {1,32}, {3,34}, {12,25}, {2,15}, {8,14}, {10,23}, {8,15}, {12,30}, {2,14}, {5,23}, {10,34}, {9,27}, {8,33}, {7,26}, {2,32}, {3,40}, {8,21}, {10,41}, {9,34}, {4,28}, {10,16}, {4,29}, {7,25}, {3,22}, {7,20}, {8,26}, {6,37}, {7,13}, {5,29}, {7,14}, {3,27}, {1,19}, {11,18}, {4,17}, {9,15}, {10,29}, {1,26}, {12,24}, {6,31}, {9,33}, {11,41}, {2,27}, {6,19}, {11,36}, {2,21}, {6,30}, {8,27}, {10,28}, {8,38}, {2,39}, {8,32}, {9,28}, {4,22}, {3,28}, {5,36}, {5,17}, {12,36}, {8,20}, {3,21}, {1,14}, {11,30}, {10,17}, {6,42}, {3,39}, {1,37}, {1,20}, {12,42}, {3,16}, {1,13}, {7,32}, {2,26}, {7,37}, {6,24}, {5,18}, {4,34}, {10,35}, {4,41}, {9,16}, {3,33}, {4,23}, {11,24}, {11,35}, {12,37}, {12,13}, {9,22} }; // ET42.54 // Bipartite(12,30) Valencies [10,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 143327232000000 EdgePairs[42][54]:={ {7,19}, {7,42}, {6,39}, {10,21}, {3,15}, {8,24}, {2,38}, {4,42}, {9,30}, {2,22}, {9,42}, {1,31}, {6,17}, {12,16}, {10,27}, {8,36}, {6,41}, {7,24}, {6,23}, {10,38}, {2,20}, {4,40}, {5,34}, {1,25}, {4,16}, {12,17}, {12,40}, {12,22}, {7,31}, {11,38}, {8,42}, {2,28}, {3,31}, {8,14}, {9,17}, {5,21}, {3,19}, {1,29}, {2,14}, {5,33}, {1,17}, {3,13}, {2,16}, {2,32}, {6,33}, {6,21}, {12,34}, {8,18}, {4,28}, {10,39}, {10,15}, {7,25}, {9,23}, {5,15}, {8,26}, {7,13}, {3,27}, {2,34}, {4,30}, {6,15}, {10,33}, {1,19}, {2,40}, {12,28}, {4,36}, {7,30}, {5,28}, {12,29}, {12,35}, {1,35}, {11,26}, {11,37}, {6,29}, {11,14}, {12,23}, {11,13}, {5,22}, {1,23}, {5,27}, {9,35}, {11,19}, {7,18}, {8,38}, {8,32}, {4,22}, {10,14}, {11,31}, {9,24}, {11,25}, {8,20}, {3,21}, {1,41}, {9,18}, {3,39}, {1,37}, {11,32}, {1,13}, {4,18}, {3,25}, {9,29}, {2,26}, {10,32}, {7,37}, {11,20}, {12,41}, {9,41}, {10,20}, {3,37}, {6,35}, {8,30}, {9,36}, {10,26}, {4,34}, {6,27}, {3,33}, {7,36}, {5,16}, {5,39}, {4,24}, {5,40} }; // ET42.55 // Bipartite(12,30) Valencies [10,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1509949440 EdgePairs[42][55]:={ {4,35}, {7,19}, {6,39}, {8,39}, {8,24}, {11,23}, {6,18}, {12,39}, {3,29}, {5,42}, {6,17}, {4,40}, {11,42}, {7,38}, {4,16}, {12,17}, {12,22}, {3,32}, {10,40}, {1,38}, {5,41}, {6,32}, {12,33}, {9,19}, {9,21}, {11,38}, {12,18}, {12,27}, {7,23}, {2,28}, {3,34}, {9,31}, {3,31}, {2,15}, {5,26}, {8,14}, {8,13}, {8,41}, {10,18}, {9,17}, {6,22}, {5,21}, {2,29}, {3,19}, {10,30}, {8,15}, {7,28}, {1,34}, {2,14}, {5,23}, {4,20}, {2,41}, {8,28}, {10,25}, {1,22}, {6,33}, {4,33}, {9,34}, {3,14}, {2,13}, {10,15}, {10,31}, {10,16}, {7,20}, {8,26}, {6,37}, {7,13}, {4,31}, {4,30}, {10,33}, {1,19}, {4,15}, {4,25}, {1,35}, {11,26}, {7,35}, {12,24}, {2,24}, {11,41}, {11,36}, {5,38}, {1,23}, {5,27}, {2,39}, {11,40}, {5,36}, {11,25}, {11,21}, {3,21}, {11,27}, {6,42}, {1,37}, {1,20}, {12,42}, {7,22}, {3,16}, {1,13}, {4,18}, {9,29}, {2,26}, {7,37}, {9,14}, {12,32}, {1,28}, {3,36}, {3,17}, {10,20}, {9,32}, {6,24}, {8,30}, {9,36}, {6,27}, {10,35}, {9,16}, {7,34}, {12,37}, {2,30}, {5,25}, {5,40}, {8,29} }; // ET42.56 // Bipartite(12,30) Valencies [10,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3932160 EdgePairs[42][56]:={ {4,35}, {5,32}, {7,39}, {6,39}, {9,40}, {11,15}, {8,39}, {8,24}, {12,26}, {10,22}, {4,14}, {5,42}, {1,31}, {8,36}, {5,35}, {7,24}, {10,38}, {7,38}, {6,13}, {12,40}, {2,33}, {11,16}, {12,27}, {7,23}, {7,15}, {8,34}, {2,28}, {3,34}, {12,25}, {2,19}, {2,18}, {2,15}, {8,14}, {4,26}, {9,17}, {5,21}, {10,23}, {3,19}, {10,30}, {5,37}, {1,29}, {3,18}, {7,28}, {3,41}, {12,21}, {1,34}, {9,38}, {4,37}, {4,20}, {1,22}, {1,16}, {8,21}, {4,33}, {2,13}, {10,15}, {10,31}, {4,29}, {10,16}, {10,37}, {9,23}, {7,13}, {8,17}, {3,27}, {2,34}, {1,19}, {2,40}, {7,30}, {9,25}, {8,19}, {11,26}, {12,23}, {6,31}, {9,33}, {11,41}, {3,42}, {5,22}, {12,38}, {5,27}, {8,32}, {4,22}, {5,20}, {11,40}, {11,31}, {5,36}, {3,26}, {3,24}, {5,17}, {11,25}, {12,36}, {6,16}, {6,20}, {1,14}, {11,30}, {9,18}, {10,17}, {6,42}, {3,39}, {1,37}, {12,42}, {1,13}, {4,18}, {9,29}, {10,32}, {7,21}, {11,20}, {12,41}, {9,14}, {2,25}, {1,28}, {6,35}, {6,24}, {9,32}, {6,27}, {4,41}, {3,33}, {7,36}, {11,35}, {2,30}, {8,29}, {6,28} }; // ET42.57 // Bipartite(21,21) Valencies [10,10] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 10080 EdgePairs[42][57]:={ {10,25}, {10,24}, {17,35}, {12,29}, {5,34}, {16,26}, {3,22}, {21,40}, {3,40}, {10,37}, {18,32}, {4,30}, {16,27}, {21,32}, {14,39}, {2,23}, {12,22}, {8,28}, {16,31}, {18,38}, {15,31}, {21,37}, {4,29}, {20,27}, {3,25}, {19,24}, {7,41}, {1,40}, {17,34}, {7,22}, {4,31}, {10,33}, {3,35}, {17,24}, {8,25}, {2,41}, {12,34}, {17,40}, {14,28}, {9,35}, {20,30}, {13,29}, {16,29}, {2,42}, {18,34}, {11,28}, {16,30}, {4,38}, {19,33}, {3,34}, {5,40}, {2,25}, {20,38}, {11,38}, {11,33}, {6,31}, {6,40}, {1,38}, {2,34}, {2,36}, {4,22}, {14,36}, {9,32}, {16,24}, {9,26}, {19,30}, {5,29}, {4,41}, {2,37}, {19,29}, {7,39}, {4,42}, {9,41}, {5,25}, {15,26}, {10,41}, {7,25}, {14,24}, {10,28}, {20,31}, {1,22}, {15,27}, {21,27}, {20,33}, {6,30}, {4,33}, {13,22}, {15,42}, {9,42}, {10,40}, {13,31}, {18,30}, {4,35}, {7,26}, {6,33}, {16,32}, {11,23}, {1,23}, {5,30}, {17,30}, {19,41}, {17,27}, {12,28}, {12,25}, {15,37}, {8,22}, {15,34}, {8,35}, {18,26}, {18,27}, {14,41}, {14,37}, {1,33}, {3,29}, {6,23}, {16,38}, {21,33}, {13,36}, {15,36}, {8,26}, {18,31}, {12,26}, {16,22}, {9,22}, {5,41}, {4,36}, {21,39}, {17,28}, {12,27}, {8,32}, {1,42}, {12,23}, {13,24}, {17,25}, {11,39}, {8,40}, {20,39}, {14,34}, {8,23}, {3,23}, {10,32}, {21,30}, {17,29}, {5,36}, {1,25}, {19,36}, {18,23}, {13,27}, {10,39}, {1,35}, {13,42}, {1,37}, {14,25}, {7,28}, {19,32}, {13,26}, {6,42}, {11,26}, {10,35}, {7,23}, {6,36}, {3,30}, {5,33}, {20,26}, {11,37}, {2,29}, {16,35}, {18,28}, {8,38}, {2,22}, {11,32}, {8,24}, {19,39}, {13,41}, {20,42}, {6,38}, {2,31}, {11,40}, {9,33}, {20,36}, {6,34}, {15,28}, {9,39}, {9,38}, {3,38}, {12,24}, {15,23}, {1,41}, {21,36}, {7,24}, {3,31}, {15,39}, {21,34}, {9,24}, {18,40}, {12,31}, {6,37}, {19,35}, {13,39}, {7,37}, {5,35}, {5,37}, {21,28}, {17,32}, {11,42}, {7,42}, {20,32}, {14,27}, {19,27}, {14,29} }; // ET42.58 // Bipartite(21,21) Valencies [10,10] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 10080 EdgePairs[42][58]:={ {21,23}, {3,33}, {16,41}, {2,24}, {13,32}, {9,28}, {2,33}, {6,32}, {11,36}, {17,36}, {18,39}, {4,27}, {11,35}, {4,24}, {15,24}, {16,33}, {18,29}, {4,26}, {17,38}, {11,25}, {8,30}, {16,40}, {5,38}, {12,32}, {7,38}, {8,42}, {1,32}, {8,33}, {10,23}, {12,38}, {20,40}, {10,26}, {12,39}, {12,41}, {2,27}, {12,42}, {21,42}, {21,35}, {3,37}, {13,35}, {14,31}, {2,26}, {8,39}, {7,34}, {11,41}, {16,25}, {12,35}, {7,36}, {2,28}, {1,30}, {5,32}, {16,23}, {4,23}, {8,31}, {8,27}, {12,37}, {10,22}, {6,22}, {15,25}, {18,42}, {18,37}, {10,30}, {6,29}, {19,28}, {15,29}, {14,23}, {14,33}, {5,22}, {10,38}, {9,29}, {19,40}, {17,37}, {19,26}, {15,32}, {9,27}, {12,36}, {15,40}, {8,41}, {2,38}, {14,30}, {14,40}, {19,22}, {2,39}, {7,32}, {17,39}, {17,23}, {1,31}, {11,22}, {11,31}, {2,35}, {17,33}, {19,38}, {5,23}, {10,29}, {21,26}, {1,29}, {3,32}, {9,25}, {15,41}, {13,33}, {19,42}, {11,30}, {21,25}, {5,24}, {9,37}, {13,23}, {14,42}, {13,25}, {18,24}, {20,28}, {13,28}, {10,42}, {19,31}, {1,28}, {3,27}, {20,22}, {18,36}, {21,31}, {18,33}, {3,26}, {8,37}, {5,28}, {21,38}, {17,31}, {5,42}, {7,31}, {13,30}, {20,29}, {9,40}, {1,24}, {14,22}, {5,31}, {11,24}, {6,27}, {6,26}, {20,23}, {12,40}, {12,30}, {21,29}, {1,39}, {18,25}, {17,41}, {7,29}, {6,41}, {6,28}, {9,30}, {16,34}, {5,39}, {20,35}, {20,37}, {4,37}, {4,40}, {16,36}, {8,34}, {3,24}, {11,27}, {10,27}, {20,34}, {1,26}, {4,34}, {10,36}, {10,34}, {15,22}, {18,22}, {15,33}, {14,32}, {6,25}, {20,24}, {2,40}, {9,36}, {16,42}, {5,27}, {15,38}, {19,25}, {3,42}, {16,39}, {13,38}, {4,25}, {3,28}, {7,27}, {20,41}, {14,35}, {13,37}, {3,41}, {17,26}, {6,39}, {7,33}, {13,34}, {11,34}, {7,35}, {17,22}, {21,24}, {2,30}, {15,30}, {19,34}, {9,31}, {1,34}, {21,41}, {6,35}, {3,36}, {4,39}, {16,28}, {18,35}, {7,40}, {9,23}, {19,37}, {8,29}, {4,32}, {1,36}, {14,26} }; // ET42.59 // Non-bipartite Valency 10 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 10080 EdgePairs[42][59]:={ {16,41}, {10,25}, {1,20}, {2,24}, {13,32}, {9,28}, {17,35}, {11,36}, {17,36}, {18,39}, {4,27}, {12,29}, {13,40}, {4,24}, {16,33}, {4,26}, {3,22}, {21,40}, {17,38}, {18,32}, {11,25}, {8,30}, {16,40}, {22,37}, {14,39}, {2,23}, {12,32}, {8,28}, {16,31}, {18,38}, {4,29}, {8,33}, {1,27}, {3,25}, {20,40}, {17,34}, {14,38}, {4,19}, {2,19}, {22,42}, {10,33}, {2,27}, {1,19}, {21,42}, {5,20}, {13,35}, {14,31}, {2,26}, {7,34}, {1,21}, {12,35}, {7,36}, {2,28}, {12,34}, {1,30}, {18,41}, {17,40}, {9,35}, {4,23}, {8,31}, {8,27}, {18,34}, {23,39}, {11,28}, {18,37}, {10,30}, {6,29}, {6,21}, {20,38}, {11,33}, {14,33}, {5,22}, {4,22}, {19,40}, {17,37}, {14,36}, {9,32}, {15,32}, {9,26}, {9,27}, {24,37}, {15,40}, {5,29}, {22,41}, {5,25}, {7,32}, {24,39}, {7,25}, {11,31}, {10,28}, {1,22}, {6,30}, {5,23}, {10,29}, {23,41}, {10,31}, {3,20}, {9,34}, {15,42}, {1,29}, {7,30}, {13,31}, {23,37}, {23,42}, {9,25}, {15,41}, {8,36}, {7,26}, {13,33}, {19,42}, {16,32}, {11,29}, {6,24}, {5,30}, {19,41}, {15,35}, {12,25}, {15,37}, {14,42}, {15,34}, {8,35}, {1,28}, {14,41}, {3,27}, {14,37}, {23,38}, {4,28}, {18,33}, {6,23}, {3,26}, {16,38}, {13,36}, {15,36}, {21,38}, {8,26}, {17,31}, {18,31}, {12,26}, {7,31}, {12,33}, {24,40}, {24,41}, {21,39}, {12,27}, {8,32}, {1,24}, {6,26}, {20,39}, {12,30}, {14,34}, {3,23}, {3,21}, {1,25}, {6,19}, {17,41}, {7,29}, {6,28}, {9,30}, {24,38}, {13,42}, {16,34}, {7,28}, {20,37}, {11,26}, {10,35}, {16,36}, {2,21}, {3,30}, {3,24}, {2,29}, {11,27}, {10,27}, {2,22}, {10,36}, {10,34}, {11,32}, {15,33}, {19,39}, {6,25}, {20,42}, {9,33}, {9,36}, {16,42}, {5,27}, {5,26}, {16,39}, {13,38}, {4,25}, {4,20}, {3,28}, {14,35}, {22,40}, {13,37}, {15,39}, {18,40}, {12,31}, {11,34}, {17,42}, {5,19}, {6,20}, {7,35}, {13,39}, {5,21}, {2,30}, {21,41}, {17,32}, {18,35}, {19,37}, {8,29}, {22,38} }; // ET42.60 // Non-bipartite Valency 10 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 10080 EdgePairs[42][60]:={ {1,11}, {38,42}, {18,39}, {4,27}, {12,29}, {13,21}, {11,35}, {14,19}, {4,24}, {4,26}, {23,29}, {35,42}, {17,38}, {23,27}, {1,10}, {10,37}, {18,32}, {32,40}, {25,39}, {26,31}, {32,35}, {1,13}, {39,42}, {7,38}, {16,31}, {4,29}, {32,34}, {34,36}, {3,25}, {2,15}, {35,40}, {22,42}, {1,19}, {12,42}, {21,35}, {25,29}, {24,30}, {29,35}, {8,39}, {11,41}, {2,9}, {29,41}, {18,21}, {8,10}, {6,7}, {24,36}, {2,14}, {5,32}, {17,40}, {6,11}, {29,39}, {3,5}, {9,11}, {19,21}, {18,37}, {3,7}, {19,33}, {7,12}, {31,33}, {31,39}, {6,31}, {40,41}, {1,7}, {26,28}, {1,18}, {3,14}, {15,32}, {16,24}, {4,8}, {18,20}, {9,27}, {27,30}, {1,5}, {12,36}, {34,38}, {31,37}, {9,41}, {26,40}, {23,34}, {11,22}, {7,25}, {14,24}, {10,28}, {24,25}, {1,22}, {19,38}, {23,26}, {5,23}, {15,19}, {24,32}, {37,40}, {28,41}, {2,20}, {14,16}, {28,29}, {30,42}, {8,17}, {23,35}, {30,36}, {6,24}, {2,6}, {19,41}, {8,11}, {11,30}, {13,23}, {33,42}, {32,38}, {13,25}, {20,28}, {26,38}, {13,28}, {10,42}, {9,20}, {18,26}, {4,13}, {3,11}, {20,22}, {31,36}, {10,12}, {2,3}, {3,10}, {22,29}, {8,37}, {15,36}, {17,31}, {8,26}, {25,37}, {27,42}, {7,31}, {6,15}, {13,30}, {2,17}, {33,35}, {4,6}, {21,39}, {5,12}, {25,32}, {8,32}, {4,9}, {14,18}, {14,22}, {17,25}, {11,39}, {30,40}, {28,33}, {33,37}, {12,40}, {3,23}, {21,30}, {36,41}, {17,19}, {5,36}, {36,39}, {13,15}, {16,34}, {16,21}, {16,17}, {20,37}, {15,18}, {38,39}, {2,21}, {3,30}, {5,33}, {16,35}, {20,34}, {1,16}, {10,34}, {15,22}, {5,8}, {16,20}, {15,33}, {20,42}, {7,9}, {9,33}, {6,34}, {6,10}, {28,38}, {5,9}, {9,38}, {27,37}, {10,19}, {1,4}, {4,12}, {3,28}, {15,23}, {22,40}, {25,27}, {23,31}, {2,12}, {2,8}, {17,22}, {13,17}, {13,20}, {22,36}, {27,34}, {37,41}, {21,41}, {24,33}, {6,35}, {7,40}, {14,27}, {19,27}, {34,41}, {24,28}, {12,21}, {14,29}, {14,26}, {26,30}, {7,18}, {5,16} }; // ET42.61 // Non-bipartite Valency 10 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 10080 EdgePairs[42][61]:={ {1,11}, {33,38}, {38,42}, {9,28}, {6,32}, {6,16}, {4,27}, {12,29}, {13,21}, {11,35}, {5,34}, {4,24}, {8,12}, {16,33}, {4,26}, {3,8}, {10,37}, {25,39}, {26,31}, {32,35}, {1,13}, {39,42}, {18,38}, {15,31}, {3,6}, {4,29}, {3,13}, {34,36}, {24,27}, {23,28}, {32,37}, {3,25}, {17,20}, {2,15}, {16,19}, {12,39}, {35,40}, {1,19}, {12,42}, {21,42}, {25,30}, {11,41}, {1,21}, {16,18}, {18,21}, {8,10}, {2,14}, {29,42}, {38,40}, {29,39}, {8,31}, {13,16}, {9,11}, {35,41}, {19,21}, {20,38}, {40,41}, {1,7}, {1,18}, {7,11}, {17,37}, {16,24}, {1,5}, {5,11}, {12,36}, {2,10}, {26,27}, {27,29}, {29,36}, {26,29}, {22,35}, {7,39}, {6,8}, {22,41}, {17,39}, {7,32}, {26,40}, {10,41}, {3,12}, {23,34}, {11,22}, {7,25}, {14,24}, {25,28}, {23,36}, {6,12}, {20,33}, {5,23}, {24,32}, {9,42}, {2,20}, {13,18}, {24,26}, {6,33}, {14,15}, {16,32}, {30,35}, {6,24}, {2,6}, {7,17}, {19,41}, {32,33}, {11,30}, {5,7}, {13,23}, {23,25}, {15,34}, {32,39}, {33,42}, {1,9}, {13,25}, {20,28}, {26,38}, {15,20}, {13,28}, {9,20}, {18,26}, {20,22}, {4,7}, {15,17}, {31,36}, {10,12}, {2,3}, {3,10}, {15,36}, {24,35}, {37,39}, {8,26}, {18,31}, {25,37}, {31,34}, {13,30}, {2,17}, {33,35}, {21,39}, {25,32}, {14,17}, {4,9}, {14,22}, {5,31}, {17,25}, {30,40}, {8,40}, {28,33}, {30,41}, {21,29}, {3,23}, {18,19}, {27,41}, {5,36}, {28,42}, {36,39}, {4,5}, {14,20}, {16,21}, {28,30}, {13,19}, {3,30}, {16,35}, {10,27}, {8,38}, {2,22}, {1,16}, {4,14}, {15,22}, {10,34}, {20,42}, {7,9}, {11,40}, {9,33}, {6,10}, {31,40}, {8,18}, {28,38}, {5,9}, {9,38}, {27,37}, {10,19}, {1,4}, {4,11}, {24,29}, {3,28}, {15,23}, {22,40}, {21,36}, {23,31}, {36,42}, {18,40}, {2,12}, {2,8}, {5,15}, {17,22}, {19,34}, {7,37}, {22,30}, {27,34}, {37,41}, {24,33}, {6,35}, {17,32}, {19,37}, {14,27}, {19,27}, {34,41}, {31,38}, {34,37}, {12,21}, {14,29}, {14,26}, {23,30} }; // ET42.62 // Bipartite(6,36) Valencies [12,2] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1671768834048000000 EdgePairs[42][62]:={ {3,22}, {5,12}, {1,26}, {2,14}, {5,36}, {5,42}, {3,40}, {6,37}, {4,23}, {1,14}, {2,26}, {4,41}, {5,24}, {2,32}, {5,29}, {4,34}, {1,32}, {1,37}, {4,11}, {2,39}, {4,10}, {3,21}, {6,31}, {4,40}, {3,27}, {6,12}, {3,33}, {5,11}, {6,30}, {1,20}, {4,16}, {1,31}, {3,9}, {6,36}, {6,7}, {2,33}, {2,21}, {5,23}, {1,38}, {1,7}, {3,16}, {3,28}, {2,20}, {3,15}, {2,38}, {5,17}, {2,15}, {6,42}, {4,17}, {5,30}, {4,28}, {2,27}, {4,22}, {6,18}, {3,39}, {6,19}, {3,34}, {5,18}, {6,25}, {1,8}, {1,13}, {5,35}, {5,41}, {1,19}, {2,9}, {4,35}, {2,8}, {1,25}, {6,13}, {6,24}, {3,10}, {4,29} }; // ET42.63 // Bipartite(6,36) Valencies [12,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 190210142896128 EdgePairs[42][63]:={ {3,32}, {1,26}, {2,14}, {5,33}, {5,42}, {4,37}, {3,12}, {6,39}, {5,24}, {2,32}, {5,29}, {4,34}, {2,24}, {6,26}, {4,11}, {4,10}, {3,21}, {1,36}, {6,31}, {5,40}, {6,12}, {5,11}, {4,7}, {6,30}, {5,15}, {2,36}, {3,23}, {3,37}, {4,16}, {6,40}, {2,33}, {5,20}, {1,7}, {5,31}, {1,16}, {3,28}, {4,38}, {5,38}, {2,18}, {4,20}, {3,19}, {3,30}, {2,15}, {3,14}, {6,21}, {1,18}, {1,27}, {4,28}, {2,27}, {1,17}, {4,25}, {3,39}, {2,42}, {6,22}, {3,41}, {6,17}, {6,35}, {2,23}, {1,8}, {2,9}, {5,13}, {1,9}, {2,41}, {1,34}, {1,35}, {4,19}, {1,25}, {5,22}, {6,13}, {6,8}, {3,10}, {4,29} }; // ET42.64 // Bipartite(6,36) Valencies [12,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 104485552128 EdgePairs[42][64]:={ {5,12}, {4,8}, {2,14}, {5,36}, {5,42}, {3,40}, {6,37}, {4,23}, {6,34}, {2,26}, {3,12}, {6,39}, {5,24}, {2,32}, {1,29}, {2,29}, {4,34}, {1,37}, {1,33}, {5,27}, {6,14}, {6,26}, {4,11}, {4,10}, {3,21}, {2,40}, {3,33}, {6,10}, {5,15}, {3,23}, {1,31}, {3,24}, {3,9}, {6,15}, {4,30}, {4,32}, {5,7}, {4,18}, {2,16}, {1,7}, {5,31}, {3,11}, {3,16}, {3,28}, {2,20}, {5,19}, {2,38}, {1,21}, {4,20}, {6,38}, {6,27}, {5,30}, {5,39}, {1,17}, {4,22}, {2,28}, {6,22}, {2,17}, {5,18}, {6,25}, {1,13}, {1,19}, {1,9}, {2,41}, {1,41}, {4,35}, {2,8}, {4,42}, {1,25}, {6,13}, {3,36}, {3,35} }; // ET42.65 // Bipartite(14,28) Valencies [12,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 336 EdgePairs[42][65]:={ {10,25}, {1,20}, {5,17}, {11,20}, {9,28}, {2,33}, {5,34}, {13,40}, {14,19}, {4,26}, {10,37}, {4,30}, {8,30}, {6,17}, {2,23}, {5,38}, {12,32}, {8,28}, {1,32}, {3,25}, {12,38}, {7,41}, {1,40}, {4,19}, {12,39}, {7,22}, {2,19}, {2,27}, {12,42}, {5,20}, {7,34}, {8,25}, {9,35}, {14,28}, {8,31}, {13,29}, {13,16}, {10,15}, {6,22}, {3,18}, {4,38}, {6,21}, {11,38}, {11,33}, {6,31}, {2,34}, {1,17}, {5,22}, {4,22}, {10,38}, {9,29}, {14,21}, {9,27}, {12,36}, {4,41}, {8,41}, {9,19}, {2,37}, {5,25}, {11,15}, {10,41}, {14,24}, {2,35}, {12,16}, {4,33}, {4,21}, {10,29}, {14,16}, {6,18}, {10,40}, {1,29}, {7,30}, {2,16}, {3,39}, {3,32}, {11,21}, {8,36}, {7,26}, {13,33}, {5,18}, {14,15}, {6,24}, {11,30}, {9,37}, {13,23}, {8,35}, {10,42}, {1,28}, {3,27}, {13,36}, {8,26}, {5,42}, {9,22}, {7,31}, {12,33}, {5,41}, {12,27}, {14,17}, {8,32}, {12,23}, {6,27}, {11,24}, {11,39}, {8,40}, {12,30}, {3,23}, {8,23}, {1,25}, {13,15}, {1,15}, {6,28}, {12,15}, {13,27}, {1,35}, {13,42}, {14,20}, {5,39}, {11,26}, {6,42}, {11,16}, {7,23}, {3,30}, {10,17}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {10,36}, {10,34}, {11,32}, {9,17}, {14,32}, {6,25}, {2,40}, {2,31}, {8,18}, {3,42}, {4,18}, {13,38}, {11,19}, {4,20}, {12,24}, {3,28}, {14,35}, {1,41}, {13,37}, {3,31}, {9,24}, {10,20}, {6,39}, {7,33}, {6,37}, {13,34}, {7,35}, {5,21}, {9,31}, {5,37}, {7,19}, {9,21}, {9,16}, {3,36}, {4,39}, {7,40}, {1,36}, {14,29}, {14,26}, {7,18} }; // ET42.66 // Bipartite(14,28) Valencies [12,6] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 336 EdgePairs[42][66]:={ {11,17}, {3,33}, {2,24}, {13,32}, {6,32}, {6,16}, {11,36}, {12,29}, {11,35}, {4,24}, {3,22}, {3,40}, {4,16}, {14,39}, {7,38}, {8,42}, {8,33}, {3,15}, {10,23}, {10,26}, {2,15}, {14,38}, {4,31}, {10,33}, {1,19}, {3,35}, {3,37}, {13,35}, {2,26}, {14,31}, {8,39}, {11,41}, {1,21}, {7,36}, {2,41}, {2,28}, {12,34}, {1,30}, {8,15}, {4,23}, {8,27}, {12,37}, {2,42}, {10,22}, {11,28}, {6,29}, {3,17}, {5,40}, {1,38}, {14,33}, {2,36}, {8,19}, {1,18}, {7,20}, {9,32}, {14,36}, {9,26}, {12,20}, {5,29}, {2,38}, {14,30}, {14,40}, {7,39}, {4,42}, {7,32}, {1,31}, {11,22}, {7,25}, {10,28}, {6,30}, {9,34}, {13,22}, {10,21}, {9,42}, {8,17}, {13,31}, {4,35}, {9,25}, {7,16}, {11,23}, {1,23}, {11,29}, {5,30}, {5,24}, {12,28}, {12,25}, {8,22}, {13,25}, {9,20}, {4,15}, {14,41}, {14,37}, {6,23}, {3,26}, {5,28}, {12,26}, {13,30}, {2,17}, {9,40}, {1,42}, {1,24}, {14,22}, {5,31}, {13,24}, {12,19}, {12,40}, {10,32}, {5,36}, {3,21}, {6,19}, {7,29}, {6,41}, {10,39}, {1,37}, {14,25}, {7,28}, {3,16}, {4,37}, {4,40}, {10,35}, {13,19}, {6,36}, {2,21}, {8,34}, {5,33}, {9,18}, {11,27}, {10,27}, {1,16}, {10,18}, {8,24}, {13,41}, {6,38}, {9,33}, {6,34}, {5,27}, {5,26}, {9,39}, {4,25}, {3,38}, {8,20}, {7,27}, {3,41}, {5,15}, {12,31}, {11,34}, {5,19}, {6,20}, {13,39}, {9,15}, {2,30}, {13,17}, {7,37}, {13,20}, {2,18}, {1,34}, {4,17}, {6,35}, {11,42}, {9,23}, {7,21}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {10,16} }; // ET42.67 // Bipartite(14,28) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 98627481501696 EdgePairs[42][67]:={ {10,25}, {2,24}, {10,24}, {2,33}, {12,29}, {13,21}, {11,35}, {5,34}, {4,26}, {11,25}, {8,30}, {6,17}, {2,23}, {12,22}, {1,32}, {3,25}, {7,41}, {4,19}, {2,19}, {12,41}, {5,20}, {13,35}, {2,26}, {8,39}, {7,34}, {8,25}, {12,34}, {1,30}, {8,15}, {14,28}, {13,29}, {6,22}, {3,18}, {11,28}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {5,40}, {14,23}, {11,33}, {6,31}, {5,22}, {10,38}, {1,18}, {7,20}, {14,21}, {9,26}, {12,20}, {12,36}, {5,29}, {2,38}, {9,19}, {2,37}, {14,30}, {4,42}, {10,41}, {1,22}, {4,33}, {4,21}, {10,31}, {3,20}, {13,22}, {14,16}, {1,29}, {7,30}, {2,16}, {3,39}, {13,31}, {3,32}, {11,21}, {4,35}, {7,16}, {8,36}, {1,23}, {6,24}, {9,37}, {8,22}, {14,42}, {13,28}, {14,41}, {3,27}, {14,37}, {4,28}, {8,37}, {13,36}, {12,26}, {12,33}, {6,15}, {5,41}, {2,17}, {12,27}, {9,40}, {8,32}, {13,24}, {11,39}, {12,19}, {12,40}, {8,23}, {14,34}, {1,39}, {10,32}, {5,36}, {1,25}, {13,15}, {1,15}, {6,28}, {12,15}, {9,30}, {10,39}, {13,42}, {1,37}, {14,20}, {7,28}, {11,26}, {6,42}, {4,40}, {7,23}, {6,36}, {5,33}, {10,17}, {3,24}, {10,27}, {1,16}, {10,34}, {11,32}, {9,17}, {10,18}, {6,38}, {2,40}, {2,31}, {11,40}, {9,33}, {5,27}, {5,26}, {8,18}, {4,18}, {13,38}, {9,38}, {11,19}, {4,25}, {3,38}, {7,27}, {14,35}, {3,41}, {3,31}, {9,24}, {10,20}, {5,15}, {5,19}, {7,35}, {2,30}, {13,17}, {7,37}, {9,31}, {6,35}, {11,42}, {9,16}, {4,39}, {7,42}, {9,23}, {7,21}, {14,27}, {8,29}, {4,32}, {11,18}, {1,36} }; // ET42.68 // Bipartite(14,28) Valencies [12,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 192631799808 EdgePairs[42][68]:={ {3,33}, {2,24}, {11,20}, {9,28}, {2,33}, {6,32}, {11,36}, {4,27}, {12,29}, {13,21}, {5,34}, {4,24}, {3,40}, {8,30}, {2,23}, {12,22}, {12,32}, {1,32}, {8,33}, {12,38}, {10,26}, {14,38}, {12,39}, {4,31}, {2,19}, {10,33}, {5,20}, {13,35}, {2,26}, {14,31}, {8,39}, {11,41}, {8,25}, {1,30}, {9,35}, {14,28}, {13,16}, {10,15}, {10,22}, {3,17}, {8,16}, {4,38}, {6,21}, {3,34}, {11,33}, {5,22}, {8,19}, {1,18}, {14,21}, {14,36}, {12,17}, {12,36}, {5,29}, {4,41}, {2,38}, {2,37}, {7,39}, {11,15}, {7,32}, {11,22}, {7,25}, {10,28}, {14,24}, {1,22}, {5,23}, {10,29}, {3,20}, {10,21}, {9,42}, {6,18}, {10,40}, {1,29}, {2,16}, {7,26}, {14,15}, {1,23}, {11,29}, {5,30}, {9,37}, {13,23}, {12,25}, {14,42}, {13,28}, {10,42}, {3,27}, {3,26}, {8,37}, {8,26}, {13,30}, {5,41}, {2,17}, {14,17}, {8,32}, {3,19}, {14,22}, {6,27}, {8,40}, {8,23}, {1,39}, {5,36}, {1,25}, {6,41}, {1,15}, {6,28}, {12,15}, {9,30}, {13,27}, {13,42}, {1,37}, {7,28}, {11,26}, {6,42}, {10,35}, {3,24}, {11,27}, {4,34}, {10,36}, {1,16}, {9,17}, {6,25}, {13,41}, {2,40}, {2,31}, {11,40}, {6,34}, {5,27}, {8,18}, {4,18}, {9,38}, {11,19}, {10,19}, {4,25}, {3,38}, {4,20}, {12,24}, {14,35}, {13,37}, {3,41}, {3,31}, {9,24}, {6,39}, {5,15}, {7,33}, {12,31}, {13,34}, {11,34}, {6,20}, {7,35}, {2,30}, {13,20}, {9,31}, {5,37}, {7,19}, {4,17}, {6,35}, {9,21}, {9,16}, {4,39}, {7,40}, {7,42}, {9,23}, {7,21}, {4,32}, {12,18}, {1,36}, {14,29}, {7,18}, {5,16} }; // ET42.69 // Bipartite(14,28) Valencies [12,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 88080384 EdgePairs[42][69]:={ {5,17}, {11,20}, {13,32}, {2,33}, {6,32}, {11,36}, {11,35}, {4,26}, {3,40}, {10,37}, {6,17}, {2,23}, {12,22}, {5,38}, {7,38}, {8,42}, {8,28}, {4,29}, {8,33}, {10,23}, {12,38}, {7,41}, {1,40}, {10,26}, {2,15}, {14,38}, {12,39}, {2,19}, {1,19}, {2,27}, {3,37}, {8,39}, {7,34}, {12,35}, {8,25}, {2,41}, {8,15}, {14,28}, {3,18}, {10,30}, {3,17}, {14,23}, {6,31}, {1,38}, {2,36}, {5,22}, {4,22}, {8,19}, {9,29}, {7,20}, {14,21}, {12,17}, {9,27}, {12,36}, {9,19}, {2,37}, {9,41}, {5,25}, {11,15}, {11,22}, {10,28}, {14,24}, {12,16}, {4,21}, {10,31}, {6,18}, {13,18}, {10,40}, {1,29}, {2,16}, {13,31}, {3,32}, {11,21}, {4,35}, {6,33}, {13,33}, {11,29}, {5,30}, {5,24}, {9,37}, {12,25}, {14,42}, {13,25}, {10,42}, {4,15}, {1,28}, {14,41}, {14,37}, {1,33}, {3,26}, {8,26}, {9,22}, {4,36}, {1,42}, {1,24}, {5,31}, {6,27}, {8,40}, {12,30}, {3,23}, {14,34}, {1,39}, {10,32}, {5,36}, {1,25}, {6,19}, {6,41}, {1,15}, {9,30}, {13,27}, {14,20}, {5,39}, {7,28}, {3,16}, {11,26}, {4,40}, {7,23}, {13,19}, {3,30}, {10,17}, {2,29}, {8,38}, {1,26}, {2,22}, {4,34}, {11,32}, {10,18}, {8,24}, {6,25}, {13,41}, {11,40}, {9,33}, {9,36}, {6,34}, {3,42}, {4,18}, {4,20}, {12,24}, {3,28}, {7,27}, {14,35}, {7,24}, {3,31}, {6,39}, {12,31}, {11,34}, {13,34}, {6,20}, {7,35}, {13,39}, {5,21}, {2,30}, {9,15}, {13,17}, {13,20}, {7,37}, {5,35}, {9,16}, {7,42}, {9,23}, {7,21}, {14,27}, {8,29}, {4,32}, {11,18}, {12,21}, {10,16}, {5,16} }; // ET42.70 // Bipartite(14,28) Valencies [12,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 21504 EdgePairs[42][70]:={ {11,17}, {13,32}, {6,32}, {12,29}, {13,21}, {11,35}, {4,26}, {4,16}, {10,37}, {4,30}, {6,17}, {12,22}, {8,28}, {1,32}, {8,33}, {3,15}, {10,26}, {4,19}, {12,39}, {1,19}, {12,42}, {3,35}, {5,20}, {3,37}, {14,31}, {8,39}, {12,35}, {7,36}, {8,25}, {2,41}, {8,15}, {4,23}, {8,31}, {10,15}, {6,22}, {3,18}, {10,30}, {6,21}, {3,34}, {11,33}, {6,31}, {1,38}, {14,33}, {2,36}, {5,22}, {10,38}, {9,29}, {8,19}, {7,20}, {9,32}, {14,21}, {14,36}, {12,20}, {5,29}, {2,38}, {2,37}, {14,40}, {4,42}, {9,41}, {5,25}, {2,39}, {11,15}, {1,31}, {10,41}, {7,25}, {10,28}, {14,24}, {12,16}, {4,33}, {4,21}, {3,20}, {13,22}, {6,18}, {13,18}, {2,16}, {13,31}, {11,21}, {4,35}, {8,36}, {2,32}, {7,26}, {5,18}, {11,23}, {1,23}, {6,24}, {11,30}, {5,24}, {9,37}, {13,23}, {12,28}, {12,25}, {4,15}, {1,28}, {3,27}, {14,37}, {1,33}, {6,23}, {3,26}, {5,28}, {5,42}, {9,22}, {7,31}, {2,17}, {9,40}, {8,32}, {6,27}, {13,24}, {12,19}, {8,23}, {1,39}, {1,25}, {7,29}, {6,41}, {1,15}, {9,30}, {13,27}, {13,42}, {14,20}, {5,39}, {14,25}, {11,26}, {6,42}, {4,40}, {10,35}, {11,16}, {3,30}, {8,34}, {2,29}, {10,27}, {8,38}, {2,22}, {10,34}, {9,17}, {10,18}, {13,41}, {2,40}, {11,40}, {9,36}, {6,34}, {9,39}, {9,38}, {11,19}, {3,38}, {12,24}, {3,28}, {7,27}, {3,41}, {7,24}, {10,20}, {7,33}, {13,34}, {5,19}, {2,30}, {13,17}, {7,37}, {5,35}, {1,34}, {4,17}, {11,42}, {9,16}, {7,40}, {7,21}, {14,27}, {12,18}, {1,36}, {14,29}, {14,26}, {5,16} }; // ET42.71 // Bipartite(14,28) Valencies [12,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1376256 EdgePairs[42][71]:={ {3,33}, {5,17}, {1,20}, {9,28}, {6,32}, {11,36}, {4,27}, {7,15}, {11,35}, {5,34}, {4,24}, {14,19}, {3,22}, {4,16}, {10,37}, {4,30}, {14,39}, {8,42}, {8,28}, {4,29}, {8,33}, {10,23}, {12,38}, {1,40}, {10,26}, {4,19}, {12,39}, {12,41}, {2,27}, {5,20}, {2,26}, {11,41}, {12,35}, {2,41}, {2,28}, {8,31}, {2,42}, {10,22}, {3,18}, {6,29}, {3,17}, {4,38}, {6,21}, {2,25}, {11,38}, {1,38}, {14,33}, {2,36}, {8,19}, {9,29}, {9,32}, {14,21}, {14,36}, {9,26}, {9,27}, {5,29}, {4,41}, {14,30}, {4,42}, {9,41}, {5,25}, {2,39}, {7,32}, {11,22}, {12,16}, {4,33}, {10,31}, {13,22}, {10,21}, {9,42}, {14,16}, {6,18}, {10,40}, {1,29}, {7,30}, {8,17}, {3,32}, {11,21}, {7,16}, {7,26}, {6,33}, {13,33}, {11,23}, {1,23}, {6,24}, {5,30}, {7,17}, {9,37}, {13,23}, {12,25}, {13,25}, {13,28}, {4,15}, {3,27}, {4,28}, {8,37}, {5,28}, {13,36}, {5,42}, {12,26}, {7,31}, {6,15}, {2,17}, {12,27}, {9,40}, {8,32}, {3,19}, {1,24}, {14,22}, {5,31}, {11,24}, {13,24}, {12,40}, {12,30}, {8,23}, {14,34}, {1,39}, {1,25}, {6,19}, {7,29}, {1,15}, {13,42}, {1,37}, {14,20}, {5,39}, {14,25}, {3,16}, {10,35}, {13,19}, {3,30}, {8,34}, {9,18}, {10,17}, {11,37}, {11,27}, {1,26}, {2,22}, {10,36}, {10,34}, {11,32}, {6,38}, {2,40}, {2,31}, {6,34}, {8,18}, {13,38}, {12,24}, {8,20}, {14,35}, {13,37}, {3,41}, {3,31}, {10,20}, {5,15}, {6,20}, {7,35}, {13,39}, {9,15}, {1,34}, {6,35}, {3,36}, {7,40}, {9,23}, {7,21}, {11,18}, {12,21}, {7,18}, {5,16} }; // ET42.72 // Bipartite(18,24) Valencies [12,9] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 300918390128640000 EdgePairs[42][72]:={ {3,33}, {10,24}, {1,20}, {2,24}, {13,32}, {2,33}, {18,39}, {5,34}, {13,40}, {4,24}, {16,26}, {4,26}, {17,38}, {4,30}, {11,25}, {16,40}, {12,22}, {5,38}, {8,28}, {18,38}, {15,31}, {1,32}, {8,33}, {1,27}, {3,25}, {12,38}, {1,40}, {10,26}, {17,34}, {12,39}, {1,19}, {12,42}, {3,35}, {3,37}, {13,35}, {11,41}, {12,35}, {7,36}, {17,21}, {8,25}, {2,41}, {2,28}, {12,34}, {9,35}, {14,28}, {18,34}, {10,22}, {6,22}, {15,25}, {18,42}, {10,30}, {16,30}, {4,38}, {15,29}, {2,25}, {11,38}, {11,33}, {6,31}, {14,33}, {2,36}, {5,22}, {4,22}, {10,38}, {9,29}, {7,20}, {17,37}, {14,21}, {14,36}, {16,24}, {9,27}, {5,29}, {8,41}, {9,19}, {2,37}, {14,40}, {7,39}, {4,42}, {9,41}, {5,25}, {7,32}, {1,31}, {11,22}, {10,28}, {14,24}, {17,33}, {15,27}, {6,30}, {15,19}, {2,20}, {10,40}, {3,39}, {13,31}, {18,30}, {11,21}, {9,25}, {15,41}, {8,36}, {2,32}, {16,32}, {1,23}, {11,29}, {5,30}, {17,30}, {11,30}, {15,35}, {9,37}, {13,23}, {15,37}, {13,28}, {10,42}, {18,26}, {1,28}, {18,27}, {14,41}, {3,27}, {14,37}, {4,28}, {3,29}, {6,23}, {16,38}, {8,37}, {13,36}, {18,31}, {5,42}, {12,26}, {16,22}, {7,31}, {5,41}, {4,36}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {13,24}, {6,27}, {17,25}, {12,19}, {8,40}, {6,26}, {12,30}, {3,23}, {18,19}, {1,39}, {10,32}, {17,29}, {3,21}, {6,19}, {17,41}, {18,23}, {13,27}, {1,35}, {14,20}, {15,21}, {16,34}, {14,25}, {7,28}, {11,26}, {6,42}, {4,40}, {7,23}, {13,19}, {16,36}, {2,21}, {5,33}, {11,37}, {2,29}, {4,34}, {10,36}, {10,34}, {18,22}, {14,32}, {15,33}, {16,20}, {8,24}, {6,38}, {2,40}, {9,33}, {16,42}, {6,34}, {5,26}, {9,39}, {4,20}, {8,20}, {7,27}, {15,23}, {3,41}, {7,24}, {3,31}, {15,39}, {10,20}, {17,26}, {6,39}, {12,31}, {11,34}, {17,42}, {7,35}, {13,39}, {17,22}, {5,21}, {13,20}, {9,31}, {5,37}, {7,19}, {6,35}, {11,42}, {9,21}, {16,28}, {18,35}, {7,40}, {9,23}, {8,29}, {4,32}, {1,36}, {14,29} }; // ET42.73 // Bipartite(18,24) Valencies [12,9] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3761479876608 EdgePairs[42][73]:={ {16,41}, {10,25}, {1,20}, {2,24}, {10,24}, {11,20}, {17,35}, {11,36}, {17,36}, {13,21}, {11,35}, {4,24}, {15,24}, {16,26}, {16,33}, {4,26}, {3,40}, {11,25}, {8,30}, {16,40}, {12,22}, {7,38}, {8,42}, {16,31}, {18,38}, {15,31}, {1,27}, {10,23}, {12,38}, {10,26}, {17,20}, {14,38}, {7,22}, {4,31}, {12,41}, {10,33}, {12,42}, {1,19}, {3,35}, {5,20}, {3,37}, {13,35}, {2,26}, {11,41}, {1,21}, {16,25}, {7,36}, {12,34}, {1,30}, {18,41}, {16,23}, {9,35}, {4,23}, {13,29}, {2,42}, {18,34}, {6,22}, {18,42}, {11,28}, {15,29}, {11,33}, {1,38}, {2,34}, {9,29}, {7,20}, {9,32}, {14,21}, {15,32}, {16,24}, {18,20}, {9,27}, {12,20}, {12,36}, {15,40}, {4,41}, {2,38}, {9,19}, {2,37}, {14,30}, {14,40}, {4,42}, {5,25}, {17,39}, {17,23}, {10,41}, {11,31}, {14,24}, {17,33}, {1,22}, {15,27}, {6,30}, {4,33}, {5,23}, {10,31}, {13,22}, {15,19}, {10,40}, {1,29}, {7,30}, {3,39}, {18,30}, {3,32}, {2,32}, {6,33}, {16,32}, {11,23}, {15,35}, {9,37}, {17,27}, {12,28}, {12,25}, {15,37}, {8,22}, {14,42}, {13,28}, {10,42}, {18,26}, {1,28}, {3,27}, {14,37}, {18,36}, {18,33}, {3,29}, {8,37}, {5,28}, {13,36}, {8,26}, {17,31}, {12,26}, {12,33}, {13,30}, {5,41}, {17,28}, {9,40}, {8,32}, {8,21}, {3,19}, {14,22}, {5,31}, {17,25}, {11,39}, {6,26}, {8,40}, {12,30}, {3,23}, {14,34}, {10,32}, {18,25}, {5,36}, {3,21}, {17,19}, {17,41}, {7,29}, {6,41}, {6,28}, {13,27}, {10,39}, {1,35}, {1,37}, {15,21}, {16,34}, {5,39}, {7,28}, {6,42}, {4,40}, {13,19}, {6,36}, {2,21}, {8,34}, {5,33}, {3,24}, {2,29}, {11,27}, {18,28}, {8,38}, {2,22}, {4,34}, {10,34}, {18,22}, {14,32}, {8,24}, {6,25}, {6,38}, {2,40}, {16,42}, {6,34}, {5,27}, {16,39}, {9,39}, {13,38}, {11,19}, {4,25}, {7,27}, {15,23}, {13,37}, {3,31}, {15,39}, {9,24}, {5,19}, {6,20}, {7,35}, {2,30}, {13,20}, {7,37}, {5,35}, {9,31}, {7,19}, {9,21}, {4,39}, {9,23}, {7,21}, {8,29}, {4,32}, {1,36}, {14,29}, {14,26} }; // ET42.74 // Bipartite(21,21) Valencies [12,12] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 60480 EdgePairs[42][74]:={ {21,23}, {3,33}, {10,25}, {10,24}, {9,28}, {6,32}, {17,35}, {18,39}, {4,27}, {12,29}, {11,35}, {13,40}, {15,24}, {16,26}, {16,33}, {18,29}, {4,26}, {3,40}, {17,38}, {10,37}, {18,32}, {8,30}, {16,40}, {21,32}, {14,39}, {2,23}, {5,38}, {12,32}, {7,38}, {8,42}, {8,28}, {16,31}, {15,31}, {4,29}, {20,27}, {1,27}, {3,25}, {19,24}, {1,40}, {10,26}, {17,34}, {14,38}, {12,39}, {4,31}, {12,41}, {2,27}, {3,35}, {21,35}, {2,26}, {8,39}, {7,34}, {11,41}, {16,25}, {12,35}, {7,36}, {2,41}, {2,28}, {5,32}, {14,28}, {9,35}, {20,30}, {8,27}, {13,29}, {16,29}, {10,22}, {11,28}, {6,29}, {4,38}, {15,29}, {19,33}, {14,23}, {20,38}, {6,40}, {6,31}, {1,38}, {2,34}, {5,22}, {4,22}, {17,37}, {15,32}, {16,24}, {12,36}, {15,40}, {8,41}, {2,38}, {2,37}, {19,29}, {14,30}, {19,22}, {4,42}, {9,41}, {2,39}, {17,39}, {17,23}, {11,22}, {7,25}, {2,35}, {1,22}, {19,38}, {6,30}, {4,33}, {5,23}, {10,29}, {10,31}, {13,22}, {16,37}, {10,40}, {1,29}, {3,39}, {13,31}, {18,30}, {3,32}, {9,25}, {15,41}, {13,33}, {6,33}, {2,32}, {7,26}, {19,42}, {5,30}, {17,30}, {11,30}, {21,25}, {12,28}, {12,25}, {14,42}, {18,24}, {8,35}, {10,42}, {19,31}, {14,41}, {20,22}, {1,33}, {21,31}, {18,33}, {3,29}, {6,23}, {16,38}, {8,37}, {21,33}, {5,28}, {13,36}, {15,36}, {8,26}, {18,31}, {5,42}, {16,22}, {7,31}, {5,41}, {4,36}, {21,39}, {17,28}, {9,40}, {1,24}, {14,22}, {13,24}, {11,39}, {20,23}, {12,40}, {20,39}, {12,30}, {21,29}, {3,23}, {8,23}, {14,34}, {18,25}, {21,30}, {1,25}, {19,36}, {6,41}, {6,28}, {18,23}, {9,30}, {13,27}, {13,42}, {1,37}, {16,34}, {20,35}, {20,37}, {4,37}, {11,26}, {13,26}, {4,40}, {6,36}, {8,34}, {11,37}, {3,24}, {11,27}, {18,28}, {10,27}, {8,38}, {20,34}, {1,26}, {2,22}, {10,36}, {10,34}, {11,32}, {14,32}, {15,33}, {6,25}, {20,42}, {9,33}, {9,36}, {16,42}, {5,27}, {19,25}, {5,26}, {15,28}, {9,39}, {13,38}, {4,25}, {12,24}, {3,28}, {7,27}, {20,41}, {15,23}, {21,36}, {3,41}, {7,24}, {15,39}, {9,24}, {18,40}, {17,26}, {7,33}, {12,31}, {13,34}, {11,34}, {17,42}, {17,22}, {21,24}, {15,30}, {19,34}, {7,37}, {5,35}, {9,31}, {1,34}, {5,37}, {21,41}, {6,35}, {17,32}, {11,42}, {3,36}, {18,35}, {7,40}, {7,42}, {9,23}, {19,37}, {20,32}, {14,27}, {19,27}, {1,36}, {14,26} }; // ET42.75 // Bipartite(21,21) Valencies [12,12] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 26330359136256 EdgePairs[42][75]:={ {16,41}, {10,24}, {9,28}, {13,32}, {2,33}, {6,32}, {17,35}, {11,36}, {17,36}, {18,39}, {4,27}, {12,29}, {16,26}, {16,33}, {18,29}, {3,22}, {21,40}, {17,38}, {18,32}, {4,30}, {11,25}, {16,27}, {16,40}, {21,32}, {14,39}, {2,23}, {12,22}, {5,38}, {7,38}, {8,42}, {8,28}, {4,29}, {1,32}, {8,33}, {12,38}, {19,24}, {7,41}, {1,40}, {17,34}, {14,38}, {2,27}, {3,35}, {13,35}, {2,26}, {14,31}, {8,39}, {7,34}, {11,41}, {17,24}, {8,25}, {2,41}, {2,28}, {18,41}, {16,23}, {9,35}, {20,30}, {4,23}, {12,37}, {2,42}, {18,34}, {10,22}, {15,25}, {18,37}, {16,30}, {15,29}, {19,33}, {3,34}, {5,40}, {20,38}, {6,31}, {2,34}, {14,33}, {5,22}, {4,22}, {10,38}, {19,40}, {19,26}, {15,32}, {9,26}, {19,30}, {9,27}, {12,36}, {15,40}, {5,29}, {4,41}, {2,37}, {19,29}, {14,40}, {19,22}, {7,39}, {9,41}, {7,32}, {15,26}, {10,41}, {11,22}, {7,25}, {10,28}, {14,24}, {20,31}, {2,35}, {1,22}, {21,27}, {19,38}, {6,30}, {5,23}, {10,29}, {21,26}, {10,31}, {9,34}, {15,42}, {9,42}, {16,37}, {1,29}, {13,31}, {18,30}, {8,36}, {7,26}, {11,23}, {11,29}, {6,24}, {5,30}, {11,30}, {15,35}, {21,25}, {5,24}, {9,37}, {17,27}, {13,23}, {8,22}, {13,25}, {20,28}, {8,35}, {10,42}, {13,28}, {19,31}, {1,28}, {18,27}, {14,41}, {3,27}, {18,36}, {1,33}, {21,31}, {3,29}, {6,23}, {21,33}, {15,36}, {21,38}, {8,26}, {17,31}, {12,26}, {7,31}, {12,33}, {13,30}, {4,36}, {21,39}, {17,28}, {9,40}, {8,32}, {1,42}, {12,23}, {5,31}, {13,24}, {11,39}, {8,40}, {20,23}, {12,40}, {20,39}, {12,30}, {14,34}, {1,39}, {18,25}, {17,29}, {20,25}, {5,36}, {1,25}, {17,41}, {19,36}, {6,28}, {18,23}, {9,30}, {1,35}, {13,42}, {16,34}, {14,25}, {20,35}, {20,37}, {4,37}, {6,42}, {10,35}, {5,33}, {11,37}, {3,24}, {11,27}, {16,35}, {10,27}, {1,26}, {4,34}, {10,36}, {10,34}, {15,22}, {18,22}, {11,32}, {14,32}, {15,33}, {6,25}, {20,42}, {6,38}, {20,24}, {2,40}, {9,33}, {16,42}, {5,26}, {3,42}, {15,28}, {13,38}, {4,25}, {3,38}, {12,24}, {3,28}, {7,27}, {13,37}, {3,41}, {7,24}, {3,31}, {15,39}, {21,34}, {6,39}, {7,33}, {6,37}, {12,31}, {11,34}, {17,42}, {13,39}, {17,22}, {21,24}, {2,30}, {19,23}, {5,37}, {21,41}, {6,35}, {3,36}, {4,39}, {16,28}, {7,40}, {9,23}, {19,37}, {20,32}, {14,27}, {8,29}, {4,32}, {1,36}, {14,26} }; // ET42.76 // Non-bipartite Valency 12 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 264241152 EdgePairs[42][76]:={ {1,11}, {3,33}, {16,41}, {10,25}, {25,31}, {4,27}, {7,15}, {29,40}, {36,38}, {13,40}, {14,19}, {4,24}, {23,29}, {3,8}, {17,38}, {10,37}, {18,32}, {32,40}, {8,30}, {26,31}, {22,37}, {14,39}, {12,22}, {12,32}, {8,42}, {18,38}, {21,37}, {1,32}, {8,33}, {7,41}, {10,26}, {2,15}, {12,39}, {21,35}, {5,20}, {3,37}, {2,26}, {24,30}, {29,35}, {7,34}, {1,21}, {17,24}, {11,14}, {27,33}, {2,41}, {8,15}, {9,35}, {14,28}, {4,23}, {29,39}, {16,29}, {2,42}, {23,39}, {3,18}, {11,28}, {18,37}, {6,29}, {3,17}, {3,7}, {8,16}, {16,30}, {23,32}, {4,38}, {15,29}, {19,33}, {3,34}, {5,40}, {2,25}, {31,39}, {6,40}, {36,37}, {14,33}, {10,38}, {35,38}, {17,37}, {19,26}, {4,8}, {9,26}, {5,29}, {8,41}, {9,19}, {28,34}, {29,36}, {14,40}, {22,35}, {11,13}, {17,23}, {24,39}, {1,31}, {11,22}, {11,31}, {22,27}, {1,22}, {21,27}, {12,13}, {20,33}, {6,30}, {4,33}, {15,42}, {24,32}, {25,41}, {30,39}, {7,30}, {2,16}, {11,21}, {9,25}, {7,16}, {15,41}, {13,33}, {1,12}, {2,32}, {19,42}, {30,36}, {30,35}, {5,30}, {19,41}, {15,35}, {9,37}, {27,38}, {28,37}, {12,28}, {32,39}, {33,42}, {18,24}, {13,28}, {5,14}, {9,20}, {18,26}, {3,27}, {4,7}, {4,28}, {33,41}, {15,36}, {21,38}, {17,31}, {18,31}, {16,22}, {24,40}, {26,42}, {12,27}, {25,32}, {1,42}, {17,25}, {11,39}, {30,40}, {28,33}, {12,40}, {3,23}, {8,23}, {14,34}, {18,25}, {12,14}, {20,25}, {5,36}, {1,25}, {6,19}, {22,28}, {6,9}, {35,37}, {25,42}, {26,32}, {26,41}, {7,29}, {1,15}, {18,23}, {6,14}, {2,11}, {13,27}, {14,20}, {15,21}, {5,39}, {16,21}, {4,37}, {23,40}, {10,35}, {7,23}, {13,19}, {16,36}, {6,36}, {2,21}, {8,34}, {9,18}, {10,17}, {20,26}, {3,24}, {11,27}, {16,35}, {20,34}, {1,26}, {2,22}, {4,34}, {10,36}, {1,16}, {15,22}, {11,32}, {9,17}, {10,18}, {8,24}, {20,42}, {2,31}, {11,40}, {9,36}, {16,42}, {6,10}, {5,10}, {31,40}, {19,25}, {4,18}, {28,38}, {5,9}, {9,38}, {27,37}, {10,19}, {3,38}, {24,29}, {5,13}, {3,28}, {20,41}, {1,41}, {21,36}, {23,31}, {7,24}, {2,12}, {10,20}, {17,26}, {6,39}, {7,33}, {12,31}, {13,34}, {5,19}, {6,20}, {13,39}, {15,30}, {19,34}, {34,42}, {6,13}, {13,20}, {5,35}, {22,36}, {27,34}, {21,28}, {4,17}, {6,35}, {17,32}, {7,42}, {14,27}, {8,29}, {34,41}, {24,31}, {12,21}, {22,38}, {23,30} }; // ET42.77 // Non-bipartite Valency 12 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 1008 EdgePairs[42][77]:={ {3,33}, {16,41}, {10,24}, {38,42}, {13,32}, {25,31}, {11,36}, {17,36}, {7,15}, {29,40}, {8,12}, {33,39}, {25,39}, {32,41}, {6,17}, {32,35}, {1,13}, {12,22}, {30,33}, {7,38}, {3,9}, {39,41}, {16,31}, {3,6}, {4,29}, {24,27}, {32,37}, {2,15}, {4,19}, {4,31}, {1,19}, {12,42}, {28,32}, {5,20}, {3,37}, {2,26}, {14,31}, {25,30}, {17,24}, {16,25}, {11,14}, {7,36}, {21,22}, {17,21}, {8,25}, {27,33}, {24,36}, {12,34}, {1,30}, {5,32}, {16,23}, {13,29}, {12,37}, {9,11}, {16,29}, {35,41}, {23,32}, {6,21}, {3,34}, {14,23}, {1,17}, {1,7}, {4,22}, {10,38}, {27,28}, {35,38}, {3,14}, {14,21}, {12,17}, {9,26}, {19,30}, {12,20}, {5,11}, {2,5}, {2,38}, {26,29}, {8,14}, {14,30}, {14,40}, {22,35}, {6,8}, {22,41}, {9,41}, {24,39}, {1,31}, {10,41}, {23,34}, {27,40}, {2,35}, {15,27}, {20,33}, {6,30}, {23,26}, {5,23}, {10,29}, {21,26}, {9,34}, {15,42}, {25,41}, {37,40}, {28,41}, {2,20}, {14,16}, {29,34}, {30,39}, {30,42}, {8,17}, {18,30}, {11,21}, {23,37}, {23,42}, {7,16}, {2,32}, {1,12}, {6,33}, {11,23}, {30,35}, {6,24}, {11,30}, {5,7}, {28,37}, {12,28}, {12,25}, {33,42}, {36,40}, {29,38}, {26,38}, {27,36}, {8,35}, {15,20}, {4,13}, {18,27}, {3,27}, {14,37}, {21,31}, {10,13}, {26,34}, {31,36}, {18,33}, {3,10}, {8,37}, {5,28}, {21,38}, {9,22}, {7,31}, {24,40}, {26,42}, {5,41}, {25,35}, {17,28}, {20,29}, {9,13}, {22,25}, {8,32}, {33,34}, {1,42}, {4,9}, {28,36}, {13,24}, {11,39}, {8,40}, {20,39}, {18,19}, {1,39}, {20,25}, {5,36}, {3,21}, {1,25}, {22,28}, {26,32}, {36,39}, {12,15}, {6,14}, {22,31}, {2,11}, {16,34}, {5,39}, {14,25}, {19,32}, {3,16}, {4,37}, {6,42}, {11,26}, {13,26}, {15,18}, {4,40}, {10,35}, {7,23}, {13,19}, {9,18}, {2,29}, {10,27}, {20,34}, {4,34}, {15,22}, {18,22}, {29,31}, {15,33}, {16,20}, {8,24}, {13,41}, {6,38}, {20,24}, {2,40}, {11,40}, {9,33}, {6,10}, {15,38}, {31,40}, {4,18}, {15,28}, {9,39}, {27,37}, {10,19}, {1,4}, {24,29}, {4,12}, {3,28}, {8,20}, {7,27}, {7,10}, {21,36}, {3,41}, {18,40}, {2,8}, {17,26}, {5,15}, {17,42}, {19,35}, {13,39}, {13,17}, {34,42}, {2,18}, {19,23}, {7,19}, {21,28}, {24,33}, {6,35}, {17,32}, {9,21}, {18,35}, {7,42}, {19,37}, {19,27}, {31,38}, {11,18}, {34,37}, {1,36}, {22,38}, {23,30}, {10,16}, {5,16} }; // ET42.78 // Non-bipartite Valency 12 // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 1404285820600320000000 EdgePairs[42][78]:={ {24,34}, {11,40}, {10,37}, {25,37}, {12,22}, {25,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {30,40}, {30,41}, {15,27}, {5,15}, {24,32}, {24,36}, {8,23}, {10,39}, {26,37}, {2,18}, {16,28}, {5,32}, {1,35}, {29,39}, {13,27}, {14,29}, {6,14}, {2,33}, {6,32}, {10,42}, {3,18}, {2,34}, {26,38}, {19,31}, {1,17}, {4,16}, {4,13}, {8,37}, {26,39}, {12,20}, {12,38}, {7,41}, {23,31}, {1,13}, {13,30}, {12,42}, {23,36}, {11,39}, {2,17}, {12,40}, {10,20}, {17,26}, {15,30}, {2,15}, {12,23}, {27,41}, {16,25}, {24,31}, {20,35}, {1,36}, {6,18}, {12,37}, {8,38}, {13,26}, {5,34}, {3,17}, {20,36}, {2,36}, {8,22}, {22,34}, {18,29}, {6,34}, {9,39}, {8,42}, {18,26}, {9,20}, {30,38}, {8,19}, {1,18}, {15,28}, {6,17}, {4,18}, {26,42}, {27,39}, {28,40}, {27,40}, {12,24}, {1,31}, {3,31}, {3,13}, {11,22}, {7,37}, {11,42}, {5,35}, {28,42}, {3,36}, {17,29}, {26,41}, {7,19}, {4,32}, {2,13}, {14,28}, {11,21}, {6,36}, {16,29}, {3,16}, {11,23}, {10,38}, {6,16}, {13,25}, {21,31}, {8,24}, {8,41}, {27,37}, {9,38}, {5,14}, {10,19}, {12,41}, {9,22}, {9,19}, {20,31}, {17,28}, {4,33}, {11,24}, {25,41}, {18,25}, {6,13}, {22,31}, {23,35}, {4,17}, {3,32}, {14,27}, {2,16}, {13,29}, {17,30}, {10,22}, {28,37}, {16,30}, {7,23}, {4,34}, {29,38}, {6,31}, {21,32}, {16,26}, {1,16}, {4,14}, {24,35}, {4,15}, {9,41}, {25,38}, {7,39}, {23,34}, {4,36}, {1,32}, {7,24}, {9,24}, {5,31}, {17,25}, {19,34}, {7,40}, {20,32}, {25,42}, {29,41}, {10,40}, {10,21}, {9,21}, {18,30}, {29,37}, {29,42}, {9,23}, {7,21}, {28,39}, {3,33}, {14,26}, {23,32}, {19,33}, {3,34}, {18,28}, {15,29}, {25,39}, {2,31}, {18,27}, {21,33}, {1,33}, {16,27}, {3,14}, {10,41}, {14,30}, {21,34}, {11,19}, {12,39}, {21,35}, {22,33}, {20,33}, {19,35}, {3,15}, {11,41}, {7,22}, {1,14}, {1,34}, {7,42}, {19,36}, {4,35}, {19,32}, {1,15}, {14,25}, {20,34}, {11,37}, {23,33}, {5,18}, {5,16}, {10,24}, {11,20}, {5,17}, {17,27}, {13,28}, {28,38}, {7,20}, {7,38}, {22,35}, {21,36}, {27,42}, {9,40}, {26,40}, {8,20}, {5,13}, {10,23}, {15,26}, {22,36}, {8,39}, {22,32}, {9,42}, {5,36}, {24,33}, {6,35}, {12,19}, {28,41}, {30,39}, {30,42}, {30,37}, {2,32}, {12,21}, {6,33}, {2,14}, {15,25}, {5,33}, {11,38}, {9,37}, {27,38}, {29,40} }; // ET42.79 // Non-bipartite Valency 13 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 2184 EdgePairs[42][79]:={ {19,28}, {6,38}, {15,38}, {19,26}, {3,8}, {9,10}, {25,40}, {5,11}, {13,37}, {1,40}, {4,31}, {6,15}, {10,33}, {8,21}, {21,30}, {30,41}, {15,27}, {24,32}, {27,33}, {8,23}, {10,39}, {3,20}, {1,21}, {3,39}, {19,37}, {16,28}, {1,35}, {4,37}, {16,21}, {13,40}, {6,32}, {10,42}, {11,27}, {3,18}, {8,16}, {10,17}, {9,18}, {19,31}, {21,40}, {16,42}, {15,32}, {8,30}, {9,33}, {1,17}, {33,39}, {28,31}, {1,10}, {8,37}, {26,39}, {21,38}, {12,38}, {12,26}, {2,5}, {23,36}, {22,42}, {23,28}, {12,40}, {20,29}, {17,26}, {13,24}, {12,23}, {20,39}, {27,41}, {13,20}, {31,38}, {34,37}, {17,36}, {30,36}, {2,29}, {5,34}, {36,38}, {2,36}, {20,36}, {20,42}, {22,34}, {18,29}, {9,29}, {8,42}, {4,22}, {30,38}, {18,33}, {29,32}, {15,28}, {6,17}, {24,41}, {38,41}, {4,18}, {26,42}, {14,35}, {28,40}, {11,22}, {35,39}, {6,27}, {34,40}, {6,12}, {19,23}, {13,17}, {1,30}, {2,13}, {23,40}, {6,36}, {22,26}, {11,16}, {10,36}, {3,24}, {14,33}, {14,23}, {15,34}, {18,22}, {21,25}, {13,25}, {14,39}, {7,12}, {31,41}, {9,38}, {27,37}, {4,10}, {18,20}, {18,38}, {28,34}, {13,36}, {2,23}, {20,22}, {10,19}, {39,42}, {9,19}, {24,39}, {3,25}, {11,34}, {11,13}, {7,35}, {22,30}, {2,12}, {1,22}, {18,25}, {24,25}, {37,40}, {22,31}, {13,31}, {17,19}, {5,39}, {3,32}, {7,28}, {25,31}, {12,18}, {2,16}, {19,41}, {13,29}, {17,30}, {5,40}, {10,25}, {12,29}, {32,42}, {21,32}, {33,40}, {27,35}, {4,14}, {23,27}, {24,35}, {9,41}, {25,38}, {6,23}, {16,31}, {7,39}, {3,41}, {4,29}, {24,29}, {8,32}, {32,37}, {10,28}, {9,24}, {19,34}, {2,19}, {6,20}, {7,40}, {17,41}, {2,26}, {12,14}, {23,37}, {26,30}, {29,37}, {29,42}, {22,38}, {28,39}, {8,36}, {14,26}, {35,41}, {10,15}, {11,30}, {3,34}, {5,24}, {8,11}, {25,36}, {2,31}, {14,19}, {1,33}, {16,27}, {1,7}, {3,14}, {5,26}, {3,11}, {4,42}, {4,8}, {4,25}, {31,35}, {3,28}, {14,30}, {7,31}, {5,9}, {30,33}, {1,4}, {20,27}, {21,35}, {27,29}, {8,14}, {3,6}, {11,31}, {20,33}, {36,42}, {11,41}, {7,22}, {26,32}, {15,42}, {14,18}, {5,21}, {6,41}, {9,15}, {17,24}, {6,28}, {16,23}, {4,35}, {1,15}, {15,21}, {7,26}, {11,37}, {23,33}, {5,16}, {16,35}, {10,24}, {11,20}, {15,16}, {7,17}, {15,22}, {14,41}, {17,37}, {16,39}, {26,34}, {7,20}, {9,27}, {2,38}, {12,32}, {18,40}, {1,27}, {5,13}, {32,34}, {4,19}, {29,35}, {7,13}, {25,28}, {9,34}, {12,35}, {21,24}, {17,32}, {1,37}, {8,25}, {2,42}, {2,9}, {12,21}, {6,7}, {18,34}, {33,36}, {5,33}, {5,30} }; // ET42.80 // Bipartite(21,21) Valencies [14,14] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 196681931556913152000000 EdgePairs[42][80]:={ {15,33}, {19,28}, {6,38}, {11,40}, {10,37}, {15,38}, {9,32}, {5,38}, {5,22}, {11,25}, {4,28}, {3,26}, {8,26}, {13,37}, {1,40}, {16,22}, {14,38}, {13,39}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {21,30}, {14,31}, {15,27}, {21,41}, {3,23}, {8,23}, {10,39}, {16,37}, {3,39}, {19,37}, {20,37}, {16,28}, {5,32}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {13,40}, {6,32}, {17,35}, {11,35}, {11,29}, {10,42}, {6,29}, {19,40}, {20,38}, {2,34}, {20,26}, {19,31}, {2,25}, {4,24}, {16,42}, {18,32}, {15,32}, {4,30}, {9,33}, {8,37}, {5,41}, {21,38}, {12,38}, {12,26}, {13,30}, {7,27}, {19,22}, {12,42}, {6,39}, {7,33}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {18,35}, {16,25}, {13,42}, {20,35}, {9,35}, {1,36}, {19,42}, {16,34}, {18,39}, {8,38}, {6,24}, {2,29}, {5,34}, {14,32}, {16,40}, {8,22}, {18,29}, {9,36}, {9,29}, {9,39}, {18,26}, {4,22}, {18,36}, {18,33}, {3,38}, {5,28}, {20,41}, {14,35}, {1,42}, {12,24}, {1,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {5,35}, {14,34}, {3,36}, {17,29}, {20,25}, {1,30}, {19,27}, {14,28}, {6,36}, {3,30}, {11,23}, {3,24}, {10,36}, {14,23}, {13,25}, {19,30}, {8,41}, {9,38}, {9,26}, {18,38}, {3,29}, {17,31}, {13,36}, {2,23}, {20,22}, {15,23}, {12,41}, {20,31}, {19,24}, {11,34}, {17,28}, {21,42}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {10,31}, {13,22}, {1,25}, {13,31}, {9,30}, {3,32}, {7,28}, {8,34}, {10,22}, {5,40}, {10,30}, {16,30}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {11,32}, {15,24}, {21,32}, {3,42}, {14,37}, {14,40}, {9,41}, {16,31}, {6,23}, {7,39}, {3,41}, {4,36}, {15,39}, {21,39}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {7,40}, {2,41}, {17,41}, {5,23}, {20,32}, {2,26}, {18,41}, {10,40}, {18,30}, {2,28}, {8,29}, {9,23}, {3,33}, {16,36}, {14,26}, {19,33}, {19,39}, {4,27}, {15,29}, {2,22}, {18,24}, {2,31}, {18,27}, {1,33}, {20,28}, {21,33}, {12,36}, {16,27}, {19,25}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {7,31}, {12,33}, {12,39}, {17,34}, {21,35}, {11,31}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {15,42}, {1,34}, {7,42}, {21,27}, {6,41}, {21,29}, {17,40}, {20,23}, {19,36}, {18,23}, {6,42}, {13,33}, {14,25}, {20,34}, {11,37}, {11,28}, {10,24}, {10,27}, {10,34}, {16,33}, {8,35}, {2,40}, {14,41}, {17,37}, {16,39}, {13,28}, {1,28}, {16,24}, {3,27}, {9,27}, {2,38}, {12,32}, {15,36}, {21,36}, {8,28}, {20,40}, {1,27}, {5,25}, {17,23}, {15,26}, {14,22}, {9,42}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {21,24}, {21,26}, {1,37}, {8,25}, {18,42}, {2,32}, {6,33}, {11,26}, {11,38}, {21,23} }; // ET42.81 // Bipartite(7,35) Valencies [15,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 5040 EdgePairs[42][81]:={ {7,42}, {5,14}, {3,15}, {2,38}, {6,10}, {6,18}, {1,11}, {3,29}, {6,14}, {5,42}, {5,30}, {4,8}, {4,27}, {1,31}, {6,41}, {5,35}, {7,24}, {6,13}, {2,37}, {3,32}, {1,38}, {5,41}, {2,33}, {6,25}, {7,27}, {1,32}, {7,23}, {2,28}, {3,34}, {2,18}, {6,9}, {4,26}, {5,9}, {5,21}, {2,29}, {5,37}, {7,10}, {2,14}, {4,37}, {6,11}, {2,31}, {2,23}, {4,39}, {1,17}, {1,22}, {2,32}, {3,40}, {1,16}, {2,36}, {4,33}, {3,9}, {7,25}, {3,22}, {7,13}, {4,31}, {4,30}, {6,26}, {6,15}, {1,19}, {2,40}, {4,36}, {4,15}, {1,35}, {6,29}, {2,24}, {7,8}, {6,19}, {5,38}, {3,35}, {1,23}, {2,21}, {5,8}, {7,18}, {4,22}, {3,24}, {3,12}, {6,20}, {7,16}, {6,42}, {3,39}, {1,20}, {1,27}, {5,11}, {1,13}, {3,25}, {2,26}, {3,20}, {7,21}, {5,12}, {1,28}, {3,17}, {4,34}, {4,41}, {3,33}, {7,34}, {7,36}, {7,17}, {1,30}, {5,39}, {5,16}, {7,12}, {4,19}, {4,10}, {5,40}, {6,28} }; // ET42.82 // Bipartite(7,35) Valencies [15,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 60197437440000000 EdgePairs[42][82]:={ {1,15}, {4,35}, {7,42}, {2,38}, {4,42}, {6,10}, {4,14}, {1,11}, {6,14}, {3,38}, {6,36}, {6,17}, {4,40}, {5,34}, {1,25}, {2,37}, {3,32}, {5,41}, {1,9}, {2,33}, {7,27}, {1,32}, {7,23}, {5,13}, {3,10}, {3,34}, {3,31}, {2,19}, {5,26}, {4,26}, {6,22}, {1,29}, {4,12}, {3,18}, {3,41}, {7,28}, {5,33}, {3,11}, {2,10}, {2,31}, {2,23}, {7,41}, {4,39}, {1,36}, {3,13}, {2,16}, {1,22}, {1,16}, {6,21}, {4,33}, {2,17}, {4,28}, {5,19}, {5,15}, {6,8}, {7,20}, {7,13}, {5,29}, {7,14}, {3,27}, {6,15}, {2,40}, {4,21}, {7,30}, {4,25}, {2,9}, {6,29}, {7,35}, {2,24}, {6,31}, {4,11}, {5,22}, {1,23}, {5,27}, {5,8}, {1,39}, {6,38}, {2,12}, {5,20}, {5,36}, {3,24}, {7,16}, {7,9}, {4,32}, {6,42}, {3,39}, {1,37}, {4,18}, {3,25}, {2,26}, {7,37}, {3,20}, {7,21}, {5,12}, {3,17}, {6,35}, {6,24}, {7,34}, {1,8}, {1,30}, {2,30}, {1,18}, {4,19}, {5,40}, {6,28} }; // ET42.83 // Bipartite(12,30) Valencies [15,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 92876046336000000 EdgePairs[42][83]:={ {11,17}, {3,33}, {10,25}, {11,20}, {6,32}, {6,16}, {12,29}, {7,15}, {11,35}, {4,24}, {4,16}, {10,37}, {4,30}, {8,30}, {1,13}, {12,22}, {7,38}, {8,42}, {8,28}, {4,29}, {1,27}, {3,15}, {7,41}, {10,26}, {2,19}, {12,41}, {1,19}, {12,42}, {3,35}, {2,26}, {11,41}, {1,21}, {11,14}, {12,35}, {2,28}, {12,34}, {2,14}, {1,30}, {4,23}, {10,22}, {6,22}, {3,17}, {8,16}, {2,25}, {11,38}, {11,33}, {6,31}, {6,40}, {2,34}, {4,22}, {10,38}, {1,18}, {3,14}, {7,20}, {12,17}, {9,27}, {12,36}, {4,41}, {8,41}, {2,38}, {9,19}, {2,37}, {7,39}, {4,42}, {5,25}, {11,15}, {7,32}, {1,31}, {10,28}, {12,16}, {10,31}, {3,20}, {9,42}, {2,13}, {2,20}, {10,40}, {8,17}, {2,16}, {3,39}, {3,32}, {11,21}, {4,35}, {9,25}, {8,36}, {2,32}, {7,26}, {5,18}, {11,23}, {11,29}, {5,30}, {7,17}, {5,24}, {9,37}, {12,28}, {8,22}, {8,35}, {7,14}, {3,27}, {4,28}, {1,33}, {10,13}, {3,29}, {3,26}, {5,42}, {4,36}, {9,13}, {1,42}, {1,24}, {12,23}, {5,31}, {11,39}, {6,26}, {8,40}, {12,40}, {12,30}, {3,23}, {8,23}, {1,39}, {10,32}, {5,36}, {3,21}, {1,25}, {6,19}, {7,29}, {1,15}, {6,28}, {6,14}, {9,30}, {1,37}, {5,39}, {11,26}, {4,40}, {7,23}, {8,34}, {5,33}, {9,18}, {11,27}, {2,22}, {4,34}, {10,34}, {11,32}, {8,24}, {6,25}, {6,38}, {2,40}, {2,31}, {9,33}, {9,36}, {6,34}, {5,27}, {8,18}, {4,18}, {9,39}, {10,19}, {3,38}, {5,13}, {12,24}, {7,27}, {3,41}, {9,24}, {10,20}, {5,15}, {7,33}, {6,37}, {10,14}, {5,19}, {6,20}, {7,35}, {5,21}, {9,15}, {6,13}, {9,31}, {5,37}, {4,17}, {9,21}, {7,21}, {8,29}, {12,18}, {1,36}, {10,16} }; // ET42.84 // Bipartite(12,30) Valencies [15,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 232190115840 EdgePairs[42][84]:={ {3,33}, {10,24}, {2,24}, {9,28}, {6,32}, {11,36}, {4,27}, {7,15}, {4,24}, {3,40}, {10,37}, {8,30}, {1,13}, {5,38}, {12,22}, {12,32}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {7,22}, {4,31}, {2,19}, {12,41}, {10,33}, {2,27}, {12,42}, {3,35}, {2,26}, {8,39}, {11,41}, {12,35}, {7,36}, {12,34}, {2,14}, {5,32}, {9,35}, {4,23}, {8,27}, {6,22}, {3,18}, {11,28}, {8,16}, {4,38}, {6,21}, {11,38}, {6,40}, {6,31}, {2,34}, {1,17}, {2,36}, {5,22}, {10,38}, {9,29}, {8,19}, {12,20}, {5,29}, {4,41}, {9,19}, {2,37}, {8,14}, {2,39}, {7,32}, {10,41}, {11,22}, {7,13}, {7,25}, {10,28}, {11,31}, {1,22}, {6,30}, {4,33}, {4,21}, {10,31}, {3,20}, {10,21}, {2,20}, {8,17}, {2,16}, {3,39}, {11,21}, {9,25}, {7,16}, {8,36}, {7,26}, {5,18}, {1,23}, {6,24}, {11,29}, {7,17}, {12,25}, {9,20}, {4,13}, {4,28}, {1,33}, {10,13}, {3,29}, {8,37}, {5,28}, {8,26}, {5,42}, {6,15}, {5,41}, {2,17}, {9,13}, {9,40}, {1,42}, {3,19}, {5,31}, {11,39}, {8,40}, {12,40}, {12,30}, {3,23}, {12,14}, {5,36}, {1,25}, {6,41}, {1,15}, {12,15}, {6,14}, {9,30}, {1,35}, {1,37}, {5,39}, {4,37}, {6,42}, {11,26}, {11,16}, {7,23}, {3,30}, {8,34}, {9,18}, {10,17}, {2,29}, {10,27}, {1,26}, {4,34}, {1,16}, {4,14}, {10,34}, {11,32}, {10,18}, {8,24}, {6,25}, {2,40}, {9,33}, {6,34}, {5,26}, {4,18}, {9,39}, {9,38}, {11,19}, {3,38}, {3,28}, {8,20}, {12,24}, {7,27}, {7,33}, {12,31}, {10,14}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {9,15}, {7,37}, {4,17}, {6,35}, {11,42}, {7,42}, {9,23}, {8,29}, {11,18}, {1,36}, {12,21}, {5,16} }; // ET42.85 // Bipartite(12,30) Valencies [15,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7255941120 EdgePairs[42][85]:={ {10,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {3,40}, {4,30}, {2,23}, {1,13}, {5,38}, {12,22}, {12,32}, {4,29}, {8,33}, {7,41}, {1,40}, {10,26}, {2,15}, {4,19}, {7,22}, {2,27}, {12,42}, {8,39}, {1,21}, {11,41}, {11,14}, {12,35}, {7,36}, {8,25}, {2,28}, {1,30}, {5,32}, {8,15}, {9,35}, {8,31}, {8,27}, {12,37}, {2,42}, {10,22}, {6,22}, {11,28}, {10,30}, {6,21}, {3,34}, {2,25}, {11,38}, {6,31}, {11,33}, {5,22}, {8,19}, {10,38}, {3,14}, {12,17}, {12,20}, {12,36}, {5,29}, {8,41}, {2,38}, {2,37}, {7,39}, {7,32}, {11,13}, {1,31}, {9,14}, {10,28}, {11,31}, {2,35}, {12,16}, {3,20}, {9,34}, {2,13}, {6,18}, {10,40}, {8,17}, {3,39}, {11,21}, {4,35}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {5,18}, {1,23}, {11,23}, {11,29}, {7,17}, {5,24}, {12,25}, {8,13}, {8,35}, {10,42}, {5,14}, {9,20}, {4,15}, {1,33}, {3,29}, {6,23}, {3,26}, {8,37}, {5,28}, {5,42}, {12,26}, {7,31}, {2,17}, {9,13}, {12,27}, {9,40}, {8,21}, {3,19}, {11,24}, {11,39}, {6,26}, {12,40}, {12,30}, {8,23}, {10,32}, {3,21}, {1,25}, {7,29}, {6,41}, {1,15}, {6,28}, {12,15}, {9,30}, {1,35}, {5,39}, {3,16}, {4,37}, {6,42}, {4,40}, {6,36}, {3,30}, {9,18}, {3,24}, {1,26}, {2,22}, {4,34}, {10,36}, {1,16}, {4,14}, {10,34}, {10,18}, {6,38}, {9,33}, {5,27}, {9,38}, {11,19}, {4,25}, {4,20}, {7,27}, {1,41}, {3,41}, {3,31}, {9,24}, {10,20}, {10,14}, {11,34}, {5,19}, {9,15}, {6,13}, {7,37}, {2,18}, {5,37}, {7,19}, {4,17}, {3,36}, {4,39}, {7,42}, {9,23}, {7,21}, {8,29}, {11,18}, {1,36}, {10,16} }; // ET42.86 // Bipartite(21,21) Valencies [15,15] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1410877440 EdgePairs[42][86]:={ {15,33}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {17,42}, {13,39}, {2,35}, {8,40}, {3,35}, {21,30}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {16,37}, {3,39}, {20,37}, {16,28}, {21,28}, {5,32}, {7,30}, {15,41}, {8,31}, {4,40}, {21,22}, {13,27}, {14,29}, {2,33}, {17,35}, {6,32}, {10,42}, {6,29}, {20,26}, {12,28}, {19,31}, {4,24}, {21,40}, {16,42}, {18,32}, {4,30}, {9,33}, {8,37}, {17,39}, {21,38}, {12,38}, {12,26}, {13,30}, {19,22}, {12,42}, {6,39}, {11,39}, {7,33}, {12,31}, {20,29}, {1,24}, {12,23}, {20,39}, {20,35}, {9,35}, {1,29}, {19,42}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {17,36}, {1,38}, {1,26}, {13,41}, {20,36}, {16,40}, {8,22}, {6,34}, {9,39}, {8,42}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {5,28}, {20,41}, {2,39}, {14,35}, {1,42}, {12,24}, {19,38}, {1,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {19,23}, {17,29}, {20,25}, {4,32}, {19,27}, {14,28}, {6,36}, {11,36}, {2,24}, {11,23}, {10,36}, {14,33}, {15,37}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {21,25}, {14,39}, {21,31}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {21,37}, {3,29}, {13,36}, {1,41}, {15,23}, {20,31}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {9,31}, {10,29}, {18,25}, {1,25}, {20,30}, {13,31}, {9,30}, {3,32}, {16,41}, {7,28}, {13,29}, {8,34}, {10,22}, {16,30}, {4,34}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {16,26}, {12,25}, {15,40}, {3,42}, {3,22}, {14,37}, {14,40}, {9,41}, {16,31}, {6,23}, {7,39}, {3,41}, {4,36}, {21,39}, {19,29}, {6,37}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {7,40}, {2,41}, {17,41}, {5,23}, {20,32}, {2,26}, {18,41}, {10,40}, {7,29}, {18,30}, {2,28}, {8,29}, {8,27}, {13,32}, {11,30}, {9,28}, {3,34}, {18,28}, {5,24}, {15,29}, {18,24}, {2,31}, {16,38}, {1,33}, {21,33}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {21,34}, {7,31}, {8,33}, {17,34}, {20,27}, {21,35}, {20,33}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {15,42}, {1,34}, {13,35}, {6,41}, {21,29}, {17,40}, {20,23}, {19,36}, {18,23}, {19,32}, {13,33}, {14,25}, {20,34}, {11,28}, {1,23}, {16,35}, {10,27}, {10,34}, {16,33}, {3,40}, {17,27}, {13,23}, {2,40}, {15,22}, {4,26}, {17,37}, {16,39}, {16,24}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {21,36}, {15,31}, {18,40}, {9,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {14,22}, {9,42}, {5,36}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {21,24}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {2,32}, {6,33}, {18,34}, {11,26}, {15,25}, {5,30}, {9,37} }; // ET42.87 // Bipartite(10,32) Valencies [16,5] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 3840 EdgePairs[42][87]:={ {1,11}, {2,24}, {10,25}, {2,33}, {6,32}, {7,15}, {4,24}, {3,22}, {4,16}, {10,37}, {8,30}, {1,13}, {5,38}, {8,42}, {8,28}, {3,13}, {8,33}, {3,25}, {3,15}, {4,19}, {7,22}, {4,31}, {2,19}, {1,19}, {2,27}, {5,20}, {8,39}, {7,34}, {7,36}, {2,41}, {2,14}, {1,30}, {5,32}, {9,11}, {2,42}, {10,22}, {6,22}, {3,18}, {10,30}, {3,17}, {4,38}, {6,21}, {7,12}, {6,40}, {6,31}, {1,17}, {9,29}, {7,11}, {7,20}, {3,14}, {9,26}, {9,27}, {5,11}, {5,29}, {4,41}, {8,41}, {2,38}, {2,37}, {7,39}, {4,42}, {7,32}, {3,12}, {10,41}, {9,14}, {7,25}, {2,35}, {5,23}, {3,20}, {10,31}, {9,34}, {2,13}, {6,18}, {10,40}, {1,29}, {7,30}, {2,16}, {4,35}, {8,36}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {7,17}, {5,24}, {9,37}, {8,35}, {10,42}, {4,15}, {1,28}, {3,11}, {3,27}, {4,28}, {10,12}, {8,37}, {5,28}, {8,26}, {9,22}, {4,36}, {9,13}, {9,40}, {8,32}, {3,19}, {6,27}, {6,26}, {8,40}, {8,23}, {3,21}, {9,12}, {1,15}, {9,30}, {10,39}, {1,35}, {1,37}, {7,28}, {3,16}, {6,42}, {7,23}, {2,21}, {8,34}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {8,38}, {10,27}, {1,16}, {10,36}, {10,34}, {6,25}, {6,38}, {2,40}, {2,31}, {9,33}, {6,34}, {5,26}, {4,25}, {10,19}, {4,20}, {5,13}, {1,41}, {3,31}, {1,14}, {6,39}, {5,15}, {10,14}, {6,20}, {5,21}, {5,35}, {4,17}, {9,21}, {4,39}, {9,23}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET42.88 // Bipartite(10,32) Valencies [16,5] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 125829120 EdgePairs[42][88]:={ {1,11}, {3,33}, {2,24}, {1,20}, {10,25}, {9,28}, {2,33}, {6,16}, {6,32}, {7,15}, {5,34}, {4,26}, {4,30}, {6,17}, {1,13}, {8,42}, {4,29}, {3,13}, {1,27}, {3,15}, {10,23}, {1,40}, {10,26}, {4,31}, {10,33}, {3,35}, {5,20}, {8,39}, {7,34}, {7,36}, {8,25}, {2,41}, {2,28}, {1,30}, {5,32}, {9,35}, {9,11}, {10,22}, {6,22}, {10,30}, {3,17}, {6,21}, {2,25}, {5,40}, {6,31}, {10,38}, {7,11}, {7,20}, {3,14}, {9,32}, {9,27}, {5,11}, {5,29}, {4,41}, {8,41}, {2,38}, {9,19}, {2,37}, {7,39}, {4,42}, {3,12}, {10,41}, {10,28}, {4,33}, {4,21}, {9,34}, {2,13}, {6,18}, {1,29}, {7,30}, {2,16}, {3,32}, {8,36}, {1,12}, {6,33}, {2,32}, {7,26}, {5,18}, {1,23}, {5,24}, {8,22}, {10,42}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {10,12}, {3,29}, {8,37}, {8,26}, {9,22}, {7,31}, {6,15}, {2,17}, {4,36}, {9,40}, {8,21}, {3,19}, {1,24}, {5,31}, {6,26}, {8,40}, {8,23}, {1,39}, {5,36}, {1,25}, {6,19}, {9,12}, {10,39}, {3,16}, {4,37}, {6,42}, {10,35}, {7,23}, {2,21}, {3,30}, {8,34}, {9,18}, {10,17}, {2,29}, {8,38}, {2,22}, {4,14}, {8,24}, {6,38}, {2,40}, {6,34}, {5,27}, {8,18}, {9,39}, {9,38}, {4,25}, {10,19}, {4,20}, {5,13}, {8,20}, {3,28}, {7,27}, {1,41}, {3,31}, {2,12}, {1,14}, {9,24}, {5,15}, {6,37}, {10,14}, {7,35}, {5,21}, {5,37}, {7,19}, {4,17}, {6,35}, {9,16}, {7,42}, {9,23}, {1,36}, {7,18}, {5,16} }; // ET42.89 // Bipartite(14,28) Valencies [16,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 98627481501696 EdgePairs[42][89]:={ {3,33}, {10,24}, {11,20}, {13,32}, {2,33}, {6,16}, {6,32}, {11,36}, {4,27}, {12,29}, {13,21}, {7,15}, {11,35}, {3,40}, {11,25}, {6,17}, {2,23}, {12,22}, {7,38}, {4,29}, {1,32}, {8,33}, {7,41}, {1,40}, {10,26}, {14,38}, {7,22}, {2,19}, {1,19}, {2,27}, {10,33}, {12,42}, {3,35}, {13,35}, {2,26}, {14,31}, {8,39}, {7,34}, {11,41}, {12,35}, {7,36}, {8,25}, {2,41}, {8,15}, {8,31}, {12,37}, {13,16}, {11,28}, {3,17}, {6,21}, {3,34}, {5,40}, {2,25}, {14,23}, {6,31}, {1,38}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {10,38}, {1,18}, {7,20}, {9,32}, {14,36}, {9,26}, {9,27}, {12,36}, {5,29}, {4,41}, {9,19}, {2,37}, {14,30}, {4,42}, {9,41}, {2,39}, {11,15}, {1,31}, {10,41}, {11,22}, {10,28}, {14,24}, {1,22}, {6,30}, {12,16}, {5,23}, {4,21}, {3,20}, {10,31}, {9,34}, {10,21}, {2,20}, {14,16}, {6,18}, {13,18}, {10,40}, {1,29}, {7,30}, {8,17}, {2,16}, {13,31}, {11,21}, {4,35}, {9,25}, {7,16}, {8,36}, {2,32}, {14,15}, {6,24}, {11,29}, {5,30}, {7,17}, {9,37}, {13,23}, {12,28}, {8,22}, {13,25}, {10,42}, {13,28}, {9,20}, {4,15}, {14,41}, {3,27}, {14,37}, {4,28}, {1,33}, {6,23}, {3,26}, {5,28}, {8,26}, {5,42}, {12,26}, {7,31}, {12,33}, {13,30}, {4,36}, {9,40}, {14,17}, {8,32}, {3,19}, {1,24}, {12,23}, {14,22}, {13,24}, {11,39}, {8,40}, {12,19}, {12,40}, {12,30}, {14,34}, {1,39}, {5,36}, {3,21}, {1,25}, {7,29}, {1,15}, {6,28}, {12,15}, {9,30}, {13,42}, {14,20}, {6,42}, {10,35}, {7,23}, {5,33}, {9,18}, {10,17}, {3,24}, {11,27}, {8,38}, {10,27}, {1,26}, {4,34}, {10,34}, {11,32}, {8,24}, {6,25}, {6,38}, {2,40}, {9,33}, {5,26}, {8,18}, {3,42}, {4,18}, {9,39}, {13,38}, {4,25}, {10,19}, {3,38}, {4,20}, {3,28}, {7,27}, {13,37}, {3,41}, {7,24}, {3,31}, {10,20}, {6,39}, {5,15}, {6,37}, {11,34}, {5,19}, {13,39}, {5,21}, {2,30}, {13,17}, {7,37}, {5,35}, {2,18}, {5,37}, {6,35}, {9,16}, {11,42}, {4,39}, {9,23}, {14,27}, {8,29}, {4,32}, {11,18}, {1,36}, {12,21}, {14,29}, {5,16} }; // ET42.90 // Bipartite(18,24) Valencies [16,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 146794677780086784000000 EdgePairs[42][90]:={ {15,33}, {10,37}, {14,36}, {6,25}, {5,38}, {4,28}, {12,22}, {8,26}, {13,37}, {1,40}, {16,22}, {14,38}, {17,42}, {2,35}, {17,33}, {4,31}, {8,21}, {3,19}, {15,27}, {1,19}, {8,23}, {3,21}, {16,37}, {3,39}, {16,28}, {5,32}, {1,35}, {4,37}, {4,40}, {14,29}, {13,40}, {2,33}, {17,35}, {4,38}, {11,35}, {11,29}, {11,27}, {1,20}, {12,28}, {8,30}, {9,33}, {5,41}, {17,39}, {7,41}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {12,31}, {12,40}, {10,20}, {17,26}, {15,30}, {13,20}, {16,25}, {15,19}, {1,29}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {1,38}, {13,19}, {14,32}, {1,26}, {2,36}, {13,41}, {16,40}, {9,36}, {6,34}, {9,39}, {8,42}, {4,22}, {18,33}, {18,36}, {5,27}, {15,28}, {2,39}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {17,29}, {18,19}, {7,19}, {4,32}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {8,24}, {4,41}, {8,41}, {14,21}, {1,41}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {7,35}, {2,27}, {12,30}, {6,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {14,27}, {16,41}, {7,28}, {13,29}, {9,25}, {17,30}, {10,22}, {7,23}, {6,22}, {4,34}, {10,25}, {17,38}, {6,31}, {11,32}, {15,24}, {16,26}, {12,25}, {15,40}, {3,42}, {3,22}, {13,38}, {18,31}, {16,31}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {10,28}, {9,24}, {7,40}, {2,41}, {17,41}, {5,23}, {5,20}, {2,26}, {10,40}, {18,21}, {9,21}, {7,29}, {18,30}, {8,29}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {18,28}, {5,24}, {16,20}, {18,24}, {16,38}, {18,27}, {12,36}, {5,26}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {8,33}, {12,39}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {15,42}, {1,34}, {13,35}, {5,21}, {17,24}, {12,34}, {17,21}, {6,28}, {16,23}, {6,42}, {4,35}, {14,20}, {15,21}, {7,26}, {1,23}, {16,35}, {11,20}, {14,42}, {10,34}, {3,40}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {14,41}, {4,26}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {15,36}, {15,31}, {18,40}, {9,40}, {4,20}, {8,20}, {17,23}, {10,23}, {4,19}, {8,39}, {3,37}, {9,42}, {16,19}, {5,36}, {9,34}, {10,32}, {17,32}, {12,19}, {1,37}, {2,42}, {18,42}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {15,25}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.91 // Bipartite(18,24) Valencies [16,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7044820107264 EdgePairs[42][91]:={ {13,21}, {15,33}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {11,25}, {4,28}, {3,26}, {8,26}, {13,37}, {1,40}, {16,22}, {14,38}, {13,39}, {17,42}, {2,35}, {17,33}, {4,31}, {3,35}, {8,21}, {3,19}, {15,27}, {1,19}, {3,23}, {3,20}, {16,28}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {4,38}, {11,35}, {11,29}, {1,20}, {2,34}, {2,25}, {16,42}, {18,32}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {12,38}, {7,41}, {12,26}, {7,27}, {12,42}, {6,39}, {10,26}, {17,20}, {7,33}, {12,31}, {10,20}, {17,26}, {15,30}, {12,23}, {13,20}, {18,35}, {9,35}, {15,19}, {1,29}, {12,37}, {16,34}, {10,35}, {18,39}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {13,19}, {14,32}, {1,26}, {2,36}, {16,40}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {3,38}, {5,27}, {15,28}, {5,28}, {14,35}, {12,24}, {1,31}, {3,31}, {11,22}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {4,32}, {14,28}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {13,25}, {14,39}, {8,24}, {9,38}, {14,21}, {9,26}, {18,20}, {18,38}, {3,29}, {17,31}, {1,41}, {2,23}, {10,19}, {12,41}, {3,25}, {11,34}, {7,35}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {10,29}, {13,22}, {1,25}, {6,19}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {16,41}, {7,28}, {17,30}, {10,22}, {5,40}, {16,30}, {7,23}, {6,22}, {4,34}, {10,25}, {17,38}, {12,29}, {6,31}, {15,24}, {12,25}, {15,40}, {3,42}, {13,38}, {14,40}, {9,41}, {7,39}, {3,41}, {15,39}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {17,25}, {2,19}, {7,40}, {2,41}, {5,23}, {5,20}, {18,41}, {10,40}, {18,21}, {9,21}, {7,29}, {18,30}, {2,28}, {9,23}, {7,21}, {8,36}, {8,27}, {16,36}, {13,32}, {14,26}, {11,30}, {4,27}, {2,22}, {18,24}, {2,31}, {18,27}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {10,41}, {4,25}, {11,19}, {8,33}, {11,31}, {13,34}, {11,41}, {7,22}, {15,42}, {1,34}, {5,21}, {7,42}, {17,24}, {17,21}, {6,28}, {16,23}, {6,42}, {18,23}, {13,33}, {14,20}, {15,21}, {11,37}, {11,28}, {1,23}, {16,35}, {10,34}, {16,33}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {9,27}, {12,32}, {15,36}, {15,31}, {4,20}, {8,20}, {10,23}, {4,19}, {14,22}, {8,39}, {3,37}, {9,42}, {10,32}, {4,39}, {12,35}, {7,36}, {17,32}, {12,19}, {1,37}, {8,25}, {2,42}, {18,42}, {6,33}, {15,25}, {5,33}, {6,40} }; // ET42.92 // Bipartite(18,24) Valencies [16,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 905969664 EdgePairs[42][92]:={ {13,21}, {6,38}, {15,38}, {9,32}, {5,38}, {5,22}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {16,22}, {14,38}, {13,39}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {15,27}, {1,19}, {3,23}, {8,23}, {1,21}, {3,39}, {16,37}, {5,32}, {1,35}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {16,21}, {13,40}, {2,33}, {6,32}, {17,35}, {11,29}, {10,42}, {6,29}, {2,34}, {2,25}, {4,24}, {18,32}, {15,32}, {4,30}, {8,37}, {17,39}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {7,33}, {12,31}, {17,26}, {1,24}, {13,24}, {12,23}, {13,20}, {18,35}, {16,25}, {13,42}, {9,35}, {1,36}, {15,19}, {1,29}, {12,37}, {16,34}, {10,35}, {8,38}, {6,24}, {2,29}, {5,34}, {13,19}, {14,32}, {18,29}, {9,36}, {6,34}, {9,29}, {9,20}, {18,26}, {18,36}, {8,19}, {3,38}, {5,27}, {15,28}, {5,28}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {3,30}, {3,24}, {10,36}, {14,33}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,41}, {9,38}, {14,21}, {9,26}, {18,20}, {18,38}, {17,31}, {13,36}, {1,41}, {10,19}, {3,25}, {11,34}, {17,28}, {7,35}, {12,30}, {4,33}, {1,22}, {7,34}, {10,31}, {10,29}, {18,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {14,27}, {16,41}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {17,38}, {6,31}, {11,32}, {15,24}, {12,25}, {15,40}, {3,42}, {3,22}, {14,40}, {9,41}, {7,39}, {4,36}, {15,39}, {7,24}, {10,28}, {9,24}, {17,25}, {2,19}, {6,20}, {2,41}, {17,41}, {5,23}, {5,20}, {2,26}, {18,41}, {10,40}, {10,21}, {7,29}, {18,30}, {8,29}, {9,23}, {7,21}, {8,27}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {15,29}, {2,22}, {16,20}, {18,24}, {2,31}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {4,42}, {10,41}, {4,25}, {14,30}, {11,19}, {8,33}, {12,39}, {11,31}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {5,21}, {6,41}, {17,40}, {12,34}, {17,21}, {6,28}, {16,23}, {18,23}, {13,33}, {14,20}, {11,37}, {1,23}, {16,35}, {10,24}, {14,42}, {11,20}, {10,34}, {16,33}, {8,35}, {17,27}, {15,22}, {15,20}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {5,42}, {2,38}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {4,20}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {8,39}, {3,37}, {9,42}, {4,39}, {12,35}, {7,36}, {12,19}, {8,25}, {2,42}, {18,42}, {16,32}, {2,32}, {11,26}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.93 // Bipartite(21,21) Valencies [16,16] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 241920 EdgePairs[42][93]:={ {15,33}, {6,38}, {19,28}, {11,40}, {15,38}, {14,36}, {9,32}, {6,25}, {5,22}, {4,28}, {12,22}, {3,26}, {8,26}, {1,40}, {16,22}, {14,38}, {13,39}, {17,42}, {2,35}, {8,40}, {3,35}, {10,33}, {14,31}, {15,27}, {21,41}, {3,23}, {8,23}, {10,39}, {16,37}, {19,37}, {21,28}, {5,32}, {1,35}, {8,31}, {4,40}, {4,37}, {21,22}, {13,27}, {14,29}, {11,35}, {6,29}, {11,27}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {21,40}, {16,42}, {18,32}, {15,32}, {8,30}, {9,33}, {20,24}, {17,39}, {21,38}, {12,38}, {7,41}, {12,26}, {13,30}, {19,22}, {12,42}, {6,39}, {11,39}, {10,26}, {7,33}, {17,26}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {13,42}, {20,35}, {12,37}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {20,36}, {16,40}, {20,42}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {4,22}, {18,33}, {18,36}, {5,27}, {15,28}, {5,28}, {20,41}, {14,35}, {1,42}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {3,36}, {19,23}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {14,33}, {15,37}, {14,23}, {11,33}, {13,25}, {21,25}, {21,31}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {18,38}, {17,31}, {13,36}, {1,41}, {20,22}, {15,23}, {12,41}, {3,25}, {19,24}, {11,34}, {17,28}, {21,42}, {7,35}, {2,27}, {12,30}, {1,22}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {16,41}, {7,28}, {19,41}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {16,30}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {21,32}, {16,26}, {15,40}, {3,42}, {14,37}, {13,38}, {14,40}, {9,41}, {16,31}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {5,31}, {17,22}, {17,25}, {19,34}, {2,41}, {2,26}, {18,41}, {10,40}, {7,29}, {18,30}, {8,29}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {19,39}, {9,28}, {3,34}, {4,27}, {5,24}, {15,29}, {2,22}, {18,24}, {2,31}, {1,33}, {20,28}, {21,33}, {16,27}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {21,34}, {7,31}, {12,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {13,35}, {7,42}, {21,27}, {21,29}, {17,24}, {17,40}, {12,34}, {19,36}, {6,28}, {16,23}, {6,42}, {18,23}, {4,35}, {13,33}, {20,34}, {7,26}, {11,37}, {1,23}, {10,24}, {14,42}, {10,34}, {16,33}, {13,23}, {8,35}, {2,40}, {15,22}, {14,41}, {4,26}, {16,39}, {17,37}, {1,28}, {16,24}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {21,36}, {8,28}, {18,40}, {9,40}, {20,40}, {1,27}, {17,23}, {10,23}, {15,26}, {3,37}, {14,22}, {8,39}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {6,35}, {17,32}, {21,24}, {1,37}, {2,42}, {18,42}, {6,33}, {2,32}, {18,34}, {11,26}, {15,25}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40}, {21,23} }; // ET42.94 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 704643072 EdgePairs[42][94]:={ {13,21}, {6,38}, {15,38}, {31,39}, {14,36}, {5,7}, {5,38}, {9,17}, {10,18}, {3,8}, {31,40}, {3,26}, {16,22}, {13,39}, {17,33}, {4,31}, {8,40}, {11,15}, {10,33}, {8,21}, {21,30}, {3,19}, {30,40}, {21,41}, {24,36}, {8,23}, {12,16}, {10,39}, {3,20}, {1,21}, {36,39}, {16,37}, {3,39}, {29,39}, {4,40}, {13,27}, {6,14}, {16,21}, {24,28}, {13,40}, {11,35}, {1,12}, {6,29}, {11,27}, {3,18}, {8,16}, {10,17}, {9,18}, {12,28}, {2,25}, {18,32}, {23,38}, {9,33}, {1,9}, {4,16}, {28,31}, {1,10}, {12,20}, {12,38}, {1,13}, {7,27}, {2,10}, {12,42}, {23,36}, {25,34}, {10,26}, {17,20}, {22,42}, {7,33}, {12,31}, {20,29}, {23,28}, {10,20}, {1,24}, {15,30}, {5,37}, {27,32}, {27,41}, {26,35}, {16,25}, {13,42}, {20,35}, {19,42}, {12,37}, {24,26}, {34,37}, {29,31}, {5,34}, {1,38}, {1,26}, {3,17}, {20,36}, {13,41}, {20,42}, {7,15}, {8,22}, {26,36}, {32,39}, {22,34}, {24,37}, {6,34}, {9,29}, {9,39}, {9,20}, {30,38}, {18,33}, {29,32}, {5,27}, {5,28}, {20,41}, {4,7}, {4,18}, {24,40}, {26,42}, {14,35}, {1,31}, {3,31}, {12,27}, {25,33}, {9,13}, {35,39}, {6,27}, {11,42}, {5,35}, {30,31}, {28,42}, {26,41}, {18,19}, {4,32}, {2,13}, {12,15}, {8,15}, {14,28}, {6,36}, {23,39}, {23,40}, {16,29}, {11,36}, {3,16}, {2,24}, {11,16}, {15,37}, {33,42}, {14,39}, {21,31}, {19,30}, {8,24}, {4,41}, {14,21}, {18,20}, {9,26}, {18,38}, {5,14}, {32,40}, {17,31}, {13,36}, {2,23}, {10,13}, {22,29}, {10,19}, {12,41}, {9,19}, {24,39}, {3,25}, {17,28}, {21,42}, {6,8}, {22,30}, {6,30}, {2,12}, {1,22}, {7,34}, {5,19}, {25,41}, {10,29}, {24,25}, {33,37}, {13,22}, {6,13}, {1,25}, {22,31}, {23,35}, {20,30}, {6,19}, {4,17}, {17,19}, {9,30}, {24,38}, {3,32}, {14,27}, {7,28}, {19,41}, {8,34}, {9,25}, {10,30}, {33,38}, {16,30}, {7,23}, {10,25}, {15,35}, {17,38}, {29,38}, {11,32}, {21,32}, {3,7}, {16,26}, {3,42}, {5,8}, {23,27}, {24,35}, {4,15}, {18,31}, {14,40}, {7,39}, {3,41}, {34,38}, {22,41}, {1,32}, {30,32}, {19,29}, {28,32}, {6,37}, {24,27}, {7,24}, {6,20}, {7,40}, {34,42}, {5,20}, {2,26}, {25,42}, {10,40}, {23,37}, {29,37}, {7,21}, {34,41}, {8,27}, {2,11}, {16,36}, {2,21}, {1,11}, {18,28}, {15,29}, {2,22}, {36,40}, {18,24}, {25,36}, {2,31}, {16,38}, {18,27}, {21,33}, {12,36}, {33,41}, {2,37}, {4,42}, {4,8}, {5,29}, {4,25}, {21,34}, {11,19}, {8,33}, {17,34}, {22,33}, {11,31}, {35,40}, {19,35}, {3,15}, {11,41}, {7,22}, {1,14}, {13,35}, {21,29}, {17,24}, {19,36}, {6,28}, {18,23}, {15,21}, {11,37}, {11,28}, {7,16}, {1,23}, {16,35}, {11,20}, {14,42}, {10,34}, {3,40}, {17,27}, {15,22}, {14,41}, {4,26}, {17,37}, {13,28}, {26,34}, {23,25}, {2,38}, {12,32}, {15,36}, {25,35}, {27,42}, {8,28}, {9,40}, {4,20}, {5,13}, {17,23}, {15,26}, {26,33}, {27,31}, {4,19}, {14,22}, {8,39}, {22,32}, {9,14}, {5,36}, {9,34}, {10,14}, {4,39}, {12,35}, {6,35}, {17,32}, {12,19}, {23,26}, {28,41}, {1,37}, {30,39}, {2,9}, {30,37}, {2,32}, {6,33}, {6,7}, {18,34}, {2,14}, {15,25}, {5,33}, {18,37}, {5,30}, {11,38}, {29,40} }; // ET42.95 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 704643072 EdgePairs[42][95]:={ {24,34}, {15,33}, {19,28}, {10,37}, {9,32}, {35,38}, {5,22}, {19,26}, {11,25}, {4,28}, {25,37}, {31,42}, {12,22}, {8,26}, {22,40}, {25,40}, {5,11}, {1,40}, {17,42}, {2,35}, {6,15}, {3,35}, {14,31}, {5,15}, {24,32}, {27,33}, {3,23}, {2,18}, {26,37}, {3,21}, {19,37}, {20,37}, {21,28}, {11,14}, {1,35}, {7,30}, {15,41}, {6,9}, {8,31}, {14,29}, {2,33}, {11,29}, {11,17}, {10,42}, {27,36}, {19,40}, {20,38}, {2,34}, {20,26}, {19,31}, {22,37}, {26,38}, {4,24}, {21,40}, {16,42}, {15,32}, {4,30}, {8,13}, {8,30}, {1,17}, {29,33}, {8,37}, {26,39}, {5,41}, {17,39}, {21,38}, {7,41}, {23,31}, {12,26}, {13,30}, {3,10}, {3,9}, {6,39}, {2,17}, {17,26}, {13,24}, {2,15}, {12,23}, {20,39}, {22,25}, {12,13}, {13,20}, {24,31}, {9,35}, {1,36}, {15,19}, {1,29}, {6,18}, {16,34}, {35,37}, {10,35}, {18,39}, {31,38}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {30,36}, {2,29}, {13,19}, {14,32}, {36,38}, {2,36}, {16,40}, {18,29}, {9,36}, {35,42}, {8,42}, {18,26}, {4,22}, {1,18}, {7,14}, {6,17}, {6,10}, {2,39}, {8,18}, {27,39}, {1,42}, {28,40}, {7,32}, {12,24}, {27,40}, {19,38}, {11,22}, {1,39}, {7,37}, {5,12}, {2,30}, {4,9}, {14,34}, {3,36}, {6,12}, {4,21}, {17,29}, {36,41}, {20,25}, {1,30}, {19,27}, {11,21}, {8,17}, {3,30}, {11,23}, {22,26}, {3,24}, {10,36}, {14,33}, {14,23}, {10,38}, {6,16}, {15,34}, {13,25}, {21,25}, {32,38}, {31,41}, {8,41}, {9,38}, {27,37}, {4,10}, {21,37}, {28,34}, {3,29}, {12,17}, {29,36}, {1,41}, {15,23}, {9,22}, {4,11}, {20,31}, {11,13}, {7,35}, {27,34}, {2,27}, {12,30}, {4,33}, {11,24}, {10,31}, {9,31}, {18,25}, {13,31}, {5,39}, {16,41}, {12,18}, {2,16}, {6,11}, {13,29}, {17,30}, {10,22}, {5,40}, {28,37}, {6,22}, {4,34}, {12,29}, {15,24}, {32,42}, {12,25}, {15,40}, {1,16}, {27,35}, {3,22}, {36,37}, {32,41}, {9,41}, {16,31}, {6,23}, {25,38}, {23,34}, {4,36}, {15,39}, {4,29}, {31,37}, {21,39}, {8,32}, {22,39}, {32,37}, {9,24}, {17,25}, {19,34}, {2,41}, {17,41}, {5,23}, {20,32}, {18,41}, {12,14}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {22,38}, {28,39}, {8,36}, {3,33}, {13,32}, {14,26}, {23,32}, {35,41}, {11,30}, {19,33}, {19,39}, {3,34}, {4,27}, {30,35}, {5,24}, {16,20}, {25,39}, {14,19}, {1,33}, {20,28}, {19,25}, {3,11}, {10,41}, {14,30}, {3,28}, {7,31}, {5,9}, {30,33}, {4,12}, {20,27}, {28,33}, {28,36}, {8,14}, {20,33}, {36,42}, {14,24}, {13,34}, {7,25}, {15,42}, {1,34}, {22,27}, {30,34}, {5,21}, {7,42}, {21,27}, {6,41}, {17,40}, {28,35}, {16,23}, {6,42}, {4,35}, {19,32}, {13,33}, {1,15}, {14,25}, {14,20}, {20,34}, {7,26}, {7,18}, {23,33}, {5,18}, {5,16}, {10,24}, {5,17}, {16,33}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,20}, {16,39}, {1,28}, {16,24}, {28,38}, {3,27}, {7,38}, {5,42}, {15,31}, {5,10}, {18,40}, {26,40}, {20,40}, {1,27}, {10,23}, {29,35}, {3,12}, {9,42}, {7,13}, {16,19}, {24,33}, {10,32}, {7,36}, {29,34}, {21,26}, {22,28}, {8,25}, {2,42}, {18,42}, {16,32}, {12,21}, {11,26}, {9,37}, {27,38}, {6,40} }; // ET42.96 // Bipartite(6,36) Valencies [18,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 416162911506546032640000 EdgePairs[42][96]:={ {1,15}, {6,39}, {5,14}, {3,15}, {4,42}, {6,10}, {6,18}, {4,14}, {1,11}, {3,29}, {6,14}, {5,30}, {5,42}, {4,8}, {3,7}, {1,31}, {6,23}, {1,40}, {2,20}, {4,40}, {5,34}, {4,16}, {2,37}, {5,41}, {2,33}, {6,7}, {1,32}, {5,13}, {2,28}, {3,31}, {6,34}, {5,26}, {4,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {5,37}, {4,12}, {3,41}, {5,33}, {3,11}, {4,20}, {6,11}, {2,41}, {1,36}, {3,13}, {2,16}, {2,32}, {1,16}, {2,36}, {2,17}, {4,28}, {2,13}, {1,12}, {3,9}, {3,23}, {5,29}, {3,27}, {4,30}, {6,15}, {6,26}, {1,19}, {2,40}, {4,36}, {2,9}, {1,35}, {4,38}, {2,24}, {6,31}, {5,22}, {6,19}, {5,38}, {3,35}, {1,23}, {2,21}, {1,7}, {6,30}, {1,39}, {6,38}, {2,12}, {4,22}, {5,17}, {3,21}, {4,32}, {6,42}, {3,39}, {2,8}, {1,20}, {1,27}, {4,18}, {5,10}, {3,25}, {2,25}, {1,28}, {3,17}, {3,37}, {6,35}, {5,18}, {4,34}, {6,27}, {3,33}, {1,8}, {5,25}, {4,10}, {4,24}, {1,24} }; // ET42.97 // Bipartite(15,27) Valencies [18,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 495432037507792896000000 EdgePairs[42][97]:={ {15,33}, {10,37}, {14,36}, {6,25}, {5,38}, {4,28}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {2,35}, {4,31}, {8,21}, {3,19}, {15,27}, {1,19}, {8,23}, {12,16}, {2,18}, {3,21}, {3,39}, {5,32}, {1,35}, {4,37}, {4,40}, {14,29}, {13,40}, {2,33}, {4,38}, {11,35}, {11,29}, {11,17}, {11,27}, {1,20}, {3,18}, {9,18}, {10,17}, {12,28}, {8,30}, {9,33}, {1,17}, {4,16}, {5,41}, {7,41}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {12,31}, {12,40}, {10,20}, {15,30}, {13,20}, {15,19}, {1,29}, {6,18}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {13,16}, {2,29}, {1,38}, {13,19}, {14,32}, {1,26}, {2,36}, {13,41}, {9,36}, {6,34}, {9,39}, {8,42}, {4,22}, {5,27}, {15,28}, {2,39}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {13,17}, {7,19}, {4,32}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {14,33}, {15,37}, {14,23}, {10,38}, {6,16}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {8,41}, {14,21}, {1,41}, {2,23}, {10,19}, {9,22}, {9,19}, {3,25}, {7,35}, {2,27}, {12,30}, {6,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {14,27}, {7,28}, {12,18}, {13,29}, {9,25}, {10,22}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,42}, {15,40}, {3,22}, {13,38}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {10,28}, {9,24}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {7,29}, {8,29}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {5,24}, {12,36}, {5,26}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {8,33}, {12,39}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {1,34}, {15,42}, {13,35}, {14,18}, {5,21}, {12,34}, {6,28}, {6,42}, {4,35}, {14,20}, {15,21}, {7,26}, {7,16}, {1,23}, {5,18}, {11,20}, {14,42}, {15,18}, {10,34}, {5,17}, {3,40}, {15,16}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {14,41}, {4,26}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {15,36}, {15,31}, {9,40}, {4,20}, {8,20}, {10,23}, {4,19}, {8,39}, {3,37}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {12,19}, {1,37}, {2,42}, {6,33}, {12,21}, {2,32}, {11,26}, {15,25}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.98 // Bipartite(21,21) Valencies [18,18] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 789910774087680 EdgePairs[42][98]:={ {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {21,30}, {14,31}, {15,27}, {21,41}, {3,23}, {16,37}, {19,37}, {20,37}, {16,28}, {21,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {19,40}, {20,38}, {2,34}, {19,31}, {2,25}, {4,24}, {21,40}, {16,42}, {18,32}, {15,32}, {4,30}, {9,33}, {20,24}, {5,41}, {21,38}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {13,42}, {20,35}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {20,36}, {16,40}, {20,42}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {20,41}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {14,34}, {3,36}, {19,23}, {17,29}, {20,25}, {4,32}, {19,27}, {14,28}, {6,36}, {16,29}, {11,36}, {3,30}, {11,23}, {3,24}, {10,36}, {14,33}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {21,25}, {14,39}, {21,31}, {19,30}, {8,24}, {8,41}, {9,26}, {18,38}, {21,37}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {20,22}, {12,41}, {9,22}, {20,31}, {19,24}, {17,28}, {21,42}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {14,27}, {16,41}, {7,28}, {19,41}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {21,32}, {12,25}, {16,26}, {3,42}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {21,39}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {5,31}, {17,22}, {19,34}, {7,40}, {2,41}, {17,41}, {5,23}, {20,32}, {2,26}, {10,40}, {18,30}, {2,28}, {8,29}, {9,23}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {18,28}, {5,24}, {15,29}, {2,22}, {18,24}, {1,33}, {20,28}, {21,33}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {21,34}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {21,35}, {11,31}, {14,24}, {13,34}, {7,25}, {1,34}, {15,42}, {13,35}, {7,42}, {21,27}, {6,41}, {17,24}, {17,40}, {20,23}, {12,34}, {19,36}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {14,25}, {20,34}, {7,26}, {11,37}, {11,28}, {16,35}, {10,24}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {15,22}, {14,41}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {3,27}, {9,27}, {7,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {8,39}, {9,42}, {5,36}, {9,34}, {4,39}, {6,35}, {21,24}, {21,26}, {8,25}, {2,42}, {18,42}, {16,32}, {2,32}, {11,26}, {15,25}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37}, {21,23} }; // ET42.99 // Bipartite(7,35) Valencies [20,4] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 5040 EdgePairs[42][99]:={ {1,15}, {4,35}, {7,19}, {5,32}, {6,39}, {7,39}, {6,12}, {4,42}, {4,14}, {2,22}, {3,38}, {6,36}, {6,17}, {7,40}, {2,11}, {6,23}, {1,40}, {2,20}, {4,40}, {5,34}, {1,25}, {7,38}, {4,16}, {7,33}, {5,24}, {1,9}, {6,32}, {7,31}, {3,30}, {6,40}, {7,15}, {5,13}, {3,10}, {3,31}, {2,19}, {6,34}, {2,15}, {5,26}, {6,22}, {7,11}, {3,19}, {1,29}, {4,12}, {3,18}, {3,41}, {7,28}, {1,34}, {3,11}, {5,23}, {5,33}, {2,10}, {4,20}, {2,41}, {1,10}, {7,26}, {7,41}, {1,36}, {3,13}, {2,16}, {6,33}, {6,21}, {2,17}, {4,28}, {7,29}, {3,14}, {2,13}, {1,12}, {4,29}, {5,19}, {5,15}, {6,8}, {7,20}, {3,23}, {6,37}, {5,29}, {7,14}, {2,42}, {3,27}, {2,34}, {4,21}, {7,30}, {4,17}, {2,35}, {5,28}, {4,25}, {2,9}, {1,26}, {7,35}, {4,38}, {6,31}, {4,11}, {3,42}, {5,22}, {2,27}, {5,27}, {6,30}, {1,39}, {6,38}, {2,39}, {2,12}, {5,20}, {3,28}, {3,26}, {5,36}, {5,17}, {5,31}, {1,42}, {6,16}, {3,21}, {1,14}, {1,41}, {7,9}, {4,32}, {2,8}, {1,37}, {7,22}, {3,16}, {4,18}, {5,10}, {7,32}, {3,8}, {7,37}, {1,33}, {2,25}, {3,36}, {4,9}, {3,37}, {6,24}, {6,35}, {5,18}, {6,27}, {4,23}, {1,8}, {4,13}, {1,21}, {2,30}, {1,18}, {5,25}, {4,24}, {1,24} }; // ET42.100 // Bipartite(7,35) Valencies [20,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 60197437440000000 EdgePairs[42][100]:={ {1,15}, {4,35}, {6,39}, {5,14}, {4,42}, {6,10}, {6,18}, {4,14}, {1,11}, {6,14}, {3,38}, {5,30}, {5,42}, {4,8}, {4,27}, {1,31}, {6,17}, {2,11}, {5,35}, {7,24}, {6,23}, {1,40}, {2,20}, {1,25}, {7,38}, {2,37}, {1,38}, {2,33}, {6,32}, {6,25}, {7,31}, {7,27}, {1,32}, {7,15}, {7,23}, {3,10}, {3,34}, {3,31}, {2,19}, {2,18}, {6,9}, {5,26}, {5,9}, {5,21}, {3,19}, {1,29}, {5,37}, {3,41}, {7,10}, {5,23}, {5,33}, {4,20}, {6,11}, {2,41}, {2,23}, {1,10}, {7,41}, {4,39}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {3,40}, {6,21}, {4,28}, {7,29}, {3,14}, {2,13}, {1,12}, {4,29}, {5,19}, {5,15}, {7,20}, {6,37}, {7,13}, {5,29}, {3,27}, {2,34}, {1,19}, {2,40}, {4,36}, {4,21}, {7,30}, {5,28}, {4,15}, {2,9}, {4,25}, {1,26}, {6,31}, {4,11}, {3,42}, {5,22}, {7,8}, {2,27}, {3,35}, {6,30}, {5,8}, {1,39}, {6,38}, {2,39}, {2,12}, {4,22}, {3,28}, {3,26}, {5,36}, {3,24}, {3,12}, {6,16}, {7,16}, {3,21}, {7,9}, {4,32}, {6,42}, {7,22}, {4,18}, {2,26}, {7,37}, {3,20}, {1,33}, {5,12}, {2,25}, {3,17}, {6,24}, {6,35}, {4,34}, {4,41}, {3,33}, {7,34}, {7,36}, {7,17}, {1,8}, {5,16}, {4,13}, {2,30}, {1,18}, {5,40}, {1,24}, {6,28} }; // ET42.101 // Bipartite(12,30) Valencies [20,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3963456300062343168000000 EdgePairs[42][101]:={ {11,17}, {3,33}, {2,24}, {1,20}, {5,17}, {10,25}, {11,20}, {9,28}, {2,33}, {6,16}, {11,36}, {11,35}, {4,26}, {3,22}, {3,40}, {4,16}, {10,37}, {8,30}, {2,23}, {1,13}, {5,38}, {12,22}, {7,38}, {8,42}, {4,29}, {1,32}, {3,13}, {8,33}, {3,25}, {3,15}, {10,23}, {7,41}, {1,40}, {10,26}, {2,15}, {4,19}, {7,22}, {12,39}, {4,31}, {1,19}, {2,27}, {12,42}, {5,20}, {3,37}, {2,26}, {7,34}, {8,39}, {11,41}, {11,14}, {2,41}, {12,34}, {2,14}, {5,32}, {8,15}, {4,23}, {8,27}, {12,37}, {2,42}, {10,22}, {6,22}, {3,18}, {4,38}, {6,21}, {3,34}, {11,38}, {6,40}, {6,31}, {11,33}, {1,38}, {1,17}, {2,36}, {4,22}, {10,38}, {7,20}, {9,27}, {12,36}, {5,29}, {4,41}, {8,41}, {2,38}, {9,19}, {8,14}, {2,39}, {7,32}, {11,15}, {1,31}, {10,41}, {7,13}, {7,25}, {10,28}, {2,35}, {1,22}, {12,13}, {6,30}, {12,16}, {5,23}, {10,29}, {10,31}, {9,34}, {9,42}, {2,20}, {6,18}, {10,40}, {1,29}, {8,17}, {3,39}, {11,21}, {4,35}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {8,36}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {5,24}, {9,37}, {12,28}, {12,25}, {8,35}, {5,14}, {1,28}, {4,13}, {7,14}, {3,27}, {4,28}, {10,13}, {8,26}, {5,42}, {9,22}, {7,31}, {12,33}, {6,15}, {5,41}, {2,17}, {9,13}, {12,27}, {9,40}, {8,32}, {8,21}, {3,19}, {6,27}, {11,24}, {11,39}, {12,19}, {12,40}, {12,30}, {8,23}, {10,32}, {5,36}, {3,21}, {1,25}, {6,19}, {7,29}, {6,28}, {12,15}, {9,30}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {6,42}, {11,26}, {4,40}, {10,35}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {10,17}, {3,24}, {2,29}, {11,27}, {8,38}, {1,26}, {4,34}, {1,16}, {4,14}, {10,34}, {11,32}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {5,27}, {5,26}, {8,18}, {3,42}, {9,39}, {4,25}, {10,19}, {4,20}, {3,28}, {8,20}, {12,24}, {1,41}, {3,31}, {1,14}, {9,24}, {10,20}, {6,39}, {5,15}, {6,37}, {12,31}, {10,14}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {3,36}, {9,16}, {9,21}, {11,42}, {7,40}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {10,16} }; // ET42.102 // Bipartite(12,30) Valencies [20,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1509949440 EdgePairs[42][102]:={ {11,17}, {3,33}, {2,24}, {1,20}, {5,17}, {10,25}, {11,20}, {9,28}, {6,16}, {11,36}, {12,29}, {11,35}, {4,26}, {3,22}, {3,40}, {10,37}, {4,30}, {11,25}, {8,30}, {2,23}, {1,13}, {5,38}, {12,22}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {12,38}, {1,40}, {10,26}, {2,15}, {4,19}, {12,39}, {2,19}, {12,41}, {1,19}, {10,33}, {12,42}, {5,20}, {3,37}, {2,26}, {7,34}, {8,39}, {1,21}, {11,41}, {7,36}, {2,41}, {2,14}, {5,32}, {8,15}, {8,31}, {12,37}, {10,15}, {10,22}, {6,22}, {3,18}, {10,30}, {6,29}, {3,17}, {8,16}, {6,21}, {3,34}, {5,40}, {11,38}, {6,31}, {11,33}, {2,34}, {1,17}, {4,22}, {8,19}, {7,20}, {9,32}, {9,27}, {12,36}, {4,41}, {8,41}, {2,38}, {9,19}, {2,37}, {8,14}, {7,39}, {5,25}, {2,39}, {7,32}, {11,15}, {1,31}, {10,41}, {7,13}, {7,25}, {10,28}, {2,35}, {12,13}, {4,33}, {12,16}, {5,23}, {4,21}, {10,29}, {9,34}, {9,42}, {10,21}, {2,20}, {6,18}, {10,40}, {1,29}, {8,17}, {2,16}, {3,32}, {11,21}, {4,35}, {9,25}, {7,16}, {2,32}, {6,33}, {5,18}, {11,23}, {6,24}, {5,30}, {7,17}, {11,30}, {5,24}, {9,37}, {12,28}, {8,22}, {8,35}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {10,13}, {6,23}, {8,37}, {8,26}, {5,42}, {12,26}, {9,22}, {7,31}, {12,33}, {5,41}, {4,36}, {2,17}, {9,13}, {12,27}, {9,40}, {8,32}, {1,42}, {3,19}, {1,24}, {12,23}, {6,27}, {11,24}, {11,39}, {6,26}, {3,23}, {8,23}, {1,39}, {12,14}, {5,36}, {1,25}, {7,29}, {6,41}, {6,28}, {6,14}, {9,30}, {1,35}, {5,39}, {7,28}, {3,16}, {4,37}, {6,42}, {11,26}, {4,40}, {10,35}, {6,36}, {3,30}, {5,33}, {8,34}, {9,18}, {2,29}, {11,27}, {8,38}, {2,22}, {4,34}, {1,16}, {10,36}, {4,14}, {10,34}, {11,32}, {9,17}, {10,18}, {8,24}, {6,38}, {2,31}, {11,40}, {9,33}, {5,27}, {5,26}, {3,42}, {4,18}, {9,38}, {4,25}, {10,19}, {3,38}, {4,20}, {3,28}, {8,20}, {12,24}, {7,27}, {7,24}, {3,31}, {1,14}, {10,20}, {6,39}, {5,15}, {6,37}, {12,31}, {10,14}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {5,35}, {1,34}, {9,31}, {7,19}, {9,16}, {11,42}, {7,40}, {7,42}, {9,23}, {7,21}, {8,29}, {12,18}, {11,18}, {1,36}, {12,21} }; // ET42.103 // Bipartite(18,24) Valencies [20,15] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6419592322744320 EdgePairs[42][103]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {11,27}, {2,34}, {12,28}, {2,25}, {18,32}, {15,32}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {16,25}, {13,42}, {9,35}, {1,36}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {6,24}, {17,36}, {2,29}, {5,34}, {13,19}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {3,38}, {5,27}, {5,28}, {14,35}, {1,42}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {15,37}, {14,23}, {10,38}, {11,33}, {18,22}, {13,25}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {18,20}, {18,38}, {3,29}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {3,32}, {16,41}, {7,28}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {14,37}, {18,31}, {14,40}, {9,41}, {16,31}, {7,39}, {3,41}, {15,39}, {4,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {17,22}, {2,19}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {5,20}, {2,26}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {3,33}, {14,26}, {11,30}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {14,19}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {2,37}, {5,29}, {10,41}, {4,25}, {14,30}, {7,31}, {12,33}, {12,39}, {17,34}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {17,24}, {17,40}, {12,34}, {17,21}, {6,28}, {6,42}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {11,28}, {1,23}, {16,35}, {11,20}, {14,42}, {10,27}, {10,34}, {16,33}, {13,23}, {8,35}, {17,27}, {2,40}, {6,21}, {14,41}, {4,26}, {15,20}, {16,39}, {13,28}, {1,28}, {3,27}, {9,27}, {5,42}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {4,20}, {8,20}, {1,27}, {17,23}, {10,23}, {15,26}, {4,19}, {14,22}, {3,37}, {9,42}, {5,36}, {16,19}, {10,32}, {4,39}, {7,36}, {17,32}, {12,19}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.104 // Bipartite(21,21) Valencies [20,20] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 102181884343418880000 EdgePairs[42][104]:={ {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {21,30}, {14,31}, {15,27}, {21,41}, {3,23}, {8,23}, {10,39}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {21,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {21,22}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {21,40}, {16,42}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {20,24}, {5,41}, {17,39}, {21,38}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {13,42}, {20,35}, {9,35}, {1,36}, {1,29}, {19,42}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {20,36}, {20,42}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {8,42}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {19,23}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {6,36}, {16,29}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {21,25}, {14,39}, {21,31}, {19,30}, {4,41}, {9,38}, {8,41}, {9,26}, {18,38}, {21,37}, {3,29}, {17,31}, {13,36}, {2,23}, {20,22}, {15,23}, {12,41}, {9,22}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {21,42}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {19,41}, {13,29}, {8,34}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {21,39}, {8,32}, {7,24}, {10,28}, {9,24}, {17,22}, {17,25}, {19,34}, {7,40}, {2,41}, {17,41}, {5,23}, {20,32}, {2,26}, {18,41}, {10,40}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {4,27}, {18,28}, {5,24}, {15,29}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {20,28}, {21,33}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {21,34}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {21,35}, {11,31}, {20,33}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {7,42}, {21,27}, {6,41}, {21,29}, {17,24}, {17,40}, {20,23}, {12,34}, {19,36}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,25}, {20,34}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {15,22}, {14,41}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {9,27}, {5,42}, {2,38}, {12,32}, {15,36}, {21,36}, {15,31}, {8,28}, {18,40}, {9,40}, {20,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {14,22}, {8,39}, {9,42}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {21,24}, {21,26}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {6,33}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40}, {21,23} }; // ET42.105 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 10569646080 EdgePairs[42][105]:={ {6,38}, {15,38}, {14,36}, {9,32}, {6,25}, {35,38}, {5,38}, {5,22}, {10,18}, {9,17}, {19,26}, {11,25}, {31,42}, {13,37}, {1,40}, {14,38}, {13,39}, {17,42}, {2,35}, {17,33}, {4,31}, {3,35}, {11,15}, {8,21}, {3,19}, {14,31}, {15,27}, {8,23}, {12,16}, {10,39}, {3,20}, {3,21}, {3,39}, {16,37}, {16,28}, {21,28}, {11,14}, {1,35}, {7,30}, {15,41}, {4,37}, {4,40}, {6,14}, {13,40}, {2,33}, {17,35}, {4,38}, {11,17}, {6,29}, {11,27}, {27,36}, {3,18}, {19,40}, {8,16}, {10,17}, {9,18}, {2,34}, {20,26}, {12,28}, {19,31}, {22,37}, {2,25}, {16,42}, {8,30}, {8,13}, {23,38}, {33,39}, {4,16}, {29,33}, {28,31}, {20,24}, {12,20}, {5,41}, {21,38}, {12,38}, {7,41}, {12,26}, {7,27}, {6,39}, {25,34}, {10,26}, {7,33}, {12,31}, {20,29}, {1,24}, {15,30}, {12,23}, {20,39}, {22,25}, {5,37}, {27,32}, {12,13}, {26,35}, {18,35}, {16,25}, {13,42}, {20,35}, {9,35}, {1,36}, {6,18}, {1,29}, {23,42}, {12,37}, {35,37}, {10,35}, {11,18}, {29,31}, {17,36}, {2,29}, {1,38}, {1,26}, {14,32}, {36,38}, {3,17}, {13,41}, {2,36}, {20,36}, {16,40}, {7,15}, {8,22}, {26,36}, {22,34}, {24,37}, {18,29}, {9,36}, {9,29}, {9,39}, {8,42}, {4,22}, {30,38}, {18,33}, {18,36}, {29,32}, {8,19}, {3,38}, {5,27}, {7,14}, {15,28}, {6,17}, {5,28}, {24,41}, {2,39}, {4,18}, {24,40}, {26,42}, {14,35}, {27,39}, {1,42}, {28,40}, {12,24}, {27,40}, {1,31}, {3,31}, {12,27}, {25,33}, {9,13}, {1,39}, {6,27}, {2,30}, {14,34}, {30,31}, {3,36}, {34,40}, {19,23}, {4,21}, {17,29}, {26,41}, {20,25}, {7,19}, {4,32}, {1,30}, {12,15}, {8,15}, {23,39}, {23,40}, {16,29}, {10,16}, {3,16}, {2,24}, {11,23}, {22,26}, {11,16}, {10,36}, {14,33}, {15,37}, {11,33}, {21,25}, {14,39}, {21,31}, {19,30}, {8,24}, {31,41}, {4,41}, {8,41}, {9,26}, {5,14}, {21,37}, {12,17}, {13,36}, {1,41}, {2,23}, {10,13}, {9,22}, {20,31}, {24,39}, {19,24}, {11,34}, {17,28}, {11,13}, {7,35}, {2,27}, {6,30}, {4,33}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {25,41}, {10,29}, {6,13}, {1,25}, {22,31}, {6,19}, {20,30}, {13,31}, {9,16}, {4,17}, {9,30}, {5,39}, {24,38}, {3,32}, {16,41}, {7,28}, {12,18}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {29,38}, {11,32}, {32,42}, {21,32}, {12,25}, {16,26}, {33,40}, {3,42}, {15,40}, {27,35}, {3,22}, {14,37}, {13,38}, {36,37}, {4,15}, {32,41}, {14,40}, {3,41}, {4,36}, {15,39}, {1,32}, {30,32}, {19,29}, {28,32}, {6,37}, {7,24}, {9,24}, {6,20}, {2,41}, {17,41}, {20,32}, {5,20}, {2,26}, {25,42}, {18,41}, {34,39}, {10,40}, {12,14}, {10,21}, {9,21}, {23,37}, {7,29}, {18,30}, {29,37}, {2,28}, {8,29}, {9,23}, {7,21}, {22,38}, {28,39}, {8,36}, {8,27}, {3,33}, {13,32}, {10,15}, {19,39}, {3,34}, {18,28}, {15,29}, {18,24}, {25,36}, {2,31}, {16,38}, {1,33}, {18,27}, {21,33}, {16,27}, {5,26}, {19,25}, {2,37}, {4,42}, {5,29}, {21,34}, {12,33}, {11,19}, {8,33}, {30,33}, {17,34}, {28,36}, {8,14}, {22,33}, {11,31}, {19,35}, {3,15}, {13,34}, {7,22}, {6,26}, {1,34}, {15,42}, {22,27}, {30,34}, {13,35}, {22,23}, {5,21}, {7,42}, {21,27}, {6,41}, {9,15}, {17,24}, {20,23}, {12,34}, {19,36}, {28,35}, {6,28}, {6,42}, {18,23}, {4,35}, {19,32}, {13,33}, {11,37}, {11,28}, {7,16}, {1,23}, {5,18}, {22,24}, {10,24}, {14,42}, {11,20}, {5,17}, {3,40}, {8,35}, {17,27}, {2,40}, {6,21}, {14,41}, {16,39}, {1,28}, {26,34}, {7,20}, {5,42}, {2,38}, {12,32}, {25,35}, {8,28}, {9,40}, {4,20}, {8,20}, {24,42}, {20,40}, {1,27}, {5,13}, {5,25}, {17,23}, {10,23}, {15,26}, {26,33}, {27,31}, {4,19}, {3,37}, {22,32}, {7,13}, {9,14}, {23,41}, {10,14}, {10,32}, {4,39}, {7,36}, {21,24}, {29,34}, {12,19}, {21,26}, {22,28}, {1,37}, {2,42}, {30,37}, {18,42}, {2,32}, {18,34}, {11,26}, {15,25}, {5,30}, {11,38}, {6,40}, {21,23} }; // ET42.106 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 10569646080 EdgePairs[42][106]:={ {13,21}, {24,34}, {15,33}, {19,28}, {11,40}, {10,37}, {31,39}, {5,7}, {23,29}, {3,8}, {4,28}, {25,37}, {31,40}, {12,22}, {3,26}, {8,26}, {22,40}, {25,40}, {5,11}, {16,22}, {1,3}, {6,15}, {8,40}, {10,33}, {21,30}, {30,40}, {30,41}, {5,15}, {24,32}, {1,19}, {27,33}, {21,41}, {24,36}, {3,23}, {2,18}, {26,37}, {1,21}, {36,39}, {19,37}, {20,37}, {5,32}, {2,7}, {29,39}, {6,9}, {8,31}, {13,27}, {14,29}, {16,21}, {24,28}, {10,11}, {19,21}, {6,32}, {11,35}, {11,29}, {1,12}, {10,42}, {9,11}, {1,20}, {20,38}, {26,38}, {4,24}, {21,40}, {2,6}, {18,32}, {32,33}, {15,32}, {4,30}, {9,33}, {8,12}, {1,17}, {1,9}, {1,10}, {8,37}, {4,13}, {26,39}, {7,11}, {17,39}, {31,36}, {23,31}, {1,13}, {13,30}, {3,10}, {2,5}, {8,9}, {2,10}, {19,22}, {3,9}, {12,42}, {23,36}, {11,39}, {26,29}, {17,20}, {2,17}, {22,42}, {33,35}, {12,40}, {23,28}, {10,20}, {17,26}, {13,24}, {24,30}, {2,15}, {27,41}, {13,20}, {24,31}, {28,30}, {15,19}, {19,42}, {16,34}, {18,39}, {24,26}, {31,38}, {40,42}, {4,23}, {8,38}, {34,37}, {13,26}, {6,24}, {30,36}, {13,16}, {5,34}, {38,42}, {13,19}, {20,42}, {32,39}, {27,30}, {6,34}, {35,42}, {9,20}, {18,26}, {1,18}, {32,35}, {38,41}, {6,10}, {20,41}, {4,7}, {8,18}, {10,12}, {7,32}, {19,38}, {3,13}, {11,22}, {35,39}, {7,37}, {5,12}, {11,42}, {2,8}, {5,35}, {4,9}, {28,42}, {6,12}, {25,29}, {36,41}, {13,17}, {18,19}, {16,18}, {2,13}, {13,18}, {19,27}, {8,10}, {14,28}, {11,21}, {34,35}, {6,36}, {8,17}, {11,36}, {16,17}, {3,30}, {3,24}, {14,15}, {14,23}, {10,38}, {6,16}, {15,34}, {18,22}, {33,42}, {13,25}, {32,38}, {7,12}, {31,33}, {9,38}, {27,37}, {4,10}, {14,21}, {18,20}, {18,38}, {32,40}, {28,34}, {3,29}, {17,31}, {29,36}, {20,22}, {22,29}, {25,32}, {10,19}, {15,23}, {12,41}, {39,42}, {4,11}, {9,19}, {3,25}, {21,42}, {34,36}, {6,8}, {25,30}, {22,30}, {27,34}, {12,30}, {2,12}, {1,22}, {1,6}, {18,25}, {24,25}, {33,37}, {13,22}, {37,40}, {23,35}, {2,20}, {17,19}, {9,12}, {14,27}, {25,31}, {2,16}, {19,41}, {6,11}, {13,29}, {4,5}, {38,40}, {28,37}, {33,38}, {17,38}, {15,35}, {12,29}, {26,31}, {6,31}, {15,24}, {3,7}, {1,16}, {4,14}, {5,8}, {23,27}, {24,35}, {18,31}, {9,41}, {16,31}, {6,23}, {25,38}, {15,17}, {37,39}, {7,39}, {23,34}, {34,38}, {22,41}, {4,29}, {1,5}, {2,3}, {24,29}, {31,37}, {21,39}, {26,27}, {8,32}, {22,39}, {24,27}, {32,37}, {10,28}, {5,31}, {17,22}, {17,25}, {19,34}, {2,19}, {7,40}, {5,23}, {34,42}, {29,41}, {18,21}, {26,30}, {29,42}, {14,16}, {34,41}, {28,29}, {2,11}, {16,36}, {14,26}, {23,32}, {35,41}, {11,30}, {3,5}, {19,33}, {9,28}, {2,21}, {1,11}, {4,27}, {30,35}, {5,24}, {2,22}, {36,40}, {16,20}, {8,11}, {25,39}, {14,19}, {20,28}, {12,36}, {33,41}, {1,7}, {26,28}, {3,14}, {3,11}, {4,8}, {10,41}, {4,25}, {14,30}, {3,28}, {31,35}, {7,31}, {5,9}, {12,39}, {39,41}, {1,4}, {4,12}, {1,8}, {20,27}, {21,35}, {28,33}, {31,34}, {7,10}, {27,29}, {3,6}, {20,33}, {36,42}, {35,40}, {14,24}, {11,41}, {7,25}, {1,14}, {26,32}, {14,18}, {21,29}, {17,40}, {2,4}, {17,21}, {23,30}, {16,23}, {13,15}, {14,25}, {15,21}, {14,20}, {1,15}, {20,34}, {7,26}, {7,18}, {23,33}, {5,16}, {16,35}, {15,18}, {10,34}, {10,27}, {16,33}, {38,39}, {7,17}, {13,23}, {32,36}, {15,22}, {4,26}, {15,20}, {17,37}, {40,41}, {13,28}, {23,25}, {16,24}, {28,38}, {3,27}, {9,27}, {7,38}, {7,9}, {15,36}, {22,35}, {21,36}, {15,31}, {5,10}, {27,42}, {18,40}, {26,40}, {25,27}, {32,34}, {22,36}, {4,6}, {8,39}, {14,22}, {29,35}, {3,12}, {9,42}, {14,17}, {25,28}, {16,19}, {5,36}, {9,34}, {24,33}, {12,35}, {6,35}, {17,32}, {23,26}, {28,41}, {37,41}, {20,21}, {8,25}, {30,39}, {30,42}, {2,9}, {16,32}, {6,33}, {12,21}, {6,7}, {2,14}, {33,36}, {5,33}, {18,37}, {9,37}, {27,38}, {37,42}, {29,40} }; // ET42.107 // Bipartite(21,21) Valencies [21,21] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 5220568743985916218538183570227200000000 EdgePairs[42][107]:={ {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {21,30}, {14,31}, {15,27}, {21,41}, {3,23}, {8,23}, {10,39}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {21,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {21,22}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {21,40}, {16,42}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {20,24}, {5,41}, {17,39}, {21,38}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {19,22}, {12,42}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {13,42}, {20,35}, {9,35}, {1,36}, {1,29}, {19,42}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {20,36}, {16,40}, {20,42}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {19,23}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {21,25}, {14,39}, {21,31}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {18,38}, {21,37}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {20,22}, {15,23}, {12,41}, {9,22}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {21,42}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {19,41}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {21,32}, {12,25}, {16,26}, {3,42}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {21,39}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {7,40}, {2,41}, {17,41}, {5,23}, {20,32}, {2,26}, {18,41}, {10,40}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {20,28}, {21,33}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {21,34}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {21,35}, {11,31}, {20,33}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {7,42}, {21,27}, {6,41}, {21,29}, {17,24}, {17,40}, {20,23}, {12,34}, {19,36}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,25}, {20,34}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {15,22}, {14,41}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {21,36}, {15,31}, {8,28}, {18,40}, {9,40}, {20,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {8,39}, {14,22}, {9,42}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {21,24}, {21,26}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {6,33}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40}, {21,23} }; // ET42.108 // Bipartite(9,33) Valencies [22,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 82427505240359043072000000 EdgePairs[42][108]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {8,12}, {4,26}, {3,22}, {3,40}, {4,16}, {1,10}, {8,30}, {2,23}, {1,13}, {5,38}, {7,38}, {8,42}, {4,29}, {1,32}, {3,13}, {8,33}, {3,25}, {3,15}, {7,41}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {5,20}, {3,37}, {2,26}, {7,34}, {8,39}, {2,41}, {2,14}, {5,32}, {8,15}, {4,23}, {8,27}, {2,42}, {6,22}, {3,18}, {4,38}, {6,21}, {3,34}, {6,40}, {6,31}, {1,38}, {4,10}, {1,17}, {2,36}, {4,22}, {7,11}, {7,20}, {9,27}, {5,11}, {5,29}, {4,41}, {8,41}, {2,38}, {9,19}, {8,14}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {5,23}, {9,34}, {9,42}, {2,20}, {6,18}, {1,29}, {8,17}, {3,39}, {4,35}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {9,37}, {8,35}, {9,10}, {5,14}, {1,28}, {4,13}, {7,14}, {3,27}, {4,28}, {3,10}, {8,26}, {5,42}, {9,22}, {7,31}, {6,15}, {5,41}, {2,17}, {9,13}, {5,12}, {9,40}, {8,32}, {8,21}, {3,19}, {6,27}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {6,28}, {2,11}, {9,30}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {3,24}, {2,29}, {8,38}, {1,26}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {6,10}, {5,27}, {5,26}, {8,18}, {3,42}, {9,39}, {4,25}, {4,11}, {4,20}, {3,28}, {8,20}, {7,10}, {1,41}, {3,31}, {2,12}, {1,14}, {9,24}, {6,39}, {5,15}, {6,37}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {3,36}, {9,16}, {9,21}, {7,40}, {8,29}, {4,32} }; // ET42.109 // Bipartite(20,22) Valencies [22,20] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2734583627802146590662858060595200000000 EdgePairs[42][109]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {16,42}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {20,24}, {5,41}, {17,39}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {19,22}, {12,42}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {13,42}, {20,35}, {9,35}, {1,36}, {1,29}, {19,42}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {20,36}, {16,40}, {20,42}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {18,38}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {20,22}, {15,23}, {12,41}, {9,22}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {19,41}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {7,40}, {2,41}, {17,41}, {5,23}, {20,32}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {20,28}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {20,23}, {12,34}, {17,21}, {19,36}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,25}, {15,21}, {20,34}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {20,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {8,39}, {14,22}, {9,42}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {20,21}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.110 // Bipartite(19,23) Valencies [23,19] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3144771171972468579262286769684480000000 EdgePairs[42][110]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {19,20}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {1,20}, {19,40}, {2,34}, {12,28}, {19,31}, {2,25}, {4,24}, {16,42}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {19,22}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {13,42}, {9,35}, {1,36}, {1,29}, {19,42}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {15,23}, {12,41}, {9,22}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {2,20}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {19,41}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {19,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {5,20}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {12,34}, {17,21}, {19,36}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {3,37}, {8,39}, {14,22}, {9,42}, {5,36}, {9,34}, {10,32}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.111 // Bipartite(6,36) Valencies [24,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5275360335382978756608000000 EdgePairs[42][111]:={ {4,35}, {5,32}, {6,39}, {6,12}, {5,14}, {3,15}, {2,38}, {6,10}, {6,18}, {4,14}, {1,11}, {5,30}, {5,42}, {6,36}, {4,8}, {3,7}, {1,31}, {2,11}, {5,35}, {1,40}, {2,20}, {4,40}, {1,25}, {4,16}, {6,13}, {5,24}, {1,38}, {5,41}, {2,33}, {6,25}, {6,7}, {3,30}, {1,32}, {6,40}, {3,10}, {3,34}, {3,31}, {6,34}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {1,29}, {3,18}, {1,34}, {2,14}, {5,23}, {5,33}, {4,37}, {4,20}, {2,41}, {2,23}, {1,10}, {4,7}, {1,17}, {3,13}, {1,22}, {2,32}, {6,33}, {3,40}, {1,16}, {6,21}, {2,36}, {2,17}, {4,28}, {3,9}, {4,29}, {3,22}, {5,15}, {6,37}, {5,29}, {4,31}, {2,42}, {3,27}, {6,15}, {1,19}, {4,17}, {2,35}, {4,25}, {2,9}, {1,35}, {1,26}, {4,38}, {2,24}, {6,31}, {4,11}, {3,42}, {2,27}, {6,19}, {5,38}, {1,23}, {2,21}, {5,27}, {1,7}, {6,30}, {5,8}, {2,39}, {2,12}, {4,22}, {5,20}, {3,28}, {5,36}, {3,24}, {5,17}, {3,12}, {6,16}, {3,21}, {1,14}, {1,41}, {4,32}, {6,42}, {3,39}, {2,8}, {1,37}, {1,20}, {5,11}, {3,16}, {1,13}, {3,25}, {2,26}, {5,12}, {1,28}, {3,36}, {3,37}, {6,24}, {5,18}, {4,34}, {6,27}, {4,41}, {3,33}, {4,23}, {1,8}, {5,39}, {4,13}, {2,30}, {4,19}, {4,10}, {6,28} }; // ET42.112 // Bipartite(6,36) Valencies [24,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 190210142896128 EdgePairs[42][112]:={ {4,35}, {6,39}, {6,12}, {3,15}, {2,38}, {6,18}, {3,29}, {6,14}, {3,38}, {5,42}, {6,36}, {4,8}, {6,17}, {2,11}, {5,35}, {6,41}, {6,23}, {2,20}, {4,40}, {5,34}, {1,25}, {4,16}, {6,13}, {2,37}, {5,24}, {3,32}, {1,9}, {2,33}, {6,32}, {3,30}, {1,32}, {6,40}, {5,7}, {5,13}, {3,10}, {2,28}, {3,31}, {2,19}, {2,18}, {2,15}, {6,9}, {4,26}, {5,26}, {5,9}, {6,22}, {2,29}, {3,19}, {4,12}, {3,41}, {1,34}, {2,14}, {3,11}, {5,33}, {4,37}, {2,10}, {4,20}, {2,41}, {2,23}, {1,10}, {4,7}, {4,39}, {1,36}, {1,17}, {3,13}, {2,16}, {2,32}, {6,33}, {3,40}, {1,16}, {6,21}, {2,36}, {4,28}, {3,14}, {1,12}, {4,29}, {3,22}, {5,15}, {6,8}, {3,23}, {5,29}, {4,31}, {2,42}, {4,30}, {2,34}, {6,15}, {6,26}, {1,19}, {4,21}, {4,17}, {4,25}, {2,9}, {1,35}, {1,26}, {4,38}, {2,24}, {6,31}, {4,11}, {3,42}, {5,22}, {2,27}, {5,38}, {1,23}, {5,27}, {1,7}, {6,30}, {5,8}, {1,39}, {4,22}, {5,20}, {3,28}, {5,36}, {3,24}, {5,17}, {5,31}, {3,12}, {3,21}, {1,14}, {1,41}, {6,42}, {3,39}, {1,37}, {1,27}, {5,11}, {3,20}, {2,25}, {1,28}, {3,37}, {6,24}, {6,35}, {2,7}, {5,18}, {4,34}, {6,27}, {3,33}, {1,8}, {1,30}, {5,16}, {4,13}, {1,21}, {1,18}, {4,19}, {5,25}, {4,10}, {5,40} }; // ET42.113 // Bipartite(14,28) Valencies [24,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2958824445050880 EdgePairs[42][113]:={ {13,21}, {6,38}, {11,40}, {14,36}, {9,32}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {2,35}, {6,15}, {8,40}, {3,35}, {11,15}, {10,33}, {3,19}, {14,31}, {5,15}, {1,19}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {3,21}, {3,39}, {5,32}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {13,40}, {2,33}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {11,39}, {10,26}, {2,17}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {13,16}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {13,41}, {7,15}, {8,22}, {6,34}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {4,32}, {1,30}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,15}, {10,38}, {14,23}, {6,16}, {11,33}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {14,37}, {13,38}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {2,41}, {5,23}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,31}, {1,33}, {12,36}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {14,24}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {6,28}, {6,42}, {4,35}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {13,23}, {2,40}, {6,21}, {14,41}, {4,26}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {4,19}, {8,39}, {14,22}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET42.114 // Bipartite(18,24) Valencies [24,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3972342533017855047489204340654080000000 EdgePairs[42][114]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {16,42}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {13,42}, {9,35}, {1,36}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {3,38}, {5,27}, {15,28}, {5,28}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {16,41}, {7,28}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {5,20}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {14,19}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {12,34}, {17,21}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {18,40}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {2,32}, {12,21}, {6,33}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.115 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 63417876480 EdgePairs[42][115]:={ {3,42}, {6,36}, {11,42}, {10,17}, {20,26}, {9,18}, {20,33}, {4,26}, {20,25}, {19,41}, {25,42}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {8,28}, {4,24}, {8,37}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,11}, {2,39}, {7,28}, {1,32}, {20,27}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {23,29}, {10,29}, {7,17}, {2,12}, {6,28}, {12,32}, {2,30}, {5,9}, {7,15}, {3,25}, {29,42}, {21,35}, {31,42}, {20,42}, {2,38}, {8,24}, {31,37}, {12,27}, {6,34}, {17,22}, {11,39}, {24,39}, {3,13}, {2,21}, {11,27}, {18,28}, {4,34}, {13,29}, {22,28}, {31,38}, {10,22}, {12,22}, {15,20}, {24,36}, {17,25}, {14,33}, {3,32}, {3,27}, {11,31}, {10,13}, {8,38}, {22,29}, {14,27}, {34,39}, {17,42}, {2,8}, {20,28}, {10,25}, {11,21}, {19,40}, {16,26}, {3,22}, {35,40}, {6,19}, {5,23}, {27,32}, {28,32}, {16,20}, {25,41}, {2,37}, {7,30}, {3,9}, {1,31}, {6,35}, {17,32}, {21,30}, {3,14}, {21,42}, {4,41}, {9,22}, {5,20}, {7,34}, {1,20}, {18,27}, {2,36}, {13,33}, {22,27}, {30,34}, {20,32}, {1,26}, {18,31}, {1,25}, {35,41}, {18,42}, {32,41}, {24,30}, {16,30}, {34,40}, {8,35}, {5,27}, {9,31}, {20,39}, {7,23}, {5,33}, {4,39}, {7,16}, {6,11}, {1,22}, {6,24}, {29,32}, {35,39}, {10,14}, {19,31}, {22,41}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {18,21}, {30,40}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {12,33}, {5,38}, {1,37}, {33,40}, {21,37}, {25,38}, {1,29}, {26,37}, {10,19}, {14,35}, {36,41}, {12,41}, {5,42}, {11,32}, {3,31}, {23,39}, {5,29}, {27,36}, {29,41}, {20,40}, {16,35}, {5,28}, {25,33}, {8,30}, {4,21}, {36,39}, {9,37}, {27,38}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {21,34}, {18,34}, {10,31}, {22,38}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,17}, {9,14}, {32,37}, {14,36}, {7,42}, {24,25}, {23,26}, {18,22}, {7,29}, {34,38}, {6,37}, {12,28}, {28,40}, {1,35}, {17,28}, {23,32}, {26,35}, {7,36}, {9,39}, {14,37}, {22,33}, {11,24}, {20,31}, {8,33}, {4,7}, {2,7}, {9,19}, {13,35}, {1,13}, {16,37}, {2,25}, {31,41}, {17,23}, {21,29}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {15,36}, {10,36}, {16,29}, {8,41}, {28,37}, {2,40}, {36,40}, {1,11}, {29,33}, {15,30}, {4,40}, {23,38}, {16,36}, {29,40}, {1,39}, {18,25}, {14,19}, {32,42}, {21,27}, {10,37}, {25,36}, {15,37}, {7,35}, {9,13}, {4,42}, {15,29}, {30,33}, {14,41}, {4,15}, {27,40}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {3,8}, {16,22}, {18,23}, {12,15}, {9,40}, {14,20}, {19,28}, {11,33}, {30,41}, {11,16}, {24,35}, {13,37}, {24,37}, {8,27}, {24,31}, {5,30}, {15,22}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {4,13}, {8,17}, {4,22}, {28,31}, {1,40}, {6,23}, {28,35}, {10,26}, {17,31}, {8,29}, {15,25}, {5,19}, {13,28}, {16,25}, {15,31}, {10,35}, {4,27}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {15,35}, {1,19}, {5,41}, {13,41}, {6,17}, {19,33}, {3,34}, {18,39}, {11,14}, {13,20}, {4,10}, {33,37}, {14,34}, {11,23}, {16,40}, {26,41}, {15,19}, {29,34}, {8,16}, {8,42}, {15,38}, {7,38}, {14,30}, {17,24}, {12,23}, {23,40}, {8,18}, {4,25}, {10,38}, {18,33}, {1,7}, {8,15}, {21,33}, {4,14}, {36,42}, {11,28}, {33,38}, {28,38}, {19,42}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {6,18}, {5,12}, {17,39}, {6,42}, {4,9}, {5,10}, {13,38}, {24,26}, {11,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {30,32}, {3,41}, {15,39}, {10,39}, {13,34}, {23,25}, {26,38}, {18,24}, {16,39}, {30,42}, {1,38}, {5,37}, {7,41}, {8,23}, {2,29}, {3,21}, {19,27}, {33,39}, {1,36}, {18,40}, {13,30}, {24,32}, {14,42}, {6,20}, {3,39}, {11,15}, {23,35}, {12,34}, {8,19}, {23,31}, {12,16}, {17,41}, {34,37}, {15,21}, {9,38}, {27,37}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {4,23}, {22,34}, {24,38}, {9,36}, {10,40}, {16,21}, {6,27}, {21,41}, {12,40}, {17,40}, {20,41}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {11,40}, {13,42}, {5,35}, {11,22}, {16,32}, {9,32}, {35,42}, {18,32}, {24,40}, {26,42}, {23,30}, {30,31}, {22,35}, {1,21}, {19,34}, {28,36}, {23,37}, {7,20}, {3,40}, {16,19}, {22,42}, {27,31}, {7,18}, {10,21}, {3,33}, {32,38}, {27,35}, {5,17}, {19,25}, {17,21}, {15,26}, {2,18}, {18,41}, {21,28}, {23,36}, {16,38}, {4,8}, {29,31}, {2,19}, {5,24}, {6,15}, {7,33}, {12,31}, {30,39}, {7,19}, {2,35}, {17,33}, {10,32}, {25,37}, {21,38}, {5,11}, {6,41}, {6,29}, {2,31} }; // ET42.116 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1008 EdgePairs[42][116]:={ {13,25}, {3,42}, {13,40}, {6,36}, {30,37}, {11,42}, {15,17}, {10,17}, {3,29}, {20,26}, {16,28}, {5,13}, {25,42}, {22,37}, {14,29}, {2,4}, {26,33}, {3,7}, {19,22}, {36,37}, {33,41}, {4,24}, {8,31}, {1,5}, {7,24}, {15,16}, {11,34}, {13,27}, {3,17}, {1,9}, {14,17}, {2,39}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {1,18}, {3,15}, {17,29}, {5,18}, {23,29}, {8,26}, {7,17}, {13,22}, {2,12}, {6,28}, {2,30}, {5,9}, {20,22}, {3,25}, {29,42}, {1,41}, {4,30}, {21,35}, {31,42}, {35,37}, {8,11}, {38,41}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {37,42}, {3,13}, {2,21}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {17,19}, {9,12}, {10,22}, {25,29}, {25,32}, {10,42}, {9,10}, {14,33}, {17,25}, {11,35}, {3,32}, {7,13}, {11,37}, {25,28}, {8,38}, {18,29}, {22,29}, {11,29}, {14,27}, {34,39}, {20,28}, {10,25}, {12,35}, {14,22}, {16,26}, {28,42}, {35,40}, {6,19}, {1,10}, {27,32}, {2,37}, {6,31}, {2,41}, {36,38}, {21,30}, {23,33}, {4,41}, {31,35}, {8,39}, {22,32}, {7,34}, {1,20}, {2,36}, {7,14}, {12,38}, {13,33}, {15,24}, {10,23}, {22,27}, {30,34}, {20,32}, {1,26}, {18,31}, {9,27}, {18,42}, {16,42}, {24,30}, {16,30}, {34,40}, {11,38}, {6,40}, {9,31}, {5,33}, {4,39}, {27,41}, {6,11}, {38,40}, {29,32}, {6,39}, {35,39}, {10,14}, {19,31}, {8,21}, {9,20}, {18,26}, {28,39}, {18,21}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {5,22}, {9,25}, {18,20}, {12,39}, {6,12}, {5,38}, {1,37}, {33,40}, {13,18}, {21,37}, {25,38}, {26,37}, {1,29}, {2,34}, {12,19}, {36,41}, {12,41}, {5,42}, {3,31}, {23,39}, {3,20}, {5,29}, {21,25}, {29,41}, {6,13}, {11,19}, {37,41}, {8,10}, {19,24}, {16,35}, {25,33}, {12,18}, {14,32}, {4,21}, {9,37}, {27,38}, {12,21}, {10,18}, {9,17}, {1,14}, {10,20}, {11,41}, {8,34}, {4,33}, {15,40}, {21,34}, {18,34}, {3,18}, {13,23}, {7,37}, {1,28}, {14,18}, {3,36}, {9,14}, {20,23}, {24,25}, {26,31}, {5,8}, {34,38}, {6,37}, {28,40}, {29,36}, {1,35}, {26,35}, {5,21}, {22,33}, {11,24}, {20,31}, {8,33}, {4,7}, {10,28}, {15,23}, {2,7}, {9,42}, {30,38}, {9,19}, {2,25}, {31,41}, {17,23}, {26,39}, {23,28}, {21,29}, {2,14}, {9,35}, {12,24}, {3,4}, {14,28}, {30,36}, {10,36}, {8,41}, {1,11}, {29,33}, {24,34}, {15,30}, {3,19}, {23,38}, {2,16}, {16,36}, {7,40}, {18,25}, {14,19}, {32,42}, {21,27}, {10,37}, {25,36}, {2,42}, {15,37}, {7,35}, {4,42}, {21,23}, {15,29}, {20,38}, {14,41}, {4,15}, {5,34}, {3,26}, {9,23}, {3,8}, {34,41}, {16,22}, {32,40}, {3,35}, {14,26}, {18,23}, {1,6}, {9,40}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {1,34}, {30,41}, {11,16}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {24,31}, {5,30}, {16,27}, {2,13}, {5,40}, {22,36}, {22,30}, {26,40}, {24,42}, {27,34}, {28,31}, {1,40}, {6,23}, {28,35}, {10,26}, {17,20}, {17,31}, {7,22}, {23,41}, {25,40}, {19,36}, {15,25}, {6,22}, {5,19}, {33,36}, {13,28}, {2,33}, {17,35}, {6,32}, {15,31}, {18,36}, {3,12}, {14,24}, {4,17}, {7,11}, {4,32}, {19,39}, {2,27}, {2,10}, {19,33}, {19,29}, {13,20}, {7,12}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {3,5}, {16,40}, {26,41}, {15,19}, {8,16}, {8,42}, {20,35}, {22,39}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {3,30}, {6,7}, {8,15}, {21,33}, {10,34}, {24,28}, {4,14}, {36,42}, {11,28}, {28,34}, {11,17}, {33,38}, {28,38}, {32,34}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {6,18}, {5,12}, {11,20}, {7,32}, {5,10}, {13,38}, {24,26}, {6,16}, {11,13}, {26,36}, {25,34}, {30,32}, {15,39}, {10,39}, {23,25}, {18,24}, {21,24}, {39,42}, {1,38}, {5,37}, {7,41}, {8,23}, {20,30}, {26,30}, {2,6}, {13,30}, {24,32}, {9,24}, {14,39}, {14,42}, {6,20}, {3,39}, {11,15}, {23,35}, {15,41}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {17,41}, {7,39}, {15,21}, {9,38}, {1,33}, {12,30}, {1,8}, {19,26}, {29,39}, {12,14}, {4,23}, {27,30}, {22,34}, {24,38}, {9,36}, {32,36}, {8,13}, {10,40}, {16,21}, {29,37}, {12,40}, {17,40}, {15,32}, {14,38}, {27,39}, {11,25}, {17,27}, {2,17}, {33,35}, {13,42}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {35,42}, {18,32}, {21,32}, {30,31}, {39,40}, {1,21}, {19,34}, {9,15}, {7,20}, {3,40}, {23,27}, {16,19}, {22,42}, {12,36}, {27,31}, {31,34}, {21,39}, {7,18}, {10,21}, {32,38}, {27,35}, {5,17}, {19,25}, {2,9}, {15,26}, {18,41}, {23,36}, {26,28}, {4,8}, {17,30}, {27,42}, {2,19}, {1,16}, {24,41}, {5,24}, {6,15}, {7,33}, {1,15}, {20,36}, {29,35}, {27,29}, {28,33}, {12,29}, {4,35}, {17,33}, {16,24}, {25,37}, {13,16}, {10,15}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET42.117 // Bipartite(12,30) Valencies [25,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 137594142720000000 EdgePairs[42][117]:={ {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {9,17}, {4,28}, {3,26}, {12,22}, {8,26}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {11,14}, {1,35}, {5,32}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {11,27}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {8,30}, {8,13}, {9,33}, {1,17}, {4,16}, {4,13}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {1,13}, {12,26}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {5,28}, {8,18}, {1,42}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {2,24}, {11,23}, {11,16}, {3,24}, {10,38}, {6,16}, {11,33}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {10,13}, {10,19}, {9,19}, {3,25}, {11,34}, {7,35}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {10,22}, {5,40}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {4,14}, {4,15}, {9,41}, {7,39}, {3,41}, {4,29}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {3,33}, {10,15}, {11,30}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {5,29}, {10,41}, {4,25}, {7,31}, {12,33}, {12,39}, {8,14}, {3,15}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {5,21}, {7,42}, {9,15}, {12,34}, {6,28}, {6,42}, {4,35}, {1,15}, {7,18}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {11,20}, {10,27}, {10,34}, {5,17}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {9,27}, {5,42}, {2,38}, {12,32}, {8,28}, {4,20}, {8,20}, {1,27}, {10,23}, {4,19}, {3,37}, {7,13}, {9,42}, {9,14}, {5,36}, {10,14}, {10,32}, {4,39}, {7,36}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.118 // Bipartite(17,25) Valencies [25,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5517142406969243121512783806464000000000 EdgePairs[42][118]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {11,25}, {4,28}, {17,18}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {16,42}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {16,41}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {12,34}, {17,21}, {6,28}, {6,42}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {15,18}, {16,33}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {2,42}, {16,32}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.119 // Bipartite(3,39) Valencies [26,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1448745832104550541033472000000 EdgePairs[42][119]:={ {2,11}, {3,22}, {1,26}, {2,14}, {3,40}, {1,14}, {2,26}, {3,12}, {2,32}, {2,30}, {1,29}, {2,29}, {1,32}, {2,24}, {1,37}, {1,40}, {1,10}, {2,39}, {3,21}, {3,42}, {3,27}, {3,33}, {2,6}, {1,4}, {1,20}, {2,36}, {3,37}, {1,31}, {3,9}, {3,24}, {2,12}, {2,33}, {2,21}, {1,38}, {1,7}, {3,4}, {1,16}, {2,20}, {3,7}, {3,16}, {3,28}, {3,15}, {2,38}, {2,18}, {3,25}, {3,19}, {3,30}, {2,15}, {2,5}, {3,18}, {3,31}, {1,5}, {2,27}, {1,17}, {3,6}, {3,39}, {2,42}, {3,34}, {1,28}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,41}, {1,41}, {1,22}, {2,8}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {3,10}, {3,36} }; // ET42.120 // Bipartite(14,28) Valencies [26,13] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1428329123020800 EdgePairs[42][120]:={ {13,21}, {6,38}, {11,40}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {8,22}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {6,17}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {1,31}, {3,31}, {12,27}, {11,22}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {13,17}, {7,19}, {4,32}, {1,30}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {14,15}, {14,33}, {10,38}, {14,23}, {6,16}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {13,29}, {9,25}, {10,22}, {5,40}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {14,37}, {13,38}, {4,15}, {14,40}, {9,41}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {10,40}, {10,21}, {9,21}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {3,15}, {13,34}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {6,28}, {6,42}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {6,21}, {14,41}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {12,32}, {8,28}, {9,40}, {4,20}, {1,27}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.121 // Bipartite(16,26) Valencies [26,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8437982504776489479960728174592000000000 EdgePairs[42][121]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {10,42}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {16,42}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {16,40}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {9,41}, {6,23}, {16,31}, {15,17}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {12,34}, {6,28}, {6,42}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {16,19}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {16,32}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.122 // Non-bipartite Valency 26 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 523069747200 EdgePairs[42][122]:={ {13,40}, {6,36}, {24,33}, {30,37}, {15,17}, {9,18}, {3,29}, {20,26}, {19,41}, {22,37}, {2,4}, {26,33}, {2,20}, {2,26}, {19,22}, {36,37}, {33,41}, {5,32}, {8,37}, {8,31}, {12,42}, {1,5}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {2,39}, {7,28}, {18,38}, {2,24}, {39,41}, {20,27}, {4,11}, {8,36}, {1,18}, {8,20}, {3,15}, {19,37}, {3,10}, {15,33}, {7,17}, {2,12}, {6,28}, {37,40}, {14,16}, {2,30}, {14,25}, {5,9}, {7,15}, {29,42}, {1,41}, {7,10}, {4,30}, {21,35}, {31,42}, {35,37}, {8,11}, {2,38}, {38,41}, {12,27}, {17,22}, {37,42}, {24,39}, {16,33}, {7,26}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {31,38}, {10,22}, {18,37}, {25,29}, {25,32}, {20,29}, {12,22}, {14,40}, {10,42}, {15,20}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {10,13}, {11,37}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {34,39}, {17,42}, {2,8}, {20,28}, {10,25}, {13,17}, {14,22}, {11,21}, {28,42}, {6,19}, {1,10}, {5,23}, {27,32}, {16,20}, {25,41}, {3,9}, {5,26}, {1,31}, {6,35}, {17,32}, {36,38}, {21,30}, {16,23}, {3,14}, {23,33}, {21,42}, {4,41}, {9,22}, {31,35}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {18,35}, {22,27}, {30,34}, {20,32}, {18,31}, {1,25}, {35,41}, {32,41}, {10,16}, {16,42}, {15,34}, {24,30}, {16,30}, {34,40}, {11,38}, {5,27}, {6,40}, {3,6}, {7,23}, {4,39}, {7,16}, {6,11}, {1,22}, {6,24}, {29,32}, {6,39}, {35,39}, {1,42}, {16,34}, {19,31}, {22,41}, {8,21}, {9,20}, {18,26}, {28,39}, {3,16}, {18,21}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {9,25}, {3,23}, {9,26}, {12,39}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {33,40}, {25,38}, {1,29}, {26,37}, {21,22}, {10,19}, {15,27}, {14,35}, {36,41}, {12,41}, {9,11}, {11,32}, {3,31}, {23,39}, {21,25}, {5,29}, {27,36}, {38,42}, {9,28}, {6,13}, {11,19}, {8,10}, {20,40}, {21,40}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {27,38}, {2,5}, {12,21}, {10,18}, {1,14}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {2,22}, {4,33}, {18,34}, {22,38}, {13,23}, {5,15}, {5,16}, {7,37}, {14,18}, {27,33}, {1,17}, {20,23}, {32,37}, {14,36}, {24,25}, {23,26}, {26,31}, {5,8}, {7,29}, {34,38}, {3,37}, {29,36}, {17,28}, {23,32}, {5,21}, {9,39}, {13,26}, {11,24}, {20,31}, {8,33}, {4,7}, {10,28}, {15,23}, {12,17}, {2,7}, {9,42}, {30,38}, {9,19}, {13,35}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {26,39}, {23,28}, {3,28}, {9,35}, {18,19}, {3,4}, {14,28}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {28,37}, {15,42}, {2,40}, {36,40}, {1,11}, {29,33}, {33,34}, {15,30}, {24,34}, {3,19}, {23,38}, {2,16}, {16,36}, {29,40}, {1,39}, {7,40}, {14,19}, {32,42}, {2,42}, {15,37}, {7,35}, {9,13}, {4,42}, {15,29}, {20,38}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {3,8}, {16,22}, {3,35}, {14,26}, {18,23}, {1,6}, {9,40}, {8,22}, {32,39}, {14,20}, {20,37}, {1,34}, {19,23}, {30,41}, {11,16}, {22,40}, {13,37}, {24,37}, {8,27}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {5,40}, {16,31}, {24,42}, {4,13}, {8,17}, {4,22}, {28,31}, {10,26}, {17,20}, {1,23}, {8,29}, {25,40}, {19,36}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {3,12}, {14,24}, {4,17}, {3,24}, {7,27}, {19,39}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {11,14}, {7,12}, {13,21}, {3,38}, {4,10}, {33,37}, {11,23}, {26,41}, {9,33}, {20,35}, {8,42}, {14,30}, {7,38}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {4,25}, {10,38}, {6,7}, {24,27}, {1,7}, {21,33}, {17,38}, {4,14}, {11,28}, {6,25}, {28,34}, {11,17}, {33,38}, {15,18}, {32,34}, {19,42}, {24,29}, {12,13}, {10,30}, {6,18}, {5,12}, {17,39}, {6,42}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {13,24}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {8,14}, {16,39}, {5,37}, {7,41}, {8,23}, {3,21}, {19,27}, {1,36}, {18,40}, {26,30}, {9,24}, {14,39}, {14,42}, {6,20}, {34,42}, {11,15}, {6,26}, {23,35}, {12,34}, {15,41}, {4,20}, {7,21}, {28,41}, {15,21}, {9,38}, {1,33}, {12,30}, {2,32}, {6,33}, {12,14}, {29,39}, {4,23}, {22,34}, {27,30}, {9,36}, {32,36}, {8,13}, {10,40}, {16,21}, {17,40}, {20,41}, {14,38}, {27,39}, {6,30}, {25,35}, {6,38}, {33,35}, {11,40}, {25,31}, {5,14}, {5,35}, {9,16}, {9,32}, {27,28}, {35,42}, {30,35}, {18,32}, {21,32}, {26,42}, {23,30}, {21,26}, {22,31}, {30,31}, {39,40}, {22,35}, {26,29}, {1,21}, {19,34}, {9,15}, {28,36}, {23,42}, {3,40}, {12,36}, {21,39}, {27,35}, {5,17}, {6,8}, {19,25}, {4,18}, {2,18}, {18,41}, {21,28}, {23,36}, {12,37}, {17,30}, {2,19}, {27,42}, {24,41}, {5,24}, {6,15}, {12,31}, {29,35}, {31,40}, {4,37}, {28,33}, {12,29}, {7,19}, {2,35}, {17,33}, {10,32}, {21,38}, {25,37}, {13,16}, {10,15}, {4,36} }; // ET42.123 // Bipartite(15,27) Valencies [27,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14239095476810325997433728794624000000000 EdgePairs[42][123]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {11,17}, {10,42}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {14,33}, {15,37}, {10,38}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,42}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {9,41}, {6,23}, {15,17}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {12,34}, {6,28}, {6,42}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {15,18}, {5,17}, {3,40}, {15,16}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {15,31}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.124 // Bipartite(14,28) Valencies [28,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 26579644890045941861876293749964800000000 EdgePairs[42][124]:={ {13,21}, {6,38}, {11,40}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {14,15}, {14,33}, {10,38}, {14,23}, {6,16}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {14,37}, {13,38}, {4,15}, {14,40}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {6,28}, {6,42}, {4,35}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {14,41}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.125 // Non-bipartite Valency 28 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 3975358563294886684595847168000000 EdgePairs[42][125]:={ {13,25}, {3,42}, {13,40}, {6,36}, {24,33}, {11,42}, {10,17}, {3,29}, {9,18}, {4,26}, {20,33}, {19,41}, {25,42}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {17,29}, {5,18}, {19,37}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {14,16}, {12,32}, {2,30}, {14,25}, {28,29}, {7,15}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {8,24}, {2,38}, {20,42}, {12,27}, {6,34}, {4,38}, {11,39}, {24,39}, {21,31}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {4,34}, {13,29}, {10,22}, {18,37}, {25,29}, {25,32}, {20,29}, {12,22}, {14,40}, {10,42}, {9,41}, {23,34}, {14,33}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {13,15}, {17,42}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {19,40}, {3,22}, {28,42}, {6,19}, {5,23}, {27,32}, {28,32}, {25,41}, {2,37}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {21,30}, {23,33}, {21,42}, {4,41}, {9,22}, {5,20}, {8,39}, {22,32}, {7,34}, {1,20}, {2,36}, {12,38}, {13,33}, {10,23}, {18,35}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {18,42}, {10,16}, {16,42}, {15,34}, {24,30}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {27,41}, {1,22}, {6,24}, {6,39}, {19,35}, {1,42}, {16,34}, {19,31}, {22,41}, {8,21}, {9,20}, {14,23}, {28,39}, {3,16}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {12,19}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {27,36}, {9,28}, {11,19}, {20,40}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {27,38}, {12,21}, {10,18}, {9,17}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {14,36}, {7,42}, {26,31}, {7,29}, {6,37}, {12,28}, {3,37}, {28,40}, {1,35}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {10,28}, {12,17}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {26,39}, {21,29}, {3,28}, {9,35}, {12,24}, {14,28}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {28,37}, {15,42}, {2,40}, {15,30}, {24,34}, {3,19}, {4,40}, {23,38}, {2,16}, {16,36}, {1,39}, {7,40}, {17,37}, {14,19}, {10,37}, {25,36}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {20,38}, {14,41}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {12,15}, {9,40}, {25,30}, {14,31}, {8,22}, {14,20}, {20,37}, {11,33}, {1,34}, {11,16}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {9,30}, {5,40}, {16,31}, {22,36}, {22,30}, {24,42}, {26,40}, {27,34}, {18,30}, {8,17}, {4,22}, {28,31}, {1,40}, {6,23}, {28,35}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {23,41}, {25,40}, {9,34}, {19,36}, {6,22}, {5,19}, {16,41}, {13,28}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {6,17}, {19,33}, {19,29}, {3,34}, {18,39}, {13,20}, {13,21}, {3,38}, {14,34}, {11,23}, {16,40}, {26,41}, {9,33}, {8,16}, {8,42}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {28,38}, {19,42}, {24,29}, {17,34}, {4,16}, {12,26}, {10,30}, {6,18}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {26,38}, {16,39}, {1,38}, {5,37}, {7,41}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {1,36}, {18,40}, {26,30}, {13,30}, {9,24}, {24,32}, {14,39}, {14,42}, {6,20}, {3,39}, {10,41}, {11,15}, {6,26}, {12,34}, {23,35}, {15,41}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {17,41}, {11,30}, {28,41}, {2,23}, {7,39}, {9,38}, {27,37}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {22,34}, {27,30}, {24,38}, {9,36}, {10,40}, {6,27}, {12,40}, {21,41}, {17,40}, {20,41}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {6,38}, {2,17}, {11,40}, {13,42}, {25,31}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {18,32}, {21,32}, {24,40}, {26,42}, {23,30}, {22,31}, {22,35}, {5,39}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {23,42}, {7,20}, {3,40}, {22,42}, {12,36}, {27,31}, {7,18}, {21,39}, {10,21}, {3,33}, {27,35}, {28,30}, {5,17}, {1,24}, {4,18}, {2,18}, {18,41}, {23,36}, {16,38}, {12,37}, {17,30}, {2,19}, {1,16}, {27,42}, {24,41}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {27,29}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {4,19}, {21,38}, {25,37}, {13,16}, {10,15}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET42.126 // Bipartite(13,29) Valencies [29,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 55057835843666593856743751339212800000000 EdgePairs[42][126]:={ {13,21}, {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {13,39}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {13,27}, {6,14}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {13,25}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {4,14}, {13,38}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {13,14}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {6,28}, {6,42}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.127 // Bipartite(6,36) Valencies [30,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 100306130042880000000 EdgePairs[42][127]:={ {1,11}, {3,33}, {2,24}, {5,17}, {6,16}, {6,32}, {4,27}, {5,34}, {4,26}, {3,8}, {4,16}, {1,10}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {3,13}, {1,27}, {3,25}, {3,15}, {1,40}, {4,19}, {4,31}, {2,19}, {1,19}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {6,7}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {3,7}, {4,38}, {6,21}, {2,25}, {5,40}, {6,31}, {6,40}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {6,8}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,26}, {5,28}, {5,42}, {6,15}, {5,41}, {2,17}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {6,27}, {6,26}, {3,23}, {1,39}, {5,36}, {3,21}, {2,7}, {1,25}, {6,19}, {6,9}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {4,37}, {6,42}, {4,40}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,27}, {5,10}, {5,26}, {3,42}, {5,9}, {4,25}, {3,38}, {4,11}, {4,20}, {1,41}, {3,41}, {3,31}, {2,12}, {2,8}, {5,15}, {6,39}, {6,37}, {6,20}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {4,17}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET42.128 // Bipartite(7,35) Valencies [30,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1805923123200000000 EdgePairs[42][128]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {4,27}, {7,15}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {7,38}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {7,41}, {1,40}, {4,19}, {7,22}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {2,26}, {7,34}, {2,9}, {7,36}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {6,21}, {3,34}, {5,40}, {2,25}, {6,31}, {6,40}, {1,38}, {2,34}, {1,17}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {4,42}, {6,8}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {7,30}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {5,42}, {7,31}, {6,15}, {2,17}, {4,36}, {5,12}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {1,39}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {7,29}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,37}, {5,39}, {7,28}, {4,37}, {6,42}, {4,40}, {7,23}, {2,21}, {6,36}, {5,33}, {3,24}, {1,26}, {4,34}, {1,16}, {4,14}, {5,8}, {7,9}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {7,10}, {7,27}, {1,41}, {3,41}, {3,31}, {7,24}, {2,12}, {5,15}, {6,37}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {5,37}, {6,35}, {3,36}, {4,39}, {7,42}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET42.129 // Bipartite(12,30) Valencies [30,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 127056544254615216592485580013568000000000 EdgePairs[42][129]:={ {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {3,26}, {12,22}, {8,26}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {1,13}, {12,26}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {3,29}, {12,17}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {12,14}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {7,13}, {9,42}, {9,14}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.130 // Non-bipartite Valency 30 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 3628800 EdgePairs[42][130]:={ {15,28}, {13,40}, {24,33}, {30,37}, {11,42}, {10,17}, {9,18}, {20,26}, {16,28}, {20,33}, {19,41}, {25,42}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {8,28}, {36,37}, {33,41}, {4,24}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {2,24}, {7,28}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {8,20}, {3,10}, {5,18}, {17,29}, {19,37}, {23,29}, {10,29}, {15,33}, {13,22}, {2,12}, {6,28}, {12,32}, {22,25}, {2,30}, {14,25}, {5,9}, {7,15}, {3,25}, {4,12}, {10,27}, {1,41}, {4,30}, {35,37}, {8,24}, {2,38}, {20,42}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {13,29}, {22,28}, {31,38}, {10,22}, {18,37}, {5,7}, {20,29}, {12,22}, {14,40}, {10,42}, {9,41}, {15,20}, {14,33}, {17,25}, {3,32}, {3,27}, {11,31}, {7,13}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {34,39}, {17,42}, {2,8}, {20,28}, {12,35}, {11,36}, {14,22}, {19,40}, {16,26}, {28,42}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {25,41}, {2,37}, {7,30}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {36,38}, {16,23}, {21,30}, {3,14}, {23,33}, {21,42}, {4,41}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {13,33}, {15,24}, {10,23}, {22,27}, {30,34}, {1,26}, {18,31}, {9,27}, {1,25}, {26,32}, {35,41}, {18,42}, {32,41}, {10,16}, {6,14}, {15,34}, {16,42}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {27,41}, {6,11}, {1,22}, {29,32}, {6,39}, {35,39}, {19,35}, {10,14}, {1,42}, {16,34}, {19,31}, {22,41}, {8,21}, {9,20}, {18,26}, {28,39}, {3,16}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {18,20}, {21,36}, {7,31}, {12,33}, {1,37}, {33,40}, {21,37}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {5,42}, {11,32}, {23,39}, {3,20}, {5,29}, {21,25}, {27,36}, {29,41}, {9,28}, {6,13}, {11,19}, {20,40}, {35,38}, {16,35}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {36,39}, 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{28,38}, {19,42}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {33,42}, {6,18}, {5,12}, {6,42}, {11,20}, {7,32}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {23,25}, {26,38}, {18,24}, {16,39}, {30,42}, {1,38}, {5,37}, {7,41}, {2,29}, {20,30}, {14,21}, {3,21}, {1,36}, {13,30}, {9,24}, {24,32}, {14,39}, {14,42}, {6,20}, {3,39}, {10,41}, {34,42}, {11,15}, {6,26}, {12,34}, {23,35}, {15,41}, {8,19}, {4,20}, {7,21}, {23,31}, {17,41}, {11,30}, {28,41}, {2,23}, {15,21}, {9,38}, {27,37}, {1,33}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {22,34}, {24,38}, {9,36}, {8,13}, {10,40}, {16,21}, {6,27}, {29,37}, {12,40}, {21,41}, {17,40}, {20,41}, {15,32}, {14,38}, {11,25}, {25,35}, {6,38}, {13,42}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {35,42}, {30,35}, {18,32}, {21,32}, {24,40}, {26,42}, {23,30}, {21,26}, {30,31}, {22,35}, {5,39}, {6,21}, {19,34}, {28,36}, {23,42}, {7,20}, {3,40}, {16,19}, {23,27}, {27,31}, {7,18}, {21,39}, {10,21}, {3,33}, {27,35}, {5,17}, {1,24}, {6,8}, {19,25}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {18,41}, {23,36}, {16,38}, {12,37}, {17,30}, {1,16}, {27,42}, {5,24}, {6,15}, {12,31}, {1,15}, {20,36}, {29,35}, {30,39}, {31,40}, {28,33}, {12,29}, {4,35}, {2,35}, {4,19}, {21,38}, {25,37}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET42.131 // Non-bipartite Valency 30 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 5040 EdgePairs[42][131]:={ {13,25}, {3,42}, {13,40}, {24,33}, {30,37}, {11,42}, {10,17}, {3,29}, {9,18}, {16,28}, {5,13}, {4,26}, {20,25}, {19,41}, {25,42}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {8,28}, {36,37}, {33,41}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {7,28}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {12,32}, {22,25}, {14,25}, {5,9}, {7,15}, {4,12}, {29,42}, {10,27}, {1,41}, {4,30}, {21,35}, {31,42}, {35,37}, {8,24}, {2,38}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {24,39}, {21,31}, {2,21}, {7,26}, {19,38}, {11,27}, {18,28}, {4,34}, {22,28}, {31,38}, {10,22}, {18,37}, {25,32}, {20,29}, {12,22}, {14,40}, {9,41}, {15,20}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {34,39}, {17,42}, {2,8}, {20,28}, {12,35}, {11,36}, {14,22}, {19,40}, {16,26}, {3,22}, {28,42}, {35,40}, {6,19}, {5,23}, {28,32}, {16,20}, {2,37}, {3,9}, {5,25}, {5,26}, {6,31}, {1,31}, {2,41}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {21,42}, {9,22}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {12,38}, {13,33}, {18,35}, {10,23}, {15,24}, {20,32}, {18,31}, {9,27}, {1,25}, {26,32}, {18,42}, {32,41}, {16,42}, {15,34}, {24,30}, {16,30}, {34,40}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, 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{20,31}, {4,7}, {10,28}, {12,17}, {2,7}, {9,42}, {30,38}, {9,19}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {31,41}, {17,23}, {26,39}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {18,19}, {14,28}, {30,36}, {15,36}, {10,36}, {16,29}, {8,41}, {28,37}, {15,42}, {2,40}, {36,40}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {4,40}, {16,36}, {1,39}, {7,40}, {17,37}, {14,19}, {21,27}, {10,37}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {20,38}, {30,33}, {14,41}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {34,41}, {16,22}, {32,40}, {3,35}, {18,23}, {9,40}, {8,22}, {32,39}, {14,20}, {20,37}, {11,33}, {30,41}, {11,16}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {5,30}, {24,31}, {15,22}, {9,30}, {2,13}, {5,40}, {16,31}, {22,30}, {24,42}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {23,41}, {25,40}, {19,36}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {18,36}, {3,12}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {2,10}, {6,17}, {19,33}, {19,29}, {3,34}, {11,14}, {13,20}, {13,21}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {16,40}, {26,41}, {15,19}, {9,33}, {29,34}, {8,16}, {8,42}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {23,40}, {5,31}, {4,25}, {10,38}, {3,30}, {6,7}, {24,27}, {18,33}, {1,7}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {36,42}, {11,28}, {6,25}, {28,34}, {13,39}, {33,38}, {28,38}, {19,42}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {33,42}, {6,18}, {5,12}, {17,39}, {11,20}, {7,32}, {5,10}, {13,38}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {2,15}, {30,32}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {23,25}, {18,24}, {8,14}, {16,39}, {1,38}, {5,37}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {33,39}, {1,36}, {18,40}, {13,30}, {14,39}, {14,42}, {6,20}, {3,39}, {10,41}, {34,42}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {7,21}, {12,16}, {17,41}, {11,30}, {28,41}, {2,23}, {7,39}, {15,21}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {4,23}, {22,34}, {24,38}, {9,36}, {8,13}, {10,40}, {6,27}, {29,37}, {12,40}, {20,41}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {11,40}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {35,42}, {30,35}, {18,32}, {21,32}, {26,42}, {21,26}, {22,31}, {30,31}, {22,35}, {5,39}, {1,21}, {9,15}, {19,34}, {28,36}, {23,37}, {23,42}, {7,20}, {3,40}, {16,19}, {23,27}, {22,42}, {27,31}, {7,18}, {21,39}, {10,21}, {32,38}, {27,35}, {5,17}, {1,24}, {19,25}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {18,41}, {21,28}, {23,36}, {4,8}, {1,16}, {2,19}, {27,42}, {24,41}, {5,24}, {6,15}, {12,31}, {20,36}, {29,35}, {30,39}, {31,40}, {4,37}, {4,35}, {7,19}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {5,11}, {6,41}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET42.132 // Bipartite(11,31) Valencies [31,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 328229405991089309530587748368384000000000 EdgePairs[42][132]:={ {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {3,26}, {8,26}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,42}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {2,31}, {1,33}, {3,14}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {6,28}, {6,42}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET42.133 // Bipartite(10,32) Valencies [32,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 954849181064987082270800722526208000000000 EdgePairs[42][133]:={ {6,38}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {1,12}, {10,42}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,42}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET42.134 // Bipartite(9,33) Valencies [33,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3151002297514457371493642384336486400000000 EdgePairs[42][134]:={ {6,38}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {4,28}, {9,10}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {9,11}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {1,10}, {8,37}, {4,13}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {2,10}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {4,10}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {9,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {3,33}, {2,11}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {5,10}, {8,28}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {4,19}, {8,39}, {3,37}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET42.135 // Bipartite(8,34) Valencies [34,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 11903786457276838958975982340826726400000000 EdgePairs[42][135]:={ {6,38}, {6,25}, {5,38}, {5,22}, {4,28}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {6,9}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {1,20}, {3,18}, {8,16}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {8,9}, {2,10}, {3,9}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {1,36}, {6,18}, {1,29}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {8,42}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {4,9}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {4,10}, {5,14}, {3,29}, {1,41}, {2,23}, {4,11}, {3,25}, {7,35}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {5,39}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,37}, {8,32}, {7,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {7,29}, {2,28}, {8,29}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {5,9}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {7,38}, {5,42}, {2,38}, {7,9}, {5,10}, {8,28}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {5,36}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,9}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {6,40} }; // ET42.136 // Bipartite(7,35) Valencies [35,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 52079065750586170445519922741116928000000000 EdgePairs[42][136]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {7,38}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {7,41}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {7,12}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {4,42}, {6,8}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {5,42}, {7,31}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {1,25}, {6,19}, {6,9}, {7,29}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {1,41}, {3,41}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {2,18}, {5,35}, {1,34}, {5,37}, {7,19}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {7,42}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET42.137 // Non-bipartite Valency 35 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 11800915893414789120000000 EdgePairs[42][137]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {24,33}, {30,37}, {11,42}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {25,42}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {19,22}, {8,28}, {33,41}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {14,16}, {12,32}, {2,30}, {14,25}, {28,29}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {29,42}, {10,27}, {1,41}, {7,10}, {4,30}, {21,35}, {31,42}, {35,37}, {8,24}, {2,38}, {20,42}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {18,28}, {4,34}, {13,29}, {31,38}, {10,22}, {18,37}, {25,29}, {25,32}, {20,29}, {12,22}, {10,42}, {14,40}, {35,36}, {9,41}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {34,39}, {13,15}, {2,8}, {17,42}, {20,28}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {28,42}, {35,40}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {25,41}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {3,14}, {23,33}, {21,42}, {4,41}, {9,22}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {34,36}, {13,33}, {10,23}, {15,24}, {18,35}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {35,41}, {18,42}, {32,41}, {10,16}, {6,14}, {15,34}, {16,42}, {24,30}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {27,41}, {6,11}, {1,22}, {6,24}, {6,39}, {35,39}, {19,35}, {1,42}, {16,34}, {19,31}, {22,41}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {31,39}, {30,40}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {33,40}, {13,18}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {21,22}, {10,19}, {12,19}, {14,35}, {15,27}, {12,41}, {5,42}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {29,41}, {9,28}, {6,13}, {11,19}, {20,40}, {19,24}, {35,38}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {27,38}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {20,23}, {32,37}, {7,42}, {14,36}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {10,28}, {15,23}, {12,17}, {9,42}, {30,38}, {9,19}, {13,35}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {31,41}, {17,36}, {17,23}, {26,39}, {21,29}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {28,37}, {15,42}, {2,40}, {1,11}, {15,30}, {24,34}, {3,19}, {4,40}, {23,38}, {2,16}, {16,36}, {29,40}, {1,39}, {7,40}, {17,37}, {14,19}, {18,25}, {32,42}, {21,27}, {10,37}, {25,36}, {2,42}, {7,8}, {15,37}, {7,35}, {4,42}, {21,23}, {15,29}, {20,38}, {14,41}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {34,41}, {16,22}, {32,40}, {3,35}, {14,26}, {18,23}, {12,15}, {9,40}, {25,30}, {14,31}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {30,41}, {11,16}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {5,40}, {16,31}, {22,36}, {22,30}, {24,42}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {1,40}, {6,23}, {28,35}, {10,26}, {1,23}, {8,29}, {17,31}, {7,22}, {23,41}, {25,40}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {16,41}, {33,36}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {2,10}, {6,17}, {19,33}, {19,29}, {3,34}, {18,39}, {13,20}, {7,12}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {16,40}, {26,41}, {9,33}, {8,16}, {8,42}, {20,35}, {8,32}, {7,38}, {14,30}, {15,38}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {33,38}, {28,38}, {19,42}, {24,29}, {17,34}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {33,42}, {6,18}, {5,12}, {17,39}, {6,42}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {13,24}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {26,38}, {18,24}, {21,24}, {16,39}, {30,42}, {1,38}, {5,37}, {7,41}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {33,39}, {1,36}, {18,40}, {26,30}, {13,30}, {9,24}, {24,32}, {14,39}, {14,42}, {6,20}, {3,39}, {10,41}, {34,42}, {11,15}, {6,26}, {12,34}, {23,35}, {15,41}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {17,41}, {11,30}, {34,37}, {28,41}, {2,23}, {7,39}, {9,38}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {29,39}, {4,23}, {22,34}, {27,30}, {24,38}, {9,36}, {32,36}, {10,40}, {6,27}, {29,37}, {12,40}, {21,41}, {17,40}, {20,41}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {11,40}, {13,42}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {35,42}, {18,32}, {21,32}, {24,40}, {26,42}, {23,30}, {21,26}, {22,31}, {22,35}, {5,39}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {23,42}, {7,20}, {3,40}, {22,42}, {12,36}, {27,31}, {7,18}, {21,39}, {10,21}, {3,33}, {32,38}, {27,35}, {28,30}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {4,18}, {15,26}, {2,18}, {18,41}, {21,28}, {23,36}, {16,38}, {12,37}, {4,8}, {1,16}, {2,19}, {17,30}, {27,42}, {24,41}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {27,29}, {30,39}, {31,40}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {13,16}, {5,11}, {6,41}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET42.138 // Bipartite(6,36) Valencies [36,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 267835195288728876576959602668601344000000000 EdgePairs[42][138]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {4,42}, {6,8}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {6,23}, {3,26}, {5,28}, {5,42}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {6,19}, {6,9}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {6,42}, {4,40}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {1,41}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {5,19}, {6,20}, {5,21}, {2,30}, {6,13}, {2,18}, {5,35}, {1,34}, {5,37}, {4,17}, {6,35}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET42.139 // Non-bipartite Valency 36 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 505542895416115200000000 EdgePairs[42][139]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {24,33}, {30,37}, {11,42}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {25,42}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {8,28}, {36,37}, {33,41}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {12,32}, {22,25}, {2,30}, {14,25}, {5,9}, {7,15}, {3,25}, {4,12}, {29,42}, {10,27}, {1,41}, {4,30}, {21,35}, {31,42}, {35,37}, {8,24}, {2,38}, {20,42}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {31,38}, {10,22}, {18,37}, {5,7}, {25,32}, {20,29}, {12,22}, {10,42}, {14,40}, {9,41}, {15,20}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {34,39}, {2,8}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {28,42}, {35,40}, {6,19}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {25,41}, {2,37}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {36,38}, {16,23}, {21,30}, {3,14}, {23,33}, {21,42}, {4,41}, {9,22}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {7,14}, {12,38}, {13,33}, {10,23}, {15,24}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {26,32}, {35,41}, {18,42}, {32,41}, {10,16}, {6,14}, {15,34}, {16,42}, {24,30}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {27,41}, {6,11}, {1,22}, {6,24}, {29,32}, {6,39}, {35,39}, {19,35}, {10,14}, {1,42}, {16,34}, {19,31}, {22,41}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {18,21}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {1,12}, {5,36}, {9,26}, {12,39}, {18,20}, {6,12}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {33,40}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {12,19}, {14,35}, {15,27}, {36,41}, {12,41}, {5,42}, {11,32}, {3,31}, {23,39}, {11,18}, {3,20}, {5,29}, {21,25}, {27,36}, {29,41}, {9,28}, {6,13}, {11,19}, {20,40}, {35,38}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {36,39}, {9,37}, {27,38}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {1,28}, {27,33}, {1,17}, {3,36}, {9,14}, {32,37}, {7,42}, {14,36}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {4,7}, {10,28}, {15,23}, {12,17}, {2,7}, {9,42}, {30,38}, {9,19}, {13,35}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {31,41}, {17,36}, {17,23}, {26,39}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {18,19}, {14,28}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {28,37}, {15,42}, {2,40}, {36,40}, {1,11}, {29,33}, {15,30}, {24,34}, {3,19}, {4,40}, {23,38}, {2,16}, {16,36}, {29,40}, {1,39}, {7,40}, {17,37}, {14,19}, {18,25}, {32,42}, {21,27}, {10,37}, {25,36}, {2,42}, {15,37}, {7,35}, {9,13}, {4,42}, {15,29}, {20,38}, {30,33}, {14,41}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {3,26}, {13,36}, {9,23}, {3,8}, {34,41}, {16,22}, {32,40}, {3,35}, {14,26}, {18,23}, {12,15}, {9,40}, {8,22}, {14,31}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {30,41}, {11,16}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {9,30}, {2,13}, {5,40}, {16,31}, {22,36}, {22,30}, {24,42}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {1,40}, {6,23}, {28,35}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {23,41}, {25,40}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {2,10}, {6,17}, {19,33}, {19,29}, {3,34}, {18,39}, {11,14}, {13,20}, {13,21}, {3,11}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {16,40}, {26,41}, {15,19}, {9,33}, {29,34}, {8,16}, {8,42}, {20,35}, {8,32}, {7,38}, {14,30}, {15,38}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {6,7}, {24,27}, {1,7}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {36,42}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {33,38}, {28,38}, {19,42}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {33,42}, {6,18}, {5,12}, {17,39}, {6,42}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {20,34}, {25,34}, {4,31}, {2,15}, {30,32}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {23,25}, {26,38}, {18,24}, {8,14}, {16,39}, {30,42}, {1,38}, {5,37}, {7,41}, {8,23}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {33,39}, {1,36}, {18,40}, {13,30}, {9,24}, {24,32}, {14,39}, {14,42}, {6,20}, {3,39}, {10,41}, {34,42}, {11,15}, {6,26}, {12,34}, {23,35}, {15,41}, {8,19}, {4,20}, {7,21}, {23,31}, {12,16}, {17,41}, {11,30}, {34,37}, {28,41}, {2,23}, {7,39}, {15,21}, {9,38}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {4,23}, {22,34}, {24,38}, {9,36}, {8,13}, {10,40}, {16,21}, {6,27}, {29,37}, {12,40}, {21,41}, {17,40}, {20,41}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {11,40}, {13,42}, {25,31}, {5,14}, {5,35}, {11,22}, {9,16}, {16,32}, {9,32}, {35,42}, {30,35}, {18,32}, {21,32}, {24,40}, {26,42}, {23,30}, {21,26}, {22,31}, {30,31}, {22,35}, {5,39}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {23,42}, {7,20}, {3,40}, {16,19}, {23,27}, {22,42}, {12,36}, {27,31}, {7,18}, {21,39}, {10,21}, {3,33}, {32,38}, {27,35}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {2,18}, {18,41}, {21,28}, {23,36}, {16,38}, {12,37}, {4,8}, {29,31}, {1,16}, {2,19}, {17,30}, {27,42}, {24,41}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {30,39}, {31,40}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {5,11}, {6,41}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET42.140 // Bipartite(5,37) Valencies [37,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1651650370947161405557917549789708288000000000 EdgePairs[42][140]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {2,42}, {3,18}, {3,17}, {3,7}, {4,38}, {3,34}, {2,25}, {5,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {4,42}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {3,29}, {3,10}, {3,26}, {5,28}, {5,42}, {2,17}, {4,36}, {5,41}, {4,6}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {1,15}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,40}, {2,31}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {1,41}, {5,6}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {2,30}, {5,21}, {2,18}, {5,35}, {1,34}, {5,37}, {4,17}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET42.141 // Bipartite(4,38) Valencies [38,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12552542819198426682240173378401782988800000000 EdgePairs[42][141]:={ {1,15}, {4,35}, {3,15}, {2,38}, {4,42}, {1,11}, {4,14}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {1,40}, {2,20}, {4,40}, {1,25}, {4,16}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {4,37}, {4,20}, {2,41}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {4,39}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {3,23}, {4,31}, {2,42}, {2,34}, {3,27}, {4,30}, {1,19}, {2,40}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,35}, {1,26}, {4,38}, {2,24}, {4,11}, {3,42}, {2,27}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {1,42}, {2,6}, {3,21}, {1,14}, {1,41}, {4,32}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {4,9}, {2,7}, {4,34}, {4,41}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET42.142 // Bipartite(3,39) Valencies [39,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 122387292487184660151841690439417384140800000000 EdgePairs[42][142]:={ {1,15}, {3,15}, {2,38}, {1,11}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {2,11}, {1,40}, {2,20}, {1,25}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {2,41}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {2,42}, {2,34}, {3,27}, {1,19}, {2,40}, {2,35}, {2,9}, {3,5}, {1,4}, {1,35}, {1,26}, {2,4}, {2,24}, {3,42}, {2,27}, {3,4}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {1,42}, {2,6}, {3,21}, {1,14}, {1,41}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET42.143 // Non-bipartite Valency 39 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 6831653917205672755200 EdgePairs[42][143]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {13,18}, {2,6}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {19,27}, {32,34}, {7,12}, {21,34}, {4,10}, {33,34}, {3,19}, {1,15}, {5,8}, {10,30}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {30,31}, {7,42}, {21,31}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {3,27}, {29,39}, {25,32}, {5,13}, {15,33}, {21,33}, {30,34}, {22,27}, {17,36}, {10,35}, {13,40}, {11,15}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {13,41}, {22,37}, {12,26}, {15,34}, {18,41}, {7,16}, {12,16}, {14,19}, {3,38}, {13,24}, {11,30}, {30,32}, {6,42}, {4,21}, {12,42}, {30,33}, {29,36}, {20,34}, {23,29}, {1,33}, {4,25}, {2,42}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, {36,42}, {1,30}, {23,42}, {14,27}, {11,35}, {2,29}, {16,39}, {15,31}, {10,21}, {17,23}, {12,19}, {3,7}, {10,25}, {6,17}, {32,35}, {20,33}, {29,42}, {2,17}, {33,35}, {36,37}, {20,32}, {18,40}, {11,33}, {19,22}, {16,26}, {3,22}, {5,24}, {11,32}, {1,5}, {28,37}, {11,20}, {24,41}, {17,28}, {1,8}, {11,24}, {1,35}, {9,17}, {10,18}, {19,38}, {8,15}, {5,20}, {14,16}, {3,12}, {3,26}, {11,31}, {16,22}, {12,39}, {6,36}, {5,15}, {20,30}, {2,36}, {4,18}, {35,41}, {22,38}, {26,39}, {8,11}, {15,35}, {30,41}, {14,38}, {5,41}, {12,27}, {11,13}, {15,30}, {7,19}, {11,34}, {8,32}, {7,39}, {22,39}, {19,26}, {8,33}, {8,20}, {5,31}, {20,35}, {16,19}, {1,13}, {26,38}, {9,23}, {7,14}, {34,41}, {5,34}, {9,29}, 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{23,30}, {29,34}, {15,23}, {17,31}, {2,31}, {13,28}, {9,18}, {20,26}, {10,17}, {11,29}, {12,15}, {3,40}, {11,42}, {11,16}, {2,34}, {8,19}, {22,40}, {20,42}, {13,37}, {33,42}, {6,34}, {2,21}, {23,35}, {18,28}, {29,33}, {32,42}, {28,41}, {29,35}, {21,23}, {23,25}, {29,32}, {23,32}, {6,21}, {1,12}, {2,32}, {6,33}, {5,19}, {18,38}, {23,33}, {7,20}, {4,29}, {1,42}, {3,8}, {10,39}, {6,25}, {4,17}, {7,31}, {12,33}, {2,25}, {17,35}, {6,32}, {2,33}, {7,15}, {12,32}, {2,4}, {1,26}, {15,26}, {12,20}, {38,41}, {11,36}, {5,14}, {5,27}, {8,27}, {15,42}, {15,16}, {3,13}, {17,30}, {30,39}, {24,37}, {4,39}, {23,31}, {25,29}, {28,40}, {35,39}, {16,35}, {24,27}, {18,37}, {13,19}, {4,36}, {10,29}, {21,42}, {14,41}, {13,22}, {14,40}, {37,40}, {9,41}, {7,11}, {26,34}, {7,34}, {23,34}, {10,23}, {33,39}, {14,24}, {21,29}, {8,22}, {32,39}, {2,10}, {5,38}, {6,10}, {25,42}, {9,40}, {1,16}, {10,36}, {16,30}, {12,34}, {7,33}, {12,31}, {15,19}, {7,32}, {13,27}, {11,39}, {19,24}, {5,7}, {7,30}, {26,31}, {9,10}, {31,39}, {8,14}, {4,23}, {8,12}, {5,22}, {22,41}, {7,35}, {17,25}, {34,39}, {3,24}, {8,38}, {17,21}, {15,27}, {3,20}, {5,12}, {26,32}, {4,9}, {26,33}, {11,22}, {16,20}, {20,39}, {27,41}, {11,26}, {34,38}, {5,26}, {16,32}, {39,41}, {31,38}, {13,16}, {16,33}, {13,38}, {16,31}, {20,27}, {16,24}, {3,15}, {26,35}, {10,28}, {16,34}, {25,36}, {12,30}, {20,38}, {3,41}, {15,39}, {18,29}, {4,42}, {24,38}, {33,38}, {32,38}, {21,36}, {1,19}, {26,30}, {19,41}, {11,14}, {12,35}, {14,35}, {19,32}, {36,40}, {19,33}, {3,34}, {3,31}, {11,19}, {24,39}, {8,16}, {13,26}, {1,39}, {4,37}, {1,14}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {25,28}, {8,26}, {30,38}, {3,32}, {10,42}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {24,26}, {8,10}, {1,22}, {27,33}, {14,34}, {17,19}, {7,24}, {9,12}, {29,40}, {11,27}, {26,41}, {27,32}, {35,38}, {10,37}, {22,30}, {27,34}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {22,35}, {32,40}, {16,41}, {33,40}, {15,18}, {2,14}, {3,35}, {27,31}, {26,28}, {13,39}, {6,14}, {14,31}, {4,8}, {17,27}, {24,25}, {13,21}, {27,29}, {5,10}, {3,17}, {12,28}, {36,38}, {19,35}, {21,24}, {1,18}, {6,22}, {22,31}, {14,32}, {22,33}, {5,39}, {25,37}, {13,25}, {14,33}, {2,22}, {3,29}, {22,32}, {8,39}, {19,30}, {7,41}, {21,41}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {18,42}, {7,37}, {38,42}, {9,16}, {3,36}, {2,40}, {11,38}, {12,41}, {4,13}, {6,40}, {31,40}, {14,17}, {5,25}, {25,41}, {5,21}, {20,40}, {18,32}, {7,28}, {14,23}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {22,42}, {1,4}, {14,29}, {18,34}, {19,23}, {18,31}, {26,37}, {14,42}, {15,40}, {2,19}, {6,19}, {4,24}, {12,37}, {17,22}, {27,28}, {14,36}, {27,36}, {26,29}, {8,18}, {8,21}, {10,15}, {12,17}, {30,40}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {17,38}, {6,27}, {16,37}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {7,17}, {20,25}, {4,41}, {3,42}, {3,28}, {9,27}, {11,25}, {11,21}, {19,42}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // ET42.144 // Bipartite(2,40) Valencies [40,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1631830566495795468691222539192231788544000000000 EdgePairs[42][144]:={ {2,11}, {1,26}, {2,14}, {1,14}, {2,37}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,37}, {1,33}, {1,40}, {1,10}, {2,39}, {1,39}, {1,36}, {1,6}, {2,40}, {2,6}, {1,4}, {1,20}, {1,12}, {2,36}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {1,38}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,38}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {2,42}, {1,28}, {2,19}, {1,42}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {2,41}, {1,41}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET42.145 // Non-bipartite Valency 40 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 107145471557284795514880000 EdgePairs[42][145]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {13,18}, {2,6}, {32,33}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {19,27}, {32,34}, {7,12}, {31,33}, {21,34}, {4,10}, {3,19}, {1,15}, {5,8}, {10,30}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {30,31}, {7,42}, {21,31}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {34,35}, {3,27}, {29,39}, {25,32}, {5,13}, 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{6,15}, {7,21}, {3,5}, {19,40}, {18,22}, {29,31}, {8,37}, {37,41}, {12,25}, {22,24}, {2,15}, {20,36}, {6,31}, {9,13}, {1,7}, {1,23}, {12,21}, {23,30}, {29,34}, {15,23}, {17,31}, {2,31}, {13,28}, {9,18}, {20,26}, {10,17}, {11,29}, {12,15}, {3,40}, {11,42}, {11,16}, {2,34}, {8,19}, {22,40}, {20,42}, {13,37}, {33,42}, {6,34}, {2,21}, {23,35}, {18,28}, {29,33}, {32,42}, {28,41}, {29,35}, {21,23}, {23,25}, {29,32}, {23,32}, {6,21}, {1,12}, {2,32}, {6,33}, {5,19}, {18,38}, {23,33}, {7,20}, {4,29}, {1,42}, {3,8}, {10,39}, {6,25}, {4,17}, {7,31}, {12,33}, {2,25}, {17,35}, {6,32}, {2,33}, {4,6}, {7,15}, {12,32}, {2,4}, {1,26}, {15,26}, {12,20}, {38,41}, {11,36}, {5,14}, {5,27}, {8,27}, {15,42}, {3,13}, {17,30}, {30,39}, {24,37}, {4,39}, {23,31}, {25,29}, {28,40}, {35,39}, {16,35}, {24,27}, {18,37}, {13,19}, {4,36}, {10,29}, {21,42}, {14,41}, {13,22}, {14,40}, {37,40}, {9,41}, {7,11}, {26,34}, {7,34}, {23,34}, {10,23}, {33,39}, {14,24}, {21,29}, {8,22}, {32,39}, {2,10}, {5,38}, {6,10}, {25,42}, {9,40}, {1,16}, {10,36}, {16,30}, {12,34}, {7,33}, {12,31}, {15,19}, {7,32}, {13,27}, {11,39}, {19,24}, {5,7}, {7,30}, {26,31}, {31,39}, {8,14}, {4,23}, {8,12}, {5,22}, {22,41}, {7,35}, {17,25}, {1,3}, {34,39}, {3,24}, {8,38}, {17,21}, {15,27}, {3,20}, {5,12}, {26,32}, {4,9}, {26,33}, {11,22}, {16,20}, {20,39}, {27,41}, {11,26}, {34,38}, {5,26}, {16,32}, {39,41}, {13,16}, {31,38}, {16,33}, {13,38}, {16,31}, {20,27}, {16,24}, {3,15}, {26,35}, {10,28}, {16,34}, {25,36}, {12,30}, {20,38}, {3,41}, {15,39}, {18,29}, {4,42}, {24,38}, {33,38}, {32,38}, {21,36}, {1,19}, {26,30}, {19,41}, {11,14}, {12,35}, {14,35}, {19,32}, {36,40}, {19,33}, {3,34}, {3,31}, {11,19}, {24,39}, {8,16}, {13,26}, {1,39}, {4,37}, {1,14}, {14,15}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {25,28}, {8,26}, {30,38}, {3,32}, {10,42}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {24,26}, {40,42}, {8,10}, {1,22}, {27,33}, {14,34}, {17,19}, {7,24}, {9,12}, {29,40}, {11,27}, {26,41}, {27,32}, {35,38}, {22,23}, {4,5}, {10,37}, {22,30}, {27,34}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {22,35}, {32,40}, {16,41}, {33,40}, {15,18}, {2,14}, {3,35}, {27,31}, {26,28}, {13,39}, {6,14}, {14,31}, {4,8}, {17,27}, {24,25}, {7,9}, {13,21}, {27,29}, {5,10}, {3,17}, {12,28}, {36,38}, {19,35}, {21,24}, {1,18}, {6,22}, {22,31}, {14,32}, {22,33}, {5,39}, {25,37}, {13,25}, {14,33}, {2,22}, {2,3}, {3,29}, {22,32}, {8,39}, {19,30}, {7,41}, {21,41}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {18,42}, {7,37}, {38,42}, {9,16}, {3,36}, {2,40}, {11,38}, {12,41}, {4,13}, {6,40}, {31,40}, {14,17}, {5,25}, {25,41}, {5,21}, {20,40}, {18,32}, {7,28}, {14,23}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {22,42}, {1,4}, {14,29}, {18,34}, {19,23}, {18,31}, {26,37}, {14,42}, {15,40}, {2,19}, {6,19}, {4,24}, {12,37}, {17,22}, {14,36}, {27,36}, {26,29}, {8,18}, {8,21}, {10,15}, {12,17}, {30,40}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {17,38}, {6,27}, {16,37}, {37,39}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {20,21}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {7,17}, {10,11}, {20,25}, {4,41}, {3,42}, {3,28}, {9,27}, {11,25}, {16,17}, {11,21}, {19,42}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // ET42.146 // Bipartite(1,41) Valencies [41,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 33452526613163807108170062053440751665152000000000 EdgePairs[42][146]:={ {1,26}, {1,14}, {1,24}, {1,29}, {1,30}, {1,32}, {1,37}, {1,33}, {1,40}, {1,10}, {1,2}, {1,39}, {1,36}, {1,6}, {1,4}, {1,20}, {1,12}, {1,31}, {1,38}, {1,7}, {1,15}, {1,16}, {1,21}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {1,28}, {1,42}, {1,8}, {1,13}, {1,19}, {1,9}, {1,41}, {1,22}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25} }; // ET42.147 // Non-bipartite Valency 41 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 1405006117752879898543142606244511569936384000000000 EdgePairs[42][147]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {13,18}, {2,6}, {32,33}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {19,27}, {32,34}, {7,12}, {31,33}, {21,34}, {4,10}, {33,34}, {3,19}, {1,15}, {5,8}, {10,30}, {31,32}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {7,42}, {30,31}, {21,31}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {34,35}, {3,27}, {29,39}, {25,32}, {5,13}, {15,33}, {21,33}, {22,27}, {30,34}, {17,36}, {10,35}, {13,40}, {11,15}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {13,41}, {22,37}, {12,26}, {15,34}, {18,41}, {7,16}, {12,16}, {14,19}, {3,38}, {13,24}, {11,30}, {30,32}, {6,42}, {4,21}, {12,42}, {29,36}, {30,33}, {20,34}, {23,29}, {1,33}, {4,25}, {2,42}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, {36,42}, {1,30}, {23,42}, {14,27}, {11,35}, {2,29}, {16,39}, {15,31}, {10,21}, {17,23}, {12,19}, {3,7}, {10,25}, {6,17}, {32,35}, {20,33}, {2,17}, {29,42}, {33,35}, {36,37}, {20,32}, {18,40}, {11,33}, {19,22}, {16,26}, {3,22}, {5,24}, {11,32}, {1,5}, {28,37}, {26,27}, {11,20}, {24,41}, {17,28}, {1,8}, {11,24}, {1,35}, {9,17}, {10,18}, {19,38}, {8,15}, {5,20}, {14,16}, {3,12}, {3,26}, {28,29}, {11,31}, {16,22}, {12,39}, {6,36}, {5,15}, {20,30}, {2,36}, {4,18}, {35,41}, {22,38}, {26,39}, {8,11}, {15,35}, {30,41}, {14,38}, {5,41}, {12,27}, {11,13}, {15,30}, {7,19}, {11,34}, {8,32}, {7,39}, {22,39}, {19,26}, {8,33}, {8,20}, {5,31}, {20,35}, {16,19}, {1,13}, {26,38}, {9,23}, {7,14}, {34,41}, {13,15}, {5,34}, {9,29}, {13,35}, {14,26}, {23,28}, {7,27}, {2,9}, {10,40}, {29,37}, {38,39}, {13,30}, {6,9}, {17,42}, {13,20}, {16,27}, {37,42}, {23,36}, {8,41}, {5,32}, {5,33}, {8,31}, {17,37}, {5,11}, {3,16}, {20,24}, {7,22}, {22,26}, {12,14}, {12,22}, {7,38}, {13,34}, {28,36}, {23,24}, {9,36}, {3,4}, {31,41}, {8,34}, {15,24}, {10,19}, {1,24}, {41,42}, {20,41}, {12,38}, {27,39}, {32,41}, {31,37}, {14,39}, {34,37}, {2,13}, {5,30}, {33,41}, {24,30}, {6,13}, {5,35}, {24,35}, {8,17}, {1,9}, {18,25}, {4,40}, {2,37}, {12,18}, {6,37}, {9,15}, {3,10}, {21,40}, {18,21}, {8,30}, {13,31}, {2,28}, {25,40}, {22,25}, {15,28}, {6,28}, {14,21}, {7,18}, {11,41}, {21,22}, {14,25}, {5,17}, {24,33}, {20,28}, {13,32}, {13,33}, {35,37}, {10,27}, {9,11}, {24,32}, {16,18}, {32,37}, {33,37}, {19,39}, {1,41}, {3,39}, {5,29}, {28,42}, {8,35}, {15,41}, {6,24}, {24,31}, {9,32}, {39,40}, {2,5}, {2,24}, {4,19}, {5,6}, {9,33}, {9,20}, {18,26}, {8,29}, {4,14}, {30,37}, {8,23}, {3,21}, {5,36}, {23,37}, {4,27}, {2,8}, {6,8}, {24,29}, {9,42}, {13,17}, {3,25}, {1,37}, {13,23}, {12,40}, {36,41}, {1,28}, {13,42}, {16,38}, {25,27}, {9,31}, {21,27}, {4,38}, {8,9}, {28,32}, {24,34}, {10,14}, {13,29}, {4,22}, {4,7}, {10,22}, {10,12}, {24,42}, {26,40}, {17,24}, {28,33}, {21,38}, {15,37}, {2,41}, {8,36}, {23,41}, {9,34}, {15,17}, {10,38}, {6,41}, {34,36}, {11,28}, {13,36}, {18,19}, {28,34}, {19,25}, {25,38}, {19,21}, {20,37}, {6,11}, {38,40}, {5,23}, {11,23}, {35,42}, {31,36}, {2,11}, {9,30}, {29,41}, {7,40}, {20,29}, {33,36}, {32,36}, {28,31}, {30,42}, {18,27}, {1,6}, {11,37}, {1,2}, {5,9}, {4,26}, {4,12}, {2,30}, {3,18}, {7,10}, {1,29}, {6,30}, {9,35}, {1,17}, {8,28}, {5,42}, {18,39}, {21,26}, {17,41}, {35,36}, {5,28}, {25,26}, {17,33}, {2,35}, {10,26}, {17,20}, {16,40}, {6,35}, {15,29}, {17,32}, {28,35}, {24,28}, {8,42}, {27,40}, {16,25}, {11,17}, {25,39}, {16,21}, {5,37}, {24,36}, {9,24}, {21,39}, {30,36}, {6,20}, {2,20}, {1,36}, {14,18}, {10,16}, {4,16}, {34,42}, {20,23}, {7,25}, {15,36}, {17,34}, {28,30}, {31,42}, {6,15}, {7,21}, {3,5}, {19,40}, {18,22}, {29,31}, {8,37}, {37,41}, {12,25}, {22,24}, {2,15}, {13,14}, {20,36}, {6,31}, {9,13}, {1,7}, {1,23}, {12,21}, {23,30}, {29,34}, {15,23}, {17,31}, {2,31}, {13,28}, {9,18}, {20,26}, {10,17}, {11,29}, {12,15}, {3,40}, {11,42}, {11,16}, {2,34}, {8,19}, {22,40}, {20,42}, {13,37}, {33,42}, {6,34}, {2,21}, {23,35}, {18,28}, {29,33}, {32,42}, {28,41}, {29,35}, {21,23}, {23,25}, {29,32}, {23,32}, {6,21}, {1,12}, {2,32}, {6,33}, {5,19}, {18,38}, {23,33}, {7,20}, {4,29}, {1,42}, {3,8}, {10,39}, {6,25}, {4,17}, {7,31}, {12,33}, {2,25}, {17,35}, {6,32}, {2,33}, {4,6}, {7,15}, {12,32}, {2,4}, {1,26}, {15,26}, {12,20}, {11,12}, {38,41}, {11,36}, {5,14}, {29,30}, {5,27}, {8,27}, {15,42}, {15,16}, {3,13}, {17,30}, {30,39}, {24,37}, {4,39}, {23,31}, {25,29}, {28,40}, {35,39}, {16,35}, {24,27}, {18,37}, {13,19}, {4,36}, {10,29}, {21,42}, {14,41}, {13,22}, {14,40}, {37,40}, {9,41}, {7,11}, {26,34}, {7,34}, {23,34}, {10,23}, {33,39}, {14,24}, {21,29}, {8,22}, {32,39}, {2,10}, {5,38}, {6,10}, {25,42}, {9,40}, {1,16}, {10,36}, {16,30}, {12,34}, {7,33}, {12,31}, {15,19}, {7,32}, {13,27}, {11,39}, {19,24}, {5,7}, {7,30}, {26,31}, {9,10}, {17,18}, {31,39}, {8,14}, {4,23}, {8,12}, {5,22}, {22,41}, {7,35}, {17,25}, {1,3}, {34,39}, {3,24}, {8,38}, {17,21}, {15,27}, {3,20}, {5,12}, {26,32}, {4,9}, {26,33}, {11,22}, {16,20}, {20,39}, {27,41}, {11,26}, {34,38}, {7,8}, {5,26}, {16,32}, {39,41}, {13,16}, {31,38}, {16,33}, {13,38}, {16,31}, {20,27}, {16,24}, {3,15}, {26,35}, {10,28}, {16,34}, {25,36}, {12,30}, {20,38}, {3,41}, {15,39}, {18,29}, {4,42}, {24,38}, {33,38}, {32,38}, {21,36}, {1,19}, {26,30}, {19,41}, {11,14}, {12,35}, {14,35}, {19,32}, {36,40}, {19,33}, {3,34}, {3,31}, {11,19}, {24,39}, {19,20}, {8,16}, {13,26}, {1,39}, {4,37}, {1,14}, {14,15}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {25,28}, {8,26}, {30,38}, {3,32}, {10,42}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {24,26}, {40,42}, {8,10}, {1,22}, {27,33}, {14,34}, {17,19}, {7,24}, {9,12}, {29,40}, {11,27}, {26,41}, {27,32}, {35,38}, {22,23}, {4,5}, {10,37}, {22,30}, {27,34}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {22,35}, {32,40}, {16,41}, {33,40}, {15,18}, {2,14}, {3,35}, {27,31}, {26,28}, {13,39}, {6,14}, {14,31}, {4,8}, {17,27}, {24,25}, {7,9}, {13,21}, {27,29}, {5,10}, {3,17}, {12,28}, {36,38}, {19,35}, {21,24}, {1,18}, {6,22}, {22,31}, {14,32}, {22,33}, {5,39}, {25,37}, {13,25}, {14,33}, {2,22}, {2,3}, {3,29}, {22,32}, {8,39}, {19,30}, {7,41}, {21,41}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {18,42}, {7,37}, {38,42}, {9,16}, {3,36}, {2,40}, {11,38}, {12,41}, {4,13}, {6,40}, {31,40}, {14,17}, {5,25}, {25,41}, {5,21}, {20,40}, {18,32}, {7,28}, {14,23}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {22,42}, {1,4}, {14,29}, {18,34}, {19,23}, {18,31}, {26,37}, {14,42}, {15,40}, {2,19}, {6,19}, {4,24}, {12,37}, {17,22}, {27,28}, {14,36}, {27,36}, {26,29}, {8,18}, {8,21}, {10,15}, {12,17}, {30,40}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {17,38}, {6,27}, {16,37}, {37,39}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {20,21}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {7,17}, {10,11}, {20,25}, {4,41}, {3,42}, {3,28}, {9,27}, {37,38}, {11,25}, {16,17}, {11,21}, {19,42}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // Total number of connected ET graphs of order 42 is 147 // ******************************************************************************************** // Order 43 // ET43.1 // Non-bipartite Valency 2 // Diameter 21 Girth 43 // Twin-free VT AT // Automorphism group of order 86 EdgePairs[43][1]:={ {11,43}, {11,22}, {30,41}, {27,38}, {13,24}, {14,25}, {2,34}, {1,33}, {10,42}, {4,36}, {3,14}, {12,23}, {4,15}, {18,29}, {21,32}, {3,35}, {5,37}, {17,28}, {31,42}, {6,38}, {22,33}, {1,12}, {2,13}, {19,30}, {6,17}, {7,18}, {15,26}, {10,21}, {29,40}, {5,16}, {8,19}, {25,36}, {9,41}, {8,40}, {9,20}, {26,37}, {23,34}, {16,27}, {28,39}, {20,31}, {32,43}, {24,35}, {7,39} }; // ET43.2 // Non-bipartite Valency 6 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 258 EdgePairs[43][2]:={ {10,19}, {11,43}, {16,25}, {7,39}, {24,33}, {18,41}, {10,21}, {5,14}, {16,36}, {14,25}, {32,41}, {8,31}, {14,34}, {2,22}, {4,27}, {6,17}, {25,34}, {2,11}, {19,39}, {13,24}, {28,37}, {28,39}, {7,27}, {6,40}, {11,22}, {27,38}, {8,42}, {20,43}, {22,33}, {26,35}, {20,40}, {10,30}, {5,37}, {12,21}, {11,34}, {23,32}, {13,33}, {7,41}, {1,10}, {19,30}, {9,43}, {8,28}, {18,38}, {21,41}, {29,40}, {2,36}, {3,14}, {2,13}, {1,12}, {15,35}, {3,23}, {8,17}, {32,43}, {2,34}, {6,26}, {6,15}, {10,33}, {4,36}, {7,30}, {26,37}, {5,28}, {12,35}, {4,15}, {1,35}, {8,19}, {8,40}, {13,22}, {18,27}, {6,29}, {15,26}, {31,40}, {4,38}, {12,23}, {33,42}, {21,30}, {3,35}, {16,27}, {27,36}, {7,18}, {6,38}, {14,23}, {14,37}, {11,31}, {3,26}, {17,37}, {3,12}, {19,42}, {30,39}, {24,35}, {7,16}, {21,32}, {18,29}, {34,43}, {29,38}, {9,18}, {22,42}, {10,42}, {31,42}, {9,29}, {20,29}, {13,36}, {15,38}, {30,41}, {11,20}, {1,33}, {12,32}, {2,25}, {9,41}, {17,26}, {20,31}, {3,37}, {9,32}, {17,28}, {23,34}, {23,43}, {22,31}, {17,40}, {5,16}, {16,39}, {5,39}, {19,28}, {4,13}, {1,21}, {15,24}, {5,25}, {4,24}, {25,36}, {9,20}, {1,24} }; // ET43.3 // Non-bipartite Valency 14 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 602 EdgePairs[43][3]:={ {13,21}, {6,38}, {10,37}, {31,39}, {14,36}, {5,7}, {9,17}, {10,18}, {9,10}, {17,18}, {31,42}, {1,40}, {1,3}, {11,43}, {17,33}, {4,31}, {8,40}, {3,35}, {11,15}, {33,34}, {5,6}, {3,19}, {30,41}, {24,32}, {12,16}, {26,37}, {2,18}, {16,37}, {5,32}, {21,22}, {6,14}, {24,28}, {19,20}, {19,21}, {10,11}, {13,40}, {1,12}, {10,42}, {9,11}, {11,27}, {19,40}, {8,16}, {2,34}, {12,28}, {4,43}, {2,6}, {32,33}, {8,30}, {8,12}, {1,17}, {1,9}, {29,33}, {27,28}, {20,24}, {7,11}, {12,20}, {17,39}, {23,31}, {8,9}, {2,10}, {10,26}, {33,35}, {13,24}, {12,23}, {5,37}, {12,13}, {28,30}, {1,36}, {15,19}, {35,37}, {16,43}, {18,39}, {24,26}, {40,42}, {29,31}, {2,29}, {38,42}, {36,38}, {20,36}, {20,42}, {7,15}, {18,29}, {9,36}, {1,43}, {9,20}, {18,26}, {30,38}, {22,43}, {8,19}, {3,38}, {5,27}, {6,17}, {6,10}, {20,41}, {24,40}, {26,42}, {14,35}, {10,12}, {1,42}, {25,33}, {25,26}, {11,22}, {9,13}, {35,39}, {6,27}, {30,31}, {19,23}, {25,29}, {13,17}, {18,19}, {16,18}, {1,2}, {2,13}, {19,27}, {8,10}, {34,35}, {23,39}, {16,17}, {3,30}, {2,24}, {22,26}, {3,24}, {14,15}, {15,37}, {11,33}, {18,22}, {39,40}, {21,25}, {19,30}, {31,33}, {8,24}, {18,20}, {32,40}, {21,37}, {2,23}, {20,22}, {15,23}, {20,31}, {39,43}, {3,25}, {21,42}, {17,28}, {34,36}, {6,8}, {11,13}, {22,30}, {2,43}, {1,22}, {7,34}, {10,31}, {9,31}, {25,41}, {7,8}, {24,25}, {33,37}, {17,19}, {9,30}, {35,43}, {7,28}, {19,41}, {13,29}, {9,25}, {4,5}, {38,40}, {5,40}, {7,23}, {6,22}, {17,38}, {11,32}, {21,32}, {3,7}, {27,35}, {3,42}, {23,27}, {24,35}, {36,37}, {4,15}, {31,32}, {9,41}, {15,17}, {37,39}, {7,39}, {13,14}, {23,34}, {34,38}, {4,36}, {1,5}, {2,3}, {30,32}, {26,27}, {28,32}, {29,30}, {17,25}, {2,41}, {34,42}, {12,14}, {10,21}, {26,30}, {7,29}, {29,37}, {8,29}, {14,16}, {22,38}, {28,39}, {28,29}, {3,5}, {36,40}, {16,20}, {25,36}, {8,43}, {16,38}, {20,28}, {1,33}, {16,27}, {33,41}, {26,28}, {3,14}, {5,26}, {3,11}, {2,37}, {4,8}, {4,25}, {31,35}, {14,30}, {12,33}, {5,9}, {11,19}, {12,39}, {39,41}, {4,12}, {28,36}, {27,29}, {22,33}, {19,35}, {13,34}, {30,34}, {15,42}, {13,35}, {22,23}, {14,18}, {21,43}, {5,21}, {7,42}, {6,41}, {21,29}, {2,4}, {12,34}, {42,43}, {17,21}, {6,28}, {13,15}, {14,25}, {11,12}, {7,18}, {1,23}, {5,16}, {22,24}, {35,36}, {3,4}, {15,16}, {38,39}, {8,35}, {32,36}, {41,43}, {14,41}, {4,26}, {40,41}, {1,28}, {26,34}, {23,25}, {16,24}, {37,38}, {7,9}, {15,36}, {15,31}, {18,40}, {32,43}, {4,20}, {27,43}, {5,13}, {25,27}, {32,34}, {15,26}, {4,6}, {27,31}, {14,22}, {10,14}, {10,32}, {4,39}, {37,41}, {20,21}, {23,24}, {16,32}, {6,33}, {6,7}, {18,34}, {11,38}, {27,38}, {41,42}, {29,40}, {21,23} }; // ET43.4 // Bipartite(21,22) Valencies [22,21] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 57426256183845078403920019272499200000000 EdgePairs[43][4]:={ {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {5,43}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {11,43}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {21,30}, {14,31}, {15,27}, {21,41}, {3,23}, {8,23}, {10,39}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {21,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {21,22}, {13,43}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {4,43}, {21,40}, {16,42}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {20,43}, {8,37}, {20,24}, {5,41}, {17,39}, {21,38}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {19,22}, {12,42}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {13,42}, {20,35}, {9,35}, {1,36}, {1,29}, {19,42}, {12,37}, {16,34}, {10,35}, {16,43}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {20,36}, {16,40}, {20,42}, {8,22}, {18,29}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {3,43}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {19,23}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {21,25}, {14,39}, {21,31}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {18,38}, {21,37}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {20,22}, {15,23}, {12,41}, {9,22}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {21,42}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {19,41}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {21,32}, {12,25}, {16,26}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {21,39}, {19,29}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {7,40}, {2,41}, {17,41}, {5,23}, {12,43}, {20,32}, {2,26}, {18,41}, {10,40}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {4,27}, {19,43}, {18,28}, {5,24}, {2,22}, {15,29}, {18,24}, {8,43}, {2,31}, {16,38}, {1,33}, {18,27}, {20,28}, {21,33}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {21,34}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {21,35}, {11,31}, {20,33}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {21,43}, {7,42}, {21,27}, {6,41}, {21,29}, {17,24}, {17,40}, {20,23}, {12,34}, {19,36}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {18,43}, {14,25}, {20,34}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {15,22}, {14,41}, {4,26}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {21,36}, {15,31}, {8,28}, {7,43}, {18,40}, {9,40}, {20,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {9,43}, {3,37}, {8,39}, {14,22}, {9,42}, {5,36}, {9,34}, {10,32}, {15,43}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {21,24}, {17,43}, {21,26}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {6,33}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40}, {21,23} }; // ET43.5 // Bipartite(20,23) Valencies [23,20] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 62895423439449371585245735393689600000000 EdgePairs[43][5]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {5,43}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {11,43}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {16,21}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {4,43}, {16,42}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {20,43}, {8,37}, {20,24}, {5,41}, {17,39}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {19,22}, {12,42}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {13,42}, {20,35}, {9,35}, {1,36}, {1,29}, {19,42}, {12,37}, {16,34}, {10,35}, {16,43}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {20,36}, {16,40}, {20,42}, {8,22}, {18,29}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {3,43}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {18,38}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {20,22}, {15,23}, {9,22}, {12,41}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {19,41}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {19,29}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {7,40}, {2,41}, {17,41}, {5,23}, {12,43}, {20,32}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {19,43}, {18,28}, {5,24}, {2,22}, {15,29}, {18,24}, {8,43}, {2,31}, {16,38}, {1,33}, {18,27}, {20,28}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {20,23}, {12,34}, {17,21}, {19,36}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {18,43}, {14,25}, {15,21}, {20,34}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {8,28}, {7,43}, {18,40}, {9,40}, {20,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {9,43}, {3,37}, {8,39}, {14,22}, {9,42}, {5,36}, {9,34}, {10,32}, {15,43}, {4,39}, {7,36}, {12,35}, {6,35}, {17,32}, {17,43}, {20,21}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET43.6 // Bipartite(19,24) Valencies [24,19] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 75474508127339245902294882472427520000000 EdgePairs[43][6]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {5,43}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {11,43}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {19,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {16,21}, {19,20}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {1,20}, {19,40}, {2,34}, {12,28}, {19,31}, {2,25}, {4,24}, {4,43}, {16,42}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {19,22}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {13,42}, {9,35}, {1,36}, {1,29}, {19,42}, {12,37}, {16,34}, {10,35}, {16,43}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {3,43}, {15,28}, {5,28}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {4,32}, {1,30}, {19,27}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {15,23}, {9,22}, {12,41}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {2,20}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {19,41}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {19,29}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {12,43}, {5,20}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {19,43}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {8,43}, {2,31}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {12,34}, {17,21}, {19,36}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {18,43}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {8,28}, {7,43}, {18,40}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {9,43}, {3,37}, {8,39}, {14,22}, {9,42}, {5,36}, {9,34}, {10,32}, {15,43}, {4,39}, {7,36}, {12,35}, {6,35}, {17,32}, {17,43}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {2,32}, {12,21}, {6,33}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET43.7 // Bipartite(18,25) Valencies [25,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 99308563325446376187230108516352000000000 EdgePairs[43][7]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {11,25}, {4,28}, {5,43}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {11,43}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,29}, {11,35}, {10,42}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {4,43}, {16,42}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {16,25}, {13,42}, {9,35}, {1,36}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {16,43}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {3,38}, {5,27}, {3,43}, {15,28}, {5,28}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {4,32}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {18,20}, {18,38}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {16,41}, {7,28}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {12,43}, {5,20}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {8,43}, {2,31}, {14,19}, {16,38}, {1,33}, {18,27}, {12,36}, {16,27}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {12,34}, {17,21}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {13,33}, {18,43}, {14,20}, {14,25}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {8,28}, {7,43}, {18,40}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {9,43}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {5,36}, {16,19}, {9,34}, {10,32}, {15,43}, {4,39}, {7,36}, {12,35}, {6,35}, {17,32}, {12,19}, {17,43}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {2,32}, {6,33}, {12,21}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET43.8 // Bipartite(17,26) Valencies [26,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 143445702581200321159332378968064000000000 EdgePairs[43][8]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {11,25}, {4,28}, {5,43}, {17,18}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {11,43}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,29}, {11,35}, {10,42}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {9,18}, {12,28}, {2,25}, {4,24}, {4,43}, {16,42}, {15,32}, {4,30}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {16,43}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {3,43}, {15,28}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {17,28}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {16,41}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {8,43}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {12,34}, {17,21}, {6,28}, {6,42}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {15,18}, {16,33}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {9,43}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {5,36}, {16,19}, {9,34}, {10,32}, {15,43}, {4,39}, {7,36}, {12,35}, {6,35}, {17,32}, {12,19}, {17,43}, {1,37}, {8,25}, {2,42}, {16,32}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET43.9 // Bipartite(16,27) Valencies [27,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 227825527628965215958939660713984000000000 EdgePairs[43][9]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {5,43}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {11,43}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {16,21}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {4,43}, {16,42}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {16,43}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {16,40}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {3,43}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {16,30}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {9,41}, {6,23}, {16,31}, {15,17}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {16,20}, {8,43}, {2,31}, {14,19}, {16,38}, {1,33}, {12,36}, {16,27}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {12,34}, {6,28}, {6,42}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {16,39}, {1,28}, {13,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {9,43}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {16,19}, {9,34}, {10,32}, {15,43}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {16,32}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET43.10 // Bipartite(15,28) Valencies [28,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 398694673350689127928144406249472000000000 EdgePairs[43][10]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {5,43}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {11,43}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,43}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {3,43}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {14,33}, {15,37}, {10,38}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {13,38}, {14,40}, {9,41}, {6,23}, {15,17}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {8,43}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {12,34}, {6,28}, {6,42}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {15,18}, {5,17}, {3,40}, {15,16}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {9,43}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {15,43}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET43.11 // Bipartite(14,29) Valencies [29,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 770809701811332313994412518748979200000000 EdgePairs[43][11]:={ {13,21}, {6,38}, {11,40}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {5,43}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {14,15}, {14,33}, {10,38}, {14,23}, {6,16}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {14,43}, {3,22}, {14,37}, {13,38}, {4,15}, {14,40}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {6,28}, {6,42}, {4,35}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {14,41}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET43.12 // Bipartite(13,30) Valencies [30,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1651735075309997815702312540176384000000000 EdgePairs[43][12]:={ {13,21}, {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {5,43}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {13,39}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {6,14}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {13,25}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {4,14}, {13,38}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {13,14}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {12,14}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {6,28}, {6,42}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET43.13 // Bipartite(12,31) Valencies [31,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3938752871893071714367052980420608000000000 EdgePairs[43][13]:={ {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {3,26}, {12,22}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {1,13}, {12,26}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {3,29}, {12,17}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {12,41}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {12,14}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET43.14 // Bipartite(11,32) Valencies [32,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10503340991714857904978807947788288000000000 EdgePairs[43][14]:={ {6,38}, {11,40}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {3,26}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {3,25}, {11,34}, {7,35}, {11,13}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,42}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {1,33}, {3,14}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {6,28}, {6,42}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET43.15 // Bipartite(10,33) Valencies [33,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31510022975144573714936423843364864000000000 EdgePairs[43][15]:={ {6,38}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {5,43}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {1,12}, {10,42}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,42}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {3,33}, {2,11}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {8,43}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET43.16 // Bipartite(9,34) Valencies [34,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 107134078115491550630783841067440537600000000 EdgePairs[43][16]:={ {6,38}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {4,28}, {5,43}, {9,10}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {9,11}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {2,10}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {4,10}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {9,22}, {4,11}, {9,19}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {9,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {3,33}, {2,11}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {8,43}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {5,10}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {9,43}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET43.17 // Bipartite(8,35) Valencies [35,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 416632526004689363564159381928935424000000000 EdgePairs[43][17]:={ {6,38}, {6,25}, {5,38}, {5,22}, {4,28}, {5,43}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {6,9}, {4,37}, {4,40}, {8,31}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {1,20}, {3,18}, {8,16}, {2,34}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {8,9}, {2,10}, {3,9}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {1,36}, {6,18}, {1,29}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {1,43}, {8,42}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {4,9}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {4,10}, {5,14}, {3,29}, {1,41}, {2,23}, {4,11}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {5,39}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {4,14}, {4,15}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {5,31}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {7,29}, {2,28}, {8,29}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {8,43}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {5,9}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {7,38}, {5,42}, {2,38}, {7,9}, {5,10}, {8,28}, {7,43}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {5,36}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {8,25}, {2,9}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {6,40} }; // ET43.18 // Bipartite(7,36) Valencies [36,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1874846367021102136038717218680209408000000000 EdgePairs[43][18]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {7,38}, {4,29}, {1,32}, {3,13}, {1,27}, {3,43}, {3,25}, {3,15}, {7,41}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {7,12}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {6,8}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {7,43}, {2,35}, {1,22}, {6,12}, {6,30}, {6,43}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {3,26}, {5,28}, {5,42}, {7,31}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {1,25}, {6,19}, {6,9}, {7,29}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {1,41}, {3,41}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {2,18}, {5,35}, {1,34}, {5,37}, {7,19}, {2,43}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {7,42}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET43.19 // Bipartite(6,37) Valencies [37,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 9909902225682968433347505298738249728000000000 EdgePairs[43][19]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {6,8}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {6,43}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {3,26}, {5,28}, {5,42}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {6,19}, {6,9}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {6,42}, {4,40}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {1,41}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {5,19}, {6,20}, {2,30}, {5,21}, {6,13}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {6,35}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET43.20 // Bipartite(5,38) Valencies [38,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 62762714095992133411200866892008914944000000000 EdgePairs[43][20]:={ {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {2,42}, {3,18}, {3,17}, {3,7}, {4,38}, {3,34}, {2,25}, {5,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {2,10}, {4,41}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {1,43}, {3,26}, {5,28}, {5,42}, {2,17}, {4,36}, {5,41}, {4,6}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {1,15}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,40}, {2,31}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {5,13}, {1,41}, {5,6}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {2,30}, {5,21}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {3,36}, {4,39}, {4,32}, {1,36}, {5,16} }; // ET43.21 // Bipartite(4,39) Valencies [39,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 489549169948738640607366761757669536563200000000 EdgePairs[43][21]:={ {1,15}, {4,35}, {3,15}, {1,43}, {2,38}, {4,42}, {1,11}, {4,14}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {1,40}, {2,20}, {4,40}, {1,25}, {4,16}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {4,5}, {1,5}, {3,30}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {4,37}, {4,20}, {2,41}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {4,39}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {4,43}, {3,23}, {4,31}, {2,42}, {2,34}, {3,27}, {4,30}, {1,19}, {2,40}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,35}, {1,26}, {4,38}, {2,24}, {4,11}, {3,42}, {2,27}, {2,43}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {1,42}, {2,6}, {3,21}, {1,14}, {1,41}, {4,32}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {3,16}, {1,13}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {4,9}, {2,7}, {3,43}, {4,34}, {4,41}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET43.22 // Bipartite(3,40) Valencies [40,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4895491699487386406073667617576695365632000000000 EdgePairs[43][22]:={ {1,15}, {3,15}, {1,43}, {2,38}, {1,11}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {2,11}, {1,40}, {2,20}, {1,25}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {1,5}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {2,41}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {3,14}, {2,13}, {1,12}, {3,9}, {3,22}, {3,23}, {2,42}, {2,34}, {3,27}, {1,19}, {2,40}, {2,35}, {2,9}, {3,5}, {1,4}, {1,35}, {1,26}, {2,4}, {2,24}, {3,42}, {2,27}, {3,4}, {2,43}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {1,42}, {2,6}, {3,21}, {1,14}, {1,41}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {1,13}, {3,16}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,43}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET43.23 // Bipartite(2,41) Valencies [41,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 66905053226327614216340124106881503330304000000000 EdgePairs[43][23]:={ {2,11}, {1,26}, {2,14}, {1,14}, {2,37}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,37}, {1,33}, {1,40}, {1,10}, {1,43}, {2,39}, {1,39}, {2,43}, {1,36}, {1,6}, {2,40}, {2,6}, {1,4}, {1,20}, {1,12}, {2,36}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {1,38}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,38}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {2,42}, {1,28}, {2,19}, {1,42}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {2,41}, {1,41}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET43.24 // Bipartite(1,42) Valencies [42,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 1405006117752879898543142606244511569936384000000000 EdgePairs[43][24]:={ {1,26}, {1,14}, {1,24}, {1,29}, {1,30}, {1,32}, {1,37}, {1,33}, {1,40}, {1,10}, {1,2}, {1,43}, {1,39}, {1,36}, {1,6}, {1,4}, {1,20}, {1,12}, {1,31}, {1,38}, {1,7}, {1,15}, {1,16}, {1,21}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {1,28}, {1,42}, {1,8}, {1,13}, {1,19}, {1,9}, {1,41}, {1,22}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25} }; // ET43.25 // Non-bipartite Valency 42 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 60415263063373835637355132068513997507264512000000000 EdgePairs[43][25]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {37,43}, {13,18}, {2,6}, {32,33}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {19,27}, {28,43}, {32,34}, {7,12}, {31,33}, {21,34}, {4,10}, {33,34}, {3,19}, {1,15}, {5,8}, {10,30}, {31,32}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {7,42}, {30,31}, {21,31}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {34,35}, {38,43}, {3,27}, {29,39}, {25,32}, {5,13}, {15,33}, {21,33}, {22,27}, {30,34}, {17,36}, {10,35}, {13,40}, {11,15}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {13,41}, {22,37}, {12,26}, {15,34}, {18,41}, {7,16}, {12,16}, {14,19}, {9,43}, {3,38}, {13,24}, {11,30}, {30,32}, {6,42}, {4,21}, {12,42}, {29,36}, {30,33}, {14,43}, {20,34}, {23,29}, {1,33}, {4,25}, {2,42}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, {36,42}, {1,30}, {23,42}, {14,27}, {11,35}, {2,29}, {16,39}, {15,31}, {10,21}, {17,23}, {12,19}, {3,7}, {10,25}, {6,17}, {32,35}, {20,33}, {2,17}, {29,42}, {33,35}, {36,37}, {20,32}, {18,40}, {11,33}, {19,22}, {16,26}, {3,22}, {5,24}, {11,32}, {22,43}, {1,5}, {28,37}, {26,27}, {11,20}, {24,41}, {17,28}, {1,8}, {11,24}, {1,35}, {9,17}, {10,18}, {19,38}, {8,15}, {5,20}, {14,16}, {3,12}, {3,26}, {28,29}, {11,31}, {16,22}, {27,43}, {12,39}, {6,36}, {5,15}, {20,30}, {2,36}, {4,18}, {35,41}, {22,38}, {26,39}, {8,11}, {15,35}, {30,41}, {14,38}, {5,41}, {39,43}, {12,27}, {11,13}, {15,30}, {3,43}, {19,43}, {7,19}, {11,34}, {8,32}, {7,39}, {22,39}, {19,26}, {8,33}, {8,20}, {5,31}, {20,35}, {16,19}, {1,13}, {26,38}, {9,23}, {7,14}, {34,41}, {13,15}, {5,34}, {9,29}, {13,35}, {14,26}, {23,28}, {7,27}, {2,9}, {10,40}, {29,37}, {38,39}, {13,30}, {6,9}, {17,42}, {13,20}, {16,27}, {37,42}, {23,36}, {8,41}, {5,32}, {5,33}, {8,31}, {17,37}, {5,11}, {3,16}, {20,24}, {7,22}, {22,26}, {12,14}, {12,22}, {7,38}, {13,34}, {28,36}, {23,24}, {9,36}, {3,4}, {31,41}, {8,34}, {26,43}, {15,24}, {10,19}, {1,24}, {41,42}, {20,41}, {12,38}, {27,39}, {32,41}, {31,37}, {14,39}, {34,37}, {2,13}, {5,30}, {33,41}, {24,30}, {6,13}, {5,35}, {24,35}, {8,17}, {1,9}, {18,25}, {4,40}, {2,37}, {12,18}, {6,37}, {9,15}, {3,10}, {21,40}, {16,43}, {18,21}, {8,30}, {13,31}, {2,28}, {25,40}, {22,25}, {15,28}, {6,28}, {14,21}, {7,18}, {11,41}, {21,22}, {14,25}, {5,17}, {24,33}, {20,28}, {13,32}, {13,33}, {35,37}, {10,27}, {9,11}, {24,32}, {16,18}, {32,37}, {33,37}, {19,39}, {1,41}, {3,39}, {5,29}, {8,35}, {28,42}, {15,41}, {6,24}, {24,31}, {9,32}, {39,40}, {2,5}, {2,24}, {4,19}, {5,6}, {9,33}, {9,20}, {18,26}, {8,29}, {4,14}, {21,43}, {7,43}, {12,43}, {30,37}, {8,23}, {3,21}, {5,36}, {23,37}, {25,43}, {4,27}, {2,8}, {6,8}, {24,29}, {9,42}, {13,17}, {3,25}, {1,37}, {13,23}, {12,40}, {36,41}, {1,28}, {13,42}, {16,38}, {25,27}, {9,31}, {21,27}, {4,38}, {8,9}, {28,32}, {24,34}, {10,14}, {13,29}, {4,22}, {4,7}, {10,22}, {10,12}, {24,42}, {26,40}, {17,24}, {28,33}, {21,38}, {15,37}, {2,41}, {8,36}, {23,41}, {9,34}, {15,17}, {10,38}, {6,41}, {34,36}, {11,28}, {13,36}, {18,19}, {28,34}, {19,25}, {25,38}, {19,21}, {20,37}, {6,11}, {38,40}, {5,23}, {11,23}, {35,42}, {31,36}, {2,11}, {9,30}, {29,41}, {7,40}, {20,29}, {33,36}, {32,36}, {28,31}, {30,42}, {18,27}, {1,6}, {11,37}, {1,2}, {5,9}, {4,26}, {4,12}, {2,30}, {3,18}, {7,10}, {1,29}, {6,30}, {9,35}, {1,17}, {8,28}, {5,42}, {18,39}, {10,43}, {21,26}, {17,41}, {4,43}, {35,36}, {5,28}, {25,26}, {17,33}, {2,35}, {10,26}, {17,20}, {16,40}, {6,35}, {15,29}, {17,32}, {8,42}, {24,28}, {28,35}, {27,40}, {16,25}, {11,17}, {25,39}, {16,21}, {5,37}, {40,43}, {24,36}, {9,24}, {21,39}, {30,36}, {6,20}, {2,20}, {1,36}, {14,18}, {10,16}, {4,16}, {34,42}, {20,23}, {7,25}, {15,36}, {17,34}, {28,30}, {31,42}, {6,15}, {7,21}, {3,5}, {19,40}, {18,22}, {29,31}, {8,37}, {37,41}, {12,25}, {22,24}, {2,15}, {13,14}, {20,36}, {6,31}, {41,43}, {9,13}, {1,7}, {1,23}, {12,21}, {23,30}, {29,34}, {15,23}, {17,31}, {2,31}, {13,28}, {9,18}, {20,26}, {10,17}, {11,29}, {12,15}, {3,40}, {11,42}, {11,16}, {2,34}, {8,19}, {22,40}, {20,42}, {13,37}, {33,42}, {6,34}, {2,21}, {23,35}, {18,28}, {29,33}, {32,42}, {28,41}, {29,35}, {21,23}, {23,25}, {29,32}, {23,32}, {6,21}, {1,12}, {2,32}, {6,33}, {5,19}, {18,38}, {23,33}, {7,20}, {4,29}, {1,42}, {3,8}, {10,39}, {6,25}, {4,17}, {7,31}, {12,33}, {2,25}, {17,35}, {6,32}, {2,33}, {4,6}, {7,15}, {12,32}, {2,4}, {1,26}, {15,26}, {12,20}, {11,12}, {38,41}, {11,36}, {5,14}, {29,30}, {5,27}, {8,27}, {15,42}, {15,16}, {3,13}, {17,30}, {30,39}, {24,37}, {4,39}, {23,31}, {25,29}, {18,43}, {28,40}, {35,39}, {16,35}, {24,27}, {18,37}, {13,19}, {4,36}, {10,29}, {21,42}, {14,41}, {13,22}, {13,43}, {14,40}, {37,40}, {9,41}, {7,11}, {26,34}, {7,34}, {23,34}, {10,23}, {33,39}, {14,24}, {21,29}, {8,22}, {32,39}, {2,10}, {5,38}, {6,10}, {25,42}, {9,40}, {1,16}, {10,36}, {16,30}, {12,34}, {7,33}, {12,31}, {15,19}, {7,32}, {13,27}, {11,39}, {19,24}, {5,7}, {7,30}, {26,31}, {9,10}, {17,18}, {24,43}, {31,39}, {8,14}, {4,23}, {8,12}, {5,22}, {22,41}, {7,35}, {17,25}, {1,3}, {34,39}, {3,24}, {8,38}, {17,21}, {15,27}, {3,20}, {5,12}, {26,32}, {4,9}, {26,33}, {11,22}, {16,20}, {20,39}, {27,41}, {11,26}, {34,38}, {7,8}, {5,26}, {16,32}, {39,41}, {13,16}, {31,38}, {16,33}, {13,38}, {16,31}, {20,27}, {16,24}, {3,15}, {26,35}, {10,28}, {16,34}, {25,36}, {12,30}, {20,38}, {3,41}, {15,39}, {18,29}, {4,42}, {35,43}, {24,38}, {33,38}, {32,38}, {21,36}, {30,43}, {1,19}, {5,43}, {26,30}, {19,41}, {11,14}, {12,35}, {14,35}, {19,32}, {36,40}, {19,33}, {3,34}, {3,31}, {11,19}, {24,39}, {19,20}, {8,16}, {13,26}, {1,39}, {4,37}, {1,14}, {8,43}, {14,15}, {34,43}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {25,28}, {8,26}, {30,38}, {3,32}, {10,42}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {24,26}, {40,42}, {8,10}, {1,22}, {27,33}, {14,34}, {17,19}, {7,24}, {9,12}, {29,40}, {11,27}, {26,41}, {27,32}, {35,38}, {22,23}, {4,5}, {32,43}, {10,37}, {22,30}, {27,34}, {31,43}, {33,43}, {42,43}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {22,35}, {20,43}, {32,40}, {16,41}, {33,40}, {15,18}, {2,14}, {3,35}, {27,31}, {26,28}, {13,39}, {6,14}, {11,43}, {14,31}, {4,8}, {17,27}, {24,25}, {7,9}, {13,21}, {27,29}, {5,10}, {3,17}, {12,28}, {36,38}, {19,35}, {21,24}, {1,18}, {6,22}, {22,31}, {14,32}, {22,33}, {5,39}, {25,37}, {13,25}, {14,33}, {2,22}, {2,3}, {3,29}, {22,32}, {8,39}, {19,30}, {1,43}, {15,43}, {7,41}, {21,41}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {18,42}, {7,37}, {38,42}, {9,16}, {3,36}, {2,40}, {11,38}, {12,41}, {4,13}, {6,40}, {31,40}, {14,17}, {5,25}, {36,43}, {25,41}, {5,21}, {20,40}, {18,32}, {7,28}, {14,23}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {22,42}, {1,4}, {14,29}, {18,34}, {19,23}, {18,31}, {26,37}, {14,42}, {15,40}, {2,19}, {23,43}, {6,19}, {4,24}, {12,37}, {17,22}, {27,28}, {14,36}, {2,43}, {27,36}, {6,43}, {26,29}, {8,18}, {8,21}, {10,15}, {12,17}, {30,40}, {29,43}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {17,38}, {6,27}, {16,37}, {37,39}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {20,21}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {7,17}, {10,11}, {17,43}, {20,25}, {4,41}, {3,42}, {3,28}, {9,27}, {37,38}, {11,25}, {16,17}, {11,21}, {19,42}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // Total number of connected ET graphs of order 43 is 25 // ******************************************************************************************** // Order 44 // ET44.1 // Bipartite(22,22) Valencies [2,2] // Diameter 22 Girth 44 // Twin-free VT AT // Automorphism group of order 88 EdgePairs[44][1]:={ {12,32}, {14,37}, {1,23}, {18,41}, {6,29}, {20,41}, {22,44}, {8,29}, {10,31}, {13,32}, {14,35}, {4,40}, {5,40}, {6,27}, {12,34}, {19,26}, {7,36}, {21,24}, {15,39}, {3,27}, {17,26}, {10,33}, {16,30}, {17,28}, {11,33}, {2,42}, {20,43}, {16,28}, {9,34}, {18,39}, {2,44}, {1,25}, {15,37}, {22,43}, {11,35}, {7,38}, {13,30}, {19,24}, {8,31}, {3,25}, {5,38}, {21,23}, {9,36}, {4,42} }; // ET44.2 // Bipartite(22,22) Valencies [4,4] // Diameter 11 Girth 4 // Has twins VT AT // Automorphism group of order 184549376 EdgePairs[44][2]:={ {5,33}, {8,28}, {3,40}, {5,29}, {21,23}, {2,24}, {7,41}, {11,24}, {1,36}, {6,31}, {5,40}, {22,35}, {18,33}, {15,38}, {15,27}, {11,37}, {4,31}, {6,43}, {7,33}, {5,44}, {9,37}, {3,29}, {6,32}, {16,33}, {18,41}, {7,30}, {17,42}, {8,32}, {20,30}, {22,24}, {8,43}, {16,40}, {15,31}, {20,37}, {19,28}, {10,23}, {22,26}, {4,38}, {12,36}, {10,34}, {14,36}, {11,35}, {2,38}, {3,25}, {4,27}, {21,28}, {12,34}, {22,37}, {12,23}, {18,30}, {6,42}, {14,40}, {9,41}, {20,41}, {13,35}, {13,38}, {21,34}, {10,39}, {2,27}, {12,25}, {17,31}, {19,43}, {19,32}, {20,26}, {13,24}, {17,32}, {17,43}, {2,35}, {10,28}, {9,30}, {18,44}, {11,26}, {13,27}, {9,26}, {14,29}, {15,42}, {21,39}, {1,34}, {1,23}, {4,42}, {14,25}, {1,25}, {16,29}, {7,44}, {19,39}, {8,39}, {3,36}, {16,44} }; // ET44.3 // Non-bipartite Valency 4 // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 45056 EdgePairs[44][3]:={ {3,22}, {11,30}, {1,26}, {15,35}, {20,42}, {17,41}, {4,24}, {18,43}, {19,37}, {19,41}, {8,28}, {21,42}, {8,31}, {17,39}, {5,29}, {20,38}, {2,24}, {12,33}, {5,27}, {6,26}, {17,44}, {18,42}, {21,44}, {12,32}, {10,30}, {6,30}, {23,44}, {14,34}, {3,23}, {15,37}, {8,29}, {10,33}, {6,32}, {16,33}, {9,32}, {7,30}, {2,21}, {16,36}, {7,27}, {9,29}, {7,32}, {16,40}, {5,25}, {5,31}, {10,31}, {3,28}, {13,33}, {13,36}, {4,27}, {3,25}, {13,39}, {9,36}, {4,21}, {23,42}, {14,35}, {17,38}, {14,40}, {7,25}, {12,29}, {9,34}, {24,43}, {11,36}, {1,27}, {16,38}, {22,41}, {2,28}, {11,34}, {14,38}, {18,37}, {8,26}, {15,34}, {12,35}, {19,40}, {15,39}, {22,43}, {4,26}, {1,22}, {6,28}, {2,25}, {19,44}, {24,41}, {13,37}, {1,23}, {20,43}, {20,39}, {11,31}, {10,35}, {18,40} }; // ET44.4 // Bipartite(11,33) Valencies [6,2] // Diameter 11 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7981535232 EdgePairs[44][4]:={ {6,41}, {11,16}, {2,44}, {8,20}, {7,16}, {5,37}, {3,12}, {5,24}, {8,31}, {4,44}, {1,32}, {2,24}, {1,43}, {11,29}, {11,27}, {10,30}, {9,15}, {6,30}, {5,15}, {1,12}, {4,31}, {3,23}, {11,38}, {6,43}, {8,29}, {9,37}, {2,33}, {6,32}, {7,36}, {7,27}, {4,33}, {8,40}, {8,42}, {1,21}, {3,25}, {4,20}, {10,41}, {11,40}, {3,14}, {6,21}, {7,25}, {7,38}, {10,39}, {4,22}, {6,19}, {3,34}, {10,19}, {10,17}, {5,26}, {5,35}, {8,18}, {2,35}, {5,13}, {10,28}, {9,26}, {2,13}, {1,34}, {9,28}, {1,23}, {4,42}, {9,39}, {7,14}, {11,18}, {2,22}, {9,17}, {3,36} }; // ET44.5 // Bipartite(20,24) Valencies [6,5] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 240 EdgePairs[44][5]:={ {16,34}, {20,27}, {14,25}, {16,36}, {8,31}, {8,24}, {4,42}, {18,44}, {3,38}, {7,40}, {8,36}, {19,39}, {10,38}, {6,23}, {4,40}, {11,42}, {7,33}, {18,42}, {20,23}, {3,32}, {19,40}, {5,41}, {16,40}, {19,24}, {11,38}, {13,43}, {12,27}, {13,42}, {18,21}, {15,29}, {13,38}, {9,31}, {16,41}, {12,25}, {6,34}, {5,26}, {5,21}, {15,28}, {10,30}, {8,22}, {19,37}, {3,41}, {6,43}, {17,30}, {20,33}, {20,38}, {2,41}, {20,35}, {2,23}, {17,24}, {9,43}, {2,32}, {6,33}, {8,21}, {4,28}, {7,29}, {10,39}, {4,29}, {3,22}, {10,37}, {4,43}, {9,23}, {11,39}, {3,27}, {2,34}, {14,26}, {10,33}, {12,28}, {2,35}, {15,33}, {14,44}, {13,30}, {9,25}, {4,25}, {2,44}, {13,22}, {7,35}, {12,24}, {15,26}, {18,35}, {12,23}, {14,32}, {11,41}, {9,44}, {17,22}, {15,21}, {6,30}, {8,27}, {1,39}, {14,37}, {11,40}, {5,36}, {3,26}, {17,37}, {19,36}, {1,42}, {16,22}, {18,29}, {17,34}, {15,27}, {7,37}, {16,43}, {14,29}, {12,32}, {1,28}, {18,31}, {20,31}, {17,32}, {13,31}, {9,36}, {10,26}, {19,25}, {5,44}, {7,34}, {1,30}, {5,39}, {11,35}, {1,21}, {1,24}, {6,28} }; // ET44.6 // Bipartite(20,24) Valencies [6,5] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 491520 EdgePairs[44][6]:={ {13,25}, {7,42}, {14,21}, {20,27}, {5,32}, {6,39}, {10,21}, {8,31}, {18,40}, {11,23}, {9,30}, {15,43}, {18,44}, {3,38}, {9,42}, {11,33}, {16,30}, {4,27}, {6,41}, {11,42}, {7,33}, {12,31}, {2,37}, {12,22}, {18,37}, {1,38}, {17,35}, {13,27}, {19,24}, {4,44}, {9,37}, {13,42}, {8,34}, {2,28}, {16,41}, {3,31}, {6,34}, {6,22}, {8,44}, {8,22}, {14,33}, {17,23}, {4,37}, {10,36}, {2,23}, {7,41}, {4,39}, {3,40}, {12,34}, {10,41}, {15,36}, {7,29}, {5,43}, {9,23}, {10,24}, {18,25}, {14,38}, {16,29}, {19,29}, {14,26}, {10,33}, {2,40}, {7,30}, {2,35}, {5,28}, {13,30}, {9,25}, {4,25}, {10,29}, {1,35}, {1,26}, {6,29}, {12,24}, {15,26}, {18,32}, {14,36}, {15,31}, {1,23}, {12,43}, {16,27}, {9,35}, {18,28}, {8,43}, {8,32}, {3,28}, {20,44}, {20,32}, {3,26}, {5,31}, {19,36}, {12,36}, {11,21}, {11,30}, {19,22}, {19,34}, {4,32}, {20,34}, {15,38}, {17,38}, {7,21}, {19,41}, {16,42}, {1,33}, {2,25}, {17,26}, {20,39}, {17,28}, {3,43}, {6,27}, {20,22}, {5,44}, {13,37}, {17,40}, {11,35}, {16,39}, {1,21}, {15,24}, {14,24}, {5,40}, {13,39} }; // ET44.7 // Non-bipartite Valency 6 // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 528 EdgePairs[44][7]:={ {1,15}, {4,35}, {11,43}, {16,25}, {27,39}, {6,39}, {24,33}, {10,21}, {14,25}, {3,15}, {8,39}, {10,22}, {11,23}, {4,14}, {7,40}, {6,17}, {23,33}, {10,43}, {28,40}, {11,42}, {28,37}, {29,43}, {7,38}, {4,16}, {28,39}, {12,22}, {2,33}, {22,35}, {13,27}, {9,21}, {21,35}, {10,44}, {6,40}, {27,38}, {22,36}, {25,40}, {3,34}, {22,33}, {31,41}, {24,34}, {31,44}, {15,28}, {14,27}, {1,34}, {32,42}, {17,31}, {2,14}, {17,30}, {19,30}, {9,43}, {1,36}, {29,42}, {13,26}, {3,13}, {2,16}, {15,25}, {26,38}, {2,36}, {4,33}, {8,18}, {2,13}, {16,26}, {14,28}, {9,23}, {10,24}, {5,19}, {7,20}, {30,44}, {6,37}, {8,17}, {32,43}, {19,29}, {31,43}, {2,35}, {26,37}, {4,15}, {25,38}, {1,35}, {8,19}, {12,24}, {15,26}, {12,23}, {25,37}, {11,41}, {9,44}, {6,19}, {18,32}, {5,38}, {12,44}, {16,27}, {7,18}, {8,38}, {5,20}, {29,41}, {13,28}, {24,35}, {20,30}, {11,21}, {6,20}, {1,14}, {18,29}, {21,36}, {26,39}, {10,42}, {12,42}, {3,16}, {1,13}, {20,29}, {7,37}, {30,41}, {12,41}, {30,42}, {18,31}, {3,36}, {21,34}, {8,37}, {9,41}, {20,31}, {17,32}, {5,18}, {19,32}, {23,34}, {4,34}, {3,33}, {32,44}, {7,17}, {11,24}, {5,39}, {23,36}, {27,40}, {5,40}, {9,22} }; // ET44.8 // Bipartite(16,28) Valencies [7,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 112 EdgePairs[44][8]:={ {7,43}, {4,35}, {10,19}, {13,25}, {5,32}, {7,39}, {10,21}, {11,17}, {2,38}, {15,43}, {3,29}, {9,42}, {6,17}, {10,27}, {5,35}, {1,40}, {14,18}, {12,40}, {13,34}, {5,41}, {2,33}, {7,31}, {6,25}, {15,40}, {11,38}, {9,37}, {12,27}, {13,42}, {8,34}, {2,28}, {8,41}, {10,18}, {13,20}, {10,30}, {11,34}, {4,37}, {10,34}, {4,20}, {2,41}, {7,26}, {9,43}, {8,28}, {13,26}, {1,17}, {15,25}, {14,30}, {2,32}, {6,33}, {4,28}, {10,39}, {16,35}, {16,19}, {14,28}, {9,23}, {14,38}, {6,37}, {16,29}, {4,31}, {1,19}, {15,33}, {14,44}, {12,29}, {1,35}, {1,26}, {8,19}, {13,40}, {12,23}, {3,42}, {5,22}, {14,36}, {2,43}, {12,44}, {15,31}, {1,23}, {2,21}, {14,22}, {5,27}, {6,30}, {15,18}, {13,32}, {5,20}, {11,31}, {3,26}, {9,24}, {12,36}, {16,22}, {11,21}, {3,21}, {3,44}, {3,39}, {7,22}, {15,27}, {4,18}, {8,25}, {11,20}, {12,41}, {16,42}, {8,37}, {9,32}, {6,24}, {16,38}, {9,36}, {6,44}, {3,33}, {7,36}, {7,17}, {4,23}, {11,24}, {1,30}, {5,39}, {8,29}, {16,24} }; // ET44.9 // Bipartite(16,28) Valencies [7,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10321920 EdgePairs[44][9]:={ {13,25}, {16,34}, {11,44}, {15,23}, {2,38}, {11,23}, {3,29}, {4,27}, {16,30}, {10,43}, {10,38}, {11,29}, {2,20}, {4,40}, {14,19}, {1,25}, {12,40}, {12,22}, {16,18}, {6,32}, {12,33}, {9,39}, {14,42}, {1,32}, {6,40}, {8,42}, {12,27}, {14,35}, {7,23}, {8,34}, {2,28}, {14,20}, {5,26}, {9,17}, {15,28}, {5,37}, {3,18}, {8,22}, {7,28}, {12,21}, {1,34}, {5,33}, {13,44}, {9,27}, {10,36}, {13,33}, {2,31}, {7,41}, {13,26}, {1,17}, {2,36}, {4,33}, {8,18}, {2,17}, {9,34}, {10,31}, {4,29}, {16,26}, {4,43}, {5,19}, {8,26}, {15,35}, {3,23}, {11,39}, {11,18}, {7,30}, {4,21}, {12,29}, {9,25}, {7,35}, {14,32}, {11,36}, {6,19}, {15,21}, {2,43}, {12,43}, {10,28}, {1,39}, {8,38}, {4,22}, {3,24}, {5,31}, {15,37}, {16,22}, {6,20}, {10,17}, {1,41}, {3,44}, {6,42}, {3,39}, {1,27}, {15,41}, {7,37}, {7,21}, {16,42}, {14,40}, {3,36}, {9,41}, {10,20}, {9,32}, {6,24}, {6,35}, {16,38}, {8,30}, {13,31}, {5,44}, {13,19}, {13,37}, {15,30}, {11,24}, {5,25}, {14,24} }; // ET44.10 // Bipartite(12,32) Valencies [8,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1536 EdgePairs[44][10]:={ {3,32}, {1,26}, {12,38}, {10,15}, {6,37}, {4,23}, {9,19}, {1,14}, {2,26}, {4,41}, {10,43}, {6,39}, {4,36}, {8,31}, {2,30}, {1,30}, {2,29}, {9,20}, {1,32}, {9,31}, {8,38}, {12,33}, {11,24}, {2,39}, {4,40}, {6,30}, {5,15}, {4,31}, {6,40}, {10,33}, {12,44}, {11,33}, {11,42}, {5,16}, {8,27}, {5,23}, {6,16}, {5,21}, {8,44}, {1,38}, {8,43}, {8,37}, {10,16}, {9,24}, {2,20}, {3,28}, {7,18}, {10,34}, {12,36}, {11,35}, {3,25}, {11,32}, {4,21}, {11,22}, {5,17}, {11,40}, {6,27}, {3,14}, {3,18}, {6,42}, {12,29}, {9,34}, {7,35}, {8,34}, {11,36}, {12,26}, {8,41}, {1,27}, {9,13}, {4,25}, {9,22}, {2,28}, {10,42}, {2,19}, {5,14}, {5,18}, {3,41}, {7,39}, {1,13}, {5,13}, {7,17}, {10,28}, {1,22}, {2,25}, {12,15}, {4,19}, {7,37}, {10,20}, {6,23}, {7,44}, {7,24}, {9,17}, {3,43}, {12,21}, {3,35}, {7,29} }; // ET44.11 // Bipartite(12,32) Valencies [8,3] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 192 EdgePairs[44][11]:={ {3,32}, {3,22}, {1,26}, {6,41}, {4,24}, {5,36}, {11,16}, {8,28}, {4,23}, {6,34}, {9,23}, {11,15}, {10,40}, {10,43}, {6,39}, {12,18}, {2,29}, {11,25}, {4,34}, {2,24}, {12,33}, {1,37}, {5,27}, {8,16}, {3,21}, {1,36}, {9,38}, {12,30}, {11,44}, {2,36}, {4,31}, {6,43}, {1,31}, {10,33}, {9,37}, {3,20}, {4,32}, {8,44}, {5,20}, {8,43}, {7,27}, {7,32}, {1,16}, {7,40}, {3,15}, {9,40}, {8,33}, {4,38}, {6,20}, {11,35}, {5,28}, {1,21}, {3,30}, {7,15}, {12,23}, {12,14}, {3,31}, {5,30}, {9,41}, {10,29}, {12,29}, {7,38}, {8,34}, {5,39}, {9,13}, {2,27}, {10,37}, {6,19}, {2,42}, {6,22}, {2,19}, {8,26}, {9,18}, {10,17}, {5,14}, {2,17}, {7,28}, {12,42}, {12,35}, {11,41}, {1,13}, {8,14}, {5,13}, {7,17}, {10,22}, {10,21}, {4,26}, {2,25}, {4,42}, {9,39}, {11,19}, {11,18}, {1,25}, {7,44}, {6,24}, {3,35} }; // ET44.12 // Bipartite(12,32) Valencies [8,3] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5283615080448 EdgePairs[44][12]:={ {11,30}, {4,24}, {5,42}, {2,44}, {6,34}, {9,23}, {8,31}, {2,32}, {1,29}, {2,24}, {9,31}, {1,37}, {1,33}, {8,23}, {6,26}, {12,16}, {2,40}, {8,15}, {4,40}, {3,27}, {7,13}, {8,25}, {11,27}, {12,32}, {9,15}, {10,36}, {2,36}, {3,23}, {11,38}, {12,40}, {4,16}, {6,36}, {10,33}, {4,30}, {4,32}, {7,27}, {2,16}, {7,43}, {2,20}, {3,15}, {8,33}, {4,38}, {5,38}, {6,20}, {11,35}, {1,21}, {11,43}, {10,41}, {11,22}, {3,19}, {12,37}, {10,44}, {9,42}, {6,42}, {3,31}, {12,13}, {12,24}, {5,30}, {12,29}, {9,34}, {7,21}, {7,35}, {8,41}, {1,17}, {7,19}, {6,18}, {4,22}, {3,39}, {2,28}, {9,18}, {10,17}, {5,14}, {5,18}, {5,26}, {5,34}, {1,13}, {10,28}, {9,26}, {1,41}, {6,28}, {4,14}, {10,25}, {9,39}, {11,19}, {7,37}, {10,20}, {11,14}, {5,22}, {1,25}, {6,44}, {8,17}, {3,43}, {8,39}, {12,21}, {3,35}, {7,29} }; // ET44.13 // Bipartite(12,32) Valencies [8,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 37748736 EdgePairs[44][13]:={ {9,13}, {10,19}, {7,39}, {8,31}, {1,43}, {12,39}, {6,17}, {4,40}, {11,42}, {4,16}, {5,24}, {3,32}, {5,41}, {2,33}, {7,31}, {9,19}, {11,38}, {12,18}, {3,30}, {6,40}, {11,22}, {7,23}, {7,15}, {5,13}, {2,28}, {2,18}, {1,29}, {8,15}, {3,41}, {7,28}, {12,21}, {1,34}, {9,38}, {5,23}, {4,37}, {10,36}, {10,25}, {2,16}, {2,32}, {6,33}, {12,34}, {8,21}, {2,17}, {10,41}, {3,14}, {8,35}, {5,29}, {7,14}, {3,27}, {2,34}, {6,26}, {6,15}, {10,33}, {7,30}, {4,21}, {1,26}, {11,26}, {8,19}, {2,44}, {11,14}, {4,38}, {12,23}, {6,31}, {9,44}, {11,36}, {8,27}, {9,35}, {8,43}, {7,44}, {4,22}, {9,28}, {12,36}, {1,42}, {11,30}, {10,17}, {4,32}, {6,42}, {1,27}, {3,16}, {1,13}, {9,29}, {3,25}, {11,20}, {8,37}, {10,20}, {6,24}, {3,43}, {10,35}, {5,39}, {12,37}, {1,18}, {12,20}, {5,25}, {4,24}, {5,40}, {9,22} }; // ET44.14 // Bipartite(12,32) Valencies [8,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12582912 EdgePairs[44][14]:={ {9,13}, {11,43}, {5,14}, {10,21}, {3,15}, {4,42}, {11,23}, {12,19}, {5,30}, {6,36}, {6,17}, {10,27}, {8,36}, {10,43}, {4,16}, {12,14}, {12,22}, {10,40}, {7,31}, {9,21}, {11,38}, {11,22}, {9,37}, {8,42}, {7,15}, {5,13}, {2,28}, {12,25}, {3,31}, {2,19}, {4,26}, {8,41}, {10,30}, {1,29}, {7,28}, {6,43}, {11,34}, {12,30}, {5,33}, {7,41}, {1,36}, {2,16}, {2,32}, {6,33}, {3,40}, {8,21}, {4,33}, {9,34}, {7,25}, {10,37}, {10,24}, {5,15}, {8,26}, {3,23}, {11,39}, {5,29}, {1,19}, {11,18}, {2,40}, {4,17}, {2,35}, {12,35}, {1,35}, {2,44}, {4,38}, {2,24}, {3,42}, {12,38}, {1,23}, {1,39}, {7,18}, {7,44}, {4,22}, {10,14}, {3,26}, {3,24}, {5,17}, {5,31}, {8,20}, {6,20}, {9,18}, {11,27}, {4,32}, {3,39}, {1,20}, {1,13}, {8,25}, {9,29}, {12,41}, {8,37}, {9,32}, {6,44}, {6,27}, {9,16}, {7,34}, {6,28} }; // ET44.15 // Non-bipartite Valency 8 // Diameter 5 Girth 4 // Has twins VT AT // Automorphism group of order 33476985149718528 EdgePairs[44][15]:={ {3,33}, {10,24}, {5,17}, {2,33}, {16,26}, {18,29}, {32,42}, {31,44}, {4,16}, {18,32}, {25,39}, {16,27}, {32,41}, {6,17}, {1,13}, {12,22}, {5,38}, {7,38}, {25,38}, {3,13}, {3,15}, {10,23}, {2,15}, {9,44}, {12,41}, {12,42}, {3,35}, {21,35}, {5,20}, {9,43}, {8,39}, {11,41}, {16,25}, {29,41}, {10,44}, {24,36}, {2,14}, {29,42}, {14,28}, {20,30}, {10,22}, {15,25}, {31,43}, {3,34}, {5,40}, {6,40}, {2,34}, {2,36}, {8,19}, {3,14}, {7,20}, {19,30}, {22,34}, {31,42}, {29,44}, {12,44}, {19,29}, {22,35}, {7,39}, {9,41}, {26,40}, {15,26}, {10,41}, {23,34}, {11,22}, {27,40}, {20,31}, {2,35}, {11,44}, {23,36}, {15,27}, {30,43}, {4,33}, {10,21}, {2,13}, {9,42}, {6,18}, {12,43}, {30,42}, {8,17}, {2,16}, {26,37}, {18,30}, {11,21}, {4,35}, {23,35}, {5,18}, {11,23}, {17,30}, {7,17}, {27,38}, {28,37}, {13,25}, {26,38}, {13,28}, {10,42}, {19,31}, {4,15}, {4,13}, {31,41}, {24,34}, {1,33}, {21,33}, {8,37}, {24,35}, {17,31}, {18,31}, {25,37}, {9,22}, {25,40}, {10,43}, {4,36}, {20,29}, {28,40}, {12,23}, {11,24}, {22,33}, {8,40}, {30,41}, {17,29}, {6,19}, {1,15}, {13,27}, {1,35}, {14,25}, {5,39}, {19,32}, {3,16}, {13,26}, {28,39}, {32,44}, {8,38}, {23,33}, {4,34}, {1,16}, {4,14}, {6,38}, {30,44}, {8,18}, {15,28}, {28,38}, {27,37}, {26,39}, {12,24}, {8,20}, {32,43}, {27,39}, {21,36}, {21,34}, {9,24}, {1,14}, {6,39}, {6,37}, {5,19}, {6,20}, {11,43}, {7,37}, {22,36}, {1,34}, {29,43}, {5,37}, {7,19}, {24,33}, {17,32}, {11,42}, {3,36}, {9,21}, {16,28}, {7,40}, {9,23}, {20,32}, {14,27}, {12,21}, {1,36}, {14,26}, {7,18} }; // ET44.16 // Bipartite(8,36) Valencies [9,2] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 104485552128 EdgePairs[44][16]:={ {5,33}, {6,41}, {4,24}, {5,42}, {3,40}, {6,37}, {7,11}, {2,37}, {1,44}, {4,36}, {4,44}, {4,34}, {1,32}, {2,24}, {7,23}, {7,31}, {8,38}, {1,33}, {6,14}, {6,26}, {1,39}, {4,10}, {2,43}, {5,40}, {1,20}, {2,36}, {3,23}, {2,12}, {3,29}, {5,9}, {5,16}, {4,32}, {5,21}, {8,10}, {4,12}, {7,27}, {1,15}, {7,43}, {3,11}, {2,31}, {3,16}, {3,28}, {3,17}, {8,42}, {5,28}, {1,21}, {4,20}, {6,38}, {7,15}, {5,30}, {7,35}, {8,34}, {8,22}, {1,27}, {7,19}, {4,22}, {2,19}, {8,26}, {5,18}, {3,41}, {6,25}, {6,17}, {7,39}, {8,14}, {8,18}, {1,9}, {2,13}, {2,25}, {8,30}, {6,29}, {6,13}, {3,35} }; // ET44.17 // Bipartite(22,22) Valencies [10,10] // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 440 EdgePairs[44][17]:={ {2,44}, {21,23}, {3,33}, {2,24}, {9,28}, {6,32}, {17,36}, {4,27}, {5,34}, {4,24}, {16,26}, {15,24}, {18,29}, {4,26}, {21,40}, {18,32}, {8,30}, {21,32}, {22,37}, {5,38}, {12,32}, {7,38}, {8,42}, {19,44}, {16,31}, {20,27}, {8,33}, {19,24}, {7,41}, {1,40}, {10,26}, {14,38}, {9,44}, {12,39}, {15,44}, {10,33}, {21,42}, {13,35}, {14,31}, {7,34}, {11,41}, {17,24}, {16,25}, {12,35}, {2,28}, {12,34}, {1,30}, {18,41}, {16,23}, {8,44}, {4,23}, {8,27}, {13,29}, {12,37}, {16,29}, {18,34}, {11,28}, {16,43}, {6,29}, {16,30}, {4,38}, {3,34}, {5,40}, {2,25}, {14,23}, {20,38}, {11,38}, {14,33}, {2,36}, {10,38}, {19,40}, {17,37}, {14,36}, {9,32}, {15,32}, {19,30}, {9,27}, {15,40}, {12,36}, {4,41}, {2,38}, {22,35}, {22,41}, {9,41}, {5,25}, {2,39}, {7,32}, {17,39}, {7,43}, {14,24}, {11,31}, {7,25}, {2,35}, {11,44}, {15,27}, {21,27}, {3,44}, {20,33}, {6,30}, {6,43}, {10,29}, {10,31}, {9,42}, {10,40}, {12,43}, {17,43}, {3,39}, {3,32}, {4,35}, {9,25}, {15,41}, {8,36}, {6,33}, {2,32}, {18,44}, {11,23}, {1,23}, {11,29}, {6,24}, {13,44}, {21,25}, {9,37}, {17,27}, {15,37}, {14,42}, {13,25}, {20,28}, {19,31}, {14,37}, {4,43}, {1,33}, {20,43}, {18,33}, {6,23}, {1,43}, {21,38}, {8,26}, {18,31}, {5,42}, {7,31}, {13,30}, {10,43}, {17,28}, {20,29}, {12,27}, {22,39}, {1,42}, {5,31}, {11,24}, {6,27}, {17,25}, {5,44}, {8,40}, {22,33}, {12,40}, {20,39}, {12,30}, {21,29}, {22,28}, {19,36}, {6,28}, {18,23}, {22,31}, {9,30}, {10,39}, {13,27}, {1,37}, {16,34}, {5,39}, {7,28}, {22,24}, {13,26}, {11,26}, {22,26}, {4,40}, {10,35}, {16,36}, {3,30}, {2,29}, {20,34}, {1,26}, {10,36}, {15,33}, {14,32}, {8,24}, {13,41}, {20,42}, {14,43}, {15,38}, {19,25}, {5,26}, {3,42}, {4,25}, {3,28}, {20,41}, {1,41}, {21,36}, {3,31}, {15,39}, {21,34}, {18,40}, {17,26}, {13,34}, {17,42}, {19,35}, {7,35}, {13,39}, {7,37}, {22,30}, {1,34}, {19,23}, {5,37}, {6,35}, {11,42}, {3,36}, {16,28}, {18,35}, {9,23}, {19,37}, {8,29} }; // ET44.18 // Bipartite(22,22) Valencies [10,10] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 5536481280 EdgePairs[44][18]:={ {2,44}, {16,41}, {10,24}, {2,24}, {13,32}, {9,28}, {2,33}, {17,35}, {17,44}, {11,36}, {17,36}, {18,39}, {4,27}, {12,29}, {5,34}, {13,40}, {4,24}, {15,24}, {18,29}, {4,26}, {21,40}, {3,40}, {11,25}, {8,30}, {8,43}, {7,38}, {8,42}, {8,28}, {18,38}, {20,27}, {3,43}, {3,25}, {1,40}, {9,44}, {12,41}, {21,42}, {21,35}, {13,35}, {14,31}, {8,39}, {22,32}, {11,41}, {17,24}, {16,25}, {7,36}, {15,43}, {2,28}, {12,34}, {1,30}, {16,23}, {4,23}, {8,31}, {13,29}, {12,37}, {18,37}, {10,30}, {16,30}, {19,28}, {4,38}, {3,34}, {14,23}, {20,38}, {11,38}, {11,33}, {6,31}, {10,38}, {17,37}, {14,36}, {19,26}, {15,32}, {16,24}, {19,30}, {9,27}, {1,44}, {8,41}, {12,44}, {14,40}, {7,39}, {22,41}, {5,25}, {2,39}, {15,26}, {10,41}, {7,25}, {20,31}, {22,27}, {2,35}, {17,33}, {11,44}, {15,27}, {21,27}, {20,33}, {5,23}, {10,29}, {10,31}, {22,44}, {9,34}, {9,42}, {10,40}, {1,29}, {3,32}, {4,35}, {13,33}, {6,33}, {2,32}, {7,26}, {19,42}, {13,43}, {1,23}, {6,24}, {20,44}, {13,44}, {5,30}, {6,44}, {19,41}, {15,35}, {11,30}, {5,24}, {15,37}, {14,42}, {15,34}, {20,28}, {13,28}, {10,42}, {18,26}, {19,31}, {18,27}, {18,36}, {4,43}, {1,33}, {21,31}, {3,29}, {22,43}, {8,37}, {5,28}, {21,38}, {8,26}, {17,31}, {12,26}, {12,33}, {5,41}, {22,25}, {8,32}, {12,23}, {13,24}, {17,25}, {6,26}, {22,33}, {20,23}, {12,40}, {20,39}, {12,30}, {21,29}, {14,34}, {3,23}, {18,25}, {21,30}, {5,36}, {7,29}, {1,37}, {16,34}, {14,25}, {5,39}, {7,28}, {19,32}, {4,37}, {6,42}, {10,35}, {16,36}, {6,36}, {2,29}, {11,27}, {16,35}, {18,28}, {10,27}, {20,34}, {1,26}, {4,34}, {11,32}, {14,32}, {19,39}, {19,43}, {6,25}, {20,42}, {2,40}, {9,33}, {14,43}, {15,38}, {3,42}, {16,39}, {9,39}, {9,38}, {7,27}, {15,23}, {1,41}, {3,31}, {18,40}, {17,26}, {6,37}, {17,42}, {13,39}, {21,24}, {11,43}, {7,37}, {5,35}, {22,30}, {22,36}, {9,31}, {1,34}, {21,41}, {2,43}, {6,35}, {3,36}, {16,28}, {7,40}, {9,23}, {19,37}, {4,32}, {14,29}, {22,38} }; // ET44.19 // Bipartite(22,22) Valencies [10,10] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 225280 EdgePairs[44][19]:={ {3,33}, {10,25}, {2,24}, {10,24}, {13,32}, {9,28}, {2,33}, {17,35}, {17,44}, {11,36}, {4,27}, {12,29}, {11,35}, {13,40}, {4,24}, {15,24}, {16,26}, {16,33}, {18,29}, {3,40}, {10,37}, {18,32}, {14,39}, {5,38}, {7,38}, {8,42}, {8,28}, {19,44}, {16,31}, {18,38}, {21,37}, {4,29}, {20,27}, {8,33}, {1,27}, {7,41}, {14,38}, {12,41}, {22,42}, {15,44}, {12,42}, {21,42}, {9,43}, {3,37}, {13,35}, {7,34}, {17,24}, {12,35}, {7,36}, {8,25}, {2,41}, {12,34}, {1,30}, {18,41}, {5,32}, {16,23}, {14,28}, {9,35}, {8,44}, {4,23}, {8,27}, {18,34}, {11,28}, {16,43}, {10,30}, {6,29}, {19,28}, {4,38}, {15,29}, {19,33}, {14,23}, {2,25}, {14,33}, {2,34}, {10,38}, {19,40}, {17,37}, {9,32}, {16,24}, {9,27}, {22,34}, {15,40}, {5,43}, {19,29}, {14,30}, {14,40}, {22,35}, {2,39}, {7,32}, {17,39}, {10,41}, {7,43}, {11,31}, {7,25}, {20,31}, {2,35}, {11,44}, {15,27}, {21,27}, {6,30}, {6,43}, {5,23}, {10,31}, {22,44}, {12,43}, {17,43}, {1,29}, {3,39}, {13,31}, {13,33}, {2,32}, {7,26}, {19,42}, {18,43}, {16,32}, {1,23}, {6,24}, {6,44}, {17,30}, {11,30}, {21,25}, {5,24}, {9,37}, {15,34}, {13,25}, {20,28}, {10,42}, {18,26}, {14,41}, {14,37}, {18,36}, {1,33}, {21,31}, {20,43}, {1,43}, {3,26}, {16,38}, {8,37}, {15,36}, {21,38}, {5,42}, {12,33}, {4,36}, {12,27}, {8,32}, {1,42}, {12,23}, {13,24}, {5,31}, {17,25}, {5,44}, {6,26}, {8,40}, {20,23}, {20,39}, {12,30}, {3,23}, {18,25}, {21,30}, {17,29}, {22,28}, {16,44}, {7,29}, {22,31}, {1,35}, {20,35}, {7,28}, {19,32}, {20,37}, {11,26}, {22,26}, {4,40}, {3,30}, {5,33}, {18,28}, {10,27}, {4,34}, {10,36}, {13,41}, {6,25}, {2,40}, {2,31}, {11,40}, {9,36}, {16,42}, {20,36}, {15,38}, {19,25}, {5,26}, {9,39}, {3,38}, {3,28}, {15,23}, {22,40}, {1,41}, {21,36}, {3,41}, {15,39}, {17,26}, {6,39}, {6,37}, {13,34}, {11,34}, {13,39}, {21,24}, {22,30}, {22,36}, {9,31}, {1,34}, {21,41}, {6,35}, {11,42}, {4,39}, {4,44}, {9,23}, {19,37}, {20,32}, {8,29}, {19,27}, {14,26} }; // ET44.20 // Bipartite(20,24) Valencies [12,10] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 2880 EdgePairs[44][20]:={ {2,44}, {16,41}, {2,24}, {13,32}, {2,33}, {17,35}, {17,44}, {11,36}, {18,39}, {13,21}, {5,34}, {13,40}, {4,24}, {16,26}, {4,26}, {3,22}, {18,32}, {4,30}, {11,25}, {8,30}, {2,23}, {8,43}, {7,38}, {19,44}, {18,38}, {15,31}, {1,32}, {1,27}, {3,43}, {3,25}, {10,23}, {12,38}, {19,24}, {1,40}, {10,26}, {17,34}, {9,44}, {14,38}, {12,39}, {7,22}, {4,31}, {15,44}, {10,33}, {9,43}, {3,37}, {14,31}, {8,39}, {11,41}, {1,21}, {17,24}, {16,25}, {12,35}, {18,21}, {2,41}, {2,28}, {12,34}, {18,41}, {5,32}, {16,23}, {17,40}, {9,35}, {14,28}, {20,30}, {8,44}, {8,31}, {13,29}, {12,37}, {2,42}, {19,21}, {6,22}, {18,42}, {16,43}, {18,37}, {10,30}, {6,29}, {19,28}, {15,29}, {6,21}, {3,34}, {5,40}, {2,25}, {20,38}, {11,33}, {1,38}, {2,36}, {10,38}, {9,29}, {19,40}, {19,26}, {16,24}, {15,40}, {8,41}, {2,37}, {5,43}, {12,44}, {14,30}, {19,22}, {4,42}, {5,25}, {2,39}, {7,32}, {17,23}, {1,31}, {10,41}, {11,22}, {7,25}, {11,31}, {10,28}, {20,31}, {17,33}, {1,22}, {15,27}, {3,44}, {20,33}, {4,33}, {4,21}, {13,22}, {15,42}, {10,21}, {9,42}, {12,43}, {1,29}, {4,35}, {9,25}, {8,36}, {6,33}, {13,33}, {19,42}, {18,43}, {16,32}, {11,29}, {5,30}, {6,44}, {17,30}, {5,24}, {9,37}, {17,27}, {13,23}, {12,28}, {15,37}, {14,42}, {14,41}, {3,27}, {18,36}, {4,28}, {3,29}, {6,23}, {1,43}, {5,28}, {13,36}, {15,36}, {8,26}, {18,31}, {16,22}, {9,22}, {20,29}, {9,40}, {8,21}, {12,23}, {13,24}, {11,24}, {5,31}, {17,25}, {6,26}, {12,40}, {20,39}, {12,30}, {3,23}, {10,32}, {17,29}, {20,25}, {5,36}, {19,36}, {6,41}, {1,35}, {15,21}, {16,34}, {14,25}, {20,35}, {7,28}, {20,37}, {11,26}, {6,42}, {4,40}, {7,23}, {8,34}, {11,27}, {16,35}, {18,28}, {10,27}, {20,34}, {1,26}, {14,44}, {10,36}, {10,34}, {18,22}, {11,32}, {15,33}, {8,24}, {19,43}, {6,38}, {5,27}, {14,43}, {15,38}, {16,39}, {9,39}, {3,38}, {7,27}, {20,41}, {14,35}, {13,37}, {3,41}, {9,24}, {17,26}, {6,39}, {7,33}, {13,34}, {7,35}, {13,39}, {2,30}, {15,30}, {7,37}, {9,31}, {1,34}, {19,23}, {5,37}, {6,35}, {11,42}, {3,36}, {4,39}, {16,28}, {7,40}, {7,42}, {20,32}, {14,27}, {8,29}, {4,32}, {19,27}, {12,21}, {14,26} }; // ET44.21 // Bipartite(20,24) Valencies [12,10] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 445805022412800000000 EdgePairs[44][21]:={ {10,25}, {13,32}, {9,28}, {2,33}, {17,44}, {11,36}, {17,36}, {4,27}, {13,21}, {11,35}, {13,40}, {15,24}, {16,26}, {18,29}, {4,26}, {3,40}, {10,37}, {4,30}, {16,27}, {8,30}, {8,43}, {12,22}, {8,42}, {19,44}, {16,31}, {18,38}, {15,31}, {20,27}, {1,32}, {3,43}, {12,38}, {19,24}, {7,44}, {1,40}, {10,26}, {9,44}, {14,38}, {12,39}, {4,31}, {15,44}, {10,33}, {12,42}, {3,35}, {2,26}, {8,39}, {1,21}, {17,24}, {12,35}, {7,36}, {15,43}, {17,21}, {18,21}, {2,41}, {12,34}, {18,41}, {5,32}, {16,23}, {17,40}, {20,30}, {4,23}, {8,31}, {8,27}, {13,29}, {2,42}, {18,34}, {10,22}, {6,22}, {18,42}, {11,28}, {16,43}, {18,37}, {10,30}, {6,29}, {16,30}, {19,28}, {4,38}, {6,21}, {2,25}, {5,40}, {20,38}, {2,34}, {14,33}, {4,22}, {10,38}, {9,29}, {19,40}, {17,37}, {9,32}, {14,21}, {15,32}, {15,40}, {1,44}, {5,29}, {2,38}, {2,37}, {14,30}, {7,39}, {4,42}, {9,41}, {5,25}, {7,32}, {10,41}, {7,43}, {11,31}, {20,31}, {17,33}, {11,44}, {15,27}, {3,44}, {6,30}, {10,29}, {10,21}, {12,43}, {1,29}, {3,39}, {18,30}, {3,32}, {4,35}, {9,25}, {13,33}, {6,33}, {11,23}, {13,44}, {15,35}, {5,24}, {9,37}, {8,22}, {14,42}, {13,25}, {8,35}, {10,42}, {13,28}, {18,26}, {19,31}, {1,28}, {14,41}, {3,27}, {14,37}, {20,22}, {4,43}, {1,33}, {20,43}, {18,33}, {16,38}, {5,28}, {13,36}, {15,36}, {8,26}, {12,26}, {16,22}, {7,31}, {5,41}, {17,28}, {12,27}, {9,40}, {1,24}, {12,23}, {14,22}, {13,24}, {11,24}, {17,25}, {11,39}, {5,44}, {6,26}, {20,23}, {20,39}, {12,30}, {3,23}, {8,23}, {14,34}, {18,25}, {17,29}, {5,36}, {1,25}, {17,41}, {19,36}, {6,41}, {1,37}, {16,34}, {14,25}, {20,35}, {7,28}, {19,32}, {6,42}, {7,23}, {2,21}, {8,34}, {5,33}, {20,26}, {3,24}, {2,29}, {11,27}, {16,35}, {8,38}, {20,34}, {2,22}, {4,34}, {10,34}, {18,22}, {11,32}, {19,39}, {19,43}, {13,41}, {6,25}, {20,42}, {6,38}, {11,40}, {9,33}, {9,36}, {16,42}, {6,34}, {15,28}, {16,39}, {3,28}, {7,27}, {15,23}, {1,41}, {13,37}, {7,24}, {3,31}, {15,39}, {9,24}, {12,31}, {6,37}, {19,35}, {7,35}, {11,43}, {5,21}, {2,30}, {19,23}, {5,37}, {17,32}, {9,21}, {3,36}, {4,39}, {7,40}, {19,27}, {1,36}, {14,29}, {14,26} }; // ET44.22 // Bipartite(20,24) Valencies [12,10] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 951050714480640000 EdgePairs[44][22]:={ {10,24}, {2,24}, {13,32}, {2,33}, {17,35}, {17,44}, {18,39}, {13,21}, {11,35}, {4,24}, {16,26}, {4,26}, {3,22}, {3,40}, {17,38}, {4,30}, {11,25}, {8,30}, {14,39}, {8,43}, {5,38}, {12,32}, {8,42}, {16,31}, {15,31}, {1,32}, {1,27}, {3,43}, {3,25}, {12,38}, {7,41}, {9,44}, {7,22}, {4,31}, {10,33}, {12,42}, {2,27}, {3,35}, {3,37}, {13,35}, {7,34}, {11,41}, {1,21}, {16,25}, {15,43}, {17,21}, {18,21}, {8,25}, {2,28}, {5,32}, {9,35}, {14,28}, {20,30}, {8,44}, {8,31}, {13,29}, {12,37}, {2,42}, {18,34}, {10,22}, {6,22}, {15,25}, {18,42}, {11,28}, {16,43}, {10,30}, {16,30}, {19,28}, {4,38}, {15,29}, {6,21}, {3,34}, {20,38}, {6,40}, {1,38}, {2,34}, {14,33}, {2,36}, {9,29}, {19,40}, {9,32}, {14,21}, {14,36}, {16,24}, {9,26}, {9,27}, {12,36}, {15,40}, {1,44}, {5,29}, {12,44}, {19,29}, {14,30}, {14,40}, {19,22}, {4,42}, {9,41}, {2,39}, {17,39}, {17,23}, {11,22}, {7,43}, {11,31}, {10,28}, {7,25}, {14,24}, {20,31}, {17,33}, {6,30}, {5,23}, {10,21}, {16,37}, {10,40}, {12,43}, {1,29}, {18,30}, {15,41}, {8,36}, {6,33}, {13,33}, {16,32}, {11,23}, {1,23}, {11,29}, {6,24}, {20,44}, {13,44}, {19,41}, {15,35}, {17,27}, {13,23}, {12,25}, {15,37}, {14,42}, {15,34}, {18,24}, {10,42}, {19,31}, {18,27}, {18,36}, {4,43}, {1,33}, {20,43}, {18,33}, {3,29}, {16,38}, {8,37}, {8,26}, {12,26}, {7,31}, {5,41}, {4,36}, {8,32}, {14,22}, {6,27}, {5,44}, {12,30}, {3,23}, {14,34}, {1,39}, {17,29}, {20,25}, {16,44}, {17,41}, {7,29}, {6,28}, {13,27}, {10,39}, {1,35}, {5,39}, {7,28}, {20,37}, {4,37}, {6,42}, {13,26}, {7,23}, {16,36}, {6,36}, {2,21}, {5,33}, {20,26}, {11,37}, {18,28}, {10,27}, {8,38}, {1,26}, {2,22}, {10,36}, {10,34}, {15,22}, {18,22}, {8,24}, {19,43}, {13,41}, {20,42}, {20,24}, {2,40}, {11,40}, {9,33}, {16,42}, {20,36}, {6,34}, {5,27}, {19,25}, {5,26}, {15,28}, {9,39}, {13,38}, {9,38}, {4,25}, {12,24}, {3,28}, {15,23}, {1,41}, {3,41}, {3,31}, {18,40}, {17,26}, {6,39}, {12,31}, {11,34}, {19,35}, {7,35}, {13,39}, {11,43}, {5,21}, {2,30}, {19,34}, {7,37}, {5,35}, {19,23}, {17,32}, {9,21}, {7,40}, {4,44}, {9,23}, {19,37}, {20,32}, {14,27}, {4,32} }; // ET44.23 // Bipartite(20,24) Valencies [12,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 11741366845440 EdgePairs[44][23]:={ {2,44}, {3,33}, {16,41}, {10,25}, {2,24}, {13,32}, {17,35}, {11,36}, {4,27}, {13,21}, {11,35}, {5,34}, {15,24}, {18,29}, {10,37}, {18,32}, {14,39}, {12,22}, {12,32}, {8,28}, {19,44}, {16,31}, {18,38}, {20,27}, {1,27}, {12,38}, {19,24}, {7,41}, {10,26}, {17,34}, {9,44}, {7,22}, {4,31}, {10,33}, {12,42}, {3,35}, {9,43}, {20,21}, {13,35}, {2,26}, {14,31}, {7,34}, {11,41}, {1,21}, {16,25}, {10,44}, {2,28}, {12,34}, {1,30}, {18,41}, {16,23}, {17,40}, {14,28}, {8,44}, {13,29}, {16,29}, {2,42}, {18,34}, {16,43}, {6,29}, {16,30}, {5,40}, {20,38}, {11,33}, {6,31}, {2,34}, {14,33}, {2,36}, {5,22}, {4,22}, {10,38}, {17,37}, {9,32}, {14,21}, {19,26}, {16,24}, {9,26}, {19,30}, {12,36}, {15,40}, {8,41}, {2,38}, {12,44}, {14,40}, {17,23}, {7,43}, {7,25}, {20,31}, {15,27}, {3,44}, {19,38}, {20,33}, {6,30}, {6,43}, {4,33}, {4,21}, {10,31}, {15,42}, {10,21}, {9,42}, {16,37}, {17,43}, {1,29}, {3,39}, {3,32}, {11,21}, {9,25}, {2,32}, {13,33}, {18,44}, {19,42}, {11,23}, {1,23}, {11,29}, {6,24}, {20,44}, {13,44}, {5,30}, {11,30}, {5,24}, {9,37}, {13,23}, {12,28}, {8,22}, {15,34}, {8,35}, {18,26}, {19,31}, {3,27}, {14,37}, {4,28}, {1,33}, {4,43}, {20,43}, {3,29}, {6,23}, {3,26}, {5,28}, {15,36}, {8,26}, {17,31}, {5,42}, {12,26}, {7,31}, {10,43}, {17,28}, {8,32}, {1,42}, {1,24}, {14,22}, {11,24}, {17,25}, {11,39}, {8,40}, {12,40}, {20,39}, {12,30}, {3,23}, {8,23}, {14,34}, {1,39}, {10,32}, {17,29}, {20,25}, {5,36}, {3,21}, {17,41}, {7,29}, {19,36}, {6,41}, {18,23}, {9,30}, {10,39}, {13,27}, {1,35}, {15,21}, {5,39}, {14,25}, {7,28}, {19,32}, {20,37}, {4,37}, {6,42}, {13,26}, {4,40}, {7,23}, {16,36}, {6,36}, {8,34}, {5,33}, {20,26}, {11,27}, {16,35}, {18,28}, {10,27}, {8,38}, {2,22}, {4,34}, {15,22}, {18,22}, {15,33}, {19,43}, {6,25}, {13,41}, {2,40}, {9,36}, {16,42}, {5,27}, {14,43}, {19,25}, {15,28}, {13,38}, {9,38}, {4,25}, {3,38}, {12,24}, {1,41}, {3,41}, {15,39}, {9,24}, {18,40}, {6,37}, {7,35}, {13,39}, {17,22}, {5,21}, {2,30}, {15,30}, {7,37}, {9,31}, {6,35}, {11,42}, {4,39}, {18,35}, {7,40}, {19,37}, {20,32}, {14,27}, {8,29}, {1,36} }; // ET44.24 // Bipartite(20,24) Valencies [12,10] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 137594142720 EdgePairs[44][24]:={ {10,25}, {2,24}, {10,24}, {9,28}, {13,32}, {2,33}, {6,32}, {17,35}, {11,36}, {17,36}, {18,39}, {5,34}, {16,26}, {16,33}, {4,26}, {3,22}, {3,40}, {10,37}, {16,27}, {8,30}, {14,39}, {8,43}, {12,22}, {12,32}, {8,42}, {19,44}, {15,31}, {4,29}, {1,32}, {8,33}, {1,27}, {3,43}, {3,25}, {12,38}, {20,40}, {7,41}, {10,26}, {14,38}, {2,27}, {3,37}, {13,35}, {14,31}, {8,39}, {1,21}, {17,24}, {7,36}, {15,43}, {18,21}, {10,44}, {8,25}, {2,28}, {12,34}, {9,35}, {4,23}, {8,31}, {8,27}, {12,37}, {13,29}, {2,42}, {18,34}, {19,21}, {15,25}, {11,28}, {18,37}, {10,30}, {6,29}, {16,30}, {19,28}, {4,38}, {15,29}, {19,33}, {3,34}, {5,40}, {11,38}, {6,31}, {1,38}, {2,34}, {14,33}, {2,36}, {5,22}, {4,22}, {10,38}, {9,29}, {19,40}, {17,37}, {14,21}, {19,26}, {16,24}, {1,44}, {4,41}, {5,29}, {12,44}, {19,22}, {7,39}, {9,41}, {2,39}, {17,23}, {11,22}, {20,31}, {11,44}, {15,27}, {19,38}, {6,43}, {5,23}, {10,31}, {9,34}, {9,42}, {12,43}, {17,43}, {1,29}, {7,30}, {4,35}, {15,41}, {8,36}, {18,43}, {16,32}, {1,23}, {13,44}, {6,44}, {17,30}, {11,30}, {15,35}, {13,23}, {12,28}, {12,25}, {15,37}, {20,28}, {10,42}, {18,27}, {14,37}, {20,22}, {4,28}, {1,33}, {20,43}, {18,33}, {6,23}, {16,38}, {8,37}, {5,28}, {13,36}, {17,31}, {18,31}, {12,26}, {9,22}, {13,30}, {10,43}, {5,41}, {20,29}, {9,40}, {8,21}, {11,24}, {13,24}, {17,25}, {6,26}, {20,23}, {12,40}, {1,39}, {10,32}, {18,25}, {17,29}, {20,25}, {16,44}, {17,41}, {7,29}, {6,41}, {9,30}, {1,35}, {13,42}, {15,21}, {5,39}, {14,25}, {16,21}, {20,35}, {19,32}, {20,37}, {11,26}, {13,26}, {4,40}, {7,23}, {16,36}, {2,21}, {3,30}, {5,33}, {3,24}, {18,28}, {20,34}, {1,26}, {2,22}, {4,34}, {14,44}, {10,36}, {18,22}, {11,32}, {14,32}, {15,33}, {8,24}, {19,39}, {6,25}, {13,41}, {6,38}, {2,40}, {11,40}, {9,36}, {16,42}, {5,27}, {14,43}, {3,42}, {16,39}, {13,38}, {3,28}, {7,27}, {20,41}, {15,23}, {1,41}, {7,24}, {3,31}, {15,39}, {9,24}, {18,40}, {7,33}, {6,37}, {12,31}, {11,34}, {17,42}, {7,35}, {5,21}, {2,30}, {19,34}, {5,35}, {6,35}, {11,42}, {3,36}, {7,42}, {9,23}, {4,44}, {7,21}, {14,27}, {4,32}, {19,27}, {14,26} }; // ET44.25 // Bipartite(20,24) Valencies [12,10] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 503316480 EdgePairs[44][25]:={ {3,33}, {16,41}, {10,25}, {2,24}, {13,32}, {9,28}, {17,35}, {17,36}, {4,27}, {12,29}, {13,21}, {5,34}, {13,40}, {15,24}, {16,26}, {18,29}, {4,26}, {3,22}, {3,40}, {10,37}, {18,32}, {4,30}, {8,30}, {14,39}, {2,23}, {8,42}, {16,31}, {20,27}, {8,33}, {1,40}, {10,26}, {14,38}, {12,41}, {15,44}, {12,42}, {9,43}, {11,41}, {1,21}, {17,24}, {16,25}, {12,35}, {7,36}, {18,21}, {10,44}, {2,41}, {18,41}, {5,32}, {17,40}, {9,35}, {20,30}, {8,44}, {4,23}, {13,29}, {12,37}, {16,29}, {2,42}, {10,22}, {19,21}, {6,22}, {15,25}, {18,42}, {11,28}, {16,43}, {10,30}, {6,29}, {16,30}, {19,28}, {4,38}, {19,33}, {3,34}, {5,40}, {2,25}, {14,23}, {20,38}, {11,38}, {11,33}, {6,31}, {1,38}, {14,33}, {2,36}, {5,22}, {10,38}, {19,40}, {17,37}, {14,21}, {19,26}, {15,32}, {9,26}, {9,27}, {12,36}, {15,40}, {8,41}, {2,37}, {14,30}, {7,39}, {4,42}, {5,25}, {17,39}, {17,23}, {1,31}, {11,22}, {7,43}, {11,31}, {7,25}, {2,35}, {1,22}, {15,27}, {3,44}, {19,38}, {6,30}, {6,43}, {4,33}, {4,21}, {13,22}, {16,37}, {12,43}, {17,43}, {1,29}, {18,30}, {3,32}, {11,21}, {4,35}, {8,36}, {13,33}, {18,44}, {11,29}, {20,44}, {13,44}, {5,24}, {17,27}, {12,25}, {15,37}, {14,42}, {15,34}, {18,24}, {8,35}, {10,42}, {13,28}, {19,31}, {1,28}, {20,22}, {18,36}, {1,33}, {18,33}, {3,29}, {1,43}, {16,38}, {5,28}, {13,36}, {15,36}, {17,31}, {16,22}, {7,31}, {17,28}, {9,40}, {8,32}, {8,21}, {12,23}, {13,24}, {17,25}, {5,44}, {6,26}, {20,39}, {12,30}, {8,23}, {10,32}, {20,25}, {5,36}, {3,21}, {6,41}, {18,23}, {10,39}, {16,34}, {5,39}, {7,28}, {20,37}, {11,26}, {6,42}, {7,23}, {20,26}, {3,24}, {2,29}, {10,27}, {20,34}, {1,26}, {14,44}, {10,34}, {15,22}, {14,32}, {8,24}, {19,39}, {19,43}, {13,41}, {6,25}, {20,42}, {6,38}, {2,31}, {11,40}, {9,33}, {16,42}, {6,34}, {5,27}, {15,28}, {9,39}, {9,38}, {12,24}, {3,28}, {7,27}, {14,35}, {1,41}, {3,41}, {7,24}, {15,39}, {12,31}, {6,37}, {13,34}, {11,34}, {19,35}, {7,35}, {11,43}, {2,30}, {7,37}, {9,31}, {1,34}, {19,23}, {5,37}, {2,43}, {9,21}, {3,36}, {4,39}, {18,35}, {7,40}, {4,44}, {9,23}, {20,32}, {14,27}, {8,29}, {4,32}, {19,27}, {14,26} }; // ET44.26 // Bipartite(20,24) Valencies [12,10] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5898240 EdgePairs[44][26]:={ {2,44}, {16,41}, {10,24}, {17,44}, {17,36}, {4,27}, {13,21}, {15,24}, {16,26}, {16,33}, {3,22}, {18,32}, {4,30}, {11,25}, {2,23}, {8,43}, {12,22}, {18,38}, {15,31}, {20,27}, {1,27}, {3,43}, {3,25}, {12,38}, {20,40}, {7,41}, {7,44}, {1,40}, {10,26}, {17,34}, {9,44}, {14,38}, {15,44}, {10,33}, {3,37}, {2,26}, {14,31}, {11,41}, {1,21}, {17,24}, {7,36}, {15,43}, {2,41}, {12,34}, {1,30}, {5,32}, {16,23}, {14,28}, {8,44}, {8,31}, {13,29}, {12,37}, {16,29}, {2,42}, {10,22}, {19,21}, {6,22}, {18,37}, {16,30}, {19,28}, {19,33}, {6,21}, {3,34}, {5,40}, {2,25}, {14,23}, {11,38}, {11,33}, {6,31}, {6,40}, {14,33}, {4,22}, {10,38}, {9,29}, {19,40}, {9,32}, {14,21}, {14,36}, {19,26}, {15,32}, {16,24}, {19,30}, {9,27}, {15,40}, {8,41}, {2,38}, {2,37}, {14,40}, {7,39}, {4,42}, {9,41}, {5,25}, {7,32}, {17,39}, {10,41}, {11,22}, {14,24}, {20,31}, {2,35}, {15,27}, {3,44}, {19,38}, {6,43}, {4,33}, {5,23}, {10,29}, {4,21}, {10,31}, {9,34}, {13,22}, {10,21}, {9,42}, {12,43}, {17,43}, {7,30}, {3,32}, {11,21}, {9,25}, {8,36}, {6,33}, {2,32}, {13,33}, {18,44}, {19,42}, {18,43}, {1,23}, {11,29}, {6,24}, {20,44}, {5,30}, {11,30}, {15,35}, {9,37}, {17,27}, {12,28}, {12,25}, {20,28}, {8,35}, {18,26}, {1,28}, {20,22}, {4,28}, {1,33}, {20,43}, {3,29}, {3,26}, {16,38}, {5,28}, {13,36}, {15,36}, {8,26}, {17,31}, {18,31}, {5,42}, {12,26}, {9,22}, {12,33}, {13,30}, {10,43}, {8,32}, {1,42}, {1,24}, {13,24}, {6,27}, {5,44}, {12,40}, {20,39}, {8,23}, {1,39}, {18,25}, {17,29}, {20,25}, {17,41}, {7,29}, {6,28}, {18,23}, {9,30}, {13,27}, {1,35}, {13,42}, {5,39}, {16,21}, {20,37}, {4,37}, {11,26}, {4,40}, {7,23}, {16,36}, {6,36}, {11,37}, {2,29}, {16,35}, {18,28}, {8,38}, {20,34}, {4,34}, {10,36}, {10,34}, {8,24}, {13,41}, {16,42}, {6,34}, {5,27}, {14,43}, {19,25}, {15,28}, {9,39}, {4,25}, {3,38}, {7,27}, {14,35}, {15,23}, {3,41}, {7,24}, {3,31}, {15,39}, {18,40}, {6,39}, {12,31}, {11,34}, {13,34}, {19,35}, {7,35}, {13,39}, {17,22}, {2,30}, {5,35}, {19,23}, {5,37}, {17,32}, {11,42}, {4,39}, {18,35}, {7,42}, {19,37}, {20,32}, {8,29}, {12,21}, {1,36}, {14,26} }; // ET44.27 // Bipartite(20,24) Valencies [12,10] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2949120 EdgePairs[44][27]:={ {3,33}, {16,41}, {10,25}, {2,24}, {2,33}, {17,35}, {11,36}, {17,36}, {18,39}, {12,29}, {13,40}, {16,26}, {16,33}, {18,29}, {4,26}, {3,40}, {17,38}, {10,37}, {11,25}, {16,27}, {8,30}, {14,39}, {2,23}, {12,22}, {5,38}, {8,42}, {8,28}, {19,44}, {15,31}, {4,29}, {8,33}, {3,25}, {19,24}, {7,41}, {7,44}, {1,40}, {4,31}, {12,41}, {15,44}, {12,42}, {3,37}, {20,21}, {13,35}, {2,26}, {14,31}, {1,21}, {17,24}, {7,36}, {15,43}, {10,44}, {2,28}, {12,34}, {18,41}, {5,32}, {9,35}, {14,28}, {8,44}, {4,23}, {16,29}, {18,34}, {10,22}, {15,25}, {10,30}, {6,29}, {4,38}, {5,40}, {11,38}, {6,40}, {6,31}, {1,38}, {14,33}, {2,36}, {4,22}, {17,37}, {14,21}, {15,32}, {16,24}, {9,26}, {19,30}, {9,27}, {12,36}, {4,41}, {8,41}, {2,38}, {14,40}, {5,25}, {7,32}, {15,26}, {17,23}, {10,41}, {11,22}, {7,43}, {11,31}, {7,25}, {2,35}, {1,22}, {20,33}, {6,30}, {6,43}, {5,23}, {10,29}, {9,34}, {13,22}, {15,42}, {9,42}, {12,43}, {1,29}, {3,39}, {13,31}, {4,35}, {19,42}, {16,32}, {13,43}, {20,44}, {17,30}, {13,23}, {15,37}, {13,25}, {18,24}, {8,35}, {10,42}, {13,28}, {19,31}, {1,28}, {18,27}, {3,27}, {20,22}, {18,36}, {4,43}, {1,33}, {16,38}, {5,28}, {9,22}, {7,31}, {12,33}, {13,30}, {8,32}, {8,21}, {14,22}, {6,27}, {11,24}, {17,25}, {11,39}, {5,44}, {6,26}, {8,40}, {20,23}, {12,30}, {8,23}, {14,34}, {10,32}, {17,29}, {20,25}, {3,21}, {1,25}, {16,44}, {17,41}, {7,29}, {19,36}, {6,41}, {6,28}, {18,23}, {9,30}, {10,39}, {13,42}, {1,37}, {15,21}, {5,39}, {16,21}, {20,35}, {7,28}, {19,32}, {20,37}, {11,26}, {6,42}, {16,36}, {2,21}, {3,30}, {11,37}, {3,24}, {11,27}, {18,28}, {10,27}, {20,34}, {1,26}, {4,34}, {14,44}, {10,34}, {18,22}, {14,32}, {15,33}, {19,39}, {19,43}, {6,38}, {20,24}, {2,40}, {2,31}, {9,33}, {20,36}, {5,27}, {14,43}, {15,38}, {5,26}, {3,42}, {16,39}, {9,39}, {9,38}, {12,24}, {3,28}, {1,41}, {13,37}, {7,24}, {18,40}, {17,26}, {6,39}, {12,31}, {13,34}, {11,34}, {17,42}, {19,35}, {11,43}, {15,30}, {7,37}, {5,35}, {1,34}, {19,23}, {5,37}, {2,43}, {9,21}, {3,36}, {18,35}, {7,40}, {4,44}, {9,23}, {20,32}, {14,27}, {8,29}, {4,32}, {19,27}, {12,21} }; // ET44.28 // Bipartite(22,22) Valencies [12,12] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 5536481280 EdgePairs[44][28]:={ {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {5,38}, {19,26}, {4,28}, {5,43}, {3,26}, {8,26}, {22,40}, {13,37}, {17,42}, {2,35}, {17,33}, {4,31}, {10,33}, {15,27}, {8,23}, {3,39}, {19,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {4,37}, {13,43}, {13,27}, {14,29}, {13,40}, {14,44}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {12,28}, {22,37}, {2,25}, {4,43}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {20,43}, {8,37}, {20,24}, {21,38}, {12,38}, {7,41}, {11,39}, {10,26}, {22,42}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {20,35}, {9,35}, {1,36}, {16,34}, {16,43}, {6,44}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {2,36}, {20,36}, {16,40}, {20,42}, {22,34}, {18,29}, {9,36}, {9,39}, {18,36}, {5,27}, {15,28}, {5,28}, {7,32}, {12,24}, {12,27}, {1,39}, {6,27}, {11,42}, {3,36}, {19,23}, {17,29}, {20,25}, {4,32}, {1,30}, {14,28}, {16,29}, {3,30}, {2,24}, {11,23}, {22,26}, {10,36}, {14,33}, {15,37}, {10,38}, {21,25}, {13,25}, {14,39}, {21,31}, {19,30}, {8,24}, {4,41}, {8,41}, {21,37}, {3,29}, {17,31}, {13,36}, {1,41}, {22,29}, {12,41}, {20,31}, {3,44}, {3,25}, {19,24}, {11,34}, {21,42}, {2,43}, {2,27}, {12,30}, {6,30}, {7,34}, {11,24}, {10,31}, {9,31}, {10,44}, {18,25}, {1,25}, {22,31}, {5,39}, {20,44}, {17,44}, {19,41}, {13,29}, {8,34}, {9,25}, {17,30}, {5,40}, {7,23}, {10,25}, {17,38}, {6,31}, {12,25}, {14,37}, {13,38}, {19,44}, {18,31}, {14,40}, {3,41}, {15,39}, {9,44}, {8,32}, {22,39}, {9,24}, {19,34}, {16,44}, {7,40}, {17,41}, {5,23}, {20,32}, {2,26}, {18,41}, {7,29}, {18,30}, {3,33}, {13,32}, {14,26}, {19,33}, {9,28}, {4,27}, {19,43}, {8,43}, {16,38}, {20,28}, {21,33}, {12,36}, {16,27}, {2,37}, {4,42}, {5,29}, {14,30}, {3,28}, {21,34}, {7,31}, {8,33}, {12,39}, {11,31}, {20,33}, {21,44}, {19,35}, {7,25}, {15,42}, {1,34}, {13,35}, {22,23}, {21,27}, {7,42}, {6,41}, {17,24}, {17,40}, {12,34}, {8,44}, {16,23}, {6,42}, {18,23}, {19,32}, {18,43}, {14,25}, {11,37}, {11,28}, {1,23}, {22,24}, {10,27}, {10,34}, {16,33}, {3,40}, {17,27}, {8,35}, {2,40}, {14,41}, {4,26}, {16,39}, {1,28}, {2,38}, {22,35}, {21,36}, {15,31}, {7,43}, {18,40}, {1,27}, {5,44}, {10,23}, {15,26}, {9,43}, {3,37}, {9,42}, {15,43}, {4,39}, {12,35}, {7,36}, {6,35}, {21,26}, {22,28}, {18,42}, {16,32}, {2,32}, {6,33}, {18,34}, {11,26}, {5,33}, {6,40}, {21,23} }; // ET44.29 // Bipartite(16,28) Valencies [14,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 672 EdgePairs[44][29]:={ {3,33}, {16,41}, {10,25}, {1,20}, {5,17}, {2,24}, {10,24}, {9,28}, {13,32}, {2,33}, {6,32}, {11,36}, {4,27}, {13,21}, {11,35}, {5,34}, {4,24}, {14,19}, {15,24}, {16,33}, {3,22}, {4,30}, {16,27}, {8,30}, {16,40}, {8,43}, {12,22}, {12,32}, {7,38}, {8,42}, {8,28}, {16,31}, {4,29}, {1,32}, {1,27}, {12,38}, {7,41}, {7,44}, {1,40}, {7,22}, {12,41}, {1,19}, {12,42}, {3,35}, {13,35}, {2,26}, {14,31}, {7,34}, {1,21}, {10,44}, {2,41}, {2,28}, {1,30}, {9,35}, {4,23}, {8,31}, {8,27}, {2,42}, {15,25}, {3,18}, {16,43}, {6,29}, {4,38}, {15,29}, {3,34}, {2,25}, {14,23}, {11,33}, {6,31}, {6,40}, {1,38}, {2,34}, {14,33}, {1,17}, {2,36}, {5,22}, {8,19}, {9,32}, {12,17}, {15,32}, {9,26}, {12,20}, {1,44}, {2,37}, {14,30}, {14,40}, {7,39}, {2,39}, {15,26}, {1,31}, {10,41}, {7,25}, {11,31}, {11,44}, {1,22}, {6,30}, {6,43}, {5,23}, {10,29}, {3,20}, {15,19}, {10,40}, {8,17}, {8,36}, {6,33}, {7,26}, {5,18}, {11,23}, {1,23}, {13,43}, {11,29}, {11,30}, {5,24}, {9,37}, {12,28}, {12,25}, {15,37}, {8,35}, {10,42}, {13,28}, {4,43}, {15,17}, {3,26}, {16,38}, {13,36}, {15,36}, {12,26}, {9,22}, {10,43}, {5,41}, {8,32}, {3,19}, {14,18}, {14,22}, {13,24}, {11,39}, {5,44}, {12,19}, {6,26}, {12,40}, {14,34}, {5,36}, {3,21}, {16,44}, {6,28}, {9,30}, {13,27}, {1,35}, {13,42}, {14,20}, {16,34}, {14,25}, {16,21}, {4,37}, {6,42}, {15,18}, {4,40}, {7,23}, {10,17}, {11,37}, {2,29}, {11,27}, {16,35}, {10,27}, {14,44}, {10,34}, {15,22}, {10,18}, {16,20}, {6,25}, {13,41}, {6,38}, {9,33}, {9,36}, {16,42}, {5,27}, {8,18}, {3,42}, {15,28}, {16,39}, {9,39}, {13,38}, {9,38}, {10,19}, {4,25}, {12,24}, {8,20}, {3,28}, {15,23}, {13,37}, {3,41}, {7,24}, {3,31}, {10,20}, {6,39}, {7,33}, {11,34}, {5,19}, {6,20}, {13,39}, {11,43}, {5,21}, {13,17}, {15,30}, {7,37}, {5,35}, {2,18}, {9,31}, {5,37}, {2,43}, {4,17}, {9,21}, {3,36}, {4,39}, {7,40}, {4,44}, {9,23}, {7,21}, {8,29}, {4,32}, {11,18}, {12,21}, {14,29}, {14,26} }; // ET44.30 // Bipartite(16,28) Valencies [14,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 21504 EdgePairs[44][30]:={ {11,17}, {16,41}, {10,24}, {2,24}, {9,28}, {13,32}, {4,27}, {12,29}, {11,35}, {15,24}, {16,33}, {3,22}, {3,40}, {10,37}, {4,30}, {11,25}, {16,27}, {8,30}, {16,40}, {14,39}, {8,43}, {5,38}, {12,22}, {7,38}, {8,42}, {16,31}, {15,31}, {4,29}, {1,32}, {3,43}, {10,23}, {12,38}, {7,44}, {1,40}, {4,19}, {12,41}, {10,33}, {3,35}, {2,26}, {14,31}, {7,34}, {16,25}, {7,36}, {15,43}, {8,25}, {10,44}, {2,41}, {2,28}, {12,34}, {4,23}, {8,27}, {13,29}, {11,28}, {10,30}, {3,17}, {15,29}, {6,21}, {14,23}, {11,38}, {6,40}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {1,18}, {14,21}, {14,36}, {12,17}, {15,32}, {9,26}, {15,40}, {1,44}, {2,38}, {9,19}, {5,43}, {12,44}, {7,39}, {5,25}, {2,39}, {15,26}, {1,31}, {10,41}, {10,28}, {2,35}, {11,44}, {3,44}, {6,30}, {6,43}, {4,33}, {4,21}, {9,34}, {13,22}, {15,19}, {9,42}, {2,20}, {12,43}, {1,29}, {8,17}, {3,39}, {3,32}, {11,21}, {4,35}, {8,36}, {6,33}, {2,32}, {13,33}, {5,18}, {16,32}, {1,23}, {13,43}, {6,24}, {13,44}, {11,30}, {15,35}, {13,23}, {15,37}, {13,25}, {10,42}, {15,20}, {9,20}, {1,28}, {14,41}, {3,27}, {14,37}, {4,28}, {6,23}, {16,38}, {8,37}, {13,36}, {5,42}, {16,22}, {9,22}, {7,31}, {13,30}, {5,41}, {2,17}, {12,27}, {14,17}, {8,32}, {3,19}, {5,31}, {5,44}, {11,39}, {6,26}, {12,40}, {12,30}, {3,23}, {10,32}, {5,36}, {1,25}, {7,29}, {6,41}, {1,37}, {14,20}, {16,34}, {14,25}, {7,28}, {6,42}, {11,26}, {13,26}, {15,18}, {4,40}, {10,35}, {13,19}, {8,34}, {5,33}, {9,18}, {3,24}, {11,37}, {2,29}, {10,27}, {8,38}, {1,26}, {2,22}, {10,36}, {9,17}, {10,18}, {15,33}, {16,20}, {11,40}, {9,36}, {16,42}, {6,34}, {14,43}, {15,38}, {5,26}, {8,18}, {3,42}, {4,18}, {16,39}, {11,19}, {4,25}, {4,20}, {8,20}, {12,24}, {7,27}, {14,35}, {1,41}, {7,24}, {3,31}, {9,24}, {6,39}, {7,33}, {6,37}, {13,34}, {6,20}, {13,39}, {5,21}, {2,30}, {7,37}, {5,35}, {9,31}, {1,34}, {7,19}, {9,21}, {11,42}, {16,28}, {9,23}, {7,21}, {14,27}, {12,18}, {12,21}, {14,29} }; // ET44.31 // Bipartite(16,28) Valencies [14,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 2688 EdgePairs[44][31]:={ {11,17}, {2,44}, {3,33}, {16,41}, {10,24}, {5,17}, {2,24}, {9,28}, {13,32}, {2,33}, {4,27}, {11,35}, {13,40}, {4,24}, {14,19}, {3,22}, {3,40}, {10,37}, {4,30}, {11,25}, {16,27}, {8,30}, {14,39}, {8,43}, {12,22}, {8,42}, {8,28}, {15,31}, {4,29}, {12,38}, {7,44}, {1,40}, {10,26}, {9,44}, {4,31}, {2,19}, {12,41}, {15,44}, {10,33}, {1,19}, {12,42}, {5,20}, {3,37}, {13,35}, {2,26}, {7,34}, {1,21}, {16,25}, {15,43}, {8,25}, {12,34}, {5,32}, {14,28}, {8,27}, {12,37}, {16,29}, {10,22}, {15,25}, {3,18}, {6,29}, {3,17}, {4,38}, {3,34}, {2,25}, {14,23}, {11,38}, {11,33}, {6,31}, {1,38}, {2,34}, {14,33}, {1,17}, {2,36}, {5,22}, {4,22}, {9,29}, {7,20}, {14,21}, {9,26}, {12,20}, {15,40}, {1,44}, {4,41}, {8,41}, {9,19}, {2,37}, {14,30}, {9,41}, {5,25}, {7,25}, {11,31}, {15,27}, {6,43}, {5,23}, {10,29}, {4,21}, {9,34}, {15,42}, {10,21}, {9,42}, {6,18}, {13,18}, {16,37}, {12,43}, {7,30}, {3,39}, {13,31}, {3,32}, {11,21}, {7,26}, {6,33}, {2,32}, {5,18}, {16,32}, {1,23}, {13,43}, {11,29}, {7,17}, {11,30}, {13,23}, {12,25}, {8,35}, {10,42}, {3,27}, {14,37}, {4,43}, {16,38}, {8,37}, {5,28}, {13,36}, {15,36}, {8,26}, {9,22}, {7,31}, {5,41}, {9,40}, {8,21}, {1,42}, {1,24}, {12,23}, {5,31}, {11,24}, {13,24}, {8,40}, {12,19}, {12,30}, {3,23}, {1,39}, {5,36}, {6,19}, {16,44}, {6,28}, {9,30}, {10,39}, {13,27}, {1,35}, {1,37}, {14,20}, {15,21}, {16,34}, {16,17}, {6,42}, {13,26}, {7,23}, {16,36}, {6,36}, {3,30}, {10,17}, {2,29}, {16,35}, {10,27}, {2,22}, {14,44}, {10,36}, {15,22}, {11,32}, {9,17}, {10,18}, {14,32}, {15,33}, {16,20}, {13,41}, {6,38}, {2,40}, {11,40}, {6,34}, {14,43}, {15,38}, {5,26}, {8,18}, {15,28}, {9,39}, {11,19}, {3,38}, {4,20}, {3,28}, {12,24}, {7,27}, {14,35}, {15,23}, {1,41}, {7,24}, {10,20}, {6,39}, {7,33}, {13,34}, {5,19}, {6,20}, {7,35}, {13,39}, {5,21}, {9,31}, {2,43}, {6,35}, {4,39}, {16,28}, {7,42}, {4,44}, {8,29}, {4,32}, {12,18}, {11,18}, {1,36}, {14,26} }; // ET44.32 // Bipartite(16,28) Valencies [14,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1712604574101012480000 EdgePairs[44][32]:={ {10,25}, {1,20}, {5,17}, {11,20}, {9,28}, {13,32}, {2,33}, {11,36}, {4,27}, {13,21}, {11,35}, {13,40}, {15,24}, {16,26}, {4,26}, {3,40}, {10,37}, {4,30}, {16,27}, {8,30}, {6,17}, {8,43}, {12,22}, {8,42}, {16,31}, {15,31}, {1,32}, {3,43}, {12,38}, {7,44}, {1,40}, {10,26}, {9,44}, {4,19}, {14,38}, {16,19}, {12,39}, {4,31}, {15,44}, {10,33}, {12,42}, {3,35}, {5,20}, {2,26}, {8,39}, {1,21}, {16,18}, {12,35}, {7,36}, {15,43}, {2,41}, {12,34}, {5,32}, {16,23}, {4,23}, {8,31}, {8,27}, {13,29}, {2,42}, {10,22}, {6,22}, {11,28}, {16,43}, {10,30}, {6,29}, {16,30}, {4,38}, {6,21}, {2,25}, {5,40}, {2,34}, {14,33}, {1,17}, {4,22}, {10,38}, {9,29}, {8,19}, {7,20}, {9,32}, {14,21}, {15,32}, {15,40}, {1,44}, {5,29}, {2,38}, {2,37}, {14,30}, {7,39}, {4,42}, {9,41}, {5,25}, {7,32}, {10,41}, {7,43}, {11,31}, {11,44}, {15,27}, {3,44}, {6,30}, {10,29}, {3,20}, {15,19}, {10,21}, {6,18}, {12,43}, {1,29}, {3,39}, {3,32}, {4,35}, {9,25}, {6,33}, {13,33}, {11,23}, {13,44}, {15,35}, {5,24}, {9,37}, {8,22}, {14,42}, {13,25}, {8,35}, {10,42}, {13,28}, {15,20}, {9,20}, {1,28}, {14,41}, {3,27}, {14,37}, {4,43}, {1,33}, {16,38}, {5,28}, {13,36}, {15,36}, {8,26}, {12,26}, {16,22}, {7,31}, {5,41}, {2,17}, {12,27}, {9,40}, {14,17}, {3,19}, {1,24}, {14,18}, {12,23}, {14,22}, {11,24}, {13,24}, {5,44}, {11,39}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {14,34}, {5,36}, {1,25}, {6,41}, {1,37}, {16,34}, {14,25}, {7,28}, {6,42}, {7,23}, {2,21}, {8,34}, {5,33}, {10,17}, {3,24}, {2,29}, {11,27}, {16,35}, {8,38}, {2,22}, {4,34}, {10,34}, {11,32}, {9,17}, {10,18}, {6,25}, {13,41}, {6,38}, {11,40}, {9,33}, {9,36}, {16,42}, {6,34}, {8,18}, {4,18}, {15,28}, {16,39}, {11,19}, {3,28}, {7,27}, {15,23}, {1,41}, {13,37}, {7,24}, {3,31}, {15,39}, {9,24}, {6,37}, {12,31}, {7,35}, {11,43}, {5,21}, {2,30}, {13,17}, {13,20}, {2,18}, {5,37}, {7,19}, {9,21}, {3,36}, {4,39}, {7,40}, {12,18}, {1,36}, {14,29}, {14,26} }; // ET44.33 // Bipartite(16,28) Valencies [14,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5637144576 EdgePairs[44][33]:={ {3,33}, {5,17}, {1,20}, {2,33}, {12,29}, {11,35}, {5,34}, {14,19}, {15,24}, {16,26}, {3,40}, {10,37}, {8,30}, {16,40}, {6,17}, {14,39}, {2,23}, {12,32}, {7,38}, {8,42}, {8,28}, {4,29}, {1,27}, {10,23}, {7,41}, {1,40}, {10,26}, {14,38}, {7,22}, {12,39}, {2,19}, {10,33}, {12,42}, {3,35}, {5,20}, {9,43}, {3,37}, {2,26}, {14,31}, {11,41}, {1,21}, {16,18}, {12,35}, {7,36}, {15,43}, {2,28}, {12,34}, {9,35}, {14,28}, {8,44}, {4,23}, {12,37}, {2,42}, {10,22}, {15,25}, {3,18}, {16,30}, {15,29}, {6,21}, {11,33}, {6,31}, {1,38}, {14,33}, {1,17}, {2,36}, {5,22}, {9,29}, {14,21}, {15,32}, {16,24}, {9,26}, {9,27}, {12,20}, {2,37}, {14,30}, {7,39}, {4,42}, {9,41}, {5,25}, {7,32}, {1,31}, {7,43}, {10,28}, {7,25}, {14,24}, {11,44}, {15,27}, {3,44}, {6,30}, {5,23}, {10,29}, {4,21}, {10,31}, {9,34}, {13,22}, {15,19}, {10,40}, {12,43}, {1,29}, {13,31}, {3,32}, {11,21}, {4,35}, {15,41}, {8,36}, {6,33}, {16,32}, {11,23}, {6,24}, {13,44}, {5,30}, {6,44}, {11,30}, {13,23}, {12,28}, {12,25}, {8,22}, {14,42}, {13,25}, {10,42}, {9,20}, {3,27}, {4,28}, {4,43}, {1,43}, {3,26}, {16,38}, {13,36}, {15,36}, {8,26}, {16,22}, {13,30}, {10,43}, {2,17}, {5,41}, {9,40}, {14,17}, {8,32}, {3,19}, {1,24}, {12,23}, {5,31}, {5,44}, {8,40}, {3,23}, {5,36}, {3,21}, {6,19}, {16,44}, {7,29}, {6,28}, {13,27}, {1,35}, {16,34}, {5,39}, {14,25}, {4,37}, {6,42}, {11,26}, {15,18}, {16,36}, {3,30}, {8,34}, {10,17}, {11,37}, {2,29}, {11,27}, {8,38}, {1,26}, {2,22}, {4,34}, {14,44}, {10,36}, {15,22}, {11,32}, {9,17}, {15,33}, {16,20}, {8,24}, {6,25}, {13,41}, {6,38}, {2,40}, {2,31}, {11,40}, {16,42}, {5,27}, {15,38}, {8,18}, {4,18}, {9,38}, {11,19}, {10,19}, {4,25}, {4,20}, {8,20}, {7,27}, {14,35}, {1,41}, {13,37}, {3,41}, {7,24}, {15,39}, {9,24}, {6,39}, {7,33}, {13,34}, {13,39}, {13,17}, {13,20}, {9,31}, {1,34}, {5,37}, {7,19}, {2,43}, {6,35}, {9,21}, {4,39}, {16,28}, {4,32}, {12,18}, {11,18}, {12,21}, {7,18} }; // ET44.34 // Bipartite(16,28) Valencies [14,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 86016 EdgePairs[44][34]:={ {2,44}, {16,41}, {10,25}, {1,20}, {13,32}, {2,33}, {11,36}, {4,27}, {12,29}, {11,35}, {5,34}, {13,40}, {4,24}, {16,26}, {16,33}, {3,22}, {3,40}, {4,30}, {8,30}, {6,17}, {14,39}, {8,43}, {5,38}, {12,32}, {7,38}, {8,42}, {8,28}, {15,31}, {4,29}, {8,33}, {1,27}, {7,44}, {1,40}, {10,26}, {9,44}, {4,19}, {16,19}, {12,39}, {15,44}, {10,33}, {3,35}, {5,20}, {9,43}, {13,35}, {2,26}, {14,31}, {11,41}, {1,21}, {16,18}, {7,36}, {15,43}, {10,44}, {2,28}, {12,34}, {1,30}, {5,32}, {4,23}, {12,37}, {2,42}, {6,22}, {15,25}, {11,28}, {16,43}, {10,30}, {6,29}, {16,30}, {6,21}, {3,34}, {5,40}, {2,25}, {14,23}, {11,38}, {6,31}, {14,33}, {1,17}, {10,38}, {8,19}, {1,18}, {7,20}, {14,21}, {12,17}, {15,32}, {9,27}, {1,44}, {8,41}, {2,38}, {5,43}, {12,44}, {5,25}, {2,39}, {7,32}, {15,26}, {1,31}, {11,22}, {7,43}, {10,28}, {7,25}, {14,24}, {1,22}, {15,27}, {10,29}, {10,31}, {9,34}, {15,42}, {10,21}, {13,18}, {16,37}, {10,40}, {8,17}, {11,21}, {8,36}, {6,33}, {7,26}, {13,33}, {5,18}, {16,32}, {11,23}, {13,43}, {11,29}, {6,24}, {15,35}, {5,24}, {12,28}, {12,25}, {15,37}, {8,22}, {13,25}, {10,42}, {15,20}, {9,20}, {14,41}, {3,27}, {14,37}, {4,28}, {3,29}, {6,23}, {1,43}, {8,37}, {15,36}, {8,26}, {16,22}, {9,22}, {7,31}, {5,41}, {12,27}, {9,40}, {14,17}, {8,32}, {3,19}, {1,24}, {12,23}, {14,22}, {13,24}, {12,19}, {6,26}, {12,30}, {3,23}, {3,21}, {6,41}, {9,30}, {10,39}, {14,20}, {5,39}, {16,17}, {4,37}, {7,23}, {13,19}, {16,36}, {2,21}, {5,33}, {9,18}, {2,29}, {11,27}, {4,34}, {9,17}, {10,18}, {13,41}, {2,40}, {2,31}, {11,40}, {9,36}, {16,42}, {15,38}, {8,18}, {3,42}, {13,38}, {11,19}, {4,25}, {3,38}, {12,24}, {3,28}, {7,27}, {14,35}, {15,23}, {3,41}, {9,24}, {6,39}, {6,37}, {11,34}, {13,34}, {5,19}, {6,20}, {7,35}, {13,39}, {2,30}, {7,37}, {13,20}, {5,35}, {2,18}, {9,31}, {1,34}, {4,17}, {6,35}, {11,42}, {3,36}, {9,21}, {4,39}, {16,28}, {7,42}, {4,44}, {4,32}, {1,36}, {14,29}, {14,26} }; // ET44.35 // Bipartite(16,28) Valencies [14,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 44040192 EdgePairs[44][35]:={ {16,41}, {10,25}, {2,24}, {11,20}, {9,28}, {2,33}, {11,36}, {4,27}, {12,29}, {11,35}, {4,24}, {15,24}, {16,33}, {4,26}, {3,22}, {3,40}, {11,25}, {16,27}, {8,30}, {2,23}, {8,43}, {5,38}, {12,32}, {16,31}, {1,27}, {3,25}, {10,26}, {14,38}, {16,19}, {7,22}, {2,19}, {15,44}, {1,19}, {3,35}, {9,43}, {3,37}, {8,39}, {7,34}, {1,21}, {16,18}, {12,35}, {7,36}, {15,43}, {10,44}, {8,25}, {12,34}, {14,28}, {8,44}, {4,23}, {8,27}, {13,29}, {10,22}, {10,30}, {6,29}, {3,17}, {16,30}, {4,38}, {15,29}, {3,34}, {11,38}, {11,33}, {6,40}, {2,34}, {1,17}, {5,22}, {4,22}, {9,29}, {7,20}, {9,32}, {14,36}, {12,17}, {15,32}, {9,26}, {9,27}, {12,20}, {4,41}, {8,41}, {2,38}, {2,37}, {12,44}, {14,30}, {14,40}, {9,41}, {5,25}, {7,32}, {1,31}, {10,41}, {11,22}, {10,28}, {14,24}, {2,35}, {11,44}, {15,27}, {6,43}, {5,23}, {4,21}, {10,31}, {3,20}, {15,19}, {15,42}, {9,42}, {2,20}, {10,40}, {12,43}, {1,29}, {3,39}, {13,31}, {11,21}, {4,35}, {15,41}, {2,32}, {13,33}, {16,32}, {1,23}, {13,43}, {6,24}, {13,44}, {7,17}, {11,30}, {5,24}, {9,37}, {14,42}, {13,25}, {8,35}, {10,42}, {13,28}, {1,33}, {6,23}, {1,43}, {3,26}, {5,28}, {8,26}, {5,42}, {12,26}, {16,22}, {7,31}, {13,30}, {5,41}, {4,36}, {9,40}, {8,21}, {14,18}, {14,22}, {11,24}, {11,39}, {6,26}, {8,40}, {12,40}, {12,30}, {3,23}, {14,34}, {1,39}, {5,36}, {3,21}, {1,25}, {16,44}, {6,28}, {10,39}, {1,35}, {13,42}, {1,37}, {14,20}, {5,39}, {16,17}, {16,21}, {7,28}, {4,37}, {6,42}, {15,18}, {4,40}, {7,23}, {13,19}, {16,36}, {2,21}, {5,33}, {9,18}, {10,17}, {2,29}, {16,35}, {10,27}, {8,38}, {14,44}, {10,36}, {9,17}, {14,32}, {15,33}, {8,24}, {6,25}, {6,38}, {6,34}, {5,27}, {15,38}, {4,18}, {15,28}, {11,19}, {1,41}, {3,31}, {6,39}, {7,33}, {6,37}, {12,31}, {11,34}, {13,34}, {5,19}, {6,20}, {13,39}, {13,17}, {15,30}, {7,37}, {13,20}, {2,18}, {9,31}, {5,37}, {7,19}, {2,43}, {3,36}, {7,42}, {9,23}, {8,29}, {4,32}, {12,18}, {12,21}, {14,26}, {7,18} }; // ET44.36 // Bipartite(11,33) Valencies [15,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 239446056960 EdgePairs[44][36]:={ {11,17}, {3,33}, {10,25}, {1,20}, {2,24}, {10,24}, {11,20}, {9,28}, {6,16}, {11,35}, {8,12}, {4,26}, {3,22}, {3,40}, {10,37}, {4,30}, {8,30}, {8,43}, {4,29}, {8,33}, {1,27}, {3,25}, {10,26}, {2,15}, {4,19}, {2,27}, {10,33}, {5,20}, {9,43}, {2,26}, {7,34}, {7,36}, {10,44}, {11,12}, {2,28}, {5,32}, {8,44}, {4,23}, {8,27}, {10,15}, {10,22}, {3,18}, {11,28}, {10,30}, {6,29}, {3,17}, {8,16}, {7,12}, {5,40}, {6,40}, {6,31}, {11,33}, {1,38}, {5,22}, {8,19}, {3,14}, {9,32}, {5,29}, {4,41}, {8,41}, {2,38}, {9,19}, {2,37}, {5,43}, {9,41}, {2,39}, {7,32}, {11,13}, {1,31}, {10,41}, {11,22}, {7,13}, {9,14}, {7,43}, {7,25}, {11,31}, {2,35}, {11,44}, {3,44}, {6,30}, {9,42}, {2,13}, {6,18}, {2,16}, {3,39}, {9,25}, {2,32}, {1,12}, {5,18}, {1,23}, {11,23}, {6,24}, {8,22}, {9,20}, {4,15}, {7,14}, {3,27}, {4,28}, {10,13}, {3,29}, {5,42}, {2,17}, {8,32}, {8,21}, {1,42}, {5,31}, {6,27}, {11,24}, {5,44}, {11,39}, {8,23}, {1,25}, {6,19}, {7,29}, {6,41}, {1,15}, {9,30}, {1,37}, {3,16}, {4,37}, {6,42}, {4,40}, {10,35}, {7,23}, {2,21}, {8,34}, {5,33}, {8,38}, {1,26}, {4,34}, {1,16}, {10,36}, {9,17}, {6,38}, {9,36}, {5,26}, {4,18}, {9,39}, {10,19}, {3,38}, {4,12}, {3,28}, {7,24}, {1,14}, {5,15}, {10,14}, {11,34}, {6,20}, {7,35}, {5,21}, {6,13}, {9,31}, {1,34}, {5,37}, {2,43}, {4,17}, {6,35}, {9,21}, {3,36}, {11,42}, {4,39}, {7,40}, {7,21}, {1,36}, {7,18} }; // ET44.37 // Bipartite(12,32) Valencies [16,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 23040 EdgePairs[44][37]:={ {2,44}, {11,17}, {3,33}, {10,25}, {1,20}, {2,24}, {11,20}, {9,28}, {4,27}, {12,29}, {7,15}, {5,34}, {3,22}, {3,40}, {4,16}, {10,37}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {5,38}, {12,32}, {4,29}, {3,13}, {3,25}, {7,41}, {7,44}, {2,15}, {4,19}, {9,44}, {7,22}, {12,39}, {4,31}, {2,19}, {12,41}, {2,27}, {10,33}, {12,42}, {3,35}, {5,20}, {9,43}, {2,26}, {8,39}, {7,34}, {11,14}, {8,25}, {10,44}, {12,34}, {2,14}, {1,30}, {5,32}, {9,35}, {4,23}, {8,31}, {8,27}, {12,37}, {10,30}, {6,29}, {3,17}, {6,21}, {3,34}, {5,40}, {6,40}, {1,38}, {1,17}, {2,36}, {4,22}, {10,38}, {1,18}, {1,44}, {4,41}, {8,41}, {2,38}, {9,19}, {2,37}, {4,42}, {5,25}, {2,39}, {7,32}, {11,13}, {11,15}, {1,31}, {10,41}, {11,22}, {7,13}, {9,14}, {7,43}, {7,25}, {10,28}, {1,22}, {6,30}, {12,16}, {3,20}, {10,31}, {9,42}, {6,18}, {10,40}, {12,43}, {11,21}, {4,35}, {7,16}, {7,26}, {2,32}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {5,24}, {9,37}, {8,22}, {10,42}, {5,14}, {4,15}, {1,28}, {7,14}, {4,43}, {3,29}, {6,23}, {5,28}, {8,26}, {7,31}, {12,33}, {4,36}, {10,43}, {9,13}, {12,27}, {8,32}, {11,24}, {5,44}, {8,40}, {12,19}, {12,40}, {8,23}, {10,32}, {12,14}, {3,21}, {1,25}, {6,19}, {1,15}, {6,28}, {10,39}, {1,35}, {3,16}, {6,42}, {11,26}, {10,35}, {11,16}, {6,36}, {3,30}, {5,33}, {8,34}, {9,18}, {11,27}, {8,38}, {1,26}, {10,36}, {9,17}, {8,24}, {6,38}, {2,31}, {9,33}, {9,36}, {5,26}, {3,42}, {11,19}, {5,13}, {8,20}, {3,28}, {12,24}, {7,27}, {3,41}, {6,39}, {7,33}, {6,37}, {11,34}, {6,20}, {7,35}, {5,21}, {9,15}, {2,18}, {5,37}, {2,43}, {4,17}, {9,21}, {9,16}, {4,39}, {8,29}, {11,18}, {1,36}, {12,21} }; // ET44.38 // Bipartite(12,32) Valencies [16,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 27401673185616199680000 EdgePairs[44][38]:={ {10,25}, {1,20}, {5,17}, {11,20}, {9,28}, {2,33}, {11,36}, {4,27}, {7,15}, {11,35}, {4,26}, {3,40}, {10,37}, {4,30}, {8,30}, {6,17}, {8,43}, {1,13}, {12,22}, {8,42}, {1,32}, {3,43}, {3,15}, {12,38}, {7,44}, {1,40}, {10,26}, {9,44}, {4,19}, {12,39}, {4,31}, {10,33}, {12,42}, {3,35}, {5,20}, {2,26}, {8,39}, {1,21}, {12,35}, {7,36}, {2,41}, {12,34}, {2,14}, {5,32}, {8,15}, {4,23}, {8,31}, {8,27}, {2,42}, {10,22}, {6,22}, {11,28}, {10,30}, {6,29}, {4,38}, {6,21}, {2,25}, {5,40}, {2,34}, {1,17}, {4,22}, {8,19}, {9,29}, {10,38}, {7,20}, {9,32}, {1,44}, {5,29}, {2,38}, {2,37}, {8,14}, {7,39}, {4,42}, {9,41}, {5,25}, {7,32}, {11,15}, {10,41}, {7,43}, {11,31}, {11,44}, {3,44}, {6,30}, {10,29}, {3,20}, {10,21}, {2,13}, {6,18}, {12,43}, {1,29}, {3,39}, {3,32}, {4,35}, {9,25}, {7,16}, {6,33}, {11,23}, {5,24}, {9,37}, {8,22}, {8,35}, {10,42}, {9,20}, {4,15}, {1,28}, {3,27}, {4,43}, {1,33}, {10,13}, {5,28}, {8,26}, {12,26}, {7,31}, {5,41}, {2,17}, {9,13}, {12,27}, {9,40}, {3,19}, {1,24}, {12,23}, {11,24}, {5,44}, {11,39}, {6,26}, {12,19}, {12,30}, {3,23}, {8,23}, {12,14}, {5,36}, {1,25}, {6,41}, {12,15}, {6,14}, {1,37}, {7,28}, {3,16}, {6,42}, {7,23}, {11,16}, {2,21}, {8,34}, {5,33}, {10,17}, {3,24}, {2,29}, {11,27}, {8,38}, {2,22}, {4,34}, {1,16}, {4,14}, {10,34}, {11,32}, {9,17}, {10,18}, {6,25}, {6,38}, {11,40}, {9,33}, {9,36}, {6,34}, {8,18}, {4,18}, {11,19}, {5,13}, {3,28}, {7,27}, {1,41}, {7,24}, {3,31}, {9,24}, {6,37}, {12,31}, {10,14}, {7,35}, {11,43}, {5,21}, {2,30}, {6,13}, {2,18}, {5,37}, {7,19}, {9,21}, {9,16}, {3,36}, {4,39}, {7,40}, {12,18}, {1,36}, {5,16} }; // ET44.39 // Bipartite(12,32) Valencies [16,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4059507138609807360000 EdgePairs[44][39]:={ {3,33}, {10,24}, {11,20}, {6,32}, {6,16}, {11,36}, {12,29}, {11,35}, {4,24}, {4,26}, {4,16}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,43}, {12,32}, {7,38}, {8,42}, {3,13}, {3,43}, {3,25}, {3,15}, {7,41}, {10,26}, {2,15}, {7,22}, {2,19}, {12,41}, {2,27}, {3,35}, {5,20}, {9,43}, {3,37}, {2,26}, {8,39}, {7,34}, {1,21}, {10,44}, {2,14}, {1,30}, {5,32}, {8,15}, {9,35}, {8,31}, {8,27}, {12,37}, {2,42}, {10,22}, {11,28}, {10,30}, {6,29}, {3,17}, {4,38}, {6,21}, {5,40}, {6,40}, {1,38}, {2,34}, {1,17}, {4,22}, {8,19}, {9,29}, {10,38}, {1,18}, {12,17}, {9,27}, {12,20}, {12,36}, {2,38}, {9,19}, {5,43}, {12,44}, {8,14}, {4,42}, {9,41}, {2,39}, {11,15}, {7,13}, {7,25}, {10,28}, {11,31}, {2,35}, {11,44}, {1,22}, {12,13}, {12,16}, {5,23}, {10,40}, {1,29}, {7,30}, {3,39}, {9,25}, {7,26}, {6,33}, {11,23}, {6,24}, {6,44}, {7,17}, {5,24}, {9,37}, {12,28}, {12,25}, {8,22}, {8,35}, {10,42}, {7,14}, {3,27}, {4,28}, {1,33}, {3,29}, {5,28}, {8,26}, {12,33}, {4,36}, {9,13}, {1,42}, {3,19}, {5,31}, {11,24}, {5,44}, {11,39}, {12,40}, {3,23}, {8,23}, {10,32}, {5,36}, {3,21}, {1,25}, {7,29}, {6,41}, {6,28}, {1,37}, {5,39}, {4,40}, {11,16}, {6,36}, {8,34}, {11,27}, {8,38}, {1,26}, {2,22}, {4,34}, {10,36}, {4,14}, {10,34}, {11,32}, {9,17}, {10,18}, {6,25}, {2,31}, {11,40}, {9,33}, {5,27}, {8,18}, {4,18}, {9,39}, {11,19}, {4,20}, {12,24}, {1,41}, {3,41}, {3,31}, {1,14}, {10,20}, {5,15}, {7,33}, {6,37}, {10,14}, {5,19}, {6,20}, {11,43}, {9,15}, {2,30}, {6,13}, {7,37}, {5,35}, {2,18}, {9,31}, {1,34}, {2,43}, {9,21}, {7,42}, {9,23}, {4,44}, {7,21}, {4,32}, {12,21}, {7,18}, {10,16}, {5,16} }; // ET44.40 // Bipartite(12,32) Valencies [16,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 338151365148672 EdgePairs[44][40]:={ {2,44}, {11,17}, {3,33}, {2,24}, {5,17}, {10,25}, {6,32}, {6,16}, {4,27}, {7,15}, {11,35}, {4,26}, {11,25}, {2,23}, {1,13}, {5,38}, {12,22}, {12,32}, {7,38}, {8,42}, {8,28}, {1,32}, {3,13}, {3,25}, {3,15}, {12,38}, {1,40}, {10,26}, {2,15}, {4,19}, {7,22}, {10,33}, {3,37}, {2,26}, {8,39}, {1,21}, {11,41}, {11,14}, {12,35}, {10,44}, {2,28}, {1,30}, {8,15}, {8,44}, {8,31}, {2,42}, {6,22}, {3,18}, {3,17}, {8,16}, {3,34}, {11,38}, {6,40}, {11,33}, {1,38}, {2,34}, {2,36}, {5,22}, {9,29}, {9,26}, {12,20}, {12,36}, {5,29}, {4,41}, {5,43}, {12,44}, {7,39}, {4,42}, {9,41}, {5,25}, {2,39}, {7,32}, {11,13}, {1,31}, {10,41}, {11,22}, {7,13}, {10,28}, {1,22}, {6,30}, {6,43}, {4,33}, {12,16}, {9,34}, {9,42}, {2,20}, {12,43}, {1,29}, {7,30}, {2,16}, {3,39}, {11,21}, {4,35}, {9,25}, {7,16}, {8,36}, {2,32}, {1,23}, {6,24}, {11,29}, {5,30}, {6,44}, {11,30}, {9,37}, {12,28}, {10,42}, {5,14}, {7,14}, {4,28}, {4,43}, {3,29}, {3,26}, {8,26}, {7,31}, {5,41}, {4,36}, {10,43}, {9,13}, {12,27}, {8,32}, {1,24}, {6,27}, {8,40}, {12,19}, {12,40}, {12,30}, {3,23}, {8,23}, {1,39}, {12,14}, {3,21}, {6,19}, {7,29}, {1,15}, {6,28}, {6,14}, {1,37}, {10,35}, {7,23}, {6,36}, {8,34}, {5,33}, {9,18}, {10,17}, {11,37}, {11,27}, {10,27}, {4,34}, {1,16}, {10,36}, {10,34}, {9,17}, {10,18}, {8,24}, {6,38}, {2,40}, {2,31}, {9,33}, {5,27}, {8,18}, {3,42}, {4,18}, {9,39}, {11,19}, {4,25}, {10,19}, {4,20}, {5,13}, {8,20}, {12,24}, {3,41}, {7,24}, {3,31}, {1,14}, {10,20}, {5,19}, {6,20}, {11,43}, {5,21}, {9,15}, {7,37}, {5,35}, {2,18}, {9,31}, {5,37}, {4,17}, {6,35}, {9,21}, {7,40}, {4,44}, {9,23}, {7,21} }; // ET44.41 // Bipartite(12,32) Valencies [16,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 21134460321792 EdgePairs[44][41]:={ {2,44}, {11,17}, {3,33}, {2,24}, {10,24}, {10,25}, {9,28}, {4,27}, {7,15}, {11,35}, {5,34}, {4,24}, {3,22}, {3,40}, {4,16}, {10,37}, {4,30}, {11,25}, {8,30}, {6,17}, {2,23}, {1,13}, {8,43}, {12,22}, {12,32}, {8,42}, {4,29}, {3,25}, {3,15}, {12,38}, {2,15}, {4,19}, {9,44}, {2,19}, {2,27}, {10,33}, {12,42}, {5,20}, {9,43}, {8,39}, {7,34}, {1,21}, {11,41}, {10,44}, {2,28}, {12,34}, {1,30}, {8,15}, {9,35}, {8,31}, {8,27}, {3,17}, {4,38}, {6,31}, {11,33}, {1,38}, {1,17}, {2,36}, {4,22}, {8,19}, {1,18}, {3,14}, {9,27}, {12,20}, {12,36}, {5,29}, {9,19}, {5,43}, {12,44}, {8,14}, {7,39}, {9,41}, {2,39}, {7,32}, {11,13}, {11,15}, {10,41}, {7,13}, {9,14}, {10,28}, {11,31}, {2,35}, {1,22}, {12,16}, {4,21}, {10,29}, {10,21}, {2,20}, {6,18}, {10,40}, {1,29}, {2,16}, {3,39}, {3,32}, {11,21}, {4,35}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {5,18}, {11,23}, {11,29}, {6,44}, {12,28}, {8,22}, {8,35}, {9,20}, {4,13}, {4,43}, {1,33}, {10,13}, {6,23}, {5,28}, {8,26}, {5,42}, {12,26}, {9,22}, {7,31}, {6,15}, {1,42}, {5,44}, {11,39}, {6,26}, {12,40}, {12,30}, {3,23}, {8,23}, {10,32}, {12,14}, {5,36}, {1,25}, {7,29}, {6,41}, {6,28}, {9,30}, {1,37}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {6,36}, {3,30}, {8,34}, {10,17}, {3,24}, {11,37}, {11,27}, {8,38}, {1,26}, {10,36}, {4,14}, {9,17}, {6,25}, {2,40}, {2,31}, {9,33}, {9,36}, {6,34}, {5,27}, {5,26}, {8,18}, {9,38}, {11,19}, {3,38}, {5,13}, {12,24}, {1,41}, {3,41}, {7,24}, {3,31}, {1,14}, {10,20}, {6,39}, {5,19}, {6,20}, {11,43}, {5,21}, {7,37}, {5,35}, {1,34}, {5,37}, {2,43}, {7,40}, {7,42}, {7,21}, {4,32}, {12,18}, {7,18}, {10,16} }; // ET44.42 // Bipartite(12,32) Valencies [16,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 50331648 EdgePairs[44][42]:={ {2,44}, {10,25}, {1,20}, {5,17}, {10,24}, {11,20}, {9,28}, {2,33}, {11,36}, {4,27}, {5,34}, {4,26}, {4,16}, {1,13}, {5,38}, {8,42}, {8,28}, {4,29}, {8,33}, {1,27}, {3,25}, {3,15}, {10,23}, {7,41}, {1,40}, {2,15}, {9,44}, {2,19}, {12,41}, {10,33}, {1,19}, {12,42}, {3,37}, {2,26}, {7,34}, {12,35}, {7,36}, {8,25}, {10,44}, {2,28}, {12,34}, {8,44}, {12,37}, {10,15}, {2,42}, {6,22}, {11,28}, {10,30}, {8,16}, {4,38}, {6,21}, {5,40}, {11,38}, {6,31}, {5,22}, {4,22}, {3,14}, {7,20}, {9,32}, {12,17}, {5,29}, {8,41}, {2,38}, {2,37}, {5,43}, {7,39}, {4,42}, {7,32}, {11,13}, {11,15}, {1,31}, {10,41}, {11,22}, {9,14}, {7,43}, {10,28}, {7,25}, {11,31}, {2,35}, {11,44}, {3,44}, {6,30}, {6,43}, {5,23}, {4,21}, {10,31}, {3,20}, {9,34}, {2,13}, {10,40}, {12,43}, {1,29}, {7,30}, {8,17}, {3,32}, {7,16}, {5,18}, {11,23}, {11,29}, {5,24}, {9,37}, {12,25}, {8,13}, {4,13}, {7,14}, {4,43}, {6,23}, {1,43}, {3,26}, {8,26}, {12,26}, {9,22}, {12,33}, {6,15}, {2,17}, {4,36}, {12,27}, {8,32}, {1,42}, {1,24}, {6,27}, {11,24}, {11,39}, {8,40}, {12,19}, {12,30}, {12,14}, {3,21}, {1,25}, {6,19}, {1,15}, {6,14}, {9,30}, {10,39}, {1,35}, {5,39}, {3,16}, {4,37}, {10,35}, {7,23}, {11,16}, {6,36}, {2,21}, {3,30}, {5,33}, {8,34}, {9,18}, {10,17}, {2,29}, {1,26}, {2,22}, {4,34}, {11,32}, {9,17}, {8,24}, {6,38}, {2,31}, {11,40}, {9,33}, {5,27}, {8,18}, {3,42}, {4,18}, {9,39}, {9,38}, {10,19}, {4,20}, {5,13}, {3,28}, {7,27}, {1,41}, {3,41}, {7,24}, {3,31}, {6,39}, {6,37}, {10,14}, {5,19}, {6,20}, {5,35}, {6,35}, {9,21}, {9,16}, {3,36}, {7,40}, {9,23}, {8,29}, {4,32}, {12,18}, {1,36}, {12,21}, {7,18} }; // ET44.43 // Bipartite(12,32) Valencies [16,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 75497472 EdgePairs[44][43]:={ {11,17}, {5,17}, {10,24}, {10,25}, {11,20}, {2,33}, {11,36}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,40}, {4,16}, {4,30}, {6,17}, {2,23}, {1,13}, {8,43}, {12,22}, {7,38}, {8,42}, {8,28}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {12,38}, {7,22}, {12,39}, {12,41}, {1,19}, {2,27}, {3,35}, {2,26}, {8,39}, {7,34}, {11,14}, {8,25}, {10,44}, {8,15}, {9,35}, {8,44}, {8,31}, {8,27}, {12,37}, {2,42}, {10,22}, {8,16}, {4,38}, {6,21}, {6,40}, {11,33}, {2,34}, {1,17}, {2,36}, {4,22}, {9,29}, {10,38}, {1,18}, {3,14}, {12,20}, {12,36}, {1,44}, {5,29}, {8,41}, {2,38}, {9,19}, {2,37}, {7,39}, {4,42}, {5,25}, {2,39}, {7,32}, {11,13}, {11,15}, {10,41}, {7,13}, {9,14}, {7,43}, {10,28}, {11,31}, {3,44}, {5,23}, {9,34}, {2,20}, {10,40}, {1,29}, {7,30}, {3,32}, {11,21}, {7,16}, {6,33}, {5,18}, {6,24}, {11,29}, {6,44}, {11,30}, {12,25}, {9,20}, {1,28}, {7,14}, {4,28}, {1,33}, {4,43}, {3,29}, {1,43}, {8,37}, {8,26}, {9,22}, {7,31}, {5,41}, {4,36}, {2,17}, {10,43}, {9,13}, {9,40}, {8,32}, {8,21}, {1,42}, {3,19}, {12,23}, {5,31}, {6,26}, {12,40}, {12,30}, {8,23}, {12,14}, {6,19}, {7,29}, {6,41}, {6,28}, {12,15}, {9,30}, {10,39}, {1,35}, {5,39}, {3,16}, {6,42}, {11,26}, {4,40}, {10,35}, {7,23}, {11,16}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {3,24}, {11,37}, {10,27}, {1,26}, {2,22}, {1,16}, {4,14}, {10,34}, {11,32}, {9,17}, {10,18}, {6,25}, {9,33}, {9,36}, {9,38}, {10,19}, {4,20}, {5,13}, {3,28}, {12,24}, {7,27}, {3,41}, {3,31}, {9,24}, {5,15}, {6,37}, {12,31}, {5,19}, {6,20}, {5,21}, {5,35}, {2,18}, {1,34}, {5,37}, {2,43}, {6,35}, {11,42}, {4,44}, {4,32}, {12,21}, {7,18} }; // ET44.44 // Bipartite(12,32) Valencies [16,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12582912 EdgePairs[44][44]:={ {2,44}, {11,17}, {5,17}, {1,20}, {10,25}, {2,33}, {5,34}, {4,24}, {4,26}, {3,40}, {4,16}, {8,30}, {8,43}, {1,13}, {5,38}, {12,22}, {8,42}, {8,28}, {1,32}, {3,13}, {1,27}, {3,25}, {3,15}, {10,23}, {12,38}, {7,41}, {7,44}, {1,40}, {4,19}, {12,39}, {12,41}, {2,27}, {12,42}, {3,35}, {7,34}, {1,21}, {11,14}, {12,35}, {8,25}, {2,28}, {2,14}, {8,15}, {9,35}, {8,44}, {8,31}, {8,27}, {10,22}, {6,22}, {3,18}, {11,28}, {8,16}, {3,34}, {6,40}, {6,31}, {11,33}, {2,36}, {5,22}, {9,29}, {10,38}, {1,18}, {12,17}, {5,29}, {4,41}, {8,41}, {2,38}, {9,19}, {2,37}, {5,43}, {12,44}, {8,14}, {7,39}, {4,42}, {7,32}, {11,13}, {11,15}, {1,31}, {10,41}, {7,13}, {7,25}, {11,31}, {11,44}, {6,30}, {6,43}, {5,23}, {4,21}, {2,20}, {1,29}, {2,16}, {3,39}, {11,21}, {4,35}, {7,16}, {2,32}, {5,18}, {6,24}, {11,29}, {5,30}, {7,17}, {11,30}, {9,37}, {12,28}, {12,25}, {5,14}, {9,20}, {4,28}, {3,29}, {1,43}, {3,26}, {8,26}, {12,26}, {9,22}, {12,33}, {6,15}, {2,17}, {4,36}, {10,43}, {9,13}, {9,40}, {8,32}, {3,19}, {1,24}, {12,23}, {5,31}, {6,27}, {11,24}, {6,26}, {12,19}, {12,30}, {3,23}, {10,32}, {12,14}, {6,19}, {7,29}, {1,15}, {6,14}, {10,39}, {1,37}, {5,39}, {7,28}, {4,37}, {6,42}, {11,26}, {4,40}, {10,35}, {7,23}, {6,36}, {2,21}, {8,34}, {5,33}, {3,24}, {11,37}, {10,27}, {2,22}, {1,16}, {10,36}, {10,34}, {9,17}, {10,18}, {6,38}, {11,40}, {9,33}, {9,36}, {5,27}, {8,18}, {3,42}, {9,39}, {9,38}, {4,25}, {10,19}, {4,20}, {5,13}, {3,41}, {3,31}, {9,24}, {10,20}, {5,15}, {7,33}, {6,20}, {2,30}, {7,37}, {1,34}, {2,43}, {6,35}, {9,21}, {11,42}, {4,44}, {9,23}, {7,21}, {4,32}, {1,36}, {7,18}, {10,16} }; // ET44.45 // Bipartite(8,36) Valencies [18,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1152 EdgePairs[44][45]:={ {1,15}, {4,35}, {7,43}, {7,19}, {6,39}, {7,39}, {6,12}, {5,14}, {8,39}, {8,24}, {4,42}, {6,10}, {3,29}, {2,22}, {6,14}, {5,42}, {3,38}, {1,31}, {4,27}, {2,11}, {8,36}, {5,35}, {6,41}, {6,23}, {1,40}, {2,20}, {4,40}, {5,34}, {7,38}, {5,24}, {3,32}, {1,38}, {1,9}, {2,33}, {6,32}, {7,31}, {7,27}, {4,44}, {6,40}, {8,42}, {7,15}, {8,34}, {3,10}, {3,31}, {2,19}, {2,15}, {6,9}, {4,26}, {5,9}, {6,22}, {2,29}, {3,19}, {5,37}, {3,18}, {8,44}, {3,41}, {7,28}, {1,34}, {3,11}, {6,11}, {2,23}, {7,26}, {8,28}, {1,17}, {2,16}, {6,33}, {6,21}, {2,36}, {4,33}, {2,17}, {8,10}, {8,18}, {8,21}, {7,29}, {3,14}, {2,13}, {1,12}, {3,22}, {5,43}, {7,20}, {8,26}, {7,13}, {5,29}, {2,42}, {3,27}, {6,15}, {4,36}, {7,30}, {4,17}, {5,28}, {4,25}, {2,9}, {1,35}, {1,26}, {2,44}, {8,40}, {6,31}, {5,38}, {2,43}, {3,35}, {1,23}, {6,30}, {7,18}, {2,39}, {8,43}, {5,20}, {8,32}, {3,28}, {3,24}, {5,17}, {8,16}, {6,16}, {3,21}, {1,14}, {1,41}, {4,32}, {1,37}, {1,20}, {1,27}, {5,11}, {7,22}, {1,13}, {4,18}, {5,10}, {3,25}, {7,37}, {7,21}, {5,12}, {2,25}, {8,37}, {8,30}, {6,44}, {4,34}, {4,41}, {3,33}, {7,36}, {4,23}, {1,30}, {5,16}, {4,13}, {5,25}, {4,19}, {4,24}, {8,12} }; // ET44.46 // Bipartite(8,36) Valencies [18,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2219535528034912174080000 EdgePairs[44][46]:={ {4,35}, {7,43}, {7,19}, {5,32}, {7,39}, {3,15}, {8,39}, {8,31}, {2,38}, {4,42}, {6,10}, {6,18}, {4,14}, {2,22}, {6,14}, {4,27}, {6,17}, {7,40}, {6,41}, {7,24}, {1,40}, {1,25}, {6,13}, {2,37}, {5,24}, {3,32}, {1,9}, {5,41}, {2,33}, {6,25}, {7,31}, {7,27}, {1,44}, {1,32}, {8,42}, {7,15}, {7,23}, {5,13}, {8,34}, {3,31}, {6,34}, {2,18}, {6,9}, {4,26}, {8,14}, {5,9}, {6,22}, {7,11}, {5,21}, {2,29}, {3,19}, {1,29}, {5,37}, {8,22}, {7,28}, {8,15}, {2,14}, {3,11}, {5,33}, {2,10}, {2,41}, {4,39}, {1,36}, {1,17}, {6,33}, {3,40}, {1,16}, {6,21}, {2,17}, {8,10}, {8,18}, {2,13}, {1,12}, {4,43}, {7,20}, {8,35}, {8,26}, {3,23}, {6,37}, {5,29}, {4,31}, {2,42}, {3,27}, {2,34}, {4,30}, {6,26}, {8,11}, {5,28}, {4,15}, {2,9}, {8,19}, {6,29}, {7,35}, {4,38}, {4,11}, {3,35}, {2,21}, {6,30}, {8,27}, {6,38}, {7,44}, {8,38}, {8,43}, {5,20}, {4,22}, {3,28}, {5,36}, {3,24}, {5,17}, {3,12}, {8,23}, {7,16}, {1,41}, {3,44}, {6,42}, {3,39}, {1,37}, {1,20}, {3,16}, {1,13}, {4,18}, {7,32}, {2,26}, {3,20}, {1,33}, {5,12}, {2,25}, {1,28}, {3,36}, {8,30}, {3,43}, {4,34}, {5,44}, {7,36}, {4,23}, {5,16}, {7,12}, {2,30}, {1,21}, {5,25}, {4,19}, {4,10}, {5,40}, {1,24} }; // ET44.47 // Bipartite(8,36) Valencies [18,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 53496602689536000000 EdgePairs[44][47]:={ {1,15}, {7,43}, {7,19}, {5,32}, {6,39}, {6,12}, {5,14}, {8,24}, {8,31}, {4,42}, {6,10}, {6,18}, {4,14}, {1,11}, {3,29}, {2,22}, {6,36}, {7,40}, {8,36}, {5,35}, {1,38}, {5,41}, {1,9}, {2,33}, {7,31}, {1,44}, {4,44}, {1,32}, {6,40}, {8,42}, {7,23}, {3,10}, {2,28}, {3,34}, {3,31}, {6,34}, {2,18}, {6,9}, {2,15}, {5,26}, {4,26}, {8,14}, {8,13}, {5,9}, {6,22}, {7,11}, {5,21}, {3,19}, {1,29}, {4,12}, {8,44}, {3,41}, {7,28}, {7,10}, {5,33}, {3,11}, {5,23}, {4,37}, {2,10}, {4,20}, {7,41}, {1,17}, {3,13}, {2,16}, {6,33}, {3,40}, {6,21}, {2,36}, {8,18}, {7,29}, {7,25}, {3,22}, {4,43}, {5,15}, {8,26}, {3,23}, {7,13}, {5,29}, {4,31}, {2,42}, {4,30}, {2,34}, {6,15}, {2,40}, {4,36}, {4,25}, {2,9}, {1,35}, {1,26}, {8,19}, {7,35}, {4,38}, {2,24}, {2,27}, {5,38}, {3,35}, {1,23}, {2,21}, {5,27}, {6,30}, {1,39}, {2,39}, {8,38}, {8,43}, {2,12}, {5,20}, {8,32}, {3,28}, {5,17}, {8,20}, {6,16}, {7,16}, {1,14}, {1,41}, {4,32}, {6,42}, {1,20}, {1,27}, {5,11}, {7,22}, {3,16}, {4,18}, {3,25}, {8,25}, {7,37}, {1,33}, {3,17}, {8,37}, {3,37}, {6,24}, {8,30}, {3,43}, {6,27}, {5,44}, {7,34}, {7,17}, {5,39}, {4,13}, {1,21}, {2,30}, {4,19}, {4,24}, {8,12}, {6,28} }; // ET44.48 // Bipartite(8,36) Valencies [18,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6687075336192000000 EdgePairs[44][48]:={ {1,15}, {7,43}, {7,19}, {7,42}, {6,12}, {3,15}, {1,43}, {8,24}, {2,38}, {6,10}, {6,18}, {4,14}, {1,11}, {3,29}, {5,30}, {5,42}, {6,36}, {1,31}, {4,27}, {6,17}, {8,36}, {5,35}, {6,41}, {7,24}, {6,23}, {2,20}, {4,40}, {1,25}, {7,38}, {4,16}, {2,37}, {5,24}, {5,41}, {1,9}, {2,33}, {7,31}, {4,44}, {6,40}, {8,42}, {5,13}, {8,34}, {3,10}, {3,34}, {2,19}, {6,34}, {2,15}, {4,26}, {8,14}, {6,22}, {5,37}, {1,29}, {8,22}, {8,44}, {3,41}, {2,14}, {5,23}, {3,11}, {4,20}, {6,11}, {2,31}, {7,26}, {8,28}, {4,39}, {1,17}, {2,32}, {3,40}, {4,33}, {8,10}, {8,18}, {4,28}, {2,13}, {3,9}, {7,25}, {3,22}, {5,43}, {5,19}, {7,20}, {8,26}, {3,23}, {7,13}, {5,29}, {7,14}, {3,27}, {1,19}, {4,21}, {7,30}, {4,15}, {2,9}, {1,35}, {2,44}, {8,40}, {6,29}, {4,38}, {2,27}, {2,43}, {3,35}, {1,23}, {2,21}, {6,30}, {1,39}, {7,18}, {2,39}, {7,44}, {8,38}, {4,22}, {8,32}, {3,28}, {5,36}, {5,31}, {5,17}, {8,16}, {8,20}, {6,16}, {3,21}, {1,41}, {4,32}, {6,42}, {3,39}, {1,37}, {1,27}, {5,11}, {3,16}, {1,13}, {7,32}, {2,26}, {7,37}, {1,33}, {5,12}, {2,25}, {3,17}, {4,9}, {6,24}, {6,35}, {5,18}, {8,30}, {4,34}, {3,33}, {7,36}, {7,12}, {1,21}, {5,25}, {4,10}, {8,12}, {6,28} }; // ET44.49 // Bipartite(8,36) Valencies [18,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 417942208512 EdgePairs[44][49]:={ {1,15}, {4,35}, {7,43}, {7,19}, {6,39}, {5,14}, {3,15}, {1,43}, {4,42}, {6,14}, {5,42}, {5,30}, {3,38}, {1,31}, {4,27}, {7,40}, {2,11}, {5,35}, {7,24}, {2,20}, {1,25}, {6,13}, {5,41}, {1,9}, {2,33}, {6,32}, {6,25}, {7,31}, {4,44}, {6,40}, {8,42}, {8,34}, {3,10}, {2,28}, {3,34}, {3,31}, {6,9}, {5,26}, {8,14}, {8,13}, {8,41}, {5,9}, {5,21}, {2,29}, {3,19}, {4,12}, {8,22}, {8,44}, {7,28}, {7,10}, {5,33}, {3,11}, {5,23}, {4,20}, {2,41}, {2,23}, {7,41}, {4,39}, {1,36}, {2,16}, {2,32}, {6,33}, {3,40}, {6,21}, {2,36}, {2,17}, {8,10}, {8,18}, {7,29}, {3,14}, {1,12}, {7,25}, {3,22}, {5,43}, {5,19}, {8,26}, {3,23}, {6,37}, {7,13}, {8,17}, {5,29}, {3,27}, {4,30}, {6,15}, {6,26}, {1,19}, {2,40}, {4,36}, {2,35}, {4,15}, {2,9}, {2,44}, {2,24}, {4,11}, {5,38}, {3,35}, {2,21}, {1,39}, {6,38}, {8,38}, {2,12}, {4,22}, {8,32}, {3,28}, {3,26}, {5,31}, {5,17}, {8,20}, {1,42}, {6,16}, {6,20}, {7,16}, {4,32}, {3,39}, {1,37}, {1,27}, {5,11}, {7,22}, {3,16}, {1,13}, {4,18}, {8,25}, {7,37}, {1,33}, {8,37}, {5,18}, {8,30}, {3,43}, {6,44}, {4,34}, {6,27}, {7,34}, {7,36}, {7,17}, {4,23}, {1,30}, {7,12}, {1,21}, {1,18}, {4,10}, {4,24}, {1,24}, {8,29}, {6,28} }; // ET44.50 // Bipartite(11,33) Valencies [18,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 239446056960 EdgePairs[44][50]:={ {2,44}, {11,17}, {2,24}, {5,17}, {10,24}, {11,20}, {9,28}, {2,33}, {6,16}, {11,36}, {5,34}, {4,24}, {8,12}, {4,26}, {3,40}, {10,37}, {4,30}, {11,25}, {8,30}, {2,23}, {5,38}, {7,38}, {8,28}, {1,32}, {3,13}, {1,27}, {3,43}, {3,25}, {7,44}, {1,40}, {10,26}, {4,19}, {9,44}, {7,22}, {2,19}, {1,19}, {3,35}, {9,43}, {8,39}, {1,21}, {11,41}, {11,14}, {7,36}, {8,25}, {2,41}, {2,28}, {1,30}, {5,32}, {8,15}, {2,42}, {10,15}, {6,22}, {3,18}, {11,28}, {10,30}, {3,34}, {11,38}, {6,31}, {1,38}, {2,34}, {4,22}, {8,19}, {9,29}, {10,38}, {1,18}, {3,14}, {9,32}, {9,26}, {1,44}, {4,41}, {8,41}, {5,43}, {8,14}, {7,39}, {2,39}, {3,12}, {10,41}, {7,13}, {7,25}, {11,31}, {2,35}, {1,22}, {6,12}, {4,33}, {5,23}, {4,21}, {10,29}, {3,20}, {10,31}, {2,13}, {9,42}, {2,20}, {10,40}, {1,29}, {8,17}, {3,32}, {11,21}, {4,35}, {7,16}, {8,36}, {1,12}, {6,33}, {1,23}, {6,44}, {7,17}, {11,30}, {5,24}, {9,37}, {10,42}, {9,20}, {4,15}, {4,13}, {7,14}, {4,43}, {1,33}, {10,13}, {3,29}, {6,23}, {1,43}, {8,37}, {5,28}, {8,26}, {9,22}, {6,15}, {2,17}, {4,36}, {5,12}, {9,40}, {6,27}, {11,39}, {6,26}, {8,40}, {3,23}, {8,23}, {3,21}, {7,29}, {6,14}, {5,39}, {7,28}, {4,37}, {6,42}, {10,35}, {11,16}, {6,36}, {8,34}, {9,18}, {3,24}, {11,27}, {10,27}, {2,22}, {1,16}, {4,14}, {11,32}, {9,17}, {10,18}, {6,25}, {6,38}, {2,31}, {9,33}, {6,34}, {5,27}, {5,26}, {8,18}, {3,42}, {9,39}, {11,19}, {4,25}, {10,19}, {5,13}, {7,27}, {1,41}, {7,24}, {3,31}, {2,12}, {10,20}, {5,15}, {7,33}, {6,37}, {6,20}, {7,35}, {11,43}, {5,21}, {2,30}, {9,15}, {5,35}, {1,34}, {9,31}, {5,37}, {3,36}, {9,21}, {11,42}, {7,40}, {4,44}, {8,29}, {4,32}, {7,18}, {10,16}, {5,16} }; // ET44.51 // Bipartite(20,24) Valencies [18,15] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1337415067238400000000 EdgePairs[44][51]:={ {13,21}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {4,28}, {3,26}, {13,37}, {1,40}, {14,38}, {17,42}, {15,44}, {11,43}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {1,21}, {3,39}, {16,37}, {20,37}, {16,28}, {5,32}, {7,30}, {8,31}, {4,40}, {4,37}, {14,29}, {16,21}, {13,40}, {2,33}, {11,35}, {10,42}, {6,29}, {11,27}, {19,40}, {2,34}, {12,28}, {19,31}, {2,25}, {4,24}, {4,43}, {15,32}, {9,33}, {20,43}, {8,37}, {20,24}, {5,41}, {13,30}, {7,27}, {19,22}, {6,39}, {11,39}, {10,26}, {12,31}, {12,40}, {20,29}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {16,25}, {13,42}, {20,35}, {1,36}, {1,29}, {19,42}, {12,37}, {10,35}, {16,43}, {18,39}, {4,23}, {13,26}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {13,41}, {20,36}, {16,40}, {18,29}, {9,36}, {6,34}, {9,29}, {18,26}, {18,33}, {3,38}, {3,43}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {19,38}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {11,42}, {14,34}, {3,36}, {19,23}, {4,21}, {17,29}, {20,25}, {4,32}, {1,30}, {19,27}, {16,29}, {11,36}, {3,30}, {11,23}, {3,24}, {14,33}, {14,23}, {10,38}, {15,34}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {4,41}, {9,38}, {8,41}, {14,21}, {9,26}, {18,38}, {13,36}, {1,41}, {2,23}, {15,23}, {12,41}, {9,22}, {11,44}, {3,44}, {20,31}, {19,24}, {11,34}, {17,28}, {7,35}, {2,43}, {2,27}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {10,29}, {18,25}, {13,22}, {1,25}, {9,30}, {3,32}, {14,27}, {16,41}, {7,28}, {20,44}, {17,44}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {14,43}, {3,42}, {15,40}, {3,22}, {14,37}, {1,44}, {13,38}, {18,31}, {19,44}, {9,41}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {9,44}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {17,22}, {17,25}, {19,34}, {16,44}, {4,44}, {7,40}, {2,41}, {17,41}, {12,43}, {20,32}, {2,26}, {18,41}, {18,21}, {10,21}, {9,21}, {18,30}, {8,29}, {8,36}, {13,44}, {8,27}, {16,36}, {13,32}, {14,26}, {11,30}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {19,43}, {5,24}, {2,22}, {8,43}, {2,31}, {1,33}, {18,27}, {20,28}, {12,36}, {16,27}, {12,44}, {5,26}, {2,37}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {19,35}, {13,34}, {7,22}, {6,26}, {1,34}, {15,42}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {20,23}, {8,44}, {17,21}, {19,36}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {18,43}, {14,25}, {7,26}, {11,28}, {16,35}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {8,35}, {6,21}, {15,22}, {14,41}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {7,44}, {8,28}, {7,43}, {9,40}, {20,40}, {5,44}, {5,25}, {10,23}, {15,26}, {8,39}, {14,22}, {9,42}, {5,36}, {9,34}, {15,43}, {4,39}, {12,35}, {7,36}, {6,35}, {17,32}, {20,21}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {6,33}, {12,21}, {18,34}, {11,26}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37} }; // ET44.52 // Bipartite(4,40) Valencies [20,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1387209705021820108800000000 EdgePairs[44][52]:={ {3,32}, {2,14}, {3,40}, {4,23}, {4,39}, {2,37}, {1,44}, {1,24}, {3,12}, {2,26}, {1,29}, {2,30}, {2,29}, {1,32}, {4,34}, {2,10}, {1,37}, {1,33}, {1,40}, {4,11}, {4,10}, {1,36}, {3,27}, {2,6}, {4,43}, {4,7}, {1,20}, {1,12}, {4,31}, {3,8}, {3,23}, {3,24}, {2,33}, {3,20}, {2,21}, {4,6}, {4,30}, {3,44}, {4,18}, {3,11}, {3,16}, {3,7}, {1,16}, {3,28}, {3,15}, {4,38}, {2,38}, {1,21}, {2,18}, {4,27}, {3,19}, {2,5}, {3,31}, {1,5}, {4,15}, {1,17}, {4,22}, {3,39}, {2,42}, {1,28}, {2,17}, {1,8}, {1,13}, {2,34}, {2,9}, {1,9}, {2,41}, {4,26}, {1,41}, {2,13}, {2,25}, {4,14}, {4,35}, {4,42}, {4,19}, {1,25}, {2,22}, {3,36}, {3,43}, {3,35} }; // ET44.53 // Bipartite(22,22) Valencies [20,20] // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 334846387814400 EdgePairs[44][53]:={ {15,33}, {6,38}, {19,28}, {11,40}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {19,26}, {11,25}, {4,28}, {5,43}, {8,26}, {22,40}, {13,37}, {1,40}, {14,38}, {13,39}, {17,42}, {15,44}, {11,43}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {21,30}, {14,31}, {21,41}, {3,23}, {8,23}, {10,39}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {21,28}, {5,32}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {13,40}, {14,44}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {22,37}, {4,24}, {4,43}, {21,40}, {16,42}, {18,32}, {15,32}, {4,30}, {20,43}, {8,37}, {20,24}, {5,41}, {21,38}, {12,38}, {7,41}, {12,26}, {13,30}, {7,27}, {12,42}, {11,39}, {10,26}, {22,42}, {7,33}, {12,31}, {12,40}, {20,29}, {17,26}, {13,24}, {15,30}, {12,23}, {20,39}, {22,25}, {5,37}, {18,35}, {16,25}, {13,42}, {20,35}, {9,35}, {1,36}, {1,29}, {19,42}, {12,37}, {16,34}, {10,35}, {16,43}, {6,44}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {14,32}, {13,41}, {20,36}, {20,42}, {18,29}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {18,26}, {18,33}, {18,36}, {22,43}, {3,38}, {5,27}, {3,43}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {1,42}, {7,32}, {19,38}, {1,31}, {3,31}, {12,27}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {19,23}, {17,29}, {20,25}, {4,32}, {2,44}, {1,30}, {19,27}, {14,28}, {6,36}, {11,36}, {3,30}, {2,24}, {22,26}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {21,25}, {14,39}, {21,31}, {8,24}, {4,41}, {9,38}, {9,26}, {18,38}, {21,37}, {3,29}, {17,31}, {1,41}, {2,23}, {22,29}, {15,23}, {12,41}, {11,44}, {3,44}, {20,31}, {3,25}, {19,24}, {21,42}, {7,35}, {2,43}, {22,30}, {2,27}, {12,30}, {6,30}, {4,33}, {22,44}, {7,34}, {11,24}, {10,31}, {9,31}, {10,44}, {10,29}, {18,25}, {1,25}, {22,31}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {18,44}, {16,41}, {7,28}, {17,44}, {13,29}, {8,34}, {9,25}, {17,30}, {10,30}, {7,23}, {16,30}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {14,43}, {15,40}, {1,44}, {13,38}, {19,44}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {22,41}, {4,29}, {1,32}, {21,39}, {19,29}, {6,43}, {6,37}, {8,32}, {22,39}, {7,24}, {10,28}, {9,24}, {5,31}, {17,25}, {19,34}, {16,44}, {4,44}, {7,40}, {2,41}, {17,41}, {5,23}, {12,43}, {20,32}, {2,26}, {18,41}, {10,40}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {22,38}, {8,36}, {13,44}, {8,27}, {3,33}, {16,36}, {13,32}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {19,43}, {18,28}, {5,24}, {15,29}, {18,24}, {8,43}, {2,31}, {16,38}, {1,33}, {18,27}, {20,28}, {21,33}, {12,36}, {16,27}, {12,44}, {5,26}, {19,25}, {2,37}, {4,42}, {10,41}, {4,25}, {3,28}, {14,30}, {21,34}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {21,35}, {22,33}, {11,31}, {21,44}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {6,26}, {1,34}, {15,42}, {22,27}, {13,35}, {21,27}, {6,41}, {21,29}, {17,24}, {17,40}, {20,23}, {12,34}, {8,44}, {19,36}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {18,43}, {14,25}, {20,34}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {22,24}, {10,24}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {8,35}, {17,27}, {2,40}, {14,41}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {22,35}, {21,36}, {15,31}, {7,44}, {8,28}, {7,43}, {18,40}, {9,40}, {20,40}, {1,27}, {5,44}, {5,25}, {17,23}, {10,23}, {15,26}, {22,36}, {9,43}, {8,39}, {22,32}, {9,42}, {5,36}, {9,34}, {15,43}, {4,39}, {7,36}, {6,35}, {17,32}, {21,24}, {17,43}, {21,26}, {22,28}, {1,37}, {8,25}, {2,42}, {16,32}, {6,33}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40}, {21,23} }; // ET44.54 // Bipartite(16,28) Valencies [21,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5137813722303037440000 EdgePairs[44][54]:={ {13,21}, {6,38}, {11,40}, {10,37}, {15,38}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {3,26}, {13,37}, {1,40}, {14,38}, {15,44}, {11,43}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,39}, {16,37}, {16,28}, {5,32}, {7,30}, {8,31}, {4,40}, {4,37}, {14,29}, {16,21}, {13,40}, {2,33}, {11,35}, {10,42}, {6,29}, {11,27}, {1,20}, {3,18}, {2,34}, {10,17}, {9,18}, {12,28}, {2,25}, {4,24}, {4,43}, {15,32}, {9,33}, {1,17}, {8,37}, {12,20}, {5,41}, {13,30}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {12,31}, {12,40}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {16,25}, {13,42}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {16,43}, {4,23}, {11,18}, {13,26}, {2,29}, {5,34}, {1,38}, {1,26}, {13,41}, {16,40}, {9,36}, {6,34}, {9,29}, {9,20}, {8,19}, {3,38}, {1,18}, {3,43}, {15,28}, {6,17}, {5,28}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {3,31}, {12,27}, {11,22}, {6,27}, {2,30}, {11,42}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {8,17}, {16,29}, {11,36}, {3,30}, {16,17}, {11,23}, {3,24}, {14,33}, {10,38}, {14,23}, {15,34}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {12,41}, {9,22}, {11,44}, {3,44}, {11,34}, {7,35}, {2,43}, {2,27}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {10,29}, {13,22}, {1,25}, {6,19}, {4,17}, {9,30}, {3,32}, {14,27}, {16,41}, {7,28}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {1,44}, {13,38}, {9,41}, {6,23}, {16,31}, {7,39}, {4,36}, {15,39}, {4,29}, {9,44}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {2,19}, {16,44}, {4,44}, {7,40}, {2,41}, {12,43}, {5,20}, {2,26}, {10,21}, {9,21}, {8,29}, {8,36}, {13,44}, {8,27}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {16,20}, {8,43}, {2,31}, {14,19}, {1,33}, {12,36}, {16,27}, {12,44}, {5,26}, {2,37}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {13,34}, {7,22}, {6,26}, {1,34}, {15,42}, {14,18}, {5,21}, {7,42}, {6,41}, {8,44}, {6,42}, {16,23}, {4,35}, {13,33}, {14,25}, {7,26}, {7,18}, {11,28}, {5,18}, {16,35}, {11,20}, {14,42}, {10,27}, {10,34}, {15,18}, {5,17}, {16,33}, {3,40}, {8,35}, {6,21}, {15,22}, {14,41}, {15,20}, {16,39}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {5,44}, {5,25}, {10,23}, {15,26}, {4,19}, {8,39}, {14,22}, {9,42}, {14,17}, {5,36}, {16,19}, {9,34}, {15,43}, {4,39}, {12,35}, {7,36}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {16,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET44.55 // Bipartite(16,28) Valencies [21,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10321920 EdgePairs[44][55]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {4,28}, {5,43}, {12,22}, {3,26}, {8,26}, {1,40}, {14,38}, {16,22}, {13,39}, {15,44}, {11,43}, {2,35}, {4,31}, {8,40}, {3,35}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {2,18}, {3,21}, {3,39}, {16,28}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {13,40}, {14,44}, {11,35}, {11,29}, {11,17}, {1,20}, {3,18}, {10,17}, {12,28}, {4,43}, {16,42}, {15,32}, {4,30}, {9,33}, {1,17}, {5,41}, {7,41}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {15,30}, {12,23}, {13,20}, {13,42}, {1,36}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {16,43}, {6,44}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {13,41}, {16,40}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {5,27}, {3,43}, {6,17}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {1,31}, {12,27}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {2,44}, {1,30}, {16,18}, {13,18}, {14,28}, {11,21}, {6,36}, {11,36}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {10,38}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {12,41}, {9,22}, {9,19}, {3,44}, {11,44}, {3,25}, {11,34}, {2,27}, {12,30}, {6,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,44}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {4,17}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {12,18}, {13,29}, {8,34}, {9,25}, {10,30}, {5,40}, {6,22}, {4,34}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {14,43}, {14,37}, {13,38}, {14,40}, {9,41}, {16,31}, {7,39}, {15,39}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {6,20}, {16,44}, {4,44}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {10,21}, {7,29}, {2,28}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {16,36}, {9,28}, {3,34}, {2,21}, {4,27}, {15,29}, {16,20}, {8,43}, {2,31}, {14,19}, {1,33}, {16,27}, {12,44}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {11,19}, {8,33}, {14,24}, {13,34}, {7,25}, {7,22}, {15,42}, {13,35}, {5,21}, {7,42}, {12,34}, {8,44}, {6,28}, {16,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {1,23}, {16,35}, {10,24}, {10,27}, {15,18}, {5,17}, {16,33}, {13,23}, {8,35}, {2,40}, {6,21}, {15,22}, {15,20}, {16,39}, {1,28}, {16,24}, {7,20}, {7,38}, {5,42}, {2,38}, {12,32}, {15,31}, {7,44}, {8,28}, {9,40}, {8,20}, {5,25}, {10,23}, {15,26}, {9,43}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {16,19}, {10,32}, {12,35}, {6,35}, {12,19}, {1,37}, {16,32}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET44.56 // Bipartite(22,22) Valencies [21,21] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 2248001455555215360000 EdgePairs[44][56]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {20,26}, {3,29}, {16,28}, {20,33}, {4,26}, {20,25}, {19,41}, {22,37}, {14,29}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {19,37}, {8,26}, {10,29}, {15,33}, {5,43}, {12,32}, {22,25}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {20,42}, {2,38}, {8,24}, {12,27}, {6,34}, {4,38}, {11,39}, {21,31}, {16,33}, {19,38}, {7,26}, {18,28}, {8,44}, {4,34}, {13,29}, {22,28}, {18,37}, {20,29}, {10,42}, {14,40}, {9,41}, {17,43}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {19,40}, {16,26}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {1,31}, {2,41}, {6,35}, {17,32}, {21,30}, {16,23}, {21,44}, {20,44}, {21,42}, {4,41}, {8,39}, {22,32}, {7,34}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {22,27}, {15,24}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {20,39}, {7,23}, {5,33}, {4,39}, {6,24}, {16,43}, {6,39}, {2,44}, {19,35}, {1,42}, {16,34}, {19,31}, {18,26}, {14,23}, {22,26}, {2,28}, {20,43}, {1,27}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {1,37}, {21,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {21,25}, {5,29}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {4,33}, {15,40}, {21,34}, {18,34}, {10,31}, {22,38}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {7,36}, {9,39}, {22,24}, {13,26}, {22,33}, {14,37}, {11,24}, {7,43}, {20,31}, {8,33}, {10,28}, {9,44}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {21,29}, {3,28}, {9,35}, {14,28}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {4,40}, {16,36}, {1,39}, {18,43}, {7,40}, {17,37}, {18,25}, {21,27}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {21,23}, {21,43}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {22,40}, {8,27}, {5,30}, {19,43}, {16,27}, {9,30}, {5,40}, {16,31}, {22,36}, {22,30}, {18,30}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {15,44}, {19,36}, {9,34}, {15,25}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,38}, {2,43}, {14,34}, {13,44}, {11,23}, {16,40}, {8,42}, {15,38}, {7,38}, {8,32}, {22,39}, {17,24}, {12,23}, {13,31}, {5,31}, {22,23}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {20,34}, {7,44}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {20,30}, {2,29}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {14,42}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {16,44}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {6,33}, {2,32}, {19,26}, {4,23}, {22,34}, {9,36}, {10,40}, {6,27}, {21,41}, {12,40}, {17,40}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {5,44}, {5,35}, {4,43}, {9,32}, {18,32}, {21,32}, {21,26}, {22,31}, {22,35}, {5,39}, {12,43}, {19,34}, {3,40}, {22,42}, {12,36}, {22,44}, {21,39}, {3,33}, {1,24}, {15,26}, {18,41}, {21,28}, {16,38}, {22,43}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET44.57 // Bipartite(22,22) Valencies [22,22] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 2526755272089183449772480847989964800000000 EdgePairs[44][57]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {20,26}, {3,29}, {16,28}, {20,33}, {4,26}, {20,25}, {19,41}, {22,37}, {14,29}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {19,37}, {17,29}, {8,26}, {10,29}, {15,33}, {6,28}, {5,43}, {12,32}, {22,25}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {20,42}, {2,38}, {8,24}, {12,27}, {6,34}, {4,38}, {11,39}, {21,31}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {22,28}, {18,37}, {20,29}, {10,42}, {14,40}, {9,41}, {17,43}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {19,40}, {16,26}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {21,30}, {16,23}, {21,44}, {20,44}, {21,42}, {4,41}, {8,39}, {22,32}, {7,34}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {20,39}, {7,23}, {5,33}, {4,39}, {6,24}, {16,43}, {6,39}, {2,44}, {19,35}, {1,42}, {16,34}, {19,31}, {22,41}, {18,26}, {14,23}, {22,26}, {2,28}, {20,43}, {1,27}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {21,25}, {5,29}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {4,33}, {15,40}, {21,34}, {18,34}, {1,44}, {10,31}, {22,38}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {7,36}, {9,39}, {22,24}, {13,26}, {14,37}, {22,33}, {11,24}, {7,43}, {20,31}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {21,29}, {3,28}, {9,35}, {12,24}, {14,28}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {4,40}, {16,36}, {1,39}, {18,43}, {7,40}, {17,37}, {18,25}, {21,27}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {21,23}, {21,43}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {22,40}, {13,37}, {8,27}, {5,30}, {19,43}, {16,27}, {9,30}, {5,40}, {16,31}, {22,36}, {22,30}, {18,30}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {15,44}, {19,36}, {9,34}, {15,25}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {20,35}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {12,23}, {13,31}, {5,31}, {22,23}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {20,34}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {20,30}, {2,29}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {14,42}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {16,44}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {6,33}, {2,32}, {19,26}, {4,23}, {22,34}, {9,36}, {10,40}, {6,27}, {21,41}, {12,40}, {17,40}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {5,44}, {5,35}, {4,43}, {16,32}, {9,32}, {18,32}, {21,32}, {21,26}, {22,31}, {22,35}, {5,39}, {12,43}, {19,34}, {3,40}, {22,42}, {12,36}, {22,44}, {21,39}, {3,33}, {1,24}, {19,25}, {15,26}, {18,41}, {21,28}, {16,38}, {22,43}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET44.58 // Bipartite(21,23) Valencies [23,21] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1320803892228436803290160443267481600000000 EdgePairs[44][58]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {20,26}, {3,29}, {16,28}, {20,33}, {4,26}, {20,25}, {19,41}, {14,29}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {19,37}, {17,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {20,22}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {20,42}, {2,38}, {8,24}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {21,31}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {10,22}, {18,37}, {20,29}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {19,40}, {16,26}, {3,22}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {21,44}, {20,44}, {21,42}, {4,41}, {9,22}, {8,39}, {7,34}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {20,39}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {19,35}, {1,42}, {16,34}, {19,31}, {18,26}, {14,23}, {2,28}, {20,43}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {1,29}, {21,22}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {5,29}, {21,25}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {20,31}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {21,29}, {3,28}, {9,35}, {12,24}, {14,28}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {4,40}, {16,36}, {1,39}, {18,43}, {7,40}, {17,37}, {18,25}, {21,27}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {21,23}, {21,43}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,22}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {19,43}, {16,27}, {9,30}, {5,40}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {19,36}, {9,34}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {20,35}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {20,34}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {20,30}, {2,29}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {14,42}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {16,44}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {6,33}, {2,32}, {19,26}, {4,23}, {9,36}, {10,40}, {6,27}, {12,40}, {21,41}, {17,40}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {5,44}, {5,35}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {21,32}, {21,26}, {5,39}, {12,43}, {19,34}, {3,40}, {12,36}, {21,39}, {3,33}, {1,24}, {19,25}, {15,26}, {18,41}, {21,28}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET44.59 // Bipartite(12,32) Valencies [24,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 82205019556848599040000 EdgePairs[44][59]:={ {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {3,26}, {1,40}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {10,33}, {8,21}, {3,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,39}, {11,14}, {5,32}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {11,35}, {10,42}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,43}, {8,13}, {9,33}, {1,17}, {4,16}, {4,13}, {8,37}, {12,20}, {5,41}, {1,13}, {7,27}, {6,39}, {11,39}, {10,26}, {2,17}, {12,31}, {12,40}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {2,29}, {5,34}, {1,38}, {1,26}, {7,15}, {9,36}, {6,34}, {9,29}, {9,20}, {8,19}, {3,38}, {1,18}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {1,42}, {7,32}, {12,24}, {3,31}, {12,27}, {11,22}, {9,13}, {6,27}, {2,30}, {11,42}, {3,36}, {4,21}, {7,19}, {4,32}, {1,30}, {2,13}, {12,15}, {8,15}, {8,17}, {11,36}, {3,30}, {3,16}, {11,23}, {11,16}, {3,24}, {10,38}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {12,17}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {12,41}, {11,44}, {3,44}, {11,34}, {7,35}, {2,43}, {2,27}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {10,29}, {6,13}, {1,25}, {6,19}, {4,17}, {9,16}, {9,30}, {3,32}, {7,28}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {1,44}, {4,15}, {9,41}, {6,23}, {7,39}, {4,36}, {4,29}, {9,44}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {2,19}, {4,44}, {7,40}, {2,41}, {12,43}, {5,20}, {2,26}, {10,21}, {9,21}, {8,29}, {8,36}, {8,27}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {12,44}, {2,37}, {5,29}, {10,41}, {4,25}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {3,15}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {8,44}, {6,42}, {4,35}, {7,26}, {7,18}, {11,28}, {7,16}, {5,16}, {5,18}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {8,35}, {6,21}, {1,28}, {3,27}, {7,20}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {5,44}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37} }; // ET44.60 // Bipartite(12,32) Valencies [24,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 37748736 EdgePairs[44][60]:={ {11,40}, {10,37}, {9,32}, {5,38}, {5,22}, {11,25}, {4,28}, {5,43}, {3,26}, {12,22}, {8,26}, {1,40}, {2,35}, {4,31}, {8,40}, {11,15}, {10,33}, {8,21}, {5,15}, {1,19}, {8,23}, {3,20}, {11,14}, {1,35}, {5,32}, {4,37}, {6,14}, {2,33}, {6,32}, {11,29}, {11,17}, {10,42}, {6,29}, {3,18}, {8,16}, {10,17}, {9,18}, {12,28}, {2,25}, {4,43}, {4,30}, {4,16}, {8,37}, {12,38}, {1,13}, {12,26}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {9,35}, {6,18}, {1,29}, {12,37}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {9,29}, {9,39}, {8,42}, {9,20}, {8,19}, {3,38}, {1,18}, {5,27}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {12,15}, {11,21}, {6,36}, {11,36}, {10,16}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {10,38}, {6,16}, {11,33}, {8,24}, {4,41}, {9,38}, {8,41}, {5,14}, {3,29}, {12,17}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {12,41}, {9,19}, {3,44}, {3,25}, {11,34}, {11,13}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {10,22}, {10,30}, {7,23}, {4,34}, {10,25}, {12,25}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {1,32}, {6,37}, {8,32}, {7,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {12,43}, {10,40}, {12,14}, {10,21}, {9,21}, {7,29}, {2,28}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {11,30}, {3,34}, {4,27}, {8,43}, {2,31}, {5,26}, {12,44}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {7,31}, {12,33}, {12,39}, {11,31}, {3,15}, {11,41}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {9,15}, {8,44}, {6,28}, {6,42}, {1,15}, {7,18}, {11,37}, {5,18}, {5,16}, {1,23}, {10,24}, {11,20}, {10,27}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {10,43}, {7,44}, {8,28}, {7,43}, {4,20}, {8,20}, {5,44}, {5,13}, {9,43}, {8,39}, {7,13}, {9,14}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {8,25}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET44.61 // Bipartite(20,24) Valencies [24,20] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1509490162546784918045897649448550400000000 EdgePairs[44][61]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {20,26}, {3,29}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {14,29}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {9,21}, {13,43}, {19,37}, {17,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {20,22}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {20,42}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {10,22}, {18,37}, {20,29}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {20,44}, {4,41}, {9,22}, {8,39}, {7,34}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {19,21}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {19,35}, {1,42}, {16,34}, {19,31}, {8,21}, {18,26}, {14,23}, {18,21}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {5,29}, {9,28}, {20,40}, {19,24}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {8,33}, {20,31}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {14,28}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {4,40}, {16,36}, {1,39}, {18,43}, {7,40}, {17,37}, {18,25}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,22}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {19,43}, {16,27}, {9,30}, {5,40}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {19,36}, {9,34}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {8,42}, {20,21}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {20,34}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {20,30}, {14,21}, {14,44}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {14,42}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {16,44}, {7,21}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {6,33}, {2,32}, {19,26}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {5,44}, {5,35}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {5,39}, {12,43}, {1,21}, {19,34}, {6,21}, {3,40}, {12,36}, {10,21}, {3,33}, {1,24}, {19,25}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET44.62 // Bipartite(19,25) Valencies [25,19] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1886862703183481147557372061810688000000000 EdgePairs[44][62]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {3,29}, {16,28}, {4,26}, {19,41}, {14,29}, {2,20}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {8,20}, {13,43}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {10,22}, {18,37}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {17,42}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {1,26}, {18,31}, {9,27}, {1,25}, {19,21}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {19,35}, {1,42}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {18,21}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {18,20}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {3,20}, {5,29}, {9,28}, {19,24}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,20}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {14,36}, {7,42}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {14,28}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {4,40}, {16,36}, {1,39}, {18,43}, {7,40}, {17,37}, {18,25}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {16,27}, {19,43}, {9,30}, {5,40}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {19,36}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {10,30}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {14,42}, {6,20}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {4,20}, {16,44}, {7,21}, {17,41}, {11,30}, {8,43}, {19,20}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {5,44}, {5,35}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {5,39}, {12,43}, {1,21}, {19,34}, {6,21}, {7,20}, {3,40}, {12,36}, {10,21}, {3,33}, {1,24}, {19,25}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET44.63 // Bipartite(18,26) Valencies [26,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2582022646461605780867982821425152000000000 EdgePairs[44][63]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {3,29}, {16,28}, {4,26}, {14,29}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {4,28}, {8,36}, {9,21}, {8,20}, {13,43}, {17,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {18,28}, {4,34}, {17,19}, {13,29}, {10,22}, {18,37}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {11,29}, {14,27}, {17,42}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {18,35}, {1,26}, {9,27}, {18,31}, {1,25}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {18,26}, {18,21}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {18,20}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {7,37}, {1,28}, {3,43}, {3,36}, {14,36}, {7,42}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {18,19}, {14,28}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {18,43}, {7,40}, {17,37}, {18,25}, {14,19}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,22}, {14,20}, {11,33}, {1,34}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {16,27}, {9,30}, {5,40}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {3,34}, {18,39}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {17,34}, {12,26}, {10,30}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {14,42}, {6,20}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {16,44}, {7,21}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {5,44}, {5,35}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {5,39}, {12,43}, {1,21}, {6,21}, {7,20}, {3,40}, {16,19}, {12,36}, {10,21}, {3,33}, {1,24}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {17,30}, {2,19}, {5,24}, {7,33}, {12,31}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET44.64 // Bipartite(8,36) Valencies [27,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6658606584104736522240000 EdgePairs[44][64]:={ {5,17}, {1,20}, {2,33}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {3,22}, {3,40}, {4,16}, {1,10}, {6,17}, {2,23}, {1,13}, {8,43}, {5,38}, {8,9}, {7,38}, {8,28}, {4,29}, {1,32}, {8,33}, {3,43}, {3,15}, {7,44}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {2,27}, {3,35}, {5,20}, {2,26}, {7,34}, {8,39}, {1,21}, {2,9}, {7,36}, {8,25}, {2,41}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {4,23}, {8,44}, {8,27}, {8,31}, {2,42}, {6,22}, {3,18}, {6,29}, {8,16}, {6,21}, {3,34}, {5,40}, {2,25}, {7,12}, {6,31}, {1,38}, {2,34}, {1,17}, {5,22}, {8,19}, {1,18}, {3,14}, {7,11}, {7,20}, {1,44}, {4,41}, {5,29}, {2,10}, {8,41}, {2,38}, {2,37}, {7,39}, {5,25}, {2,39}, {7,32}, {3,12}, {7,43}, {2,35}, {1,22}, {3,44}, {6,30}, {6,43}, {4,33}, {4,21}, {3,20}, {2,13}, {6,18}, {1,29}, {7,30}, {8,17}, {3,39}, {3,32}, {4,35}, {7,16}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {5,30}, {8,11}, {5,24}, {8,13}, {1,9}, {8,35}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {4,43}, {3,10}, {6,23}, {3,26}, {8,37}, {5,28}, {5,42}, {7,31}, {6,15}, {5,41}, {4,36}, {2,17}, {5,12}, {8,32}, {1,42}, {8,21}, {3,19}, {4,9}, {1,24}, {6,27}, {5,44}, {6,26}, {8,40}, {3,23}, {8,23}, {5,36}, {1,25}, {6,19}, {6,9}, {6,41}, {6,14}, {2,11}, {1,37}, {7,28}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {1,16}, {8,24}, {6,25}, {6,38}, {2,31}, {6,34}, {6,10}, {5,10}, {5,26}, {3,42}, {5,9}, {4,25}, {3,38}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {7,27}, {1,41}, {3,31}, {7,24}, {1,14}, {6,39}, {6,37}, {7,35}, {5,21}, {2,30}, {6,13}, {2,18}, {1,34}, {5,37}, {7,19}, {2,43}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {4,44}, {7,42}, {8,29}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET44.65 // Bipartite(17,27) Valencies [27,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3873033969692408671301974232137728000000000 EdgePairs[44][65]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {9,18}, {3,29}, {16,28}, {4,26}, {14,29}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {17,29}, {5,18}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {4,34}, {17,19}, {13,29}, {10,22}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {17,18}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {17,42}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {1,26}, {9,27}, {1,25}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,18}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {7,37}, {1,28}, {14,18}, {3,43}, {3,36}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {3,28}, {9,35}, {12,24}, {14,28}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {7,40}, {17,37}, {14,19}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {9,40}, {14,31}, {8,22}, {14,20}, {11,33}, {1,34}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {16,27}, {9,30}, {5,40}, {16,31}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {14,24}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {15,18}, {17,34}, {12,26}, {10,30}, {6,18}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {14,42}, {6,20}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {16,44}, {7,21}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {16,18}, {5,44}, {5,35}, {4,43}, {11,22}, {16,32}, {9,32}, {5,39}, {12,43}, {1,21}, {6,21}, {7,20}, {3,40}, {16,19}, {12,36}, {7,18}, {10,21}, {3,33}, {1,24}, {17,21}, {4,18}, {15,26}, {2,18}, {16,38}, {12,37}, {17,30}, {2,19}, {5,24}, {7,33}, {12,31}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET44.66 // Bipartite(16,28) Valencies [28,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 6379114773611026046850310499991552000000000 EdgePairs[44][66]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {15,17}, {10,17}, {3,29}, {9,18}, {16,28}, {4,26}, {14,29}, {2,20}, {2,26}, {16,17}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {5,18}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {4,34}, {13,29}, {10,22}, {12,22}, {14,40}, {10,42}, {9,41}, {15,20}, {14,33}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {16,23}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {1,26}, {9,27}, {1,25}, {15,34}, {12,44}, {16,42}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,18}, {9,17}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {7,37}, {1,28}, {14,18}, {3,43}, {1,17}, {3,36}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {8,33}, {10,28}, {9,44}, {15,23}, {12,17}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {3,28}, {9,35}, {12,24}, {14,28}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {7,40}, {14,19}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {9,40}, {14,31}, {8,22}, {14,20}, {11,33}, {1,34}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {16,27}, {9,30}, {5,40}, {16,31}, {8,17}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {8,29}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {2,33}, {6,32}, {15,31}, {10,35}, {4,27}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {6,17}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {11,17}, {15,18}, {12,26}, {10,30}, {6,18}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {14,42}, {6,20}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {7,21}, {16,44}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {15,32}, {14,38}, {6,30}, {11,25}, {6,38}, {2,17}, {11,40}, {13,42}, {16,18}, {5,44}, {5,35}, {4,43}, {11,22}, {16,32}, {9,32}, {5,39}, {12,43}, {1,21}, {6,21}, {7,20}, {3,40}, {16,19}, {12,36}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {15,26}, {2,18}, {16,38}, {12,37}, {2,19}, {5,24}, {7,33}, {12,31}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {10,32}, {16,24}, {4,19}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET44.67 // Bipartite(15,29) Valencies [29,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 11562145527169984709916187781234688000000000 EdgePairs[44][67]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {5,43}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {15,44}, {11,43}, {2,35}, {4,31}, {8,40}, {3,35}, {8,21}, {10,33}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {13,40}, {14,44}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,43}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {3,43}, {15,28}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {2,44}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {14,33}, {15,37}, {10,38}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,44}, {11,44}, {3,25}, {11,34}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {1,44}, {13,38}, {14,40}, {9,41}, {6,23}, {15,17}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {9,44}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {13,44}, {8,27}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {15,29}, {8,43}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {15,18}, {5,17}, {3,40}, {15,16}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {14,41}, {4,26}, {15,20}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,25}, {10,23}, {15,26}, {9,43}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {15,43}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET44.68 // Bipartite(4,40) Valencies [30,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4161629115065460326400000000 EdgePairs[44][68]:={ {4,35}, {3,15}, {2,38}, {2,22}, {3,38}, {3,7}, {4,8}, {4,27}, {2,11}, {1,40}, {4,40}, {1,25}, {4,16}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {4,5}, {1,5}, {1,44}, {3,30}, {4,44}, {1,32}, {3,10}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {1,34}, {2,14}, {3,11}, {2,10}, {4,37}, {4,20}, {2,41}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {4,39}, {1,17}, {1,22}, {1,16}, {3,40}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {4,29}, {3,22}, {4,43}, {3,23}, {4,31}, {2,42}, {3,27}, {2,34}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {1,26}, {4,11}, {3,42}, {2,27}, {2,43}, {3,35}, {2,21}, {2,39}, {3,28}, {3,26}, {3,24}, {3,12}, {1,42}, {2,6}, {1,14}, {1,41}, {3,44}, {4,32}, {3,39}, {1,37}, {1,20}, {3,16}, {1,13}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {4,9}, {2,7}, {3,43}, {4,41}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {2,5}, {4,24}, {1,24} }; // ET44.69 // Bipartite(11,33) Valencies [30,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14481697524940800 EdgePairs[44][69]:={ {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {3,26}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {11,15}, {8,21}, {10,33}, {3,19}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {5,41}, {7,41}, {1,13}, {11,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {9,36}, {6,34}, {1,43}, {9,39}, {8,42}, {9,20}, {4,22}, {1,18}, {3,38}, {5,27}, {7,14}, {3,43}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {11,22}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {7,12}, {8,24}, {4,41}, {9,38}, {9,26}, {5,14}, {3,29}, {1,41}, {10,13}, {10,19}, {9,22}, {9,19}, {3,44}, {11,44}, {3,25}, {11,34}, {7,35}, {11,13}, {2,43}, {2,27}, {6,30}, {4,33}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,42}, {3,22}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {3,14}, {2,37}, {4,42}, {5,29}, {10,41}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,42}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {5,18}, {5,16}, {1,23}, {10,24}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {5,42}, {2,38}, {7,44}, {8,28}, {7,43}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {9,42}, {5,36}, {9,34}, {10,14}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET44.70 // Bipartite(14,30) Valencies [30,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23124291054339969419832375562469376000000000 EdgePairs[44][70]:={ {13,21}, {6,38}, {11,40}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {4,28}, {11,25}, {5,43}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {13,40}, {14,44}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {2,44}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {14,15}, {14,33}, {10,38}, {14,23}, {6,16}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {9,22}, {12,41}, {9,19}, {3,44}, {11,44}, {3,25}, {11,34}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {14,43}, {3,22}, {14,37}, {1,44}, {13,38}, {4,15}, {14,40}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {9,44}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {13,44}, {8,27}, {3,33}, {13,32}, {14,26}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {14,19}, {1,33}, {12,36}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {14,41}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET44.71 // Non-bipartite Valency 30 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 958003200 EdgePairs[44][71]:={ {13,25}, {3,42}, {15,28}, {24,33}, {30,37}, {15,17}, {3,29}, {16,28}, {5,13}, {4,26}, {20,33}, {20,25}, {30,43}, {25,42}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {36,37}, {33,41}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {1,5}, {7,24}, {11,34}, {13,27}, {3,17}, {2,11}, {1,9}, {2,39}, {7,28}, {18,38}, {2,24}, {39,41}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {13,43}, {3,10}, {5,18}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {22,25}, {30,44}, {2,30}, {14,25}, {28,29}, {5,9}, {7,15}, {3,25}, {4,12}, {29,42}, {1,41}, {4,30}, {31,42}, {8,11}, {2,38}, {38,41}, {31,37}, {12,27}, {37,44}, {6,34}, {17,22}, {4,38}, {37,42}, {11,39}, {24,39}, {21,31}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {4,34}, {13,29}, {22,28}, {38,44}, {31,38}, {10,22}, {18,37}, {25,32}, {20,29}, {36,44}, {12,22}, {14,40}, {10,42}, {4,5}, {9,41}, {23,34}, {17,25}, {24,36}, {11,35}, {3,27}, {11,31}, {7,13}, {10,13}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {34,39}, {28,43}, {17,42}, {2,8}, {20,28}, {10,25}, {13,17}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {28,42}, {35,40}, {6,19}, {1,10}, {5,23}, {27,32}, {16,20}, {7,30}, {5,26}, {6,31}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {21,44}, {3,14}, {20,44}, {31,44}, {35,44}, {21,42}, {4,41}, {9,22}, {31,35}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {26,44}, {18,35}, {15,24}, {22,27}, {30,34}, {20,32}, {18,31}, {9,27}, {1,25}, {26,32}, {18,42}, {32,41}, {10,16}, {6,14}, {12,44}, {15,34}, {16,42}, {24,30}, {16,30}, {8,35}, {5,27}, {6,40}, {9,31}, {3,6}, {20,39}, {5,33}, {7,16}, {27,41}, {6,24}, {16,43}, {6,39}, {24,43}, {2,44}, {35,39}, {16,34}, {19,31}, {22,41}, {8,21}, {9,20}, {18,26}, {28,39}, {3,16}, {18,21}, {30,40}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {3,23}, {4,44}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {39,44}, {12,33}, {26,43}, {5,38}, {1,37}, {33,40}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {15,27}, {14,35}, {36,41}, {5,42}, {11,32}, {3,31}, {11,18}, {3,20}, {27,36}, {6,13}, {11,19}, {8,10}, {20,40}, {19,24}, {35,38}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {36,39}, {9,37}, {27,38}, {10,18}, {9,17}, {1,14}, {10,20}, {17,26}, {11,41}, {19,44}, {40,41}, {13,19}, {9,29}, {2,22}, {15,40}, {21,34}, {1,44}, {13,23}, {5,15}, {19,32}, {6,10}, {7,37}, {1,28}, {14,18}, {3,43}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {7,42}, {24,25}, {6,43}, {23,26}, {26,31}, {18,22}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {7,36}, {9,39}, {13,26}, {14,37}, {22,33}, {11,24}, {8,33}, {20,31}, {10,28}, {15,23}, {12,17}, {2,7}, {9,42}, {9,19}, {13,35}, {1,13}, {10,24}, {31,41}, {17,36}, {26,39}, {23,28}, {2,14}, {9,35}, {12,24}, {14,28}, {10,36}, {12,20}, {8,41}, {28,37}, {2,40}, {9,43}, {36,40}, {29,33}, {3,19}, {4,40}, {23,38}, {16,36}, {29,40}, {1,39}, {18,43}, {7,40}, {17,37}, {18,25}, {14,19}, {32,42}, {21,27}, {10,37}, {6,44}, {25,36}, {2,42}, {15,37}, {7,35}, {4,42}, {21,43}, {15,29}, {30,33}, {14,41}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,43}, {3,26}, {13,36}, {9,23}, {34,41}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {29,44}, {25,30}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {30,41}, {11,16}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {24,31}, {16,27}, {19,43}, {23,44}, {9,30}, {2,13}, {5,40}, {16,31}, {24,42}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {32,43}, {1,40}, {6,23}, {28,35}, {10,26}, {1,23}, {8,29}, {7,22}, {15,44}, {23,41}, {25,40}, {19,36}, {15,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {18,36}, {3,12}, {14,24}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {13,41}, {2,10}, {6,17}, {32,35}, {19,33}, {18,39}, {11,14}, {7,12}, {13,20}, {13,21}, {3,11}, {2,43}, {3,38}, {33,37}, {14,34}, {11,23}, {3,5}, {16,40}, {26,41}, {36,43}, {15,19}, {9,33}, {29,34}, {8,16}, {8,42}, {20,21}, {20,35}, {14,30}, {7,38}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {5,31}, {29,43}, {4,25}, {10,38}, {3,30}, {24,27}, {18,33}, {1,7}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {35,43}, {11,28}, {6,25}, {37,43}, {13,39}, {11,43}, {11,17}, {33,38}, {28,38}, {15,18}, {19,42}, {24,29}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {33,42}, {6,18}, {33,44}, {7,32}, {5,10}, {13,38}, {4,9}, {24,26}, {40,42}, {6,16}, {11,13}, {7,44}, {20,34}, {25,34}, {27,44}, {2,15}, {3,41}, {15,39}, {20,24}, {23,25}, {8,14}, {39,42}, {16,39}, {25,43}, {38,43}, {7,41}, {8,23}, {14,21}, {14,44}, {3,21}, {19,27}, {2,6}, {13,30}, {32,33}, {14,42}, {4,6}, {3,39}, {10,41}, {34,42}, {12,34}, {23,35}, {15,41}, {8,19}, {4,20}, {16,44}, {7,21}, {17,41}, {34,37}, {8,43}, {28,41}, {2,23}, {15,21}, {9,38}, {10,44}, {27,37}, {1,33}, {12,30}, {1,8}, {2,32}, {6,33}, {19,26}, {12,14}, {29,39}, {22,34}, {27,30}, {24,38}, {9,36}, {32,36}, {10,40}, {6,27}, {12,40}, {17,40}, {20,41}, {15,32}, {14,38}, {11,25}, {2,17}, {11,40}, {13,42}, {25,31}, {16,18}, {5,14}, {5,44}, {9,16}, {16,32}, {35,42}, {30,35}, {25,44}, {21,32}, {23,30}, {21,26}, {22,31}, {22,35}, {5,39}, {12,43}, {26,29}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {23,42}, {8,12}, {7,20}, {12,36}, {22,44}, {31,34}, {7,18}, {21,39}, {10,21}, {40,43}, {3,33}, {32,38}, {27,35}, {28,30}, {5,17}, {1,24}, {17,21}, {2,9}, {4,18}, {2,18}, {18,41}, {21,28}, {23,36}, {16,38}, {22,43}, {4,8}, {17,30}, {1,16}, {27,42}, {24,41}, {5,24}, {12,31}, {27,29}, {30,39}, {31,40}, {4,37}, {28,33}, {4,35}, {7,19}, {10,32}, {16,24}, {4,19}, {21,38}, {34,43}, {5,11}, {6,41}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET44.72 // Bipartite(13,31) Valencies [31,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 51203787334609932286771688745467904000000000 EdgePairs[44][72]:={ {13,21}, {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {13,39}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {6,14}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {2,44}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {13,25}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {10,19}, {9,22}, {12,41}, {9,19}, {3,44}, {11,44}, {3,25}, {11,34}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {13,38}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {13,14}, {4,36}, {4,29}, {9,44}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {12,14}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {13,44}, {8,27}, {3,33}, {13,32}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET44.73 // Bipartite(12,32) Valencies [32,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 126040091900578294859745695373459456000000000 EdgePairs[44][73]:={ {6,38}, {11,40}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {3,26}, {12,22}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {1,13}, {12,26}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {3,29}, {12,17}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {12,41}, {9,19}, {3,44}, {11,44}, {3,25}, {11,34}, {7,35}, {11,13}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {3,32}, {7,28}, {12,18}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {12,14}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {1,33}, {12,36}, {3,14}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET44.74 // Bipartite(11,33) Valencies [33,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 346610252726590310864300662277013504000000000 EdgePairs[44][74]:={ {6,38}, {11,40}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {3,26}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {3,44}, {9,19}, {11,44}, {3,25}, {11,34}, {7,35}, {11,13}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {3,33}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {1,33}, {3,14}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {3,12}, {9,14}, {7,13}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET44.75 // Non-bipartite Valency 33 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 60930411873673404638822400000000 EdgePairs[44][75]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {30,37}, {11,42}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {30,43}, {19,41}, {25,42}, {22,37}, {14,29}, {2,20}, {2,26}, {8,28}, {11,12}, {33,41}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {13,43}, {5,18}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {7,17}, {2,12}, {6,28}, {5,43}, {12,32}, {22,25}, {30,44}, {2,30}, {14,25}, {7,15}, {3,25}, {4,12}, {29,42}, {10,27}, {1,41}, {4,30}, {21,35}, {31,42}, {8,24}, {2,38}, {20,42}, {31,37}, {12,27}, {6,34}, {4,38}, {11,39}, {24,39}, {21,31}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {11,27}, {8,44}, {18,28}, {4,34}, {13,29}, {22,28}, {9,12}, {31,38}, {10,22}, {18,37}, {20,29}, {10,42}, {14,40}, {9,41}, {17,43}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {28,43}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {28,44}, {11,21}, {19,40}, {16,26}, {3,22}, {28,42}, {6,19}, {5,23}, {25,41}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {21,44}, {3,14}, {20,44}, {31,44}, {21,42}, {4,41}, {9,22}, {31,35}, {5,20}, {29,38}, {8,39}, {22,32}, {7,34}, {1,20}, {15,43}, {18,27}, {2,36}, {7,14}, {12,38}, {11,44}, {13,33}, {26,44}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {18,42}, {32,41}, {10,16}, {6,14}, {12,44}, {15,34}, {16,42}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {24,44}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {7,16}, {27,41}, {1,22}, {6,24}, {16,43}, {6,39}, {24,43}, {2,44}, {19,35}, {10,14}, {1,42}, {16,34}, {19,31}, {22,41}, {8,21}, {9,20}, {14,23}, {18,26}, {28,39}, {3,16}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {3,23}, {4,44}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {21,36}, {7,31}, {12,33}, {26,43}, {5,38}, {1,37}, {33,40}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {14,35}, {15,27}, {12,41}, {5,42}, {11,32}, {3,31}, {23,39}, {11,18}, {10,43}, {3,20}, {5,29}, {21,25}, {27,36}, {29,41}, {9,28}, {6,13}, {11,19}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {4,21}, {14,32}, {33,43}, {9,37}, {27,38}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {1,44}, {10,31}, {22,38}, {3,18}, {13,23}, {5,15}, {5,16}, {19,32}, {7,37}, {1,28}, {3,43}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {26,35}, {5,21}, {7,36}, {9,39}, {22,24}, {13,26}, {14,37}, {22,33}, {11,24}, {7,43}, {8,33}, {20,31}, {10,28}, {10,12}, {9,44}, {15,23}, {9,42}, {30,38}, {9,19}, {13,35}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {31,41}, {17,36}, {17,23}, {26,39}, {18,44}, {21,29}, {3,28}, {2,14}, {9,35}, {12,24}, {14,28}, {30,36}, {15,36}, {10,36}, {16,29}, {8,41}, {28,37}, {15,42}, {2,40}, {9,43}, {33,34}, {15,30}, {24,34}, {3,19}, {4,40}, {23,38}, {2,16}, {16,36}, {29,40}, {32,44}, {1,39}, {18,43}, {7,40}, {17,37}, {18,25}, {32,42}, {21,27}, {10,37}, {6,44}, {25,36}, {2,42}, {15,37}, {7,35}, {9,13}, {4,42}, {21,23}, {21,43}, {15,29}, {20,38}, {14,41}, {4,15}, {4,29}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {32,40}, {3,35}, {14,26}, {18,23}, {29,44}, {9,40}, {14,31}, {8,22}, {32,39}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {30,41}, {11,16}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {5,30}, {16,27}, {19,43}, {23,44}, {9,30}, {2,13}, {5,40}, {16,31}, {22,36}, {22,30}, {24,42}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {32,43}, {1,40}, {6,23}, {28,35}, {10,26}, {1,23}, {8,29}, {17,31}, {7,22}, {15,44}, {23,41}, {25,40}, {9,34}, {19,36}, {15,25}, {6,22}, {5,19}, {16,41}, {33,36}, {13,28}, {16,25}, {17,44}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {18,39}, {11,14}, {7,12}, {3,38}, {2,43}, {33,37}, {14,34}, {13,44}, {11,23}, {16,40}, {26,41}, {9,33}, {29,34}, {8,16}, {8,42}, {20,35}, {8,32}, {7,38}, {14,30}, {15,38}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {22,23}, {29,43}, {4,25}, {10,38}, {3,30}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {11,28}, {6,25}, {28,34}, {13,39}, {11,43}, {11,17}, {33,38}, {28,38}, {32,34}, {19,42}, {17,34}, {4,16}, {12,26}, {10,30}, {33,42}, {6,18}, {5,12}, {17,39}, {33,44}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {11,13}, {6,16}, {26,36}, {7,44}, {20,34}, {25,34}, {27,44}, {4,31}, {2,15}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {26,38}, {18,24}, {21,24}, {8,14}, {16,39}, {30,42}, {1,38}, {5,37}, {25,43}, {7,41}, {3,44}, {8,23}, {2,29}, {20,30}, {14,44}, {3,21}, {19,27}, {33,39}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {14,42}, {6,20}, {3,39}, {10,41}, {11,15}, {6,26}, {12,34}, {23,35}, {15,41}, {8,19}, {4,20}, {7,21}, {16,44}, {17,41}, {11,30}, {8,43}, {28,41}, {2,23}, {7,39}, {9,38}, {10,44}, {27,37}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {29,39}, {4,23}, {22,34}, {24,38}, {9,36}, {32,36}, {8,13}, {10,40}, {6,27}, {29,37}, {12,40}, {21,41}, {17,40}, {20,41}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {25,35}, {17,27}, {6,38}, {2,17}, {33,35}, {11,40}, {13,42}, {5,14}, {5,44}, {5,35}, {4,43}, {11,22}, {9,16}, {16,32}, {9,32}, {30,35}, {25,44}, {18,32}, {21,32}, {24,40}, {26,42}, {21,26}, {22,31}, {31,43}, {22,35}, {5,39}, {12,43}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,37}, {23,42}, {8,12}, {7,20}, {3,40}, {27,43}, {22,42}, {12,36}, {22,44}, {31,34}, {7,18}, {21,39}, {10,21}, {3,33}, {32,38}, {27,35}, {5,17}, {1,24}, {19,25}, {4,18}, {15,26}, {2,18}, {18,41}, {23,43}, {21,28}, {23,36}, {16,38}, {22,43}, {12,37}, {1,16}, {2,19}, {17,30}, {27,42}, {24,41}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {30,39}, {31,40}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {25,37}, {10,15}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET44.76 // Bipartite(10,34) Valencies [34,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1071340781154915506307838410674405376000000000 EdgePairs[44][76]:={ {6,38}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {5,43}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {1,12}, {10,42}, {6,29}, {9,11}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {6,44}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {4,11}, {3,44}, {9,19}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {3,33}, {2,11}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {8,43}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET44.77 // Bipartite(9,35) Valencies [35,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3749692734042204272077434437360418816000000000 EdgePairs[44][77]:={ {6,38}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {4,28}, {5,43}, {9,10}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {4,37}, {4,40}, {8,31}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {9,11}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {2,10}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {6,44}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {4,10}, {9,26}, {5,14}, {3,29}, {1,41}, {2,23}, {9,22}, {4,11}, {3,44}, {9,19}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {9,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {3,33}, {2,11}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {8,43}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {5,10}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {9,43}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET44.78 // Bipartite(8,36) Valencies [36,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14998770936168817088309737749441675264000000000 EdgePairs[44][78]:={ {6,38}, {6,25}, {5,38}, {5,22}, {4,28}, {5,43}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {6,9}, {4,37}, {4,40}, {8,31}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {1,20}, {3,18}, {8,16}, {2,34}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {8,9}, {2,10}, {3,9}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {1,36}, {6,18}, {1,29}, {6,44}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {1,43}, {8,42}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {4,9}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {4,10}, {5,14}, {3,29}, {1,41}, {2,23}, {4,11}, {3,44}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {5,39}, {3,32}, {7,28}, {2,16}, {6,11}, {8,34}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {7,29}, {2,28}, {8,29}, {7,21}, {8,36}, {8,27}, {3,33}, {2,11}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {8,43}, {2,31}, {1,33}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {5,9}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {7,38}, {5,42}, {2,38}, {7,9}, {5,10}, {7,44}, {8,28}, {7,43}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {5,36}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {8,25}, {2,9}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {6,40} }; // ET44.79 // Bipartite(7,37) Valencies [37,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 69369315579780779033432537091167748096000000000 EdgePairs[44][79]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {7,38}, {4,29}, {1,32}, {3,13}, {1,27}, {3,43}, {3,25}, {3,15}, {7,41}, {7,44}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {7,12}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {4,22}, {5,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {1,44}, {4,41}, {2,10}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {6,8}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {7,43}, {2,35}, {1,22}, {3,44}, {6,12}, {6,30}, {6,43}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {6,44}, {7,17}, {5,24}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {3,26}, {5,28}, {5,42}, {7,31}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {5,44}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {1,25}, {6,19}, {6,9}, {7,29}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {1,41}, {3,41}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {6,13}, {7,37}, {2,18}, {5,35}, {1,34}, {5,37}, {7,19}, {2,43}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {4,44}, {7,42}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET44.80 // Bipartite(6,38) Valencies [38,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 376576284575952800467205201352053489664000000000 EdgePairs[44][80]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {1,44}, {4,41}, {2,10}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {6,8}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {3,44}, {6,12}, {6,30}, {6,43}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {6,44}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {3,26}, {5,28}, {5,42}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {5,44}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {6,19}, {6,9}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {6,42}, {4,40}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {1,41}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {5,19}, {6,20}, {2,30}, {5,21}, {6,13}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {6,35}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36}, {5,16} }; // ET44.81 // Bipartite(5,39) Valencies [39,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2447745849743693203036833808788347682816000000000 EdgePairs[44][81]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {2,42}, {3,18}, {3,17}, {3,7}, {4,38}, {3,34}, {2,25}, {5,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {1,44}, {4,41}, {2,10}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {5,25}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {3,44}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {1,43}, {3,26}, {5,28}, {5,42}, {2,17}, {4,36}, {5,41}, {4,6}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {5,44}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {1,15}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,40}, {2,31}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {5,13}, {1,41}, {5,6}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {2,30}, {5,21}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36}, {5,16} }; // ET44.82 // Bipartite(4,40) Valencies [40,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 19581966797949545624294670470306781462528000000000 EdgePairs[44][82]:={ {1,15}, {4,35}, {3,15}, {1,43}, {2,38}, {4,42}, {1,11}, {4,14}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {4,8}, {4,27}, {2,11}, {1,40}, {2,20}, {4,40}, {1,25}, {4,16}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {4,5}, {1,5}, {1,44}, {3,30}, {4,44}, {1,32}, {4,6}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {4,26}, {2,29}, {3,19}, {1,29}, {4,12}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {4,37}, {4,20}, {2,41}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {4,39}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {4,33}, {4,28}, {3,14}, {2,13}, {1,12}, {3,9}, {4,29}, {3,22}, {4,43}, {3,23}, {4,31}, {2,42}, {2,34}, {3,27}, {4,30}, {1,19}, {2,40}, {4,21}, {4,36}, {2,35}, {4,17}, {2,9}, {4,15}, {4,25}, {3,5}, {1,35}, {1,26}, {2,44}, {4,38}, {2,24}, {4,11}, {3,42}, {2,27}, {2,43}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {4,22}, {3,28}, {3,26}, {3,24}, {3,12}, {1,42}, {2,6}, {3,21}, {1,14}, {1,41}, {3,44}, {4,32}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {1,13}, {3,16}, {4,18}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {4,9}, {2,7}, {3,43}, {4,34}, {4,41}, {3,33}, {1,8}, {4,23}, {1,30}, {2,30}, {1,21}, {4,13}, {1,6}, {1,18}, {4,19}, {4,10}, {2,5}, {4,24}, {1,24} }; // ET44.83 // Non-bipartite Valency 40 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 60740641855649297203200 EdgePairs[44][83]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {37,43}, {13,18}, {2,6}, {32,33}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {5,44}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {8,44}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {19,27}, {28,43}, {32,34}, {7,12}, {31,33}, {21,34}, {4,10}, {3,19}, {1,15}, {10,30}, {24,44}, {40,44}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {7,42}, {21,31}, {13,44}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {38,43}, {3,27}, {29,39}, {25,32}, {5,13}, {15,33}, {21,33}, {22,27}, {30,34}, {17,36}, {10,35}, {13,40}, {11,15}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {13,41}, {22,37}, {12,26}, {15,34}, {18,41}, {7,16}, {12,16}, {14,19}, {9,43}, {3,38}, {13,24}, {11,30}, {6,42}, {4,21}, {12,42}, {29,36}, {30,33}, {14,43}, {20,34}, {23,29}, {1,33}, {4,25}, {2,42}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, {36,42}, {1,30}, {23,42}, {14,27}, {11,35}, {2,29}, {16,39}, {15,31}, {10,21}, {17,23}, {12,19}, {3,7}, {10,25}, {6,17}, {32,35}, {20,33}, {2,17}, {29,42}, {36,37}, {20,32}, {18,40}, {11,33}, {18,44}, {19,22}, {16,26}, {3,22}, {5,24}, {11,32}, {22,43}, {1,5}, {28,37}, {11,20}, {24,41}, {17,28}, {1,8}, {11,24}, {1,35}, {9,17}, {10,18}, {19,38}, {8,15}, {5,20}, {3,12}, {3,26}, {28,29}, {11,31}, {16,22}, {27,43}, {12,39}, {6,36}, {5,15}, {20,30}, {2,36}, {4,18}, {35,41}, {22,38}, {26,39}, {8,11}, {15,35}, {30,41}, {14,38}, {5,41}, {39,43}, {12,27}, {11,13}, {15,30}, {3,43}, {19,43}, {7,19}, {11,34}, {8,32}, {7,39}, {22,39}, {19,26}, {8,33}, {8,20}, {5,31}, {20,35}, {16,19}, {1,13}, {26,38}, {9,23}, {7,14}, {34,41}, {5,34}, {9,29}, {13,35}, {14,26}, {23,28}, {7,27}, {2,9}, {10,40}, {29,37}, {13,30}, {6,9}, {17,42}, {13,20}, {16,27}, {37,42}, {23,36}, {8,41}, {5,32}, {5,33}, {8,31}, {17,37}, {5,11}, {3,16}, {20,24}, {7,22}, {22,26}, {12,14}, {12,22}, {7,38}, {13,34}, {28,36}, {9,36}, {4,44}, {31,41}, {8,34}, {26,43}, {15,24}, {10,19}, {1,24}, {20,41}, {12,38}, {27,39}, {32,41}, {31,37}, {14,39}, {34,37}, {2,13}, {5,30}, {33,41}, {24,30}, {6,13}, {5,35}, {24,35}, {8,17}, {1,9}, {18,25}, {4,40}, {2,37}, {12,18}, {6,37}, {25,44}, {9,15}, {3,10}, {21,40}, {16,43}, {18,21}, {8,30}, {21,44}, {10,44}, {13,31}, {2,28}, {25,40}, {22,25}, {15,28}, {6,28}, {14,21}, {7,18}, {11,41}, {14,25}, {5,17}, {24,33}, {20,28}, {13,32}, {13,33}, {35,37}, {10,27}, {24,32}, {16,18}, {32,37}, {33,37}, {19,39}, {1,41}, {3,39}, {5,29}, {28,42}, {8,35}, {15,41}, {6,24}, {24,31}, {9,32}, {2,5}, {2,24}, {4,19}, {9,33}, {9,20}, {18,26}, {8,29}, {4,14}, {21,43}, {7,43}, {12,43}, {30,37}, {8,23}, {3,21}, {5,36}, {23,37}, {25,43}, {4,27}, {2,8}, {24,29}, {9,42}, {13,17}, {3,25}, {26,44}, {1,37}, {13,23}, {12,40}, {36,41}, {1,28}, {13,42}, {16,38}, {9,31}, {21,27}, {4,38}, {8,9}, {28,32}, {24,34}, {10,14}, {13,29}, {4,22}, {4,7}, {10,22}, {24,42}, {26,40}, {17,24}, {28,33}, {21,38}, {15,37}, {7,44}, {2,41}, {8,36}, {23,41}, {39,44}, {9,34}, {15,17}, {10,38}, {6,41}, {11,28}, {13,36}, {28,34}, {19,25}, {25,38}, {19,21}, {20,37}, {6,11}, {5,23}, {12,44}, {11,23}, {35,42}, {31,36}, {2,11}, {9,30}, {29,41}, {38,44}, {7,40}, {20,29}, {32,36}, {28,31}, {30,42}, {18,27}, {1,6}, {11,37}, {5,9}, {4,26}, {4,12}, {2,30}, {3,18}, {7,10}, {1,29}, {6,30}, {9,35}, {1,17}, {8,28}, {5,42}, {18,39}, {10,43}, {16,44}, {21,26}, {17,41}, {4,43}, {5,28}, {2,35}, {17,33}, {10,26}, {16,40}, {6,35}, {15,29}, {17,32}, {28,35}, {24,28}, {8,42}, {27,40}, {16,25}, {11,17}, {25,39}, {16,21}, {5,37}, {40,43}, {24,36}, {9,24}, {21,39}, {30,36}, {6,20}, {2,20}, {1,36}, {14,18}, {10,16}, {4,16}, {34,42}, {20,23}, {7,25}, {15,36}, {17,34}, {28,30}, {31,42}, {6,15}, {7,21}, {3,5}, {19,40}, {18,22}, {8,37}, {37,41}, {12,25}, {2,15}, {20,36}, {6,31}, {27,44}, {9,13}, {1,7}, {1,23}, {12,21}, {23,30}, {29,34}, {15,23}, {17,31}, {2,31}, {13,28}, {9,18}, {20,26}, {10,17}, {11,29}, {19,44}, {12,15}, {3,40}, {3,44}, {11,42}, {11,16}, {2,34}, {8,19}, {37,44}, {22,40}, {20,42}, {13,37}, {33,42}, {6,34}, {2,21}, {23,35}, {18,28}, {29,33}, {32,42}, {28,41}, {29,35}, {23,25}, {23,32}, {6,21}, {1,12}, {2,32}, {6,33}, {5,19}, {18,38}, {23,33}, {7,20}, {4,29}, {1,42}, {3,8}, {10,39}, {6,25}, {4,17}, {7,31}, {12,33}, {2,25}, {17,35}, {6,32}, {2,33}, {4,6}, {7,15}, {12,32}, {22,44}, {1,26}, {14,44}, {15,26}, {12,20}, {38,41}, {11,36}, {5,14}, {5,27}, {8,27}, {15,42}, {3,13}, {17,30}, {30,39}, {24,37}, {4,39}, {23,31}, {25,29}, {18,43}, {28,40}, {35,39}, {16,35}, {24,27}, {18,37}, {13,19}, {4,36}, {10,29}, {21,42}, {14,41}, {13,22}, {13,43}, {14,40}, {9,41}, {7,11}, {26,34}, {7,34}, {23,34}, {10,23}, {33,39}, {14,24}, {21,29}, {8,22}, {32,39}, {2,10}, {5,38}, {6,10}, {25,42}, {9,40}, {28,44}, {1,16}, {10,36}, {16,30}, {12,34}, {7,33}, {12,31}, {15,19}, {7,32}, {13,27}, {11,39}, {19,24}, {7,30}, {26,31}, {24,43}, {31,39}, {8,14}, {4,23}, {8,12}, {5,22}, {22,41}, {7,35}, {17,25}, {9,44}, {34,39}, {3,24}, {8,38}, {17,21}, {15,27}, {3,20}, {5,12}, {26,32}, {4,9}, {26,33}, {11,22}, {16,20}, {20,39}, {27,41}, {11,26}, {34,38}, {5,26}, {16,32}, {39,41}, {31,38}, {16,33}, {13,38}, {16,31}, {20,27}, {16,24}, {3,15}, {26,35}, {36,44}, {10,28}, {16,34}, {25,36}, {12,30}, {20,38}, {3,41}, {15,39}, {18,29}, {4,42}, {35,43}, {24,38}, {33,38}, {32,38}, {21,36}, {30,43}, {29,44}, {1,19}, {5,43}, {26,30}, {19,41}, {11,14}, {12,35}, {14,35}, {19,32}, {36,40}, {19,33}, {3,34}, {3,31}, {11,19}, {24,39}, {8,16}, {13,26}, {1,39}, {4,37}, {1,14}, {8,43}, {34,43}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {8,26}, {30,38}, {3,32}, {10,42}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {24,26}, {40,42}, {8,10}, {1,22}, {27,33}, {14,34}, {7,24}, {29,40}, {11,27}, {26,41}, {27,32}, {35,38}, {4,5}, {32,43}, {10,37}, {22,30}, {27,34}, {31,43}, {33,43}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {22,35}, {20,43}, {32,40}, {16,41}, {33,40}, {15,18}, {2,14}, {17,44}, {3,35}, {27,31}, {13,39}, {6,14}, {11,43}, {14,31}, {4,8}, {17,27}, {24,25}, {7,9}, {13,21}, {27,29}, {5,10}, {23,44}, {3,17}, {12,28}, {34,44}, {36,38}, {19,35}, {1,18}, {6,44}, {22,31}, {6,22}, {31,44}, {14,32}, {22,33}, {2,44}, {5,39}, {25,37}, {13,25}, {14,33}, {2,22}, {3,29}, {22,32}, {8,39}, {19,30}, {1,43}, {15,43}, {7,41}, {21,41}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {18,42}, {7,37}, {38,42}, {9,16}, {3,36}, {2,40}, {33,44}, {11,38}, {12,41}, {4,13}, {6,40}, {31,40}, {32,44}, {14,17}, {5,25}, {36,43}, {25,41}, {5,21}, {20,40}, {18,32}, {7,28}, {14,23}, {35,44}, {20,44}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {22,42}, {30,44}, {14,29}, {18,34}, {19,23}, {18,31}, {26,37}, {14,42}, {15,40}, {1,44}, {2,19}, {23,43}, {6,19}, {4,24}, {12,37}, {17,22}, {14,36}, {2,43}, {27,36}, {6,43}, {26,29}, {8,18}, {8,21}, {10,15}, {12,17}, {30,40}, {29,43}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {15,44}, {17,38}, {6,27}, {16,37}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {20,21}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {7,17}, {17,43}, {20,25}, {4,41}, {3,42}, {3,28}, {9,27}, {11,25}, {16,17}, {11,44}, {11,21}, {19,42}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // ET44.84 // Bipartite(3,41) Valencies [41,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 200715159678982842649020372320644509990912000000000 EdgePairs[44][84]:={ {1,15}, {3,15}, {1,43}, {2,38}, {1,11}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {2,11}, {1,40}, {2,20}, {1,25}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {1,5}, {1,44}, {3,30}, {1,32}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {2,41}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {2,13}, {3,14}, {1,12}, {3,9}, {3,22}, {3,23}, {2,42}, {2,34}, {3,27}, {1,19}, {2,40}, {2,35}, {2,9}, {3,5}, {1,4}, {1,35}, {1,26}, {2,44}, {2,4}, {2,24}, {3,42}, {2,27}, {3,4}, {2,43}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {1,42}, {2,6}, {3,21}, {1,14}, {1,41}, {3,44}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {1,13}, {3,16}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,43}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24} }; // ET44.85 // Bipartite(2,42) Valencies [42,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2810012235505759797086285212489023139872768000000000 EdgePairs[44][85]:={ {2,11}, {1,26}, {2,14}, {2,44}, {1,14}, {1,44}, {2,37}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,37}, {1,33}, {1,40}, {1,10}, {1,43}, {2,39}, {1,39}, {2,43}, {1,36}, {1,6}, {2,40}, {2,6}, {1,4}, {1,20}, {1,12}, {2,36}, {1,31}, {2,12}, {2,4}, {2,33}, {2,21}, {1,38}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,38}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {2,42}, {1,28}, {2,19}, {1,42}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {2,41}, {1,41}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET44.86 // Non-bipartite Valency 42 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 4714400748520531002654720000 EdgePairs[44][86]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {37,43}, {13,18}, {2,6}, {32,33}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {5,44}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {8,44}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {19,27}, {28,43}, {32,34}, {7,12}, {31,33}, {21,34}, {4,10}, {3,19}, {1,15}, {5,8}, {10,30}, {24,44}, {40,44}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {7,42}, {30,31}, {21,31}, {13,44}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {34,35}, {38,43}, {3,27}, {29,39}, {25,32}, {5,13}, {15,33}, {21,33}, {22,27}, {30,34}, {17,36}, {10,35}, {13,40}, {11,15}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {13,41}, {22,37}, {12,26}, {15,34}, {18,41}, {7,16}, {12,16}, {14,19}, {9,43}, {3,38}, {13,24}, {11,30}, {30,32}, {6,42}, {4,21}, {12,42}, {29,36}, {30,33}, {14,43}, {20,34}, {23,29}, {1,33}, {4,25}, {2,42}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, {36,42}, {1,30}, {23,42}, {14,27}, {11,35}, {2,29}, {16,39}, {15,31}, {10,21}, {17,23}, {12,19}, {3,7}, {10,25}, {6,17}, {32,35}, {20,33}, {2,17}, {29,42}, {33,35}, {36,37}, 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{12,37}, {17,22}, {14,36}, {2,43}, {27,36}, {6,43}, {26,29}, {8,18}, {8,21}, {10,15}, {12,17}, {30,40}, {29,43}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {15,44}, {17,38}, {6,27}, {16,37}, {37,39}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {20,21}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {7,17}, {10,11}, {17,43}, {20,25}, {4,41}, {41,44}, {3,42}, {3,28}, {9,27}, {11,25}, {16,17}, {11,44}, {11,21}, {19,42}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // ET44.87 // Bipartite(1,43) Valencies [43,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 60415263063373835637355132068513997507264512000000000 EdgePairs[44][87]:={ {1,26}, {1,14}, {1,44}, {1,24}, {1,29}, {1,30}, {1,32}, {1,37}, {1,33}, {1,40}, {1,10}, {1,2}, {1,43}, {1,39}, {1,36}, {1,6}, {1,4}, {1,20}, {1,12}, {1,31}, {1,38}, {1,7}, {1,15}, {1,16}, {1,21}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {1,28}, {1,42}, {1,8}, {1,13}, {1,19}, {1,9}, {1,41}, {1,22}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25} }; // ET44.88 // Non-bipartite Valency 43 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 2658271574788448768043625811014615890319638528000000000 EdgePairs[44][88]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {37,43}, {13,18}, {2,6}, {32,33}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {5,44}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {8,44}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {19,27}, {28,43}, {32,34}, {7,12}, {31,33}, {21,34}, {4,10}, {33,34}, {3,19}, {1,15}, {5,8}, {10,30}, {24,44}, {31,32}, {40,44}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {7,42}, 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{18,38}, {23,33}, {7,20}, {4,29}, {1,42}, {3,8}, {10,39}, {6,25}, {4,17}, {7,31}, {12,33}, {2,25}, {17,35}, {6,32}, {2,33}, {4,6}, {7,15}, {12,32}, {2,4}, {22,44}, {1,26}, {14,44}, {15,26}, {12,20}, {11,12}, {38,41}, {11,36}, {5,14}, {29,30}, {5,27}, {8,27}, {15,42}, {15,16}, {3,13}, {17,30}, {30,39}, {24,37}, {4,39}, {23,31}, {25,29}, {18,43}, {28,40}, {35,39}, {16,35}, {24,27}, {18,37}, {13,19}, {4,36}, {10,29}, {21,42}, {14,41}, {13,22}, {13,43}, {14,40}, {37,40}, {9,41}, {7,11}, {26,34}, {7,34}, {23,34}, {10,23}, {33,39}, {14,24}, {21,29}, {8,22}, {32,39}, {2,10}, {5,38}, {6,10}, {25,42}, {9,40}, {1,16}, {28,44}, {10,36}, {16,30}, {12,34}, {7,33}, {12,31}, {15,19}, {7,32}, {13,27}, {11,39}, {19,24}, {5,7}, {7,30}, {26,31}, {9,10}, {17,18}, {24,43}, {31,39}, {8,14}, {4,23}, {8,12}, {5,22}, {22,41}, {7,35}, {17,25}, {1,3}, {9,44}, {34,39}, {3,24}, {8,38}, {17,21}, {15,27}, {3,20}, {5,12}, {26,32}, {4,9}, {26,33}, {11,22}, {16,20}, {20,39}, {11,26}, {27,41}, {34,38}, {7,8}, {5,26}, {16,32}, {39,41}, {13,16}, {31,38}, {16,33}, {13,38}, {16,31}, {20,27}, {16,24}, {3,15}, {26,35}, {36,44}, {10,28}, {16,34}, {25,36}, {12,30}, {20,38}, {3,41}, {15,39}, {18,29}, {4,42}, {35,43}, {42,44}, {24,38}, {33,38}, {32,38}, {21,36}, {30,43}, {29,44}, {1,19}, {5,43}, {26,30}, {19,41}, {11,14}, {12,35}, {14,35}, {19,32}, {36,40}, {19,33}, {3,34}, {3,31}, {11,19}, {24,39}, {19,20}, {8,16}, {13,26}, {1,39}, {4,37}, {1,14}, {8,43}, {14,15}, {34,43}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {25,28}, {8,26}, {30,38}, {3,32}, {10,42}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {24,26}, {40,42}, {8,10}, {1,22}, {14,34}, {27,33}, {17,19}, {7,24}, {9,12}, {29,40}, {11,27}, {26,41}, {27,32}, {35,38}, {22,23}, {4,5}, {32,43}, {10,37}, {22,30}, {27,34}, {31,43}, {33,43}, {42,43}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {22,35}, {20,43}, {32,40}, {16,41}, {33,40}, {15,18}, {2,14}, {17,44}, {3,35}, {26,28}, {27,31}, {13,39}, {6,14}, {11,43}, {14,31}, {4,8}, {17,27}, {24,25}, {7,9}, {13,21}, {27,29}, {5,10}, {23,44}, {3,17}, {12,28}, {34,44}, {36,38}, {19,35}, {21,24}, {1,18}, {6,44}, {22,31}, {6,22}, {31,44}, {14,32}, {22,33}, {2,44}, {5,39}, {25,37}, {13,25}, {14,33}, {2,22}, {2,3}, {3,29}, {22,32}, {8,39}, {19,30}, {1,43}, {15,43}, {7,41}, {21,41}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {18,42}, {7,37}, {38,42}, {9,16}, {3,36}, {2,40}, {33,44}, {11,38}, {12,41}, {4,13}, {6,40}, {31,40}, {32,44}, {14,17}, {5,25}, {36,43}, {25,41}, {5,21}, {20,40}, {18,32}, {7,28}, {14,23}, {35,44}, {20,44}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {22,42}, {30,44}, {1,4}, {14,29}, {18,34}, {19,23}, {18,31}, {26,37}, {14,42}, {15,40}, {1,44}, {2,19}, {23,43}, {6,19}, {4,24}, {12,37}, {17,22}, {27,28}, {14,36}, {2,43}, {27,36}, {6,43}, {26,29}, {8,18}, {8,21}, {10,15}, {12,17}, {30,40}, {29,43}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {15,44}, {17,38}, {6,27}, {16,37}, {37,39}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {20,21}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {7,17}, {10,11}, {17,43}, {20,25}, {4,41}, {41,44}, {3,42}, {3,28}, {9,27}, {37,38}, {11,25}, {16,17}, {11,44}, {11,21}, {19,42}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // Total number of connected ET graphs of order 44 is 88 // ******************************************************************************************** // Order 45 // ET45.1 // Non-bipartite Valency 2 // Diameter 22 Girth 45 // Twin-free VT AT // Automorphism group of order 90 EdgePairs[45][1]:={ {11,43}, {8,20}, {4,38}, {19,32}, {27,37}, {22,35}, {24,34}, {6,39}, {9,19}, {30,40}, {14,25}, {7,41}, {20,33}, {7,21}, {1,15}, {31,43}, {18,29}, {4,18}, {29,42}, {6,16}, {5,37}, {12,24}, {26,38}, {9,42}, {13,27}, {10,22}, {2,35}, {16,28}, {23,36}, {15,26}, {1,36}, {25,39}, {17,30}, {3,34}, {5,17}, {11,23}, {21,31}, {33,45}, {28,41}, {32,44}, {8,40}, {3,13}, {12,44}, {2,14}, {10,45} }; // ET45.2 // Bipartite(18,27) Valencies [3,2] // Diameter 8 Girth 12 // Twin-free Non-VT Non-AT // Automorphism group of order 216 EdgePairs[45][2]:={ {15,32}, {18,32}, {5,36}, {18,22}, {17,34}, {2,37}, {1,44}, {15,36}, {6,33}, {5,29}, {4,44}, {9,21}, {7,41}, {7,31}, {16,41}, {6,26}, {11,28}, {5,43}, {2,43}, {8,25}, {1,20}, {4,31}, {12,40}, {17,25}, {2,45}, {3,24}, {8,29}, {10,45}, {11,42}, {16,30}, {13,40}, {10,23}, {12,39}, {3,28}, {4,38}, {13,33}, {11,35}, {17,27}, {12,19}, {7,35}, {9,22}, {3,34}, {14,38}, {14,27}, {14,23}, {1,19}, {10,21}, {9,26}, {18,20}, {15,42}, {16,37}, {13,30}, {6,24}, {8,39} }; // ET45.3 // Bipartite(15,30) Valencies [4,2] // Diameter 6 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[45][3]:={ {12,27}, {12,20}, {11,16}, {8,19}, {6,34}, {1,44}, {2,30}, {5,29}, {7,41}, {9,31}, {15,20}, {1,39}, {3,27}, {14,45}, {12,30}, {13,26}, {10,36}, {3,37}, {7,33}, {15,37}, {5,44}, {8,32}, {4,32}, {5,21}, {8,43}, {4,18}, {13,40}, {1,16}, {12,39}, {4,45}, {11,35}, {13,36}, {2,38}, {11,40}, {9,42}, {3,18}, {6,42}, {7,22}, {15,28}, {14,33}, {14,21}, {10,19}, {8,26}, {15,34}, {6,25}, {2,23}, {5,35}, {10,22}, {10,38}, {2,41}, {9,28}, {1,23}, {11,31}, {14,25}, {13,17}, {7,24}, {9,17}, {6,24}, {3,43}, {4,29} }; // ET45.4 // Bipartite(15,30) Valencies [4,2] // Diameter 6 Girth 8 // Twin-free Non-VT Non-AT // Automorphism group of order 60 EdgePairs[45][4]:={ {1,26}, {5,33}, {6,41}, {4,24}, {8,28}, {4,23}, {8,20}, {4,36}, {11,25}, {15,20}, {3,42}, {9,38}, {15,27}, {14,34}, {11,37}, {6,43}, {12,31}, {5,44}, {10,45}, {6,36}, {9,37}, {15,21}, {4,18}, {7,32}, {10,31}, {1,16}, {7,40}, {9,40}, {13,33}, {2,38}, {13,39}, {3,25}, {14,43}, {3,19}, {3,30}, {12,34}, {14,32}, {12,24}, {15,17}, {5,30}, {7,21}, {8,41}, {10,42}, {12,22}, {1,28}, {2,17}, {2,23}, {13,29}, {11,39}, {2,35}, {1,19}, {13,27}, {9,26}, {11,18}, {8,45}, {6,29}, {14,16}, {5,22}, {7,44}, {10,35} }; // ET45.5 // Bipartite(15,30) Valencies [4,2] // Diameter 15 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 983040 EdgePairs[45][5]:={ {8,28}, {9,19}, {5,32}, {10,27}, {10,40}, {1,44}, {2,32}, {2,30}, {1,29}, {9,21}, {11,20}, {3,33}, {15,24}, {4,43}, {11,37}, {2,45}, {1,31}, {7,33}, {15,37}, {4,30}, {8,43}, {3,16}, {12,39}, {1,16}, {4,45}, {7,18}, {13,36}, {5,19}, {11,35}, {9,36}, {11,22}, {12,41}, {5,17}, {6,27}, {3,18}, {6,42}, {3,31}, {12,24}, {14,40}, {9,34}, {7,35}, {12,26}, {8,41}, {13,38}, {7,20}, {13,23}, {4,28}, {13,21}, {14,38}, {10,42}, {8,26}, {14,23}, {2,17}, {15,39}, {5,34}, {10,25}, {14,25}, {6,29}, {6,44}, {15,22} }; // ET45.6 // Non-bipartite Valency 4 // Diameter 7 Girth 4 // Twin-free VT AT // Automorphism group of order 180 EdgePairs[45][6]:={ {9,19}, {1,14}, {8,20}, {31,44}, {4,37}, {5,37}, {10,43}, {6,39}, {33,45}, {9,20}, {21,33}, {14,26}, {7,41}, {11,24}, {8,21}, {12,45}, {13,25}, {22,35}, {30,40}, {11,44}, {15,27}, {26,39}, {32,45}, {2,36}, {11,23}, {33,43}, {4,16}, {12,43}, {27,38}, {5,16}, {18,28}, {8,40}, {16,30}, {31,43}, {28,42}, {29,42}, {10,23}, {3,15}, {9,40}, {4,38}, {24,36}, {23,36}, {6,38}, {32,44}, {2,15}, {10,44}, {3,14}, {9,42}, {20,31}, {12,24}, {4,17}, {29,40}, {7,21}, {23,35}, {8,41}, {25,38}, {27,39}, {5,39}, {7,19}, {6,18}, {19,33}, {22,34}, {12,22}, {5,18}, {16,28}, {6,17}, {17,30}, {18,29}, {30,41}, {11,45}, {1,13}, {2,34}, {19,31}, {26,37}, {10,22}, {13,27}, {15,26}, {2,13}, {7,42}, {20,32}, {1,34}, {1,35}, {24,34}, {21,32}, {25,37}, {17,29}, {14,25}, {28,41}, {3,36}, {3,35} }; // ET45.7 // Non-bipartite Valency 4 // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 180 EdgePairs[45][7]:={ {4,9}, {11,15}, {41,45}, {4,37}, {40,43}, {23,25}, {33,45}, {31,34}, {9,20}, {21,33}, {27,29}, {20,23}, {7,12}, {8,11}, {11,24}, {1,43}, {8,21}, {35,38}, {13,25}, {27,37}, {30,40}, {1,4}, {19,22}, {26,39}, {2,36}, {2,45}, {10,45}, {33,36}, {12,44}, {30,31}, {6,16}, {18,28}, {10,13}, {3,44}, {5,7}, {4,18}, {8,40}, {31,43}, {1,15}, {28,42}, {21,24}, {10,23}, {9,10}, {42,44}, {17,19}, {24,36}, {11,43}, {29,33}, {6,38}, {5,17}, {32,44}, {3,14}, {12,14}, {2,5}, {16,21}, {9,41}, {36,39}, {39,42}, {23,35}, {25,38}, {5,39}, {7,19}, {3,6}, {22,34}, {28,32}, {14,27}, {12,22}, {24,26}, {17,30}, {32,35}, {22,27}, {34,37}, {19,31}, {18,20}, {37,41}, {38,40}, {15,26}, {2,13}, {7,42}, {20,32}, {1,34}, {25,30}, {29,41}, {15,18}, {14,16}, {16,29}, {13,17}, {26,28}, {6,8}, {3,35} }; // ET45.8 // Non-bipartite Valency 4 // Diameter 5 Girth 4 // Twin-free VT AT // Automorphism group of order 180 EdgePairs[45][8]:={ {11,43}, {16,34}, {5,32}, {7,39}, {21,39}, {6,17}, {11,29}, {1,40}, {2,20}, {26,44}, {30,43}, {25,44}, {17,35}, {24,43}, {34,45}, {33,44}, {22,41}, {22,33}, {27,45}, {10,23}, {15,28}, {14,27}, {28,41}, {12,30}, {24,37}, {20,33}, {19,30}, {7,26}, {29,42}, {13,26}, {2,36}, {8,21}, {15,36}, {3,14}, {2,13}, {1,12}, {10,16}, {7,25}, {10,37}, {13,45}, {32,43}, {4,31}, {2,34}, {1,19}, {4,17}, {4,15}, {10,29}, {25,38}, {8,19}, {11,37}, {8,40}, {23,42}, {4,38}, {12,38}, {21,45}, {12,44}, {3,35}, {25,31}, {16,27}, {15,42}, {6,30}, {8,27}, {7,18}, {6,38}, {9,28}, {24,35}, {21,32}, {18,29}, {20,26}, {5,11}, {3,16}, {31,42}, {35,41}, {1,33}, {14,40}, {18,31}, {14,41}, {3,37}, {6,24}, {17,28}, {5,18}, {9,36}, {19,32}, {23,34}, {22,40}, {5,39}, {23,36}, {9,20}, {13,39}, {9,22} }; // ET45.9 // Non-bipartite Valency 4 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[45][9]:={ {17,41}, {18,32}, {34,45}, {4,24}, {15,43}, {27,33}, {5,32}, {1,14}, {15,40}, {2,37}, {40,43}, {8,31}, {6,33}, {24,27}, {9,25}, {11,17}, {20,22}, {7,34}, {9,31}, {13,16}, {15,20}, {8,11}, {1,43}, {14,39}, {3,21}, {6,12}, {25,28}, {30,40}, {12,30}, {11,44}, {4,7}, {11,23}, {3,29}, {12,44}, {32,41}, {7,45}, {20,29}, {8,44}, {8,10}, {16,36}, {22,24}, {35,39}, {21,29}, {13,40}, {10,31}, {2,31}, {41,43}, {26,36}, {5,38}, {19,27}, {5,19}, {2,38}, {37,38}, {23,36}, {19,38}, {12,34}, {6,42}, {7,25}, {21,45}, {39,42}, {10,29}, {16,35}, {33,42}, {18,21}, {4,25}, {3,39}, {19,33}, {14,42}, {18,45}, {1,28}, {24,26}, {5,18}, {17,32}, {22,27}, {30,34}, {35,36}, {2,9}, {23,26}, {4,26}, {1,41}, {16,37}, {9,28}, {13,37}, {13,30}, {14,28}, {10,20}, {6,44}, {15,22}, {17,23}, {3,35} }; // ET45.10 // Bipartite(20,25) Valencies [5,4] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 800 EdgePairs[45][10]:={ {17,41}, {15,43}, {8,28}, {6,37}, {5,32}, {19,24}, {1,24}, {2,26}, {17,28}, {2,30}, {19,26}, {4,44}, {20,38}, {7,41}, {7,31}, {1,37}, {1,40}, {8,23}, {5,27}, {11,24}, {16,23}, {15,44}, {8,25}, {20,21}, {9,44}, {18,33}, {10,30}, {13,26}, {19,22}, {8,24}, {11,38}, {6,43}, {10,45}, {6,32}, {17,42}, {5,23}, {13,32}, {15,21}, {4,33}, {16,40}, {5,31}, {15,31}, {7,40}, {8,33}, {4,38}, {13,42}, {19,27}, {13,33}, {11,35}, {1,21}, {3,25}, {13,39}, {9,36}, {9,27}, {5,45}, {12,41}, {12,34}, {12,23}, {12,37}, {18,30}, {9,42}, {14,40}, {18,31}, {16,35}, {9,34}, {7,38}, {15,28}, {11,36}, {20,34}, {10,39}, {20,25}, {4,22}, {3,39}, {2,28}, {18,37}, {19,43}, {12,22}, {14,27}, {1,42}, {3,41}, {6,35}, {11,45}, {2,35}, {2,34}, {16,39}, {10,22}, {10,21}, {14,29}, {20,32}, {17,45}, {17,29}, {14,25}, {6,29}, {18,36}, {3,43}, {3,36}, {14,30}, {16,44}, {7,26}, {4,29} }; // ET45.11 // Bipartite(20,25) Valencies [5,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 29491200 EdgePairs[45][11]:={ {14,39}, {9,40}, {19,45}, {2,38}, {4,42}, {11,23}, {5,42}, {5,30}, {8,36}, {9,45}, {13,24}, {5,34}, {1,25}, {7,33}, {20,23}, {19,40}, {10,40}, {6,32}, {13,27}, {4,44}, {14,42}, {11,22}, {12,25}, {3,31}, {17,44}, {5,26}, {20,40}, {10,23}, {8,22}, {16,21}, {15,34}, {10,34}, {2,41}, {7,41}, {8,33}, {9,43}, {4,39}, {18,33}, {1,22}, {6,21}, {4,28}, {7,29}, {10,31}, {16,26}, {10,37}, {14,28}, {14,45}, {13,35}, {4,45}, {16,29}, {11,28}, {3,27}, {6,26}, {2,35}, {17,33}, {14,44}, {12,35}, {6,29}, {18,27}, {19,43}, {20,37}, {15,26}, {12,38}, {5,38}, {2,43}, {3,35}, {1,23}, {12,43}, {15,42}, {8,27}, {7,44}, {17,37}, {3,24}, {19,36}, {11,25}, {11,21}, {3,39}, {17,41}, {18,30}, {17,29}, {20,34}, {7,37}, {15,38}, {12,41}, {2,25}, {1,28}, {18,36}, {20,31}, {9,32}, {6,24}, {18,22}, {8,30}, {13,31}, {9,36}, {19,32}, {16,32}, {15,30}, {1,21}, {13,39}, {16,24} }; // ET45.12 // Bipartite(15,30) Valencies [6,3] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 360 EdgePairs[45][12]:={ {11,30}, {1,26}, {12,27}, {3,40}, {6,37}, {13,19}, {2,44}, {6,34}, {10,40}, {4,41}, {5,24}, {8,31}, {2,32}, {14,18}, {2,29}, {5,29}, {4,34}, {13,34}, {14,26}, {8,23}, {12,16}, {14,39}, {5,43}, {1,36}, {3,27}, {12,45}, {8,25}, {3,38}, {15,27}, {4,31}, {6,40}, {8,29}, {6,32}, {7,36}, {13,43}, {1,38}, {3,44}, {4,18}, {2,16}, {7,43}, {1,16}, {3,28}, {2,20}, {10,23}, {15,19}, {8,33}, {5,28}, {1,21}, {9,36}, {11,32}, {4,21}, {9,33}, {11,22}, {9,42}, {3,31}, {12,24}, {15,17}, {7,25}, {15,25}, {7,35}, {13,38}, {7,20}, {13,23}, {10,39}, {14,33}, {10,42}, {2,19}, {15,41}, {5,18}, {12,42}, {12,35}, {6,17}, {11,41}, {11,45}, {11,39}, {14,37}, {9,30}, {10,21}, {14,44}, {15,26}, {1,22}, {4,35}, {9,28}, {13,30}, {7,37}, {10,20}, {8,45}, {5,22}, {9,17}, {6,24} }; // ET45.13 // Bipartite(15,30) Valencies [6,3] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7255941120 EdgePairs[45][13]:={ {3,32}, {3,22}, {1,26}, {15,35}, {5,33}, {12,27}, {6,34}, {8,31}, {14,18}, {5,29}, {11,17}, {9,16}, {12,33}, {6,26}, {8,21}, {5,43}, {2,43}, {3,42}, {1,36}, {4,40}, {8,25}, {9,38}, {11,27}, {15,29}, {11,37}, {1,31}, {3,24}, {12,43}, {6,36}, {2,33}, {11,21}, {4,30}, {15,45}, {6,16}, {5,23}, {13,32}, {7,27}, {3,44}, {7,32}, {13,40}, {1,16}, {15,19}, {4,45}, {10,34}, {13,42}, {5,19}, {2,38}, {1,21}, {2,18}, {9,36}, {4,20}, {12,23}, {12,37}, {10,44}, {13,20}, {14,40}, {15,25}, {7,22}, {10,29}, {8,35}, {10,24}, {13,22}, {8,41}, {5,39}, {10,39}, {4,25}, {2,28}, {3,34}, {10,19}, {14,38}, {9,18}, {11,41}, {15,39}, {2,23}, {14,20}, {7,17}, {9,26}, {1,41}, {7,42}, {4,35}, {9,28}, {13,30}, {14,28}, {7,37}, {12,17}, {8,45}, {11,31}, {6,44}, {6,24}, {14,30} }; // ET45.14 // Bipartite(15,30) Valencies [6,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23592960 EdgePairs[45][14]:={ {3,32}, {5,33}, {12,20}, {11,16}, {6,37}, {9,19}, {10,27}, {15,40}, {4,41}, {10,43}, {4,36}, {13,31}, {14,18}, {11,25}, {6,45}, {7,41}, {8,38}, {1,37}, {13,16}, {8,23}, {14,39}, {5,43}, {12,45}, {15,44}, {12,30}, {15,29}, {6,30}, {8,24}, {2,36}, {12,40}, {7,33}, {8,29}, {9,32}, {2,21}, {5,16}, {4,32}, {8,44}, {5,31}, {9,24}, {2,20}, {3,28}, {7,18}, {3,17}, {13,36}, {5,28}, {4,21}, {6,38}, {14,35}, {3,30}, {11,40}, {10,44}, {4,17}, {15,25}, {7,22}, {10,29}, {9,34}, {1,27}, {13,38}, {13,23}, {13,21}, {2,27}, {12,25}, {14,33}, {3,45}, {2,42}, {11,34}, {6,22}, {10,42}, {1,42}, {15,41}, {5,18}, {12,35}, {14,20}, {2,35}, {14,24}, {1,19}, {10,28}, {4,26}, {15,26}, {1,22}, {1,34}, {9,39}, {11,19}, {7,37}, {11,31}, {6,23}, {9,17}, {3,43}, {8,39}, {7,26} }; // ET45.15 // Bipartite(18,27) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 432 EdgePairs[45][15]:={ {11,43}, {9,40}, {2,38}, {4,42}, {12,39}, {18,44}, {14,34}, {5,42}, {5,30}, {3,38}, {7,40}, {10,27}, {8,36}, {7,24}, {9,45}, {11,29}, {10,43}, {4,40}, {17,35}, {16,23}, {7,27}, {1,44}, {3,30}, {14,42}, {6,40}, {13,43}, {12,27}, {14,35}, {13,42}, {6,45}, {16,41}, {2,19}, {15,32}, {6,22}, {2,29}, {1,29}, {18,24}, {7,28}, {12,21}, {11,34}, {17,23}, {15,34}, {9,27}, {2,41}, {13,33}, {7,26}, {8,28}, {10,25}, {18,38}, {1,22}, {6,33}, {12,34}, {4,33}, {4,28}, {10,39}, {16,26}, {7,25}, {3,22}, {10,37}, {5,19}, {15,35}, {8,26}, {14,43}, {1,19}, {15,33}, {5,28}, {10,29}, {17,36}, {18,35}, {6,31}, {18,32}, {15,31}, {2,21}, {6,30}, {5,45}, {14,31}, {1,39}, {13,32}, {14,23}, {4,22}, {5,31}, {15,37}, {9,24}, {11,25}, {8,20}, {11,21}, {3,21}, {1,41}, {3,44}, {16,44}, {3,39}, {17,41}, {8,25}, {13,23}, {8,45}, {17,38}, {11,20}, {17,26}, {18,36}, {9,36}, {16,32}, {13,37}, {12,37}, {2,30}, {12,20}, {4,19}, {9,20}, {16,24} }; // ET45.16 // Bipartite(18,27) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 216 EdgePairs[45][16]:={ {10,19}, {16,34}, {13,41}, {18,41}, {11,44}, {13,29}, {8,39}, {1,43}, {12,26}, {2,38}, {15,43}, {18,44}, {14,34}, {5,30}, {6,36}, {4,27}, {7,24}, {9,45}, {6,23}, {10,38}, {14,19}, {4,40}, {7,38}, {3,32}, {5,41}, {2,33}, {17,35}, {7,27}, {14,42}, {12,27}, {18,23}, {9,31}, {15,32}, {15,28}, {8,22}, {12,21}, {17,30}, {4,37}, {10,34}, {2,31}, {13,33}, {17,24}, {13,26}, {15,25}, {3,40}, {6,21}, {10,39}, {7,29}, {9,23}, {8,35}, {15,35}, {3,23}, {2,42}, {10,33}, {1,19}, {17,33}, {14,44}, {5,28}, {8,40}, {6,29}, {12,24}, {11,36}, {14,36}, {12,43}, {14,22}, {5,45}, {6,38}, {11,40}, {9,28}, {4,22}, {11,31}, {3,24}, {11,25}, {8,20}, {9,26}, {18,20}, {3,21}, {1,41}, {3,44}, {4,32}, {13,21}, {6,42}, {1,37}, {1,20}, {15,27}, {16,28}, {17,29}, {7,37}, {16,43}, {16,42}, {2,25}, {10,20}, {17,32}, {18,22}, {8,30}, {16,37}, {9,36}, {7,34}, {1,45}, {16,31}, {5,39}, {11,35}, {2,30}, {5,25}, {4,19}, {12,45}, {18,26}, {13,39} }; // ET45.17 // Bipartite(18,27) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 108 EdgePairs[45][17]:={ {11,43}, {13,41}, {5,32}, {7,39}, {10,21}, {1,43}, {4,42}, {12,39}, {2,22}, {9,42}, {5,30}, {11,29}, {6,23}, {1,40}, {4,40}, {13,24}, {1,25}, {15,44}, {12,31}, {1,38}, {5,41}, {10,44}, {13,43}, {17,42}, {12,27}, {14,35}, {13,38}, {6,45}, {3,34}, {2,28}, {9,31}, {16,41}, {13,20}, {5,21}, {10,23}, {11,45}, {17,23}, {15,34}, {10,34}, {2,41}, {18,33}, {13,26}, {10,25}, {15,25}, {6,33}, {4,29}, {14,28}, {7,20}, {8,35}, {6,37}, {4,31}, {1,19}, {15,19}, {12,28}, {15,33}, {12,35}, {18,19}, {1,35}, {11,26}, {2,44}, {4,38}, {5,22}, {9,44}, {17,22}, {18,32}, {14,36}, {16,27}, {14,22}, {8,27}, {8,43}, {14,37}, {9,28}, {3,24}, {17,37}, {12,36}, {8,23}, {9,26}, {18,29}, {17,21}, {10,42}, {11,32}, {18,30}, {8,25}, {7,32}, {9,29}, {2,26}, {8,45}, {18,45}, {11,20}, {7,21}, {3,20}, {14,40}, {3,36}, {3,37}, {6,24}, {16,38}, {6,27}, {7,34}, {15,30}, {3,33}, {7,36}, {17,40}, {5,39}, {16,31}, {16,39}, {2,30}, {4,19}, {16,24} }; // ET45.18 // Bipartite(18,27) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1296 EdgePairs[45][18]:={ {10,19}, {4,35}, {13,25}, {16,34}, {9,40}, {18,41}, {17,39}, {12,39}, {18,44}, {14,34}, {9,42}, {11,33}, {7,40}, {13,24}, {12,40}, {5,24}, {3,32}, {6,32}, {7,31}, {7,27}, {4,44}, {1,32}, {16,20}, {17,42}, {18,21}, {13,38}, {3,34}, {16,33}, {10,23}, {3,19}, {5,37}, {15,39}, {17,23}, {5,33}, {9,27}, {2,23}, {13,26}, {15,25}, {1,22}, {2,36}, {7,25}, {3,22}, {14,28}, {10,37}, {4,43}, {10,24}, {8,35}, {14,43}, {4,45}, {4,31}, {15,45}, {2,42}, {4,30}, {10,33}, {1,19}, {12,29}, {13,30}, {9,25}, {8,19}, {11,26}, {6,29}, {17,36}, {18,35}, {5,22}, {9,44}, {2,43}, {16,27}, {18,28}, {6,38}, {8,38}, {14,37}, {5,36}, {3,26}, {5,31}, {8,20}, {8,23}, {11,21}, {6,20}, {11,30}, {1,41}, {11,27}, {6,42}, {13,21}, {3,39}, {17,34}, {7,22}, {15,41}, {16,28}, {15,38}, {11,20}, {16,43}, {12,41}, {14,29}, {14,40}, {1,28}, {18,31}, {17,26}, {9,32}, {6,44}, {10,35}, {7,36}, {12,37}, {2,30}, {1,21}, {15,24}, {12,45}, {8,29}, {2,45} }; // ET45.19 // Bipartite(18,27) Valencies [6,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 216 EdgePairs[45][19]:={ {7,19}, {14,21}, {10,21}, {15,23}, {11,23}, {12,39}, {15,43}, {9,42}, {8,36}, {5,35}, {4,40}, {13,24}, {11,42}, {1,25}, {7,33}, {3,32}, {9,19}, {4,44}, {3,30}, {1,32}, {13,43}, {6,40}, {8,42}, {6,45}, {2,28}, {16,33}, {6,22}, {10,30}, {14,27}, {5,37}, {8,22}, {12,21}, {6,43}, {1,34}, {11,34}, {17,31}, {9,38}, {4,37}, {13,44}, {10,36}, {17,24}, {7,41}, {8,33}, {18,38}, {3,40}, {12,34}, {10,39}, {7,29}, {4,43}, {5,19}, {7,20}, {18,25}, {14,45}, {16,29}, {15,45}, {2,34}, {14,26}, {2,40}, {2,35}, {17,33}, {14,44}, {1,35}, {11,26}, {18,27}, {15,26}, {12,23}, {11,41}, {16,27}, {5,45}, {18,28}, {14,31}, {8,38}, {2,39}, {5,20}, {4,22}, {3,28}, {12,36}, {8,20}, {6,20}, {18,29}, {11,30}, {13,21}, {3,39}, {1,37}, {10,42}, {15,27}, {16,28}, {9,29}, {13,23}, {17,38}, {12,41}, {2,25}, {18,31}, {9,41}, {3,37}, {17,32}, {6,35}, {13,31}, {10,26}, {5,44}, {16,32}, {7,36}, {1,30}, {15,24}, {4,19}, {17,25}, {9,22}, {16,24} }; // ET45.20 // Bipartite(18,27) Valencies [6,4] // Diameter 9 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 92876046336 EdgePairs[45][20]:={ {10,19}, {13,25}, {9,40}, {7,39}, {2,38}, {18,40}, {12,39}, {12,19}, {9,42}, {4,27}, {16,30}, {11,29}, {2,20}, {15,44}, {18,42}, {13,34}, {16,23}, {13,27}, {1,44}, {11,38}, {10,44}, {3,30}, {13,43}, {17,43}, {7,23}, {8,34}, {9,31}, {14,20}, {16,41}, {8,41}, {2,29}, {11,45}, {3,19}, {18,24}, {12,21}, {12,30}, {16,21}, {17,23}, {7,41}, {18,33}, {6,33}, {2,36}, {4,43}, {10,37}, {15,35}, {13,45}, {14,38}, {4,45}, {5,29}, {6,26}, {1,19}, {12,28}, {4,36}, {7,30}, {15,33}, {4,25}, {1,35}, {1,26}, {15,26}, {9,33}, {5,22}, {11,36}, {2,27}, {5,38}, {15,42}, {14,22}, {10,28}, {14,31}, {8,43}, {8,32}, {5,20}, {3,28}, {5,31}, {9,24}, {8,23}, {3,21}, {11,27}, {6,42}, {3,39}, {17,34}, {1,37}, {17,41}, {8,25}, {7,32}, {13,36}, {11,20}, {7,21}, {14,29}, {14,40}, {1,28}, {18,31}, {3,37}, {6,24}, {6,35}, {17,32}, {18,22}, {10,26}, {6,44}, {4,34}, {10,35}, {16,32}, {12,37}, {16,39}, {15,24}, {5,40}, {17,25}, {2,45}, {9,22} }; // ET45.21 // Bipartite(18,27) Valencies [6,4] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 725594112 EdgePairs[45][21]:={ {11,43}, {7,19}, {7,42}, {5,32}, {12,26}, {2,38}, {11,23}, {9,30}, {3,29}, {3,38}, {6,36}, {10,27}, {18,39}, {8,36}, {7,24}, {2,20}, {4,40}, {12,40}, {7,33}, {12,31}, {15,44}, {12,22}, {5,41}, {2,33}, {6,25}, {9,39}, {16,23}, {1,44}, {9,21}, {10,44}, {17,42}, {18,21}, {6,45}, {3,34}, {16,41}, {10,45}, {16,33}, {6,34}, {8,41}, {2,29}, {14,27}, {5,37}, {7,28}, {6,43}, {11,34}, {15,39}, {17,31}, {9,38}, {5,23}, {4,20}, {10,36}, {17,24}, {4,29}, {5,19}, {18,25}, {14,45}, {15,35}, {4,31}, {2,42}, {18,34}, {1,19}, {17,33}, {5,28}, {13,30}, {12,35}, {1,35}, {1,26}, {15,26}, {4,38}, {2,24}, {11,41}, {17,22}, {14,36}, {15,21}, {12,44}, {14,22}, {8,27}, {14,31}, {8,32}, {4,22}, {11,25}, {13,28}, {8,23}, {18,43}, {13,21}, {1,37}, {11,32}, {18,30}, {9,29}, {3,25}, {8,45}, {7,37}, {3,20}, {16,42}, {14,40}, {1,28}, {10,26}, {3,43}, {6,27}, {10,35}, {13,19}, {13,37}, {15,30}, {16,32}, {17,40}, {9,20}, {13,39}, {16,24} }; // ET45.22 // Bipartite(18,27) Valencies [6,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 663552 EdgePairs[45][22]:={ {10,19}, {7,42}, {7,39}, {15,23}, {8,39}, {8,24}, {17,39}, {15,43}, {2,22}, {17,27}, {5,42}, {3,38}, {11,33}, {5,35}, {6,23}, {17,19}, {7,38}, {1,25}, {12,40}, {2,33}, {1,44}, {9,21}, {10,44}, {3,30}, {14,42}, {1,32}, {11,22}, {13,43}, {12,27}, {14,35}, {18,21}, {8,34}, {15,29}, {2,28}, {9,31}, {14,20}, {12,25}, {6,34}, {13,20}, {15,28}, {18,24}, {17,45}, {12,30}, {6,43}, {5,23}, {15,34}, {4,20}, {2,41}, {13,33}, {17,24}, {7,26}, {10,25}, {3,40}, {4,33}, {10,41}, {7,29}, {16,26}, {4,43}, {10,37}, {13,45}, {6,37}, {4,45}, {16,29}, {11,28}, {3,27}, {4,30}, {1,19}, {2,40}, {4,36}, {14,44}, {12,35}, {13,30}, {8,19}, {6,29}, {11,41}, {12,38}, {18,32}, {3,35}, {2,21}, {8,27}, {14,31}, {14,23}, {5,20}, {11,40}, {5,31}, {15,37}, {9,24}, {16,22}, {11,21}, {9,26}, {1,41}, {17,34}, {1,37}, {7,22}, {3,25}, {10,32}, {8,45}, {13,36}, {16,42}, {18,31}, {18,36}, {9,32}, {16,38}, {9,36}, {5,44}, {16,39}, {18,26}, {6,28} }; // ET45.23 // Non-bipartite Valency 6 // Diameter 7 Girth 4 // Has twins VT AT // Automorphism group of order 14105549537280 EdgePairs[45][23]:={ {1,15}, {11,43}, {7,19}, {27,39}, {13,25}, {7,42}, {6,39}, {9,40}, {11,44}, {14,25}, {3,15}, {21,31}, {10,22}, {11,23}, {6,18}, {9,42}, {16,30}, {6,17}, {7,40}, {10,43}, {28,40}, {32,45}, {4,16}, {12,22}, {33,43}, {19,31}, {22,35}, {9,19}, {13,27}, {9,21}, {10,44}, {11,22}, {27,38}, {8,42}, {22,36}, {33,44}, {19,33}, {3,34}, {10,45}, {2,15}, {24,34}, {31,44}, {8,41}, {10,23}, {14,27}, {11,45}, {5,37}, {28,41}, {1,34}, {2,14}, {27,37}, {17,30}, {4,37}, {20,33}, {7,41}, {33,45}, {4,39}, {1,36}, {29,42}, {13,26}, {3,13}, {15,25}, {29,40}, {26,38}, {2,36}, {8,21}, {3,14}, {2,13}, {30,40}, {10,24}, {7,20}, {6,37}, {32,43}, {16,29}, {31,43}, {2,34}, {21,33}, {14,26}, {4,17}, {2,35}, {26,37}, {25,38}, {1,35}, {8,19}, {8,40}, {12,24}, {15,26}, {31,45}, {4,38}, {12,23}, {25,37}, {5,38}, {12,44}, {3,35}, {25,39}, {12,43}, {18,28}, {6,38}, {20,32}, {5,17}, {29,41}, {22,34}, {8,20}, {24,35}, {6,16}, {21,32}, {1,14}, {18,29}, {26,39}, {15,27}, {1,13}, {4,18}, {18,30}, {16,28}, {17,29}, {28,42}, {30,41}, {7,21}, {30,42}, {3,36}, {9,41}, {20,31}, {17,28}, {5,18}, {23,34}, {19,32}, {23,35}, {32,44}, {11,24}, {5,16}, {5,39}, {23,36}, {9,20}, {12,45}, {24,36} }; // ET45.24 // Non-bipartite Valency 6 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 77760 EdgePairs[45][24]:={ {14,39}, {10,19}, {20,27}, {19,45}, {21,43}, {6,12}, {24,33}, {5,14}, {22,32}, {35,44}, {9,30}, {35,40}, {2,22}, {5,42}, {3,38}, {27,32}, {11,33}, {3,7}, {4,27}, {18,39}, {38,45}, {1,40}, {28,37}, {12,17}, {6,13}, {27,34}, {12,31}, {18,42}, {24,29}, {13,34}, {1,9}, {7,31}, {6,25}, {16,40}, {16,23}, {22,44}, {21,25}, {6,40}, {34,45}, {14,35}, {22,28}, {24,45}, {6,45}, {14,20}, {31,41}, {5,26}, {9,17}, {23,30}, {21,28}, {32,39}, {8,15}, {12,21}, {7,28}, {11,34}, {3,11}, {2,41}, {10,36}, {17,24}, {1,10}, {19,30}, {9,43}, {19,26}, {8,18}, {15,36}, {4,28}, {10,16}, {25,33}, {4,43}, {18,25}, {7,13}, {3,23}, {34,41}, {5,29}, {26,31}, {28,36}, {11,18}, {12,35}, {4,15}, {13,22}, {39,43}, {37,44}, {30,34}, {33,42}, {9,33}, {4,11}, {3,42}, {36,42}, {36,43}, {15,21}, {31,38}, {29,35}, {16,27}, {6,30}, {2,39}, {7,44}, {14,23}, {2,12}, {8,32}, {20,44}, {17,37}, {23,31}, {19,42}, {30,39}, {7,16}, {29,38}, {2,8}, {1,37}, {1,27}, {17,41}, {5,10}, {20,29}, {3,25}, {2,26}, {8,45}, {10,32}, {33,37}, {15,38}, {11,20}, {25,35}, {21,40}, {9,14}, {26,36}, {17,26}, {18,22}, {16,38}, {23,43}, {4,41}, {5,44}, {13,19}, {13,37}, {15,24}, {32,40}, {20,41}, {1,24}, {8,29} }; // ET45.25 // Non-bipartite Valency 6 // Diameter 4 Girth 3 // Twin-free VT AT // Automorphism group of order 2160 EdgePairs[45][25]:={ {21,23}, {1,11}, {38,42}, {29,45}, {11,20}, {12,29}, {7,15}, {29,40}, {4,26}, {35,42}, {3,8}, {4,16}, {32,40}, {11,25}, {6,17}, {2,23}, {5,38}, {17,34}, {10,26}, {21,35}, {3,37}, {12,35}, {2,9}, {8,25}, {2,28}, {1,30}, {14,28}, {8,31}, {28,43}, {23,44}, {3,18}, {39,40}, {15,45}, {15,29}, {22,45}, {6,31}, {4,10}, {1,7}, {8,19}, {35,38}, {9,32}, {9,27}, {5,11}, {31,42}, {2,10}, {2,38}, {24,43}, {39,43}, {8,14}, {19,22}, {7,39}, {22,41}, {5,25}, {24,42}, {15,26}, {17,23}, {3,12}, {10,28}, {22,27}, {21,44}, {1,22}, {6,12}, {6,43}, {28,41}, {14,16}, {13,18}, {30,42}, {24,26}, {7,26}, {5,18}, {16,32}, {13,44}, {11,30}, {23,25}, {15,34}, {36,40}, {18,24}, {19,31}, {9,20}, {18,36}, {15,17}, {33,41}, {20,43}, {18,33}, {3,29}, {21,33}, {8,37}, {13,36}, {17,31}, {29,32}, {16,22}, {25,40}, {26,42}, {13,30}, {2,17}, {9,13}, {12,27}, {6,27}, {28,33}, {1,39}, {27,41}, {19,45}, {36,39}, {19,36}, {13,27}, {37,44}, {14,25}, {23,40}, {4,37}, {5,33}, {3,24}, {16,35}, {20,34}, {10,36}, {1,16}, {20,24}, {30,44}, {14,43}, {38,45}, {9,38}, {10,19}, {14,35}, {5,45}, {30,31}, {6,39}, {7,33}, {11,34}, {37,41}, {4,44}, {20,32}, {7,21}, {4,32}, {34,41}, {34,37}, {12,21} }; // ET45.26 // Bipartite(9,36) Valencies [8,2] // Diameter 4 Girth 6 // Twin-free Non-VT Non-AT // Automorphism group of order 362880 EdgePairs[45][26]:={ {2,11}, {5,12}, {5,33}, {4,13}, {8,19}, {8,28}, {6,39}, {5,24}, {1,29}, {1,30}, {9,25}, {4,44}, {7,23}, {2,10}, {7,31}, {1,37}, {1,10}, {6,14}, {5,43}, {2,43}, {2,40}, {4,40}, {3,38}, {9,15}, {1,20}, {2,36}, {9,11}, {2,45}, {6,36}, {9,32}, {5,16}, {8,27}, {1,38}, {4,12}, {7,32}, {1,15}, {3,16}, {6,20}, {8,42}, {4,21}, {9,27}, {9,33}, {8,13}, {3,14}, {3,18}, {3,31}, {4,17}, {5,30}, {3,26}, {7,21}, {8,35}, {8,41}, {7,19}, {3,34}, {6,22}, {9,18}, {1,42}, {3,41}, {6,25}, {7,39}, {2,23}, {5,35}, {2,34}, {4,26}, {6,28}, {7,37}, {8,45}, {6,44}, {5,22}, {7,24}, {9,17}, {4,29} }; // ET45.27 // Bipartite(9,36) Valencies [8,2] // Diameter 9 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 47552535724032 EdgePairs[45][27]:={ {2,11}, {1,26}, {1,44}, {3,12}, {4,36}, {6,33}, {2,29}, {5,29}, {4,34}, {7,23}, {7,41}, {9,31}, {1,37}, {7,12}, {8,16}, {8,23}, {1,10}, {6,26}, {3,21}, {5,40}, {8,25}, {5,11}, {4,43}, {9,15}, {2,36}, {3,37}, {2,45}, {4,16}, {6,15}, {7,30}, {8,32}, {5,20}, {8,43}, {4,18}, {7,32}, {5,31}, {9,24}, {2,20}, {3,28}, {4,45}, {9,40}, {5,38}, {2,38}, {2,18}, {4,27}, {9,33}, {3,19}, {3,30}, {9,42}, {6,42}, {7,21}, {8,34}, {8,41}, {9,13}, {2,27}, {1,17}, {4,25}, {3,39}, {9,22}, {1,28}, {6,35}, {6,17}, {7,39}, {8,14}, {5,13}, {1,19}, {1,35}, {7,14}, {6,44}, {5,22}, {6,24}, {3,10} }; // ET45.28 // Bipartite(9,36) Valencies [8,2] // Diameter 6 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 18874368 EdgePairs[45][28]:={ {2,11}, {3,22}, {4,13}, {8,19}, {3,40}, {8,28}, {4,39}, {5,32}, {4,23}, {9,19}, {1,14}, {6,34}, {9,23}, {4,41}, {2,30}, {2,29}, {4,44}, {1,32}, {7,12}, {1,40}, {1,10}, {6,26}, {5,43}, {8,21}, {3,42}, {3,27}, {9,15}, {2,36}, {4,31}, {8,24}, {6,43}, {3,24}, {7,33}, {2,12}, {9,37}, {7,30}, {7,45}, {6,16}, {8,10}, {5,20}, {7,27}, {8,37}, {5,25}, {2,31}, {1,16}, {5,38}, {8,42}, {2,18}, {4,21}, {9,33}, {5,17}, {7,15}, {3,18}, {9,41}, {7,38}, {9,35}, {7,20}, {3,45}, {1,28}, {5,14}, {6,25}, {5,35}, {6,11}, {4,26}, {1,22}, {2,13}, {1,34}, {6,29}, {6,44}, {9,17}, {3,36}, {8,39} }; // ET45.29 // Bipartite(15,30) Valencies [8,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[45][29]:={ {13,41}, {7,39}, {15,23}, {8,31}, {8,24}, {12,26}, {10,22}, {9,30}, {12,19}, {14,34}, {3,29}, {11,33}, {1,31}, {6,17}, {12,16}, {11,29}, {10,38}, {2,20}, {13,24}, {11,42}, {14,18}, {12,40}, {15,44}, {7,31}, {9,39}, {6,25}, {7,27}, {15,40}, {1,44}, {9,21}, {10,44}, {12,18}, {14,42}, {13,42}, {6,45}, {3,31}, {2,19}, {5,26}, {9,17}, {6,22}, {5,21}, {10,23}, {15,28}, {2,29}, {5,37}, {8,44}, {7,28}, {6,43}, {11,34}, {13,16}, {9,38}, {4,20}, {2,41}, {4,39}, {15,25}, {1,22}, {2,32}, {6,33}, {1,16}, {12,34}, {2,17}, {10,37}, {8,35}, {14,43}, {15,20}, {4,45}, {8,17}, {11,28}, {3,27}, {4,30}, {14,26}, {11,37}, {13,40}, {7,35}, {4,38}, {3,42}, {5,22}, {5,38}, {15,21}, {2,21}, {12,43}, {5,27}, {10,28}, {8,43}, {14,23}, {12,36}, {6,16}, {9,18}, {4,32}, {3,39}, {11,32}, {15,27}, {4,18}, {8,25}, {7,32}, {9,29}, {13,23}, {13,36}, {1,33}, {3,36}, {9,41}, {10,20}, {14,41}, {3,37}, {6,35}, {8,30}, {10,26}, {7,34}, {3,33}, {1,45}, {13,19}, {7,36}, {1,30}, {11,35}, {5,25}, {4,19}, {14,24}, {5,40}, {1,24}, {2,45} }; // ET45.30 // Bipartite(15,30) Valencies [8,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[45][30]:={ {4,35}, {11,43}, {7,39}, {13,29}, {14,25}, {6,18}, {2,22}, {6,17}, {12,16}, {10,27}, {5,35}, {7,24}, {10,38}, {2,20}, {13,24}, {7,38}, {1,25}, {14,18}, {7,33}, {15,44}, {12,22}, {10,40}, {2,33}, {6,32}, {7,45}, {9,21}, {11,16}, {4,44}, {12,27}, {3,31}, {5,26}, {9,17}, {15,32}, {15,28}, {10,30}, {3,18}, {8,22}, {12,21}, {11,34}, {1,34}, {14,33}, {9,38}, {5,33}, {5,23}, {4,37}, {15,34}, {2,23}, {1,36}, {13,26}, {3,40}, {1,16}, {9,34}, {4,28}, {15,36}, {7,25}, {3,22}, {4,43}, {5,43}, {5,19}, {10,24}, {8,35}, {14,45}, {8,26}, {13,35}, {2,42}, {3,27}, {2,40}, {7,30}, {14,44}, {13,30}, {10,29}, {11,37}, {11,26}, {8,40}, {6,29}, {14,32}, {6,31}, {11,41}, {3,42}, {15,21}, {15,31}, {1,23}, {6,30}, {5,45}, {8,27}, {11,19}, {1,39}, {6,38}, {14,31}, {2,39}, {8,43}, {14,23}, {3,28}, {9,24}, {12,36}, {8,20}, {15,16}, {11,21}, {1,41}, {3,44}, {4,32}, {10,42}, {12,42}, {4,18}, {9,29}, {13,17}, {12,41}, {2,25}, {8,37}, {10,20}, {9,41}, {9,36}, {1,45}, {13,19}, {13,37}, {7,17}, {5,39}, {12,20}, {4,19}, {6,28} }; // ET45.31 // Bipartite(15,30) Valencies [8,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[45][31]:={ {14,39}, {7,42}, {13,41}, {10,21}, {13,29}, {8,31}, {12,39}, {9,30}, {6,36}, {11,33}, {13,18}, {5,35}, {7,24}, {9,45}, {10,38}, {11,29}, {4,40}, {4,16}, {12,17}, {10,40}, {1,38}, {5,41}, {2,33}, {12,33}, {9,39}, {6,25}, {11,16}, {10,44}, {11,38}, {3,30}, {13,42}, {7,23}, {6,45}, {14,20}, {2,18}, {8,41}, {15,28}, {3,19}, {11,45}, {1,29}, {8,22}, {12,21}, {11,34}, {1,34}, {2,23}, {1,36}, {14,16}, {6,33}, {1,16}, {10,41}, {8,18}, {2,17}, {4,28}, {3,22}, {10,37}, {14,45}, {15,20}, {15,35}, {4,31}, {3,27}, {2,34}, {4,30}, {6,26}, {1,19}, {4,36}, {13,30}, {1,26}, {2,44}, {12,24}, {15,26}, {3,42}, {6,19}, {5,38}, {15,21}, {2,43}, {12,43}, {14,22}, {5,27}, {8,27}, {10,28}, {7,18}, {14,31}, {2,39}, {7,44}, {8,43}, {14,23}, {5,20}, {9,28}, {5,17}, {15,37}, {11,25}, {4,32}, {12,42}, {15,27}, {8,25}, {3,25}, {7,32}, {15,17}, {7,21}, {12,32}, {14,40}, {3,37}, {6,24}, {6,35}, {9,32}, {10,26}, {3,43}, {9,36}, {13,31}, {5,44}, {13,19}, {7,34}, {13,37}, {4,23}, {11,35}, {5,40}, {9,20}, {1,24}, {8,29}, {9,22} }; // ET45.32 // Bipartite(15,30) Valencies [8,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 120 EdgePairs[45][32]:={ {10,19}, {14,39}, {7,42}, {10,21}, {12,26}, {2,38}, {11,23}, {6,36}, {13,18}, {4,27}, {7,40}, {10,27}, {11,29}, {10,38}, {1,40}, {13,24}, {5,34}, {14,18}, {4,16}, {12,22}, {12,33}, {6,25}, {15,40}, {1,44}, {9,21}, {11,38}, {4,44}, {14,42}, {1,32}, {9,37}, {8,42}, {14,35}, {7,23}, {8,34}, {3,45}, {13,38}, {15,29}, {14,20}, {5,26}, {9,17}, {15,28}, {3,19}, {11,45}, {5,37}, {8,22}, {3,41}, {12,30}, {1,34}, {6,43}, {5,23}, {15,22}, {2,41}, {2,31}, {9,43}, {2,16}, {15,25}, {2,32}, {3,40}, {1,16}, {2,17}, {7,25}, {10,24}, {14,45}, {8,26}, {15,35}, {4,31}, {4,30}, {6,26}, {10,33}, {11,18}, {2,35}, {13,30}, {4,25}, {11,37}, {12,24}, {14,32}, {9,33}, {11,41}, {6,19}, {2,43}, {12,44}, {14,22}, {8,27}, {1,39}, {7,18}, {8,43}, {5,20}, {9,28}, {8,16}, {5,17}, {5,31}, {13,28}, {6,20}, {3,21}, {11,27}, {3,44}, {10,42}, {15,41}, {9,29}, {10,32}, {13,36}, {3,20}, {7,21}, {1,33}, {1,28}, {3,17}, {6,35}, {6,24}, {9,36}, {13,31}, {7,34}, {15,30}, {7,36}, {4,23}, {12,37}, {5,39}, {4,19}, {12,45}, {8,29}, {13,39} }; // ET45.33 // Bipartite(15,30) Valencies [8,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 11796480 EdgePairs[45][33]:={ {11,43}, {7,42}, {10,21}, {13,29}, {11,17}, {8,31}, {11,23}, {6,18}, {12,39}, {15,43}, {5,42}, {5,30}, {1,31}, {7,40}, {6,23}, {2,20}, {4,40}, {13,24}, {5,34}, {10,40}, {7,31}, {12,33}, {7,27}, {9,19}, {1,44}, {9,21}, {12,18}, {10,44}, {11,38}, {14,42}, {11,22}, {9,37}, {12,27}, {14,35}, {2,28}, {3,34}, {14,20}, {4,26}, {15,28}, {3,19}, {14,27}, {1,29}, {3,18}, {12,21}, {1,34}, {5,23}, {13,44}, {10,36}, {2,31}, {8,33}, {4,39}, {10,25}, {2,16}, {6,33}, {3,40}, {1,16}, {8,18}, {9,34}, {15,36}, {7,25}, {5,19}, {13,45}, {8,17}, {11,28}, {15,45}, {14,26}, {1,19}, {2,35}, {13,30}, {4,25}, {10,29}, {1,26}, {11,37}, {13,22}, {6,29}, {12,24}, {15,26}, {4,38}, {14,32}, {2,24}, {5,38}, {14,17}, {15,21}, {2,43}, {5,27}, {5,45}, {9,35}, {6,38}, {2,39}, {8,32}, {3,28}, {8,16}, {12,36}, {7,16}, {6,20}, {10,17}, {1,41}, {12,42}, {11,32}, {7,22}, {15,41}, {3,25}, {10,32}, {8,45}, {7,37}, {14,41}, {6,35}, {8,30}, {9,36}, {3,43}, {6,44}, {4,41}, {3,33}, {13,37}, {15,30}, {4,23}, {4,24}, {9,20}, {9,22}, {13,39} }; // ET45.34 // Bipartite(15,30) Valencies [8,4] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1966080 EdgePairs[45][34]:={ {4,35}, {7,19}, {11,43}, {7,42}, {7,39}, {13,29}, {14,25}, {11,23}, {5,42}, {5,30}, {1,31}, {6,17}, {8,36}, {7,24}, {10,43}, {2,20}, {13,24}, {12,40}, {15,44}, {10,40}, {6,32}, {9,39}, {7,27}, {9,19}, {13,27}, {1,44}, {9,21}, {11,16}, {11,38}, {13,42}, {14,35}, {15,29}, {9,31}, {14,20}, {12,25}, {10,45}, {3,31}, {6,34}, {8,41}, {10,18}, {6,22}, {10,30}, {5,37}, {1,29}, {3,18}, {1,34}, {15,39}, {4,20}, {13,44}, {8,33}, {10,25}, {2,32}, {1,16}, {8,21}, {8,18}, {2,17}, {4,33}, {9,34}, {15,36}, {8,26}, {6,37}, {4,45}, {11,28}, {2,42}, {4,30}, {10,33}, {1,19}, {12,28}, {2,35}, {12,35}, {1,26}, {11,26}, {6,29}, {15,26}, {4,38}, {12,23}, {14,32}, {11,41}, {5,22}, {12,38}, {2,27}, {6,19}, {14,17}, {15,21}, {12,43}, {14,22}, {5,27}, {5,45}, {10,28}, {8,38}, {13,32}, {14,37}, {3,28}, {11,31}, {9,24}, {8,23}, {3,21}, {1,41}, {7,22}, {3,16}, {4,18}, {15,41}, {7,37}, {13,17}, {14,40}, {3,36}, {9,36}, {3,43}, {6,44}, {9,16}, {7,34}, {3,33}, {4,23}, {2,30}, {12,20}, {15,24}, {5,25}, {5,40}, {2,45}, {13,39} }; // ET45.35 // Bipartite(21,24) Valencies [8,7] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 336 EdgePairs[45][35]:={ {2,44}, {13,32}, {9,28}, {16,33}, {4,26}, {17,38}, {12,45}, {18,32}, {8,30}, {16,40}, {2,23}, {9,45}, {5,38}, {12,22}, {12,32}, {15,31}, {4,29}, {1,32}, {3,43}, {1,40}, {17,34}, {15,44}, {12,42}, {3,37}, {17,24}, {21,43}, {8,25}, {2,41}, {18,41}, {5,32}, {16,23}, {14,28}, {9,35}, {8,44}, {4,23}, {13,29}, {12,37}, {6,22}, {18,42}, {10,30}, {19,28}, {3,34}, {2,25}, {14,23}, {11,33}, {6,40}, {14,33}, {2,36}, {10,38}, {19,40}, {17,37}, {14,36}, {19,30}, {9,27}, {15,40}, {8,41}, {2,38}, {19,22}, {7,39}, {4,42}, {7,32}, {10,41}, {7,43}, {20,31}, {2,35}, {11,44}, {1,22}, {15,27}, {6,30}, {6,43}, {21,26}, {10,31}, {13,22}, {18,30}, {7,26}, {6,33}, {18,43}, {11,29}, {20,44}, {15,35}, {5,24}, {9,37}, {17,27}, {12,28}, {12,25}, {14,42}, {1,45}, {15,34}, {8,22}, {13,25}, {1,28}, {3,27}, {14,37}, {1,33}, {3,26}, {21,33}, {21,38}, {18,31}, {7,31}, {10,43}, {1,24}, {12,23}, {13,24}, {11,24}, {5,31}, {11,39}, {8,40}, {20,23}, {20,39}, {21,29}, {1,39}, {18,25}, {17,29}, {20,25}, {16,44}, {19,45}, {6,41}, {6,28}, {5,39}, {20,35}, {4,37}, {11,26}, {10,35}, {16,36}, {6,36}, {3,30}, {8,34}, {2,29}, {16,35}, {10,27}, {4,34}, {10,36}, {18,22}, {13,41}, {20,42}, {11,40}, {9,36}, {14,43}, {5,27}, {3,42}, {16,39}, {13,38}, {9,38}, {4,25}, {17,45}, {5,45}, {21,36}, {7,24}, {15,39}, {3,31}, {17,26}, {7,33}, {11,34}, {21,24}, {13,45}, {15,30}, {19,34}, {5,35}, {21,41}, {16,28}, {7,42}, {9,23}, {4,44}, {19,37}, {20,32}, {8,29}, {19,27}, {14,26} }; // ET45.36 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[45][36]:={ {2,44}, {10,24}, {5,17}, {38,42}, {6,16}, {36,38}, {18,29}, {31,44}, {1,13}, {30,33}, {39,42}, {39,41}, {25,38}, {3,13}, {32,34}, {24,27}, {3,43}, {3,15}, {33,45}, {2,15}, {3,35}, {2,4}, {25,30}, {11,14}, {29,41}, {21,22}, {17,21}, {10,44}, {8,10}, {6,7}, {2,14}, {29,42}, {38,40}, {3,5}, {13,16}, {10,15}, {10,22}, {32,36}, {31,43}, {2,45}, {16,30}, {4,38}, {7,12}, {36,37}, {2,34}, {2,36}, {26,28}, {8,19}, {7,11}, {7,20}, {4,8}, {18,20}, {27,30}, {1,5}, {31,35}, {33,43}, {8,41}, {34,38}, {27,29}, {12,44}, {26,29}, {22,35}, {19,22}, {9,41}, {11,13}, {15,26}, {23,34}, {11,22}, {25,28}, {22,27}, {23,36}, {15,27}, {3,44}, {12,13}, {20,33}, {23,26}, {37,40}, {9,42}, {14,16}, {6,18}, {12,43}, {24,26}, {18,30}, {3,4}, {11,23}, {2,6}, {8,11}, {23,25}, {40,43}, {1,45}, {13,25}, {26,38}, {9,10}, {19,31}, {9,20}, {24,34}, {4,7}, {21,31}, {15,17}, {10,45}, {31,36}, {1,43}, {30,32}, {21,33}, {24,35}, {25,37}, {29,32}, {33,35}, {28,40}, {17,28}, {22,25}, {32,45}, {33,34}, {8,21}, {14,18}, {12,23}, {30,40}, {28,33}, {30,41}, {8,40}, {40,45}, {20,23}, {42,43}, {18,19}, {17,29}, {17,19}, {28,42}, {34,39}, {9,12}, {6,9}, {35,37}, {41,44}, {12,15}, {1,35}, {41,45}, {14,25}, {5,39}, {16,21}, {19,32}, {4,37}, {13,26}, {15,18}, {32,44}, {5,8}, {29,31}, {42,44}, {16,20}, {20,24}, {6,38}, {4,18}, {5,9}, {27,37}, {26,39}, {11,45}, {12,24}, {28,31}, {27,39}, {1,14}, {1,6}, {6,39}, {35,39}, {10,14}, {21,24}, {11,43}, {13,17}, {22,36}, {19,23}, {1,34}, {5,37}, {37,41}, {7,19}, {4,17}, {9,21}, {3,36}, {16,28}, {7,40}, {7,42}, {20,32}, {14,27}, {5,16} }; // ET45.37 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[45][37]:={ {36,44}, {3,33}, {10,24}, {2,33}, {17,44}, {5,34}, {8,12}, {16,26}, {21,40}, {33,39}, {4,30}, {16,27}, {25,39}, {26,31}, {16,40}, {22,37}, {1,13}, {9,45}, {12,22}, {25,38}, {15,31}, {4,29}, {1,32}, {3,13}, {23,28}, {32,37}, {3,15}, {10,23}, {20,40}, {7,44}, {17,20}, {2,15}, {4,19}, {16,19}, {25,33}, {12,42}, {21,42}, {2,4}, {5,20}, {9,43}, {26,33}, {11,41}, {11,14}, {7,36}, {18,21}, {17,21}, {8,10}, {18,41}, {2,14}, {27,44}, {20,30}, {8,44}, {3,5}, {9,11}, {16,43}, {6,29}, {19,28}, {3,34}, {7,12}, {31,39}, {14,33}, {2,34}, {26,45}, {7,11}, {15,32}, {19,30}, {1,5}, {15,40}, {8,45}, {14,40}, {11,15}, {24,39}, {1,31}, {10,41}, {11,22}, {7,43}, {2,35}, {12,13}, {4,21}, {27,31}, {9,34}, {30,39}, {10,40}, {13,31}, {26,37}, {3,32}, {29,37}, {4,35}, {23,37}, {15,41}, {18,44}, {19,42}, {3,4}, {13,33}, {18,43}, {5,30}, {2,6}, {19,41}, {36,45}, {17,27}, {28,37}, {14,42}, {8,22}, {29,38}, {32,38}, {26,38}, {9,10}, {8,35}, {18,26}, {23,38}, {25,45}, {10,13}, {35,45}, {22,29}, {5,28}, {9,22}, {34,44}, {4,36}, {20,29}, {25,32}, {16,45}, {22,39}, {12,23}, {11,24}, {17,25}, {33,37}, {12,40}, {21,29}, {18,19}, {18,25}, {6,19}, {34,43}, {17,41}, {27,32}, {12,15}, {6,28}, {24,38}, {1,35}, {13,42}, {28,39}, {25,43}, {7,23}, {6,36}, {8,34}, {16,20}, {14,32}, {8,24}, {13,41}, {30,38}, {2,31}, {16,42}, {9,36}, {6,34}, {27,37}, {17,45}, {24,29}, {26,44}, {20,41}, {27,39}, {27,43}, {7,24}, {18,40}, {1,14}, {1,6}, {17,42}, {10,14}, {6,20}, {7,35}, {5,21}, {5,35}, {22,30}, {21,28}, {11,42}, {3,36}, {9,23}, {24,28}, {31,38}, {35,43}, {1,36}, {23,30} }; // ET45.38 // Non-bipartite Valency 8 // Diameter 4 Girth 4 // Twin-free VT AT // Automorphism group of order 2160 EdgePairs[45][38]:={ {33,38}, {16,41}, {2,24}, {5,17}, {25,31}, {7,15}, {29,40}, {8,12}, {18,29}, {4,26}, {3,8}, {21,40}, {4,16}, {12,45}, {32,35}, {5,38}, {12,32}, {39,42}, {19,44}, {8,28}, {25,38}, {29,33}, {18,38}, {20,27}, {3,45}, {3,13}, {8,33}, {24,27}, {23,28}, {32,37}, {17,20}, {33,45}, {16,19}, {14,38}, {28,32}, {25,29}, {13,35}, {17,24}, {21,43}, {11,14}, {18,21}, {10,44}, {27,33}, {6,7}, {24,36}, {2,14}, {16,23}, {17,40}, {38,40}, {13,16}, {35,41}, {10,15}, {10,22}, {23,44}, {18,42}, {15,25}, {31,43}, {37,45}, {16,30}, {2,25}, {31,39}, {11,33}, {36,37}, {38,43}, {2,34}, {27,28}, {7,11}, {17,37}, {14,21}, {9,32}, {14,36}, {19,26}, {12,17}, {22,34}, {5,11}, {2,5}, {12,36}, {1,44}, {5,29}, {34,38}, {9,19}, {8,14}, {19,22}, {9,41}, {1,22}, {12,13}, {6,30}, {6,43}, {23,26}, {10,31}, {15,19}, {28,41}, {6,18}, {29,34}, {30,42}, {23,35}, {3,4}, {19,42}, {24,45}, {30,35}, {21,25}, {15,34}, {36,40}, {1,9}, {9,10}, {20,45}, {19,31}, {3,27}, {4,28}, {22,43}, {21,33}, {31,34}, {7,31}, {17,28}, {9,13}, {22,25}, {14,17}, {1,42}, {4,9}, {12,23}, {28,36}, {11,24}, {8,40}, {40,45}, {20,23}, {42,43}, {3,23}, {2,7}, {26,32}, {41,44}, {7,29}, {1,15}, {9,30}, {1,35}, {33,36}, {4,37}, {13,26}, {15,18}, {10,35}, {32,44}, {1,26}, {5,8}, {18,22}, {6,25}, {2,40}, {6,10}, {5,27}, {16,39}, {27,37}, {24,29}, {26,39}, {4,12}, {8,20}, {20,41}, {13,37}, {5,45}, {3,41}, {15,39}, {1,6}, {30,31}, {6,39}, {35,39}, {11,34}, {21,24}, {11,43}, {34,42}, {13,20}, {22,30}, {37,41}, {2,43}, {3,36}, {7,42}, {20,32}, {4,44}, {14,27}, {7,21}, {39,44}, {11,18}, {26,30}, {10,16} }; // ET45.39 // Non-bipartite Valency 8 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[45][39]:={ {11,17}, {21,23}, {10,24}, {5,17}, {38,42}, {4,27}, {29,40}, {3,8}, {4,16}, {12,45}, {4,30}, {1,13}, {12,22}, {5,38}, {12,32}, {39,41}, {8,28}, {18,38}, {3,6}, {3,45}, {32,34}, {1,27}, {3,25}, {19,24}, {1,40}, {33,45}, {2,15}, {35,40}, {3,35}, {25,29}, {2,4}, {26,33}, {2,26}, {10,44}, {2,41}, {6,11}, {16,29}, {15,16}, {15,25}, {6,29}, {31,43}, {11,33}, {36,37}, {4,10}, {2,36}, {19,40}, {27,28}, {3,14}, {17,37}, {14,21}, {16,24}, {4,8}, {18,20}, {1,5}, {12,36}, {1,44}, {34,38}, {24,43}, {23,45}, {5,43}, {39,43}, {22,35}, {9,41}, {5,25}, {11,15}, {4,45}, {22,27}, {23,36}, {21,44}, {20,33}, {12,16}, {21,26}, {22,44}, {10,31}, {27,31}, {15,19}, {37,40}, {28,41}, {6,18}, {29,34}, {30,42}, {24,26}, {11,23}, {1,23}, {30,35}, {6,44}, {17,30}, {15,35}, {8,11}, {5,7}, {23,25}, {40,43}, {8,13}, {32,39}, {1,9}, {26,38}, {9,20}, {24,34}, {7,14}, {14,37}, {20,22}, {21,31}, {10,13}, {20,43}, {31,36}, {22,29}, {30,32}, {5,28}, {13,36}, {25,37}, {33,35}, {25,32}, {5,12}, {8,32}, {8,21}, {14,18}, {28,36}, {28,33}, {8,40}, {6,26}, {33,37}, {14,34}, {12,14}, {20,25}, {17,19}, {2,7}, {9,12}, {6,9}, {19,45}, {17,41}, {7,29}, {18,23}, {9,30}, {37,44}, {41,45}, {16,21}, {19,32}, {4,37}, {13,26}, {10,35}, {32,44}, {3,24}, {18,28}, {2,22}, {29,31}, {42,44}, {10,18}, {20,42}, {16,42}, {15,38}, {3,42}, {16,39}, {38,45}, {7,10}, {27,39}, {36,42}, {18,40}, {6,39}, {35,39}, {7,33}, {11,34}, {17,22}, {13,39}, {11,43}, {9,15}, {13,17}, {13,20}, {9,31}, {1,34}, {7,19}, {21,41}, {2,43}, {7,42}, {14,27}, {19,27}, {34,41}, {24,28}, {31,38}, {23,30}, {26,30} }; // ET45.40 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[45][40]:={ {11,17}, {16,41}, {9,28}, {18,39}, {5,34}, {13,40}, {4,24}, {15,24}, {18,29}, {21,40}, {17,38}, {12,45}, {33,39}, {4,30}, {16,27}, {26,31}, {8,30}, {1,13}, {15,31}, {21,37}, {20,27}, {32,34}, {32,37}, {3,15}, {7,41}, {1,40}, {33,45}, {1,19}, {25,29}, {9,43}, {22,32}, {11,41}, {11,14}, {7,36}, {17,21}, {10,44}, {8,10}, {27,33}, {24,36}, {2,14}, {17,40}, {27,44}, {9,35}, {8,44}, {12,37}, {10,15}, {2,42}, {10,22}, {23,39}, {18,42}, {6,22}, {6,29}, {31,43}, {19,28}, {20,38}, {2,25}, {14,23}, {11,38}, {26,28}, {7,11}, {14,21}, {19,26}, {4,8}, {24,37}, {22,34}, {27,30}, {1,5}, {25,36}, {28,34}, {29,36}, {11,31}, {2,35}, {3,44}, {12,13}, {12,16}, {5,23}, {4,21}, {3,20}, {13,22}, {15,19}, {15,42}, {9,42}, {30,39}, {16,37}, {17,43}, {8,17}, {23,35}, {13,33}, {19,42}, {3,4}, {2,32}, {11,23}, {30,35}, {17,30}, {2,6}, {21,25}, {36,45}, {5,7}, {28,37}, {8,22}, {1,45}, {29,38}, {26,38}, {10,42}, {5,14}, {4,15}, {14,41}, {25,45}, {14,37}, {3,27}, {1,33}, {26,34}, {31,36}, {22,29}, {5,28}, {25,37}, {12,33}, {34,44}, {5,41}, {4,36}, {33,35}, {20,29}, {25,32}, {8,40}, {40,45}, {12,40}, {42,43}, {18,19}, {18,25}, {10,32}, {21,30}, {9,12}, {16,44}, {6,9}, {41,44}, {7,29}, {10,39}, {6,42}, {4,40}, {7,23}, {2,21}, {8,34}, {32,44}, {1,26}, {23,33}, {16,20}, {14,32}, {10,18}, {19,39}, {27,35}, {18,45}, {13,38}, {12,24}, {20,41}, {7,45}, {27,39}, {3,41}, {3,31}, {15,39}, {9,24}, {17,26}, {26,43}, {5,19}, {6,20}, {11,43}, {6,13}, {13,20}, {1,34}, {2,43}, {6,35}, {3,36}, {9,16}, {16,28}, {24,31}, {24,28}, {31,38}, {35,43}, {22,38}, {23,30}, {7,18} }; // ET45.41 // Non-bipartite Valency 8 // Diameter 3 Girth 3 // Twin-free VT AT // Automorphism group of order 720 EdgePairs[45][41]:={ {2,44}, {3,33}, {10,24}, {1,20}, {25,31}, {13,21}, {14,19}, {8,12}, {23,29}, {31,44}, {10,37}, {25,39}, {16,40}, {32,35}, {8,43}, {9,45}, {8,42}, {18,38}, {3,6}, {4,29}, {1,32}, {3,45}, {12,38}, {7,44}, {17,20}, {16,19}, {4,19}, {14,38}, {2,19}, {10,33}, {12,42}, {2,27}, {5,20}, {26,33}, {25,30}, {24,30}, {29,35}, {16,25}, {18,21}, {6,7}, {18,41}, {20,30}, {9,11}, {16,29}, {16,43}, {8,16}, {6,21}, {3,34}, {31,39}, {6,40}, {14,33}, {2,36}, {4,22}, {19,40}, {27,28}, {3,14}, {17,37}, {15,32}, {2,5}, {33,43}, {15,40}, {4,41}, {12,44}, {26,29}, {19,29}, {9,41}, {11,15}, {10,41}, {23,34}, {11,22}, {30,34}, {19,38}, {25,34}, {35,44}, {21,26}, {9,34}, {24,32}, {36,43}, {2,13}, {34,45}, {26,35}, {26,37}, {13,31}, {18,30}, {29,37}, {4,35}, {23,37}, {18,44}, {8,36}, {42,45}, {5,30}, {7,17}, {5,24}, {27,38}, {17,27}, {15,37}, {14,42}, {32,38}, {27,36}, {15,20}, {18,26}, {10,13}, {6,23}, {1,43}, {3,26}, {24,35}, {5,42}, {9,22}, {31,34}, {6,15}, {10,43}, {21,39}, {17,28}, {22,39}, {32,45}, {4,9}, {12,23}, {28,36}, {14,22}, {13,24}, {11,39}, {22,33}, {27,45}, {33,37}, {8,23}, {12,14}, {20,25}, {5,36}, {3,21}, {1,25}, {22,28}, {27,32}, {1,15}, {6,28}, {9,30}, {24,38}, {1,35}, {33,36}, {7,28}, {20,37}, {40,44}, {28,39}, {25,43}, {11,16}, {41,43}, {9,18}, {10,17}, {4,14}, {5,8}, {11,32}, {13,41}, {20,42}, {30,38}, {2,40}, {2,31}, {11,40}, {6,34}, {3,42}, {16,39}, {17,45}, {1,4}, {11,45}, {26,44}, {5,13}, {7,10}, {15,23}, {1,41}, {23,31}, {7,24}, {12,31}, {17,42}, {7,35}, {13,39}, {22,36}, {21,41}, {21,28}, {7,40}, {8,29}, {19,27}, {12,18} }; // ET45.42 // Non-bipartite Valency 8 // Diameter 2 Girth 4 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[45][42]:={ {1,11}, {37,42}, {2,24}, {5,17}, {38,42}, {17,36}, {12,29}, {7,15}, {29,40}, {4,26}, {3,22}, {4,16}, {1,10}, {32,40}, {11,25}, {30,45}, {6,17}, {5,38}, {3,9}, {39,41}, {19,44}, {28,45}, {29,33}, {16,31}, {8,33}, {24,27}, {10,26}, {35,40}, {3,37}, {17,24}, {21,22}, {24,44}, {8,25}, {2,28}, {12,34}, {1,30}, {16,23}, {6,11}, {8,31}, {35,41}, {18,34}, {15,16}, {23,44}, {15,25}, {3,18}, {11,28}, {39,40}, {3,17}, {15,45}, {15,29}, {4,38}, {22,45}, {6,31}, {8,19}, {35,38}, {14,36}, {9,32}, {2,38}, {29,44}, {5,43}, {39,43}, {8,14}, {19,22}, {22,41}, {5,25}, {2,39}, {7,32}, {3,12}, {27,40}, {7,13}, {9,14}, {10,28}, {22,27}, {17,33}, {21,44}, {23,26}, {4,33}, {25,41}, {10,21}, {13,18}, {30,42}, {1,29}, {2,16}, {23,42}, {9,25}, {7,26}, {13,43}, {13,44}, {6,44}, {15,35}, {23,25}, {15,34}, {33,42}, {1,9}, {13,25}, {18,24}, {20,45}, {13,28}, {21,31}, {15,17}, {4,43}, {33,41}, {20,43}, {22,43}, {21,33}, {8,37}, {30,32}, {13,36}, {18,31}, {38,44}, {12,26}, {16,22}, {27,42}, {24,41}, {13,30}, {28,40}, {5,12}, {14,18}, {1,24}, {5,31}, {12,19}, {6,26}, {28,33}, {30,41}, {20,23}, {12,30}, {3,23}, {2,7}, {34,39}, {35,37}, {26,41}, {36,39}, {19,36}, {37,43}, {1,37}, {19,32}, {23,40}, {14,45}, {10,35}, {16,36}, {11,27}, {6,45}, {20,34}, {10,36}, {1,16}, {20,24}, {5,27}, {5,10}, {31,40}, {4,18}, {9,39}, {38,45}, {9,38}, {11,19}, {4,11}, {3,28}, {8,20}, {7,27}, {36,42}, {21,34}, {2,12}, {2,8}, {10,20}, {30,31}, {6,39}, {6,37}, {11,34}, {19,35}, {34,42}, {7,37}, {29,43}, {17,32}, {9,21}, {18,35}, {20,32}, {14,27}, {7,21}, {4,32}, {14,29}, {14,26} }; // ET45.43 // Bipartite(18,27) Valencies [9,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 3888 EdgePairs[45][43]:={ {16,41}, {2,24}, {13,32}, {2,33}, {17,35}, {18,39}, {5,34}, {16,26}, {15,24}, {18,29}, {4,26}, {17,38}, {18,32}, {4,30}, {11,25}, {16,27}, {2,23}, {9,45}, {12,32}, {7,38}, {8,28}, {16,31}, {15,31}, {3,45}, {8,33}, {3,43}, {3,25}, {10,23}, {12,38}, {7,44}, {14,38}, {12,39}, {10,33}, {12,42}, {1,19}, {3,37}, {2,26}, {1,21}, {17,24}, {12,35}, {7,36}, {15,43}, {18,21}, {1,30}, {5,32}, {14,28}, {9,35}, {8,27}, {2,42}, {6,22}, {18,42}, {6,29}, {15,29}, {4,38}, {6,31}, {2,34}, {7,20}, {17,37}, {14,21}, {12,36}, {4,41}, {14,40}, {9,41}, {15,26}, {10,41}, {11,22}, {7,43}, {2,35}, {17,33}, {11,44}, {1,22}, {3,44}, {4,33}, {5,23}, {10,29}, {9,34}, {13,22}, {2,20}, {1,29}, {3,32}, {11,21}, {9,25}, {13,33}, {18,43}, {6,24}, {13,44}, {17,30}, {11,30}, {12,28}, {15,37}, {8,22}, {1,28}, {14,41}, {3,27}, {4,43}, {10,45}, {8,37}, {15,36}, {8,26}, {12,26}, {16,22}, {10,43}, {17,28}, {8,32}, {11,24}, {8,40}, {1,39}, {18,25}, {5,36}, {17,19}, {16,44}, {6,28}, {18,23}, {9,30}, {13,42}, {14,20}, {16,34}, {14,25}, {6,42}, {4,40}, {16,36}, {13,19}, {11,37}, {10,27}, {6,45}, {16,20}, {6,25}, {2,40}, {11,40}, {5,27}, {9,39}, {10,19}, {17,45}, {3,38}, {15,23}, {14,35}, {1,41}, {7,24}, {3,31}, {18,40}, {10,20}, {12,31}, {13,34}, {11,34}, {5,19}, {6,20}, {13,39}, {5,21}, {13,45}, {15,30}, {5,35}, {9,31}, {5,37}, {7,19}, {4,39}, {7,42}, {9,23}, {4,44}, {14,27}, {7,21}, {8,29}, {1,36} }; // ET45.44 // Bipartite(18,27) Valencies [9,6] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1296 EdgePairs[45][44]:={ {16,41}, {10,25}, {9,28}, {6,32}, {11,36}, {18,39}, {4,27}, {12,29}, {5,34}, {16,26}, {4,30}, {16,27}, {8,30}, {14,39}, {8,43}, {9,45}, {12,22}, {18,38}, {3,45}, {3,43}, {10,26}, {17,34}, {16,19}, {9,44}, {14,38}, {2,19}, {12,41}, {15,44}, {2,27}, {5,20}, {8,39}, {7,34}, {1,21}, {17,24}, {12,35}, {1,30}, {2,42}, {15,25}, {18,42}, {10,30}, {6,29}, {6,21}, {3,34}, {2,25}, {6,40}, {6,31}, {2,36}, {4,22}, {10,38}, {9,29}, {8,19}, {7,20}, {17,37}, {14,21}, {15,32}, {18,20}, {12,20}, {15,40}, {4,41}, {2,37}, {4,42}, {9,41}, {1,31}, {4,45}, {7,25}, {14,24}, {10,28}, {2,35}, {17,33}, {11,44}, {1,22}, {3,44}, {6,43}, {5,23}, {10,31}, {3,20}, {15,19}, {10,40}, {12,43}, {17,43}, {13,31}, {3,32}, {11,21}, {7,26}, {6,33}, {18,44}, {16,32}, {13,43}, {1,23}, {17,30}, {5,24}, {8,22}, {15,34}, {8,35}, {13,28}, {1,28}, {1,33}, {10,45}, {3,26}, {8,37}, {5,28}, {13,36}, {18,31}, {16,22}, {7,31}, {12,33}, {13,30}, {12,27}, {9,40}, {8,32}, {1,24}, {12,23}, {11,24}, {17,25}, {11,39}, {1,39}, {17,29}, {18,23}, {13,42}, {16,21}, {14,45}, {16,36}, {6,36}, {11,37}, {2,29}, {8,38}, {15,22}, {11,32}, {15,33}, {13,41}, {6,38}, {2,40}, {9,36}, {5,26}, {10,19}, {4,25}, {17,45}, {3,38}, {7,27}, {15,23}, {14,35}, {13,37}, {3,41}, {9,24}, {18,40}, {7,33}, {11,34}, {5,19}, {13,20}, {5,35}, {5,37}, {11,42}, {4,39}, {16,28}, {18,35}, {7,42}, {9,23}, {4,44}, {14,27}, {7,21}, {14,29}, {14,26} }; // ET45.45 // Bipartite(18,27) Valencies [9,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 33853318889472 EdgePairs[45][45]:={ {2,44}, {3,33}, {16,41}, {1,20}, {11,36}, {17,36}, {12,29}, {13,21}, {5,34}, {15,24}, {18,29}, {3,22}, {3,40}, {10,37}, {11,25}, {8,30}, {16,40}, {14,39}, {7,38}, {16,31}, {18,38}, {15,31}, {10,23}, {12,38}, {17,34}, {16,19}, {4,19}, {9,44}, {4,31}, {15,44}, {1,19}, {12,42}, {2,27}, {3,35}, {2,26}, {8,39}, {11,41}, {1,21}, {12,34}, {1,30}, {5,32}, {16,23}, {9,35}, {8,44}, {4,23}, {8,27}, {13,29}, {18,34}, {10,22}, {18,42}, {6,29}, {2,45}, {1,38}, {2,36}, {4,22}, {7,20}, {14,21}, {14,36}, {9,26}, {18,20}, {12,20}, {15,40}, {4,41}, {5,43}, {14,30}, {8,45}, {7,39}, {5,25}, {2,39}, {15,26}, {17,23}, {10,41}, {10,28}, {2,35}, {3,44}, {6,43}, {5,23}, {10,31}, {15,42}, {9,42}, {16,37}, {10,40}, {12,43}, {17,43}, {1,29}, {7,30}, {8,36}, {6,33}, {18,43}, {16,32}, {11,23}, {6,24}, {15,35}, {17,27}, {12,25}, {18,24}, {8,35}, {13,28}, {1,28}, {4,28}, {18,33}, {3,26}, {8,26}, {16,22}, {9,22}, {12,33}, {13,30}, {5,41}, {9,40}, {8,21}, {17,25}, {1,39}, {10,32}, {18,25}, {5,36}, {17,41}, {7,29}, {1,37}, {7,28}, {4,37}, {6,42}, {14,45}, {4,40}, {13,19}, {2,21}, {3,24}, {11,27}, {14,44}, {15,22}, {11,32}, {15,33}, {6,25}, {6,38}, {9,33}, {6,34}, {5,27}, {3,42}, {13,38}, {10,19}, {17,45}, {11,45}, {12,24}, {14,35}, {13,37}, {5,45}, {3,31}, {9,24}, {11,34}, {6,20}, {13,39}, {11,43}, {2,30}, {13,20}, {7,37}, {9,31}, {7,19}, {17,32}, {16,28}, {14,27}, {7,21}, {4,32}, {14,26} }; // ET45.46 // Bipartite(18,27) Valencies [9,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 557256278016 EdgePairs[45][46]:={ {2,44}, {3,33}, {10,25}, {11,20}, {4,27}, {13,21}, {11,35}, {5,34}, {4,24}, {16,26}, {17,38}, {10,37}, {18,32}, {4,30}, {14,39}, {2,23}, {9,45}, {5,38}, {12,32}, {8,42}, {15,31}, {8,33}, {7,44}, {1,40}, {17,20}, {16,19}, {14,38}, {12,41}, {15,44}, {1,19}, {12,42}, {5,20}, {9,43}, {3,37}, {2,26}, {17,24}, {11,41}, {2,41}, {18,41}, {17,40}, {8,31}, {12,37}, {18,34}, {10,22}, {6,22}, {16,30}, {15,45}, {11,38}, {6,40}, {6,31}, {14,21}, {9,32}, {9,27}, {15,40}, {5,29}, {2,38}, {5,43}, {14,30}, {7,39}, {4,42}, {9,41}, {5,25}, {15,26}, {1,31}, {4,45}, {10,28}, {2,35}, {17,33}, {11,44}, {1,22}, {15,27}, {4,33}, {4,21}, {10,31}, {9,34}, {2,20}, {16,37}, {10,40}, {7,30}, {3,32}, {9,25}, {13,33}, {2,32}, {7,26}, {18,43}, {11,23}, {11,29}, {5,30}, {6,44}, {15,35}, {12,28}, {8,22}, {1,28}, {18,27}, {18,36}, {1,43}, {15,36}, {13,36}, {17,31}, {12,33}, {13,30}, {10,43}, {4,36}, {3,19}, {12,23}, {13,24}, {6,27}, {12,19}, {8,40}, {6,26}, {14,34}, {3,23}, {18,25}, {17,29}, {1,25}, {16,44}, {18,23}, {13,27}, {13,42}, {14,20}, {1,37}, {14,25}, {5,39}, {16,21}, {7,28}, {11,26}, {6,36}, {3,24}, {2,29}, {16,35}, {6,45}, {8,38}, {10,34}, {15,22}, {11,32}, {8,24}, {9,36}, {14,43}, {18,45}, {3,42}, {16,39}, {10,19}, {12,24}, {8,20}, {3,28}, {3,41}, {17,42}, {7,35}, {13,39}, {17,22}, {5,21}, {13,45}, {7,37}, {1,34}, {7,19}, {6,35}, {4,39}, {16,28}, {9,23}, {7,21}, {8,29}, {14,29} }; // ET45.47 // Bipartite(18,27) Valencies [9,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1088391168 EdgePairs[45][47]:={ {10,24}, {9,28}, {17,35}, {17,44}, {11,36}, {18,39}, {12,29}, {11,35}, {13,40}, {16,33}, {15,24}, {4,26}, {3,22}, {3,40}, {2,23}, {8,43}, {12,22}, {5,38}, {7,38}, {8,28}, {3,45}, {3,43}, {3,25}, {10,23}, {12,38}, {1,40}, {16,19}, {4,19}, {10,33}, {1,19}, {5,20}, {9,43}, {14,31}, {11,41}, {12,35}, {18,21}, {8,25}, {2,41}, {17,40}, {4,23}, {13,29}, {18,34}, {16,30}, {15,29}, {6,21}, {3,34}, {2,25}, {14,33}, {2,34}, {8,19}, {7,20}, {17,37}, {14,36}, {15,32}, {16,24}, {12,20}, {5,29}, {4,41}, {8,41}, {2,38}, {9,19}, {12,44}, {14,40}, {7,39}, {1,31}, {10,41}, {14,24}, {11,44}, {1,22}, {6,30}, {9,34}, {13,22}, {15,42}, {2,20}, {16,37}, {7,30}, {13,31}, {18,30}, {4,35}, {9,25}, {15,41}, {2,32}, {18,43}, {11,23}, {13,43}, {5,30}, {6,44}, {9,37}, {14,42}, {13,25}, {15,20}, {10,42}, {1,28}, {18,27}, {3,27}, {18,36}, {4,28}, {1,33}, {10,45}, {8,37}, {17,31}, {12,26}, {17,28}, {8,32}, {1,42}, {1,24}, {14,22}, {6,27}, {5,44}, {6,26}, {12,40}, {8,23}, {10,32}, {18,25}, {17,19}, {7,29}, {9,30}, {1,37}, {16,21}, {5,39}, {4,37}, {11,26}, {14,45}, {6,36}, {8,34}, {2,29}, {11,27}, {10,27}, {6,45}, {10,36}, {11,32}, {15,33}, {16,42}, {15,38}, {5,26}, {18,45}, {16,39}, {9,39}, {13,38}, {11,45}, {15,23}, {7,24}, {3,31}, {17,26}, {6,39}, {7,33}, {12,31}, {13,34}, {17,22}, {5,21}, {13,20}, {5,35}, {2,43}, {6,35}, {9,21}, {3,36}, {16,28}, {7,42}, {4,44}, {14,27}, {7,21}, {4,32} }; // ET45.48 // Bipartite(18,27) Valencies [9,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 663552 EdgePairs[45][48]:={ {10,19}, {7,19}, {13,25}, {5,32}, {6,39}, {18,41}, {12,26}, {2,38}, {10,22}, {15,43}, {18,44}, {11,33}, {4,27}, {10,27}, {18,39}, {8,36}, {5,35}, {7,24}, {9,45}, {2,20}, {11,42}, {1,25}, {12,40}, {12,31}, {5,24}, {5,41}, {2,33}, {6,32}, {17,35}, {7,31}, {9,39}, {16,23}, {13,27}, {9,21}, {11,38}, {1,32}, {16,20}, {14,35}, {7,23}, {18,21}, {8,34}, {3,45}, {6,45}, {3,34}, {9,31}, {3,31}, {17,44}, {8,41}, {15,32}, {13,20}, {10,23}, {1,29}, {8,44}, {7,28}, {6,43}, {1,34}, {15,39}, {16,21}, {17,30}, {10,34}, {4,20}, {13,33}, {7,26}, {9,43}, {4,39}, {10,25}, {1,22}, {6,33}, {3,40}, {12,34}, {4,33}, {16,26}, {16,19}, {5,43}, {10,37}, {14,28}, {7,20}, {8,35}, {14,38}, {14,43}, {6,37}, {3,23}, {5,29}, {15,45}, {2,42}, {4,30}, {1,19}, {2,40}, {4,36}, {4,21}, {2,35}, {15,33}, {5,28}, {13,30}, {4,25}, {10,29}, {11,26}, {8,40}, {17,36}, {12,23}, {14,32}, {2,24}, {3,42}, {5,22}, {9,44}, {5,38}, {12,44}, {1,23}, {15,42}, {14,22}, {18,28}, {6,38}, {9,28}, {11,40}, {3,26}, {15,37}, {16,22}, {18,43}, {11,30}, {3,44}, {6,42}, {13,21}, {17,34}, {1,37}, {1,27}, {12,42}, {7,22}, {15,27}, {17,41}, {16,28}, {8,25}, {17,29}, {2,26}, {10,32}, {13,36}, {15,38}, {18,45}, {7,21}, {11,20}, {14,29}, {18,31}, {9,41}, {14,41}, {18,36}, {3,37}, {8,30}, {9,36}, {6,27}, {13,19}, {17,40}, {11,24}, {11,35}, {12,37}, {16,31}, {2,30}, {4,19}, {14,24}, {12,45}, {17,25}, {8,29}, {13,39}, {16,24} }; // ET45.49 // Bipartite(15,30) Valencies [10,5] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2149908480000000 EdgePairs[45][49]:={ {2,24}, {11,20}, {13,32}, {12,29}, {4,24}, {12,45}, {4,30}, {2,23}, {8,43}, {8,28}, {3,43}, {3,25}, {1,40}, {14,38}, {4,19}, {9,44}, {12,39}, {7,22}, {4,31}, {12,41}, {15,44}, {10,33}, {3,35}, {3,37}, {7,34}, {12,35}, {7,36}, {8,25}, {2,41}, {8,31}, {2,42}, {10,22}, {11,28}, {3,17}, {8,16}, {15,45}, {6,21}, {14,23}, {11,38}, {6,31}, {1,17}, {2,36}, {8,19}, {9,32}, {12,17}, {15,32}, {9,26}, {4,42}, {15,26}, {11,22}, {10,28}, {2,35}, {11,44}, {1,22}, {15,27}, {6,43}, {10,21}, {9,42}, {10,40}, {1,29}, {7,30}, {13,31}, {7,16}, {6,33}, {5,18}, {13,43}, {1,23}, {13,44}, {5,30}, {5,24}, {8,22}, {13,25}, {15,20}, {9,20}, {1,28}, {14,41}, {4,43}, {10,45}, {3,29}, {8,37}, {5,42}, {12,33}, {2,17}, {4,36}, {12,27}, {14,17}, {3,19}, {12,23}, {6,27}, {8,40}, {3,23}, {5,36}, {6,19}, {9,30}, {10,39}, {1,35}, {14,20}, {15,21}, {5,39}, {7,28}, {4,37}, {11,26}, {13,26}, {11,16}, {13,19}, {8,34}, {5,33}, {9,18}, {2,29}, {10,27}, {6,45}, {14,44}, {1,16}, {10,34}, {11,32}, {14,32}, {15,33}, {6,25}, {11,40}, {9,36}, {5,27}, {15,38}, {4,18}, {13,38}, {9,38}, {4,25}, {14,35}, {1,41}, {13,37}, {5,45}, {3,41}, {7,24}, {3,31}, {15,39}, {9,24}, {6,39}, {6,37}, {11,34}, {5,21}, {2,30}, {13,20}, {2,18}, {1,34}, {7,40}, {7,42}, {12,21}, {14,29}, {14,26}, {7,18}, {10,16} }; // ET45.50 // Bipartite(20,25) Valencies [10,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 28800 EdgePairs[45][50]:={ {3,33}, {16,41}, {2,24}, {13,32}, {2,33}, {18,39}, {13,21}, {11,35}, {5,34}, {13,40}, {4,24}, {16,33}, {10,37}, {14,39}, {2,23}, {8,43}, {16,31}, {18,38}, {8,33}, {3,25}, {10,23}, {12,38}, {19,24}, {7,44}, {10,26}, {17,34}, {9,44}, {7,22}, {10,33}, {2,27}, {3,35}, {9,43}, {3,37}, {11,41}, {1,21}, {18,21}, {2,41}, {2,28}, {12,34}, {18,41}, {5,32}, {17,40}, {9,35}, {20,30}, {4,23}, {8,31}, {12,37}, {15,25}, {18,42}, {11,28}, {18,37}, {10,30}, {6,29}, {2,45}, {19,28}, {4,38}, {15,29}, {3,34}, {5,40}, {2,25}, {11,33}, {1,38}, {5,22}, {4,22}, {10,38}, {9,29}, {19,40}, {9,32}, {14,36}, {19,26}, {15,32}, {12,36}, {1,44}, {8,41}, {19,29}, {7,39}, {4,42}, {5,25}, {2,39}, {7,32}, {15,26}, {17,23}, {4,45}, {10,28}, {11,31}, {14,24}, {17,33}, {15,27}, {19,38}, {6,30}, {6,43}, {9,34}, {13,22}, {10,21}, {12,43}, {1,29}, {13,31}, {11,21}, {7,26}, {6,33}, {11,29}, {20,44}, {6,44}, {17,30}, {5,24}, {12,25}, {15,37}, {15,34}, {18,24}, {8,35}, {10,42}, {20,45}, {18,26}, {18,27}, {14,41}, {20,22}, {4,43}, {10,45}, {6,23}, {1,43}, {15,36}, {17,31}, {16,22}, {9,22}, {5,41}, {17,28}, {9,40}, {16,45}, {8,21}, {1,42}, {12,23}, {5,31}, {8,40}, {12,40}, {20,39}, {12,30}, {8,23}, {18,25}, {20,25}, {3,21}, {16,44}, {7,29}, {6,28}, {1,35}, {13,42}, {1,37}, {5,39}, {14,25}, {16,21}, {7,28}, {19,32}, {20,37}, {13,26}, {11,26}, {4,40}, {6,36}, {3,30}, {11,27}, {16,35}, {6,45}, {8,38}, {20,34}, {1,26}, {14,44}, {11,32}, {8,24}, {19,43}, {20,42}, {9,36}, {16,42}, {20,36}, {5,27}, {14,43}, {15,28}, {16,39}, {13,38}, {17,45}, {12,24}, {7,27}, {7,45}, {14,35}, {13,37}, {3,41}, {3,31}, {13,34}, {17,22}, {2,30}, {15,30}, {9,31}, {19,23}, {6,35}, {17,32}, {3,36}, {4,39}, {7,42}, {4,44}, {14,27}, {19,27}, {1,36}, {14,29} }; // ET45.51 // Bipartite(20,25) Valencies [10,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 200 EdgePairs[45][51]:={ {2,44}, {10,25}, {13,32}, {17,35}, {11,36}, {17,36}, {12,29}, {13,21}, {11,35}, {5,34}, {4,24}, {15,24}, {16,26}, {4,26}, {17,38}, {12,45}, {10,37}, {18,32}, {11,25}, {8,30}, {2,23}, {8,42}, {19,44}, {16,31}, {8,33}, {1,27}, {3,25}, {10,23}, {7,41}, {1,40}, {17,34}, {9,44}, {15,44}, {12,42}, {9,43}, {3,37}, {20,21}, {14,31}, {8,39}, {11,41}, {1,21}, {16,25}, {18,41}, {17,40}, {8,31}, {16,29}, {18,34}, {19,21}, {6,22}, {2,45}, {15,45}, {16,30}, {19,28}, {15,29}, {14,23}, {2,25}, {11,38}, {6,31}, {1,38}, {9,29}, {17,37}, {14,36}, {9,32}, {15,32}, {16,24}, {9,26}, {9,27}, {5,29}, {4,41}, {2,38}, {12,44}, {14,30}, {14,40}, {8,45}, {19,22}, {4,42}, {9,41}, {7,32}, {1,31}, {7,43}, {11,31}, {10,28}, {7,25}, {20,31}, {17,33}, {1,22}, {3,44}, {6,30}, {4,33}, {13,22}, {10,21}, {16,37}, {10,40}, {1,29}, {3,39}, {3,32}, {4,35}, {7,26}, {6,33}, {2,32}, {19,42}, {11,23}, {6,24}, {20,44}, {6,44}, {17,30}, {19,41}, {5,24}, {12,28}, {15,37}, {14,42}, {1,45}, {8,22}, {13,25}, {10,42}, {20,45}, {18,27}, {18,36}, {4,28}, {10,45}, {20,43}, {18,33}, {1,43}, {3,26}, {16,38}, {8,37}, {5,42}, {12,26}, {12,33}, {5,41}, {4,36}, {12,27}, {16,45}, {13,24}, {6,27}, {5,31}, {11,39}, {12,40}, {20,39}, {12,30}, {3,23}, {8,23}, {17,29}, {20,25}, {7,29}, {18,23}, {15,21}, {7,28}, {4,37}, {10,35}, {6,36}, {3,30}, {5,33}, {8,34}, {20,26}, {16,35}, {18,28}, {2,22}, {10,34}, {15,22}, {18,22}, {15,33}, {19,39}, {19,43}, {13,41}, {20,42}, {6,38}, {20,24}, {2,40}, {9,36}, {14,43}, {5,27}, {15,28}, {13,38}, {9,38}, {3,28}, {14,35}, {13,37}, {9,24}, {18,40}, {6,39}, {13,34}, {11,34}, {7,35}, {13,39}, {11,43}, {5,21}, {2,30}, {5,35}, {1,34}, {19,23}, {2,43}, {17,32}, {3,36}, {4,39}, {7,40}, {14,27}, {7,21}, {19,27}, {14,26} }; // ET45.52 // Bipartite(20,25) Valencies [10,8] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1981355655168000000 EdgePairs[45][52]:={ {3,33}, {16,41}, {10,24}, {9,28}, {17,35}, {11,36}, {13,21}, {5,34}, {16,26}, {15,24}, {12,45}, {10,37}, {4,30}, {8,43}, {9,45}, {12,22}, {12,32}, {8,28}, {16,31}, {18,38}, {20,27}, {8,33}, {3,43}, {14,38}, {7,22}, {15,44}, {2,27}, {12,42}, {9,43}, {11,41}, {1,21}, {12,35}, {18,21}, {10,44}, {18,41}, {5,32}, {17,40}, {14,28}, {9,35}, {4,23}, {8,31}, {12,37}, {16,29}, {2,42}, {10,22}, {6,29}, {2,45}, {19,28}, {15,29}, {4,38}, {19,33}, {6,21}, {14,23}, {2,25}, {6,31}, {14,33}, {5,22}, {19,40}, {17,37}, {15,32}, {16,24}, {19,30}, {1,44}, {5,29}, {8,41}, {2,37}, {14,30}, {14,40}, {7,32}, {1,31}, {4,45}, {7,25}, {11,31}, {2,35}, {11,44}, {15,27}, {19,38}, {4,33}, {10,29}, {15,42}, {1,29}, {7,30}, {13,31}, {11,21}, {4,35}, {9,25}, {8,36}, {2,32}, {13,33}, {18,43}, {13,43}, {11,29}, {6,24}, {20,44}, {6,44}, {17,30}, {5,24}, {17,27}, {13,23}, {12,25}, {15,37}, {15,34}, {13,28}, {10,42}, {18,26}, {20,22}, {18,36}, {4,28}, {4,43}, {18,33}, {3,26}, {13,36}, {8,26}, {18,31}, {5,42}, {20,29}, {12,27}, {9,40}, {8,21}, {1,24}, {11,24}, {17,25}, {11,39}, {5,44}, {6,26}, {12,40}, {20,39}, {12,30}, {3,23}, {8,23}, {1,39}, {10,32}, {3,21}, {16,44}, {19,45}, {6,41}, {18,23}, {9,30}, {10,39}, {16,34}, {14,25}, {5,39}, {16,21}, {20,37}, {13,26}, {11,26}, {14,45}, {4,40}, {16,36}, {6,36}, {18,28}, {10,27}, {8,38}, {20,34}, {1,26}, {2,22}, {10,34}, {15,22}, {19,43}, {13,41}, {20,42}, {20,24}, {2,40}, {9,33}, {6,34}, {14,43}, {5,27}, {19,25}, {16,39}, {13,38}, {9,38}, {4,25}, {17,45}, {3,38}, {3,28}, {7,27}, {7,45}, {14,35}, {1,41}, {3,41}, {3,31}, {15,39}, {6,39}, {11,34}, {17,42}, {19,35}, {7,35}, {17,22}, {2,30}, {7,37}, {1,34}, {19,23}, {5,37}, {17,32}, {3,36}, {7,40}, {7,42}, {9,23}, {20,32}, {1,36} }; // ET45.53 // Bipartite(20,25) Valencies [10,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3057647616000000 EdgePairs[45][53]:={ {3,33}, {10,25}, {13,32}, {17,44}, {11,36}, {5,34}, {15,24}, {16,33}, {4,26}, {3,22}, {12,45}, {18,32}, {9,45}, {12,22}, {12,32}, {8,42}, {3,43}, {10,23}, {20,40}, {7,44}, {17,34}, {14,38}, {7,22}, {4,31}, {15,44}, {10,33}, {12,42}, {2,27}, {3,37}, {14,31}, {7,34}, {11,41}, {1,21}, {17,24}, {12,35}, {18,21}, {18,41}, {16,23}, {9,35}, {14,28}, {20,30}, {4,23}, {8,31}, {8,27}, {12,37}, {16,29}, {2,42}, {19,21}, {15,25}, {18,42}, {16,43}, {18,37}, {10,30}, {6,29}, {2,45}, {15,45}, {4,38}, {15,29}, {14,23}, {5,40}, {2,25}, {20,38}, {14,33}, {10,38}, {19,40}, {17,37}, {14,21}, {14,36}, {19,26}, {16,24}, {9,26}, {19,30}, {15,40}, {1,44}, {4,41}, {5,29}, {8,41}, {2,37}, {7,39}, {9,41}, {5,25}, {7,32}, {17,39}, {1,31}, {10,28}, {11,31}, {2,35}, {11,44}, {20,33}, {6,43}, {4,33}, {4,21}, {13,22}, {10,40}, {1,29}, {3,32}, {11,21}, {9,25}, {8,36}, {6,33}, {2,32}, {13,33}, {13,43}, {11,29}, {6,24}, {5,30}, {6,44}, {19,41}, {15,35}, {5,24}, {17,27}, {13,23}, {12,25}, {8,22}, {15,34}, {20,28}, {13,28}, {20,45}, {18,26}, {19,31}, {18,27}, {14,41}, {3,27}, {18,36}, {4,28}, {4,43}, {10,45}, {20,43}, {6,23}, {16,38}, {8,37}, {8,26}, {18,31}, {10,43}, {4,36}, {12,27}, {9,40}, {8,32}, {8,21}, {1,24}, {11,24}, {11,39}, {5,44}, {20,23}, {12,40}, {12,30}, {3,23}, {1,39}, {17,29}, {20,25}, {16,44}, {19,45}, {7,29}, {19,36}, {6,28}, {9,30}, {13,27}, {13,42}, {16,34}, {5,39}, {20,35}, {11,26}, {10,35}, {1,26}, {2,22}, {18,22}, {6,38}, {2,40}, {9,36}, {6,34}, {14,43}, {19,25}, {3,42}, {16,39}, {13,38}, {3,38}, {3,28}, {7,27}, {1,41}, {13,37}, {5,45}, {7,24}, {15,39}, {6,39}, {11,34}, {17,42}, {19,35}, {17,22}, {2,30}, {15,30}, {7,37}, {5,35}, {9,31}, {1,34}, {17,32}, {9,21}, {16,28}, {7,42}, {1,36}, {14,26} }; // ET45.54 // Bipartite(20,25) Valencies [10,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 204800 EdgePairs[45][54]:={ {2,44}, {3,33}, {2,24}, {9,28}, {6,32}, {17,35}, {4,27}, {13,40}, {4,24}, {18,29}, {3,40}, {17,38}, {12,45}, {18,32}, {4,30}, {11,25}, {16,27}, {14,39}, {7,38}, {8,42}, {16,31}, {18,38}, {15,31}, {8,33}, {3,43}, {3,25}, {10,23}, {19,24}, {20,40}, {7,41}, {1,40}, {10,26}, {17,34}, {12,39}, {12,41}, {15,44}, {10,33}, {2,26}, {7,34}, {1,21}, {16,25}, {15,43}, {10,44}, {2,41}, {12,34}, {14,28}, {8,31}, {13,29}, {12,37}, {16,29}, {19,21}, {6,22}, {18,42}, {6,29}, {2,45}, {15,45}, {16,30}, {19,28}, {6,21}, {20,38}, {11,33}, {6,31}, {2,34}, {10,38}, {17,37}, {14,21}, {9,32}, {19,26}, {9,26}, {2,37}, {5,43}, {12,44}, {14,30}, {19,22}, {9,41}, {2,39}, {7,32}, {10,41}, {11,22}, {14,24}, {1,22}, {15,27}, {3,44}, {19,38}, {20,33}, {6,30}, {4,21}, {9,34}, {15,42}, {10,40}, {12,43}, {1,29}, {7,30}, {3,39}, {13,31}, {11,21}, {8,36}, {13,33}, {16,32}, {11,23}, {1,23}, {13,43}, {11,29}, {20,44}, {13,44}, {5,30}, {17,30}, {19,41}, {15,35}, {15,37}, {8,22}, {13,25}, {8,35}, {10,42}, {20,45}, {3,27}, {14,37}, {18,36}, {4,28}, {1,33}, {4,43}, {10,45}, {18,33}, {3,29}, {13,36}, {15,36}, {18,31}, {5,42}, {12,26}, {16,22}, {9,22}, {17,28}, {8,32}, {1,24}, {5,31}, {11,24}, {6,27}, {11,39}, {5,44}, {20,23}, {12,40}, {14,34}, {8,23}, {1,39}, {5,36}, {1,25}, {17,41}, {6,28}, {18,23}, {13,27}, {14,25}, {16,21}, {7,28}, {19,32}, {4,37}, {11,26}, {20,26}, {16,35}, {8,38}, {1,26}, {4,34}, {10,36}, {18,22}, {6,25}, {20,42}, {2,40}, {11,40}, {20,36}, {14,43}, {5,27}, {9,38}, {4,25}, {17,45}, {12,24}, {20,41}, {7,45}, {5,45}, {3,31}, {9,24}, {17,42}, {7,35}, {13,39}, {15,30}, {19,34}, {7,37}, {5,35}, {19,23}, {5,37}, {2,43}, {6,35}, {17,32}, {9,21}, {3,36}, {4,39}, {16,28}, {18,35}, {7,42}, {9,23}, {14,27}, {8,29} }; // ET45.55 // Non-bipartite Valency 10 // Diameter 4 Girth 4 // Has twins VT AT // Automorphism group of order 92876046336000000000 EdgePairs[45][55]:={ {3,33}, {33,38}, {37,42}, {10,24}, {9,28}, {7,15}, {36,38}, {5,34}, {16,33}, {4,26}, {35,42}, {3,40}, {12,45}, {11,25}, {16,40}, {22,37}, {30,45}, {32,35}, {5,38}, {30,33}, {7,38}, {39,41}, {18,38}, {4,29}, {20,27}, {3,45}, {8,33}, {24,27}, {32,37}, {20,40}, {7,41}, {10,26}, {16,19}, {4,19}, {14,38}, {25,33}, {21,35}, {2,4}, {25,29}, {5,20}, {13,35}, {34,40}, {17,21}, {10,44}, {6,7}, {24,36}, {18,41}, {23,43}, {16,23}, {29,42}, {38,40}, {28,35}, {13,29}, {3,5}, {16,29}, {10,15}, {2,42}, {3,18}, {3,7}, {15,45}, {6,21}, {2,25}, {7,12}, {31,39}, {2,34}, {1,17}, {26,28}, {8,19}, {3,14}, {7,20}, {9,32}, {18,20}, {27,30}, {33,43}, {12,36}, {1,44}, {5,43}, {8,14}, {14,30}, {19,22}, {22,35}, {5,25}, {17,39}, {11,13}, {24,39}, {28,44}, {1,31}, {10,41}, {23,34}, {11,22}, {15,27}, {21,44}, {20,33}, {21,26}, {10,31}, {22,44}, {27,31}, {9,42}, {2,13}, {28,41}, {14,16}, {6,18}, {29,34}, {16,37}, {7,30}, {2,16}, {18,30}, {4,35}, {2,32}, {19,42}, {30,36}, {24,45}, {13,44}, {5,30}, {8,11}, {27,38}, {23,25}, {40,43}, {1,9}, {18,24}, {9,10}, {20,45}, {3,27}, {23,38}, {21,31}, {31,36}, {22,29}, {8,37}, {15,36}, {18,31}, {25,37}, {29,32}, {9,22}, {7,31}, {12,33}, {25,40}, {26,42}, {17,28}, {9,13}, {12,27}, {5,12}, {33,34}, {4,9}, {1,24}, {12,23}, {6,27}, {30,40}, {8,40}, {20,23}, {12,40}, {14,34}, {8,23}, {3,23}, {27,41}, {12,14}, {36,41}, {26,32}, {1,15}, {6,28}, {37,43}, {1,35}, {14,20}, {41,45}, {15,21}, {14,25}, {19,32}, {4,37}, {13,26}, {15,18}, {22,26}, {10,35}, {11,16}, {13,19}, {6,36}, {32,44}, {10,17}, {6,45}, {1,26}, {2,22}, {5,8}, {42,44}, {11,32}, {19,43}, {20,36}, {6,10}, {14,43}, {19,25}, {15,28}, {9,39}, {38,45}, {4,11}, {26,39}, {28,31}, {1,41}, {13,37}, {7,24}, {15,39}, {2,8}, {1,6}, {6,39}, {35,39}, {17,42}, {11,34}, {17,22}, {21,24}, {11,43}, {13,17}, {19,34}, {29,43}, {21,41}, {2,43}, {4,17}, {17,32}, {11,42}, {3,36}, {9,21}, {31,45}, {4,44}, {8,29}, {39,44}, {12,18}, {24,28}, {34,37}, {23,30}, {5,16} }; // ET45.56 // Bipartite(9,36) Valencies [12,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10030613004288000000 EdgePairs[45][56]:={ {5,32}, {7,39}, {6,39}, {6,12}, {5,14}, {1,43}, {8,24}, {4,42}, {6,18}, {3,29}, {2,22}, {6,36}, {1,31}, {8,36}, {1,40}, {7,38}, {1,25}, {7,33}, {2,33}, {7,45}, {7,27}, {8,42}, {7,15}, {5,13}, {3,10}, {6,45}, {3,34}, {2,28}, {2,15}, {5,26}, {8,41}, {9,17}, {5,37}, {4,12}, {3,41}, {1,34}, {9,38}, {3,11}, {4,37}, {2,10}, {1,10}, {7,26}, {2,16}, {1,22}, {6,33}, {3,40}, {6,21}, {1,16}, {8,18}, {3,22}, {4,43}, {5,43}, {5,19}, {9,23}, {7,20}, {8,35}, {3,23}, {8,17}, {7,14}, {4,31}, {4,30}, {2,34}, {6,15}, {1,19}, {8,11}, {2,40}, {4,36}, {4,25}, {2,27}, {9,44}, {5,38}, {3,35}, {2,21}, {6,30}, {9,35}, {2,39}, {7,44}, {5,20}, {3,28}, {5,31}, {8,23}, {9,26}, {6,42}, {1,37}, {9,11}, {3,16}, {1,13}, {4,18}, {7,32}, {9,29}, {7,21}, {9,14}, {1,28}, {3,17}, {9,41}, {6,24}, {9,32}, {8,30}, {6,27}, {5,44}, {4,13}, {5,25}, {4,19}, {4,24}, {8,12}, {9,20}, {8,29}, {2,45} }; // ET45.57 // Bipartite(9,36) Valencies [12,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 285315214344192 EdgePairs[45][57]:={ {7,19}, {7,39}, {3,15}, {8,31}, {8,24}, {1,43}, {2,38}, {4,42}, {6,18}, {5,30}, {6,36}, {1,31}, {6,17}, {4,27}, {2,11}, {9,45}, {1,40}, {2,20}, {5,34}, {1,25}, {6,13}, {3,32}, {6,40}, {8,42}, {3,10}, {6,45}, {8,13}, {6,22}, {5,21}, {2,29}, {3,19}, {4,12}, {8,22}, {8,15}, {3,41}, {7,28}, {1,34}, {7,10}, {2,14}, {2,41}, {9,27}, {2,23}, {1,10}, {7,26}, {8,33}, {9,43}, {4,39}, {1,22}, {2,32}, {1,16}, {4,33}, {2,17}, {9,34}, {3,14}, {5,43}, {9,23}, {3,23}, {4,45}, {5,29}, {4,30}, {6,26}, {1,19}, {8,11}, {4,36}, {4,21}, {7,30}, {2,35}, {9,25}, {4,15}, {2,44}, {8,40}, {7,35}, {6,31}, {3,42}, {5,38}, {8,38}, {7,44}, {5,20}, {3,28}, {3,24}, {8,20}, {9,18}, {1,37}, {5,11}, {1,13}, {4,18}, {2,26}, {7,37}, {7,21}, {5,12}, {9,14}, {1,28}, {9,41}, {3,37}, {6,35}, {9,32}, {6,44}, {9,36}, {6,27}, {9,16}, {3,33}, {7,17}, {7,12}, {5,39}, {5,16}, {5,25}, {4,24}, {8,29} }; // ET45.58 // Bipartite(9,36) Valencies [12,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 28311552 EdgePairs[45][58]:={ {3,15}, {8,39}, {1,43}, {8,31}, {6,10}, {9,30}, {2,22}, {5,42}, {1,31}, {7,40}, {2,11}, {6,41}, {5,35}, {6,23}, {9,45}, {4,40}, {1,25}, {9,12}, {5,24}, {3,32}, {6,25}, {7,45}, {7,27}, {9,19}, {1,44}, {4,44}, {9,37}, {3,45}, {5,13}, {3,34}, {6,34}, {8,14}, {4,26}, {8,13}, {7,11}, {2,29}, {5,37}, {4,12}, {3,18}, {8,44}, {8,15}, {6,43}, {2,14}, {9,38}, {9,27}, {1,10}, {8,33}, {4,39}, {1,36}, {1,17}, {2,16}, {2,32}, {8,21}, {4,28}, {7,29}, {3,14}, {5,19}, {9,23}, {8,26}, {6,37}, {5,29}, {2,42}, {3,27}, {2,34}, {4,30}, {2,40}, {7,30}, {4,21}, {9,15}, {1,35}, {1,26}, {7,35}, {2,24}, {9,33}, {6,19}, {5,38}, {2,21}, {7,18}, {2,39}, {8,38}, {5,20}, {4,22}, {8,32}, {5,31}, {5,17}, {8,20}, {6,16}, {6,42}, {5,11}, {7,22}, {3,16}, {1,13}, {3,25}, {1,28}, {3,36}, {9,41}, {6,24}, {3,43}, {4,41}, {3,33}, {7,36}, {7,17}, {4,23}, {7,12}, {1,18}, {4,10}, {9,20}, {6,28} }; // ET45.59 // Bipartite(9,36) Valencies [12,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 940369969152 EdgePairs[45][59]:={ {7,43}, {9,13}, {7,19}, {5,32}, {6,12}, {8,39}, {2,38}, {4,14}, {1,11}, {9,30}, {6,14}, {9,42}, {6,36}, {1,40}, {5,34}, {9,12}, {7,33}, {3,32}, {7,31}, {7,45}, {4,44}, {6,40}, {9,37}, {6,45}, {3,31}, {2,19}, {9,10}, {2,18}, {2,15}, {4,26}, {8,13}, {3,19}, {1,29}, {8,15}, {7,10}, {2,14}, {3,11}, {4,37}, {4,20}, {2,31}, {7,41}, {8,33}, {1,17}, {6,33}, {1,16}, {6,21}, {8,21}, {7,29}, {9,34}, {4,29}, {5,15}, {8,35}, {3,23}, {2,42}, {6,26}, {8,11}, {4,17}, {5,28}, {9,25}, {4,25}, {1,35}, {4,38}, {5,22}, {2,27}, {2,43}, {3,35}, {1,23}, {5,27}, {8,27}, {6,38}, {2,39}, {5,20}, {3,24}, {9,24}, {3,12}, {8,23}, {1,42}, {6,16}, {1,41}, {9,18}, {3,44}, {4,32}, {7,22}, {5,10}, {8,25}, {2,26}, {8,45}, {3,20}, {7,21}, {1,28}, {3,36}, {8,37}, {6,24}, {3,43}, {9,36}, {4,41}, {5,44}, {7,34}, {7,17}, {1,30}, {5,39}, {5,16}, {4,13}, {2,30}, {1,18}, {5,40}, {6,28}, {9,22} }; // ET45.60 // Bipartite(15,30) Valencies [12,6] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 360 EdgePairs[45][60]:={ {10,25}, {1,20}, {5,17}, {11,20}, {13,32}, {6,32}, {11,36}, {12,29}, {13,21}, {11,35}, {15,24}, {3,40}, {4,16}, {11,25}, {8,30}, {12,22}, {5,38}, {7,38}, {8,42}, {8,28}, {15,31}, {4,29}, {8,33}, {3,25}, {10,26}, {14,38}, {12,39}, {2,19}, {15,44}, {2,27}, {5,20}, {9,43}, {13,35}, {8,39}, {7,34}, {1,21}, {12,35}, {15,43}, {2,41}, {2,28}, {1,30}, {9,35}, {13,29}, {2,42}, {10,22}, {6,22}, {15,25}, {11,28}, {6,29}, {8,16}, {2,45}, {3,34}, {11,38}, {11,33}, {14,33}, {5,22}, {10,38}, {9,32}, {14,21}, {12,17}, {9,27}, {1,44}, {4,41}, {9,19}, {2,37}, {12,44}, {8,45}, {14,30}, {14,40}, {15,26}, {4,45}, {6,43}, {5,23}, {10,31}, {3,20}, {13,22}, {15,42}, {10,21}, {9,42}, {1,29}, {3,39}, {13,31}, {4,35}, {7,16}, {15,41}, {7,26}, {6,33}, {6,44}, {5,24}, {9,37}, {13,23}, {12,25}, {8,22}, {1,45}, {14,41}, {3,27}, {4,28}, {4,43}, {10,45}, {1,43}, {3,26}, {15,36}, {8,26}, {5,42}, {12,33}, {10,43}, {4,36}, {5,41}, {14,17}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {11,24}, {11,39}, {5,44}, {6,26}, {12,40}, {12,30}, {3,23}, {14,34}, {1,39}, {5,36}, {6,28}, {9,30}, {13,27}, {1,37}, {15,21}, {14,25}, {3,16}, {6,42}, {15,18}, {4,40}, {7,23}, {10,17}, {11,37}, {2,29}, {11,27}, {14,44}, {1,16}, {9,17}, {10,18}, {14,32}, {8,24}, {13,41}, {2,40}, {2,31}, {9,36}, {6,34}, {4,18}, {13,38}, {10,19}, {3,28}, {15,23}, {5,45}, {7,24}, {10,20}, {7,33}, {6,37}, {12,31}, {13,34}, {5,19}, {6,20}, {7,35}, {13,39}, {2,30}, {7,37}, {2,18}, {9,31}, {1,34}, {7,19}, {4,17}, {3,36}, {9,16}, {7,40}, {14,27}, {4,32}, {11,18}, {7,18} }; // ET45.61 // Bipartite(15,30) Valencies [12,6] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[45][61]:={ {11,17}, {9,28}, {6,16}, {12,29}, {13,21}, {14,19}, {15,24}, {4,26}, {3,22}, {10,37}, {11,25}, {8,43}, {8,42}, {1,32}, {12,38}, {7,44}, {10,26}, {9,44}, {14,38}, {12,39}, {4,31}, {2,19}, {3,35}, {13,35}, {8,39}, {11,41}, {1,21}, {12,35}, {7,36}, {5,32}, {8,27}, {10,22}, {15,16}, {15,29}, {6,21}, {3,34}, {5,40}, {2,25}, {11,38}, {11,33}, {6,31}, {14,33}, {1,17}, {4,22}, {8,19}, {7,20}, {12,36}, {5,29}, {8,41}, {2,38}, {9,19}, {2,37}, {5,43}, {12,44}, {8,45}, {14,40}, {4,42}, {9,41}, {2,39}, {7,32}, {1,31}, {4,45}, {7,25}, {10,28}, {14,24}, {15,27}, {3,44}, {6,30}, {12,16}, {9,34}, {13,22}, {10,21}, {2,20}, {10,40}, {8,17}, {3,39}, {7,16}, {2,32}, {6,33}, {5,18}, {1,23}, {13,43}, {13,44}, {5,30}, {7,17}, {11,30}, {15,35}, {5,24}, {13,23}, {14,42}, {1,28}, {14,41}, {3,27}, {4,28}, {10,45}, {3,29}, {6,23}, {1,43}, {8,37}, {15,36}, {9,22}, {7,31}, {10,43}, {4,36}, {2,17}, {1,42}, {3,19}, {14,18}, {12,23}, {6,27}, {11,39}, {12,19}, {12,30}, {3,23}, {10,32}, {3,21}, {1,25}, {6,41}, {6,28}, {13,42}, {14,20}, {15,21}, {14,25}, {11,26}, {14,45}, {15,18}, {4,40}, {10,35}, {7,23}, {5,33}, {9,18}, {3,24}, {2,29}, {11,27}, {1,26}, {4,34}, {10,36}, {1,16}, {15,22}, {11,32}, {15,33}, {8,24}, {6,38}, {2,40}, {9,33}, {9,36}, {6,34}, {5,27}, {5,26}, {15,28}, {9,38}, {4,25}, {4,20}, {8,20}, {13,37}, {5,45}, {3,41}, {9,24}, {6,39}, {12,31}, {13,34}, {7,35}, {11,43}, {2,30}, {13,17}, {13,45}, {15,30}, {13,20}, {7,37}, {2,18}, {9,31}, {1,34}, {5,37}, {11,42}, {7,40}, {4,44}, {8,29}, {12,18}, {14,26}, {10,16} }; // ET45.62 // Bipartite(15,30) Valencies [12,6] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 15045919506432000000 EdgePairs[45][62]:={ {3,33}, {10,24}, {5,17}, {9,28}, {6,16}, {11,36}, {13,21}, {5,34}, {15,24}, {12,45}, {10,37}, {4,30}, {8,43}, {9,45}, {12,22}, {12,32}, {8,28}, {8,33}, {3,43}, {14,38}, {7,22}, {15,44}, {1,19}, {12,42}, {2,27}, {9,43}, {11,41}, {1,21}, {12,35}, {10,44}, {5,32}, {9,35}, {14,28}, {4,23}, {8,31}, {12,37}, {13,16}, {2,42}, {10,22}, {3,18}, {6,29}, {8,16}, {2,45}, {4,38}, {15,29}, {6,21}, {2,25}, {14,23}, {6,31}, {14,33}, {5,22}, {7,20}, {12,17}, {15,32}, {12,20}, {1,44}, {5,29}, {8,41}, {2,37}, {14,30}, {14,40}, {7,32}, {1,31}, {4,45}, {7,25}, {11,31}, {2,35}, {11,44}, {15,27}, {4,33}, {10,29}, {15,19}, {15,42}, {2,20}, {13,18}, {1,29}, {7,30}, {13,31}, {11,21}, {4,35}, {9,25}, {8,36}, {2,32}, {13,33}, {13,43}, {11,29}, {6,24}, {6,44}, {7,17}, {5,24}, {13,23}, {12,25}, {15,37}, {15,34}, {13,28}, {10,42}, {9,20}, {4,28}, {4,43}, {15,17}, {3,26}, {13,36}, {8,26}, {5,42}, {2,17}, {12,27}, {9,40}, {8,21}, {1,24}, {14,18}, {11,24}, {11,39}, {5,44}, {6,26}, {12,40}, {12,30}, {3,23}, {8,23}, {1,39}, {10,32}, {3,21}, {6,19}, {6,41}, {9,30}, {10,39}, {14,20}, {5,39}, {14,25}, {3,16}, {13,26}, {11,26}, {14,45}, {4,40}, {11,16}, {6,36}, {9,18}, {10,17}, {10,27}, {8,38}, {1,26}, {2,22}, {1,16}, {10,34}, {15,22}, {13,41}, {2,40}, {9,33}, {6,34}, {5,27}, {14,43}, {8,18}, {4,18}, {13,38}, {9,38}, {11,19}, {10,19}, {4,25}, {3,38}, {4,20}, {3,28}, {7,27}, {7,45}, {14,35}, {1,41}, {3,41}, {3,31}, {15,39}, {6,39}, {11,34}, {5,19}, {7,35}, {2,30}, {7,37}, {1,34}, {5,37}, {3,36}, {7,40}, {7,42}, {9,23}, {1,36} }; // ET45.63 // Bipartite(15,30) Valencies [12,6] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 56422198149120 EdgePairs[45][63]:={ {10,25}, {5,17}, {10,24}, {2,33}, {6,16}, {11,36}, {13,21}, {5,34}, {15,24}, {4,26}, {4,16}, {10,37}, {4,30}, {2,23}, {12,22}, {12,32}, {7,38}, {8,28}, {3,45}, {3,25}, {12,38}, {7,22}, {4,31}, {15,44}, {1,19}, {12,42}, {2,27}, {3,35}, {5,20}, {13,35}, {14,31}, {8,39}, {10,44}, {8,25}, {2,28}, {8,31}, {13,29}, {12,37}, {2,42}, {15,25}, {3,18}, {10,30}, {6,29}, {15,45}, {5,40}, {11,33}, {4,22}, {8,19}, {9,32}, {14,21}, {14,36}, {12,17}, {9,26}, {15,40}, {1,44}, {4,41}, {8,41}, {2,38}, {2,37}, {8,45}, {14,30}, {14,40}, {4,42}, {9,41}, {5,25}, {7,32}, {7,43}, {11,44}, {15,27}, {6,43}, {4,21}, {9,42}, {14,16}, {13,18}, {10,40}, {12,43}, {1,29}, {3,39}, {13,31}, {2,32}, {6,33}, {11,23}, {1,23}, {11,29}, {6,24}, {5,30}, {6,44}, {7,17}, {15,35}, {5,24}, {12,28}, {15,37}, {14,42}, {15,34}, {13,25}, {8,35}, {13,28}, {15,20}, {9,20}, {14,41}, {1,33}, {15,17}, {10,45}, {3,29}, {6,23}, {1,43}, {9,22}, {12,33}, {2,17}, {4,36}, {12,27}, {9,40}, {8,21}, {3,19}, {1,24}, {12,23}, {14,22}, {11,24}, {11,39}, {5,44}, {6,26}, {1,39}, {3,21}, {6,19}, {9,30}, {14,20}, {7,28}, {11,26}, {4,40}, {10,35}, {11,16}, {13,19}, {7,23}, {6,36}, {10,17}, {10,27}, {8,38}, {1,26}, {2,22}, {1,16}, {10,34}, {14,32}, {13,41}, {9,36}, {6,34}, {5,27}, {8,18}, {13,38}, {11,19}, {3,38}, {4,20}, {3,28}, {7,27}, {5,45}, {3,41}, {3,31}, {10,20}, {6,39}, {7,33}, {11,34}, {13,39}, {11,43}, {13,45}, {15,30}, {7,37}, {5,35}, {2,18}, {9,31}, {1,34}, {5,37}, {2,43}, {9,21}, {9,16}, {7,42}, {8,29}, {4,32}, {12,18}, {1,36}, {14,26}, {7,18} }; // ET45.64 // Bipartite(15,30) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 43535646720 EdgePairs[45][64]:={ {11,17}, {2,44}, {10,25}, {1,20}, {2,24}, {9,28}, {2,33}, {6,16}, {6,32}, {11,36}, {13,21}, {4,24}, {14,19}, {4,26}, {3,40}, {4,16}, {12,45}, {10,37}, {4,30}, {6,17}, {14,39}, {2,23}, {8,42}, {15,31}, {1,32}, {12,38}, {1,40}, {9,44}, {14,38}, {12,41}, {5,20}, {3,37}, {1,21}, {12,35}, {15,43}, {8,25}, {2,28}, {1,30}, {5,32}, {14,28}, {8,44}, {8,31}, {13,29}, {2,42}, {10,22}, {15,16}, {6,22}, {3,18}, {3,17}, {15,29}, {5,40}, {11,33}, {2,34}, {5,22}, {9,29}, {7,20}, {14,36}, {5,29}, {8,41}, {2,38}, {9,19}, {5,43}, {8,45}, {15,26}, {1,31}, {4,45}, {7,43}, {7,25}, {11,44}, {1,22}, {5,23}, {10,29}, {3,20}, {9,34}, {15,19}, {14,16}, {6,18}, {12,43}, {7,30}, {13,31}, {4,35}, {15,41}, {2,32}, {11,23}, {13,44}, {5,30}, {7,17}, {12,28}, {12,25}, {8,22}, {8,35}, {10,42}, {9,20}, {3,27}, {10,45}, {15,36}, {5,42}, {12,33}, {4,36}, {9,40}, {8,32}, {8,21}, {1,42}, {14,18}, {12,23}, {6,27}, {11,24}, {13,24}, {6,26}, {10,32}, {3,21}, {6,28}, {9,30}, {10,39}, {13,27}, {15,21}, {5,39}, {14,25}, {11,26}, {6,42}, {14,45}, {4,40}, {10,35}, {11,16}, {7,23}, {13,19}, {6,36}, {3,30}, {5,33}, {8,34}, {9,18}, {10,17}, {11,37}, {11,27}, {10,27}, {1,26}, {2,22}, {4,34}, {1,16}, {15,33}, {8,24}, {13,41}, {6,38}, {9,39}, {9,38}, {10,19}, {4,25}, {3,38}, {4,20}, {3,28}, {7,27}, {7,45}, {14,35}, {15,23}, {1,41}, {13,37}, {3,41}, {3,31}, {15,39}, {9,24}, {7,33}, {6,37}, {12,31}, {11,34}, {13,34}, {5,19}, {7,35}, {13,39}, {11,43}, {13,17}, {7,37}, {2,18}, {2,43}, {7,40}, {4,44}, {12,18}, {12,21}, {1,36}, {14,29}, {14,26} }; // ET45.65 // Bipartite(15,30) Valencies [12,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23592960 EdgePairs[45][65]:={ {11,17}, {3,33}, {10,25}, {1,20}, {10,24}, {11,20}, {9,28}, {6,16}, {13,21}, {11,35}, {13,40}, {14,19}, {4,24}, {4,26}, {10,37}, {4,30}, {8,30}, {2,23}, {7,38}, {8,42}, {3,45}, {8,33}, {12,38}, {4,19}, {7,22}, {15,44}, {1,19}, {2,27}, {5,20}, {9,43}, {14,31}, {2,26}, {1,21}, {2,41}, {12,34}, {8,27}, {2,42}, {10,22}, {6,22}, {15,25}, {3,18}, {6,29}, {3,17}, {15,29}, {6,21}, {11,38}, {11,33}, {6,31}, {5,22}, {8,19}, {7,20}, {15,32}, {9,26}, {9,27}, {12,36}, {15,40}, {1,44}, {4,41}, {8,41}, {2,38}, {5,43}, {14,30}, {8,45}, {9,41}, {7,32}, {4,45}, {7,43}, {7,25}, {2,35}, {11,44}, {1,22}, {3,44}, {6,30}, {4,21}, {10,31}, {9,42}, {2,20}, {14,16}, {13,18}, {10,40}, {12,43}, {1,29}, {2,16}, {3,32}, {9,25}, {13,33}, {2,32}, {11,23}, {11,29}, {6,24}, {6,44}, {7,17}, {5,24}, {12,28}, {12,25}, {15,37}, {13,25}, {10,42}, {1,28}, {14,41}, {3,27}, {4,28}, {4,43}, {15,17}, {3,29}, {1,43}, {5,28}, {13,36}, {15,36}, {8,26}, {12,33}, {13,30}, {5,41}, {4,36}, {2,17}, {9,40}, {12,23}, {13,24}, {5,31}, {12,19}, {12,40}, {8,23}, {14,34}, {10,32}, {13,27}, {10,39}, {1,35}, {13,42}, {14,20}, {1,37}, {15,21}, {5,39}, {7,28}, {3,16}, {14,45}, {15,18}, {7,23}, {6,36}, {3,30}, {8,34}, {10,17}, {10,27}, {8,38}, {6,45}, {4,34}, {14,44}, {15,22}, {11,32}, {15,33}, {2,31}, {5,26}, {8,18}, {3,42}, {9,39}, {9,38}, {11,19}, {14,35}, {3,31}, {9,24}, {6,39}, {6,37}, {11,34}, {7,35}, {13,39}, {13,45}, {7,37}, {5,35}, {1,34}, {5,37}, {4,39}, {7,40}, {9,23}, {12,18}, {11,18}, {12,21}, {14,29}, {1,36}, {14,26}, {10,16}, {5,16} }; // ET45.66 // Bipartite(18,27) Valencies [12,8] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 432 EdgePairs[45][66]:={ {2,44}, {3,33}, {16,41}, {10,24}, {2,24}, {13,32}, {9,28}, {2,33}, {6,32}, {17,35}, {17,44}, {11,36}, {18,39}, {12,29}, {11,35}, {4,26}, {3,40}, {17,38}, {4,30}, {11,25}, {14,39}, {8,43}, {5,38}, {12,32}, {15,31}, {1,32}, {8,33}, {10,23}, {7,41}, {1,40}, {10,26}, {9,44}, {4,19}, {14,38}, {16,19}, {12,39}, {2,19}, {1,19}, {2,27}, {13,35}, {14,31}, {1,21}, {17,24}, {8,25}, {1,30}, {16,23}, {8,44}, {8,31}, {18,34}, {6,22}, {15,25}, {18,42}, {18,37}, {10,30}, {6,29}, {4,38}, {15,29}, {3,34}, {6,40}, {1,38}, {2,36}, {5,22}, {8,19}, {7,20}, {15,32}, {16,24}, {9,26}, {18,20}, {12,20}, {12,36}, {5,29}, {4,41}, {8,41}, {2,38}, {5,43}, {12,44}, {8,45}, {14,30}, {4,42}, {5,25}, {2,39}, {17,39}, {15,26}, {7,43}, {11,31}, {10,28}, {2,35}, {17,33}, {11,44}, {15,27}, {3,44}, {4,21}, {10,21}, {9,42}, {16,37}, {10,40}, {3,39}, {3,32}, {11,21}, {9,25}, {8,36}, {6,33}, {7,26}, {18,44}, {13,43}, {1,23}, {11,29}, {5,30}, {11,30}, {9,37}, {17,27}, {13,23}, {12,28}, {12,25}, {15,37}, {8,22}, {15,34}, {15,20}, {9,20}, {1,28}, {18,27}, {14,41}, {3,27}, {4,43}, {10,45}, {18,33}, {3,29}, {16,38}, {17,31}, {18,31}, {12,26}, {9,22}, {13,30}, {10,43}, {5,41}, {9,40}, {16,45}, {8,21}, {1,42}, {1,24}, {12,23}, {14,22}, {6,27}, {11,24}, {11,39}, {6,26}, {12,40}, {3,23}, {10,32}, {5,36}, {17,19}, {17,41}, {18,23}, {1,35}, {16,34}, {14,25}, {7,28}, {4,37}, {6,42}, {13,26}, {14,45}, {4,40}, {10,35}, {6,36}, {2,21}, {5,33}, {2,29}, {16,35}, {18,28}, {4,34}, {15,22}, {18,22}, {16,20}, {8,24}, {13,41}, {6,25}, {9,33}, {9,36}, {16,42}, {6,34}, {5,27}, {14,43}, {3,42}, {13,38}, {17,45}, {11,45}, {3,28}, {7,45}, {14,35}, {15,23}, {13,37}, {7,24}, {15,39}, {10,20}, {12,31}, {6,37}, {13,34}, {5,19}, {17,22}, {11,43}, {5,21}, {2,30}, {13,45}, {13,20}, {7,37}, {9,31}, {1,34}, {7,19}, {3,36}, {16,28}, {7,40}, {7,42}, {7,21}, {14,27}, {4,32}, {14,29} }; // ET45.67 // Bipartite(18,27) Valencies [12,8] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 216 EdgePairs[45][67]:={ {3,33}, {16,41}, {1,20}, {13,32}, {9,28}, {17,35}, {17,44}, {17,36}, {18,39}, {12,29}, {11,35}, {5,34}, {13,40}, {4,24}, {14,19}, {16,26}, {3,22}, {10,37}, {4,30}, {11,25}, {8,30}, {16,40}, {14,39}, {2,23}, {8,43}, {4,29}, {3,43}, {7,44}, {17,20}, {17,34}, {9,44}, {14,38}, {16,19}, {4,31}, {10,33}, {2,27}, {1,19}, {9,43}, {8,39}, {7,34}, {12,35}, {17,21}, {18,21}, {10,44}, {8,25}, {2,41}, {18,41}, {5,32}, {16,23}, {14,28}, {4,23}, {8,31}, {18,34}, {10,22}, {18,42}, {16,43}, {2,45}, {16,30}, {4,38}, {15,29}, {11,38}, {1,38}, {2,36}, {10,38}, {17,37}, {14,36}, {15,32}, {9,26}, {9,27}, {12,20}, {15,40}, {1,44}, {4,41}, {5,29}, {2,38}, {12,44}, {8,45}, {14,30}, {7,39}, {4,42}, {5,25}, {7,32}, {17,23}, {1,31}, {11,22}, {10,28}, {3,44}, {4,21}, {10,31}, {9,34}, {13,22}, {15,42}, {2,20}, {16,37}, {10,40}, {12,43}, {17,43}, {9,25}, {15,41}, {13,33}, {6,33}, {18,44}, {1,23}, {11,29}, {6,24}, {5,30}, {17,30}, {15,35}, {9,37}, {12,28}, {12,25}, {1,45}, {14,42}, {15,34}, {13,25}, {8,35}, {15,20}, {18,26}, {3,27}, {14,37}, {4,28}, {1,33}, {10,45}, {3,29}, {6,23}, {3,26}, {13,36}, {8,26}, {12,33}, {5,41}, {9,40}, {8,32}, {16,45}, {8,21}, {1,42}, {3,19}, {1,24}, {5,31}, {11,24}, {6,27}, {12,19}, {8,40}, {6,26}, {12,40}, {18,19}, {10,32}, {5,36}, {3,21}, {6,28}, {9,30}, {14,20}, {14,25}, {7,28}, {6,42}, {7,23}, {13,19}, {16,36}, {6,36}, {2,21}, {5,33}, {11,37}, {3,24}, {2,29}, {11,27}, {10,27}, {1,26}, {2,22}, {15,22}, {18,22}, {11,32}, {15,33}, {16,20}, {8,24}, {6,25}, {13,41}, {6,38}, {2,31}, {6,34}, {5,27}, {5,26}, {18,45}, {3,42}, {15,28}, {16,39}, {13,38}, {11,19}, {11,45}, {12,24}, {7,27}, {7,45}, {14,35}, {1,41}, {13,37}, {7,24}, {18,40}, {10,20}, {6,39}, {12,31}, {13,34}, {17,42}, {7,35}, {13,39}, {17,22}, {11,43}, {5,21}, {15,30}, {7,37}, {9,31}, {2,43}, {3,36}, {4,39}, {18,35}, {9,23}, {7,21}, {4,32}, {14,29} }; // ET45.68 // Bipartite(18,27) Valencies [12,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 371504185344 EdgePairs[45][68]:={ {2,44}, {10,25}, {1,20}, {2,24}, {11,20}, {2,33}, {6,32}, {17,35}, {17,44}, {11,36}, {18,39}, {4,27}, {12,29}, {11,35}, {4,24}, {3,22}, {3,40}, {10,37}, {16,27}, {8,30}, {16,40}, {14,39}, {12,22}, {5,38}, {12,32}, {8,42}, {16,31}, {15,31}, {8,33}, {12,38}, {10,26}, {4,19}, {14,38}, {16,19}, {7,22}, {12,41}, {15,44}, {1,19}, {2,27}, {5,20}, {9,43}, {3,37}, {2,26}, {8,39}, {17,24}, {7,36}, {15,43}, {17,21}, {18,21}, {10,44}, {5,32}, {8,44}, {12,37}, {2,42}, {18,34}, {6,22}, {15,25}, {18,42}, {2,45}, {16,30}, {14,23}, {11,38}, {11,33}, {6,31}, {6,40}, {1,38}, {2,36}, {10,38}, {14,21}, {14,36}, {15,32}, {12,20}, {15,40}, {1,44}, {5,29}, {8,41}, {2,38}, {14,30}, {7,39}, {4,42}, {17,39}, {15,26}, {17,23}, {4,45}, {10,28}, {2,35}, {17,33}, {11,44}, {6,43}, {4,33}, {5,23}, {10,29}, {3,20}, {9,34}, {9,42}, {2,20}, {16,37}, {1,29}, {7,30}, {18,30}, {3,32}, {9,25}, {15,41}, {13,33}, {18,43}, {13,43}, {11,29}, {5,30}, {6,44}, {17,30}, {15,35}, {12,28}, {15,34}, {13,25}, {18,24}, {8,35}, {13,28}, {1,28}, {14,41}, {4,28}, {4,43}, {18,33}, {3,29}, {6,23}, {1,43}, {13,36}, {8,26}, {18,31}, {16,22}, {9,22}, {7,31}, {10,43}, {4,36}, {5,41}, {9,40}, {8,32}, {16,45}, {8,21}, {3,19}, {12,23}, {13,24}, {11,24}, {12,19}, {6,26}, {12,40}, {3,23}, {8,23}, {18,25}, {5,36}, {1,25}, {17,41}, {6,41}, {9,30}, {13,27}, {1,35}, {13,42}, {1,37}, {14,20}, {5,39}, {16,21}, {7,28}, {4,37}, {11,26}, {14,45}, {10,35}, {13,19}, {16,36}, {2,29}, {11,27}, {1,26}, {4,34}, {10,34}, {15,22}, {18,22}, {14,32}, {8,24}, {6,25}, {9,33}, {6,34}, {5,27}, {16,39}, {9,39}, {10,19}, {4,25}, {3,38}, {11,45}, {3,28}, {7,27}, {7,45}, {15,23}, {13,37}, {5,45}, {3,41}, {3,31}, {9,24}, {18,40}, {10,20}, {17,26}, {12,31}, {13,34}, {17,42}, {5,21}, {13,45}, {7,37}, {9,31}, {1,34}, {7,19}, {6,35}, {17,32}, {11,42}, {9,21}, {16,28}, {7,40}, {7,21}, {14,27}, {14,29} }; // ET45.69 // Bipartite(18,27) Valencies [12,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1451188224 EdgePairs[45][69]:={ {3,33}, {10,24}, {1,20}, {11,20}, {9,28}, {6,32}, {17,36}, {12,29}, {11,35}, {14,19}, {16,33}, {18,29}, {4,26}, {3,22}, {3,40}, {17,38}, {18,32}, {11,25}, {8,30}, {16,40}, {8,43}, {9,45}, {12,22}, {16,31}, {18,38}, {15,31}, {3,45}, {10,23}, {12,38}, {10,26}, {17,20}, {12,39}, {7,22}, {4,31}, {10,33}, {2,27}, {1,19}, {9,43}, {13,35}, {14,31}, {8,39}, {1,21}, {16,25}, {12,35}, {7,36}, {17,21}, {10,44}, {8,25}, {1,30}, {18,41}, {5,32}, {14,28}, {8,44}, {4,23}, {8,27}, {13,29}, {18,34}, {18,42}, {11,28}, {16,43}, {10,30}, {2,45}, {16,30}, {15,29}, {6,21}, {2,25}, {11,38}, {1,38}, {2,34}, {14,33}, {2,36}, {4,22}, {15,32}, {16,24}, {18,20}, {9,27}, {12,20}, {15,40}, {4,41}, {2,38}, {9,19}, {12,44}, {8,45}, {14,40}, {7,39}, {17,39}, {17,23}, {10,41}, {14,24}, {11,44}, {6,30}, {6,43}, {5,23}, {9,34}, {15,19}, {10,21}, {9,42}, {2,20}, {1,29}, {7,30}, {3,32}, {4,35}, {9,25}, {15,41}, {8,36}, {13,33}, {18,43}, {11,29}, {13,44}, {17,30}, {9,37}, {17,27}, {15,37}, {14,42}, {18,24}, {8,35}, {10,42}, {15,20}, {1,28}, {3,27}, {14,37}, {4,43}, {1,33}, {18,33}, {6,23}, {5,28}, {13,36}, {8,26}, {12,26}, {16,22}, {7,31}, {5,41}, {8,21}, {1,42}, {1,24}, {14,22}, {13,24}, {5,44}, {12,40}, {12,30}, {3,23}, {1,39}, {10,32}, {18,25}, {17,29}, {5,36}, {6,19}, {17,41}, {6,41}, {6,28}, {18,23}, {10,39}, {13,27}, {13,42}, {1,37}, {16,34}, {16,21}, {7,28}, {11,26}, {13,26}, {4,40}, {10,35}, {8,34}, {11,37}, {3,24}, {2,29}, {2,22}, {4,34}, {14,44}, {15,22}, {6,25}, {2,40}, {2,31}, {9,33}, {9,36}, {16,42}, {6,34}, {5,27}, {15,38}, {5,26}, {3,42}, {15,28}, {16,39}, {13,38}, {11,19}, {4,25}, {17,45}, {7,27}, {7,45}, {14,35}, {15,23}, {5,45}, {3,41}, {3,31}, {9,24}, {6,39}, {12,31}, {6,37}, {11,34}, {5,19}, {11,43}, {13,45}, {7,37}, {13,20}, {5,35}, {5,37}, {7,19}, {2,43}, {17,32}, {3,36}, {7,40}, {4,44}, {7,21}, {4,32}, {12,21}, {14,26} }; // ET45.70 // Bipartite(18,27) Valencies [12,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 663552 EdgePairs[45][70]:={ {3,33}, {16,41}, {10,25}, {1,20}, {10,24}, {11,20}, {9,28}, {6,32}, {17,35}, {17,36}, {18,39}, {12,29}, {13,21}, {11,35}, {5,34}, {13,40}, {4,24}, {16,33}, {3,40}, {17,38}, {12,45}, {18,32}, {11,25}, {16,27}, {14,39}, {2,23}, {8,43}, {5,38}, {7,38}, {15,31}, {4,29}, {3,45}, {8,33}, {12,38}, {7,41}, {7,44}, {1,40}, {10,26}, {14,38}, {12,39}, {7,22}, {15,44}, {1,19}, {3,37}, {2,26}, {18,21}, {8,25}, {2,28}, {12,34}, {1,30}, {16,23}, {14,28}, {8,31}, {13,29}, {12,37}, {2,42}, {18,34}, {10,22}, {15,25}, {11,28}, {16,43}, {10,30}, {15,45}, {16,30}, {3,34}, {2,25}, {6,31}, {8,19}, {7,20}, {17,37}, {9,32}, {14,36}, {15,32}, {4,41}, {9,19}, {5,43}, {12,44}, {8,45}, {4,42}, {2,39}, {7,32}, {17,23}, {7,43}, {11,31}, {14,24}, {2,35}, {17,33}, {1,22}, {15,27}, {3,44}, {6,30}, {4,33}, {4,21}, {10,29}, {9,34}, {15,19}, {2,20}, {10,40}, {17,43}, {1,29}, {7,30}, {3,39}, {18,30}, {11,21}, {15,41}, {8,36}, {2,32}, {13,33}, {16,32}, {11,23}, {13,43}, {11,29}, {13,44}, {6,44}, {5,24}, {15,37}, {8,22}, {14,42}, {18,24}, {8,35}, {10,42}, {13,28}, {15,20}, {14,41}, {3,27}, {4,28}, {4,43}, {3,29}, {3,26}, {16,38}, {8,37}, {5,28}, {13,36}, {15,36}, {17,31}, {18,31}, {5,42}, {12,26}, {16,22}, {9,22}, {12,33}, {5,41}, {4,36}, {12,27}, {9,40}, {1,42}, {1,24}, {13,24}, {6,27}, {17,25}, {11,39}, {12,40}, {8,23}, {14,34}, {18,19}, {5,36}, {3,21}, {17,19}, {1,25}, {6,19}, {16,44}, {6,41}, {18,23}, {9,30}, {1,35}, {13,42}, {5,39}, {4,37}, {11,26}, {14,45}, {4,40}, {10,35}, {7,23}, {6,36}, {2,21}, {2,29}, {16,35}, {18,28}, {6,45}, {8,38}, {1,26}, {10,34}, {18,22}, {11,32}, {16,20}, {6,25}, {13,41}, {2,31}, {5,27}, {14,43}, {5,26}, {9,39}, {10,19}, {17,45}, {3,38}, {7,27}, {13,37}, {5,45}, {9,24}, {18,40}, {10,20}, {7,33}, {6,37}, {6,20}, {7,35}, {17,22}, {15,30}, {9,31}, {1,34}, {11,42}, {9,21}, {4,44}, {9,23}, {14,27}, {12,21}, {14,26} }; // ET45.71 // Non-bipartite Valency 12 // Diameter 3 Girth 4 // Has twins VT AT // Automorphism group of order 28211099074560 EdgePairs[45][71]:={ {24,34}, {6,38}, {5,7}, {40,43}, {35,38}, {5,38}, {25,37}, {9,10}, {33,43}, {12,22}, {11,43}, {2,35}, {8,40}, {3,35}, {11,15}, {8,21}, {33,34}, {30,40}, {30,41}, {15,27}, {24,36}, {26,37}, {36,39}, {16,28}, {11,14}, {1,35}, {6,9}, {21,22}, {4,37}, {13,27}, {16,21}, {4,38}, {9,11}, {33,44}, {2,34}, {26,38}, {19,31}, {2,6}, {8,12}, {33,45}, {4,16}, {29,33}, {28,31}, {27,28}, {26,39}, {20,24}, {7,11}, {31,36}, {7,41}, {1,13}, {2,5}, {19,22}, {23,36}, {6,39}, {26,29}, {17,20}, {33,35}, {2,15}, {12,23}, {22,25}, {5,37}, {12,13}, {1,36}, {6,18}, {35,37}, {24,26}, {34,37}, {13,26}, {29,31}, {32,44}, {13,16}, {31,43}, {38,42}, {36,38}, {2,36}, {22,34}, {27,30}, {18,29}, {31,44}, {1,43}, {8,42}, {32,45}, {9,20}, {29,32}, {8,19}, {3,43}, {6,17}, {32,35}, {38,41}, {4,7}, {4,18}, {27,39}, {28,40}, {12,24}, {3,13}, {11,22}, {35,39}, {42,45}, {4,9}, {30,31}, {28,42}, {3,36}, {19,23}, {25,29}, {17,29}, {13,17}, {18,19}, {7,19}, {2,44}, {2,13}, {41,44}, {13,18}, {12,15}, {8,10}, {16,29}, {11,23}, {22,26}, {6,16}, {39,40}, {13,25}, {21,31}, {7,12}, {8,41}, {27,37}, {42,44}, {18,20}, {20,22}, {10,13}, {39,42}, {9,19}, {3,44}, {11,44}, {20,31}, {19,24}, {17,28}, {6,8}, {11,13}, {25,30}, {2,43}, {11,24}, {1,6}, {10,44}, {24,25}, {37,40}, {23,35}, {4,17}, {17,19}, {5,39}, {9,12}, {14,27}, {38,40}, {17,30}, {10,22}, {16,30}, {12,45}, {21,32}, {1,44}, {5,8}, {23,27}, {24,35}, {36,37}, {9,41}, {25,38}, {15,17}, {34,38}, {23,34}, {1,5}, {30,32}, {28,32}, {6,37}, {24,27}, {7,40}, {12,43}, {20,32}, {29,41}, {34,39}, {12,14}, {18,21}, {9,21}, {26,30}, {18,30}, {29,42}, {7,21}, {14,16}, {2,45}, {14,26}, {1,45}, {10,15}, {3,5}, {19,33}, {3,34}, {18,28}, {16,20}, {8,11}, {25,39}, {11,45}, {21,33}, {40,45}, {3,45}, {26,28}, {3,14}, {12,44}, {4,8}, {31,35}, {5,9}, {30,33}, {39,41}, {1,4}, {31,45}, {31,34}, {28,33}, {41,45}, {27,29}, {7,10}, {3,6}, {20,33}, {3,15}, {1,14}, {22,27}, {1,34}, {14,18}, {7,42}, {20,23}, {2,4}, {42,43}, {17,21}, {19,32}, {1,15}, {14,25}, {40,44}, {5,18}, {5,16}, {10,24}, {15,18}, {5,17}, {3,4}, {15,16}, {10,45}, {32,36}, {41,43}, {23,25}, {7,20}, {22,35}, {10,43}, {32,43}, {9,40}, {8,20}, {32,34}, {10,23}, {15,26}, {22,36}, {9,42}, {14,17}, {25,28}, {16,19}, {10,14}, {4,39}, {21,24}, {23,26}, {28,41}, {37,41}, {30,42}, {6,7}, {2,14}, {33,36}, {15,25}, {27,38}, {37,42}, {29,40}, {21,23} }; // ET45.72 // Non-bipartite Valency 12 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 77760 EdgePairs[45][72]:={ {13,21}, {19,28}, {15,38}, {31,39}, {14,36}, {9,32}, {6,25}, {38,43}, {23,29}, {9,17}, {10,18}, {3,8}, {31,40}, {5,45}, {3,26}, {5,11}, {13,37}, {1,40}, {16,22}, {14,38}, {17,42}, {13,39}, {6,15}, {10,33}, {21,30}, {24,32}, {5,15}, {3,23}, {12,16}, {3,39}, {29,39}, {8,31}, {23,44}, {6,14}, {24,28}, {35,45}, {11,17}, {1,12}, {27,36}, {19,40}, {8,16}, {20,26}, {10,17}, {9,18}, {2,25}, {21,40}, {4,43}, {16,42}, {4,30}, {8,13}, {8,30}, {9,33}, {20,43}, {1,9}, {7,45}, {1,10}, {4,13}, {12,20}, {17,39}, {23,31}, {3,10}, {12,31}, {10,20}, {17,26}, {1,24}, {27,32}, {26,35}, {16,25}, {24,45}, {23,43}, {15,19}, {10,35}, {6,44}, {31,38}, {30,36}, {13,19}, {1,26}, {20,42}, {7,15}, {32,39}, {35,42}, {9,29}, {18,26}, {3,38}, {5,27}, {7,14}, {5,28}, {6,10}, {20,41}, {8,18}, {7,32}, {25,33}, {9,13}, {1,39}, {5,12}, {6,27}, {2,8}, {14,34}, {34,40}, {37,45}, {36,41}, {20,25}, {21,45}, {19,27}, {11,21}, {11,36}, {2,24}, {11,16}, {10,36}, {15,34}, {11,33}, {33,42}, {31,41}, {4,41}, {4,10}, {14,21}, {18,38}, {8,45}, {28,34}, {29,36}, {13,36}, {1,41}, {2,23}, {4,45}, {25,32}, {10,19}, {15,23}, {39,43}, {3,25}, {11,34}, {21,42}, {19,45}, {22,30}, {27,34}, {2,27}, {6,30}, {2,12}, {1,22}, {22,44}, {10,31}, {33,37}, {13,22}, {22,31}, {20,30}, {34,43}, {9,30}, {22,45}, {16,41}, {7,28}, {20,44}, {12,18}, {19,41}, {6,11}, {5,40}, {28,37}, {33,38}, {15,35}, {29,38}, {26,31}, {11,32}, {15,24}, {32,42}, {3,7}, {33,40}, {3,42}, {3,22}, {14,37}, {4,14}, {32,41}, {19,44}, {24,43}, {15,39}, {4,29}, {9,44}, {24,29}, {19,29}, {6,43}, {32,37}, {17,22}, {17,25}, {2,41}, {34,42}, {18,41}, {36,43}, {7,29}, {37,44}, {2,11}, {35,41}, {36,40}, {18,24}, {25,36}, {16,38}, {20,28}, {18,27}, {16,27}, {1,7}, {19,25}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {14,24}, {30,34}, {13,35}, {21,43}, {21,27}, {6,41}, {9,15}, {21,29}, {17,24}, {17,40}, {12,34}, {8,44}, {28,35}, {23,30}, {6,28}, {16,23}, {18,23}, {14,20}, {23,33}, {7,16}, {3,40}, {7,17}, {13,23}, {4,26}, {15,20}, {17,37}, {16,39}, {26,34}, {28,38}, {5,42}, {2,38}, {12,32}, {25,35}, {8,28}, {7,43}, {18,40}, {34,44}, {1,27}, {5,44}, {5,13}, {9,43}, {26,33}, {27,31}, {29,35}, {14,22}, {22,32}, {24,33}, {12,35}, {35,44}, {36,45}, {21,26}, {22,28}, {1,37}, {2,42}, {30,39}, {2,9}, {30,37}, {39,44}, {12,21}, {38,45}, {18,37}, {6,40} }; // ET45.73 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 4320 EdgePairs[45][73]:={ {6,38}, {9,32}, {6,25}, {38,43}, {5,38}, {3,8}, {31,40}, {5,45}, {8,26}, {22,40}, {25,40}, {16,22}, {28,44}, {15,44}, {17,33}, {4,31}, {8,21}, {30,40}, {30,41}, {15,27}, {3,23}, {2,18}, {14,45}, {3,39}, {5,32}, {21,22}, {4,37}, {8,31}, {13,43}, {14,29}, {23,44}, {14,44}, {6,32}, {17,35}, {11,35}, {11,29}, {1,12}, {11,27}, {3,18}, {12,28}, {19,31}, {4,43}, {18,32}, {8,13}, {9,33}, {20,43}, {1,17}, {1,9}, {29,33}, {28,31}, {1,10}, {8,37}, {29,44}, {12,26}, {3,10}, {7,27}, {38,44}, {6,39}, {22,42}, {2,17}, {7,33}, {10,20}, {1,24}, {15,30}, {5,37}, {27,41}, {18,35}, {24,45}, {23,43}, {20,35}, {6,18}, {23,42}, {1,29}, {35,37}, {16,34}, {37,43}, {24,26}, {8,38}, {13,26}, {29,31}, {17,36}, {13,16}, {1,38}, {38,42}, {36,38}, {20,36}, {35,42}, {9,39}, {3,38}, {5,27}, {7,14}, {15,28}, {24,41}, {38,41}, {6,10}, {2,39}, {4,18}, {24,40}, {26,42}, {14,35}, {28,40}, {27,40}, {35,39}, {7,37}, {5,12}, {2,30}, {2,8}, {14,34}, {28,42}, {34,40}, {19,23}, {37,45}, {26,41}, {7,19}, {1,30}, {39,45}, {13,18}, {8,15}, {11,21}, {3,16}, {2,24}, {22,26}, {10,36}, {6,16}, {15,34}, {39,40}, {33,42}, {13,25}, {21,31}, {31,41}, {9,38}, {9,26}, {3,29}, {13,36}, {20,22}, {10,19}, {39,42}, {4,11}, {9,19}, {13,45}, {19,24}, {11,34}, {19,45}, {4,33}, {2,12}, {22,44}, {24,25}, {37,40}, {4,17}, {14,27}, {22,45}, {6,45}, {6,11}, {13,29}, {9,25}, {10,30}, {10,25}, {12,29}, {28,45}, {32,42}, {3,7}, {12,25}, {33,40}, {1,16}, {3,22}, {23,27}, {36,37}, {32,41}, {19,44}, {18,31}, {24,43}, {16,31}, {15,17}, {34,38}, {7,39}, {30,32}, {28,32}, {6,43}, {8,32}, {10,28}, {5,31}, {17,22}, {19,34}, {4,44}, {20,32}, {29,41}, {25,42}, {34,39}, {9,21}, {2,28}, {29,42}, {14,16}, {34,41}, {8,27}, {2,11}, {16,36}, {14,26}, {30,45}, {35,41}, {11,30}, {4,27}, {2,22}, {36,40}, {18,24}, {21,33}, {12,36}, {1,7}, {5,26}, {3,11}, {2,37}, {4,25}, {14,30}, {21,34}, {3,28}, {7,31}, {30,33}, {4,12}, {21,44}, {20,33}, {36,42}, {19,35}, {7,25}, {6,26}, {22,27}, {13,35}, {21,43}, {9,15}, {20,23}, {18,23}, {19,32}, {20,45}, {1,23}, {5,16}, {11,20}, {15,18}, {10,34}, {10,27}, {5,17}, {16,33}, {13,28}, {23,25}, {16,24}, {7,20}, {15,36}, {21,36}, {5,10}, {8,20}, {5,44}, {17,23}, {7,13}, {23,41}, {9,14}, {14,17}, {30,43}, {15,43}, {29,43}, {4,39}, {12,35}, {21,24}, {17,32}, {12,19}, {37,41}, {1,37}, {2,9}, {39,44}, {6,33}, {12,21}, {18,34}, {11,26}, {15,25} }; // ET45.74 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 2160 EdgePairs[45][74]:={ {37,42}, {10,25}, {5,17}, {2,24}, {6,32}, {6,16}, {17,35}, {11,36}, {17,36}, {4,27}, {21,45}, {11,35}, {36,38}, {16,33}, {32,42}, {3,22}, {23,27}, {1,10}, {18,32}, {21,32}, {30,45}, {38,41}, {32,41}, {30,33}, {39,42}, {7,38}, {3,9}, {39,41}, {19,44}, {28,45}, {29,33}, {16,31}, {8,33}, {24,27}, {19,24}, {35,40}, {4,31}, {22,42}, {15,44}, {28,32}, {13,35}, {34,40}, {8,39}, {17,24}, {21,43}, {29,41}, {21,22}, {15,43}, {24,44}, {12,34}, {23,43}, {5,32}, {6,11}, {8,15}, {16,23}, {29,42}, {38,40}, {8,27}, {13,29}, {13,16}, {35,41}, {18,34}, {15,16}, {15,25}, {11,28}, {10,30}, {3,17}, {3,7}, {37,45}, {4,38}, {19,33}, {36,37}, {1,38}, {38,43}, {1,17}, {1,18}, {7,20}, {14,36}, {16,24}, {9,26}, {12,20}, {12,36}, {34,38}, {29,44}, {9,19}, {2,37}, {23,45}, {5,43}, {14,30}, {2,39}, {7,32}, {26,40}, {28,44}, {4,45}, {27,40}, {7,13}, {9,14}, {7,25}, {20,31}, {17,33}, {24,25}, {15,27}, {20,33}, {30,43}, {23,26}, {4,33}, {10,29}, {23,41}, {22,44}, {25,41}, {37,40}, {10,21}, {6,18}, {1,29}, {2,16}, {3,39}, {11,21}, {23,42}, {9,25}, {6,33}, {1,12}, {13,43}, {1,23}, {24,45}, {11,29}, {20,44}, {6,44}, {15,35}, {9,37}, {12,28}, {12,25}, {8,13}, {33,40}, {33,42}, {1,9}, {13,25}, {13,28}, {20,45}, {39,45}, {1,28}, {31,41}, {3,11}, {7,14}, {20,22}, {4,43}, {21,31}, {3,10}, {22,43}, {30,32}, {15,36}, {8,26}, {18,31}, {38,44}, {12,26}, {27,42}, {7,31}, {24,40}, {24,41}, {28,40}, {5,12}, {22,25}, {14,17}, {8,32}, {8,21}, {14,18}, {1,24}, {5,31}, {5,44}, {30,40}, {12,19}, {6,26}, {30,41}, {20,23}, {12,30}, {14,34}, {3,23}, {36,41}, {28,42}, {2,7}, {34,39}, {35,37}, {25,42}, {26,41}, {18,23}, {37,43}, {2,11}, {1,37}, {16,34}, {5,39}, {20,35}, {19,32}, {3,16}, {13,26}, {11,26}, {14,45}, {15,18}, {22,26}, {10,35}, {16,36}, {3,30}, {2,29}, {11,27}, {10,27}, {8,38}, {6,45}, {2,22}, {14,44}, {10,34}, {18,22}, {29,31}, {19,43}, {6,25}, {6,38}, {9,33}, {20,36}, {6,10}, {5,27}, {5,10}, {31,40}, {5,26}, {15,28}, {4,18}, {9,39}, {11,19}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {3,28}, {8,20}, {7,27}, {28,31}, {22,40}, {21,36}, {36,42}, {21,34}, {2,12}, {2,8}, {10,20}, {35,39}, {6,37}, {13,34}, {19,35}, {17,22}, {21,24}, {9,15}, {2,30}, {13,17}, {13,45}, {15,30}, {19,34}, {34,42}, {7,37}, {2,18}, {9,31}, {19,23}, {29,43}, {5,37}, {7,19}, {4,17}, {17,32}, {9,21}, {4,39}, {18,35}, {14,27}, {39,44}, {14,29}, {14,26}, {5,16} }; // ET45.75 // Non-bipartite Valency 12 // Diameter 3 Girth 3 // Has twins VT AT // Automorphism group of order 56422198149120 EdgePairs[45][75]:={ {13,21}, {24,34}, {10,37}, {15,38}, {5,7}, {40,43}, {5,22}, {10,18}, {9,17}, {19,26}, {33,43}, {3,26}, {13,37}, {1,40}, {14,38}, {13,39}, {11,43}, {6,15}, {8,40}, {10,33}, {33,34}, {3,19}, {24,32}, {5,15}, {1,19}, {24,36}, {12,16}, {10,39}, {3,20}, {1,21}, {3,21}, {16,37}, {19,37}, {20,37}, {16,28}, {7,30}, {6,9}, {4,40}, {6,14}, {11,17}, {1,20}, {27,36}, {20,38}, {8,16}, {20,26}, {10,17}, {9,18}, {33,44}, {2,25}, {4,24}, {8,30}, {33,45}, {4,13}, {27,28}, {5,41}, {17,39}, {31,36}, {21,38}, {12,38}, {7,41}, {23,31}, {23,36}, {25,34}, {11,39}, {26,29}, {33,35}, {12,31}, {13,24}, {20,39}, {13,20}, {26,35}, {24,31}, {15,19}, {12,37}, {18,39}, {4,23}, {11,18}, {32,44}, {30,36}, {6,24}, {31,43}, {13,19}, {1,26}, {26,36}, {22,34}, {27,30}, {18,29}, {31,44}, {1,43}, {9,29}, {8,42}, {32,45}, {4,22}, {3,43}, {32,35}, {4,7}, {8,18}, {1,42}, {19,38}, {42,45}, {4,9}, {25,29}, {17,29}, {20,25}, {2,44}, {41,44}, {19,27}, {8,17}, {16,29}, {10,16}, {11,16}, {15,37}, {14,23}, {10,38}, {11,33}, {21,25}, {14,39}, {4,41}, {8,41}, {42,44}, {14,21}, {18,38}, {5,14}, {21,37}, {28,34}, {12,17}, {29,36}, {1,41}, {15,23}, {11,44}, {3,44}, {3,25}, {17,28}, {6,8}, {25,30}, {27,34}, {2,43}, {2,27}, {10,31}, {10,44}, {13,22}, {6,13}, {1,25}, {22,31}, {23,35}, {2,20}, {9,16}, {9,30}, {7,28}, {12,18}, {17,30}, {5,40}, {16,30}, {12,45}, {6,22}, {17,38}, {11,32}, {15,24}, {27,35}, {3,42}, {14,37}, {1,44}, {13,38}, {4,14}, {5,8}, {24,35}, {4,15}, {9,41}, {6,23}, {23,34}, {3,41}, {15,39}, {21,39}, {2,19}, {7,40}, {2,41}, {5,23}, {12,43}, {2,26}, {26,30}, {7,29}, {18,30}, {8,29}, {2,45}, {1,45}, {23,32}, {19,39}, {9,28}, {2,21}, {30,35}, {18,28}, {5,24}, {25,36}, {14,19}, {16,38}, {11,45}, {40,45}, {3,45}, {26,28}, {12,44}, {19,25}, {4,42}, {4,8}, {31,35}, {12,33}, {5,9}, {12,39}, {31,45}, {20,27}, {28,36}, {31,34}, {41,45}, {27,29}, {22,33}, {11,31}, {14,24}, {30,34}, {21,27}, {7,42}, {6,41}, {42,43}, {28,35}, {6,42}, {14,20}, {15,21}, {7,18}, {11,37}, {23,33}, {40,44}, {7,16}, {3,40}, {7,17}, {10,45}, {13,23}, {32,36}, {2,40}, {41,43}, {15,22}, {15,20}, {17,37}, {16,39}, {26,34}, {3,27}, {5,42}, {12,32}, {25,35}, {22,35}, {10,43}, {8,28}, {32,43}, {9,40}, {1,27}, {5,13}, {32,34}, {22,36}, {29,35}, {14,22}, {22,32}, {9,42}, {25,28}, {24,33}, {10,32}, {29,34}, {21,26}, {2,42}, {6,7}, {33,36}, {18,37}, {11,38}, {6,40} }; // ET45.76 // Non-bipartite Valency 12 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 51840 EdgePairs[45][76]:={ {24,34}, {11,40}, {10,37}, {15,38}, {31,39}, {35,38}, {9,17}, {10,18}, {19,26}, {3,8}, {25,37}, {12,22}, {5,11}, {16,22}, {1,3}, {17,42}, {2,35}, {6,15}, {3,19}, {1,19}, {3,23}, {26,37}, {2,18}, {19,37}, {2,7}, {8,31}, {13,43}, {24,28}, {10,11}, {35,45}, {11,29}, {11,17}, {1,12}, {11,27}, {19,40}, {8,16}, {33,44}, {12,28}, {2,25}, {16,42}, {18,32}, {8,13}, {23,38}, {33,39}, {29,33}, {4,13}, {26,39}, {5,41}, {1,13}, {2,5}, {8,9}, {2,10}, {3,9}, {12,42}, {23,36}, {23,28}, {10,20}, {17,26}, {22,25}, {20,39}, {13,20}, {16,25}, {9,35}, {37,43}, {18,39}, {6,44}, {40,42}, {11,18}, {36,44}, {29,31}, {31,43}, {5,34}, {36,38}, {13,41}, {16,40}, {8,22}, {32,39}, {24,37}, {31,44}, {18,26}, {4,22}, {30,38}, {3,38}, {7,14}, {6,10}, {20,41}, {4,7}, {27,45}, {27,39}, {28,40}, {7,32}, {12,24}, {25,26}, {1,39}, {7,37}, {2,30}, {4,9}, {3,36}, {6,12}, {37,45}, {26,41}, {1,2}, {2,13}, {39,45}, {41,44}, {11,21}, {10,16}, {11,23}, {10,36}, {14,33}, {6,16}, {15,34}, {11,33}, {18,22}, {14,39}, {21,31}, {32,38}, {42,44}, {14,21}, {9,26}, {32,40}, {5,14}, {21,37}, {12,17}, {34,45}, {25,30}, {27,34}, {12,30}, {4,33}, {22,44}, {25,41}, {1,6}, {20,30}, {6,19}, {13,31}, {4,17}, {24,38}, {3,32}, {12,18}, {19,41}, {13,29}, {17,30}, {29,38}, {26,31}, {28,45}, {6,31}, {15,24}, {32,42}, {33,40}, {14,37}, {5,8}, {23,27}, {36,37}, {43,45}, {4,15}, {31,32}, {18,31}, {25,38}, {15,17}, {34,38}, {4,36}, {24,29}, {19,29}, {7,24}, {6,20}, {4,44}, {7,40}, {12,43}, {34,42}, {34,39}, {36,43}, {8,29}, {7,21}, {34,41}, {8,27}, {2,11}, {1,45}, {23,32}, {10,15}, {3,5}, {19,33}, {9,28}, {30,35}, {18,28}, {15,29}, {16,20}, {18,24}, {8,43}, {20,28}, {40,45}, {16,27}, {1,7}, {3,14}, {19,25}, {31,35}, {14,30}, {5,9}, {11,19}, {30,33}, {1,4}, {21,35}, {8,14}, {3,6}, {22,33}, {21,44}, {20,33}, {35,40}, {14,24}, {26,32}, {22,27}, {1,34}, {21,27}, {7,42}, {9,15}, {20,23}, {2,4}, {42,43}, {17,21}, {28,35}, {14,20}, {7,16}, {5,18}, {22,24}, {15,16}, {17,27}, {10,45}, {13,23}, {32,36}, {6,21}, {9,45}, {4,26}, {15,20}, {13,28}, {5,42}, {2,38}, {25,35}, {10,43}, {5,10}, {9,40}, {34,44}, {1,27}, {5,44}, {25,27}, {17,23}, {15,26}, {22,36}, {3,12}, {23,41}, {9,14}, {7,13}, {30,43}, {29,43}, {29,34}, {6,35}, {21,24}, {35,44}, {12,19}, {28,41}, {36,45}, {17,43}, {37,41}, {22,28}, {8,25}, {30,39}, {30,42}, {16,32}, {33,36}, {41,42}, {29,40}, {21,23} }; // ET45.77 // Bipartite(10,35) Valencies [14,4] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1040645140512768000000 EdgePairs[45][77]:={ {4,35}, {9,13}, {10,19}, {7,42}, {5,32}, {6,39}, {9,40}, {5,14}, {8,31}, {10,22}, {1,11}, {9,30}, {2,22}, {6,14}, {5,42}, {3,38}, {6,36}, {1,31}, {7,40}, {10,27}, {8,36}, {6,41}, {9,45}, {2,20}, {4,40}, {5,34}, {2,37}, {5,24}, {7,27}, {7,45}, {1,44}, {10,44}, {7,15}, {3,31}, {6,34}, {2,15}, {8,13}, {8,41}, {5,37}, {1,29}, {3,18}, {3,41}, {1,34}, {9,38}, {3,11}, {4,20}, {10,34}, {6,11}, {8,33}, {9,43}, {8,28}, {1,36}, {3,13}, {10,12}, {2,32}, {1,16}, {6,21}, {4,33}, {2,17}, {8,18}, {8,21}, {4,28}, {10,39}, {7,25}, {4,43}, {10,37}, {5,19}, {9,23}, {10,24}, {7,20}, {8,26}, {3,23}, {4,45}, {5,29}, {2,42}, {4,30}, {6,26}, {1,19}, {2,40}, {8,11}, {7,30}, {2,35}, {9,25}, {4,15}, {4,25}, {9,15}, {10,29}, {1,26}, {6,29}, {7,35}, {4,38}, {6,31}, {9,33}, {5,22}, {2,27}, {6,19}, {5,27}, {9,35}, {1,39}, {8,38}, {8,43}, {2,12}, {9,28}, {10,14}, {3,28}, {3,26}, {5,17}, {8,16}, {8,23}, {6,16}, {3,21}, {1,14}, {1,41}, {9,18}, {10,17}, {10,42}, {7,22}, {3,16}, {4,18}, {7,32}, {10,32}, {7,37}, {5,12}, {2,25}, {3,36}, {6,24}, {6,44}, {3,43}, {5,44}, {3,33}, {7,17}, {4,23}, {7,12}, {5,39}, {4,13}, {1,21}, {2,30}, {9,20}, {1,24}, {2,45} }; // ET45.78 // Bipartite(10,35) Valencies [14,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 390241927692288000000 EdgePairs[45][78]:={ {1,11}, {3,33}, {10,25}, {5,34}, {8,12}, {4,26}, {3,22}, {4,16}, {9,45}, {8,42}, {3,13}, {3,43}, {10,23}, {7,44}, {2,15}, {7,22}, {4,31}, {10,33}, {2,27}, {1,19}, {5,20}, {3,37}, {7,34}, {1,21}, {9,35}, {4,23}, {8,31}, {8,27}, {9,11}, {10,15}, {2,42}, {3,18}, {10,30}, {6,29}, {3,17}, {8,16}, {2,45}, {4,38}, {2,25}, {5,40}, {7,12}, {10,38}, {9,26}, {1,44}, {4,41}, {5,29}, {8,41}, {2,37}, {7,39}, {9,41}, {5,25}, {7,32}, {1,31}, {3,12}, {10,28}, {2,35}, {6,43}, {4,33}, {4,21}, {2,20}, {6,18}, {10,40}, {1,29}, {8,17}, {3,32}, {9,25}, {8,36}, {6,33}, {2,32}, {6,24}, {5,30}, {6,44}, {7,17}, {8,11}, {5,24}, {8,22}, {5,14}, {9,20}, {4,13}, {7,14}, {3,27}, {4,28}, {4,43}, {10,13}, {10,45}, {6,23}, {8,37}, {8,26}, {2,17}, {4,36}, {10,43}, {9,40}, {8,32}, {8,21}, {1,24}, {5,44}, {3,23}, {1,39}, {6,19}, {7,29}, {6,28}, {6,14}, {9,30}, {5,39}, {10,35}, {1,26}, {2,22}, {1,16}, {10,18}, {6,38}, {2,40}, {9,36}, {6,34}, {3,42}, {4,18}, {3,38}, {4,11}, {3,28}, {7,27}, {1,41}, {5,45}, {7,24}, {2,12}, {1,14}, {10,20}, {6,39}, {5,15}, {5,19}, {9,15}, {2,30}, {6,13}, {7,37}, {5,35}, {9,31}, {1,34}, {7,19}, {9,21}, {9,16}, {7,42}, {1,36} }; // ET45.79 // Bipartite(15,30) Valencies [14,7] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 660602880 EdgePairs[45][79]:={ {2,44}, {10,24}, {1,20}, {13,32}, {2,33}, {6,16}, {6,32}, {4,27}, {13,21}, {14,19}, {3,22}, {4,16}, {4,30}, {6,17}, {8,43}, {7,38}, {8,42}, {8,28}, {4,29}, {3,45}, {1,27}, {10,23}, {12,38}, {1,40}, {7,22}, {4,31}, {15,44}, {10,33}, {5,20}, {3,37}, {2,26}, {14,31}, {8,39}, {11,41}, {1,21}, {15,43}, {10,44}, {8,25}, {2,41}, {12,34}, {1,30}, {9,35}, {8,44}, {8,27}, {6,22}, {15,29}, {2,25}, {11,38}, {11,33}, {6,31}, {6,40}, {2,36}, {5,22}, {10,38}, {1,18}, {7,20}, {9,32}, {9,26}, {9,27}, {12,36}, {8,41}, {2,37}, {5,43}, {14,30}, {14,40}, {4,42}, {9,41}, {7,32}, {11,22}, {4,45}, {7,43}, {7,25}, {15,27}, {3,44}, {12,16}, {4,33}, {10,29}, {15,19}, {15,42}, {9,42}, {14,16}, {12,43}, {7,30}, {3,39}, {2,32}, {5,18}, {11,23}, {13,43}, {6,24}, {7,17}, {11,30}, {15,35}, {5,24}, {12,28}, {12,25}, {15,37}, {1,45}, {15,34}, {13,28}, {15,20}, {9,20}, {14,41}, {4,28}, {1,33}, {4,43}, {3,29}, {5,28}, {13,36}, {15,36}, {8,26}, {12,33}, {13,30}, {5,41}, {2,17}, {1,42}, {1,24}, {12,23}, {5,31}, {6,27}, {13,24}, {12,19}, {8,40}, {12,40}, {3,23}, {8,23}, {14,34}, {1,39}, {10,32}, {3,21}, {1,25}, {6,19}, {10,39}, {1,35}, {14,20}, {15,21}, {5,39}, {14,25}, {7,28}, {3,16}, {11,26}, {6,42}, {13,26}, {14,45}, {10,35}, {7,23}, {13,19}, {2,21}, {3,30}, {5,33}, {10,17}, {11,37}, {3,24}, {2,29}, {11,27}, {8,38}, {2,22}, {14,44}, {10,34}, {15,22}, {9,17}, {10,18}, {8,24}, {6,25}, {13,41}, {2,40}, {9,36}, {6,34}, {5,26}, {4,18}, {15,28}, {9,38}, {11,19}, {10,19}, {3,38}, {11,45}, {7,45}, {14,35}, {3,31}, {10,20}, {6,39}, {12,31}, {6,37}, {11,34}, {13,34}, {7,35}, {13,39}, {13,17}, {13,45}, {7,37}, {5,35}, {2,18}, {9,31}, {5,37}, {4,17}, {11,42}, {9,16}, {3,36}, {9,21}, {7,40}, {4,44}, {9,23}, {8,29}, {4,32}, {12,18}, {11,18}, {12,21}, {1,36}, {14,29}, {14,26}, {5,16} }; // ET45.80 // Bipartite(20,25) Valencies [15,12] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 28800 EdgePairs[45][80]:={ {18,45}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {19,26}, {11,25}, {4,28}, {5,45}, {12,22}, {3,26}, {8,26}, {14,38}, {13,39}, {11,43}, {2,35}, {17,33}, {4,31}, {8,40}, {14,31}, {15,27}, {8,23}, {1,21}, {14,45}, {3,21}, {16,37}, {3,39}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {19,21}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {2,34}, {20,26}, {2,25}, {4,24}, {16,42}, {8,30}, {20,43}, {8,37}, {5,41}, {17,39}, {12,38}, {13,30}, {7,27}, {12,42}, {6,39}, {10,26}, {7,33}, {12,31}, {20,29}, {17,26}, {13,24}, {20,39}, {5,37}, {13,42}, {20,35}, {9,35}, {1,36}, {1,29}, {19,42}, {16,34}, {15,45}, {10,35}, {18,39}, {8,38}, {13,26}, {6,24}, {5,34}, {1,38}, {14,32}, {2,36}, {16,40}, {8,22}, {18,29}, {9,39}, {8,42}, {18,26}, {4,22}, {18,33}, {3,43}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {12,24}, {19,38}, {1,31}, {3,31}, {11,22}, {5,35}, {14,34}, {3,36}, {19,23}, {4,21}, {20,25}, {4,32}, {2,44}, {14,28}, {11,21}, {3,30}, {2,24}, {3,24}, {10,36}, {15,37}, {15,34}, {8,41}, {9,26}, {17,31}, {13,36}, {1,41}, {2,23}, {20,22}, {4,45}, {12,41}, {3,44}, {20,31}, {3,25}, {19,24}, {17,28}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {10,31}, {10,44}, {18,25}, {13,22}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {18,44}, {7,28}, {6,45}, {20,44}, {17,44}, {19,41}, {8,34}, {9,25}, {17,30}, {10,30}, {6,22}, {12,29}, {11,32}, {15,24}, {16,26}, {12,25}, {15,40}, {3,42}, {14,37}, {1,44}, {13,38}, {19,44}, {14,40}, {9,41}, {16,45}, {4,36}, {4,29}, {19,29}, {6,43}, {9,24}, {17,22}, {19,34}, {16,44}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {20,32}, {18,41}, {10,40}, {18,21}, {10,21}, {7,29}, {8,29}, {9,23}, {7,21}, {13,44}, {2,45}, {16,36}, {13,32}, {11,30}, {19,33}, {19,39}, {2,21}, {4,27}, {19,43}, {18,28}, {5,24}, {15,29}, {8,43}, {2,31}, {16,38}, {11,45}, {1,33}, {18,27}, {12,36}, {16,27}, {3,45}, {19,25}, {2,37}, {5,29}, {10,41}, {4,25}, {14,30}, {7,31}, {8,33}, {11,31}, {20,33}, {14,24}, {13,34}, {11,41}, {7,22}, {6,26}, {15,42}, {1,34}, {13,35}, {7,42}, {17,40}, {20,23}, {12,34}, {19,36}, {6,28}, {16,23}, {6,42}, {18,23}, {13,33}, {18,43}, {15,21}, {7,26}, {11,37}, {11,28}, {1,23}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {17,27}, {8,35}, {13,23}, {17,45}, {9,45}, {17,37}, {16,39}, {1,28}, {16,24}, {3,27}, {7,38}, {12,32}, {15,36}, {10,43}, {7,44}, {8,28}, {7,43}, {18,40}, {9,40}, {1,27}, {5,25}, {17,23}, {10,23}, {9,43}, {14,22}, {9,42}, {9,34}, {15,43}, {4,39}, {12,35}, {7,36}, {17,32}, {20,21}, {1,37}, {6,33}, {12,21}, {2,32}, {15,25}, {5,33}, {18,37}, {9,37}, {6,40} }; // ET45.81 // Bipartite(20,25) Valencies [15,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3057647616000000 EdgePairs[45][81]:={ {13,21}, {15,33}, {19,28}, {11,40}, {10,37}, {15,38}, {9,32}, {6,25}, {5,38}, {19,26}, {11,25}, {5,43}, {3,26}, {8,26}, {1,40}, {16,22}, {17,42}, {15,44}, {11,43}, {2,35}, {17,33}, {3,35}, {10,33}, {8,21}, {3,23}, {10,39}, {3,21}, {14,45}, {16,37}, {19,37}, {20,37}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {14,29}, {16,21}, {19,21}, {13,40}, {14,44}, {6,32}, {17,35}, {11,35}, {11,29}, {10,42}, {20,38}, {2,34}, {19,31}, {2,25}, {4,24}, {16,42}, {18,32}, {4,30}, {9,33}, {20,43}, {7,45}, {8,37}, {20,24}, {5,41}, {12,26}, {13,30}, {7,27}, {19,22}, {11,39}, {7,33}, {12,31}, {12,40}, {20,29}, {1,24}, {20,39}, {16,25}, {1,29}, {19,42}, {18,39}, {13,26}, {2,29}, {5,34}, {1,38}, {14,32}, {2,36}, {13,41}, {16,40}, {20,42}, {8,22}, {18,29}, {9,36}, {1,43}, {8,42}, {18,26}, {4,22}, {18,36}, {3,38}, {3,43}, {15,28}, {5,28}, {2,39}, {14,35}, {7,32}, {12,24}, {19,38}, {3,31}, {1,39}, {7,37}, {6,27}, {2,30}, {14,34}, {3,36}, {19,23}, {4,32}, {2,44}, {1,30}, {19,27}, {6,36}, {3,30}, {2,24}, {11,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {8,24}, {8,41}, {9,38}, {9,26}, {13,36}, {20,22}, {4,45}, {15,23}, {12,41}, {9,22}, {11,44}, {13,45}, {3,25}, {11,34}, {17,28}, {7,35}, {12,30}, {6,30}, {11,24}, {9,31}, {10,44}, {10,29}, {1,25}, {13,31}, {5,39}, {14,27}, {18,44}, {16,41}, {7,28}, {6,45}, {20,44}, {19,41}, {8,34}, {17,30}, {10,22}, {16,30}, {7,23}, {12,45}, {6,22}, {4,34}, {17,38}, {12,29}, {6,31}, {15,24}, {16,26}, {12,25}, {14,37}, {1,44}, {13,38}, {18,31}, {14,40}, {9,41}, {16,31}, {16,45}, {3,41}, {15,39}, {4,29}, {6,37}, {8,32}, {10,28}, {5,31}, {17,22}, {17,25}, {4,44}, {7,40}, {2,41}, {5,23}, {20,32}, {2,26}, {18,41}, {18,21}, {9,21}, {8,29}, {9,23}, {8,36}, {8,27}, {2,45}, {3,33}, {16,36}, {1,45}, {11,30}, {19,33}, {9,28}, {2,21}, {4,27}, {19,43}, {5,24}, {15,29}, {18,24}, {2,31}, {11,45}, {1,33}, {18,27}, {20,28}, {12,36}, {16,27}, {3,45}, {12,44}, {5,26}, {4,42}, {5,29}, {4,25}, {14,30}, {3,28}, {12,39}, {20,27}, {20,33}, {14,24}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {5,21}, {7,42}, {6,41}, {17,40}, {20,23}, {12,34}, {8,44}, {19,36}, {6,42}, {4,35}, {19,32}, {13,33}, {15,21}, {14,25}, {20,34}, {11,28}, {1,23}, {16,35}, {10,24}, {14,42}, {10,27}, {10,34}, {3,40}, {17,27}, {13,23}, {2,40}, {6,21}, {17,45}, {17,37}, {13,28}, {1,28}, {9,27}, {7,38}, {15,36}, {10,43}, {15,31}, {7,43}, {5,44}, {17,23}, {10,23}, {15,26}, {9,43}, {8,39}, {14,22}, {9,42}, {5,36}, {15,43}, {10,32}, {4,39}, {12,35}, {6,35}, {17,32}, {17,43}, {18,42}, {16,32}, {12,21}, {18,34}, {5,33}, {18,37}, {11,38}, {9,37}, {6,40} }; // ET45.82 // Bipartite(5,40) Valencies [16,2] // Diameter 5 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1065620623885074432000000 EdgePairs[45][82]:={ {5,12}, {1,26}, {4,8}, {4,13}, {5,42}, {4,23}, {5,32}, {1,14}, {2,37}, {1,44}, {1,24}, {5,37}, {5,24}, {2,32}, {2,30}, {1,29}, {5,29}, {2,10}, {5,27}, {1,39}, {4,10}, {3,21}, {2,40}, {1,6}, {1,36}, {4,40}, {3,33}, {3,38}, {4,43}, {3,8}, {3,23}, {2,45}, {1,31}, {2,12}, {5,44}, {4,30}, {5,9}, {5,7}, {4,18}, {4,33}, {2,7}, {3,11}, {3,16}, {3,28}, {2,20}, {1,16}, {4,45}, {4,38}, {5,19}, {1,21}, {4,20}, {5,17}, {2,15}, {3,18}, {3,31}, {3,26}, {4,15}, {4,28}, {5,39}, {2,27}, {3,6}, {4,25}, {2,42}, {5,14}, {2,17}, {3,41}, {3,13}, {5,34}, {2,35}, {1,19}, {1,9}, {1,41}, {2,25}, {4,35}, {1,34}, {1,11}, {5,22}, {2,22}, {3,36}, {3,43} }; // ET45.83 // Bipartite(5,40) Valencies [16,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7608405715845120 EdgePairs[45][83]:={ {1,26}, {1,14}, {2,37}, {1,44}, {1,24}, {4,41}, {5,37}, {4,36}, {5,24}, {2,32}, {1,29}, {1,33}, {5,27}, {1,43}, {4,11}, {1,39}, {4,10}, {5,10}, {3,21}, {2,43}, {1,36}, {1,6}, {4,40}, {5,40}, {3,38}, {5,15}, {4,31}, {3,8}, {4,16}, {3,9}, {2,12}, {5,44}, {3,29}, {2,33}, {4,6}, {4,30}, {4,32}, {4,12}, {5,20}, {5,7}, {5,25}, {2,7}, {3,11}, {1,16}, {3,28}, {3,15}, {2,38}, {3,25}, {2,18}, {4,21}, {4,20}, {5,45}, {3,19}, {5,17}, {3,18}, {3,31}, {5,30}, {2,27}, {4,22}, {3,45}, {3,39}, {2,28}, {2,42}, {5,14}, {2,17}, {3,41}, {2,23}, {5,34}, {1,13}, {5,35}, {1,19}, {1,9}, {4,26}, {2,13}, {2,8}, {1,34}, {1,23}, {4,42}, {2,22}, {3,35} }; // ET45.84 // Bipartite(9,36) Valencies [16,4] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 144 EdgePairs[45][84]:={ {2,44}, {3,33}, {5,17}, {2,33}, {6,32}, {4,27}, {4,24}, {4,26}, {3,40}, {1,10}, {2,23}, {8,43}, {7,38}, {8,42}, {8,28}, {3,13}, {3,25}, {7,41}, {7,44}, {7,22}, {4,31}, {2,27}, {5,20}, {3,37}, {7,34}, {7,36}, {8,25}, {2,14}, {8,15}, {9,35}, {8,44}, {8,27}, {9,11}, {6,22}, {6,29}, {3,17}, {2,45}, {2,25}, {6,40}, {1,38}, {1,17}, {5,22}, {4,22}, {8,19}, {1,18}, {7,11}, {9,32}, {2,10}, {9,19}, {9,41}, {2,39}, {1,31}, {7,43}, {6,12}, {6,30}, {4,21}, {9,34}, {2,20}, {6,18}, {1,29}, {9,25}, {7,16}, {8,36}, {2,32}, {5,30}, {5,24}, {9,37}, {8,13}, {8,35}, {5,14}, {9,20}, {1,28}, {4,13}, {7,14}, {3,27}, {4,28}, {6,23}, {3,10}, {1,43}, {8,26}, {5,42}, {5,12}, {8,32}, {3,19}, {1,39}, {5,36}, {3,21}, {9,12}, {6,41}, {1,15}, {6,28}, {2,11}, {1,37}, {5,39}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {3,30}, {5,33}, {8,34}, {9,18}, {2,29}, {6,45}, {1,26}, {1,16}, {9,17}, {8,24}, {6,38}, {2,31}, {9,33}, {6,10}, {5,26}, {3,42}, {4,18}, {3,38}, {4,11}, {4,12}, {4,20}, {7,45}, {1,41}, {5,45}, {7,24}, {3,31}, {1,14}, {5,15}, {9,15}, {2,30}, {6,13}, {5,35}, {1,34}, {7,19}, {2,43}, {6,35}, {9,21}, {3,36}, {4,39}, {7,40}, {4,44}, {9,23}, {7,21}, {8,29}, {5,16} }; // ET45.85 // Bipartite(9,36) Valencies [16,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 190210142896128 EdgePairs[45][85]:={ {2,44}, {1,11}, {2,24}, {1,20}, {2,33}, {6,16}, {6,32}, {4,27}, {4,24}, {8,12}, {3,22}, {3,40}, {4,16}, {1,10}, {8,30}, {6,17}, {5,38}, {8,42}, {3,13}, {8,33}, {2,15}, {4,19}, {7,22}, {1,19}, {2,27}, {5,20}, {3,37}, {9,43}, {2,26}, {8,39}, {7,36}, {5,32}, {8,15}, {8,44}, {2,42}, {6,22}, {2,45}, {7,12}, {6,40}, {6,31}, {1,38}, {4,10}, {1,17}, {2,36}, {3,14}, {5,11}, {1,44}, {5,29}, {8,41}, {2,38}, {8,14}, {7,39}, {4,42}, {4,45}, {7,13}, {2,35}, {6,43}, {4,33}, {5,23}, {3,20}, {9,34}, {9,42}, {2,20}, {1,29}, {7,30}, {8,17}, {3,32}, {9,25}, {5,18}, {5,30}, {6,44}, {8,35}, {5,14}, {4,15}, {1,28}, {3,11}, {4,28}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {8,26}, {9,22}, {7,31}, {5,41}, {4,36}, {2,17}, {9,13}, {5,12}, {9,40}, {8,32}, {8,21}, {3,19}, {6,26}, {3,23}, {8,23}, {5,36}, {1,25}, {9,12}, {6,41}, {6,14}, {9,30}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {4,37}, {2,29}, {1,26}, {4,34}, {1,16}, {8,24}, {6,25}, {9,33}, {6,34}, {5,27}, {4,18}, {9,39}, {4,25}, {3,38}, {3,28}, {7,27}, {7,10}, {7,45}, {5,45}, {3,41}, {3,31}, {9,24}, {5,21}, {9,15}, {6,13}, {7,37}, {2,18}, {9,31}, {1,34}, {7,19}, {6,35}, {9,21}, {9,16}, {7,40}, {7,21}, {7,18} }; // ET45.86 // Bipartite(9,36) Valencies [16,4] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 37748736 EdgePairs[45][86]:={ {1,15}, {7,43}, {5,32}, {9,40}, {6,12}, {5,14}, {3,15}, {8,39}, {8,31}, {2,38}, {4,42}, {6,10}, {6,18}, {9,30}, {2,22}, {5,30}, {5,42}, {6,36}, {2,11}, {6,41}, {6,23}, {2,20}, {7,38}, {4,16}, {9,12}, {7,33}, {5,24}, {1,38}, {6,25}, {7,31}, {7,27}, {7,45}, {1,32}, {6,40}, {7,15}, {5,13}, {3,10}, {2,28}, {3,34}, {6,45}, {5,26}, {8,14}, {8,13}, {8,41}, {9,17}, {6,22}, {7,11}, {2,29}, {3,19}, {4,12}, {5,37}, {8,22}, {1,34}, {6,43}, {5,33}, {2,10}, {1,10}, {4,39}, {1,36}, {1,16}, {8,21}, {7,29}, {9,34}, {4,29}, {7,25}, {4,43}, {5,19}, {5,15}, {7,20}, {8,35}, {6,37}, {7,13}, {8,17}, {4,31}, {2,42}, {4,30}, {2,40}, {4,21}, {4,25}, {8,19}, {2,44}, {8,40}, {7,35}, {2,24}, {4,11}, {2,27}, {6,19}, {9,44}, {3,35}, {1,23}, {2,21}, {5,27}, {5,45}, {6,30}, {9,35}, {7,18}, {2,39}, {8,38}, {8,32}, {3,28}, {3,26}, {5,31}, {8,20}, {8,23}, {1,42}, {9,26}, {3,21}, {1,14}, {1,41}, {9,18}, {3,44}, {3,39}, {1,20}, {9,11}, {3,16}, {3,25}, {9,29}, {2,26}, {1,33}, {5,12}, {9,14}, {1,28}, {3,17}, {8,37}, {3,37}, {9,32}, {3,43}, {9,36}, {4,34}, {6,27}, {4,41}, {5,44}, {9,16}, {3,33}, {7,36}, {7,17}, {4,23}, {4,13}, {1,18}, {4,24}, {1,24}, {2,45}, {6,28}, {9,22} }; // ET45.87 // Bipartite(15,30) Valencies [16,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 660602880 EdgePairs[45][87]:={ {3,33}, {2,24}, {5,17}, {11,20}, {9,28}, {13,32}, {2,33}, {6,32}, {4,27}, {11,35}, {5,34}, {13,40}, {14,19}, {15,24}, {4,26}, {12,45}, {11,25}, {8,30}, {6,17}, {14,39}, {2,23}, {8,43}, {5,38}, {12,22}, {12,32}, {8,28}, {8,33}, {1,27}, {10,23}, {7,44}, {1,40}, {10,26}, {4,19}, {9,44}, {14,38}, {2,27}, {10,33}, {9,43}, {14,31}, {8,39}, {1,21}, {12,35}, {7,36}, {8,25}, {10,44}, {2,28}, {12,34}, {1,30}, {5,32}, {14,28}, {8,44}, {12,37}, {13,16}, {2,42}, {6,22}, {15,25}, {3,18}, {10,30}, {6,29}, {3,34}, {5,40}, {14,23}, {11,38}, {11,33}, {2,36}, {8,19}, {9,29}, {10,38}, {7,20}, {9,32}, {12,17}, {9,26}, {12,20}, {12,36}, {15,40}, {5,29}, {4,41}, {2,38}, {9,19}, {2,37}, {8,45}, {14,30}, {7,39}, {4,42}, {9,41}, {5,25}, {2,39}, {7,32}, {15,26}, {1,31}, {10,41}, {11,22}, {7,43}, {7,25}, {10,28}, {11,31}, {14,24}, {11,44}, {1,22}, {3,44}, {6,30}, {4,33}, {12,16}, {5,23}, {10,29}, {9,34}, {15,19}, {10,21}, {14,16}, {13,18}, {3,39}, {13,31}, {4,35}, {7,16}, {15,41}, {2,32}, {13,33}, {11,23}, {6,24}, {11,29}, {5,30}, {6,44}, {7,17}, {15,35}, {9,37}, {13,23}, {15,37}, {8,22}, {1,45}, {14,42}, {15,34}, {13,25}, {15,20}, {1,28}, {3,27}, {4,28}, {4,43}, {10,45}, {3,29}, {1,43}, {3,26}, {8,37}, {15,36}, {5,42}, {9,22}, {7,31}, {12,33}, {13,30}, {2,17}, {10,43}, {1,42}, {3,19}, {6,27}, {13,24}, {5,44}, {6,26}, {8,40}, {12,19}, {12,30}, {14,34}, {5,36}, {3,21}, {1,25}, {7,29}, {6,41}, {1,37}, {14,20}, {15,21}, {7,28}, {3,16}, {6,42}, {13,26}, {14,45}, {4,40}, {10,35}, {11,16}, {2,21}, {8,34}, {3,24}, {11,37}, {11,27}, {6,45}, {1,26}, {2,22}, {4,34}, {1,16}, {10,36}, {15,22}, {9,17}, {10,18}, {8,24}, {13,41}, {11,40}, {5,27}, {14,43}, {15,38}, {8,18}, {3,42}, {4,18}, {13,38}, {9,38}, {4,25}, {4,20}, {14,35}, {15,23}, {1,41}, {5,45}, {3,41}, {7,24}, {3,31}, {15,39}, {10,20}, {6,39}, {6,37}, {12,31}, {5,19}, {6,20}, {7,35}, {13,39}, {5,21}, {13,17}, {13,45}, {2,18}, {9,31}, {2,43}, {4,17}, {6,35}, {3,36}, {9,16}, {11,42}, {7,40}, {9,23}, {7,21}, {14,27}, {8,29}, {4,32}, {12,18}, {11,18}, {1,36}, {12,21} }; // ET45.88 // Bipartite(15,30) Valencies [16,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23592960 EdgePairs[45][88]:={ {2,44}, {11,17}, {3,33}, {2,24}, {10,25}, {11,20}, {13,32}, {2,33}, {6,16}, {6,32}, {13,21}, {11,35}, {5,34}, {4,24}, {14,19}, {15,24}, {4,26}, {3,40}, {4,30}, {11,25}, {8,30}, {6,17}, {14,39}, {2,23}, {9,45}, {12,22}, {12,32}, {8,42}, {4,29}, {1,32}, {3,45}, {3,43}, {3,25}, {10,23}, {12,38}, {10,26}, {7,22}, {12,41}, {15,44}, {1,19}, {2,27}, {13,35}, {14,31}, {8,39}, {12,35}, {7,36}, {8,25}, {10,44}, {9,35}, {14,28}, {4,23}, {8,31}, {8,27}, {12,37}, {13,29}, {2,42}, {6,22}, {3,18}, {11,28}, {6,29}, {8,16}, {2,45}, {4,38}, {15,29}, {3,34}, {5,40}, {11,38}, {6,40}, {6,31}, {1,38}, {14,33}, {1,17}, {5,22}, {8,19}, {10,38}, {9,32}, {14,21}, {14,36}, {12,17}, {15,32}, {9,26}, {9,27}, {12,20}, {1,44}, {4,41}, {2,38}, {5,43}, {8,45}, {5,25}, {9,41}, {2,39}, {15,26}, {1,31}, {10,41}, {4,45}, {11,22}, {7,43}, {7,25}, {10,28}, {14,24}, {2,35}, {11,44}, {1,22}, {15,27}, {4,33}, {12,16}, {4,21}, {10,29}, {10,31}, {15,42}, {9,42}, {2,20}, {14,16}, {10,40}, {12,43}, {1,29}, {7,30}, {3,39}, {4,35}, {7,16}, {15,41}, {8,36}, {2,32}, {5,18}, {1,23}, {11,23}, {11,29}, {13,44}, {5,30}, {6,44}, {5,24}, {12,28}, {12,25}, {8,22}, {14,42}, {9,20}, {1,28}, {14,37}, {15,17}, {1,43}, {8,37}, {5,28}, {13,36}, {15,36}, {5,42}, {12,26}, {7,31}, {13,30}, {2,17}, {4,36}, {10,43}, {8,21}, {3,19}, {14,18}, {12,23}, {14,22}, {13,24}, {6,26}, {8,40}, {12,40}, {14,34}, {3,21}, {6,19}, {6,41}, {9,30}, {13,27}, {13,42}, {1,37}, {15,21}, {5,39}, {7,28}, {3,16}, {13,26}, {15,18}, {10,35}, {3,30}, {5,33}, {8,34}, {9,18}, {3,24}, {11,37}, {2,29}, {1,26}, {1,16}, {10,34}, {11,32}, {9,17}, {15,33}, {8,24}, {6,25}, {13,41}, {11,40}, {9,33}, {9,36}, {6,34}, {5,27}, {14,43}, {15,38}, {4,18}, {9,38}, {11,19}, {10,19}, {4,20}, {3,28}, {7,27}, {7,45}, {15,23}, {1,41}, {5,45}, {3,31}, {15,39}, {10,20}, {7,33}, {6,37}, {12,31}, {11,34}, {5,19}, {6,20}, {13,39}, {11,43}, {2,30}, {13,17}, {13,45}, {7,37}, {13,20}, {2,18}, {1,34}, {5,37}, {6,35}, {9,21}, {3,36}, {4,39}, {7,40}, {7,42}, {9,23}, {4,44}, {7,21}, {14,27}, {7,18}, {10,16} }; // ET45.89 // Bipartite(21,24) Valencies [16,14] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 50350574478569766912000000 EdgePairs[45][89]:={ {15,33}, {18,45}, {19,28}, {10,37}, {14,36}, {6,25}, {5,38}, {19,26}, {4,28}, {5,45}, {12,22}, {8,26}, {13,37}, {1,40}, {16,22}, {14,38}, {17,42}, {2,35}, {17,33}, {4,31}, {21,30}, {15,27}, {8,23}, {14,45}, {16,37}, {3,39}, {19,37}, {16,28}, {21,28}, {5,32}, {1,35}, {4,37}, {4,40}, {21,22}, {13,43}, {14,29}, {13,40}, {14,44}, {2,33}, {17,35}, {4,38}, {11,35}, {11,29}, {11,27}, {19,40}, {20,38}, {20,26}, {12,28}, {19,31}, {4,43}, {21,40}, {8,30}, {9,33}, {20,24}, {5,41}, {17,39}, {7,41}, {19,22}, {12,42}, {6,39}, {11,39}, {10,26}, {12,31}, {12,40}, {20,29}, {17,26}, {15,30}, {20,39}, {16,25}, {20,35}, {1,29}, {12,37}, {16,34}, {16,43}, {10,35}, {15,45}, {18,39}, {4,23}, {8,38}, {13,26}, {17,36}, {6,24}, {2,29}, {1,38}, {1,26}, {14,32}, {2,36}, {13,41}, {20,36}, {16,40}, {20,42}, {9,36}, {6,34}, {1,43}, {9,39}, {8,42}, {4,22}, {18,33}, {18,36}, {5,27}, {3,43}, {15,28}, {20,41}, {2,39}, {14,35}, {7,32}, {12,24}, {19,38}, {1,31}, {3,31}, {12,27}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {19,23}, {17,29}, {4,32}, {2,44}, {21,45}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {21,25}, {14,39}, {21,31}, {8,24}, {4,41}, {8,41}, {21,37}, {8,45}, {1,41}, {2,23}, {9,22}, {11,44}, {3,25}, {21,42}, {7,35}, {2,27}, {12,30}, {6,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,44}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {14,27}, {16,41}, {7,28}, {6,45}, {20,44}, {17,44}, {19,41}, {13,29}, {9,25}, {17,30}, {10,22}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {17,38}, {6,31}, {11,32}, {15,24}, {16,26}, {12,25}, {15,40}, {3,42}, {3,22}, {1,44}, {13,38}, {18,31}, {19,44}, {16,31}, {15,39}, {4,29}, {1,32}, {21,39}, {19,29}, {6,43}, {6,37}, {8,32}, {10,28}, {9,24}, {19,34}, {16,44}, {4,44}, {7,40}, {2,41}, {17,41}, {5,23}, {12,43}, {20,32}, {2,26}, {10,40}, {7,29}, {18,30}, {8,29}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {19,43}, {18,28}, {5,24}, {18,24}, {16,38}, {11,45}, {18,27}, {21,33}, {12,36}, {3,45}, {5,26}, {19,25}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {21,34}, {7,31}, {12,33}, {8,33}, {12,39}, {20,27}, {20,33}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {15,42}, {1,34}, {13,35}, {21,43}, {21,27}, {17,24}, {20,23}, {12,34}, {8,44}, {6,28}, {16,23}, {6,42}, {4,35}, {19,32}, {18,43}, {7,26}, {20,45}, {1,23}, {16,35}, {14,42}, {10,34}, {3,40}, {17,27}, {8,35}, {13,23}, {15,22}, {17,45}, {9,45}, {14,41}, {4,26}, {13,28}, {1,28}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {15,36}, {10,43}, {21,36}, {15,31}, {7,44}, {7,43}, {18,40}, {9,40}, {5,44}, {17,23}, {10,23}, {9,43}, {3,37}, {8,39}, {9,42}, {5,36}, {9,34}, {15,43}, {10,32}, {17,32}, {21,24}, {1,37}, {2,42}, {18,42}, {16,32}, {6,33}, {2,32}, {18,34}, {11,26}, {15,25}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.90 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 8640 EdgePairs[45][90]:={ {24,34}, {15,38}, {5,7}, {40,43}, {6,25}, {35,38}, {38,43}, {5,38}, {23,29}, {10,18}, {4,28}, {9,10}, {5,45}, {33,43}, {12,22}, {5,11}, {1,40}, {16,22}, {17,42}, {13,39}, {11,43}, {2,35}, {8,40}, {3,35}, {11,15}, {10,33}, {8,21}, {33,34}, {30,40}, {30,41}, {27,33}, {21,41}, {3,23}, {12,16}, {26,37}, {36,39}, {16,37}, {7,30}, {6,9}, {21,22}, {4,37}, {8,31}, {13,27}, {16,21}, {23,44}, {4,38}, {11,35}, {11,17}, {9,11}, {6,29}, {19,40}, {20,26}, {19,31}, {2,25}, {21,40}, {4,43}, {16,42}, {2,6}, {23,45}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {20,43}, {33,45}, {33,39}, {4,16}, {29,33}, {28,31}, {20,24}, {26,39}, {27,28}, {7,11}, {31,36}, {7,41}, {2,5}, {19,22}, {3,9}, {6,39}, {23,36}, {26,29}, {33,35}, {7,33}, {12,31}, {23,28}, {1,24}, {24,30}, {22,25}, {27,32}, {13,20}, {24,45}, {1,36}, {15,19}, {19,42}, {6,18}, {10,35}, {18,39}, {31,38}, {11,18}, {34,37}, {13,26}, {32,44}, {30,36}, {13,16}, {31,43}, {38,42}, {13,19}, {1,26}, {2,36}, {16,40}, {20,42}, {32,39}, {27,30}, {18,29}, {31,44}, {9,29}, {8,42}, {9,20}, {32,45}, {22,43}, {29,32}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {20,41}, {4,18}, {14,35}, {28,40}, {7,32}, {12,24}, {25,33}, {3,13}, {11,22}, {35,39}, {42,45}, {6,27}, {2,8}, {4,9}, {14,34}, {30,31}, {28,42}, {6,12}, {19,23}, {25,29}, {37,45}, {13,17}, {18,19}, {20,25}, {7,19}, {2,44}, {21,45}, {2,13}, {19,27}, {12,15}, {8,10}, {8,15}, {16,29}, {10,16}, {2,24}, {11,23}, {22,26}, {10,36}, {15,37}, {18,22}, {14,39}, {21,31}, {32,38}, {7,12}, {27,37}, {42,44}, {14,21}, {18,20}, {18,38}, {28,34}, {12,17}, {29,36}, {13,36}, {1,41}, {2,23}, {10,13}, {39,42}, {4,11}, {9,19}, {39,43}, {3,25}, {11,34}, {17,28}, {11,13}, {19,45}, {22,30}, {2,43}, {6,30}, {1,22}, {22,44}, {1,6}, {9,31}, {10,44}, {24,25}, {33,37}, {37,40}, {17,19}, {5,39}, {14,27}, {7,28}, {6,45}, {20,44}, {25,31}, {38,40}, {17,30}, {16,30}, {12,45}, {17,38}, {15,35}, {26,31}, {11,32}, {3,7}, {3,42}, {3,22}, {14,37}, {1,44}, {13,38}, {5,8}, {23,27}, {24,35}, {36,37}, {24,43}, {9,41}, {25,38}, {23,34}, {34,38}, {24,29}, {31,37}, {28,32}, {6,43}, {6,37}, {8,32}, {24,27}, {4,44}, {2,41}, {17,41}, {20,32}, {34,42}, {2,26}, {29,41}, {18,41}, {12,14}, {26,30}, {29,42}, {8,29}, {7,21}, {34,41}, {37,44}, {1,45}, {35,41}, {3,5}, {9,28}, {3,34}, {19,43}, {18,28}, {36,40}, {16,20}, {18,24}, {25,39}, {11,45}, {21,33}, {12,36}, {3,45}, {1,7}, {12,44}, {5,26}, {19,25}, {4,8}, {5,29}, {4,25}, {31,35}, {12,33}, {30,33}, {39,41}, {1,4}, {4,12}, {1,8}, {41,45}, {11,31}, {20,33}, {21,44}, {36,42}, {35,40}, {3,15}, {13,34}, {1,14}, {26,32}, {1,34}, {30,34}, {14,18}, {21,27}, {7,42}, {9,15}, {17,24}, {20,23}, {12,34}, {17,21}, {28,35}, {16,23}, {19,32}, {1,15}, {14,25}, {15,21}, {14,20}, {40,44}, {5,16}, {10,24}, {15,18}, {5,17}, {3,4}, {3,40}, {15,16}, {32,36}, {41,43}, {4,26}, {17,37}, {16,39}, {3,27}, {15,36}, {22,35}, {10,43}, {5,10}, {18,40}, {9,40}, {8,20}, {1,27}, {5,44}, {32,34}, {17,23}, {10,23}, {15,26}, {22,36}, {29,35}, {7,13}, {9,14}, {14,17}, {25,28}, {10,14}, {10,32}, {21,24}, {23,26}, {37,41}, {21,26}, {22,28}, {2,42}, {2,9}, {39,44}, {6,7}, {2,14}, {38,45}, {15,25}, {27,38} }; // ET45.91 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 4320 EdgePairs[45][91]:={ {24,34}, {18,45}, {19,28}, {5,7}, {40,43}, {23,29}, {5,22}, {10,18}, {9,17}, {19,26}, {9,10}, {33,43}, {12,22}, {14,38}, {17,42}, {13,39}, {11,43}, {2,35}, {8,40}, {10,33}, {21,30}, {3,19}, {5,15}, {8,23}, {10,39}, {26,37}, {1,21}, {3,21}, {16,37}, {19,37}, {20,37}, {21,28}, {11,14}, {1,35}, {29,39}, {15,41}, {6,9}, {4,40}, {6,14}, {16,21}, {24,28}, {13,40}, {35,45}, {2,33}, {11,17}, {10,42}, {9,11}, {6,29}, {1,20}, {27,36}, {20,38}, {8,16}, {9,18}, {2,34}, {22,37}, {26,38}, {4,24}, {21,40}, {2,6}, {15,32}, {4,30}, {8,30}, {23,38}, {8,12}, {33,45}, {33,39}, {7,45}, {4,13}, {27,28}, {17,39}, {21,38}, {31,36}, {12,38}, {7,41}, {1,13}, {23,36}, {25,34}, {11,39}, {26,29}, {17,20}, {33,35}, {20,29}, {12,40}, {17,26}, {24,30}, {2,15}, {27,32}, {12,13}, {13,20}, {16,25}, {24,31}, {13,42}, {1,36}, {19,42}, {12,37}, {18,39}, {31,38}, {36,44}, {32,44}, {6,24}, {30,36}, {5,34}, {13,19}, {14,32}, {1,26}, {16,40}, {8,22}, {26,36}, {32,39}, {18,29}, {31,44}, {9,36}, {1,43}, {9,29}, {8,42}, {18,26}, {4,22}, {5,28}, {32,35}, {20,41}, {4,7}, {27,45}, {8,18}, {27,39}, {1,42}, {12,24}, {1,31}, {25,33}, {3,13}, {42,45}, {11,42}, {5,35}, {3,36}, {4,21}, {20,25}, {25,44}, {2,44}, {41,44}, {12,15}, {6,36}, {16,29}, {10,16}, {11,23}, {11,16}, {14,33}, {15,37}, {10,38}, {32,38}, {7,12}, {4,41}, {27,37}, {42,44}, {14,21}, {18,20}, {5,14}, {28,34}, {12,17}, {1,41}, {26,44}, {22,29}, {15,23}, {12,41}, {9,22}, {3,44}, {24,39}, {34,45}, {3,25}, {17,28}, {21,42}, {6,8}, {7,35}, {11,13}, {25,30}, {2,43}, {2,27}, {11,24}, {10,31}, {5,19}, {10,44}, {18,25}, {33,37}, {13,22}, {6,13}, {1,25}, {22,31}, {20,30}, {34,43}, {2,20}, {13,31}, {17,19}, {9,30}, {24,38}, {3,32}, {16,41}, {7,28}, {12,18}, {25,31}, {17,44}, {19,41}, {8,34}, {17,30}, {10,22}, {5,40}, {28,37}, {16,30}, {7,23}, {12,45}, {4,34}, {17,38}, {29,38}, {11,32}, {15,24}, {27,35}, {14,37}, {13,38}, {24,35}, {4,15}, {14,40}, {9,41}, {6,23}, {16,45}, {25,38}, {3,41}, {23,34}, {4,36}, {15,39}, {4,29}, {9,44}, {1,32}, {1,5}, {31,37}, {21,39}, {19,29}, {22,39}, {7,24}, {9,24}, {2,19}, {6,20}, {16,44}, {5,23}, {5,20}, {2,26}, {18,41}, {10,40}, {18,21}, {23,37}, {26,30}, {36,43}, {7,29}, {25,43}, {3,33}, {1,45}, {23,32}, {10,15}, {3,5}, {19,39}, {3,34}, {30,35}, {18,28}, {8,11}, {8,43}, {25,39}, {2,31}, {14,19}, {16,38}, {11,45}, {40,45}, {16,27}, {3,45}, {12,44}, {19,25}, {4,8}, {12,33}, {5,9}, {1,4}, {31,45}, {20,27}, {28,36}, {31,34}, {7,10}, {27,29}, {3,6}, {11,31}, {14,24}, {3,15}, {11,41}, {1,14}, {26,32}, {15,42}, {7,42}, {21,27}, {6,41}, {17,40}, {2,4}, {8,44}, {23,30}, {6,28}, {6,42}, {13,33}, {18,43}, {15,21}, {11,37}, {23,33}, {7,16}, {3,40}, {7,17}, {8,35}, {13,23}, {17,27}, {2,40}, {41,43}, {6,21}, {9,45}, {14,41}, {15,20}, {26,34}, {28,38}, {3,27}, {5,42}, {12,32}, {25,35}, {22,35}, {10,43}, {15,31}, {8,28}, {7,43}, {32,43}, {9,40}, {27,43}, {20,40}, {32,34}, {10,23}, {22,36}, {26,33}, {27,31}, {4,19}, {14,22}, {22,32}, {29,35}, {25,28}, {16,19}, {9,34}, {10,14}, {24,33}, {7,36}, {6,35}, {29,34}, {35,44}, {17,43}, {21,26}, {22,28}, {2,42}, {30,39}, {30,37}, {18,42}, {26,45}, {2,14}, {33,36}, {18,37}, {5,30} }; // ET45.92 // Non-bipartite Valency 16 // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 3628800 EdgePairs[45][92]:={ {13,21}, {15,33}, {18,45}, {6,38}, {10,37}, {15,38}, {31,39}, {14,36}, {5,7}, {40,43}, {9,32}, {35,38}, {5,38}, {5,22}, {10,18}, {9,17}, {19,26}, {25,37}, {5,43}, {3,26}, {8,26}, {22,40}, {11,43}, {2,35}, {4,31}, {8,40}, {26,43}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {24,32}, {1,19}, {24,36}, {3,20}, {3,21}, {19,37}, {20,37}, {16,28}, {21,28}, {5,32}, {7,30}, {8,31}, {4,37}, {6,14}, {19,21}, {13,40}, {17,35}, {11,29}, {10,42}, {9,11}, {6,29}, {20,38}, {8,16}, {10,17}, {2,34}, {19,31}, {26,38}, {2,25}, {15,32}, {23,45}, {8,30}, {20,43}, {33,45}, {1,9}, {4,16}, {7,45}, {28,31}, {26,39}, {12,20}, {17,39}, {21,38}, {23,31}, {1,13}, {13,30}, {3,10}, {2,10}, {19,22}, {6,39}, {23,36}, {11,39}, {12,40}, {1,24}, {2,15}, {5,37}, {13,20}, {18,35}, {24,31}, {6,18}, {19,42}, {1,29}, {16,34}, {35,37}, {16,43}, {6,44}, {24,26}, {31,38}, {40,42}, {11,18}, {34,37}, {36,44}, {13,26}, {29,31}, {32,44}, {6,24}, {13,16}, {2,29}, {31,43}, {1,38}, {14,32}, {13,41}, {20,42}, {7,15}, {32,39}, {22,34}, {24,37}, {31,44}, {9,36}, {6,34}, {1,43}, {35,42}, {18,26}, {32,45}, {4,22}, {30,38}, {18,36}, {29,32}, {1,18}, {5,27}, {7,14}, {15,28}, {5,28}, {24,41}, {38,41}, {4,7}, {27,45}, {2,39}, {27,39}, {10,12}, {28,40}, {12,24}, {27,40}, {3,31}, {25,33}, {1,39}, {5,12}, {2,30}, {3,36}, {37,45}, {4,21}, {17,29}, {7,19}, {4,32}, {2,44}, {19,27}, {8,15}, {23,40}, {16,29}, {3,30}, {3,16}, {2,24}, {11,23}, {15,37}, {10,38}, {11,33}, {13,25}, {4,41}, {8,41}, {14,21}, {9,26}, {32,40}, {8,45}, {29,36}, {13,36}, {20,22}, {10,13}, {26,44}, {22,29}, {25,32}, {15,23}, {9,22}, {39,42}, {4,11}, {11,44}, {13,45}, {3,25}, {11,34}, {34,36}, {7,35}, {22,30}, {27,34}, {12,30}, {22,44}, {7,34}, {11,24}, {9,31}, {18,25}, {6,13}, {23,35}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,12}, {14,27}, {22,45}, {35,43}, {17,44}, {19,41}, {17,30}, {10,22}, {12,45}, {12,29}, {28,45}, {12,25}, {33,40}, {27,35}, {14,37}, {1,44}, {5,8}, {18,31}, {9,41}, {6,23}, {25,38}, {15,17}, {7,39}, {3,41}, {4,36}, {21,39}, {30,32}, {6,43}, {22,39}, {24,27}, {7,24}, {10,28}, {17,25}, {2,19}, {16,44}, {7,40}, {5,23}, {20,32}, {34,42}, {25,42}, {29,41}, {18,41}, {18,21}, {9,21}, {36,43}, {7,29}, {18,30}, {29,37}, {29,42}, {14,16}, {8,36}, {34,41}, {2,45}, {37,44}, {25,43}, {14,26}, {4,27}, {8,11}, {16,38}, {20,28}, {1,33}, {21,33}, {3,45}, {33,41}, {12,44}, {3,11}, {4,42}, {21,34}, {11,19}, {12,39}, {30,33}, {39,41}, {1,8}, {4,12}, {20,27}, {17,34}, {28,36}, {3,6}, {20,33}, {21,44}, {3,15}, {7,25}, {1,14}, {15,42}, {1,34}, {13,35}, {21,43}, {21,29}, {17,24}, {20,23}, {17,40}, {12,34}, {19,36}, {28,35}, {23,30}, {6,28}, {16,23}, {27,44}, {19,32}, {11,28}, {5,18}, {1,23}, {14,42}, {15,18}, {10,27}, {5,17}, {16,33}, {3,40}, {8,35}, {2,40}, {15,22}, {17,45}, {14,41}, {4,26}, {16,39}, {1,28}, {26,34}, {16,24}, {7,20}, {9,27}, {5,42}, {22,35}, {10,43}, {7,44}, {18,40}, {8,20}, {24,42}, {5,13}, {25,27}, {10,23}, {26,33}, {4,6}, {14,22}, {9,42}, {23,41}, {14,17}, {25,28}, {30,43}, {15,43}, {10,32}, {12,35}, {12,19}, {23,26}, {28,41}, {8,25}, {30,42}, {2,9}, {30,37}, {6,33}, {2,14}, {33,36}, {38,45}, {5,33}, {11,38}, {9,37} }; // ET45.93 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[45][93]:={ {6,38}, {10,37}, {15,38}, {14,36}, {5,38}, {23,29}, {9,17}, {10,18}, {19,26}, {11,25}, {4,28}, {25,37}, {31,40}, {8,26}, {22,40}, {16,22}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {26,43}, {3,35}, {8,21}, {21,30}, {5,6}, {15,27}, {24,32}, {1,19}, {27,33}, {24,36}, {12,16}, {3,20}, {26,37}, {16,37}, {16,28}, {5,32}, {7,30}, {4,37}, {24,28}, {10,11}, {13,40}, {6,32}, {17,35}, {11,35}, {11,29}, {11,17}, {6,29}, {27,36}, {19,40}, {8,16}, {10,17}, {2,34}, {19,31}, {4,43}, {16,42}, {2,6}, {23,45}, {4,30}, {8,30}, {9,33}, {8,12}, {33,45}, {33,39}, {4,16}, {29,33}, {1,10}, {20,24}, {7,11}, {5,41}, {21,38}, {7,41}, {23,31}, {1,13}, {13,30}, {38,44}, {3,9}, {6,39}, {23,36}, {11,39}, {7,33}, {12,31}, {12,40}, {13,24}, {24,30}, {2,15}, {12,23}, {20,39}, {5,37}, {26,35}, {18,35}, {16,25}, {24,31}, {9,35}, {15,19}, {6,18}, {16,34}, {37,43}, {18,39}, {4,23}, {13,26}, {32,44}, {17,36}, {6,24}, {30,36}, {31,43}, {1,38}, {38,42}, {13,19}, {13,41}, {20,36}, {16,40}, {22,34}, {24,37}, {31,44}, {9,36}, {35,42}, {8,42}, {18,26}, {32,45}, {1,18}, {15,28}, {24,41}, {20,41}, {27,45}, {2,39}, {14,35}, {1,42}, {19,38}, {3,31}, {25,33}, {25,26}, {11,22}, {9,13}, {35,39}, {1,39}, {5,12}, {2,8}, {30,31}, {3,36}, {34,40}, {6,12}, {19,23}, {25,29}, {17,29}, {13,17}, {7,19}, {4,32}, {1,30}, {39,45}, {19,27}, {23,40}, {16,29}, {3,16}, {22,26}, {3,24}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {18,22}, {32,38}, {4,10}, {9,26}, {28,34}, {3,29}, {13,36}, {2,23}, {4,45}, {26,44}, {25,32}, {9,22}, {4,11}, {11,44}, {13,45}, {3,44}, {39,43}, {19,45}, {2,43}, {12,30}, {1,22}, {22,44}, {10,31}, {10,44}, {33,37}, {13,22}, {1,25}, {23,35}, {6,19}, {2,20}, {9,16}, {4,17}, {18,44}, {14,27}, {22,45}, {35,43}, {6,45}, {12,18}, {20,44}, {8,34}, {17,30}, {10,22}, {28,37}, {12,45}, {17,38}, {12,29}, {29,38}, {28,45}, {11,32}, {15,24}, {3,7}, {3,42}, {3,22}, {14,37}, {23,27}, {18,31}, {6,23}, {16,45}, {25,38}, {7,39}, {34,38}, {4,36}, {31,37}, {21,39}, {28,32}, {8,32}, {22,39}, {7,24}, {10,28}, {2,19}, {7,40}, {2,41}, {17,41}, {20,32}, {34,42}, {2,26}, {25,42}, {29,41}, {9,21}, {7,29}, {18,30}, {2,28}, {29,42}, {28,39}, {8,36}, {34,41}, {25,43}, {13,32}, {14,26}, {1,45}, {2,21}, {19,43}, {5,24}, {18,24}, {20,28}, {1,33}, {21,33}, {33,41}, {1,7}, {12,44}, {5,26}, {19,25}, {3,11}, {4,8}, {5,29}, {10,41}, {4,25}, {21,34}, {7,31}, {12,33}, {5,9}, {12,39}, {4,12}, {20,27}, {17,34}, {8,14}, {20,33}, {21,44}, {36,42}, {3,15}, {13,34}, {7,25}, {1,14}, {26,32}, {15,42}, {1,34}, {30,34}, {14,18}, {21,43}, {5,21}, {21,27}, {9,15}, {17,21}, {8,44}, {6,28}, {6,42}, {27,44}, {19,32}, {14,20}, {14,25}, {15,21}, {11,28}, {40,44}, {5,18}, {11,20}, {14,42}, {35,36}, {10,27}, {10,34}, {5,17}, {16,33}, {3,40}, {15,16}, {2,40}, {32,36}, {9,45}, {14,41}, {40,41}, {3,27}, {7,20}, {9,27}, {22,35}, {15,31}, {7,43}, {8,20}, {24,42}, {26,40}, {1,27}, {5,44}, {5,13}, {17,23}, {10,23}, {9,43}, {27,31}, {29,35}, {7,13}, {23,41}, {30,43}, {10,14}, {15,43}, {6,35}, {28,41}, {36,45}, {17,43}, {37,41}, {20,21}, {22,28}, {8,25}, {30,39}, {30,42}, {18,42}, {12,21}, {2,14}, {18,37}, {5,33}, {11,38}, {9,37}, {27,38}, {29,40} }; // ET45.94 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 1440 EdgePairs[45][94]:={ {15,33}, {18,45}, {19,28}, {11,40}, {15,38}, {31,39}, {40,43}, {23,29}, {10,18}, {19,26}, {25,37}, {9,10}, {33,43}, {12,22}, {3,26}, {13,37}, {1,40}, {14,38}, {17,42}, {13,39}, {11,43}, {2,35}, {6,15}, {8,40}, {26,43}, {3,35}, {10,33}, {21,30}, {33,34}, {3,19}, {14,31}, {5,15}, {24,32}, {21,41}, {24,36}, {8,23}, {12,16}, {10,39}, {26,37}, {1,21}, {3,21}, {19,37}, {16,28}, {21,28}, {11,14}, {29,39}, {4,40}, {24,28}, {13,40}, {35,45}, {2,33}, {9,11}, {6,29}, {1,20}, {27,36}, {19,40}, {20,38}, {8,16}, {20,26}, {10,17}, {9,18}, {22,37}, {26,38}, {2,25}, {16,42}, {2,6}, {15,32}, {4,30}, {8,30}, {23,38}, {8,12}, {33,45}, {33,39}, {7,45}, {4,13}, {27,28}, {7,11}, {31,36}, {23,31}, {2,5}, {12,42}, {25,34}, {26,29}, {17,20}, {20,29}, {17,26}, {13,24}, {20,39}, {27,32}, {12,13}, {13,20}, {26,35}, {16,25}, {9,35}, {1,36}, {19,42}, {12,37}, {16,43}, {18,39}, {4,23}, {11,18}, {36,44}, {32,44}, {6,24}, {30,36}, {5,34}, {13,19}, {14,32}, {1,26}, {2,36}, {13,41}, {22,34}, {27,30}, {18,29}, {31,44}, {9,36}, {6,34}, {1,43}, {18,26}, {4,22}, {30,38}, {5,28}, {32,35}, {20,41}, {4,7}, {27,39}, {12,24}, {19,38}, {1,31}, {3,31}, {25,33}, {3,13}, {11,42}, {5,35}, {4,9}, {25,29}, {4,21}, {18,19}, {20,25}, {25,44}, {2,13}, {41,44}, {19,27}, {12,15}, {8,10}, {6,36}, {8,17}, {16,29}, {11,23}, {11,16}, {15,37}, {10,38}, {21,25}, {14,39}, {32,38}, {7,12}, {8,24}, {4,41}, {8,41}, {42,44}, {14,21}, {5,14}, {21,37}, {8,45}, {28,34}, {12,17}, {29,36}, {1,41}, {25,32}, {15,23}, {12,41}, {9,22}, {3,44}, {24,39}, {3,25}, {17,28}, {21,42}, {6,8}, {7,35}, {11,13}, {2,43}, {22,30}, {2,27}, {7,34}, {11,24}, {10,31}, {5,19}, {10,44}, {6,13}, {22,31}, {23,35}, {20,30}, {34,43}, {2,20}, {9,16}, {13,31}, {9,30}, {24,38}, {3,32}, {18,44}, {16,41}, {35,43}, {7,28}, {17,44}, {8,34}, {17,30}, {10,22}, {5,40}, {25,45}, {28,37}, {33,38}, {7,23}, {12,45}, {6,22}, {17,38}, {26,31}, {11,32}, {15,40}, {3,42}, {27,35}, {1,44}, {4,14}, {5,8}, {24,35}, {9,41}, {16,45}, {23,34}, {4,36}, {4,29}, {9,44}, {1,5}, {24,29}, {31,37}, {21,39}, {19,29}, {22,39}, {32,37}, {9,24}, {17,25}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {18,41}, {10,40}, {18,21}, {23,37}, {26,30}, {7,29}, {18,30}, {29,37}, {8,29}, {8,36}, {2,45}, {10,15}, {9,28}, {3,34}, {5,24}, {16,20}, {25,36}, {8,43}, {25,39}, {14,19}, {16,38}, {11,45}, {18,27}, {1,33}, {40,45}, {16,27}, {3,45}, {12,44}, {10,41}, {31,35}, {12,33}, {5,9}, {12,39}, {1,4}, {31,45}, {41,45}, {3,6}, {11,31}, {14,24}, {3,15}, {7,22}, {1,14}, {15,42}, {1,34}, {30,34}, {7,42}, {21,27}, {6,41}, {17,40}, {42,43}, {17,21}, {28,35}, {23,30}, {6,28}, {6,42}, {27,44}, {4,35}, {13,33}, {1,15}, {15,21}, {7,18}, {11,37}, {23,33}, {14,42}, {3,4}, {3,40}, {7,17}, {13,23}, {6,21}, {15,22}, {14,41}, {15,20}, {17,37}, {16,39}, {26,34}, {28,38}, {5,42}, {12,32}, {10,43}, {7,44}, {18,40}, {32,43}, {27,43}, {20,40}, {34,44}, {1,27}, {32,34}, {10,23}, {22,36}, {9,43}, {26,33}, {27,31}, {4,19}, {14,22}, {22,32}, {29,35}, {9,42}, {25,28}, {16,19}, {10,14}, {24,33}, {36,45}, {17,43}, {22,28}, {2,42}, {30,39}, {26,45}, {2,32}, {6,7}, {2,14}, {33,36}, {18,37}, {5,30}, {11,38}, {27,38} }; // ET45.95 // Non-bipartite Valency 16 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 3628800 EdgePairs[45][95]:={ {24,34}, {15,33}, {6,38}, {10,37}, {14,36}, {44,45}, {5,7}, {35,38}, {5,22}, {10,18}, {19,26}, {3,8}, {25,37}, {5,43}, {3,26}, {8,26}, {5,11}, {1,3}, {13,39}, {11,43}, {2,35}, {4,31}, {8,21}, {21,30}, {33,34}, {5,6}, {14,31}, {30,41}, {21,41}, {3,23}, {12,16}, {10,39}, {2,18}, {26,37}, {1,35}, {2,7}, {21,22}, {14,29}, {16,21}, {24,28}, {19,20}, {19,21}, {35,45}, {14,44}, {2,33}, {17,35}, {11,35}, {11,29}, {9,11}, {1,20}, {27,36}, {10,17}, {20,26}, {19,31}, {16,42}, {32,33}, {15,32}, {4,30}, {8,30}, {4,16}, {8,37}, {26,39}, {21,38}, {29,44}, {23,31}, {1,13}, {7,27}, {22,42}, {33,35}, {12,31}, {22,25}, {20,39}, {12,23}, {27,32}, {13,20}, {18,35}, {24,45}, {20,35}, {23,43}, {15,19}, {12,37}, {16,34}, {37,43}, {16,43}, {10,35}, {18,39}, {11,18}, {8,38}, {34,37}, {36,44}, {13,26}, {32,44}, {6,24}, {30,36}, {2,29}, {5,34}, {38,42}, {13,19}, {14,32}, {36,38}, {2,36}, {13,41}, {8,22}, {9,29}, {9,39}, {8,42}, {9,20}, {30,38}, {18,33}, {29,32}, {1,18}, {7,14}, {15,28}, {6,17}, {38,41}, {6,10}, {20,41}, {4,18}, {24,40}, {27,39}, {10,12}, {28,40}, {7,32}, {27,40}, {1,31}, {3,31}, {12,27}, {3,13}, {9,13}, {2,30}, {11,42}, {4,21}, {36,41}, {26,41}, {2,44}, {1,30}, {1,2}, {39,45}, {41,44}, {12,15}, {8,15}, {23,39}, {16,29}, {16,17}, {11,16}, {14,15}, {15,37}, {10,38}, {15,34}, {11,33}, {21,25}, {21,31}, {8,41}, {27,37}, {14,21}, {18,20}, {9,26}, {32,40}, {28,34}, {17,31}, {12,17}, {29,36}, {26,44}, {4,11}, {9,19}, {13,45}, {39,43}, {11,34}, {21,42}, {17,28}, {19,45}, {25,30}, {22,30}, {2,27}, {4,33}, {1,22}, {11,24}, {1,6}, {25,41}, {18,25}, {33,37}, {13,22}, {6,13}, {22,31}, {20,30}, {34,43}, {2,20}, {9,16}, {4,17}, {13,31}, {17,19}, {24,38}, {3,32}, {14,27}, {6,45}, {20,44}, {12,18}, {19,41}, {8,34}, {38,40}, {28,37}, {7,23}, {6,22}, {10,25}, {17,38}, {28,45}, {6,31}, {3,7}, {12,25}, {3,22}, {4,14}, {23,27}, {24,35}, {4,15}, {19,44}, {14,40}, {24,43}, {9,41}, {16,31}, {6,23}, {25,38}, {15,17}, {37,39}, {22,41}, {9,44}, {1,5}, {24,29}, {28,32}, {8,32}, {32,37}, {10,28}, {9,24}, {5,31}, {7,40}, {5,23}, {12,43}, {34,42}, {25,42}, {10,40}, {12,14}, {23,37}, {7,29}, {18,30}, {29,42}, {14,16}, {22,38}, {8,36}, {13,44}, {25,43}, {3,33}, {2,11}, {11,30}, {3,5}, {19,39}, {3,34}, {1,11}, {30,35}, {5,24}, {36,40}, {25,36}, {25,39}, {14,19}, {18,27}, {1,33}, {40,45}, {1,7}, {26,28}, {5,29}, {3,28}, {7,31}, {5,9}, {8,33}, {12,39}, {30,33}, {39,41}, {1,4}, {4,12}, {28,33}, {41,45}, {27,29}, {3,6}, {20,33}, {36,42}, {35,40}, {3,15}, {7,22}, {26,32}, {22,23}, {17,24}, {17,40}, {2,4}, {42,43}, {17,21}, {28,35}, {6,28}, {18,23}, {27,44}, {4,35}, {18,43}, {15,21}, {20,45}, {40,44}, {1,23}, {5,16}, {10,24}, {11,20}, {10,27}, {15,16}, {13,23}, {10,45}, {2,40}, {32,36}, {17,45}, {9,45}, {26,34}, {23,25}, {16,24}, {28,38}, {5,42}, {10,43}, {21,36}, {15,31}, {7,44}, {8,28}, {4,20}, {24,42}, {27,43}, {5,13}, {25,27}, {32,34}, {10,23}, {15,26}, {22,36}, {9,43}, {26,33}, {4,19}, {3,37}, {7,13}, {9,42}, {14,17}, {16,19}, {9,34}, {29,43}, {7,36}, {6,35}, {29,34}, {12,19}, {8,25}, {30,42}, {39,44}, {26,45}, {2,32}, {12,21}, {6,7}, {2,14}, {38,45}, {18,37}, {41,42}, {6,40}, {29,40} }; // ET45.96 // Bipartite(15,30) Valencies [18,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 56422198149120 EdgePairs[45][96]:={ {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {5,38}, {5,22}, {10,18}, {9,17}, {12,22}, {3,26}, {8,26}, {1,40}, {11,43}, {2,35}, {8,40}, {3,35}, {15,27}, {10,39}, {3,20}, {1,21}, {14,45}, {5,32}, {15,41}, {4,37}, {4,40}, {14,29}, {13,40}, {2,33}, {11,17}, {10,42}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {2,34}, {2,25}, {4,43}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {7,45}, {5,41}, {7,41}, {13,30}, {12,42}, {10,26}, {7,33}, {12,31}, {1,24}, {13,24}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {15,19}, {6,18}, {6,44}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {13,16}, {2,29}, {1,38}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {1,18}, {3,38}, {5,27}, {15,28}, {6,17}, {5,28}, {2,39}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {6,27}, {3,36}, {7,19}, {2,44}, {1,30}, {13,18}, {11,21}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {10,38}, {11,33}, {13,25}, {14,39}, {8,24}, {9,26}, {8,45}, {13,36}, {1,41}, {2,23}, {4,45}, {10,19}, {12,41}, {9,19}, {13,45}, {3,44}, {11,44}, {3,25}, {11,34}, {7,35}, {2,43}, {6,30}, {4,33}, {7,34}, {11,24}, {10,31}, {5,19}, {10,29}, {13,22}, {4,17}, {9,16}, {9,30}, {5,39}, {3,32}, {14,27}, {8,34}, {9,25}, {10,22}, {7,23}, {12,45}, {12,29}, {6,31}, {12,25}, {14,43}, {3,42}, {3,22}, {14,37}, {1,44}, {13,38}, {14,40}, {6,23}, {15,17}, {7,39}, {4,36}, {15,39}, {4,29}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {5,31}, {2,19}, {6,20}, {2,41}, {12,43}, {10,21}, {7,29}, {9,23}, {7,21}, {14,16}, {8,36}, {13,44}, {2,45}, {13,32}, {14,26}, {11,30}, {3,34}, {2,21}, {4,27}, {15,29}, {2,22}, {2,31}, {14,19}, {1,33}, {3,45}, {12,44}, {5,26}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {12,39}, {11,31}, {13,34}, {11,41}, {7,25}, {7,22}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {12,34}, {8,44}, {6,28}, {4,35}, {14,20}, {14,25}, {15,21}, {11,37}, {11,28}, {5,18}, {5,16}, {1,23}, {11,20}, {15,18}, {10,27}, {5,17}, {3,40}, {15,16}, {8,35}, {6,21}, {15,22}, {9,45}, {4,26}, {13,28}, {1,28}, {9,27}, {5,42}, {12,32}, {15,36}, {15,31}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {15,26}, {9,43}, {4,19}, {14,17}, {5,36}, {10,32}, {4,39}, {12,35}, {12,19}, {1,37}, {8,25}, {2,42}, {6,33}, {12,21}, {2,32}, {11,38}, {9,37}, {6,40} }; // ET45.97 // Bipartite(15,30) Valencies [18,9] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 43535646720 EdgePairs[45][97]:={ {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {5,38}, {9,17}, {4,28}, {5,43}, {5,45}, {3,26}, {13,37}, {15,44}, {11,43}, {4,31}, {8,40}, {3,35}, {10,33}, {3,19}, {14,31}, {1,19}, {8,23}, {3,20}, {1,21}, {14,45}, {3,39}, {1,35}, {4,37}, {13,27}, {13,40}, {14,44}, {2,33}, {6,32}, {4,38}, {10,42}, {6,29}, {3,18}, {10,17}, {4,24}, {8,30}, {5,41}, {13,30}, {7,27}, {6,39}, {10,26}, {2,17}, {7,33}, {12,31}, {13,24}, {12,23}, {5,37}, {13,20}, {13,42}, {1,36}, {15,19}, {1,29}, {6,18}, {12,37}, {10,35}, {15,45}, {11,18}, {2,29}, {1,38}, {1,26}, {14,32}, {3,17}, {2,36}, {8,22}, {9,36}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {5,28}, {2,39}, {4,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {12,27}, {1,39}, {7,37}, {2,30}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {4,32}, {13,18}, {11,21}, {11,36}, {10,16}, {3,30}, {3,16}, {11,23}, {11,16}, {10,36}, {15,34}, {11,33}, {13,25}, {8,24}, {4,41}, {14,21}, {9,26}, {8,45}, {3,29}, {12,17}, {1,41}, {2,23}, {15,23}, {12,41}, {9,19}, {13,45}, {11,44}, {3,25}, {11,34}, {2,43}, {2,27}, {6,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {7,28}, {2,16}, {8,34}, {10,22}, {5,40}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {15,24}, {12,25}, {1,16}, {13,38}, {14,40}, {9,41}, {6,23}, {15,39}, {4,29}, {9,44}, {1,32}, {6,43}, {8,32}, {7,24}, {9,24}, {5,31}, {2,19}, {6,20}, {4,44}, {5,23}, {12,43}, {5,20}, {2,26}, {10,21}, {9,21}, {8,29}, {14,16}, {13,44}, {13,32}, {14,26}, {1,45}, {11,30}, {4,27}, {15,29}, {2,22}, {8,43}, {3,45}, {12,44}, {2,37}, {4,42}, {10,41}, {14,30}, {3,28}, {12,33}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {11,41}, {7,22}, {13,35}, {5,21}, {7,42}, {6,41}, {12,34}, {8,44}, {6,28}, {6,42}, {14,20}, {14,25}, {7,26}, {7,18}, {11,28}, {7,16}, {5,18}, {11,20}, {14,42}, {15,18}, {10,27}, {5,17}, {3,40}, {15,16}, {7,17}, {10,45}, {8,35}, {2,40}, {6,21}, {14,41}, {13,28}, {1,28}, {3,27}, {9,27}, {7,38}, {15,36}, {10,43}, {7,44}, {7,43}, {9,40}, {8,20}, {5,25}, {10,23}, {15,26}, {4,19}, {14,22}, {8,39}, {3,37}, {9,34}, {10,32}, {15,43}, {4,39}, {12,35}, {7,36}, {12,19}, {8,25}, {2,42}, {6,33}, {12,21}, {2,32}, {11,26}, {15,25}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.98 // Bipartite(18,27) Valencies [18,12] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 3888 EdgePairs[45][98]:={ {15,33}, {18,45}, {6,38}, {14,36}, {9,32}, {5,22}, {11,25}, {4,28}, {5,43}, {5,45}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {17,42}, {15,44}, {2,35}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {1,19}, {8,23}, {10,39}, {1,21}, {14,45}, {3,39}, {16,37}, {16,28}, {5,32}, {8,31}, {4,37}, {13,27}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {6,29}, {11,27}, {1,20}, {12,28}, {2,25}, {4,24}, {4,43}, {18,32}, {8,30}, {9,33}, {7,45}, {8,37}, {5,41}, {17,39}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {17,20}, {12,40}, {10,20}, {13,24}, {15,30}, {13,20}, {16,25}, {15,19}, {1,29}, {12,37}, {16,43}, {6,44}, {8,38}, {13,26}, {1,26}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {18,29}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {3,38}, {3,43}, {15,28}, {5,28}, {2,39}, {7,32}, {1,31}, {3,31}, {11,22}, {6,27}, {11,42}, {14,34}, {3,36}, {2,44}, {1,30}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,23}, {10,38}, {15,34}, {18,22}, {14,39}, {8,24}, {8,41}, {14,21}, {18,20}, {18,38}, {3,29}, {1,41}, {2,23}, {4,45}, {10,19}, {12,41}, {9,19}, {13,45}, {3,44}, {11,44}, {11,34}, {17,28}, {7,35}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,44}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {18,44}, {7,28}, {17,44}, {13,29}, {9,25}, {17,30}, {10,22}, {5,40}, {7,23}, {16,30}, {12,45}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {16,26}, {14,43}, {3,42}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {9,44}, {6,37}, {9,24}, {5,31}, {17,22}, {2,19}, {6,20}, {7,40}, {17,41}, {5,23}, {12,43}, {18,41}, {10,40}, {18,21}, {7,29}, {2,28}, {7,21}, {8,36}, {13,44}, {2,45}, {3,33}, {16,36}, {13,32}, {14,26}, {1,45}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {15,29}, {8,43}, {14,19}, {16,27}, {5,26}, {2,37}, {4,42}, {10,41}, {4,25}, {12,33}, {8,33}, {12,39}, {17,34}, {11,31}, {14,24}, {7,25}, {7,22}, {1,34}, {15,42}, {13,35}, {5,21}, {6,41}, {17,24}, {12,34}, {17,21}, {16,23}, {4,35}, {13,33}, {15,21}, {14,25}, {7,26}, {11,37}, {11,28}, {1,23}, {16,35}, {10,24}, {14,42}, {11,20}, {10,27}, {16,33}, {13,23}, {10,45}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {17,45}, {9,45}, {14,41}, {4,26}, {15,20}, {16,39}, {13,28}, {1,28}, {16,24}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {7,44}, {7,43}, {18,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,25}, {17,23}, {10,23}, {4,19}, {9,42}, {16,19}, {9,34}, {15,43}, {12,35}, {7,36}, {6,35}, {12,19}, {17,43}, {1,37}, {2,42}, {18,42}, {16,32}, {2,32}, {12,21}, {18,34}, {11,26}, {15,25}, {5,33}, {18,37}, {5,30}, {9,37}, {6,40} }; // ET45.99 // Bipartite(18,27) Valencies [18,12] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 1296 EdgePairs[45][99]:={ {13,21}, {18,45}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {11,25}, {4,28}, {5,43}, {5,45}, {8,26}, {1,40}, {13,39}, {17,42}, {11,43}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {3,21}, {3,39}, {16,37}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {13,40}, {14,44}, {2,33}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {11,27}, {1,20}, {2,34}, {12,28}, {4,24}, {4,43}, {16,42}, {18,32}, {9,33}, {7,45}, {5,41}, {17,39}, {12,38}, {7,41}, {12,26}, {12,42}, {6,39}, {17,20}, {12,31}, {12,40}, {10,20}, {17,26}, {13,24}, {15,30}, {16,25}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {15,45}, {16,43}, {6,44}, {4,23}, {13,26}, {6,24}, {17,36}, {1,38}, {13,19}, {14,32}, {1,26}, {16,40}, {18,29}, {6,34}, {1,43}, {9,39}, {8,42}, {9,20}, {18,26}, {18,33}, {18,36}, {5,27}, {15,28}, {2,39}, {1,42}, {7,32}, {12,24}, {3,31}, {11,22}, {7,37}, {6,27}, {2,30}, {14,34}, {3,36}, {4,21}, {18,19}, {7,19}, {4,32}, {2,44}, {14,28}, {16,29}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {14,33}, {15,37}, {14,23}, {11,33}, {18,22}, {13,25}, {8,24}, {8,41}, {9,38}, {9,26}, {8,45}, {3,29}, {17,31}, {1,41}, {2,23}, {9,22}, {9,19}, {13,45}, {3,25}, {17,28}, {7,35}, {2,43}, {12,30}, {6,30}, {4,33}, {9,31}, {10,44}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {9,30}, {5,39}, {17,19}, {7,28}, {6,45}, {17,44}, {13,29}, {8,34}, {9,25}, {10,22}, {5,40}, {7,23}, {16,30}, {12,45}, {6,22}, {4,34}, {15,35}, {17,38}, {15,24}, {12,25}, {14,43}, {3,42}, {3,22}, {14,37}, {1,44}, {13,38}, {14,40}, {6,23}, {16,31}, {16,45}, {7,39}, {4,36}, {15,39}, {4,29}, {1,32}, {6,37}, {7,24}, {5,31}, {17,22}, {6,20}, {16,44}, {7,40}, {2,41}, {17,41}, {2,26}, {18,41}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {13,32}, {1,45}, {11,30}, {2,21}, {18,28}, {2,22}, {15,29}, {16,20}, {18,24}, {2,31}, {14,19}, {16,38}, {11,45}, {18,27}, {12,36}, {12,44}, {5,29}, {10,41}, {14,30}, {3,28}, {11,19}, {8,33}, {12,39}, {11,31}, {13,34}, {11,41}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {6,41}, {17,40}, {12,34}, {8,44}, {17,21}, {6,28}, {6,42}, {16,23}, {4,35}, {13,33}, {18,43}, {14,20}, {14,25}, {15,21}, {11,28}, {16,35}, {10,24}, {14,42}, {11,20}, {10,27}, {10,34}, {16,33}, {3,40}, {13,23}, {17,27}, {14,41}, {4,26}, {15,20}, {16,39}, {16,24}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {7,44}, {8,28}, {7,43}, {4,20}, {8,20}, {1,27}, {5,44}, {5,25}, {17,23}, {10,23}, {15,26}, {9,43}, {4,19}, {14,22}, {3,37}, {9,42}, {5,36}, {9,34}, {10,32}, {15,43}, {7,36}, {6,35}, {17,32}, {12,19}, {1,37}, {8,25}, {2,32}, {12,21}, {18,34}, {11,26}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37} }; // ET45.100 // Bipartite(18,27) Valencies [18,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 107013320101683265536000000 EdgePairs[45][100]:={ {15,33}, {18,45}, {10,37}, {14,36}, {6,25}, {5,38}, {4,28}, {5,45}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {17,42}, {2,35}, {17,33}, {4,31}, {8,21}, {3,19}, {15,27}, {1,19}, {8,23}, {3,21}, {14,45}, {3,39}, {16,37}, {16,28}, {5,32}, {1,35}, {4,37}, {4,40}, {13,43}, {14,29}, {13,40}, {14,44}, {2,33}, {17,35}, {4,38}, {11,35}, {11,29}, {11,27}, {1,20}, {12,28}, {4,43}, {8,30}, {9,33}, {5,41}, {17,39}, {7,41}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {12,31}, {12,40}, {10,20}, {17,26}, {15,30}, {13,20}, {16,25}, {15,19}, {1,29}, {12,37}, {16,34}, {10,35}, {15,45}, {16,43}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {1,38}, {13,19}, {14,32}, {1,26}, {2,36}, {13,41}, {16,40}, {9,36}, {6,34}, {1,43}, {9,39}, {8,42}, {4,22}, {18,33}, {18,36}, {5,27}, {3,43}, {15,28}, {2,39}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {17,29}, {18,19}, {7,19}, {4,32}, {2,44}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {8,24}, {4,41}, {8,41}, {14,21}, {8,45}, {1,41}, {2,23}, {10,19}, {9,22}, {9,19}, {11,44}, {3,25}, {7,35}, {2,27}, {12,30}, {6,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,44}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {14,27}, {16,41}, {7,28}, {6,45}, {17,44}, {13,29}, {9,25}, {17,30}, {10,22}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {17,38}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {15,40}, {3,22}, {1,44}, {13,38}, {18,31}, {16,31}, {15,39}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {10,28}, {9,24}, {16,44}, {4,44}, {7,40}, {2,41}, {17,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {18,21}, {9,21}, {7,29}, {18,30}, {8,29}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {18,28}, {5,24}, {16,20}, {18,24}, {16,38}, {11,45}, {18,27}, {12,36}, {3,45}, {5,26}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {7,31}, {12,33}, {8,33}, {12,39}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {1,34}, {15,42}, {13,35}, {5,21}, {17,24}, {12,34}, {8,44}, {17,21}, {6,28}, {6,42}, {16,23}, {4,35}, {18,43}, {14,20}, {15,21}, {7,26}, {1,23}, {16,35}, {11,20}, {14,42}, {10,34}, {3,40}, {13,23}, {8,35}, {17,27}, {6,21}, {15,22}, {17,45}, {9,45}, {14,41}, {4,26}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {15,36}, {10,43}, {15,31}, {7,44}, {7,43}, {18,40}, {9,40}, {4,20}, {8,20}, {5,44}, {17,23}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {9,42}, {5,36}, {16,19}, {9,34}, {10,32}, {15,43}, {17,32}, {12,19}, {1,37}, {2,42}, {18,42}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.101 // Bipartite(18,27) Valencies [18,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 33853318889472 EdgePairs[45][101]:={ {13,21}, {15,33}, {18,45}, {6,38}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {11,25}, {4,28}, {5,43}, {5,45}, {3,26}, {8,26}, {13,37}, {1,40}, {16,22}, {13,39}, {15,44}, {11,43}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {1,21}, {14,45}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,40}, {14,44}, {4,38}, {11,29}, {10,42}, {6,29}, {11,27}, {1,20}, {4,24}, {4,43}, {16,42}, {15,32}, {8,30}, {9,33}, {8,37}, {12,20}, {5,41}, {17,39}, {12,38}, {12,26}, {13,30}, {12,42}, {6,39}, {11,39}, {17,20}, {7,33}, {10,20}, {1,24}, {13,24}, {5,37}, {13,20}, {18,35}, {16,25}, {13,42}, {9,35}, {1,29}, {16,34}, {15,45}, {16,43}, {6,44}, {18,39}, {4,23}, {13,26}, {6,24}, {17,36}, {5,34}, {1,38}, {13,19}, {14,32}, {1,26}, {2,36}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {5,27}, {3,43}, {5,28}, {2,39}, {14,35}, {1,42}, {12,24}, {1,31}, {3,31}, {12,27}, {1,39}, {7,37}, {6,27}, {2,30}, {3,36}, {17,29}, {7,19}, {4,32}, {2,44}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {11,23}, {3,24}, {14,23}, {10,38}, {15,34}, {14,39}, {4,41}, {8,41}, {14,21}, {9,26}, {18,20}, {18,38}, {8,45}, {2,23}, {10,19}, {15,23}, {9,22}, {3,44}, {3,25}, {11,34}, {17,28}, {7,35}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {10,31}, {9,31}, {5,19}, {10,29}, {18,25}, {13,22}, {13,31}, {5,39}, {17,19}, {3,32}, {14,27}, {18,44}, {16,41}, {7,28}, {6,45}, {13,29}, {9,25}, {17,30}, {10,22}, {12,45}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {11,32}, {15,24}, {12,25}, {15,40}, {3,42}, {3,22}, {14,37}, {1,44}, {13,38}, {14,40}, {9,41}, {16,31}, {7,39}, {3,41}, {4,29}, {9,44}, {6,43}, {8,32}, {7,24}, {10,28}, {9,24}, {17,25}, {2,19}, {6,20}, {7,40}, {2,41}, {17,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {18,21}, {7,29}, {18,30}, {2,28}, {9,23}, {7,21}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {14,26}, {11,30}, {3,34}, {2,21}, {2,22}, {16,20}, {18,24}, {2,31}, {14,19}, {16,38}, {11,45}, {1,33}, {18,27}, {12,36}, {3,45}, {12,44}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {14,30}, {7,31}, {12,33}, {11,19}, {12,39}, {17,34}, {11,41}, {7,22}, {6,26}, {15,42}, {13,35}, {5,21}, {7,42}, {12,34}, {8,44}, {17,21}, {6,42}, {16,23}, {13,33}, {18,43}, {7,26}, {11,37}, {11,28}, {10,24}, {11,20}, {10,34}, {16,33}, {3,40}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {17,45}, {9,45}, {14,41}, {17,37}, {13,28}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {15,36}, {10,43}, {15,31}, {7,44}, {8,28}, {9,40}, {4,20}, {5,25}, {17,23}, {10,23}, {15,26}, {9,43}, {4,19}, {14,22}, {8,39}, {9,42}, {16,19}, {5,36}, {9,34}, {15,43}, {10,32}, {12,35}, {6,35}, {17,32}, {17,43}, {1,37}, {18,42}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {15,25}, {5,30}, {11,38} }; // ET45.102 // Bipartite(18,27) Valencies [18,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 557256278016 EdgePairs[45][102]:={ {13,21}, {18,45}, {11,40}, {10,37}, {14,36}, {6,25}, {5,38}, {5,22}, {11,25}, {4,28}, {5,43}, {5,45}, {12,22}, {3,26}, {8,26}, {13,37}, {14,38}, {16,22}, {13,39}, {17,42}, {15,44}, {11,43}, {2,35}, {17,33}, {4,31}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {10,39}, {1,21}, {14,45}, {16,37}, {16,28}, {5,32}, {15,41}, {4,37}, {4,40}, {14,29}, {13,40}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {5,41}, {17,39}, {7,41}, {12,26}, {13,30}, {12,42}, {6,39}, {11,39}, {17,20}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {16,25}, {13,42}, {15,19}, {1,29}, {12,37}, {16,34}, {15,45}, {16,43}, {6,44}, {18,39}, {8,38}, {13,26}, {17,36}, {2,29}, {5,34}, {1,38}, {13,19}, {14,32}, {2,36}, {16,40}, {9,36}, {6,34}, {1,43}, {9,39}, {8,42}, {4,22}, {18,33}, {18,36}, {5,27}, {15,28}, {2,39}, {1,42}, {7,32}, {12,24}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {2,44}, {1,30}, {11,21}, {6,36}, {16,29}, {11,36}, {3,24}, {14,33}, {15,37}, {14,23}, {10,38}, {15,34}, {18,22}, {8,24}, {8,41}, {8,45}, {1,41}, {10,19}, {15,23}, {12,41}, {9,22}, {9,19}, {3,44}, {11,44}, {11,34}, {7,35}, {2,43}, {2,27}, {6,30}, {4,33}, {7,34}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {3,32}, {14,27}, {16,41}, {7,28}, {6,45}, {17,44}, {13,29}, {9,25}, {17,30}, {10,30}, {5,40}, {7,23}, {12,45}, {10,25}, {15,35}, {17,38}, {16,26}, {14,43}, {3,42}, {3,22}, {13,38}, {18,31}, {14,40}, {6,23}, {16,31}, {3,41}, {15,39}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {10,28}, {9,24}, {5,31}, {16,44}, {4,44}, {7,40}, {17,41}, {5,23}, {5,20}, {2,26}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {8,29}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {11,30}, {9,28}, {2,21}, {18,28}, {5,24}, {2,22}, {16,20}, {18,24}, {2,31}, {16,38}, {11,45}, {1,33}, {18,27}, {12,36}, {3,45}, {12,44}, {4,42}, {5,29}, {10,41}, {3,28}, {7,31}, {12,33}, {8,33}, {11,31}, {14,24}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {6,41}, {17,24}, {8,44}, {17,21}, {6,28}, {16,23}, {4,35}, {13,33}, {18,43}, {14,20}, {14,25}, {15,21}, {7,26}, {1,23}, {16,35}, {10,24}, {14,42}, {11,20}, {10,34}, {3,40}, {8,35}, {17,27}, {2,40}, {6,21}, {17,45}, {9,45}, {14,41}, {4,26}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {7,44}, {7,43}, {18,40}, {9,40}, {4,20}, {8,20}, {5,25}, {17,23}, {10,23}, {15,26}, {9,43}, {4,19}, {14,22}, {8,39}, {3,37}, {9,42}, {16,19}, {5,36}, {9,34}, {15,43}, {10,32}, {4,39}, {12,35}, {6,35}, {17,32}, {12,19}, {1,37}, {18,42}, {16,32}, {18,34}, {11,26}, {15,25}, {5,33}, {18,37}, {11,38}, {9,37} }; // ET45.103 // Bipartite(18,27) Valencies [18,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 663552 EdgePairs[45][103]:={ {13,21}, {18,45}, {6,38}, {11,40}, {15,38}, {9,32}, {6,25}, {5,22}, {11,25}, {12,22}, {16,22}, {15,44}, {11,43}, {17,33}, {4,31}, {8,40}, {10,33}, {8,21}, {14,31}, {1,19}, {3,23}, {8,23}, {1,21}, {3,39}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {13,43}, {13,27}, {14,29}, {16,21}, {13,40}, {14,44}, {6,32}, {17,35}, {4,38}, {11,29}, {10,42}, {6,29}, {11,27}, {2,34}, {12,28}, {2,25}, {4,43}, {16,42}, {18,32}, {15,32}, {4,30}, {9,33}, {8,37}, {5,41}, {12,38}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {7,33}, {12,40}, {15,30}, {12,23}, {5,37}, {13,20}, {18,35}, {13,42}, {9,35}, {1,36}, {1,29}, {12,37}, {16,34}, {10,35}, {15,45}, {16,43}, {6,44}, {18,39}, {4,23}, {13,26}, {17,36}, {2,29}, {5,34}, {1,38}, {13,19}, {14,32}, {1,26}, {2,36}, {8,22}, {6,34}, {9,39}, {9,20}, {18,33}, {8,19}, {3,38}, {3,43}, {5,28}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {12,27}, {11,22}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {7,19}, {4,32}, {1,30}, {14,28}, {6,36}, {11,36}, {2,24}, {11,23}, {3,24}, {10,36}, {15,37}, {10,38}, {15,34}, {13,25}, {14,39}, {8,24}, {8,41}, {14,21}, {18,20}, {8,45}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {4,45}, {10,19}, {12,41}, {3,44}, {13,45}, {11,34}, {17,28}, {2,43}, {2,27}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,44}, {10,29}, {1,25}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {18,44}, {7,28}, {6,45}, {10,22}, {10,30}, {7,23}, {16,30}, {12,45}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {16,26}, {3,42}, {15,40}, {3,22}, {14,37}, {1,44}, {13,38}, {18,31}, {9,41}, {7,39}, {3,41}, {4,36}, {15,39}, {9,44}, {6,43}, {6,37}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {2,19}, {16,44}, {17,41}, {12,43}, {5,20}, {2,26}, {18,41}, {18,21}, {10,21}, {9,21}, {18,30}, {8,29}, {7,21}, {8,36}, {8,27}, {3,33}, {13,32}, {14,26}, {1,45}, {9,28}, {3,34}, {4,27}, {18,28}, {5,24}, {15,29}, {2,22}, {16,20}, {18,24}, {2,31}, {14,19}, {16,38}, {1,33}, {18,27}, {12,36}, {3,45}, {16,27}, {12,44}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {14,30}, {3,28}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {12,34}, {17,21}, {6,42}, {16,23}, {4,35}, {13,33}, {18,43}, {14,20}, {14,25}, {7,26}, {11,37}, {1,23}, {11,20}, {10,34}, {16,33}, {3,40}, {13,23}, {10,45}, {8,35}, {17,27}, {2,40}, {17,45}, {9,45}, {14,41}, {4,26}, {16,39}, {17,37}, {1,28}, {16,24}, {3,27}, {7,20}, {9,27}, {7,38}, {2,38}, {15,36}, {15,31}, {7,44}, {8,28}, {7,43}, {18,40}, {9,40}, {4,20}, {8,20}, {5,44}, {5,25}, {17,23}, {10,23}, {15,26}, {9,43}, {4,19}, {14,22}, {3,37}, {9,42}, {16,19}, {15,43}, {6,35}, {8,25}, {18,42}, {16,32}, {2,32}, {11,26}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.104 // Non-bipartite Valency 18 // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 62923832219789760135168000000 EdgePairs[45][104]:={ {24,34}, {15,33}, {18,45}, {6,38}, {10,37}, {5,7}, {40,43}, {35,38}, {5,38}, {5,22}, {25,37}, {9,10}, {33,43}, {12,22}, {8,26}, {22,40}, {11,43}, {2,35}, {4,31}, {8,40}, {26,43}, {3,35}, {11,15}, {8,21}, {33,34}, {3,19}, {14,31}, {30,40}, {30,41}, {15,27}, {1,19}, {24,36}, {10,39}, {3,20}, {26,37}, {1,21}, {3,21}, {36,39}, {19,37}, {20,37}, {16,28}, {11,14}, {1,35}, {5,32}, {15,41}, {6,9}, {4,37}, {21,22}, {13,27}, {16,21}, {13,40}, {6,32}, {17,35}, {4,38}, {11,29}, {9,11}, {1,20}, {20,38}, {2,34}, {33,44}, {12,28}, {19,31}, {26,38}, {4,24}, {2,6}, {15,32}, {8,12}, {33,45}, {4,16}, {29,33}, {28,31}, {20,24}, {26,39}, {27,28}, {7,11}, {21,38}, {31,36}, {12,38}, {7,41}, {1,13}, {2,5}, {7,27}, {19,22}, {6,39}, {23,36}, {11,39}, {26,29}, {17,20}, {22,42}, {33,35}, {2,15}, {12,23}, {20,39}, {22,25}, {5,37}, {12,13}, {18,35}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {23,42}, {12,37}, {16,34}, {35,37}, {16,43}, {24,26}, {4,23}, {34,37}, {13,26}, {29,31}, {32,44}, {17,36}, {6,24}, {13,16}, {2,29}, {31,43}, {38,42}, {14,32}, {36,38}, {2,36}, {13,41}, {22,34}, {27,30}, {18,29}, {31,44}, {9,36}, {1,43}, {8,42}, {9,20}, {32,45}, {4,22}, {18,36}, {29,32}, {8,19}, {3,43}, {6,17}, {24,41}, {32,35}, {38,41}, {4,7}, {27,45}, {4,18}, {24,40}, {27,39}, {28,40}, {12,24}, {19,38}, {3,13}, {11,22}, {35,39}, {42,45}, {2,30}, {4,9}, {30,31}, {28,42}, {3,36}, {19,23}, {25,29}, {17,29}, {13,17}, {18,19}, {7,19}, {4,32}, {25,44}, {2,44}, {1,30}, {2,13}, {41,44}, {13,18}, {12,15}, {8,10}, {23,40}, {16,29}, {3,30}, {11,23}, {22,26}, {14,33}, {10,38}, {6,16}, {39,40}, {13,25}, {21,31}, {7,12}, {8,41}, {27,37}, {42,44}, {9,26}, {18,20}, {21,37}, {3,29}, {10,13}, {20,22}, {26,44}, {39,42}, {9,19}, {3,44}, {11,44}, {20,31}, {19,24}, {17,28}, {6,8}, {7,35}, {11,13}, {25,30}, {2,43}, {12,30}, {4,33}, {7,34}, {11,24}, {1,6}, {10,44}, {10,29}, {24,25}, {37,40}, {23,35}, {2,20}, {4,17}, {13,31}, {17,19}, {5,39}, {9,12}, {18,44}, {14,27}, {17,44}, {8,34}, {9,25}, {38,40}, {17,30}, {10,22}, {10,30}, {25,45}, {16,30}, {12,45}, {6,22}, {12,29}, {6,31}, {21,32}, {15,40}, {1,44}, {5,8}, {23,27}, {24,35}, {36,37}, {14,40}, {9,41}, {6,23}, {16,45}, {25,38}, {15,17}, {23,34}, {34,38}, {22,41}, {1,5}, {21,39}, {30,32}, {28,32}, {6,37}, {24,27}, {10,28}, {5,31}, {2,19}, {16,44}, {7,40}, {5,23}, {12,43}, {20,32}, {29,41}, {34,39}, {12,14}, {18,21}, {9,21}, {26,30}, {18,30}, {2,28}, {29,42}, {7,21}, {14,16}, {8,36}, {8,27}, {2,45}, {25,43}, {16,36}, {13,32}, {14,26}, {1,45}, {10,15}, {11,30}, {3,5}, {19,33}, {19,39}, {3,34}, {2,21}, {18,28}, {5,24}, {16,20}, {8,11}, {25,39}, {11,45}, {21,33}, {40,45}, {3,45}, {26,28}, {3,14}, {12,44}, {4,8}, {3,28}, {31,35}, {5,9}, {12,39}, {30,33}, {39,41}, {1,4}, {31,45}, {17,34}, {28,33}, {31,34}, {41,45}, {7,10}, {27,29}, {3,6}, {20,33}, {3,15}, {7,25}, {1,14}, {15,42}, {1,34}, {22,27}, {14,18}, {7,42}, {20,23}, {2,4}, {42,43}, {17,21}, {27,44}, {19,32}, {13,33}, {18,43}, {1,15}, {14,25}, {7,26}, {11,37}, {11,28}, {40,44}, {5,18}, {5,16}, {16,35}, {10,24}, {14,42}, {15,18}, {5,17}, {3,4}, {15,16}, {8,35}, {10,45}, {32,36}, {41,43}, {17,45}, {14,41}, {1,28}, {23,25}, {7,20}, {9,27}, {22,35}, {10,43}, {15,31}, {32,43}, {9,40}, {8,20}, {24,42}, {27,43}, {32,34}, {10,23}, {15,26}, {22,36}, {9,42}, {23,41}, {14,17}, {25,28}, {16,19}, {9,34}, {10,14}, {4,39}, {7,36}, {21,24}, {23,26}, {28,41}, {17,43}, {37,41}, {8,25}, {30,42}, {26,45}, {6,33}, {6,7}, {18,34}, {2,14}, {33,36}, {15,25}, {5,33}, {11,38}, {27,38}, {37,42}, {29,40}, {21,23} }; // ET45.105 // Non-bipartite Valency 18 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 338533188894720 EdgePairs[45][105]:={ {6,38}, {14,36}, {9,32}, {6,25}, {35,38}, {38,43}, {5,38}, {3,8}, {11,25}, {5,43}, {31,40}, {5,45}, {31,42}, {8,26}, {22,40}, {25,40}, {5,11}, {16,22}, {28,44}, {15,44}, {17,33}, {4,31}, {8,21}, {30,40}, {30,41}, {15,27}, {3,23}, {2,18}, {14,45}, {36,39}, {3,39}, {5,32}, {2,7}, {8,31}, {4,37}, {21,22}, {13,43}, {13,27}, {14,29}, {23,44}, {14,44}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {1,12}, {11,27}, {3,18}, {12,28}, {19,31}, {4,43}, {18,32}, {23,45}, {8,13}, {9,33}, {20,43}, {1,17}, {1,9}, {4,16}, {29,33}, {28,31}, {1,10}, {8,37}, {20,24}, {12,20}, {29,44}, {12,26}, {13,30}, {3,10}, {7,27}, {38,44}, {2,10}, {19,22}, {3,9}, {6,39}, {10,26}, {2,17}, {22,42}, {7,33}, {10,20}, {1,24}, {15,30}, {22,25}, {5,37}, {27,41}, {18,35}, {24,45}, {20,35}, {23,43}, {6,18}, {1,29}, {23,42}, {16,34}, {35,37}, {37,43}, {15,45}, {10,35}, {6,44}, {24,26}, {28,43}, {8,38}, {34,37}, {13,26}, {29,31}, {17,36}, {13,16}, {2,29}, {1,38}, {38,42}, {36,38}, {3,17}, {20,36}, {7,15}, {35,42}, {9,39}, {9,20}, {18,36}, {18,33}, {22,43}, {29,32}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {15,28}, {6,17}, {24,41}, {38,41}, {6,10}, {2,39}, {4,18}, {24,40}, {26,42}, {14,35}, {28,40}, {7,32}, {27,40}, {12,27}, {9,13}, {35,39}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {2,8}, {14,34}, {30,31}, {28,42}, {34,40}, {6,12}, {19,23}, {37,45}, {36,41}, {13,17}, {26,41}, {7,19}, {4,32}, {1,30}, {21,45}, {39,45}, {13,18}, {8,15}, {14,28}, {11,21}, {23,40}, {11,36}, {3,30}, {3,16}, {2,24}, {22,26}, {3,24}, {10,36}, {6,16}, {15,34}, {18,22}, {39,40}, {33,42}, {13,25}, {21,31}, {31,41}, {9,38}, {4,10}, {9,26}, {32,40}, {3,29}, {17,31}, {13,36}, {2,23}, {20,22}, {4,45}, {10,19}, {39,42}, {4,11}, {9,19}, {13,45}, {20,31}, {39,43}, {19,24}, {11,34}, {19,45}, {12,30}, {4,33}, {2,12}, {1,22}, {22,44}, {9,31}, {25,41}, {10,29}, {24,25}, {37,40}, {4,17}, {5,39}, {14,27}, {22,45}, {6,45}, {20,44}, {2,16}, {6,11}, {13,29}, {9,25}, {38,40}, {10,30}, {10,25}, {15,35}, {12,29}, {28,45}, {6,31}, {32,42}, {21,32}, {3,7}, {12,25}, {33,40}, {1,16}, {14,43}, {3,22}, {23,27}, {30,44}, {36,37}, {32,41}, {18,31}, {19,44}, {24,43}, {16,31}, {15,17}, {7,39}, {34,38}, {22,41}, {30,32}, {28,32}, {6,43}, {6,37}, {8,32}, {24,27}, {10,28}, {5,31}, {17,22}, {19,34}, {4,44}, {20,32}, {34,42}, {25,42}, {29,41}, {34,39}, {29,45}, {10,21}, {9,21}, {2,28}, {29,42}, {7,21}, {14,16}, {13,44}, {34,41}, {8,27}, {37,44}, {2,11}, {16,36}, {14,26}, {30,45}, {35,41}, {11,30}, {19,33}, {1,11}, {4,27}, {19,43}, {15,29}, {2,22}, {36,40}, {18,24}, {21,33}, {12,36}, {33,41}, {1,7}, {5,26}, {3,11}, {2,37}, {4,25}, {14,30}, {3,28}, {21,34}, {7,31}, {11,19}, {8,33}, {30,33}, {39,41}, {1,8}, {4,12}, {17,34}, {21,35}, {28,33}, {8,14}, {20,33}, {21,44}, {36,42}, {35,40}, {19,35}, {13,34}, {7,25}, {6,26}, {22,27}, {13,35}, {14,18}, {21,43}, {9,15}, {17,24}, {20,23}, {24,44}, {12,34}, {19,36}, {16,23}, {18,23}, {19,32}, {14,25}, {20,34}, {7,26}, {20,45}, {11,28}, {5,18}, {5,16}, {1,23}, {16,35}, {11,20}, {15,18}, {10,34}, {10,27}, {5,17}, {16,33}, {15,16}, {4,26}, {13,28}, {1,28}, {23,25}, {16,24}, {7,20}, {9,27}, {7,38}, {2,38}, {15,36}, {21,36}, {5,10}, {27,42}, {8,20}, {24,42}, {26,40}, {5,44}, {5,25}, {17,23}, {15,26}, {3,37}, {8,39}, {3,12}, {9,14}, {7,13}, {23,41}, {14,17}, {30,43}, {15,43}, {4,39}, {29,43}, {12,35}, {17,32}, {21,24}, {12,19}, {23,26}, {28,41}, {37,41}, {1,37}, {8,25}, {30,42}, {2,9}, {16,32}, {39,44}, {6,33}, {12,21}, {18,34}, {11,26}, {38,45}, {15,25}, {5,33}, {9,37}, {37,42}, {29,40}, {21,23} }; // ET45.106 // Bipartite(15,30) Valencies [20,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 495432037507792896000000000 EdgePairs[45][106]:={ {15,33}, {10,37}, {14,36}, {6,25}, {5,38}, {4,28}, {5,45}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {2,35}, {4,31}, {8,21}, {3,19}, {15,27}, {1,19}, {8,23}, {12,16}, {2,18}, {3,21}, {14,45}, {3,39}, {5,32}, {1,35}, {4,37}, {4,40}, {13,43}, {14,29}, {13,40}, {14,44}, {2,33}, {4,38}, {11,35}, {11,29}, {11,17}, {11,27}, {1,20}, {3,18}, {9,18}, {10,17}, {12,28}, {4,43}, {8,30}, {9,33}, {1,17}, {4,16}, {5,41}, {7,41}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {12,31}, {12,40}, {10,20}, {15,30}, {13,20}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {15,45}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {13,16}, {2,29}, {1,38}, {13,19}, {1,26}, {14,32}, {2,36}, {13,41}, {9,36}, {6,34}, {1,43}, {9,39}, {8,42}, {4,22}, {5,27}, {3,43}, {15,28}, {2,39}, {8,18}, {14,35}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {13,17}, {7,19}, {4,32}, {2,44}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {14,33}, {15,37}, {10,38}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {8,41}, {14,21}, {8,45}, {1,41}, {2,23}, {10,19}, {9,22}, {9,19}, {11,44}, {3,25}, {7,35}, {2,27}, {12,30}, {6,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,44}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {14,27}, {7,28}, {6,45}, {12,18}, {13,29}, {9,25}, {10,22}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,42}, {15,40}, {3,22}, {1,44}, {13,38}, {15,39}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {10,28}, {9,24}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {9,21}, {7,29}, {8,29}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {5,24}, {11,45}, {12,36}, {3,45}, {5,26}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {1,34}, {15,42}, {13,35}, {14,18}, {5,21}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {14,20}, {15,21}, {7,26}, {7,16}, {1,23}, {5,18}, {11,20}, {14,42}, {10,34}, {15,18}, {5,17}, {3,40}, {15,16}, {7,17}, {8,35}, {13,23}, {6,21}, {15,22}, {9,45}, {14,41}, {4,26}, {13,28}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {15,36}, {10,43}, {15,31}, {7,44}, {7,43}, {9,40}, {4,20}, {8,20}, {5,44}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {15,43}, {12,19}, {1,37}, {2,42}, {6,33}, {12,21}, {2,32}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.107 // Bipartite(15,30) Valencies [20,10] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2149908480000000 EdgePairs[45][107]:={ {15,33}, {6,38}, {10,37}, {15,38}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {4,28}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {15,44}, {2,35}, {8,40}, {3,35}, {10,33}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {1,21}, {14,45}, {5,32}, {7,30}, {8,31}, {4,40}, {13,43}, {14,29}, {13,40}, {14,44}, {2,33}, {6,32}, {11,35}, {11,29}, {11,17}, {10,42}, {11,27}, {3,18}, {8,16}, {10,17}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {9,33}, {4,16}, {8,37}, {12,20}, {5,41}, {12,38}, {7,41}, {12,26}, {13,30}, {6,39}, {11,39}, {2,17}, {12,40}, {1,24}, {13,24}, {15,30}, {12,23}, {13,20}, {13,42}, {1,36}, {6,18}, {10,35}, {15,45}, {6,44}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {13,16}, {2,29}, {5,34}, {13,19}, {14,32}, {3,17}, {8,22}, {1,43}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {3,43}, {15,28}, {5,28}, {2,39}, {4,18}, {14,35}, {1,42}, {1,31}, {3,31}, {12,27}, {1,39}, {7,37}, {6,27}, {11,42}, {5,35}, {3,36}, {4,21}, {7,19}, {1,30}, {13,18}, {11,21}, {6,36}, {8,17}, {11,36}, {3,30}, {11,23}, {3,24}, {10,36}, {14,33}, {14,23}, {15,34}, {11,33}, {13,25}, {14,39}, {4,41}, {9,38}, {8,41}, {14,21}, {9,26}, {3,29}, {12,17}, {13,36}, {2,23}, {4,45}, {10,19}, {12,41}, {9,22}, {9,19}, {3,44}, {11,44}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {13,22}, {1,25}, {6,19}, {13,31}, {9,16}, {4,17}, {3,32}, {14,27}, {7,28}, {6,45}, {2,16}, {8,34}, {9,25}, {10,30}, {5,40}, {7,23}, {12,45}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {15,24}, {1,16}, {3,42}, {14,43}, {15,40}, {14,37}, {13,38}, {3,41}, {4,36}, {15,39}, {4,29}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {2,19}, {6,20}, {7,40}, {2,41}, {5,23}, {5,20}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {13,44}, {2,45}, {13,32}, {14,26}, {1,45}, {11,30}, {9,28}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {14,19}, {11,45}, {1,33}, {12,44}, {5,26}, {2,37}, {4,42}, {5,29}, {10,41}, {7,31}, {12,33}, {12,39}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {7,42}, {12,34}, {8,44}, {6,42}, {4,35}, {14,20}, {14,25}, {15,21}, {7,18}, {7,16}, {5,16}, {5,18}, {10,24}, {11,20}, {10,27}, {15,18}, {5,17}, {15,16}, {7,17}, {10,45}, {8,35}, {2,40}, {6,21}, {15,22}, {9,45}, {14,41}, {15,20}, {13,28}, {1,28}, {9,27}, {5,42}, {12,32}, {15,36}, {10,43}, {8,28}, {7,43}, {9,40}, {8,20}, {1,27}, {5,44}, {10,23}, {15,26}, {9,43}, {3,37}, {14,17}, {5,36}, {9,34}, {4,39}, {12,35}, {7,36}, {1,37}, {8,25}, {6,33}, {12,21}, {11,26}, {5,30}, {11,38}, {9,37} }; // ET45.108 // Bipartite(20,25) Valencies [20,16] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 800 EdgePairs[45][108]:={ {13,21}, {15,33}, {6,38}, {19,28}, {11,40}, {15,38}, {14,36}, {6,25}, {5,38}, {5,22}, {11,25}, {5,45}, {12,22}, {3,26}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {15,44}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {10,39}, {3,21}, {14,45}, {3,39}, {16,37}, {20,37}, {16,28}, {5,32}, {7,30}, {15,41}, {8,31}, {4,40}, {13,43}, {13,27}, {19,21}, {13,40}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {11,29}, {10,42}, {11,27}, {19,40}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {4,43}, {16,42}, {18,32}, {15,32}, {9,33}, {20,43}, {7,45}, {8,37}, {20,24}, {5,41}, {17,39}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {7,33}, {12,31}, {20,29}, {17,26}, {13,24}, {12,23}, {20,39}, {5,37}, {18,35}, {13,42}, {9,35}, {1,36}, {1,29}, {16,34}, {15,45}, {16,43}, {6,44}, {18,39}, {4,23}, {8,38}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {2,36}, {13,41}, {20,36}, {16,40}, {20,42}, {8,22}, {18,29}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {18,26}, {4,22}, {18,33}, {18,36}, {5,27}, {3,43}, {15,28}, {5,28}, {2,39}, {14,35}, {1,42}, {7,32}, {19,38}, {1,31}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {5,35}, {14,34}, {19,23}, {4,21}, {20,25}, {4,32}, {1,30}, {19,27}, {14,28}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {15,37}, {14,23}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {19,30}, {8,24}, {4,41}, {8,41}, {14,21}, {9,26}, {18,38}, {8,45}, {17,31}, {1,41}, {2,23}, {20,22}, {15,23}, {12,41}, {9,22}, {11,44}, {13,45}, {3,44}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {19,45}, {2,43}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,29}, {18,25}, {13,22}, {1,25}, {20,30}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {7,28}, {6,45}, {20,44}, {17,44}, {19,41}, {13,29}, {8,34}, {10,22}, {10,30}, {7,23}, {16,30}, {12,45}, {4,34}, {10,25}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {14,43}, {15,40}, {3,22}, {14,37}, {1,44}, {13,38}, {19,44}, {14,40}, {9,41}, {6,23}, {16,31}, {16,45}, {3,41}, {4,36}, {15,39}, {4,29}, {9,44}, {19,29}, {6,43}, {6,37}, {8,32}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {16,44}, {4,44}, {7,40}, {17,41}, {5,23}, {12,43}, {20,32}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {13,44}, {2,45}, {3,33}, {13,32}, {14,26}, {1,45}, {11,30}, {19,33}, {19,39}, {9,28}, {3,34}, {2,21}, {4,27}, {19,43}, {18,28}, {5,24}, {15,29}, {18,24}, {8,43}, {2,31}, {16,38}, {1,33}, {18,27}, {12,36}, {3,45}, {12,44}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {12,33}, {12,39}, {20,27}, {11,31}, {14,24}, {19,35}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {17,40}, {20,23}, {12,34}, {8,44}, {17,21}, {19,36}, {6,42}, {16,23}, {4,35}, {13,33}, {18,43}, {14,25}, {15,21}, {20,34}, {20,45}, {11,37}, {11,28}, {16,35}, {10,24}, {14,42}, {10,27}, {10,34}, {16,33}, {3,40}, {8,35}, {10,45}, {17,27}, {2,40}, {17,45}, {14,41}, {4,26}, {17,37}, {1,28}, {16,24}, {3,27}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {7,44}, {8,28}, {7,43}, {9,40}, {20,40}, {1,27}, {5,44}, {17,23}, {10,23}, {15,26}, {9,43}, {3,37}, {14,22}, {8,39}, {9,42}, {5,36}, {10,32}, {15,43}, {12,35}, {7,36}, {6,35}, {17,32}, {20,21}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {2,32}, {12,21}, {6,33}, {18,34}, {11,26}, {18,37}, {5,30}, {11,38}, {9,37} }; // ET45.109 // Bipartite(20,25) Valencies [20,16] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23776267862016000000 EdgePairs[45][109]:={ {13,21}, {15,33}, {18,45}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {5,38}, {5,22}, {19,26}, {5,43}, {5,45}, {12,22}, {3,26}, {8,26}, {16,22}, {13,39}, {17,42}, {11,43}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {1,21}, {3,21}, {14,45}, {3,39}, {16,37}, {19,37}, {20,37}, {16,28}, {5,32}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {14,29}, {16,21}, {19,21}, {13,40}, {14,44}, {2,33}, {6,32}, {17,35}, {11,29}, {10,42}, {6,29}, {11,27}, {19,40}, {20,38}, {2,34}, {20,26}, {12,28}, {19,31}, {2,25}, {4,24}, {16,42}, {15,32}, {4,30}, {8,30}, {20,43}, {7,45}, {5,41}, {17,39}, {12,38}, {13,30}, {7,27}, {19,22}, {12,42}, {6,39}, {11,39}, {10,26}, {7,33}, {12,40}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {18,35}, {20,35}, {9,35}, {1,36}, {1,29}, {19,42}, {12,37}, {16,34}, {10,35}, {15,45}, {16,43}, {6,44}, {18,39}, {8,38}, {13,26}, {6,24}, {2,29}, {1,38}, {1,26}, {14,32}, {13,41}, {20,36}, {20,42}, {18,29}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {18,26}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {3,43}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {20,25}, {4,32}, {2,44}, {19,27}, {11,21}, {6,36}, {16,29}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {15,37}, {10,38}, {11,33}, {13,25}, {14,39}, {19,30}, {8,24}, {4,41}, {8,41}, {9,26}, {14,21}, {18,38}, {8,45}, {3,29}, {13,36}, {1,41}, {2,23}, {20,22}, {4,45}, {15,23}, {9,22}, {11,44}, {3,44}, {13,45}, {20,31}, {3,25}, {19,24}, {11,34}, {17,28}, {7,35}, {19,45}, {2,43}, {2,27}, {12,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {18,25}, {20,30}, {13,31}, {9,30}, {14,27}, {18,44}, {16,41}, {7,28}, {17,44}, {19,41}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {10,30}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {12,25}, {16,26}, {15,40}, {14,37}, {1,44}, {13,38}, {18,31}, {19,44}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {4,36}, {4,29}, {9,44}, {1,32}, {19,29}, {6,43}, {6,37}, {7,24}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {16,44}, {4,44}, {7,40}, {5,23}, {12,43}, {20,32}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {2,28}, {8,29}, {8,36}, {13,44}, {2,45}, {3,33}, {16,36}, {14,26}, {19,39}, {3,34}, {4,27}, {18,28}, {2,22}, {18,24}, {8,43}, {16,38}, {1,33}, {20,28}, {3,45}, {16,27}, {12,44}, {5,26}, {19,25}, {2,37}, {4,42}, {10,41}, {4,25}, {3,28}, {14,30}, {12,33}, {8,33}, {12,39}, {17,34}, {20,27}, {11,31}, {20,33}, {14,24}, {19,35}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {17,24}, {17,40}, {20,23}, {12,34}, {8,44}, {19,36}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {18,43}, {14,25}, {15,21}, {20,45}, {11,37}, {11,28}, {1,23}, {14,42}, {10,27}, {16,33}, {3,40}, {13,23}, {10,45}, {8,35}, {17,27}, {2,40}, {6,21}, {15,22}, {17,45}, {9,45}, {14,41}, {4,26}, {16,39}, {17,37}, {13,28}, {1,28}, {16,24}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {7,44}, {8,28}, {7,43}, {18,40}, {9,40}, {20,40}, {1,27}, {5,25}, {17,23}, {10,23}, {15,26}, {8,39}, {14,22}, {9,42}, {5,36}, {9,34}, {10,32}, {15,43}, {4,39}, {12,35}, {17,32}, {17,43}, {20,21}, {1,37}, {8,25}, {2,42}, {16,32}, {2,32}, {6,33}, {18,34}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37} }; // ET45.110 // Bipartite(20,25) Valencies [20,16] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 29491200 EdgePairs[45][110]:={ {13,21}, {15,33}, {18,45}, {6,38}, {19,28}, {11,40}, {10,37}, {15,38}, {9,32}, {5,38}, {19,26}, {11,25}, {4,28}, {5,43}, {5,45}, {3,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {15,44}, {11,43}, {17,33}, {4,31}, {10,33}, {8,21}, {14,31}, {15,27}, {3,23}, {8,23}, {10,39}, {1,21}, {3,21}, {14,45}, {3,39}, {19,37}, {20,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,27}, {14,29}, {16,21}, {19,21}, {14,44}, {2,33}, {6,32}, {17,35}, {4,38}, {11,35}, {10,42}, {6,29}, {11,27}, {19,40}, {20,38}, {20,26}, {2,25}, {4,24}, {4,43}, {16,42}, {18,32}, {15,32}, {4,30}, {8,30}, {20,43}, {7,45}, {8,37}, {5,41}, {17,39}, {12,38}, {7,41}, {12,26}, {7,27}, {19,22}, {12,42}, {11,39}, {10,26}, {7,33}, {12,40}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {20,39}, {5,37}, {18,35}, {13,42}, {20,35}, {9,35}, {1,36}, {19,42}, {12,37}, {16,34}, {10,35}, {15,45}, {6,44}, {18,39}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {2,36}, {13,41}, {20,36}, {16,40}, {20,42}, {8,22}, {18,29}, {9,36}, {6,34}, {1,43}, {9,29}, {4,22}, {18,33}, {18,36}, {3,38}, {5,27}, {15,28}, {5,28}, {20,41}, {2,39}, {14,35}, {1,42}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {19,23}, {4,21}, {17,29}, {20,25}, {2,44}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {2,24}, {11,23}, {3,24}, {10,36}, {15,37}, {10,38}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {19,30}, {8,24}, {8,41}, {14,21}, {9,26}, {8,45}, {3,29}, {17,31}, {2,23}, {20,22}, {4,45}, {12,41}, {9,22}, {3,44}, {13,45}, {20,31}, {3,25}, {19,24}, {7,35}, {19,45}, {2,43}, {2,27}, {12,30}, {6,30}, {1,22}, {7,34}, {11,24}, {10,31}, {10,44}, {18,25}, {13,22}, {1,25}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {16,41}, {20,44}, {17,44}, {19,41}, {13,29}, {8,34}, {9,25}, {17,30}, {10,22}, {5,40}, {7,23}, {16,30}, {12,45}, {6,22}, {4,34}, {10,25}, {15,35}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {13,38}, {18,31}, {19,44}, {14,40}, {9,41}, {6,23}, {16,31}, {7,39}, {3,41}, {15,39}, {4,29}, {9,44}, {1,32}, {19,29}, {8,32}, {10,28}, {9,24}, {5,31}, {17,22}, {17,25}, {19,34}, {16,44}, {4,44}, {7,40}, {2,41}, {17,41}, {12,43}, {20,32}, {2,26}, {18,41}, {10,40}, {18,21}, {9,21}, {7,29}, {18,30}, {8,29}, {9,23}, {7,21}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {19,43}, {18,28}, {5,24}, {15,29}, {18,24}, {8,43}, {16,38}, {1,33}, {18,27}, {20,28}, {12,36}, {3,45}, {16,27}, {12,44}, {19,25}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {17,34}, {11,31}, {20,33}, {14,24}, {19,35}, {13,34}, {7,25}, {7,22}, {6,26}, {15,42}, {6,41}, {17,40}, {20,23}, {17,21}, {19,36}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {19,32}, {13,33}, {18,43}, {14,25}, {20,34}, {7,26}, {20,45}, {11,37}, {11,28}, {1,23}, {16,35}, {14,42}, {10,34}, {16,33}, {13,23}, {10,45}, {8,35}, {17,27}, {2,40}, {6,21}, {17,45}, {9,45}, {4,26}, {13,28}, {1,28}, {16,24}, {3,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {7,44}, {8,28}, {7,43}, {9,40}, {20,40}, {1,27}, {5,44}, {17,23}, {10,23}, {9,43}, {3,37}, {14,22}, {8,39}, {9,42}, {5,36}, {9,34}, {10,32}, {15,43}, {4,39}, {7,36}, {6,35}, {17,43}, {1,37}, {8,25}, {2,42}, {16,32}, {6,33}, {12,21}, {2,32}, {18,34}, {11,26}, {5,33}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.111 // Non-bipartite Valency 20 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 371504185344000000000 EdgePairs[45][111]:={ {13,25}, {3,42}, {15,28}, {15,17}, {10,17}, {20,26}, {16,28}, {4,26}, {30,43}, {19,41}, {25,42}, {41,44}, {26,33}, {2,26}, {3,7}, {8,28}, {36,37}, {8,37}, {8,31}, {12,42}, {30,45}, {1,5}, {15,16}, {11,34}, {13,27}, {12,25}, {1,9}, {14,17}, {18,38}, {7,28}, {39,41}, {1,32}, {20,27}, {4,28}, {9,21}, {1,18}, {3,15}, {17,29}, {5,18}, {6,28}, {22,25}, {20,22}, {3,25}, {4,12}, {29,42}, {10,27}, {7,10}, {35,37}, {20,42}, {8,11}, {8,24}, {31,37}, {12,27}, {37,44}, {6,34}, {4,38}, {37,42}, {31,36}, {18,28}, {4,34}, {13,29}, {38,44}, {31,38}, {10,22}, {18,37}, {5,7}, {15,45}, {25,32}, {10,42}, {28,45}, {9,41}, {15,20}, {9,10}, {23,34}, {24,36}, {3,27}, {7,13}, {10,13}, {25,28}, {18,29}, {22,29}, {14,27}, {34,39}, {17,42}, {2,8}, {12,35}, {11,36}, {28,44}, {28,42}, {35,40}, {6,19}, {27,32}, {14,43}, {5,25}, {8,40}, {2,41}, {1,31}, {6,35}, {3,14}, {20,44}, {5,45}, {5,20}, {8,39}, {22,45}, {15,43}, {2,36}, {7,14}, {42,45}, {22,27}, {30,34}, {20,32}, {1,26}, {35,41}, {16,42}, {12,44}, {15,34}, {16,30}, {5,27}, {9,31}, {3,6}, {7,23}, {27,41}, {6,11}, {1,22}, {38,40}, {29,32}, {6,39}, {24,43}, {2,45}, {19,35}, {1,42}, {19,31}, {8,21}, {9,20}, {4,45}, {3,16}, {30,40}, {20,43}, {1,27}, {3,23}, {5,36}, {18,20}, {6,12}, {21,36}, {12,33}, {5,38}, {13,18}, {40,45}, {21,22}, {2,34}, {14,35}, {12,41}, {9,11}, {11,32}, {3,31}, {23,39}, {10,43}, {21,25}, {5,29}, {38,42}, {37,41}, {20,40}, {35,38}, {19,24}, {21,40}, {12,18}, {33,43}, {8,30}, {36,39}, {27,38}, {2,5}, {10,18}, {11,41}, {19,44}, {31,45}, {9,29}, {2,22}, {21,34}, {1,44}, {10,31}, {22,38}, {3,18}, {5,16}, {7,37}, {21,45}, {27,33}, {14,18}, {1,17}, {3,36}, {9,14}, {24,25}, {6,43}, {26,31}, {23,26}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {1,35}, {5,21}, {9,39}, {14,37}, {20,31}, {11,45}, {41,43}, {9,42}, {39,45}, {13,35}, {1,13}, {16,37}, {10,24}, {2,25}, {17,23}, {26,39}, {23,28}, {2,14}, {12,24}, {18,19}, {3,4}, {30,36}, {12,45}, {14,28}, {15,36}, {37,45}, {2,40}, {36,40}, {33,34}, {24,34}, {2,16}, {29,40}, {32,44}, {7,40}, {14,19}, {6,44}, {15,37}, {21,23}, {21,43}, {15,29}, {30,33}, {27,40}, {4,29}, {1,43}, {13,36}, {9,23}, {3,8}, {34,41}, {16,22}, {3,35}, {14,26}, {18,23}, {29,44}, {12,15}, {25,30}, {8,22}, {32,39}, {11,33}, {1,34}, {19,23}, {30,41}, {11,16}, {1,4}, {24,37}, {5,30}, {23,44}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {28,31}, {1,40}, {28,35}, {10,26}, {17,20}, {17,31}, {7,22}, {25,40}, {19,36}, {15,25}, {2,33}, {10,35}, {4,17}, {3,24}, {6,17}, {32,35}, {19,33}, {11,14}, {7,12}, {13,20}, {13,21}, {2,43}, {4,10}, {33,37}, {14,34}, {13,44}, {11,23}, {16,40}, {26,41}, {15,19}, {9,33}, {29,34}, {20,35}, {8,42}, {15,38}, {7,38}, {14,30}, {22,39}, {8,32}, {17,24}, {12,23}, {29,43}, {4,25}, {6,7}, {18,33}, {1,7}, {8,15}, {42,43}, {21,33}, {17,38}, {10,34}, {25,39}, {24,28}, {36,42}, {13,39}, {11,43}, {11,17}, {19,42}, {24,29}, {4,16}, {6,9}, {6,18}, {39,43}, {33,44}, {17,39}, {7,32}, {5,10}, {13,38}, {4,9}, {24,26}, {11,26}, {11,13}, {20,34}, {30,32}, {3,41}, {20,24}, {26,38}, {16,39}, {38,43}, {7,41}, {3,44}, {14,21}, {14,44}, {19,27}, {33,39}, {18,40}, {26,30}, {2,6}, {13,30}, {9,24}, {14,39}, {32,45}, {34,42}, {6,26}, {23,35}, {8,19}, {4,20}, {19,45}, {12,16}, {17,41}, {28,41}, {2,23}, {9,38}, {10,44}, {27,37}, {2,32}, {12,14}, {24,38}, {32,36}, {8,13}, {10,40}, {16,21}, {6,27}, {21,41}, {6,30}, {11,25}, {2,17}, {33,35}, {11,40}, {25,31}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {24,45}, {16,32}, {27,28}, {18,32}, {26,42}, {21,32}, {23,30}, {21,26}, {31,43}, {39,40}, {22,35}, {5,39}, {26,29}, {28,36}, {6,21}, {9,15}, {23,37}, {8,12}, {7,20}, {23,27}, {16,19}, {12,36}, {22,44}, {31,34}, {32,38}, {3,33}, {1,24}, {19,25}, {17,21}, {2,9}, {15,26}, {18,41}, {23,43}, {4,8}, {29,31}, {17,30}, {7,33}, {1,15}, {12,31}, {29,35}, {27,29}, {13,45}, {4,37}, {40,44}, {28,33}, {7,19}, {17,33}, {10,32}, {16,24}, {25,37}, {4,19}, {13,16}, {5,11}, {10,15}, {4,36} }; // ET45.112 // Bipartite(10,35) Valencies [21,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 390241927692288000000 EdgePairs[45][112]:={ {2,44}, {3,33}, {2,24}, {1,20}, {10,24}, {9,28}, {6,32}, {6,16}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {3,40}, {10,37}, {4,30}, {6,17}, {1,13}, {5,38}, {7,38}, {8,42}, {4,29}, {3,45}, {3,13}, {3,43}, {3,25}, {3,15}, {10,23}, {1,40}, {2,15}, {4,19}, {7,22}, {2,19}, {1,19}, {10,33}, {3,35}, {9,43}, {2,26}, {8,39}, {10,44}, {2,41}, {2,14}, {1,30}, {6,11}, {8,44}, {8,27}, {8,31}, {9,11}, {10,22}, {6,22}, {3,18}, {8,16}, {2,45}, {6,21}, {2,25}, {7,12}, {6,40}, {6,31}, {1,38}, {2,34}, {2,36}, {4,22}, {8,19}, {10,38}, {1,18}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {1,44}, {5,29}, {8,41}, {5,43}, {8,14}, {4,42}, {9,41}, {2,39}, {7,32}, {4,45}, {7,13}, {7,43}, {7,25}, {10,28}, {2,35}, {6,12}, {6,30}, {5,23}, {10,29}, {3,20}, {9,42}, {2,20}, {1,29}, {7,30}, {8,17}, {2,16}, {4,35}, {8,36}, {5,18}, {1,23}, {7,17}, {8,11}, {5,24}, {9,37}, {8,22}, {1,45}, {10,42}, {5,14}, {4,15}, {1,28}, {3,11}, {1,33}, {10,13}, {10,12}, {1,43}, {3,26}, {8,37}, {5,28}, {8,26}, {9,22}, {6,15}, {5,41}, {10,43}, {9,13}, {8,32}, {8,21}, {1,24}, {5,31}, {6,27}, {5,44}, {6,26}, {3,23}, {1,39}, {10,32}, {5,36}, {3,21}, {1,25}, {9,12}, {6,41}, {1,15}, {2,11}, {10,39}, {1,35}, {5,39}, {7,28}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {8,34}, {9,18}, {10,17}, {2,29}, {6,45}, {10,27}, {4,34}, {4,14}, {10,34}, {9,17}, {10,18}, {8,24}, {6,25}, {2,40}, {2,31}, {9,33}, {9,36}, {5,26}, {9,38}, {4,25}, {10,19}, {3,38}, {4,12}, {4,20}, {5,13}, {3,28}, {7,27}, {7,45}, {3,41}, {3,31}, {1,14}, {7,33}, {6,37}, {10,14}, {5,19}, {6,20}, {7,35}, {5,21}, {2,30}, {7,37}, {1,34}, {9,31}, {4,17}, {6,35}, {3,36}, {9,16}, {9,21}, {4,39}, {7,40}, {7,42}, {4,44}, {9,23}, {8,29}, {4,32}, {7,18}, {5,16} }; // ET45.113 // Bipartite(12,33) Valencies [22,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5275360335382978756608000000 EdgePairs[45][113]:={ {10,37}, {6,25}, {5,38}, {4,28}, {5,45}, {12,22}, {8,26}, {1,40}, {2,35}, {4,31}, {6,15}, {11,15}, {8,21}, {3,19}, {5,15}, {1,19}, {8,23}, {12,16}, {2,18}, {3,21}, {3,39}, {11,14}, {1,35}, {5,32}, {4,37}, {4,40}, {2,33}, {4,38}, {11,35}, {11,29}, {11,17}, {11,27}, {1,20}, {3,18}, {9,18}, {10,17}, {12,28}, {4,43}, {8,30}, {9,33}, {1,17}, {4,16}, {4,13}, {5,41}, {7,41}, {1,13}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {12,31}, {12,40}, {10,20}, {2,15}, {12,13}, {6,18}, {1,29}, {12,37}, {10,35}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {1,38}, {1,26}, {2,36}, {9,36}, {6,34}, {1,43}, {9,39}, {8,42}, {4,22}, {5,27}, {7,14}, {3,43}, {2,39}, {8,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {9,13}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {7,19}, {4,32}, {2,44}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,38}, {6,16}, {11,33}, {8,24}, {4,41}, {8,41}, {5,14}, {8,45}, {1,41}, {2,23}, {10,13}, {10,19}, {9,22}, {9,19}, {11,44}, {3,25}, {7,35}, {2,27}, {12,30}, {6,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {5,39}, {7,28}, {6,45}, {12,18}, {9,25}, {10,22}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {10,28}, {9,24}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {9,21}, {7,29}, {8,29}, {8,36}, {8,27}, {2,45}, {3,33}, {11,30}, {9,28}, {3,34}, {2,21}, {5,24}, {11,45}, {12,36}, {3,45}, {5,26}, {5,29}, {10,41}, {4,25}, {3,28}, {7,31}, {12,33}, {8,33}, {12,39}, {8,14}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {1,34}, {5,21}, {9,15}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {7,26}, {7,16}, {1,23}, {5,18}, {11,20}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {7,44}, {7,43}, {9,40}, {4,20}, {8,20}, {5,44}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {7,13}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {12,19}, {1,37}, {2,42}, {6,33}, {12,21}, {2,32}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.114 // Bipartite(22,23) Valencies [23,22] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 29057685629025609672383529751884595200000000 EdgePairs[45][114]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {20,26}, {3,29}, {16,28}, {20,33}, {4,26}, {20,25}, {19,41}, {22,37}, {14,29}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {19,37}, {17,29}, {8,26}, {10,29}, {15,33}, {6,28}, {5,43}, {12,32}, {22,25}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {20,42}, {2,38}, {8,24}, {12,27}, {6,34}, {4,38}, {11,39}, {21,31}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {22,28}, {18,37}, {15,45}, {20,29}, {10,42}, {14,40}, {9,41}, {17,43}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {19,40}, {16,26}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {21,44}, {20,44}, {5,45}, {21,42}, {4,41}, {8,39}, {22,32}, {7,34}, {22,45}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {20,39}, {7,23}, {5,33}, {4,39}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {22,41}, {18,26}, {14,23}, {4,45}, {22,26}, {2,28}, {20,43}, {1,27}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {5,29}, {21,25}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {4,33}, {15,40}, {18,34}, {21,34}, {1,44}, {10,31}, {22,38}, {13,23}, {19,32}, {7,37}, {21,45}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {7,36}, {9,39}, {22,24}, {13,26}, {14,37}, {22,33}, {11,24}, {7,43}, {20,31}, {8,33}, {11,45}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {21,29}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {4,40}, {16,36}, {1,39}, {18,43}, {6,45}, {7,40}, {17,37}, {18,25}, {21,27}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {21,23}, {21,43}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {22,40}, {13,37}, {8,27}, {5,30}, {19,43}, {16,27}, {9,30}, {5,40}, {16,31}, {22,36}, {22,30}, {18,30}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {15,44}, {19,36}, {9,34}, {15,25}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {20,35}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {12,23}, {13,31}, {5,31}, {22,23}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {20,34}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {20,30}, {2,29}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {19,45}, {16,44}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {6,33}, {2,32}, {19,26}, {4,23}, {22,34}, {9,36}, {10,40}, {6,27}, {12,40}, {21,41}, {17,40}, {7,45}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {16,32}, {9,32}, {18,32}, {21,32}, {21,26}, {22,31}, {16,45}, {22,35}, {5,39}, {12,43}, {19,34}, {10,45}, {3,40}, {22,42}, {12,36}, {22,44}, {21,39}, {3,33}, {1,24}, {19,25}, {15,26}, {18,41}, {21,28}, {16,38}, {22,43}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET45.115 // Bipartite(5,40) Valencies [24,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 7608405715845120 EdgePairs[45][115]:={ {4,35}, {5,32}, {3,15}, {1,43}, {1,11}, {2,22}, {3,38}, {5,42}, {1,31}, {4,27}, {2,11}, {1,40}, {4,40}, {4,16}, {3,32}, {1,38}, {5,41}, {2,33}, {1,44}, {3,30}, {5,7}, {4,6}, {3,45}, {3,10}, {3,34}, {2,19}, {2,15}, {4,26}, {5,26}, {5,9}, {5,21}, {2,29}, {5,6}, {5,37}, {3,18}, {1,34}, {2,14}, {4,37}, {4,20}, {2,41}, {2,31}, {2,23}, {1,10}, {4,7}, {4,39}, {1,17}, {2,32}, {3,40}, {4,33}, {3,14}, {2,13}, {4,29}, {3,22}, {4,43}, {5,19}, {4,45}, {5,29}, {2,42}, {4,30}, {2,34}, {4,36}, {4,17}, {2,35}, {5,28}, {4,15}, {2,9}, {4,25}, {2,44}, {2,24}, {3,42}, {5,22}, {5,38}, {2,43}, {3,35}, {1,23}, {2,21}, {5,27}, {1,7}, {5,8}, {2,39}, {2,12}, {3,28}, {3,26}, {5,36}, {3,24}, {5,17}, {5,31}, {3,12}, {1,14}, {1,41}, {3,44}, {1,37}, {1,20}, {1,27}, {5,11}, {3,16}, {1,13}, {3,25}, {3,8}, {3,20}, {1,33}, {3,6}, {2,25}, {5,12}, {1,28}, {3,36}, {4,9}, {5,18}, {4,23}, {1,8}, {1,30}, {5,16}, {5,39}, {4,13}, {1,21}, {1,18}, {4,19}, {4,10}, {1,24}, {2,45} }; // ET45.116 // Bipartite(9,36) Valencies [24,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 142434729055340426428416000000 EdgePairs[45][116]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,16}, {8,12}, {4,26}, {3,22}, {3,40}, {4,16}, {1,10}, {8,30}, {2,23}, {1,13}, {5,38}, {9,45}, {7,38}, {8,42}, {4,29}, {1,32}, {3,13}, {3,45}, {8,33}, {3,43}, {3,25}, {3,15}, {7,41}, {7,44}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {5,20}, {3,37}, {9,43}, {2,26}, {7,34}, {8,39}, {2,41}, {2,14}, {5,32}, {8,15}, {4,23}, {8,44}, {8,27}, {2,42}, {6,22}, {3,18}, {2,45}, {4,38}, {6,21}, {3,34}, {6,40}, {6,31}, {1,38}, {4,10}, {1,17}, {2,36}, {4,22}, {7,11}, {7,20}, {9,27}, {5,11}, {1,44}, {4,41}, {5,29}, {8,41}, {2,38}, {9,19}, {8,14}, {8,45}, {2,39}, {7,32}, {1,31}, {3,12}, {7,13}, {7,25}, {7,43}, {2,35}, {1,22}, {6,12}, {6,30}, {6,43}, {5,23}, {9,34}, {9,42}, {2,20}, {6,18}, {1,29}, {8,17}, {3,39}, {4,35}, {9,25}, {7,16}, {7,26}, {6,33}, {2,32}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {7,17}, {8,11}, {5,24}, {9,37}, {8,35}, {9,10}, {5,14}, {1,28}, {4,13}, {7,14}, {3,27}, {4,28}, {4,43}, {3,10}, {1,43}, {8,26}, {5,42}, {9,22}, {7,31}, {6,15}, {5,41}, {2,17}, {9,13}, {5,12}, {9,40}, {8,32}, {8,21}, {3,19}, {6,27}, {5,44}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {7,29}, {6,28}, {2,11}, {9,30}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {6,36}, {2,21}, {3,30}, {5,33}, {9,18}, {3,24}, {2,29}, {6,45}, {8,38}, {1,26}, {4,34}, {1,16}, {4,14}, {8,24}, {6,25}, {9,33}, {9,36}, {6,34}, {6,10}, {5,27}, {5,26}, {8,18}, {3,42}, {9,39}, {4,25}, {4,11}, {4,20}, {3,28}, {8,20}, {7,10}, {1,41}, {5,45}, {3,31}, {2,12}, {1,14}, {9,24}, {6,39}, {5,15}, {6,37}, {7,35}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {2,18}, {1,34}, {9,31}, {7,19}, {4,17}, {3,36}, {9,16}, {9,21}, {7,40}, {4,44}, {8,29}, {4,32} }; // ET45.117 // Bipartite(9,36) Valencies [24,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10030613004288000000 EdgePairs[45][117]:={ {2,44}, {1,11}, {3,33}, {5,17}, {1,20}, {2,33}, {6,16}, {7,15}, {4,24}, {8,12}, {3,22}, {3,40}, {4,16}, {1,10}, {4,30}, {8,30}, {1,13}, {5,38}, {9,45}, {7,38}, {8,42}, {8,28}, {4,29}, {1,32}, {3,45}, {8,33}, {3,15}, {7,44}, {1,40}, {2,15}, {4,19}, {9,44}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {2,26}, {8,39}, {7,36}, {8,10}, {2,28}, {2,14}, {5,32}, {8,15}, {9,35}, {4,23}, {8,27}, {9,11}, {6,22}, {3,17}, {8,16}, {2,45}, {6,21}, {3,34}, {7,12}, {2,25}, {6,40}, {6,31}, {1,38}, {4,10}, {2,34}, {1,17}, {4,22}, {9,29}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {1,44}, {4,41}, {5,29}, {2,10}, {8,41}, {2,38}, {2,37}, {5,43}, {8,45}, {4,42}, {7,39}, {5,25}, {9,41}, {2,39}, {7,32}, {1,31}, {7,13}, {9,14}, {7,25}, {7,43}, {1,22}, {6,12}, {3,44}, {6,30}, {6,43}, {5,23}, {3,20}, {2,13}, {9,42}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {8,11}, {5,24}, {8,22}, {8,35}, {5,14}, {9,20}, {1,28}, {4,13}, {3,11}, {7,14}, {3,27}, {4,28}, {4,43}, {3,29}, {3,10}, {1,43}, {3,26}, {5,42}, {7,31}, {6,15}, {5,41}, {4,36}, {5,12}, {8,21}, {5,31}, {6,27}, {5,44}, {8,40}, {3,23}, {8,23}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {6,28}, {9,30}, {1,35}, {1,37}, {3,16}, {4,37}, {6,42}, {4,40}, {6,36}, {2,21}, {8,34}, {9,18}, {6,45}, {1,26}, {2,22}, {4,34}, {1,16}, {9,17}, {8,24}, {6,25}, {2,40}, {2,31}, {9,33}, {9,36}, {6,34}, {6,10}, {5,26}, {8,18}, {4,18}, {9,39}, {9,38}, {4,25}, {3,38}, {4,11}, {4,12}, {5,13}, {3,28}, {7,27}, {7,45}, {1,41}, {3,41}, {7,24}, {1,14}, {9,24}, {6,39}, {6,37}, {7,33}, {5,19}, {9,15}, {6,13}, {7,37}, {5,35}, {1,34}, {5,37}, {7,19}, {2,43}, {4,17}, {9,21}, {7,42}, {9,23}, {7,21}, {8,29}, {7,18} }; // ET45.118 // Bipartite(9,36) Valencies [24,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 285315214344192 EdgePairs[45][118]:={ {2,44}, {1,11}, {3,33}, {1,20}, {9,28}, {6,32}, {6,16}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {3,40}, {1,10}, {4,30}, {8,30}, {6,17}, {5,38}, {9,45}, {7,38}, {8,42}, {4,29}, {1,32}, {3,13}, {3,45}, {8,33}, {3,15}, {7,41}, {7,44}, {4,19}, {7,22}, {4,31}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {9,43}, {2,26}, {7,34}, {8,39}, {1,21}, {1,30}, {5,32}, {8,15}, {8,44}, {8,27}, {3,18}, {3,17}, {2,45}, {4,38}, {6,21}, {2,25}, {5,40}, {1,38}, {4,10}, {2,34}, {2,36}, {5,22}, {4,22}, {7,11}, {7,20}, {3,14}, {9,27}, {5,11}, {5,29}, {8,41}, {2,38}, {9,19}, {5,43}, {8,14}, {8,45}, {4,42}, {5,25}, {2,39}, {7,32}, {7,13}, {7,25}, {7,43}, {2,35}, {6,12}, {3,44}, {6,30}, {6,43}, {4,33}, {5,23}, {4,21}, {9,34}, {2,13}, {9,42}, {2,20}, {6,18}, {1,29}, {8,17}, {2,16}, {3,32}, {4,35}, {9,25}, {7,16}, {7,26}, {1,12}, {8,36}, {5,18}, {1,23}, {6,44}, {7,17}, {8,11}, {5,24}, {9,37}, {8,35}, {9,10}, {5,14}, {4,15}, {4,13}, {1,28}, {7,14}, {3,27}, {4,28}, {1,33}, {6,23}, {3,10}, {1,43}, {3,26}, {8,26}, {5,42}, {9,22}, {7,31}, {5,41}, {2,17}, {9,13}, {9,40}, {8,32}, {1,42}, {8,21}, {3,19}, {1,24}, {5,31}, {6,27}, {6,26}, {3,23}, {8,23}, {1,39}, {5,36}, {1,25}, {6,19}, {9,12}, {7,29}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {9,30}, {1,37}, {7,28}, {4,37}, {4,40}, {7,23}, {6,36}, {2,21}, {5,33}, {9,18}, {3,24}, {2,29}, {6,45}, {8,38}, {2,22}, {1,16}, {8,24}, {6,25}, {2,40}, {2,31}, {9,33}, {9,36}, {6,34}, {6,10}, {5,27}, {8,18}, {3,42}, {9,39}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {8,20}, {7,10}, {1,41}, {5,45}, {3,41}, {3,31}, {2,12}, {1,14}, {9,24}, {6,39}, {5,15}, {6,37}, {7,35}, {2,30}, {9,15}, {7,37}, {2,18}, {1,34}, {9,31}, {7,19}, {2,43}, {4,17}, {6,35}, {3,36}, {9,16}, {9,21}, {4,39}, {7,40}, {4,44}, {8,29}, {5,16} }; // ET45.119 // Bipartite(9,36) Valencies [24,6] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 940369969152 EdgePairs[45][119]:={ {2,44}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {6,32}, {4,27}, {7,15}, {4,24}, {8,12}, {3,22}, {3,40}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {2,23}, {1,13}, {8,43}, {5,38}, {9,45}, {7,38}, {8,42}, {8,28}, {1,32}, {3,13}, {3,45}, {1,27}, {3,25}, {3,15}, {7,44}, {4,19}, {9,44}, {4,31}, {1,19}, {3,37}, {9,43}, {1,21}, {7,36}, {8,10}, {2,41}, {2,28}, {6,11}, {9,35}, {4,23}, {8,44}, {8,31}, {9,11}, {6,22}, {3,18}, {6,29}, {3,17}, {8,16}, {2,45}, {3,34}, {7,12}, {2,25}, {6,31}, {1,38}, {4,10}, {2,34}, {2,36}, {4,22}, {8,19}, {9,29}, {7,11}, {7,20}, {3,14}, {9,32}, {9,26}, {9,27}, {5,11}, {1,44}, {5,29}, {2,10}, {8,41}, {9,19}, {2,37}, {5,43}, {8,14}, {4,42}, {7,39}, {5,25}, {9,41}, {7,32}, {1,31}, {4,45}, {7,13}, {9,14}, {7,25}, {2,35}, {1,22}, {6,30}, {6,43}, {4,33}, {5,23}, {4,21}, {2,13}, {2,20}, {6,18}, {7,30}, {8,17}, {2,16}, {3,39}, {4,35}, {7,16}, {2,32}, {1,12}, {7,26}, {8,36}, {5,18}, {5,30}, {6,44}, {5,24}, {1,45}, {8,22}, {5,14}, {9,20}, {4,15}, {7,14}, {3,27}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {3,26}, {8,26}, {5,42}, {6,15}, {5,41}, {4,36}, {2,17}, {5,12}, {9,40}, {8,32}, {1,24}, {5,31}, {6,27}, {8,40}, {1,39}, {5,36}, {3,21}, {1,25}, {6,19}, {6,41}, {1,15}, {2,11}, {1,37}, {7,28}, {3,16}, {6,42}, {4,40}, {7,23}, {2,21}, {3,30}, {5,33}, {8,34}, {2,29}, {8,38}, {1,26}, {2,22}, {4,34}, {9,17}, {8,24}, {6,25}, {2,40}, {9,33}, {6,34}, {6,10}, {5,26}, {8,18}, {3,42}, {4,18}, {9,39}, {9,38}, {3,38}, {4,11}, {4,12}, {5,13}, {3,28}, {8,20}, {7,27}, {5,45}, {3,41}, {7,24}, {2,12}, {1,14}, {6,39}, {6,37}, {5,19}, {6,20}, {7,35}, {5,21}, {9,15}, {6,13}, {7,37}, {5,35}, {1,34}, {9,31}, {5,37}, {6,35}, {9,16}, {9,21}, {4,39}, {7,40}, {7,42}, {9,23}, {8,29}, {1,36}, {7,18} }; // ET45.120 // Bipartite(15,30) Valencies [24,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 180551034077184000000 EdgePairs[45][120]:={ {13,21}, {15,33}, {6,38}, {10,37}, {15,38}, {14,36}, {9,32}, {5,38}, {5,22}, {10,18}, {9,17}, {5,43}, {5,45}, {12,22}, {3,26}, {8,26}, {13,39}, {11,43}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {14,45}, {3,39}, {5,32}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {14,29}, {13,40}, {14,44}, {2,33}, {6,32}, {11,29}, {11,17}, {10,42}, {6,29}, {11,27}, {3,18}, {8,16}, {10,17}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {1,17}, {4,16}, {7,45}, {12,20}, {5,41}, {12,38}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {15,45}, {6,44}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {1,38}, {1,26}, {13,19}, {14,32}, {13,41}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {3,43}, {15,28}, {6,17}, {5,28}, {2,39}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {7,19}, {4,32}, {2,44}, {13,18}, {11,21}, {6,36}, {11,36}, {10,16}, {3,30}, {3,16}, {2,24}, {11,23}, {11,16}, {10,36}, {3,24}, {15,37}, {10,38}, {6,16}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {8,41}, {9,26}, {14,21}, {8,45}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {4,45}, {15,23}, {9,22}, {9,19}, {3,44}, {11,44}, {13,45}, {3,25}, {11,34}, {7,35}, {2,43}, {2,27}, {12,30}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {14,27}, {7,28}, {12,18}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {15,40}, {14,37}, {1,44}, {13,38}, {14,40}, {9,41}, {6,23}, {15,17}, {7,39}, {3,41}, {4,36}, {4,29}, {9,44}, {1,32}, {6,43}, {6,37}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {4,44}, {7,40}, {5,23}, {12,43}, {5,20}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {14,16}, {8,36}, {13,44}, {2,45}, {3,33}, {14,26}, {3,34}, {4,27}, {2,22}, {8,43}, {14,19}, {1,33}, {3,45}, {5,26}, {12,44}, {2,37}, {4,42}, {10,41}, {4,25}, {3,28}, {14,30}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,18}, {11,37}, {11,28}, {5,18}, {5,16}, {1,23}, {14,42}, {10,27}, {15,18}, {5,17}, {3,40}, {15,16}, {7,17}, {10,45}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {9,45}, {14,41}, {4,26}, {15,20}, {1,28}, {13,28}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,25}, {10,23}, {15,26}, {4,19}, {8,39}, {14,22}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {15,43}, {4,39}, {12,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37} }; // ET45.121 // Bipartite(15,30) Valencies [24,12] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23592960 EdgePairs[45][121]:={ {15,33}, {10,37}, {15,38}, {14,36}, {6,25}, {5,38}, {5,22}, {10,18}, {4,28}, {5,45}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {11,43}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {3,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {14,45}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {13,40}, {14,44}, {2,33}, {6,32}, {4,38}, {11,35}, {11,29}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {4,43}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {7,45}, {8,37}, {5,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {12,31}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {15,45}, {6,44}, {4,23}, {11,18}, {13,26}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {13,41}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {15,28}, {6,17}, {2,39}, {4,18}, {8,18}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {13,17}, {7,19}, {2,44}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {11,36}, {10,16}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {15,37}, {10,38}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {8,41}, {9,38}, {9,26}, {14,21}, {8,45}, {3,29}, {12,17}, {1,41}, {2,23}, {4,45}, {10,19}, {15,23}, {9,22}, {12,41}, {11,44}, {3,44}, {13,45}, {3,25}, {7,35}, {2,43}, {4,33}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {13,22}, {1,25}, {6,19}, {9,16}, {9,30}, {5,39}, {14,27}, {7,28}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {1,16}, {3,42}, {14,43}, {3,22}, {14,37}, {1,44}, {14,40}, {9,41}, {15,17}, {7,39}, {3,41}, {15,39}, {4,29}, {9,44}, {1,32}, {6,43}, {8,32}, {7,24}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {9,23}, {7,21}, {14,16}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {13,32}, {14,26}, {1,45}, {11,30}, {9,28}, {3,34}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {14,19}, {11,45}, {1,33}, {12,36}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {10,41}, {4,25}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {13,34}, {11,41}, {7,25}, {6,26}, {15,42}, {13,35}, {5,21}, {7,42}, {6,41}, {12,34}, {6,28}, {6,42}, {4,35}, {13,33}, {14,25}, {15,21}, {11,37}, {11,28}, {7,16}, {1,23}, {10,24}, {11,20}, {14,42}, {10,34}, {15,18}, {5,17}, {3,40}, {15,16}, {7,17}, {10,45}, {8,35}, {2,40}, {6,21}, {15,22}, {9,45}, {14,41}, {15,20}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {15,31}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {5,44}, {5,25}, {10,23}, {9,43}, {4,19}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {10,32}, {15,43}, {4,39}, {7,36}, {6,35}, {12,19}, {8,25}, {2,32}, {12,21}, {6,33}, {11,26}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.122 // Bipartite(18,27) Valencies [24,16] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1872381094133760 EdgePairs[45][122]:={ {13,21}, {15,33}, {18,45}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {11,25}, {4,28}, {5,43}, {5,45}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {16,22}, {13,39}, {17,42}, {11,43}, {2,35}, {17,33}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {15,27}, {1,19}, {3,23}, {10,39}, {3,20}, {1,21}, {14,45}, {16,37}, {16,28}, {5,32}, {1,35}, {7,30}, {15,41}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {16,21}, {13,40}, {14,44}, {2,33}, {6,32}, {17,35}, {11,35}, {11,29}, {10,42}, {6,29}, {11,27}, {1,20}, {2,34}, {12,28}, {2,25}, {4,24}, {4,43}, {18,32}, {15,32}, {4,30}, {8,30}, {9,33}, {7,45}, {8,37}, {12,20}, {5,41}, {17,39}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {17,20}, {12,31}, {12,40}, {10,20}, {17,26}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {18,35}, {16,25}, {13,42}, {9,35}, {1,29}, {15,19}, {12,37}, {16,34}, {10,35}, {15,45}, {16,43}, {18,39}, {4,23}, {8,38}, {13,26}, {6,24}, {17,36}, {2,29}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {2,36}, {13,41}, {16,40}, {8,22}, {18,29}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {18,26}, {4,22}, {18,33}, {18,36}, {8,19}, {3,38}, {5,27}, {3,43}, {15,28}, {5,28}, {2,39}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {17,29}, {18,19}, {7,19}, {4,32}, {2,44}, {1,30}, {14,28}, {11,21}, {6,36}, {16,29}, {11,36}, {2,24}, {11,23}, {3,24}, {14,33}, {15,37}, {10,38}, {14,23}, {15,34}, {11,33}, {18,22}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {9,26}, {14,21}, {18,20}, {18,38}, {8,45}, {3,29}, {17,31}, {13,36}, {1,41}, {2,23}, {4,45}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,44}, {11,44}, {13,45}, {3,25}, {11,34}, {17,28}, {7,35}, {2,43}, {2,27}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,44}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {13,31}, {9,30}, {5,39}, {17,19}, {3,32}, {14,27}, {18,44}, {16,41}, {7,28}, {6,45}, {17,44}, {8,34}, {17,30}, {10,22}, {10,30}, {7,23}, {16,30}, {12,45}, {6,22}, {4,34}, {10,25}, {17,38}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {16,26}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {1,44}, {18,31}, {9,41}, {6,23}, {16,31}, {16,45}, {7,39}, {3,41}, {4,36}, {15,39}, {1,32}, {9,44}, {6,43}, {6,37}, {10,28}, {9,24}, {17,22}, {17,25}, {6,20}, {16,44}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {18,41}, {10,40}, {18,21}, {10,21}, {9,21}, {7,29}, {18,30}, {8,29}, {9,23}, {7,21}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {16,36}, {13,32}, {14,26}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {18,28}, {5,24}, {2,22}, {15,29}, {16,20}, {18,24}, {8,43}, {2,31}, {14,19}, {16,38}, {11,45}, {1,33}, {18,27}, {12,36}, {3,45}, {16,27}, {5,26}, {12,44}, {4,42}, {5,29}, {10,41}, {4,25}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {17,34}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {1,34}, {15,42}, {13,35}, {5,21}, {6,41}, {17,24}, {17,40}, {12,34}, {8,44}, {17,21}, {6,28}, {6,42}, {16,23}, {18,23}, {4,35}, {13,33}, {14,20}, {14,25}, {15,21}, {7,26}, {1,23}, {16,35}, {10,24}, {11,20}, {14,42}, {10,34}, {3,40}, {8,35}, {13,23}, {17,27}, {2,40}, {6,21}, {15,22}, {17,45}, {9,45}, {14,41}, {4,26}, {15,20}, {16,39}, {17,37}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {7,44}, {8,28}, {7,43}, {18,40}, {9,40}, {8,20}, {5,44}, {5,25}, {10,23}, {4,19}, {8,39}, {3,37}, {9,42}, {5,36}, {16,19}, {10,32}, {15,43}, {4,39}, {7,36}, {12,35}, {12,19}, {17,43}, {1,37}, {8,25}, {2,42}, {18,42}, {16,32}, {2,32}, {6,33}, {11,26}, {5,33}, {15,25}, {18,37}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.123 // Bipartite(21,24) Valencies [24,21] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 31699293413482483278963850638419558400000000 EdgePairs[45][123]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {20,26}, {3,29}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {14,29}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {19,37}, {17,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {20,22}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {8,24}, {2,38}, {20,42}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {21,31}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {10,22}, {18,37}, {15,45}, {20,29}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {19,40}, {16,26}, {3,22}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, 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{14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {8,42}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {20,34}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {20,30}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {19,45}, {16,44}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {9,36}, {10,40}, {6,27}, {12,40}, {21,41}, {17,40}, {7,45}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {21,32}, {21,26}, {16,45}, {5,39}, {12,43}, {19,34}, {10,45}, {3,40}, {12,36}, {21,39}, {3,33}, {1,24}, {19,25}, {15,26}, {18,41}, {21,28}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET45.124 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 338533188894720 EdgePairs[45][124]:={ {13,25}, {3,42}, {33,45}, {15,17}, {10,17}, {20,26}, {16,28}, {20,33}, {4,26}, {20,25}, {19,41}, {41,44}, {2,4}, {26,33}, {2,26}, {3,7}, {19,22}, {8,28}, {36,37}, {8,31}, {1,5}, {15,16}, {11,34}, {13,27}, {1,9}, {14,17}, {2,24}, {7,28}, {18,38}, {39,41}, {20,27}, {4,28}, {4,11}, {9,21}, {3,15}, {8,20}, {17,29}, {5,18}, {23,29}, {6,28}, {37,40}, {5,43}, {14,16}, {12,32}, {22,25}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {29,42}, {1,41}, {7,10}, {4,30}, {35,37}, {20,42}, {8,11}, {23,45}, {38,41}, {31,37}, {37,44}, {17,22}, {4,38}, {37,42}, {21,31}, {3,13}, {31,36}, {18,28}, {17,19}, {22,28}, {9,12}, {38,44}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {12,22}, {9,41}, {15,20}, {9,10}, {23,34}, {24,36}, {11,35}, {3,27}, {11,31}, {7,13}, {10,13}, {25,28}, {18,29}, {22,29}, {14,27}, {34,39}, {17,42}, {2,8}, {12,35}, {13,17}, {11,36}, {19,40}, {28,42}, {3,22}, {35,40}, {27,32}, {28,32}, {16,20}, {7,30}, {5,25}, {3,9}, {5,26}, {8,40}, {2,41}, {36,38}, {16,23}, {21,44}, {3,14}, {20,44}, {5,45}, {31,44}, {21,42}, {31,35}, {22,45}, {2,36}, {7,14}, {42,45}, {11,44}, {22,27}, {10,23}, {30,34}, {20,32}, {1,26}, {1,25}, {26,32}, {35,41}, {18,42}, {10,16}, {16,42}, {12,44}, {15,34}, {24,30}, {16,30}, {34,40}, {5,27}, {24,44}, {9,31}, {3,6}, {4,39}, {6,11}, {1,22}, {38,40}, {29,32}, {6,39}, {24,43}, {2,44}, {35,39}, {2,45}, {10,14}, {1,42}, {19,31}, {8,21}, {9,20}, {4,45}, {18,21}, {31,39}, {22,26}, {30,40}, {20,43}, 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{6,45}, {7,40}, {17,37}, {14,19}, {21,27}, {6,44}, {2,42}, {15,37}, {9,13}, {21,23}, {21,43}, {30,33}, {4,29}, {1,43}, {3,26}, {13,36}, {3,8}, {34,41}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {25,30}, {9,40}, {32,39}, {14,20}, {11,33}, {1,34}, {19,23}, {30,41}, {11,16}, {1,4}, {24,35}, {13,37}, {5,30}, {23,44}, {19,43}, {9,30}, {2,13}, {22,36}, {22,30}, {18,30}, {28,31}, {32,43}, {1,40}, {28,35}, {17,20}, {1,23}, {8,29}, {15,25}, {41,45}, {16,41}, {33,36}, {10,35}, {4,27}, {4,17}, {3,24}, {7,11}, {2,27}, {15,35}, {6,17}, {32,35}, {19,33}, {3,34}, {18,39}, {11,14}, {7,12}, {13,20}, {13,21}, {2,43}, {4,10}, {33,37}, {14,34}, {11,23}, {3,5}, {16,40}, {15,19}, {9,33}, {29,34}, {8,42}, {15,38}, {8,32}, {17,24}, {12,23}, {4,25}, {24,27}, {6,7}, {1,7}, {8,15}, {42,43}, {21,33}, {17,38}, {10,34}, {25,39}, {24,28}, {36,42}, {6,25}, {28,34}, {37,43}, {13,39}, {11,43}, {11,17}, {33,38}, {15,18}, {32,34}, {19,42}, {24,29}, {12,13}, {4,16}, {6,9}, {1,45}, {6,18}, {5,12}, {39,43}, {17,39}, {33,44}, {7,32}, {5,10}, {13,38}, {4,9}, {24,26}, {6,16}, {11,13}, {2,15}, {30,32}, {3,41}, {15,39}, {10,33}, {13,34}, {20,24}, {23,25}, {26,38}, {18,24}, {21,24}, {8,14}, {39,42}, {16,39}, {30,42}, {5,37}, {38,43}, {7,41}, {3,44}, {14,21}, {19,27}, {33,39}, {1,36}, {18,40}, {26,30}, {42,44}, {2,6}, {14,39}, {32,45}, {34,42}, {11,15}, {6,26}, {23,35}, {12,34}, {8,19}, {19,45}, {7,21}, {12,16}, {17,41}, {34,37}, {28,41}, {2,23}, {15,21}, {27,37}, {10,44}, {1,8}, {19,26}, {12,14}, {22,34}, {27,30}, {32,36}, {8,13}, {16,21}, {6,27}, {21,41}, {17,40}, {20,41}, {14,38}, {27,39}, {6,30}, {6,38}, {33,35}, {25,31}, {5,44}, {3,45}, {4,43}, {11,22}, {24,45}, {9,32}, {27,28}, {35,42}, {30,35}, {21,32}, {23,30}, {21,26}, {30,31}, {31,43}, {39,40}, {22,35}, {5,39}, {12,43}, {26,29}, {28,36}, {9,15}, {10,45}, {8,12}, {7,20}, {3,40}, {23,27}, {16,19}, {12,36}, {27,31}, {22,44}, {31,34}, {40,43}, {32,38}, {5,17}, {1,24}, {19,25}, {6,8}, {17,21}, {2,9}, {4,18}, {15,26}, {18,41}, {23,43}, {23,36}, {26,28}, {16,38}, {22,43}, {4,8}, {29,31}, {17,30}, {7,33}, {1,15}, {12,31}, {20,45}, {29,35}, {27,29}, {4,37}, {40,44}, {28,33}, {7,19}, {2,35}, {10,32}, {16,24}, {25,37}, {13,16}, {5,11}, {10,15}, {6,29} }; // ET45.125 // Non-bipartite Valency 24 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 338533188894720 EdgePairs[45][125]:={ {3,42}, {13,40}, {24,33}, {6,36}, {30,37}, {11,42}, {33,45}, {10,17}, {20,26}, {9,18}, {16,28}, {5,13}, {20,25}, {19,41}, {22,37}, {41,44}, {2,4}, {26,33}, {2,20}, {2,26}, {8,28}, {4,24}, {12,42}, {1,5}, {7,24}, {18,38}, {7,28}, {1,32}, {20,27}, {4,28}, {8,36}, {3,15}, {19,37}, {17,29}, {23,29}, {15,33}, {7,17}, {13,22}, {6,28}, {12,32}, {5,9}, {3,25}, {1,41}, {7,10}, {4,30}, {20,42}, {8,11}, {8,24}, {31,37}, {6,34}, {11,39}, {24,39}, {3,13}, {2,21}, {19,38}, {31,36}, {18,28}, {8,44}, {4,34}, {17,19}, {22,28}, {9,12}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {36,44}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {9,10}, {23,34}, {17,45}, {24,36}, {17,25}, {14,33}, {3,32}, {3,27}, {11,31}, {10,13}, {25,28}, {11,37}, {18,29}, {19,30}, {22,29}, {17,42}, {20,28}, {14,22}, {19,40}, {16,26}, {6,19}, {27,32}, {5,23}, {16,20}, {25,45}, {7,30}, {8,40}, {2,41}, {1,31}, {6,35}, {21,30}, {3,14}, {23,33}, {31,44}, {35,44}, {21,42}, {4,41}, {9,22}, {31,35}, {5,20}, {29,38}, {22,32}, {7,34}, {1,20}, {18,27}, {2,36}, {42,45}, {12,38}, {11,44}, {13,33}, {26,44}, {15,24}, {10,23}, {30,34}, {1,26}, {1,25}, {26,32}, {18,42}, {10,16}, {6,14}, {12,44}, {24,30}, {16,42}, {16,30}, {8,35}, {11,38}, {6,40}, {3,6}, {20,39}, {7,23}, {7,16}, {6,24}, {16,43}, {34,45}, {2,44}, {2,45}, {10,14}, {1,42}, {18,26}, {14,23}, {28,39}, {18,21}, {31,39}, {1,27}, {5,22}, {5,36}, {18,20}, {12,39}, {12,33}, {26,43}, {40,45}, {21,37}, {25,38}, {26,37}, {2,34}, {12,41}, {5,42}, {9,11}, {11,32}, {3,31}, {23,39}, {11,18}, {10,43}, {3,20}, {5,29}, {21,25}, {27,36}, {9,28}, {6,13}, {8,10}, {20,40}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {33,43}, {27,38}, {2,5}, {10,18}, {9,17}, {1,14}, {17,26}, {11,41}, {35,45}, {31,45}, {8,34}, {13,19}, {9,29}, {15,40}, {1,44}, {10,31}, {22,38}, {13,23}, {5,15}, {27,33}, {3,43}, {3,36}, {32,37}, {7,42}, {26,31}, {5,8}, {7,29}, {29,36}, {1,35}, {17,28}, {26,35}, {23,32}, {5,21}, {7,36}, {14,37}, {22,33}, {11,24}, {7,43}, {11,45}, {4,7}, {41,43}, {9,44}, {15,23}, {12,17}, {9,42}, {30,38}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {27,45}, {26,39}, {18,44}, {23,28}, {21,29}, {2,14}, {9,35}, {12,24}, {18,19}, {3,4}, {12,45}, {30,36}, {16,29}, {8,41}, {28,37}, {15,42}, {2,40}, {9,43}, {33,34}, {24,34}, {3,19}, {4,40}, {23,38}, {32,44}, {18,43}, {7,40}, {17,37}, {18,25}, {14,19}, {21,27}, {36,45}, {10,37}, {25,36}, {2,42}, {15,37}, {7,35}, {4,42}, {20,38}, {14,41}, {4,15}, {4,29}, {5,34}, {26,34}, {1,43}, {3,26}, {9,23}, {3,35}, {12,15}, {1,6}, {25,30}, {9,40}, {14,31}, {8,45}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {11,16}, {1,4}, {24,35}, {13,37}, {24,37}, {24,31}, {5,30}, {15,22}, {16,27}, {9,30}, {2,13}, {5,40}, {22,36}, {22,30}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {32,43}, {1,40}, {6,23}, {28,35}, {17,20}, {8,29}, {7,22}, {9,34}, {41,45}, {6,22}, {5,19}, {16,41}, {33,36}, {16,25}, {17,44}, {2,33}, {15,31}, {14,24}, {7,11}, {19,39}, {2,27}, {1,19}, {5,41}, {13,41}, {32,35}, {19,29}, {3,34}, {18,39}, {11,14}, {7,12}, {13,20}, {13,21}, {2,43}, {33,37}, {11,23}, {3,5}, {16,40}, {36,43}, {15,19}, {29,34}, {8,16}, {8,42}, {15,38}, {22,39}, {12,23}, {13,31}, {8,18}, {10,38}, {6,7}, {42,43}, {17,38}, {25,39}, {24,28}, {4,14}, {35,43}, {28,34}, {13,39}, {11,43}, {11,17}, {33,38}, {28,38}, {32,34}, {19,42}, {24,29}, {12,13}, {6,9}, {1,45}, {17,39}, {33,44}, {6,42}, {4,9}, {13,38}, {13,24}, {11,13}, {26,36}, {7,44}, {25,34}, {27,44}, {2,15}, {3,41}, {15,39}, {10,33}, {10,39}, {26,38}, {16,39}, {25,43}, {7,41}, {3,44}, {8,23}, {20,30}, {14,21}, {3,21}, {19,27}, {33,39}, {1,36}, {18,40}, {26,30}, {42,44}, {2,6}, {24,32}, {9,24}, {14,39}, {9,45}, {32,45}, {14,42}, {6,20}, {18,45}, {10,41}, {11,15}, {23,35}, {15,41}, {4,20}, {16,44}, {23,31}, {12,16}, {17,41}, {8,43}, {15,21}, {27,37}, {10,44}, {1,33}, {2,32}, {19,26}, {12,14}, {29,39}, {4,23}, {27,30}, {22,34}, {24,38}, {9,36}, {32,36}, {10,40}, {16,21}, {29,37}, {21,41}, {12,40}, {17,40}, {7,45}, {20,41}, {15,32}, {14,38}, {27,39}, {6,30}, {25,35}, {17,27}, {33,35}, {11,40}, {13,42}, {25,31}, {5,14}, {5,35}, {3,45}, {11,22}, {9,16}, {27,28}, {30,35}, {25,44}, {23,30}, {34,44}, {21,26}, {22,31}, {16,45}, {31,43}, {22,35}, {12,43}, {26,29}, {1,21}, {6,21}, {28,36}, {23,37}, {10,45}, {8,12}, {3,40}, {16,19}, {27,43}, {27,31}, {31,34}, {21,39}, {7,18}, {40,43}, {3,33}, {32,38}, {27,35}, {6,8}, {19,25}, {17,21}, {18,41}, {21,28}, {23,36}, {26,28}, {16,38}, {12,37}, {4,8}, {17,30}, {2,19}, {5,24}, {6,15}, {12,31}, {1,15}, {29,35}, {27,29}, {30,39}, {26,45}, {40,44}, {4,35}, {2,35}, {10,32}, {25,37}, {4,19}, {21,38}, {34,43}, {10,15}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET45.126 // Bipartite(20,25) Valencies [25,20] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 37737254063669622951147441236213760000000000 EdgePairs[45][126]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {3,29}, {20,26}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {14,29}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {9,21}, {13,43}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {20,22}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {20,42}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {10,22}, {18,37}, {15,45}, {20,29}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {20,44}, {5,45}, {4,41}, {9,22}, {8,39}, {7,34}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {19,21}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {8,21}, {18,26}, {14,23}, {4,45}, {18,21}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {5,29}, {9,28}, {20,40}, {19,24}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {11,45}, {8,33}, {20,31}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {4,40}, {16,36}, {1,39}, {18,43}, {6,45}, {7,40}, {17,37}, {18,25}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {8,22}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {16,27}, {19,43}, {9,30}, {5,40}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {19,36}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {8,42}, {20,21}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {20,34}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {20,30}, {14,21}, {14,44}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {16,44}, {7,21}, {19,45}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {7,45}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {19,34}, {10,45}, {3,40}, {12,36}, {10,21}, {3,33}, {1,24}, {19,25}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET45.127 // Bipartite(6,39) Valencies [26,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 11589966656836404328267776000000 EdgePairs[45][127]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {4,26}, {3,22}, {3,40}, {4,16}, {1,10}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {3,45}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {1,19}, {2,27}, {5,20}, {3,37}, {2,26}, {2,9}, {6,7}, {2,41}, {2,14}, {5,32}, {4,23}, {2,42}, {6,22}, {3,18}, {3,7}, {2,45}, {4,38}, {6,21}, {3,34}, {6,40}, {6,31}, {1,38}, {4,10}, {1,17}, {2,36}, {1,7}, {4,22}, {4,8}, {5,11}, {1,44}, {4,41}, {5,29}, {2,38}, {2,39}, {1,31}, {3,12}, {2,35}, {1,22}, {6,12}, {6,30}, {6,43}, {5,23}, {2,20}, {6,18}, {1,29}, {3,39}, {4,35}, {2,32}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {5,24}, {5,14}, {1,28}, {4,13}, {3,27}, {4,7}, {4,28}, {4,43}, {3,10}, {1,43}, {5,42}, {6,15}, {5,41}, {2,17}, {5,12}, {3,19}, {6,27}, {5,44}, {5,36}, {3,21}, {1,25}, {6,19}, {6,9}, {6,28}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {6,42}, {4,40}, {6,36}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {6,45}, {1,26}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,34}, {6,10}, {5,27}, {5,26}, {3,42}, {5,9}, {4,25}, {4,11}, {1,8}, {4,20}, {3,28}, {1,41}, {5,45}, {3,31}, {2,12}, {1,14}, {2,8}, {6,39}, {5,15}, {6,37}, {5,21}, {2,30}, {6,13}, {5,35}, {2,18}, {1,34}, {4,17}, {3,36}, {4,44}, {4,32} }; // ET45.128 // Bipartite(19,26) Valencies [26,19] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 49058430282770509836491673607077888000000000 EdgePairs[45][128]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {3,29}, {16,28}, {4,26}, {19,41}, {14,29}, {2,20}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {4,28}, {8,36}, {9,21}, {8,20}, {13,43}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {10,22}, {18,37}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {17,42}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {1,26}, {18,31}, {9,27}, {1,25}, {18,42}, {19,21}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {4,45}, {18,21}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {18,20}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {3,20}, {5,29}, {9,28}, {19,24}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,20}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {14,36}, {7,42}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {4,40}, {16,36}, {1,39}, {6,45}, {18,43}, {7,40}, {17,37}, {18,25}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {16,27}, {19,43}, {9,30}, {5,40}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {19,36}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {1,45}, {10,30}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {18,45}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {4,20}, {16,44}, {7,21}, {19,45}, {17,41}, {11,30}, {8,43}, {2,23}, {19,20}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {7,45}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {19,34}, {10,45}, {7,20}, {3,40}, {12,36}, {10,21}, {3,33}, {1,24}, {19,25}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET45.129 // Bipartite(18,27) Valencies [27,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 69714611454463356083435536178479104000000000 EdgePairs[45][129]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {3,29}, {16,28}, {4,26}, {14,29}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {4,28}, {8,36}, {9,21}, {8,20}, {13,43}, {17,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {18,28}, {4,34}, {17,19}, {13,29}, {10,22}, {18,37}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {11,29}, {14,27}, {17,42}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {18,35}, {1,26}, {9,27}, {18,31}, {1,25}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {18,26}, {4,45}, {18,21}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {18,20}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {7,37}, {1,28}, {3,43}, {3,36}, {14,36}, {7,42}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {18,19}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {6,45}, {18,43}, {7,40}, {17,37}, {14,19}, {18,25}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {8,22}, {14,20}, {11,33}, {1,34}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {16,27}, {9,30}, {5,40}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {3,34}, {18,39}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {17,34}, {12,26}, {1,45}, {10,30}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {18,45}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {16,44}, {7,21}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {7,45}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {10,45}, {7,20}, {3,40}, {16,19}, {12,36}, {10,21}, {3,33}, {1,24}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {17,30}, {2,19}, {5,24}, {7,33}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET45.130 // Bipartite(3,42) Valencies [28,2] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3975358563294886684595847168000000 EdgePairs[45][130]:={ {2,11}, {3,22}, {1,26}, {2,14}, {3,40}, {2,44}, {1,14}, {1,44}, {2,26}, {3,12}, {2,32}, {2,30}, {1,29}, {2,29}, {1,32}, {2,24}, {1,37}, {1,40}, {1,10}, {1,43}, {2,39}, {3,21}, {3,42}, {3,27}, {3,33}, {2,6}, {1,4}, {1,20}, {2,36}, {3,37}, {1,31}, {2,45}, {3,9}, {3,24}, {2,12}, {2,33}, {2,21}, {1,38}, {1,7}, {3,4}, {1,16}, {2,20}, {3,7}, {3,16}, {3,28}, {3,15}, {2,18}, {2,38}, {3,25}, {3,19}, {3,30}, {2,15}, {2,5}, {3,18}, {3,31}, {1,5}, {2,27}, {1,17}, {3,6}, {3,45}, {3,39}, {2,42}, {3,34}, {1,28}, {2,17}, {3,13}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,41}, {1,41}, {1,22}, {2,8}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {3,10}, {3,36}, {3,43} }; // ET45.131 // Bipartite(9,36) Valencies [28,7] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 362880 EdgePairs[45][131]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {9,28}, {2,33}, {4,27}, {7,15}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {3,40}, {4,16}, {1,10}, {4,30}, {8,30}, {6,17}, {7,38}, {8,42}, {8,28}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {7,41}, {7,44}, {4,19}, {2,19}, {1,19}, {3,35}, {5,20}, {9,43}, {2,26}, {1,21}, {7,36}, {8,10}, {2,28}, {1,30}, {5,32}, {6,11}, {8,15}, {9,35}, {4,23}, {8,44}, {8,27}, {8,31}, {9,11}, {2,42}, {6,22}, {3,18}, {3,17}, {8,16}, {2,45}, {4,38}, {6,21}, {3,34}, {5,40}, {2,25}, {6,31}, {6,40}, {1,38}, {2,34}, {1,17}, {2,36}, {5,22}, {4,22}, {8,19}, {9,29}, {3,14}, {7,20}, {9,32}, {9,26}, {9,27}, {2,10}, {4,41}, {5,29}, {8,41}, {2,38}, {9,19}, {2,37}, {5,43}, {8,14}, {7,39}, {5,25}, {2,39}, {7,32}, {4,45}, {7,13}, {9,14}, {7,43}, {6,12}, {3,44}, {6,43}, {4,33}, {5,23}, {2,13}, {9,42}, {2,20}, {6,18}, {1,29}, {7,30}, {8,17}, {2,16}, {3,39}, {3,32}, {4,35}, {9,25}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {8,36}, {5,18}, {1,23}, {6,24}, {5,30}, {6,44}, {7,17}, {8,11}, {5,24}, {9,37}, {1,45}, {8,13}, {8,22}, {8,35}, {9,10}, {5,14}, {9,20}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {3,26}, {5,28}, {8,26}, {9,22}, {7,31}, {5,41}, {4,36}, {2,17}, {9,13}, {5,12}, {9,40}, {1,42}, {8,21}, {1,24}, {5,31}, {6,27}, {5,44}, {8,23}, {1,39}, {5,36}, {3,21}, {1,25}, {6,19}, {9,12}, {6,41}, {1,15}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {6,36}, {2,21}, {3,30}, {8,34}, {9,18}, {2,29}, {6,45}, {8,38}, {2,22}, {4,34}, {1,16}, {8,24}, {6,25}, {6,38}, {2,40}, {2,31}, {9,33}, {9,36}, {6,34}, {5,10}, {5,26}, {8,18}, {3,42}, {4,18}, {9,39}, {4,25}, {3,38}, {4,11}, {4,12}, {8,20}, {7,10}, {7,27}, {7,45}, {1,41}, {5,45}, {3,41}, {3,31}, {7,24}, {2,12}, {1,14}, {5,15}, {6,39}, {6,37}, {7,33}, {6,20}, {5,21}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {1,34}, {9,31}, {5,37}, {7,19}, {6,35}, {9,16}, {9,21}, {7,40}, {4,44}, {7,42}, {9,23}, {8,29}, {4,32}, {7,18} }; // ET45.132 // Bipartite(10,35) Valencies [28,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12487741686153216000000 EdgePairs[45][132]:={ {6,38}, {10,37}, {9,32}, {5,38}, {5,22}, {10,18}, {9,17}, {5,43}, {5,45}, {3,26}, {8,26}, {5,11}, {2,35}, {4,31}, {8,40}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {1,12}, {10,42}, {9,11}, {6,29}, {3,18}, {8,16}, {10,17}, {2,34}, {2,25}, {4,24}, {4,30}, {8,13}, {8,30}, {1,17}, {4,16}, {7,45}, {5,41}, {1,13}, {7,27}, {6,39}, {10,26}, {2,17}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {6,44}, {8,38}, {6,24}, {2,29}, {1,38}, {1,26}, {7,15}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {8,18}, {10,12}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {2,13}, {8,15}, {6,36}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,26}, {8,45}, {3,29}, {1,41}, {2,23}, {10,13}, {4,45}, {9,22}, {4,11}, {9,19}, {3,44}, {3,25}, {7,35}, {2,43}, {2,27}, {2,12}, {1,22}, {7,34}, {10,31}, {9,31}, {6,13}, {6,19}, {2,20}, {9,16}, {4,17}, {9,30}, {9,12}, {7,28}, {6,11}, {8,34}, {9,25}, {10,22}, {5,40}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {9,44}, {1,32}, {6,43}, {6,37}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {4,44}, {7,40}, {5,23}, {5,20}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {8,36}, {2,45}, {3,33}, {10,15}, {3,34}, {1,11}, {4,27}, {2,22}, {8,11}, {8,43}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {4,25}, {10,41}, {3,28}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {7,18}, {5,18}, {5,16}, {1,23}, {10,27}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,13}, {5,25}, {10,23}, {4,19}, {8,39}, {7,13}, {9,42}, {9,14}, {5,36}, {9,34}, {10,32}, {4,39}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37} }; // ET45.133 // Bipartite(15,30) Valencies [28,14] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 42849873690624000 EdgePairs[45][133]:={ {13,21}, {15,33}, {6,38}, {11,40}, {10,37}, {15,38}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {10,18}, {9,17}, {11,25}, {5,43}, {5,45}, {3,26}, {12,22}, {8,26}, {1,40}, {14,38}, {13,39}, {15,44}, {11,43}, {2,35}, {4,31}, {8,40}, {3,35}, {10,33}, {8,21}, {3,19}, {14,31}, {15,27}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {14,45}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {13,40}, {14,44}, {2,33}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {10,17}, {9,18}, {2,34}, {12,28}, {2,25}, {4,24}, {15,32}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {7,45}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {10,26}, {2,17}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {15,30}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {15,19}, {12,37}, {10,35}, {15,45}, {6,44}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {9,20}, {4,22}, {8,19}, {3,38}, {5,27}, {3,43}, {15,28}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {12,24}, {1,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {1,30}, {13,18}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {14,33}, {15,37}, {10,38}, {14,23}, {6,16}, {15,34}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {8,45}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {4,45}, {10,19}, {15,23}, {9,22}, {12,41}, {9,19}, {3,44}, {11,44}, {13,45}, {3,25}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {10,31}, {9,31}, {5,19}, {10,44}, {10,29}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {3,32}, {14,27}, {7,28}, {6,45}, {12,18}, {2,16}, {8,34}, {13,29}, {10,22}, {5,40}, {12,45}, {6,22}, {4,34}, {10,25}, {15,35}, {12,29}, {6,31}, {11,32}, {15,24}, {12,25}, {1,16}, {3,42}, {14,43}, {15,40}, {3,22}, {14,37}, {1,44}, {13,38}, {14,40}, {9,41}, {6,23}, {15,17}, {7,39}, {3,41}, {4,36}, {15,39}, {4,29}, {9,44}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {10,21}, {9,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {13,44}, {2,45}, {3,33}, {13,32}, {14,26}, {1,45}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {2,22}, {15,29}, {8,43}, {2,31}, {14,19}, {11,45}, {3,45}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {14,30}, {7,31}, {12,33}, {8,33}, {12,39}, {11,31}, {14,24}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {15,42}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {13,33}, {14,25}, {15,21}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {15,18}, {5,17}, {3,40}, {15,16}, {7,17}, {8,35}, {13,23}, {2,40}, {6,21}, {15,22}, {9,45}, {14,41}, {4,26}, {15,20}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {5,42}, {2,38}, {12,32}, {15,36}, {10,43}, {15,31}, {7,44}, {8,28}, {7,43}, {4,20}, {8,20}, {1,27}, {5,44}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {15,43}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {11,26}, {5,33}, {15,25}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.134 // Bipartite(17,28) Valencies [28,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 108444951151387442796455278499856384000000000 EdgePairs[45][134]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {9,18}, {3,29}, {16,28}, {4,26}, {14,29}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {5,18}, {17,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {4,34}, {17,19}, {13,29}, {10,22}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {17,18}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {17,42}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {1,26}, {9,27}, {1,25}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {4,45}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,18}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {7,37}, {1,28}, {14,18}, {3,43}, {3,36}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {6,45}, {7,40}, {17,37}, {14,19}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {8,22}, {14,20}, {11,33}, {1,34}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {16,27}, {9,30}, {5,40}, {16,31}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {14,24}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {17,38}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {15,18}, {17,34}, {12,26}, {1,45}, {10,30}, {6,18}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {16,44}, {7,21}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {7,45}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {14,45}, {16,18}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {10,45}, {7,20}, {3,40}, {16,19}, {12,36}, {7,18}, {10,21}, {3,33}, {1,24}, {17,21}, {4,18}, {15,26}, {2,18}, {16,38}, {12,37}, {2,19}, {17,30}, {5,24}, {7,33}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET45.135 // Non-bipartite Valency 28 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 7846046208000 EdgePairs[45][135]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {15,17}, {10,17}, {3,29}, {9,18}, {20,26}, {5,13}, {20,25}, {19,41}, {25,42}, {22,37}, {14,29}, {41,44}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {8,28}, {36,37}, {33,41}, {5,32}, {4,24}, {8,37}, {8,31}, {30,45}, {1,5}, {7,24}, {15,16}, {13,27}, {12,25}, {3,17}, {1,9}, {14,17}, {2,39}, {7,28}, {18,38}, {2,24}, {39,41}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {13,43}, {19,37}, {23,29}, {10,29}, {15,33}, {7,17}, {2,12}, {37,40}, {22,25}, {30,44}, {14,25}, {5,9}, {20,22}, {3,25}, {1,41}, {7,10}, {4,30}, {21,35}, {31,42}, {35,37}, {8,24}, {2,38}, {8,11}, {20,42}, {23,45}, {38,41}, {12,27}, {37,44}, {6,34}, {37,42}, {11,39}, {3,13}, {7,26}, {31,36}, {11,27}, {18,28}, {4,34}, {22,28}, {9,12}, {31,38}, {10,22}, {25,29}, {15,45}, {25,32}, {20,29}, {10,42}, {9,41}, {17,43}, {15,20}, {17,45}, {17,25}, {24,36}, {11,35}, {3,32}, {7,13}, {10,13}, {25,28}, {18,29}, {19,30}, {11,29}, {34,39}, {28,43}, {2,8}, {10,25}, {12,35}, {11,36}, {14,22}, {28,44}, {19,40}, {16,26}, {3,22}, {28,42}, {6,19}, {1,10}, {27,32}, {28,32}, {14,43}, {25,45}, {5,26}, {6,31}, {8,40}, {1,31}, {16,23}, {21,44}, {23,33}, {20,44}, {5,45}, {31,44}, {35,44}, {21,42}, {4,41}, {9,22}, {31,35}, {5,20}, {8,39}, {22,45}, {1,20}, {18,27}, {2,36}, {7,14}, {42,45}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {22,27}, {20,32}, {1,25}, {35,41}, {18,42}, {32,41}, {16,42}, {24,30}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {24,44}, {9,31}, {5,33}, {4,39}, {7,16}, {27,41}, {6,11}, {38,40}, {16,43}, {24,43}, {34,45}, {2,44}, {2,45}, {19,35}, {16,34}, {19,31}, {22,41}, {8,21}, {18,26}, {14,23}, {4,45}, {31,39}, {30,40}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {3,23}, {5,36}, {9,26}, {12,39}, {18,20}, {6,12}, {21,36}, {39,44}, {12,33}, {26,43}, {5,38}, {1,37}, {13,18}, {25,38}, {26,37}, {21,22}, {10,19}, {15,27}, {36,41}, {12,41}, {5,42}, {9,11}, {11,32}, {3,31}, {23,39}, {10,43}, {5,29}, {27,36}, {29,41}, {6,13}, {11,19}, {8,10}, {19,24}, {35,38}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {33,43}, {36,39}, {9,37}, {27,38}, {12,21}, {10,18}, {9,17}, {1,14}, {31,45}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {10,31}, {3,18}, {13,23}, {5,16}, {21,45}, {1,28}, {14,18}, {3,43}, {3,36}, {20,23}, {32,37}, {14,36}, {7,42}, {24,25}, {6,43}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {23,32}, {26,35}, {7,36}, {14,37}, {22,33}, {11,24}, {11,45}, {8,33}, {20,31}, {4,7}, {9,44}, {9,42}, {30,38}, {9,19}, {13,35}, {16,37}, {17,23}, {26,39}, {18,44}, {21,29}, {23,28}, {2,14}, {12,24}, {18,19}, {3,4}, {12,45}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {28,37}, {37,45}, {15,42}, {2,40}, 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{15,19}, {29,34}, {8,16}, {15,38}, {7,38}, {14,30}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {29,43}, {4,25}, {10,38}, {3,30}, {6,7}, {18,33}, {1,7}, {8,15}, {42,43}, {21,33}, {10,34}, {25,39}, {4,14}, {35,43}, {11,28}, {6,25}, {28,34}, {13,39}, {11,17}, {33,38}, {28,38}, {32,34}, {24,29}, {17,34}, {4,16}, {1,45}, {10,30}, {33,42}, {6,18}, {5,12}, {39,43}, {17,39}, {33,44}, {6,42}, {11,20}, {7,32}, {5,10}, {4,9}, {11,26}, {24,26}, {13,24}, {11,13}, {7,44}, {20,34}, {27,44}, {4,31}, {30,32}, {3,41}, {15,39}, {13,34}, {18,24}, {21,24}, {8,14}, {39,42}, {30,42}, {38,43}, {3,44}, {8,23}, {2,29}, {20,30}, {14,21}, {14,44}, {3,21}, {19,27}, {18,40}, {26,30}, {2,6}, {13,30}, {24,32}, {32,45}, {14,42}, {18,45}, {10,41}, {34,42}, {6,26}, {12,34}, {23,35}, {4,20}, {16,44}, {19,45}, {12,16}, {17,41}, {8,43}, {28,41}, {7,39}, {9,38}, {10,44}, {27,37}, {1,33}, {12,30}, {2,32}, {12,14}, {29,39}, {4,23}, {22,34}, {27,30}, {24,38}, {9,36}, {16,21}, {29,37}, {12,40}, {17,40}, {7,45}, {20,41}, {15,32}, {14,38}, {6,30}, {25,35}, {17,27}, {6,38}, {2,17}, {11,40}, {5,14}, {5,44}, {5,35}, {4,43}, {11,22}, {16,32}, {9,32}, {35,42}, {30,35}, {25,44}, {18,32}, {21,32}, {34,44}, {21,26}, {22,31}, {22,35}, {5,39}, {12,43}, {1,21}, {9,15}, {6,21}, {19,34}, {28,36}, {23,42}, {7,20}, {16,19}, {23,27}, {27,43}, {27,31}, {21,39}, {10,21}, {40,43}, {5,17}, {1,24}, {6,8}, {19,25}, {17,21}, {2,9}, {4,18}, {15,26}, {21,28}, {23,36}, {26,28}, {16,38}, {22,43}, {12,37}, {29,31}, {17,30}, {2,19}, {1,16}, {27,42}, {24,41}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {27,29}, {13,45}, {30,39}, {26,45}, {31,40}, {4,37}, {40,44}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {21,38}, {13,16}, {10,15}, {6,41}, {6,29} }; // ET45.136 // Non-bipartite Valency 28 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 3628800 EdgePairs[45][136]:={ {13,25}, {3,42}, {13,40}, {24,33}, {30,37}, {33,45}, {15,17}, {3,29}, {20,26}, {16,28}, {20,33}, {19,41}, {25,42}, {22,37}, {14,29}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {4,24}, {43,45}, {8,37}, {8,31}, {12,42}, {30,45}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {8,36}, {9,21}, {1,18}, {8,20}, {5,18}, {19,37}, {23,29}, {8,26}, {10,29}, {15,33}, {13,22}, {2,12}, {5,43}, {12,32}, {30,44}, {2,30}, {14,25}, {5,9}, {7,15}, {3,25}, {29,42}, {10,27}, {1,41}, {7,10}, {21,35}, {35,37}, {8,24}, {2,38}, {8,11}, {20,42}, {23,45}, {38,41}, {31,37}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {24,39}, {7,26}, {31,36}, {11,27}, {8,44}, {4,34}, {17,19}, {13,29}, {22,28}, {31,38}, {10,22}, {18,37}, {5,7}, {15,45}, {25,32}, {20,29}, {14,40}, {9,41}, {17,43}, {23,34}, {14,33}, {11,35}, {3,27}, {11,37}, {25,28}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {1,3}, {28,43}, {13,15}, {20,28}, {10,25}, {13,17}, {11,36}, {14,22}, {28,44}, {11,21}, {38,39}, {16,26}, {3,22}, {28,42}, {35,40}, {6,19}, {1,10}, {14,43}, {25,45}, {7,30}, {5,25}, {3,9}, {6,31}, {8,40}, {2,41}, {1,31}, {17,32}, {36,38}, {21,44}, {3,14}, {23,33}, {5,45}, {31,44}, {25,26}, {35,44}, {21,42}, {4,41}, {9,22}, {31,35}, {5,20}, {22,32}, {7,34}, {22,45}, {1,20}, {15,43}, {18,27}, {2,36}, {7,14}, {12,38}, {11,44}, {13,33}, {26,44}, {18,35}, {30,34}, {20,32}, {9,27}, {37,38}, {35,41}, {19,21}, {32,41}, {10,16}, {6,14}, {12,44}, {15,34}, {16,42}, {24,30}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {7,23}, {20,39}, {5,33}, {6,11}, {38,40}, {16,43}, {2,44}, {35,39}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {8,21}, {9,20}, {18,26}, {4,45}, {3,16}, {18,21}, {31,39}, {30,40}, {2,28}, {1,27}, {9,25}, {4,44}, {5,36}, {9,26}, {12,39}, {18,20}, {21,36}, {7,31}, {12,33}, {26,43}, {5,38}, {1,37}, {13,18}, {40,45}, {25,38}, {26,37}, {2,34}, {10,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {23,39}, {10,43}, {3,20}, {5,29}, {27,36}, {29,41}, {38,42}, {9,28}, {8,10}, {20,40}, {16,35}, {21,40}, {5,28}, {12,18}, {14,32}, {4,21}, {33,43}, {9,37}, {12,21}, {1,14}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {1,44}, {22,38}, {5,15}, {5,16}, {19,32}, {6,10}, {7,37}, {21,45}, {1,28}, {27,33}, {3,43}, {3,36}, {14,36}, {7,42}, {24,25}, {23,26}, {26,31}, {18,22}, {5,8}, {6,37}, {12,28}, {28,40}, {29,36}, {1,35}, {31,32}, {17,28}, {9,39}, {22,24}, {13,26}, {14,37}, {22,33}, {11,24}, {4,7}, {10,28}, {10,12}, {9,44}, {12,17}, {30,38}, {39,45}, {9,19}, {1,13}, {16,37}, {10,24}, {17,36}, {17,23}, {26,39}, {18,44}, {21,29}, {23,28}, {2,14}, {18,19}, {14,28}, {12,45}, {30,36}, {15,36}, {10,36}, {12,20}, {8,41}, {28,37}, {37,45}, {15,42}, {2,40}, {24,34}, {3,19}, {16,36}, {29,40}, {32,44}, {1,39}, {18,43}, {6,45}, {7,40}, {17,37}, {18,25}, {32,42}, {36,45}, {6,44}, {25,36}, {2,42}, {15,37}, {4,42}, {15,29}, {30,33}, {14,41}, {4,29}, {27,40}, {5,34}, {1,30}, {1,43}, {3,26}, {9,23}, {16,22}, {32,40}, {3,35}, {14,26}, {18,23}, {12,15}, {29,44}, {1,6}, {9,40}, {8,22}, {8,45}, {32,39}, {19,28}, {20,37}, {11,33}, {1,34}, {11,16}, {24,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {19,43}, {44,45}, {9,30}, {16,31}, {22,36}, {24,42}, {4,13}, {43,44}, {28,31}, {32,43}, {6,23}, {10,26}, {17,20}, {1,23}, {7,22}, {23,41}, {5,6}, {25,40}, {9,34}, {19,36}, {15,25}, {41,45}, {6,22}, {16,41}, {13,28}, {17,44}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {18,36}, {3,12}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {6,17}, {19,33}, {19,29}, {3,34}, {13,20}, {31,33}, {3,38}, {3,11}, {2,43}, {4,10}, {14,34}, {13,44}, {11,23}, {16,40}, {26,41}, {9,33}, {8,42}, {20,35}, {8,9}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {5,31}, {22,23}, {29,43}, {4,25}, {10,38}, {24,27}, {18,33}, {42,43}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {11,28}, {6,25}, {37,43}, {13,39}, {11,43}, {33,38}, {19,42}, {24,29}, {17,34}, {4,16}, {1,45}, {10,30}, {39,43}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {4,9}, {24,26}, {6,16}, {11,13}, {26,36}, {7,44}, {20,34}, {25,34}, {27,44}, {4,31}, {2,15}, {30,32}, {3,41}, {10,33}, {10,39}, {13,34}, {23,25}, {18,24}, {21,24}, {8,14}, {16,39}, {30,42}, {1,38}, {38,43}, {7,41}, {3,44}, {8,23}, {14,21}, {19,27}, {1,36}, {18,40}, {26,30}, {2,6}, {13,30}, {32,33}, {24,32}, {14,39}, {6,20}, {10,41}, {11,15}, {6,26}, {12,34}, {23,35}, {15,41}, {8,19}, {4,20}, {7,21}, {19,45}, {23,31}, {12,16}, {17,41}, {11,30}, {8,43}, {28,41}, {7,39}, {15,21}, {9,38}, {10,44}, {27,37}, {12,30}, {6,33}, {12,14}, {29,39}, {4,23}, {22,34}, {32,36}, {8,13}, {10,40}, {16,21}, {6,27}, {29,37}, {17,40}, {7,45}, {15,32}, {29,30}, {27,39}, {11,25}, {25,35}, {17,27}, {6,38}, {33,35}, {13,42}, {16,18}, {5,14}, {5,44}, {5,35}, {3,45}, {4,43}, {24,45}, {9,16}, {16,32}, {9,32}, {35,42}, {30,35}, {25,44}, {18,32}, {24,40}, {26,42}, {23,30}, {21,26}, {16,45}, {22,35}, {5,39}, {1,21}, {13,14}, {6,21}, {9,15}, {19,34}, {28,36}, {23,42}, {8,12}, {7,20}, {3,40}, {23,27}, {22,42}, {22,44}, {31,34}, {7,18}, {21,39}, {40,43}, {3,33}, {5,17}, {1,24}, {19,25}, {17,21}, {2,9}, {15,26}, {2,18}, {18,41}, {23,43}, {21,28}, {23,36}, {12,37}, {29,31}, {17,30}, {2,19}, {27,42}, {24,41}, {5,24}, {12,31}, {1,15}, {20,36}, {20,45}, {13,45}, {31,40}, {4,37}, {28,33}, {12,29}, {4,35}, {7,19}, {2,35}, {21,38}, {25,37}, {13,16}, {34,43}, {10,15}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET45.137 // Bipartite(16,29) Valencies [29,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 184994328434719755358659004499755008000000000 EdgePairs[45][137]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {15,17}, {10,17}, {3,29}, {9,18}, {16,28}, {4,26}, {14,29}, {2,20}, {2,26}, {16,17}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {5,18}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {4,34}, {13,29}, {10,22}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {15,20}, {14,33}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {1,26}, {9,27}, {1,25}, {15,34}, {12,44}, {16,42}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {4,45}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,18}, {9,17}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {7,37}, {1,28}, {14,18}, {3,43}, {1,17}, {3,36}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {12,17}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {6,45}, {7,40}, {14,19}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {8,22}, {14,20}, {11,33}, {1,34}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {16,27}, {9,30}, {5,40}, {16,31}, {8,17}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {8,29}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {2,33}, {6,32}, {15,31}, {10,35}, {4,27}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {6,17}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {11,17}, {15,18}, {12,26}, {1,45}, {10,30}, {6,18}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {7,21}, {16,44}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {7,45}, {15,32}, {14,38}, {6,30}, {11,25}, {6,38}, {2,17}, {11,40}, {13,42}, {14,45}, {16,18}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {10,45}, {7,20}, {3,40}, {16,19}, {12,36}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {15,26}, {2,18}, {16,38}, {12,37}, {2,19}, {5,24}, {7,33}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {10,32}, {16,24}, {4,19}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET45.138 // Bipartite(15,30) Valencies [30,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 346864365815099541297485633437040640000000000 EdgePairs[45][138]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {15,17}, {10,17}, {3,29}, {9,18}, {4,26}, {14,29}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {15,16}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {5,18}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {5,43}, {14,16}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {2,21}, {7,26}, {11,27}, {8,44}, {4,34}, {13,29}, {10,22}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {15,20}, {14,33}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {3,22}, {6,19}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {1,26}, {9,27}, {1,25}, {10,16}, {15,34}, {12,44}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {7,16}, {1,22}, {6,24}, {6,39}, {2,44}, {2,45}, {1,42}, {8,21}, {9,20}, {14,23}, {4,45}, {3,16}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,18}, {9,17}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {5,16}, {7,37}, {1,28}, {14,18}, {3,43}, {1,17}, {3,36}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {12,17}, {9,42}, {9,19}, {13,35}, {13,32}, {10,24}, {2,25}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {8,41}, {15,42}, {2,40}, {9,43}, {15,30}, {3,19}, {4,40}, {2,16}, {1,39}, {6,45}, {7,40}, {14,19}, {10,37}, {6,44}, {2,42}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {8,22}, {14,20}, {11,33}, {1,34}, {11,16}, {7,25}, {13,37}, {8,27}, {5,30}, {15,22}, {9,30}, {5,40}, {8,17}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {8,29}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {13,28}, {2,33}, {6,32}, {15,31}, {10,35}, {4,27}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {6,17}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {15,19}, {9,33}, {8,16}, {8,42}, {8,32}, {7,38}, {14,30}, {15,38}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {11,17}, {15,18}, {4,16}, {12,26}, {1,45}, {10,30}, {6,18}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {6,16}, {7,44}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {7,21}, {12,16}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {6,27}, {12,40}, {7,45}, {15,32}, {14,38}, {6,30}, {11,25}, {6,38}, {2,17}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {9,16}, {9,32}, {5,39}, {12,43}, {1,21}, {6,21}, {10,45}, {7,20}, {3,40}, {12,36}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {15,26}, {2,18}, {12,37}, {1,16}, {2,19}, {5,24}, {7,33}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {10,32}, {4,19}, {13,16}, {6,41}, {4,36}, {6,29}, {2,31} }; // ET45.139 // Non-bipartite Valency 30 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 13416835151120242560510984192000000000 EdgePairs[45][139]:={ {13,25}, {3,42}, {15,28}, {6,36}, {11,42}, {33,45}, {15,17}, {10,17}, {20,26}, {16,28}, {4,26}, {20,33}, {20,25}, {30,43}, {19,41}, {25,42}, {22,37}, {14,29}, {41,44}, {2,4}, {26,33}, {2,26}, {3,7}, {19,22}, {8,28}, {36,37}, {8,37}, {8,31}, {12,42}, {30,45}, {1,5}, {7,24}, {15,16}, {11,34}, {13,27}, {12,25}, {3,17}, {1,9}, {14,17}, {2,24}, {7,28}, {18,38}, {39,41}, {1,32}, {20,27}, {4,28}, {4,11}, {9,21}, {1,18}, {8,20}, {3,15}, {13,43}, {17,29}, {5,18}, {23,29}, {6,28}, {37,40}, {5,43}, {14,16}, {12,32}, {22,25}, {30,44}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {29,42}, {10,27}, {1,41}, {7,10}, {4,30}, {21,35}, {35,37}, {8,24}, {8,11}, {20,42}, {23,45}, {38,41}, {31,37}, {12,27}, {37,44}, {6,34}, {17,22}, {4,38}, {37,42}, {24,39}, {21,31}, {3,13}, {16,33}, {31,36}, {11,27}, {18,28}, {4,34}, {17,19}, {13,29}, {22,28}, {9,12}, {38,44}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {15,45}, {25,32}, {12,22}, {10,42}, {28,45}, {9,41}, {15,20}, {9,10}, {23,34}, {24,36}, {11,35}, {3,27}, {3,32}, {11,31}, {7,13}, {10,13}, {25,28}, {8,38}, {18,29}, {22,29}, {14,27}, {34,39}, {28,43}, {17,42}, {2,8}, {10,25}, {12,35}, {13,17}, {11,36}, {28,44}, {19,40}, {3,22}, {28,42}, {35,40}, {6,19}, {27,32}, {28,32}, {16,20}, {25,41}, {14,43}, {7,30}, {5,25}, {3,9}, {5,26}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {36,38}, {16,23}, {21,44}, {3,14}, {20,44}, {5,45}, {31,44}, {21,42}, {9,22}, {31,35}, {5,20}, {8,39}, {22,45}, {15,43}, {2,36}, {7,14}, {42,45}, {11,44}, {10,23}, {22,27}, {30,34}, {20,32}, {1,26}, {18,31}, {1,25}, {26,32}, {35,41}, {18,42}, {10,16}, {16,42}, {12,44}, {15,34}, {24,30}, {16,30}, {34,40}, {5,27}, {24,44}, {9,31}, {3,6}, {7,23}, {4,39}, {27,41}, {6,11}, {1,22}, {38,40}, {29,32}, {6,39}, {24,43}, {2,44}, {35,39}, {2,45}, {19,35}, {10,14}, {1,42}, {19,31}, {8,21}, {9,20}, {4,45}, {3,16}, {18,21}, {31,39}, {22,26}, {30,40}, {1,27}, {20,43}, {3,23}, {4,44}, {5,36}, {18,20}, {6,12}, {21,36}, {39,44}, {7,31}, {12,33}, {5,38}, {13,18}, {40,45}, {25,38}, {26,37}, {2,34}, {21,22}, {15,27}, {14,35}, {36,41}, {12,41}, {9,11}, {11,32}, {3,31}, {23,39}, {11,18}, {10,43}, {5,29}, {21,25}, {29,41}, {38,42}, {9,28}, {37,41}, {8,10}, {20,40}, {19,24}, {35,38}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {33,43}, {36,39}, {9,37}, {27,38}, {2,5}, {10,18}, {1,14}, {11,41}, {19,44}, {31,45}, {13,19}, {9,29}, {2,22}, {21,34}, {1,44}, {10,31}, {22,38}, {3,18}, {5,16}, {19,32}, {6,10}, {7,37}, {21,45}, {14,18}, {27,33}, {3,43}, {1,17}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {7,42}, {24,25}, {6,43}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {28,40}, {29,36}, {1,35}, {17,28}, {5,21}, {9,39}, {13,26}, {14,37}, {11,24}, {11,45}, {8,33}, {20,31}, {4,7}, {41,43}, {12,17}, {2,7}, {9,42}, {39,45}, {9,19}, {13,35}, {1,13}, {16,37}, {10,24}, {2,25}, {17,23}, {26,39}, {23,28}, {2,14}, {12,24}, {18,19}, {3,4}, {14,28}, {12,45}, {30,36}, {15,36}, {10,36}, {16,29}, {8,41}, {37,45}, {2,40}, {29,45}, {36,40}, {38,45}, {29,33}, {33,34}, {15,30}, {24,34}, {23,38}, {2,16}, {29,40}, {32,44}, {6,45}, {7,40}, {17,37}, {14,19}, {21,27}, {6,44}, {2,42}, {15,37}, {9,13}, {21,23}, {21,43}, {15,29}, {30,33}, {4,29}, {27,40}, {5,34}, {1,43}, {3,26}, {13,36}, {9,23}, {3,8}, {34,41}, {16,22}, {3,35}, {14,26}, {18,23}, {12,15}, {29,44}, {1,6}, {9,40}, {25,30}, {8,22}, {32,39}, {14,20}, {11,33}, {1,34}, {19,23}, {30,41}, {11,16}, {1,4}, {24,35}, {13,37}, {24,37}, {5,30}, {19,43}, {23,44}, {9,30}, {2,13}, {16,31}, {22,36}, {22,30}, {26,40}, {18,30}, {28,31}, {32,43}, {1,40}, {28,35}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {25,40}, {19,36}, {15,25}, {41,45}, {5,19}, {16,41}, {33,36}, {13,28}, {2,33}, {10,35}, {4,27}, {4,17}, {3,24}, {7,11}, {2,27}, {15,35}, {6,17}, {32,35}, {19,33}, {3,34}, {18,39}, {11,14}, {7,12}, {13,20}, {13,21}, {2,43}, {4,10}, {33,37}, {14,34}, {13,44}, {11,23}, {3,5}, {16,40}, {26,41}, {15,19}, {9,33}, {29,34}, {8,42}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {12,23}, {29,43}, {4,25}, {6,7}, {24,27}, {18,33}, {1,7}, {8,15}, {42,43}, {21,33}, {17,38}, {10,34}, {25,39}, {24,28}, {36,42}, {6,25}, {28,34}, {37,43}, {13,39}, {11,43}, {11,17}, {33,38}, {15,18}, {32,34}, {19,42}, {24,29}, {12,13}, {4,16}, {12,26}, {6,9}, {1,45}, {6,18}, {5,12}, {39,43}, {17,39}, {33,44}, {7,32}, {5,10}, {13,38}, {4,9}, {11,26}, {24,26}, {6,16}, {11,13}, {20,34}, {2,15}, {30,32}, {3,41}, {15,39}, {10,33}, {13,34}, {20,24}, {23,25}, {26,38}, {18,24}, {21,24}, {8,14}, {39,42}, {16,39}, {30,42}, {5,37}, {38,43}, {7,41}, {3,44}, {8,23}, {14,21}, {14,44}, {19,27}, {33,39}, {1,36}, {18,40}, {26,30}, {42,44}, {2,6}, {13,30}, {9,24}, {14,39}, {32,45}, {6,20}, {10,41}, {34,42}, {11,15}, {6,26}, {12,34}, {23,35}, {8,19}, {4,20}, {19,45}, {7,21}, {12,16}, {17,41}, {34,37}, {28,41}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {27,37}, {1,33}, {1,8}, {2,32}, {19,26}, {12,14}, {22,34}, {27,30}, {24,38}, {32,36}, {8,13}, {10,40}, {16,21}, {6,27}, {12,40}, {21,41}, {17,40}, {20,41}, {14,38}, {27,39}, {6,30}, {11,25}, {6,38}, {2,17}, {33,35}, {11,40}, {25,31}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {24,45}, {16,32}, {9,32}, {27,28}, {35,42}, {30,35}, {18,32}, {21,32}, {26,42}, {23,30}, {21,26}, {30,31}, {31,43}, {39,40}, {22,35}, {5,39}, {12,43}, {26,29}, {19,34}, {6,21}, {9,15}, {28,36}, {10,45}, {23,37}, {8,12}, {7,20}, {3,40}, {16,19}, {23,27}, {12,36}, {27,31}, {22,44}, {31,34}, {40,43}, {3,33}, {32,38}, {5,17}, {1,24}, {19,25}, {6,8}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {18,41}, {23,43}, {23,36}, {26,28}, {16,38}, {22,43}, {4,8}, {29,31}, {17,30}, {1,16}, {27,42}, {7,33}, {1,15}, {12,31}, {20,36}, {20,45}, {29,35}, {27,29}, {13,45}, {4,37}, {40,44}, {28,33}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {25,37}, {13,16}, {5,11}, {10,15}, {4,36}, {6,29}, {2,31} }; // ET45.140 // Bipartite(14,31) Valencies [31,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 716853022684539052014803642436550656000000000 EdgePairs[45][140]:={ {13,21}, {6,38}, {11,40}, {10,37}, {14,36}, {9,32}, {6,25}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {5,45}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {14,38}, {13,39}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {14,31}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {14,45}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {14,29}, {13,40}, {14,44}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {7,45}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {14,32}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {14,35}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {2,44}, {1,30}, {13,18}, {12,15}, {8,15}, {14,28}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {14,15}, {14,33}, {10,38}, {14,23}, {6,16}, {11,33}, {13,25}, {14,39}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {14,21}, {8,45}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {4,45}, {10,19}, {9,22}, {12,41}, {9,19}, {3,44}, {11,44}, {13,45}, {3,25}, {11,34}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {14,27}, {7,28}, {6,45}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {14,43}, {3,22}, {14,37}, {1,44}, {13,38}, {4,15}, {14,40}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {9,44}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {14,16}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {13,32}, {14,26}, {1,45}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {14,19}, {11,45}, {1,33}, {12,36}, {3,45}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {14,30}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {11,31}, {14,24}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {6,26}, {1,34}, {13,35}, {14,18}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {13,33}, {1,15}, {13,15}, {14,20}, {14,25}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {14,42}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {13,23}, {2,40}, {6,21}, {9,45}, {14,41}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {14,22}, {9,42}, {14,17}, {5,36}, {9,34}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.141 // Bipartite(5,40) Valencies [32,4] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 12787447486620893184000000 EdgePairs[45][141]:={ {2,44}, {1,11}, {3,33}, {2,24}, {5,17}, {2,33}, {4,27}, {4,24}, {4,26}, {3,8}, {3,40}, {4,16}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {1,21}, {2,9}, {2,28}, {2,14}, {5,32}, {2,42}, {3,18}, {2,45}, {3,34}, {2,25}, {5,40}, {1,38}, {4,10}, {2,34}, {1,17}, {1,7}, {5,22}, {4,22}, {1,18}, {3,14}, {5,11}, {1,44}, {4,41}, {2,10}, {2,38}, {2,37}, {5,43}, {4,42}, {5,25}, {2,39}, {1,31}, {4,45}, {2,35}, {1,22}, {3,44}, {5,23}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {3,39}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {5,7}, {1,9}, {4,15}, {1,28}, {3,11}, {4,7}, {1,33}, {3,29}, {3,10}, {1,43}, {3,26}, {5,28}, {5,42}, {2,17}, {4,36}, {5,41}, {4,6}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,37}, {3,16}, {4,37}, {4,40}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,40}, {5,27}, {5,10}, {5,26}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {1,41}, {5,45}, {5,6}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,21}, {2,30}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36}, {5,16} }; // ET45.142 // Bipartite(9,36) Valencies [32,8] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 958659120196485120 EdgePairs[45][142]:={ {6,38}, {6,25}, {9,32}, {5,38}, {9,17}, {4,28}, {5,43}, {9,10}, {5,45}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {3,20}, {2,18}, {1,21}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {1,12}, {9,11}, {6,29}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {7,45}, {1,10}, {8,37}, {4,13}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {6,39}, {2,17}, {1,24}, {2,15}, {5,37}, {9,35}, {6,18}, {1,29}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {5,27}, {7,14}, {3,43}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {9,38}, {4,10}, {9,26}, {5,14}, {8,45}, {3,29}, {1,41}, {2,23}, {4,45}, {9,22}, {9,19}, {3,44}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {8,34}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {1,32}, {9,44}, {6,43}, {6,37}, {9,24}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {9,21}, {7,29}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {2,45}, {3,33}, {2,11}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {8,43}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {1,34}, {5,21}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {5,10}, {7,44}, {8,28}, {7,43}, {9,40}, {8,20}, {5,44}, {5,25}, {4,19}, {8,39}, {3,37}, {7,13}, {9,14}, {9,42}, {5,36}, {4,39}, {7,36}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET45.143 // Bipartite(13,32) Valencies [32,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1638521194707517833176694039854972928000000000 EdgePairs[45][143]:={ {13,21}, {6,38}, {11,40}, {10,37}, {9,32}, {6,25}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {5,45}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {13,39}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {13,43}, {13,27}, {6,14}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,30}, {9,33}, {1,17}, {4,16}, {7,45}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {9,36}, {6,34}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {2,44}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {13,25}, {8,24}, {4,41}, {9,38}, {8,41}, {9,26}, {5,14}, {8,45}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {4,45}, {10,19}, {9,22}, {12,41}, {9,19}, {3,44}, {11,44}, {13,45}, {3,25}, {11,34}, {7,35}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {9,30}, {5,39}, {3,32}, {7,28}, {6,45}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {13,38}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {13,14}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {12,14}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {13,44}, {8,27}, {2,45}, {3,33}, {13,32}, {1,45}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {11,45}, {1,33}, {12,36}, {3,45}, {3,14}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {13,23}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.144 // Non-bipartite Valency 32 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 43545600 EdgePairs[45][144]:={ {13,25}, {3,42}, {15,28}, {13,40}, {24,33}, {30,37}, {11,42}, {33,45}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {16,28}, {5,13}, {4,26}, {20,33}, {30,43}, {19,41}, {25,42}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {33,41}, {5,32}, {8,37}, {8,31}, {7,24}, {15,16}, {11,34}, {13,27}, {12,25}, {3,17}, {2,11}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {39,41}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {5,18}, {17,29}, {19,37}, {23,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {14,16}, {30,44}, {2,30}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {29,42}, {10,27}, {4,30}, {21,35}, {31,42}, {35,37}, {8,24}, {2,38}, {8,11}, {20,42}, {23,45}, {38,41}, {31,37}, {37,44}, {6,34}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {8,44}, {13,29}, {22,28}, {9,12}, {38,44}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {36,44}, {10,42}, {14,40}, {28,45}, {35,36}, {9,41}, {17,43}, {17,45}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {3,32}, {7,13}, {10,13}, {11,37}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {2,8}, {20,28}, {12,35}, {13,17}, {14,22}, {28,44}, {19,40}, {3,22}, {28,42}, {6,19}, {1,10}, {5,23}, {28,32}, {25,41}, {14,43}, {7,30}, {3,9}, {5,26}, {8,40}, {2,41}, {6,35}, {16,23}, {21,30}, {21,44}, {3,14}, {20,44}, {31,44}, {25,26}, {35,44}, {21,42}, {4,41}, {9,22}, {29,38}, {8,39}, {7,34}, {22,45}, {1,20}, {15,43}, {18,27}, {2,36}, {7,14}, {12,38}, {34,36}, {11,44}, {26,44}, {15,24}, {10,23}, {18,35}, {30,34}, {20,32}, {9,27}, {18,31}, {1,25}, {26,32}, {35,41}, {18,42}, {19,21}, {32,41}, {10,16}, {6,14}, {12,44}, {15,34}, {16,42}, {24,30}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {3,6}, {7,23}, {20,39}, {5,33}, {7,16}, {27,41}, {1,22}, {25,27}, {6,24}, {29,32}, {16,43}, {6,39}, {24,43}, {34,45}, {2,44}, {35,39}, {2,45}, {19,35}, {10,14}, {1,42}, {16,34}, {19,31}, {22,41}, {8,21}, {9,20}, {14,23}, {18,26}, {4,45}, {28,39}, {3,16}, {18,21}, {31,39}, {22,26}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {1,12}, {5,36}, {9,26}, {12,39}, {6,12}, {7,31}, {12,33}, {26,43}, {5,38}, {1,37}, {33,40}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {9,11}, {11,32}, {3,31}, {23,39}, {11,18}, {10,43}, {3,20}, {5,29}, {27,36}, {29,41}, {38,42}, {9,28}, {6,13}, {11,19}, {37,41}, {35,38}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {27,38}, {12,21}, {9,17}, {10,18}, {1,14}, {17,26}, {40,41}, {31,45}, {8,34}, {13,19}, {4,33}, {18,34}, {21,34}, {1,44}, {10,31}, {22,38}, {5,16}, {19,32}, {21,45}, {1,28}, {14,18}, {27,33}, {1,17}, {3,36}, {20,23}, {14,36}, {6,43}, {23,26}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {5,21}, {7,36}, {13,26}, {14,37}, {22,33}, {11,24}, {7,43}, {11,45}, {20,31}, {4,7}, {10,28}, {10,12}, {15,23}, {9,42}, {30,38}, {39,45}, {13,35}, {10,11}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {27,45}, {17,36}, {17,23}, {26,39}, {18,44}, {21,29}, {2,14}, {9,35}, {12,24}, {14,28}, {12,45}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {28,37}, {37,45}, {15,42}, {2,40}, {9,43}, {29,45}, {38,45}, {29,33}, {3,19}, {4,40}, {2,16}, {29,40}, {32,44}, {1,39}, {6,45}, {7,40}, {18,25}, {21,27}, {36,45}, {10,37}, {6,44}, {25,36}, {15,37}, {7,35}, {9,13}, {4,42}, {21,43}, {15,29}, {20,38}, {30,33}, {14,41}, {4,15}, {27,40}, {8,25}, {5,34}, {26,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {34,41}, {16,22}, {32,40}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {8,22}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {30,41}, {7,25}, {22,40}, {24,35}, {13,37}, {24,37}, {8,27}, {24,31}, {15,22}, {16,27}, {19,43}, {23,44}, {9,30}, {2,13}, {22,36}, {22,30}, {24,42}, {26,40}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {32,43}, {1,40}, {6,23}, {28,35}, {10,26}, {1,23}, {17,31}, {8,29}, {15,44}, {23,41}, {5,6}, {19,36}, {6,22}, {5,19}, {33,36}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {4,27}, {3,12}, {18,36}, {4,17}, {3,24}, {7,11}, {4,32}, {1,19}, {5,41}, {13,41}, {2,10}, {6,17}, {19,33}, {3,34}, {18,39}, {13,20}, {13,21}, {3,11}, {2,43}, {4,10}, {33,37}, {13,44}, {11,23}, {16,40}, {36,43}, {15,19}, {9,33}, {8,16}, {8,42}, {20,21}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {12,23}, {13,31}, {23,40}, {5,31}, {29,43}, {4,25}, {10,38}, {3,30}, {24,27}, {1,7}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {24,28}, {36,42}, {35,43}, {11,28}, {6,25}, {28,34}, {37,43}, {13,39}, {11,43}, {11,17}, {15,18}, {19,42}, {17,34}, {4,16}, {12,26}, {1,45}, {33,42}, {6,18}, {5,12}, {39,43}, {17,39}, {33,44}, {6,42}, {11,20}, {24,26}, {40,42}, {13,24}, {7,44}, {20,34}, {25,34}, {27,44}, {4,31}, {2,15}, {30,32}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {26,38}, {18,24}, {8,14}, {39,42}, {16,39}, {30,42}, {1,38}, {5,37}, {25,43}, {7,41}, {3,44}, {2,29}, {14,21}, {3,21}, {19,27}, {33,39}, {18,40}, {2,6}, {13,30}, {24,32}, {9,45}, {32,45}, {14,42}, {4,6}, {6,20}, {18,45}, {3,39}, {10,41}, {34,42}, {12,34}, {23,35}, {15,41}, {8,19}, {4,20}, {16,44}, {7,21}, {19,45}, {23,31}, {12,16}, {17,41}, {11,30}, {34,37}, {28,41}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {1,8}, {6,33}, {19,26}, {4,23}, {22,34}, {24,38}, {9,36}, {32,36}, {6,27}, {29,37}, {12,40}, {17,40}, {7,45}, {20,41}, {15,32}, {14,38}, {27,39}, {6,30}, {11,25}, {6,38}, {11,40}, {13,42}, {25,31}, {14,45}, {5,14}, {5,44}, {3,45}, {4,43}, {11,22}, {24,45}, {9,16}, {16,32}, {9,32}, {35,42}, {25,44}, {18,32}, {21,32}, {24,40}, {26,42}, {23,30}, {22,31}, {30,31}, {16,45}, {31,43}, {22,35}, {5,39}, {12,43}, {9,15}, {28,36}, {23,37}, {23,42}, {8,12}, {7,20}, {3,40}, {23,27}, {27,43}, {12,36}, {27,31}, {22,44}, {7,18}, {21,39}, {10,21}, {40,43}, {32,38}, {27,35}, {5,17}, {1,24}, {19,25}, {17,21}, {2,9}, {4,18}, {15,26}, {2,18}, {18,41}, {21,28}, {23,36}, {16,38}, {22,43}, {4,8}, {29,31}, {17,30}, {2,19}, {24,41}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,36}, {29,35}, {13,45}, {30,39}, {26,45}, {31,40}, {4,37}, {40,44}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {25,37}, {13,16}, {34,43}, {5,11}, {4,36}, {6,29}, {2,31} }; // ET45.145 // Non-bipartite Valency 32 // Diameter 2 Girth 3 // Twin-free VT AT // Automorphism group of order 51840 EdgePairs[45][145]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {24,33}, {30,37}, {11,42}, {33,45}, {10,17}, {3,29}, {9,18}, {20,26}, {16,28}, {5,13}, {20,25}, {25,42}, {22,37}, {14,29}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {16,17}, {8,28}, {11,12}, {33,41}, {5,32}, {4,24}, {8,37}, {30,45}, {1,5}, {26,27}, {11,34}, {13,27}, {12,25}, {3,17}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {18,38}, {39,41}, {1,32}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {3,10}, {17,29}, {14,15}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {37,40}, {5,43}, {14,16}, {12,32}, {30,44}, {14,25}, {28,29}, {20,22}, {7,15}, {3,25}, {4,12}, {29,42}, {10,27}, {1,41}, {7,10}, {4,30}, {31,42}, {35,37}, {8,24}, {8,11}, {20,42}, {23,45}, {38,41}, {31,37}, {12,27}, {37,44}, {6,34}, {17,22}, {4,38}, {37,42}, {11,39}, {24,39}, {3,13}, {2,21}, {16,33}, {7,26}, {19,38}, {31,36}, {8,44}, {4,34}, {17,19}, {9,12}, {38,44}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {15,45}, {25,32}, {20,29}, {10,42}, {14,40}, {35,36}, {4,5}, {9,41}, {9,10}, {17,18}, {17,45}, {23,34}, {17,25}, {24,36}, {11,35}, {3,27}, {11,31}, {10,13}, {11,37}, {25,28}, {8,38}, {18,29}, {19,30}, {22,29}, {14,27}, {28,43}, {13,15}, {2,8}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {28,44}, {38,39}, {16,26}, {3,22}, {28,42}, {1,10}, {5,23}, {27,32}, {28,32}, {2,37}, {14,43}, {25,45}, {7,30}, {5,25}, {5,26}, {8,40}, {2,41}, {1,31}, {17,32}, {16,23}, {21,30}, {23,33}, {20,44}, {5,45}, {21,42}, {4,41}, {9,22}, {5,20}, {8,39}, {22,32}, {7,34}, {22,45}, {1,20}, {15,43}, {18,27}, {2,36}, {42,45}, {12,38}, {34,36}, {11,44}, {13,33}, {23,24}, {26,44}, {10,23}, {18,35}, {30,34}, {20,32}, {1,26}, {9,27}, {37,38}, {1,25}, {35,41}, {18,42}, {19,21}, {32,41}, {6,14}, {12,44}, {24,30}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {24,44}, {9,31}, {7,23}, {5,33}, {4,39}, {27,41}, {6,11}, {1,22}, {38,40}, {6,24}, {29,32}, {16,43}, {6,39}, {24,43}, {2,44}, {35,39}, {2,45}, {19,35}, {10,14}, {1,42}, {16,34}, {19,31}, {22,41}, {8,21}, {9,20}, {14,23}, {4,45}, {28,39}, {3,16}, {18,21}, {22,26}, {30,40}, {2,28}, {20,43}, {5,22}, {9,25}, {5,36}, {12,39}, {18,20}, {21,36}, {39,44}, {7,31}, {12,33}, {26,43}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {21,22}, {10,19}, {15,27}, {14,35}, {36,41}, {12,41}, {9,11}, {11,32}, {3,31}, {23,39}, {3,20}, {5,29}, {21,25}, {27,36}, {29,41}, {38,42}, {6,13}, {8,10}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {25,33}, {8,30}, {4,21}, {14,32}, {33,43}, {36,39}, {9,37}, {27,38}, {12,21}, {1,14}, {11,41}, {19,44}, {40,41}, {31,45}, {8,34}, {13,19}, {9,29}, {2,22}, {37,39}, {15,40}, {18,34}, {21,34}, {1,44}, {10,31}, {22,38}, {3,18}, {5,15}, {5,16}, {19,32}, {21,45}, {1,28}, {14,18}, {27,33}, {3,43}, {1,17}, {32,37}, {14,36}, {24,25}, {6,43}, {23,26}, {7,29}, {6,37}, {3,37}, {29,36}, {1,35}, {17,28}, {26,35}, {5,21}, {7,36}, {9,39}, {13,26}, {11,24}, {7,43}, {11,45}, {8,33}, {20,31}, {10,28}, {41,43}, {10,12}, {9,44}, {15,23}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {31,41}, {17,36}, {18,44}, {21,29}, {3,28}, {2,14}, {3,4}, {18,19}, {14,28}, {2,3}, {12,45}, {30,36}, {15,36}, {12,20}, {16,29}, {8,41}, {28,37}, {15,42}, {2,40}, {9,43}, {29,45}, {36,40}, {38,45}, {1,11}, {33,34}, {15,30}, {4,40}, {2,16}, {16,36}, {32,44}, {6,45}, {18,43}, {17,37}, {14,19}, {18,25}, {25,36}, {2,42}, {7,8}, {15,37}, {7,35}, {9,13}, {4,42}, {21,43}, {20,38}, {14,41}, {4,29}, {27,40}, {26,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {18,23}, {12,15}, {29,44}, {14,31}, {8,45}, {19,28}, {20,37}, {19,23}, {30,41}, {11,16}, {7,25}, {22,40}, {24,35}, {13,37}, {5,30}, {24,31}, {15,22}, {19,43}, {23,44}, {44,45}, {9,30}, {5,40}, {16,31}, {22,30}, {24,42}, {26,40}, {18,30}, {43,44}, {8,17}, {28,31}, {32,43}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {7,22}, {15,44}, {5,6}, {25,40}, {9,34}, {19,36}, {15,25}, {41,45}, {6,22}, {5,19}, {16,41}, {17,44}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {18,36}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {6,17}, {32,35}, {3,34}, {11,14}, {7,12}, {31,33}, {13,21}, {3,11}, {2,43}, {4,10}, {33,37}, {14,34}, {13,44}, {15,19}, {9,33}, {8,42}, {20,21}, {20,35}, {8,32}, {7,38}, {22,39}, {17,24}, {12,23}, {23,40}, {8,18}, {5,31}, {22,23}, {4,25}, {10,38}, {3,30}, {6,7}, {24,27}, {18,33}, {8,15}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {36,42}, {35,43}, {11,28}, {6,25}, {28,34}, {13,39}, {11,43}, {33,38}, {28,38}, {15,18}, {32,34}, {19,42}, {17,34}, {12,13}, {4,16}, {12,26}, {6,9}, {10,30}, {7,9}, {33,42}, {6,18}, {5,12}, {39,43}, {17,39}, {6,42}, {11,20}, {13,38}, {11,26}, {24,26}, {13,24}, {11,13}, {26,36}, {7,44}, {20,34}, {25,34}, {27,44}, {4,31}, {2,15}, {30,32}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {23,25}, {26,38}, {39,42}, {16,39}, {1,38}, {5,37}, {25,43}, {38,43}, {7,41}, {3,44}, {8,23}, {2,29}, {14,44}, {3,21}, {19,27}, {1,36}, {18,40}, {26,30}, {2,6}, {13,30}, {32,33}, {9,24}, {24,32}, {32,45}, {14,42}, {4,6}, {18,45}, {3,39}, {10,41}, {11,15}, {6,26}, {12,34}, {23,35}, {15,41}, {8,19}, {4,20}, {16,44}, {19,45}, {23,31}, {12,16}, {17,41}, {11,30}, {34,37}, {2,23}, {19,20}, {7,39}, {15,21}, {9,38}, {10,44}, {27,37}, {1,33}, {1,8}, {2,32}, {6,33}, {12,14}, {29,39}, {4,23}, {22,34}, {27,30}, {9,36}, {10,40}, {16,21}, {6,27}, {29,37}, {12,40}, {21,41}, {17,40}, {7,45}, {15,32}, {14,38}, {29,30}, {6,30}, {11,25}, {6,38}, {2,17}, {33,35}, {13,42}, {25,31}, {14,45}, {16,18}, {5,35}, {3,45}, {4,43}, {11,22}, {24,45}, {9,16}, {9,32}, {27,28}, {35,42}, {25,44}, {21,32}, {24,40}, {26,42}, {23,30}, {21,26}, {22,31}, {30,31}, {16,45}, {39,40}, {22,35}, {5,39}, {26,29}, {1,21}, {13,14}, {19,34}, {28,36}, {23,37}, {23,42}, {8,12}, {7,20}, {3,40}, {16,19}, {27,43}, {34,35}, {22,42}, {12,36}, {27,31}, {31,34}, {7,18}, {21,39}, {10,21}, {40,43}, {3,33}, {27,35}, {28,30}, {5,17}, {1,24}, {6,8}, {2,9}, {4,18}, {18,41}, {23,43}, {21,28}, {26,28}, {16,38}, {22,43}, {12,37}, {4,8}, {1,16}, {2,19}, {27,42}, {24,41}, {5,24}, {7,33}, {1,15}, {12,31}, {20,36}, {20,45}, {29,35}, {27,29}, {13,45}, {26,45}, {31,40}, {4,37}, {40,44}, {28,33}, {12,29}, {4,35}, {7,19}, {17,33}, {10,32}, {16,24}, {4,19}, {21,38}, {13,16}, {34,43}, {6,41}, {6,29}, {2,31} }; // ET45.146 // Bipartite(12,33) Valencies [33,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4159323032719083730371607947324162048000000000 EdgePairs[45][146]:={ {6,38}, {11,40}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {5,45}, {3,26}, {12,22}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {1,17}, {4,16}, {7,45}, {4,13}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {1,13}, {12,26}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {8,45}, {3,29}, {12,17}, {1,41}, {2,23}, {10,13}, {4,45}, {10,19}, {9,22}, {12,41}, {9,19}, {3,44}, {11,44}, {3,25}, {11,34}, {7,35}, {11,13}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {5,39}, {9,30}, {3,32}, {7,28}, {6,45}, {12,18}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {12,14}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {2,45}, {3,33}, {1,45}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {11,45}, {1,33}, {12,36}, {3,45}, {3,14}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.147 // Bipartite(11,34) Valencies [34,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 11784748592704070569386222517418459136000000000 EdgePairs[45][147]:={ {6,38}, {11,40}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {5,45}, {3,26}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {7,45}, {4,13}, {8,37}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {11,33}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {8,45}, {3,29}, {1,41}, {2,23}, {10,13}, {4,45}, {10,19}, {9,22}, {3,44}, {9,19}, {11,44}, {3,25}, {11,34}, {7,35}, {11,13}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {6,45}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {2,45}, {3,33}, {1,45}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {8,43}, {2,31}, {11,45}, {1,33}, {3,45}, {3,14}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {4,19}, {8,39}, {3,37}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET45.148 // Bipartite(10,35) Valencies [35,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 37496927340422042720774344373604188160000000000 EdgePairs[45][148]:={ {6,38}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {5,43}, {5,45}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {8,31}, {4,40}, {4,37}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {1,12}, {10,42}, {6,29}, {9,11}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {7,45}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {10,35}, {6,44}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {8,45}, {3,29}, {1,41}, {2,23}, {10,13}, {4,45}, {10,19}, {9,22}, {4,11}, {3,44}, {9,19}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {2,45}, {3,33}, {2,11}, {1,45}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {8,43}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET45.149 // Bipartite(9,36) Valencies [36,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 134988938425519353794787639744975077376000000000 EdgePairs[45][149]:={ {6,38}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {4,28}, {5,43}, {9,10}, {5,45}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {4,37}, {4,40}, {8,31}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {9,11}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {7,45}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {2,10}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {6,44}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {4,10}, {9,26}, {5,14}, {8,45}, {3,29}, {1,41}, {2,23}, {4,45}, {9,22}, {4,11}, {3,44}, {9,19}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {9,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {2,45}, {8,27}, {3,33}, {2,11}, {1,45}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {8,43}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {5,10}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {9,43}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {8,25}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET45.150 // Non-bipartite Valency 36 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 755085986637477121622016000000 EdgePairs[45][150]:={ {13,25}, {3,42}, {13,40}, {24,33}, {30,37}, {33,45}, {15,17}, {9,18}, {3,29}, {10,17}, {20,26}, {5,13}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {41,44}, {2,4}, {26,33}, {2,20}, {2,26}, {3,7}, {19,22}, {8,28}, {36,37}, {33,41}, {5,32}, {4,24}, {8,31}, {1,5}, {15,16}, {11,34}, {13,27}, {2,11}, {1,9}, {14,17}, {2,39}, {7,28}, {2,24}, {18,38}, {39,41}, {20,27}, {4,28}, {4,11}, {8,36}, {9,21}, {3,15}, {8,20}, {3,10}, {5,18}, {17,29}, {19,37}, {23,29}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {2,12}, {6,28}, {37,40}, {5,43}, {14,16}, {12,32}, {22,25}, {2,30}, {14,25}, {5,9}, {20,22}, {7,15}, {3,25}, {4,12}, {29,42}, {1,41}, {7,10}, {4,30}, {31,42}, {35,37}, {8,11}, {2,38}, {20,42}, {23,45}, {38,41}, {31,37}, {37,44}, {17,22}, {4,38}, {37,42}, {11,39}, {21,31}, {3,13}, {2,21}, {7,26}, {19,38}, {31,36}, {8,44}, {18,28}, {17,19}, {22,28}, {9,12}, {38,44}, {31,38}, {10,22}, {18,37}, {25,29}, {5,7}, {25,32}, {20,29}, {36,44}, {12,22}, {14,40}, {9,41}, {17,43}, {15,20}, {9,10}, {17,45}, {23,34}, {14,33}, {17,25}, {24,36}, {11,35}, {3,27}, {11,31}, {7,13}, {10,13}, {11,37}, {25,28}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {34,39}, {2,8}, {17,42}, {20,28}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {28,42}, {35,40}, {1,10}, {5,23}, {27,32}, {28,32}, {16,20}, {2,37}, {25,45}, {7,30}, {5,25}, {3,9}, {5,26}, {6,31}, {8,40}, {2,41}, {36,38}, {16,23}, {21,30}, {21,44}, {3,14}, {23,33}, {20,44}, {5,45}, {31,44}, {35,44}, {21,42}, {4,41}, {31,35}, {29,38}, {22,32}, {7,34}, {22,45}, {1,20}, {18,27}, {2,36}, {7,14}, {42,45}, {12,38}, {11,44}, {13,33}, {26,44}, {15,24}, {10,23}, {18,35}, {22,27}, {30,34}, {20,32}, {1,26}, {9,27}, {1,25}, {26,32}, {35,41}, {18,42}, {32,41}, {10,16}, {6,14}, {12,44}, {15,34}, {16,42}, {24,30}, {16,30}, {34,40}, {8,35}, {11,38}, {5,27}, {6,40}, {24,44}, {9,31}, {3,6}, {20,39}, {5,33}, {4,39}, {7,16}, {6,11}, {1,22}, {38,40}, {6,24}, {29,32}, {16,43}, {6,39}, {24,43}, {34,45}, {2,44}, {35,39}, {2,45}, {10,14}, {1,42}, {16,34}, {19,31}, {22,41}, {8,21}, {9,20}, {14,23}, {18,26}, {4,45}, {28,39}, {18,21}, {31,39}, {22,26}, {30,40}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {3,23}, {4,44}, {1,12}, {9,26}, {12,39}, {18,20}, {6,12}, {39,44}, {7,31}, {12,33}, {26,43}, {5,38}, {1,37}, {33,40}, {13,18}, {40,45}, {21,37}, {25,38}, {1,29}, {26,37}, {2,34}, {21,22}, {10,19}, {12,19}, {15,27}, {14,35}, {36,41}, {5,42}, {9,11}, {11,32}, {11,18}, {10,43}, {3,20}, {5,29}, {21,25}, {27,36}, {29,41}, {38,42}, {9,28}, {6,13}, {11,19}, {37,41}, {8,10}, {20,40}, {19,24}, {35,38}, {16,35}, {21,40}, {5,28}, {25,33}, {12,18}, {8,30}, {14,32}, {33,43}, {36,39}, {27,38}, {2,5}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {17,26}, {19,44}, {35,45}, {31,45}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {5,15}, {5,16}, {19,32}, {6,10}, {21,45}, {1,28}, {14,18}, {27,33}, {3,43}, {3,36}, {9,14}, {20,23}, {32,37}, {14,36}, {7,42}, {24,25}, {6,43}, {23,26}, {26,31}, {18,22}, {5,8}, {7,29}, {34,38}, {6,37}, {12,28}, {3,37}, {28,40}, {29,36}, {1,35}, {17,28}, {23,32}, {26,35}, {7,36}, {13,26}, {14,37}, {22,33}, {11,24}, {7,43}, {11,45}, {8,33}, {20,31}, {4,7}, {10,28}, {41,43}, {9,44}, {15,23}, {12,17}, {2,7}, {9,42}, {30,38}, {39,45}, {9,19}, {13,35}, {1,13}, {16,37}, {13,32}, {10,24}, {2,25}, {27,45}, {31,41}, {17,36}, {17,23}, {26,39}, {18,44}, {21,29}, {23,28}, {3,28}, {2,14}, {9,35}, {12,24}, {3,4}, {18,19}, {12,45}, {30,36}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {28,37}, {37,45}, {15,42}, {2,40}, {9,43}, {36,40}, {38,45}, {1,11}, {29,33}, {33,34}, {24,34}, {3,19}, {4,40}, {16,36}, {29,40}, {32,44}, {1,39}, {6,45}, {18,43}, {7,40}, {17,37}, {14,19}, {18,25}, {32,42}, {21,27}, {36,45}, {10,37}, {6,44}, {25,36}, {2,42}, {15,37}, {7,35}, {9,13}, {4,42}, {21,23}, {21,43}, {20,38}, {30,33}, {14,41}, {4,15}, {4,29}, {8,25}, {26,34}, {1,30}, {1,43}, {3,26}, {13,36}, {3,8}, {34,41}, {16,22}, {32,40}, {3,35}, {14,26}, {18,23}, {12,15}, {1,6}, {9,40}, {25,30}, {14,31}, {8,45}, {32,39}, {14,20}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {30,41}, {11,16}, {1,4}, {7,25}, {22,40}, {24,35}, {13,37}, {8,27}, {5,30}, {24,31}, {15,22}, {16,27}, {19,43}, {23,44}, {9,30}, {2,13}, {5,40}, {22,36}, {22,30}, {24,42}, {27,34}, {4,13}, {18,30}, {8,17}, {4,22}, {28,31}, {32,43}, {1,40}, {6,23}, {28,35}, {17,20}, {1,23}, {8,29}, {23,41}, {9,34}, {15,25}, {41,45}, {6,22}, {16,41}, {33,36}, {16,25}, {17,44}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {3,12}, {18,36}, {14,24}, {4,17}, {3,24}, {7,27}, {7,11}, {4,32}, {19,39}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {2,10}, {6,17}, {32,35}, {19,33}, {19,29}, {3,34}, {18,39}, {11,14}, {7,12}, {13,20}, {13,21}, {3,11}, {2,43}, {3,38}, {4,10}, {33,37}, {14,34}, {11,23}, {3,5}, {16,40}, {36,43}, {15,19}, {9,33}, {29,34}, {8,16}, {8,42}, {15,38}, {8,32}, {17,24}, {12,23}, {13,31}, {23,40}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {6,7}, {24,27}, {1,7}, {8,15}, {42,43}, {21,33}, {17,38}, {10,34}, {25,39}, {4,14}, {24,28}, {36,42}, {35,43}, {11,28}, {6,25}, {28,34}, {37,43}, {13,39}, {11,43}, {11,17}, {33,38}, {28,38}, {15,18}, {32,34}, {19,42}, {24,29}, {17,34}, {12,13}, {4,16}, {6,9}, {1,45}, {10,30}, {33,42}, {6,18}, {5,12}, {39,43}, {17,39}, {33,44}, {6,42}, {11,20}, {7,32}, {5,10}, {13,38}, {4,9}, {24,26}, {13,24}, {11,13}, {6,16}, {26,36}, {7,44}, {25,34}, {27,44}, {4,31}, {2,15}, {30,32}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {23,25}, {26,38}, {18,24}, {21,24}, {8,14}, {39,42}, {16,39}, {30,42}, {1,38}, {5,37}, {25,43}, {38,43}, {7,41}, {3,44}, {2,29}, {20,30}, {14,21}, {3,21}, {19,27}, {33,39}, {1,36}, {18,40}, {26,30}, {42,44}, {2,6}, {24,32}, {14,39}, {9,45}, {32,45}, {14,42}, {18,45}, {3,39}, {34,42}, {11,15}, {6,26}, {12,34}, {23,35}, {15,41}, {8,19}, {7,21}, {16,44}, {19,45}, {23,31}, {12,16}, {17,41}, {11,30}, {34,37}, {8,43}, {28,41}, {2,23}, {15,21}, {10,44}, {27,37}, {12,30}, {1,8}, {6,33}, {19,26}, {12,14}, {29,39}, {4,23}, {22,34}, {27,30}, {9,36}, {32,36}, {8,13}, {16,21}, {6,27}, {29,37}, {21,41}, {17,40}, {7,45}, {20,41}, {15,32}, {14,38}, {27,39}, {6,30}, {25,35}, {17,27}, {6,38}, {33,35}, {13,42}, {25,31}, {5,14}, {5,44}, {3,45}, {4,43}, {11,22}, {24,45}, {9,16}, {9,32}, {27,28}, {35,42}, {30,35}, {25,44}, {21,32}, {24,40}, {23,30}, {34,44}, {21,26}, {22,31}, {30,31}, {16,45}, {31,43}, {39,40}, {22,35}, {5,39}, {12,43}, {26,29}, {1,21}, {9,15}, {28,36}, {10,45}, {23,42}, {8,12}, {7,20}, {3,40}, {16,19}, {23,27}, {27,43}, {22,42}, {12,36}, {27,31}, {22,44}, {31,34}, {7,18}, {21,39}, {10,21}, {40,43}, {32,38}, {27,35}, {5,17}, {1,24}, {6,8}, {19,25}, {2,9}, {17,21}, {4,18}, {15,26}, {18,41}, {23,43}, {21,28}, {23,36}, {26,28}, {16,38}, {22,43}, {12,37}, {4,8}, {29,31}, {2,19}, {17,30}, {24,41}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {20,45}, {29,35}, {27,29}, {30,39}, {26,45}, {31,40}, {4,37}, {40,44}, {28,33}, {12,29}, {7,19}, {2,35}, {10,32}, {16,24}, {21,38}, {25,37}, {13,16}, {34,43}, {5,11}, {6,41}, {10,15}, {6,29} }; // ET45.151 // Bipartite(8,37) Valencies [37,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 554954524638246232267460296729341984768000000000 EdgePairs[45][151]:={ {6,38}, {6,25}, {5,38}, {5,22}, {4,28}, {5,43}, {5,45}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {6,9}, {4,37}, {4,40}, {8,31}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {1,20}, {3,18}, {2,34}, {8,16}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {7,45}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {8,9}, {2,10}, {3,9}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {1,36}, {6,18}, {1,29}, {6,44}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {1,43}, {8,42}, {4,22}, {1,18}, {3,38}, {8,19}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {4,9}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {4,10}, {5,14}, {8,45}, {3,29}, {1,41}, {2,23}, {4,45}, {4,11}, {3,44}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {5,39}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {8,34}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {7,29}, {2,28}, {8,29}, {7,21}, {8,36}, {2,45}, {8,27}, {3,33}, {2,11}, {1,45}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {8,43}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {5,9}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {7,38}, {5,42}, {2,38}, {7,9}, {5,10}, {7,44}, {8,28}, {7,43}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {5,36}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {8,25}, {2,9}, {2,32}, {6,33}, {2,14}, {5,33}, {5,30}, {6,40} }; // ET45.152 // Bipartite(7,38) Valencies [38,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2636033992031669603270436409464374427648000000000 EdgePairs[45][152]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {7,15}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {7,38}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {7,41}, {7,44}, {1,40}, {2,15}, {4,19}, {7,22}, {4,31}, {2,19}, {7,8}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {7,34}, {1,21}, {2,9}, {7,36}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {2,45}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {7,12}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {4,22}, {5,22}, {1,18}, {3,14}, {7,11}, {7,20}, {4,8}, {5,11}, {1,44}, {4,41}, {2,10}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {6,8}, {7,39}, {5,25}, {2,39}, {7,32}, {1,31}, {3,12}, {4,45}, {7,13}, {7,25}, {7,43}, {2,35}, {1,22}, {3,44}, {6,12}, {6,30}, {6,43}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {7,30}, {2,16}, {3,39}, {3,32}, {4,35}, {7,16}, {2,32}, {1,12}, {6,33}, {7,26}, {5,18}, {1,23}, {6,24}, {5,30}, {6,44}, {7,17}, {5,24}, {1,45}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {7,14}, {3,27}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {3,26}, {5,28}, {5,42}, {7,31}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {5,44}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {1,25}, {6,19}, {6,9}, {7,29}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {7,28}, {3,16}, {4,37}, {6,42}, {4,40}, {7,23}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {6,45}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {7,9}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {5,13}, {3,28}, {7,10}, {7,27}, {7,45}, {1,41}, {5,45}, {3,41}, {3,31}, {7,24}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {7,33}, {5,19}, {6,20}, {7,35}, {2,30}, {5,21}, {6,13}, {7,37}, {2,18}, {5,35}, {1,34}, {5,37}, {7,19}, {2,43}, {4,17}, {6,35}, {3,36}, {4,39}, {7,40}, {4,44}, {7,42}, {7,21}, {4,32}, {1,36}, {7,18}, {5,16} }; // ET45.153 // Bipartite(6,39) Valencies [39,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14686475098462159218221002852730086096896000000000 EdgePairs[45][153]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {2,45}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {1,44}, {4,41}, {2,10}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {6,8}, {5,25}, {2,39}, {1,31}, {3,12}, {4,45}, {2,35}, {1,22}, {3,44}, {6,12}, {6,30}, {6,43}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {6,44}, {5,24}, {5,7}, {1,45}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {3,26}, {5,28}, {5,42}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {5,44}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {6,19}, {6,9}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {6,42}, {4,40}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {6,45}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {5,13}, {1,41}, {5,45}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {5,19}, {6,20}, {2,30}, {5,21}, {6,13}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {6,35}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36}, {5,16} }; // ET45.154 // Bipartite(5,40) Valencies [40,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 97909833989747728121473352351533907312640000000000 EdgePairs[45][154]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {2,42}, {3,18}, {3,17}, {3,7}, {2,45}, {4,38}, {3,34}, {2,25}, {5,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {1,44}, {4,41}, {2,10}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {5,25}, {2,39}, {1,31}, {3,12}, {4,45}, {2,35}, {1,22}, {3,44}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {1,45}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {1,43}, {3,26}, {5,28}, {5,42}, {2,17}, {4,36}, {5,41}, {4,6}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {5,44}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {1,15}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,40}, {2,31}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {5,13}, {1,41}, {5,45}, {5,6}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {2,30}, {5,21}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36}, {5,16} }; // ET45.155 // Non-bipartite Valency 40 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 1872381094133760000000000 EdgePairs[45][155]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {37,43}, {13,18}, {2,6}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {18,45}, {5,44}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {8,44}, {14,37}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {19,27}, {28,43}, {7,12}, {21,34}, {4,10}, {3,19}, {1,15}, {5,8}, {10,30}, {24,44}, {40,44}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {7,42}, {30,31}, {21,45}, {21,31}, {13,44}, {3,14}, {17,39}, {1,31}, {6,23}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {38,43}, {3,27}, {29,39}, {25,32}, {25,45}, {5,13}, {4,45}, {15,33}, {21,33}, {22,27}, {30,34}, {17,36}, {10,35}, {13,40}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {13,41}, {22,37}, {12,26}, {15,34}, {18,41}, {7,16}, {12,16}, {14,19}, {9,43}, {3,38}, {13,24}, {11,30}, {30,32}, {40,45}, {6,42}, {4,21}, {12,42}, {29,36}, {30,33}, {14,43}, {20,34}, {23,29}, {1,33}, {4,25}, {2,42}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, {36,42}, {1,30}, {23,42}, {14,27}, {11,35}, {2,29}, {16,39}, {15,31}, {10,21}, {17,23}, {10,45}, {12,19}, {3,7}, {10,25}, {6,17}, {20,33}, {2,17}, {29,42}, {20,32}, {18,40}, {11,33}, {18,44}, {19,22}, {16,26}, {3,22}, {5,24}, {11,32}, {22,43}, {28,37}, {11,20}, {24,41}, {17,28}, {1,8}, {11,24}, {1,35}, {9,17}, {10,18}, {19,38}, {8,15}, {5,20}, {14,16}, {3,12}, {11,45}, {3,26}, {11,31}, {16,22}, {27,43}, {12,39}, {6,36}, {5,15}, {20,30}, {2,36}, {4,18}, {35,41}, {22,38}, {26,39}, {8,11}, {15,35}, {30,41}, {14,38}, {5,41}, {39,43}, {12,27}, {15,30}, {3,43}, {19,43}, {7,19}, {1,45}, {11,34}, {8,32}, {7,39}, {22,39}, {19,26}, {8,33}, {8,20}, {5,31}, {20,35}, {30,45}, {1,13}, {26,38}, {9,23}, {7,14}, {34,41}, {5,34}, {9,29}, {13,35}, {14,26}, {23,28}, {7,27}, {2,9}, {10,40}, {29,37}, {13,30}, {17,42}, {35,45}, {13,20}, {16,27}, {37,42}, {23,36}, {8,41}, {5,32}, {5,33}, {8,31}, {17,37}, {5,11}, {3,16}, {20,24}, {7,22}, {22,26}, {12,22}, {20,45}, {7,38}, {13,34}, {28,36}, {15,45}, {9,36}, {4,44}, {31,41}, {8,34}, {26,43}, {15,24}, {10,19}, {1,24}, {20,41}, {12,38}, {27,39}, {32,41}, {31,37}, {14,39}, {31,45}, {34,37}, {2,13}, {5,30}, {33,41}, {24,30}, {6,13}, {5,35}, {24,35}, {8,17}, {1,9}, {18,25}, {4,40}, {2,37}, {12,18}, {6,37}, {25,44}, {9,15}, {3,10}, {21,40}, {16,43}, {13,45}, {18,21}, {8,30}, {21,44}, {10,44}, {13,31}, {2,28}, {25,40}, {15,28}, {6,28}, {14,21}, {7,18}, {11,41}, {34,45}, {14,25}, {5,17}, {24,33}, {20,28}, {13,32}, {13,33}, {35,37}, {10,27}, {9,11}, {24,32}, {32,37}, {33,37}, {19,39}, {1,41}, {3,39}, {5,29}, {33,45}, {8,35}, {28,42}, {15,41}, {6,24}, {24,31}, {32,45}, {9,32}, {2,24}, {4,19}, {5,6}, {9,33}, {9,20}, {18,26}, {8,29}, {24,45}, {4,14}, {21,43}, {7,43}, {12,43}, {30,37}, {8,23}, {5,45}, {3,21}, {5,36}, {23,37}, {25,43}, {4,27}, {2,8}, {24,29}, {9,42}, {13,17}, {3,25}, {26,44}, {1,37}, {13,23}, {12,40}, {36,41}, {1,28}, {8,45}, {13,42}, {16,38}, {25,27}, {9,31}, {21,27}, {4,38}, {28,32}, {24,34}, {10,14}, {13,29}, {4,22}, {4,7}, {10,22}, {10,12}, {24,42}, {26,40}, {17,24}, {28,33}, {21,38}, {15,37}, {7,44}, {2,41}, {8,36}, {23,41}, {39,44}, {9,34}, {15,17}, {10,38}, {6,41}, {34,36}, {11,28}, {13,36}, {28,34}, {19,25}, {25,38}, {19,21}, {20,37}, {6,11}, {5,23}, {12,44}, {11,23}, {35,42}, {31,36}, {2,11}, {9,30}, {29,41}, {38,44}, {7,40}, {20,29}, {33,36}, {32,36}, {28,31}, {30,42}, {18,27}, {1,6}, {11,37}, {5,9}, {4,26}, {4,12}, {2,30}, {3,18}, {1,29}, {6,30}, {9,35}, {1,17}, {8,28}, {5,42}, {18,39}, {10,43}, {16,44}, {21,26}, {17,41}, {4,43}, {35,36}, {5,28}, {25,26}, {17,33}, {2,35}, {10,26}, {16,40}, {6,35}, {15,29}, {17,32}, {8,42}, {24,28}, {28,35}, {27,40}, {16,25}, {11,17}, {25,39}, {16,21}, {5,37}, {40,43}, {24,36}, {9,24}, {21,39}, {30,36}, {6,20}, {2,20}, {1,36}, {14,18}, {10,16}, {4,16}, {34,42}, {20,23}, {7,25}, {15,36}, {17,34}, {31,42}, {6,15}, {9,45}, {7,21}, {19,40}, {18,22}, {29,31}, {8,37}, {37,41}, {12,25}, {2,15}, {20,36}, {6,31}, {27,44}, {9,13}, {1,7}, {1,23}, {6,45}, {12,21}, {23,30}, {29,34}, {15,23}, {17,31}, {2,45}, {2,31}, {13,28}, {9,18}, {20,26}, {10,17}, {11,29}, {19,44}, {3,40}, {3,44}, {11,42}, {11,16}, {2,34}, {8,19}, {37,44}, {22,40}, {20,42}, {13,37}, {33,42}, {6,34}, {2,21}, {23,35}, {18,28}, {29,33}, {32,42}, {28,41}, {29,35}, {29,32}, {23,32}, {37,45}, {6,21}, {1,12}, {2,32}, {6,33}, {5,19}, {18,38}, {23,33}, {7,20}, {4,29}, {1,42}, {3,8}, {10,39}, {6,25}, {4,17}, {7,31}, {12,33}, {2,25}, {17,35}, {6,32}, {2,33}, {4,6}, {7,15}, {12,32}, {22,44}, {1,26}, {28,45}, {14,44}, {15,26}, {12,20}, {38,41}, {11,36}, {5,14}, {5,27}, {8,27}, {15,42}, {15,16}, {3,13}, {17,30}, {30,39}, {24,37}, {4,39}, {23,31}, {25,29}, {18,43}, {28,40}, {35,39}, {23,45}, 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{6,40}, {31,40}, {32,44}, {14,17}, {5,25}, {36,43}, {25,41}, {5,21}, {3,45}, {20,40}, {18,32}, {7,28}, {14,23}, {35,44}, {20,44}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {9,26}, {22,34}, {10,24}, {29,38}, {16,28}, {22,42}, {30,44}, {14,29}, {18,34}, {19,23}, {18,31}, {26,37}, {14,42}, {15,40}, {1,44}, {2,19}, {23,43}, {6,19}, {4,24}, {12,37}, {17,22}, {14,36}, {2,43}, {27,36}, {6,43}, {8,18}, {19,45}, {8,21}, {10,15}, {12,17}, {30,40}, {29,43}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {15,44}, {17,38}, {6,27}, {16,37}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {27,45}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {20,21}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {38,45}, {7,17}, {10,11}, {17,43}, {20,25}, {4,41}, {3,42}, {3,28}, {9,27}, {11,25}, {11,44}, {11,21}, {19,42}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // ET45.156 // Bipartite(4,41) Valencies [41,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 802860638715931370596081489282578039963648000000000 EdgePairs[45][156]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {2,33}, {4,27}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {2,28}, {2,14}, {1,30}, {4,23}, {3,5}, {2,42}, {3,18}, {3,17}, {3,7}, {2,45}, {4,38}, {3,34}, {2,25}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {1,18}, {3,14}, {4,8}, {1,5}, {2,5}, {1,44}, {4,41}, {2,10}, {2,38}, {2,37}, {4,42}, {2,39}, {1,31}, {3,12}, {4,45}, {2,35}, {1,22}, {3,44}, {4,33}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {1,23}, {2,6}, {1,45}, {1,9}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {1,43}, {3,26}, {2,17}, {4,36}, {4,6}, {1,42}, {3,19}, {4,9}, {1,24}, {3,23}, {1,39}, {3,21}, {2,7}, {1,25}, {1,15}, {2,11}, {4,5}, {1,35}, {1,37}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {2,40}, {2,31}, {3,42}, {4,18}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {1,41}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {2,30}, {2,18}, {1,34}, {2,43}, {4,17}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36} }; // ET45.157 // Bipartite(3,42) Valencies [42,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8430036706517279391258855637467069419618304000000000 EdgePairs[45][157]:={ {1,15}, {3,15}, {1,43}, {2,38}, {1,11}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {2,11}, {1,40}, {2,20}, {1,25}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {1,5}, {1,44}, {3,30}, {1,32}, {3,45}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {2,41}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {2,13}, {3,14}, {1,12}, {3,9}, {3,22}, {3,23}, {2,42}, {2,34}, {3,27}, {1,19}, {2,40}, {2,35}, {2,9}, {1,4}, {3,5}, {1,35}, {1,26}, {2,44}, {2,4}, {2,24}, {3,42}, {2,27}, {3,4}, {2,43}, {3,35}, {1,23}, {2,21}, {1,7}, {1,39}, {2,39}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {1,42}, {2,6}, {3,21}, {1,14}, {1,41}, {3,44}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {1,13}, {3,16}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {2,25}, {3,6}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,43}, {1,45}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24}, {2,45} }; // ET45.158 // Non-bipartite Valency 42 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 614848852548510547968000 EdgePairs[45][158]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {37,43}, {13,18}, {2,6}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {18,45}, {5,44}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {8,44}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {19,27}, {28,43}, {32,34}, {7,12}, {21,34}, {4,10}, {33,34}, {3,19}, {1,15}, {5,8}, {10,30}, {24,44}, {40,44}, {9,28}, {25,31}, {2,23}, {16,36}, {7,26}, {7,42}, {30,31}, {21,45}, {21,31}, {13,44}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {38,43}, {3,27}, {29,39}, {25,32}, {25,45}, {5,13}, {4,45}, {15,33}, {21,33}, {22,27}, {30,34}, {17,36}, {10,35}, {13,40}, {11,15}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {13,41}, {22,37}, {12,26}, {15,34}, {18,41}, {7,16}, {12,16}, {14,19}, {9,43}, {3,38}, {13,24}, {11,30}, {30,32}, {40,45}, {6,42}, {4,21}, {12,42}, {29,36}, {30,33}, {14,43}, {20,34}, {23,29}, {1,33}, {4,25}, {2,42}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, 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{14,17}, {5,25}, {36,43}, {25,41}, {5,21}, {3,45}, {20,40}, {18,32}, {7,28}, {14,23}, {35,44}, {20,44}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {22,42}, {30,44}, {1,4}, {14,29}, {18,34}, {19,23}, {18,31}, {26,37}, {14,42}, {15,40}, {1,44}, {2,19}, {23,43}, {6,19}, {4,24}, {12,37}, {17,22}, {27,28}, {14,36}, {2,43}, {27,36}, {6,43}, {26,29}, {8,18}, {19,45}, {8,21}, {10,15}, {12,17}, {30,40}, {29,43}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {15,44}, {17,38}, {6,27}, {16,37}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {27,45}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {38,45}, {7,17}, {17,43}, {20,25}, {4,41}, {41,44}, {3,42}, {3,28}, {9,27}, {11,25}, {11,44}, {11,21}, {19,42}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // ET45.159 // Bipartite(2,43) Valencies [43,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 120830526126747671274710264137027995014529024000000000 EdgePairs[45][159]:={ {2,11}, {1,26}, {2,14}, {2,44}, {1,14}, {1,44}, {2,37}, {1,24}, {2,26}, {1,29}, {2,30}, {2,32}, {1,30}, {2,29}, {1,32}, {2,24}, {2,10}, {1,37}, {1,33}, {1,40}, {1,10}, {1,43}, {2,39}, {1,39}, {2,43}, {1,36}, {1,6}, {1,45}, {2,40}, {2,6}, {1,4}, {1,20}, {1,12}, {2,36}, {1,31}, {2,45}, {2,12}, {2,4}, {2,33}, {2,21}, {1,38}, {2,16}, {1,7}, {1,15}, {2,7}, {2,31}, {1,16}, {2,20}, {1,21}, {2,18}, {2,38}, {2,3}, {2,15}, {2,5}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {2,27}, {2,28}, {2,42}, {1,28}, {2,19}, {1,42}, {2,17}, {2,23}, {1,8}, {1,13}, {2,35}, {1,19}, {2,9}, {2,34}, {1,9}, {2,41}, {1,41}, {1,22}, {2,13}, {2,8}, {2,25}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25}, {2,22} }; // ET45.160 // Bipartite(1,44) Valencies [44,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 2658271574788448768043625811014615890319638528000000000 EdgePairs[45][160]:={ {1,26}, {1,14}, {1,44}, {1,24}, {1,29}, {1,30}, {1,32}, {1,37}, {1,33}, {1,40}, {1,10}, {1,2}, {1,43}, {1,39}, {1,36}, {1,6}, {1,45}, {1,4}, {1,20}, {1,12}, {1,31}, {1,38}, {1,7}, {1,15}, {1,16}, {1,21}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {1,28}, {1,42}, {1,8}, {1,13}, {1,19}, {1,9}, {1,41}, {1,22}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25} }; // ET45.161 // Non-bipartite Valency 44 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 119622220865480194561963161495657715064383733760000000000 EdgePairs[45][161]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {37,43}, {13,18}, {2,6}, {32,33}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {18,45}, {5,44}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {8,44}, 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{34,43}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {25,28}, {8,26}, {30,38}, {3,32}, {10,42}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {12,45}, {24,26}, {40,42}, {8,10}, {1,22}, {14,34}, {27,33}, {17,19}, {7,24}, {9,12}, {29,40}, {11,27}, {26,41}, {27,32}, {35,38}, {22,23}, {4,5}, {32,43}, {10,37}, {22,30}, {27,34}, {31,43}, {33,43}, {42,43}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {26,45}, {22,35}, {20,43}, {32,40}, {16,41}, {33,40}, {15,18}, {2,14}, {17,44}, {3,35}, {26,28}, {27,31}, {13,39}, {6,14}, {11,43}, {14,31}, {4,8}, {17,27}, {24,25}, {7,9}, {13,21}, {27,29}, {5,10}, {39,45}, {23,44}, {3,17}, {12,28}, {34,44}, {14,45}, {36,38}, {19,35}, {21,24}, {1,18}, {6,44}, {22,31}, {6,22}, {31,44}, {14,32}, {22,33}, {2,44}, {5,39}, {25,37}, {13,25}, {14,33}, {2,22}, {2,3}, {3,29}, {22,32}, {8,39}, {19,30}, {1,43}, {15,43}, {7,41}, {21,41}, {22,45}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {18,42}, {7,37}, {38,42}, {9,16}, {3,36}, {2,40}, {33,44}, {11,38}, {12,41}, {4,13}, {6,40}, {31,40}, {32,44}, {14,17}, {5,25}, {36,43}, {25,41}, {5,21}, {3,45}, {20,40}, {18,32}, {7,28}, {14,23}, {35,44}, {20,44}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {22,42}, {30,44}, {1,4}, {14,29}, {18,34}, {19,23}, {18,31}, {15,40}, {14,42}, {26,37}, {1,44}, {2,19}, {23,43}, {6,19}, {4,24}, {12,37}, {17,22}, {27,28}, {14,36}, {2,43}, {27,36}, {6,43}, {26,29}, {8,18}, {19,45}, {8,21}, {10,15}, {12,17}, {30,40}, {29,43}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {15,44}, {43,45}, {17,38}, {6,27}, {16,37}, {37,39}, {19,28}, {18,35}, {2,27}, {1,10}, {4,20}, {27,45}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {3,9}, {23,38}, {7,29}, {20,21}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {38,45}, {7,17}, {10,11}, {17,43}, {20,25}, {4,41}, {41,44}, {3,42}, {3,28}, {9,27}, {37,38}, {11,25}, {16,17}, {11,44}, {11,21}, {19,42}, {23,39}, {10,41}, {12,29}, {22,28}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // Total number of connected ET graphs of order 45 is 161 // ******************************************************************************************** // Order 46 // ET46.1 // Bipartite(23,23) Valencies [2,2] // Diameter 23 Girth 46 // Twin-free VT AT // Automorphism group of order 92 EdgePairs[46][1]:={ {14,46}, {3,24}, {15,41}, {22,26}, {17,37}, {21,33}, {4,30}, {23,29}, {14,43}, {5,27}, {12,46}, {10,42}, {6,30}, {1,24}, {13,45}, {20,35}, {12,42}, {2,25}, {10,38}, {7,36}, {16,39}, {3,27}, {11,40}, {19,37}, {8,38}, {9,40}, {18,35}, {22,31}, {17,41}, {13,44}, {19,33}, {18,39}, {21,28}, {4,25}, {23,28}, {5,32}, {2,29}, {7,32}, {15,45}, {11,44}, {8,34}, {1,26}, {20,31}, {6,34}, {9,36}, {16,43} }; // ET46.2 // Non-bipartite Valency 4 // Diameter 11 Girth 4 // Has twins VT AT // Automorphism group of order 385875968 EdgePairs[46][2]:={ {1,15}, {4,35}, {11,43}, {7,39}, {11,44}, {31,46}, {8,39}, {12,26}, {9,42}, {23,38}, {7,40}, {16,30}, {32,45}, {29,43}, {30,43}, {2,33}, {22,35}, {13,27}, {21,35}, {22,36}, {19,33}, {15,29}, {25,40}, {12,25}, {13,46}, {2,15}, {14,46}, {10,23}, {14,27}, {5,37}, {3,18}, {8,22}, {28,41}, {1,34}, {17,31}, {26,40}, {24,37}, {20,33}, {2,16}, {1,16}, {24,38}, {8,21}, {10,41}, {14,28}, {9,23}, {10,24}, {5,19}, {30,44}, {14,45}, {13,45}, {6,37}, {29,44}, {16,29}, {2,34}, {4,36}, {4,17}, {11,26}, {8,40}, {31,45}, {6,19}, {18,32}, {5,38}, {12,44}, {3,35}, {25,39}, {12,43}, {6,38}, {5,20}, {23,37}, {27,42}, {9,24}, {11,25}, {13,28}, {6,20}, {21,36}, {19,34}, {26,39}, {10,42}, {7,22}, {4,18}, {32,46}, {28,42}, {20,34}, {7,21}, {1,33}, {18,31}, {3,36}, {3,17}, {9,41}, {17,32}, {27,41}, {15,30} }; // ET46.3 // Bipartite(23,23) Valencies [11,11] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 506 EdgePairs[46][3]:={ {3,33}, {16,41}, {10,25}, {2,33}, {11,36}, {18,39}, {4,27}, {11,35}, {13,40}, {16,33}, {23,29}, {3,40}, {17,38}, {12,45}, {15,46}, {10,37}, {18,32}, {16,27}, {8,30}, {16,40}, {18,46}, {12,32}, {8,42}, {19,44}, {15,31}, {21,37}, {4,29}, {20,27}, {22,46}, {1,32}, {8,33}, {1,27}, {19,24}, {1,40}, {17,34}, {9,44}, {12,39}, {4,31}, {12,41}, {10,33}, {12,42}, {2,27}, {21,42}, {13,35}, {2,26}, {8,39}, {7,34}, {17,24}, {21,43}, {7,36}, {15,43}, {10,44}, {8,25}, {2,41}, {1,30}, {5,32}, {17,40}, {9,35}, {14,28}, {20,30}, {13,29}, {12,37}, {16,29}, {2,45}, {16,30}, {23,32}, {4,38}, {2,25}, {11,38}, {6,40}, {6,31}, {21,46}, {2,34}, {2,36}, {10,38}, {9,32}, {14,36}, {19,26}, {16,24}, {9,26}, {19,30}, {12,36}, {15,40}, {5,29}, {12,46}, {2,37}, {5,43}, {8,45}, {14,30}, {22,35}, {4,42}, {9,41}, {7,32}, {17,39}, {15,26}, {10,41}, {4,45}, {7,43}, {22,27}, {15,27}, {21,44}, {19,38}, {6,30}, {23,26}, {23,41}, {21,26}, {9,34}, {15,42}, {10,40}, {17,43}, {7,30}, {3,39}, {13,31}, {4,35}, {23,42}, {15,41}, {18,44}, {11,29}, {20,44}, {13,44}, {5,30}, {6,44}, {6,46}, {15,35}, {12,28}, {23,25}, {14,42}, {15,34}, {13,25}, {8,35}, {10,42}, {18,26}, {19,31}, {1,28}, {14,41}, {3,27}, {23,38}, {4,28}, {20,43}, {18,33}, {3,29}, {3,26}, {22,43}, {8,37}, {21,33}, {5,28}, {13,36}, {18,31}, {7,31}, {10,43}, {5,41}, {17,28}, {20,29}, {12,27}, {22,25}, {16,45}, {1,24}, {13,24}, {5,31}, {17,25}, {22,33}, {20,39}, {21,29}, {10,32}, {18,25}, {17,29}, {20,25}, {1,25}, {22,28}, {11,46}, {16,44}, {19,45}, {17,41}, {20,46}, {6,41}, {6,28}, {22,31}, {1,35}, {13,42}, {1,37}, {5,39}, {14,25}, {22,24}, {11,26}, {14,45}, {6,36}, {3,30}, {5,33}, {8,34}, {11,37}, {2,29}, {16,35}, {18,28}, {10,27}, {8,38}, {20,34}, {1,26}, {4,34}, {14,44}, {23,46}, {11,32}, {19,39}, {19,43}, {6,38}, {2,31}, {11,40}, {9,33}, {9,36}, {20,36}, {6,34}, {14,43}, {16,46}, {18,45}, {3,42}, {9,39}, {9,38}, {17,45}, {3,38}, {11,45}, {12,24}, {3,28}, {7,45}, {8,46}, {14,35}, {13,37}, {23,31}, {7,24}, {15,39}, {21,34}, {9,24}, {18,40}, {7,33}, {6,37}, {13,39}, {21,24}, {11,43}, {5,35}, {22,36}, {1,34}, {5,37}, {21,28}, {23,24}, {3,36}, {7,40}, {7,42}, {4,44}, {19,37}, {20,32}, {4,32}, {19,27}, {22,38}, {14,26}, {23,30} }; // ET46.4 // Bipartite(22,24) Valencies [12,11] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 15840 EdgePairs[46][4]:={ {15,33}, {18,45}, {19,28}, {11,40}, {9,32}, {6,25}, {5,38}, {19,26}, {11,25}, {4,28}, {5,45}, {8,26}, {1,40}, {14,38}, {13,39}, {17,33}, {8,40}, {10,33}, {21,30}, {14,31}, {21,41}, {10,39}, {3,39}, {20,37}, {21,28}, {1,35}, {7,30}, {8,31}, {4,37}, {2,46}, {13,43}, {13,27}, {14,29}, {13,40}, {14,44}, {6,32}, {17,35}, {4,38}, {11,35}, {6,29}, {12,28}, {22,37}, {2,25}, {21,40}, {4,43}, {16,42}, {15,32}, {12,46}, {20,43}, {7,45}, {8,37}, {20,24}, {5,41}, {21,38}, {13,30}, {6,39}, {10,26}, {7,33}, {12,31}, {12,23}, {22,25}, {5,37}, {16,25}, {13,42}, {20,35}, {1,36}, {16,34}, {6,46}, {15,45}, {10,35}, {18,39}, {6,44}, {4,23}, {17,36}, {6,24}, {2,29}, {1,26}, {20,36}, {20,42}, {22,34}, {18,29}, {9,36}, {6,34}, {9,29}, {8,42}, {18,26}, {22,43}, {5,27}, {19,46}, {15,28}, {5,28}, {14,46}, {9,46}, {7,32}, {19,38}, {3,31}, {12,27}, {1,39}, {2,30}, {11,42}, {5,35}, {14,34}, {3,36}, {4,32}, {19,27}, {6,36}, {3,30}, {2,24}, {22,26}, {3,24}, {14,33}, {15,37}, {14,23}, {10,38}, {13,25}, {8,41}, {18,38}, {7,46}, {3,29}, {13,36}, {1,41}, {15,23}, {20,31}, {13,45}, {3,25}, {11,34}, {17,28}, {21,42}, {7,35}, {19,45}, {2,43}, {12,30}, {7,34}, {11,24}, {10,31}, {10,44}, {17,46}, {22,31}, {20,30}, {9,30}, {22,45}, {16,41}, {20,44}, {17,44}, {19,41}, {17,30}, {5,40}, {16,30}, {7,23}, {10,25}, {12,29}, {11,32}, {15,24}, {21,32}, {15,40}, {14,37}, {1,44}, {18,31}, {9,41}, {16,31}, {7,39}, {3,41}, {1,32}, {21,39}, {19,29}, {6,43}, {7,24}, {10,28}, {5,31}, {17,25}, {16,44}, {4,44}, {17,41}, {5,23}, {12,43}, {10,40}, {2,28}, {8,29}, {9,23}, {8,36}, {8,27}, {2,45}, {3,33}, {13,32}, {14,26}, {19,33}, {19,39}, {3,34}, {4,27}, {16,46}, {15,29}, {4,46}, {2,31}, {16,38}, {11,45}, {18,27}, {1,33}, {12,36}, {16,27}, {3,45}, {12,44}, {19,25}, {2,37}, {4,42}, {12,33}, {12,39}, {22,33}, {21,44}, {14,24}, {11,41}, {6,26}, {1,34}, {22,27}, {13,35}, {21,29}, {17,24}, {20,23}, {8,44}, {18,23}, {6,42}, {4,35}, {19,32}, {18,43}, {20,34}, {11,37}, {1,23}, {16,35}, {10,24}, {3,40}, {9,45}, {14,41}, {4,26}, {22,46}, {17,37}, {16,39}, {13,28}, {9,27}, {7,38}, {2,38}, {15,36}, {22,35}, {10,43}, {8,28}, {7,43}, {18,40}, {20,40}, {1,27}, {15,26}, {22,36}, {9,42}, {9,34}, {15,43}, {21,24}, {17,32}, {8,25}, {2,42}, {18,42}, {18,34}, {11,26}, {5,33}, {5,30}, {11,38}, {9,37}, {21,23} }; // ET46.5 // Bipartite(22,24) Valencies [12,11] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 32440320 EdgePairs[46][5]:={ {15,33}, {19,28}, {6,38}, {11,40}, {14,36}, {6,25}, {5,43}, {5,45}, {3,26}, {8,26}, {22,40}, {11,43}, {4,31}, {8,40}, {20,46}, {10,33}, {14,31}, {15,27}, {14,45}, {16,37}, {19,37}, {20,37}, {21,28}, {16,28}, {1,35}, {15,41}, {4,37}, {13,43}, {14,29}, {2,33}, {4,38}, {11,29}, {10,42}, {11,27}, {19,40}, {22,37}, {2,25}, {4,24}, {4,43}, {21,40}, {16,42}, {18,32}, {4,30}, {20,43}, {17,39}, {7,41}, {7,27}, {11,39}, {10,26}, {12,31}, {20,29}, {17,26}, {1,24}, {12,23}, {22,25}, {18,35}, {16,25}, {20,35}, {9,35}, {1,36}, {1,29}, {19,42}, {12,37}, {6,46}, {15,45}, {10,35}, {18,39}, {8,38}, {13,26}, {6,24}, {2,29}, {5,34}, {18,46}, {13,41}, {16,40}, {20,42}, {9,36}, {6,34}, {9,29}, {9,39}, {18,26}, {3,38}, {5,27}, {19,46}, {15,28}, {20,41}, {2,39}, {1,42}, {7,32}, {12,27}, {7,37}, {2,30}, {11,42}, {3,36}, {20,25}, {4,32}, {1,30}, {14,28}, {6,36}, {3,30}, {22,26}, {3,24}, {14,33}, {10,38}, {15,34}, {21,31}, {19,30}, {8,24}, {9,38}, {9,26}, {18,38}, {7,46}, {8,45}, {3,29}, {17,31}, {1,41}, {22,29}, {15,23}, {20,31}, {13,45}, {11,44}, {17,28}, {19,45}, {2,27}, {22,44}, {7,34}, {10,31}, {9,31}, {17,46}, {20,30}, {13,31}, {5,39}, {18,44}, {6,45}, {13,29}, {15,46}, {10,30}, {16,30}, {12,45}, {17,38}, {15,35}, {11,32}, {21,32}, {12,25}, {15,40}, {3,42}, {14,43}, {14,37}, {1,44}, {13,38}, {19,44}, {14,40}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {15,39}, {22,41}, {1,32}, {6,37}, {8,32}, {7,24}, {10,28}, {9,24}, {5,31}, {17,25}, {19,34}, {4,44}, {2,41}, {12,43}, {2,26}, {10,40}, {7,29}, {18,30}, {9,23}, {22,38}, {8,36}, {13,44}, {8,27}, {2,45}, {21,46}, {5,46}, {16,36}, {13,32}, {1,45}, {11,30}, {19,33}, {3,34}, {5,24}, {15,29}, {18,27}, {1,33}, {16,27}, {12,44}, {19,25}, {2,37}, {4,42}, {4,25}, {3,28}, {21,34}, {12,33}, {8,33}, {12,39}, {17,34}, {21,35}, {11,31}, {21,44}, {14,24}, {13,34}, {11,41}, {7,25}, {6,26}, {21,43}, {22,23}, {17,40}, {20,23}, {8,44}, {16,23}, {18,23}, {19,32}, {13,33}, {14,25}, {20,34}, {11,28}, {1,23}, {16,35}, {3,40}, {17,27}, {10,45}, {14,41}, {4,26}, {17,37}, {16,39}, {16,24}, {9,27}, {5,42}, {2,38}, {12,32}, {22,35}, {10,43}, {21,36}, {7,44}, {8,28}, {10,23}, {9,43}, {8,39}, {22,32}, {5,36}, {13,46}, {12,35}, {7,36}, {21,24}, {6,35}, {17,43}, {22,28}, {2,42}, {18,42}, {6,33}, {18,34}, {3,46}, {5,33}, {5,30}, {21,23} }; // ET46.6 // Bipartite(18,28) Valencies [14,9] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 722505054698864640000 EdgePairs[46][6]:={ {2,44}, {3,33}, {10,24}, {1,20}, {2,24}, {13,32}, {2,33}, {18,39}, {5,34}, {13,40}, {4,24}, {16,26}, {4,26}, {17,38}, {4,30}, {11,25}, {16,40}, {18,46}, {9,45}, {5,38}, {12,22}, {8,28}, {18,38}, {15,31}, {1,32}, {3,45}, {8,33}, {1,27}, {3,43}, {3,25}, {12,38}, {7,44}, {1,40}, {10,26}, {17,34}, {12,39}, {1,19}, {12,42}, {3,35}, {9,43}, {3,37}, {13,35}, {11,41}, {12,35}, {7,36}, {15,43}, {17,21}, {10,44}, {8,25}, {2,41}, {2,28}, {12,34}, {9,35}, {14,28}, {8,44}, {17,46}, {18,34}, {10,22}, {6,22}, {15,25}, {18,42}, {10,30}, {2,45}, {15,45}, {16,30}, {4,38}, {15,29}, {2,25}, {11,38}, {11,33}, {6,31}, {14,33}, {2,36}, {5,22}, {4,22}, {10,38}, {9,29}, {7,20}, {17,37}, {14,21}, {14,36}, {16,24}, {9,27}, {1,44}, {5,29}, {8,41}, {12,46}, {9,19}, {2,37}, {8,45}, {14,40}, {7,39}, {4,42}, {9,41}, {5,25}, {7,32}, {1,31}, {11,22}, {7,43}, {10,28}, {14,24}, {17,33}, {15,27}, {6,30}, {6,43}, {15,19}, {2,20}, {10,40}, {12,43}, {3,39}, {13,31}, {18,30}, {11,21}, {9,25}, {15,41}, {8,36}, {2,32}, {18,43}, {16,32}, {1,23}, {13,43}, {11,29}, {13,44}, {5,30}, {17,30}, {6,46}, {11,30}, {15,35}, {9,37}, {5,46}, {13,23}, {15,37}, {10,42}, {13,28}, {18,26}, {1,28}, {18,27}, {14,41}, {3,27}, {14,37}, {10,46}, {4,28}, {3,29}, {6,23}, {1,43}, {4,46}, {16,38}, {8,37}, {13,36}, {18,31}, {5,42}, {12,26}, {16,22}, {7,31}, {5,41}, {4,36}, {12,27}, {8,32}, {8,21}, {3,19}, {1,24}, {12,23}, {6,27}, {13,24}, {17,25}, {6,26}, {8,40}, {12,19}, {12,30}, {3,23}, {18,19}, {1,39}, {10,32}, {17,29}, {3,21}, {6,19}, {11,46}, {16,44}, {17,41}, {18,23}, {13,27}, {1,35}, {14,20}, {15,21}, {16,34}, {14,25}, {7,28}, {11,26}, {6,42}, {14,45}, {4,40}, {7,23}, {13,19}, {16,36}, {2,21}, {5,33}, {11,37}, {2,29}, {4,34}, {14,44}, {10,36}, {10,34}, {18,22}, {14,32}, {15,33}, {16,20}, {8,24}, {6,38}, {2,40}, {9,33}, {16,42}, {6,34}, {5,26}, {16,46}, {9,39}, {17,45}, {4,20}, {11,45}, {8,20}, {7,27}, {15,23}, {5,45}, {3,41}, {7,24}, {3,31}, {15,39}, {10,20}, {17,26}, {6,39}, {12,31}, {11,34}, {17,42}, {7,35}, {13,39}, {17,22}, {5,21}, {13,20}, {9,31}, {5,37}, {7,19}, {6,35}, {9,21}, {11,42}, {16,28}, {18,35}, {7,40}, {4,44}, {9,23}, {8,29}, {4,32}, {1,36}, {14,29} }; // ET46.7 // Bipartite(16,30) Valencies [15,8] // Diameter 4 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 322560 EdgePairs[46][7]:={ {16,41}, {10,25}, {5,17}, {2,24}, {10,24}, {11,20}, {9,28}, {2,33}, {6,32}, {11,36}, {2,46}, {12,29}, {13,40}, {4,24}, {15,24}, {16,33}, {3,22}, {10,37}, {11,25}, {16,27}, {8,30}, {6,17}, {14,39}, {9,45}, {5,38}, {12,32}, {7,38}, {8,42}, {8,28}, {16,31}, {4,29}, {1,32}, {3,45}, {3,43}, {1,40}, {10,26}, {4,19}, {16,19}, {12,39}, {4,31}, {12,41}, {15,44}, {12,42}, {5,20}, {9,43}, {13,35}, {2,26}, {8,39}, {7,34}, {1,21}, {16,25}, {7,36}, {15,43}, {10,44}, {2,41}, {12,34}, {1,30}, {16,23}, {14,28}, {8,44}, {8,27}, {13,29}, {16,29}, {2,42}, {11,28}, {16,43}, {10,30}, {4,38}, {3,34}, {14,23}, {11,38}, {6,31}, {11,33}, {2,34}, {1,17}, {5,22}, {4,22}, {8,19}, {9,29}, {10,38}, {9,32}, {12,20}, {1,44}, {5,29}, {12,46}, {5,43}, {7,46}, {14,30}, {14,40}, {2,39}, {15,26}, {1,31}, {4,45}, {7,25}, {10,28}, {2,35}, {3,44}, {6,43}, {4,33}, {3,20}, {9,34}, {15,19}, {15,42}, {10,21}, {2,20}, {6,18}, {13,18}, {16,37}, {12,43}, {1,29}, {7,30}, {3,32}, {11,21}, {15,41}, {7,26}, {6,33}, {13,33}, {5,18}, {1,23}, {13,44}, {5,30}, {6,44}, {15,35}, {5,46}, {12,28}, {12,25}, {15,37}, {8,22}, {13,25}, {8,35}, {13,28}, {14,41}, {3,27}, {14,37}, {10,45}, {6,23}, {3,26}, {13,36}, {15,36}, {5,42}, {9,22}, {7,31}, {2,17}, {10,43}, {14,17}, {16,45}, {8,21}, {1,42}, {3,19}, {1,24}, {14,18}, {14,22}, {5,31}, {6,27}, {6,26}, {8,40}, {12,19}, {12,30}, {8,23}, {5,36}, {3,21}, {1,25}, {11,46}, {10,39}, {13,27}, {1,37}, {16,21}, {4,37}, {6,42}, {11,26}, {14,45}, {15,18}, {4,40}, {10,35}, {7,23}, {2,21}, {3,30}, {8,34}, {10,17}, {11,37}, {11,27}, {16,35}, {8,38}, {2,22}, {15,22}, {11,32}, {9,17}, {14,32}, {15,33}, {6,25}, {13,41}, {6,38}, {2,40}, {2,31}, {11,40}, {9,33}, {9,36}, {6,34}, {5,27}, {16,46}, {4,18}, {15,28}, {16,39}, {9,38}, {11,19}, {4,20}, {12,24}, {7,45}, {15,23}, {1,41}, {3,41}, {7,24}, {3,31}, {9,24}, {9,46}, {10,20}, {6,39}, {14,46}, {13,34}, {7,35}, {13,17}, {13,45}, {13,20}, {5,35}, {5,37}, {7,19}, {9,21}, {3,36}, {11,42}, {4,39}, {7,40}, {4,44}, {9,23}, {14,27}, {8,29}, {4,32}, {12,18}, {1,36}, {14,26}, {7,18} }; // ET46.8 // Bipartite(16,30) Valencies [15,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 23776267862016000000 EdgePairs[46][8]:={ {2,44}, {3,33}, {2,24}, {5,17}, {10,24}, {9,28}, {6,32}, {11,36}, {4,27}, {5,34}, {13,40}, {15,24}, {16,26}, {16,33}, {4,26}, {12,45}, {11,25}, {16,27}, {16,40}, {6,17}, {2,23}, {12,22}, {12,32}, {8,28}, {15,31}, {3,45}, {8,33}, {3,43}, {3,25}, {10,23}, {12,38}, {1,40}, {10,26}, {14,38}, {12,39}, {1,19}, {9,43}, {3,37}, {13,35}, {2,26}, {8,39}, {7,36}, {15,43}, {10,44}, {2,41}, {12,34}, {9,35}, {8,44}, {8,27}, {13,29}, {2,42}, {15,25}, {3,18}, {10,30}, {6,29}, {15,45}, {4,38}, {5,40}, {14,23}, {11,33}, {1,17}, {2,36}, {5,22}, {4,22}, {9,29}, {10,38}, {14,36}, {12,20}, {5,29}, {2,38}, {12,46}, {9,19}, {5,43}, {12,44}, {8,45}, {14,30}, {7,39}, {9,41}, {5,25}, {1,31}, {10,41}, {4,45}, {7,43}, {7,25}, {11,31}, {14,24}, {2,35}, {1,22}, {15,27}, {6,30}, {4,33}, {5,23}, {4,21}, {10,29}, {9,34}, {13,22}, {15,19}, {15,42}, {2,20}, {6,18}, {1,29}, {7,30}, {3,39}, {13,31}, {11,21}, {9,25}, {2,32}, {16,32}, {1,23}, {13,43}, {6,24}, {6,44}, {11,30}, {9,37}, {5,46}, {13,23}, {12,28}, {15,37}, {8,22}, {14,42}, {13,25}, {10,42}, {13,28}, {1,28}, {14,41}, {3,27}, {4,28}, {6,23}, {1,43}, {4,46}, {16,38}, {5,28}, {15,36}, {8,26}, {12,26}, {16,22}, {9,22}, {7,31}, {12,33}, {5,41}, {2,17}, {12,27}, {9,40}, {14,17}, {8,32}, {16,45}, {8,21}, {3,19}, {14,18}, {5,31}, {11,24}, {11,39}, {6,26}, {8,40}, {12,40}, {10,32}, {3,21}, {1,25}, {1,46}, {16,44}, {6,41}, {1,35}, {13,46}, {1,37}, {14,20}, {15,21}, {16,34}, {16,21}, {6,42}, {15,18}, {4,40}, {10,35}, {13,19}, {6,36}, {3,30}, {8,34}, {10,17}, {3,24}, {11,37}, {2,29}, {11,27}, {8,38}, {4,34}, {14,44}, {10,36}, {9,17}, {10,18}, {14,32}, {15,33}, {16,20}, {13,41}, {6,38}, {16,46}, {3,42}, {16,39}, {11,19}, {4,20}, {11,45}, {8,20}, {7,27}, {7,45}, {8,46}, {14,35}, {1,41}, {13,37}, {7,24}, {3,31}, {15,39}, {9,46}, {10,20}, {7,33}, {13,34}, {5,19}, {6,20}, {11,43}, {2,30}, {13,17}, {15,30}, {7,37}, {5,35}, {2,18}, {9,31}, {1,34}, {5,37}, {7,19}, {6,35}, {3,36}, {11,42}, {4,39}, {16,28}, {7,42}, {9,23}, {4,44}, {7,21}, {4,32}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18} }; // ET46.9 // Bipartite(16,30) Valencies [15,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 36691771392000000 EdgePairs[46][9]:={ {11,17}, {13,32}, {2,33}, {6,32}, {11,36}, {2,46}, {12,29}, {13,21}, {11,35}, {4,24}, {14,19}, {16,26}, {15,46}, {4,30}, {11,25}, {8,30}, {16,40}, {2,23}, {9,45}, {5,38}, {12,22}, {7,38}, {8,42}, {8,28}, {4,29}, {1,27}, {3,43}, {3,25}, {10,23}, {7,44}, {14,38}, {7,22}, {12,41}, {15,44}, {10,33}, {2,27}, {1,19}, {12,42}, {3,35}, {5,20}, {9,43}, {3,37}, {14,31}, {7,34}, {1,21}, {11,41}, {16,18}, {12,35}, {2,41}, {2,28}, {12,34}, {5,32}, {9,35}, {8,44}, {4,23}, {10,22}, {3,18}, {3,17}, {2,45}, {15,45}, {16,30}, {6,31}, {2,34}, {1,17}, {4,22}, {9,29}, {7,20}, {14,36}, {12,17}, {15,32}, {16,24}, {9,27}, {12,36}, {15,40}, {4,41}, {12,46}, {9,19}, {5,43}, {7,46}, {14,30}, {7,39}, {4,42}, {9,41}, {5,25}, {2,39}, {7,32}, {15,26}, {1,31}, {10,41}, {10,28}, {11,31}, {14,24}, {2,35}, {15,27}, {6,30}, {6,43}, {10,29}, {10,21}, {6,18}, {10,40}, {1,29}, {13,31}, {4,35}, {9,25}, {8,36}, {7,26}, {13,33}, {16,32}, {1,23}, {11,23}, {13,43}, {6,24}, {11,29}, {13,44}, {6,44}, {11,30}, {9,37}, {12,28}, {8,22}, {1,45}, {14,42}, {15,34}, {13,25}, {15,20}, {14,37}, {10,46}, {4,28}, {1,33}, {10,45}, {3,29}, {1,43}, {4,46}, {16,38}, {8,26}, {16,22}, {2,17}, {4,36}, {8,32}, {3,19}, {14,18}, {12,23}, {5,31}, {11,24}, {5,44}, {6,26}, {8,40}, {12,40}, {12,30}, {3,23}, {1,39}, {1,25}, {6,19}, {16,44}, {10,39}, {13,27}, {1,35}, {1,37}, {14,20}, {15,21}, {16,34}, {5,39}, {14,25}, {7,28}, {6,42}, {13,26}, {4,40}, {10,35}, {13,19}, {16,36}, {6,36}, {2,21}, {3,30}, {5,33}, {8,34}, {10,17}, {3,24}, {11,37}, {2,29}, {10,27}, {8,38}, {2,22}, {4,34}, {14,44}, {10,34}, {15,22}, {9,17}, {14,32}, {15,33}, {16,20}, {8,24}, {6,25}, {6,38}, {2,40}, {9,33}, {16,42}, {5,27}, {14,43}, {15,38}, {5,26}, {8,18}, {16,46}, {3,42}, {4,18}, {15,28}, {9,39}, {13,38}, {11,19}, {8,20}, {12,24}, {7,27}, {7,45}, {8,46}, {1,41}, {13,37}, {5,45}, {3,41}, {3,31}, {15,39}, {7,33}, {6,37}, {5,19}, {6,20}, {13,39}, {11,43}, {5,21}, {13,45}, {13,20}, {9,31}, {5,37}, {4,17}, {9,21}, {3,36}, {11,42}, {16,28}, {7,40}, {9,23}, {7,21}, {12,18}, {11,18}, {14,26} }; // ET46.10 // Bipartite(16,30) Valencies [15,8] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 116095057920 EdgePairs[46][10]:={ {10,24}, {11,20}, {6,32}, {4,27}, {2,46}, {15,24}, {16,26}, {16,33}, {4,26}, {3,40}, {12,45}, {15,46}, {10,37}, {4,30}, {16,40}, {8,43}, {9,45}, {12,22}, {12,32}, {7,38}, {8,42}, {4,29}, {8,33}, {1,27}, {10,23}, {12,38}, {4,19}, {14,38}, {7,22}, {2,19}, {15,44}, {1,19}, {2,27}, {10,33}, {12,42}, {5,20}, {9,43}, {3,37}, {13,35}, {2,26}, {14,31}, {1,21}, {11,41}, {12,35}, {7,36}, {8,25}, {10,44}, {2,28}, {12,34}, {5,32}, {16,23}, {9,35}, {14,28}, {8,44}, {4,23}, {8,31}, {6,22}, {3,18}, {11,28}, {16,43}, {10,30}, {6,29}, {3,17}, {2,45}, {16,30}, {6,21}, {2,25}, {5,40}, {11,38}, {6,31}, {1,17}, {2,36}, {5,22}, {9,29}, {7,20}, {9,32}, {14,21}, {16,24}, {9,26}, {12,36}, {15,40}, {5,29}, {8,41}, {2,38}, {12,46}, {9,19}, {2,37}, {5,43}, {12,44}, {7,46}, {8,45}, {7,39}, {2,39}, {7,32}, {15,26}, {1,31}, {10,41}, {11,22}, {11,31}, {14,24}, {2,35}, {11,44}, {15,27}, {4,33}, {5,23}, {3,20}, {10,31}, {9,42}, {10,21}, {6,18}, {10,40}, {1,29}, {7,30}, {3,39}, {11,21}, {9,25}, {7,26}, {13,33}, {16,32}, {1,23}, {13,43}, {13,44}, {5,30}, {11,30}, {13,23}, {12,28}, {12,25}, {15,37}, {8,22}, {1,45}, {15,34}, {13,25}, {8,35}, {15,20}, {14,41}, {3,27}, {14,37}, {4,43}, {1,33}, {15,17}, {3,29}, {1,43}, {4,46}, {13,36}, {15,36}, {5,42}, {12,26}, {16,22}, {9,22}, {5,41}, {4,36}, {2,17}, {10,43}, {14,17}, {8,32}, {8,21}, {3,19}, {14,18}, {5,31}, {11,24}, {13,24}, {8,23}, {14,34}, {1,39}, {3,21}, {1,25}, {6,19}, {16,44}, {7,29}, {6,41}, {6,28}, {13,27}, {1,35}, {13,46}, {1,37}, {16,34}, {5,39}, {14,25}, {7,28}, {4,37}, {6,42}, {13,26}, {14,45}, {15,18}, {4,40}, {16,36}, {3,30}, {5,33}, {8,34}, {10,17}, {2,29}, {6,45}, {10,27}, {14,44}, {10,34}, {11,32}, {16,20}, {8,24}, {6,25}, {6,38}, {11,40}, {9,33}, {9,36}, {16,42}, {15,38}, {16,46}, {15,28}, {9,39}, {3,38}, {4,20}, {3,28}, {12,24}, {14,35}, {1,41}, {13,37}, {3,41}, {3,31}, {9,46}, {10,20}, {6,39}, {11,34}, {13,34}, {5,19}, {5,21}, {13,17}, {13,45}, {15,30}, {2,18}, {7,19}, {4,17}, {6,35}, {11,42}, {4,39}, {7,40}, {7,42}, {9,23}, {14,27}, {12,18}, {11,18}, {7,18} }; // ET46.11 // Bipartite(14,32) Valencies [16,7] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 147941222252544 EdgePairs[46][11]:={ {11,17}, {3,33}, {5,17}, {1,20}, {10,24}, {10,25}, {9,28}, {13,32}, {2,33}, {6,16}, {6,32}, {4,27}, {2,46}, {13,21}, {11,35}, {5,34}, {13,40}, {14,19}, {4,26}, {3,40}, {4,30}, {11,25}, {8,30}, {9,45}, {12,22}, {12,32}, {8,28}, {1,32}, {3,45}, {1,27}, {3,25}, {10,23}, {12,38}, {7,41}, {1,40}, {4,19}, {9,44}, {14,38}, {4,31}, {1,19}, {10,33}, {12,42}, {5,20}, {3,37}, {9,43}, {2,26}, {8,39}, {7,34}, {11,41}, {2,41}, {12,34}, {8,15}, {9,35}, {14,28}, {8,44}, {4,23}, {8,31}, {13,29}, {13,16}, {2,42}, {10,15}, {10,22}, {6,22}, {10,30}, {6,29}, {3,17}, {2,45}, {4,38}, {6,21}, {2,25}, {6,40}, {11,33}, {2,34}, {14,33}, {4,22}, {9,29}, {10,38}, {14,36}, {9,26}, {9,27}, {12,20}, {12,36}, {1,44}, {2,38}, {12,46}, {9,19}, {2,37}, {12,44}, {8,45}, {14,30}, {4,42}, {5,25}, {7,32}, {11,15}, {1,31}, {10,41}, {7,43}, {7,25}, {11,31}, {3,44}, {6,30}, {6,43}, {12,16}, {5,23}, {3,20}, {10,31}, {9,34}, {9,42}, {13,18}, {10,40}, {13,31}, {3,32}, {11,21}, {4,35}, {7,16}, {8,36}, {7,26}, {5,18}, {1,23}, {11,23}, {6,24}, {11,29}, {7,17}, {6,46}, {9,37}, {13,23}, {12,28}, {8,22}, {9,20}, {4,15}, {1,28}, {14,41}, {10,46}, {4,43}, {3,29}, {1,43}, {4,46}, {8,37}, {5,28}, {5,42}, {12,26}, {5,41}, {2,17}, {14,17}, {8,21}, {1,24}, {14,22}, {5,31}, {6,27}, {13,24}, {5,44}, {11,39}, {12,40}, {12,30}, {8,23}, {1,39}, {10,32}, {5,36}, {3,21}, {6,19}, {13,15}, {1,15}, {10,39}, {1,35}, {13,42}, {14,20}, {5,39}, {14,25}, {3,16}, {13,26}, {2,21}, {5,33}, {9,18}, {10,17}, {3,24}, {11,37}, {2,29}, {11,27}, {6,45}, {8,38}, {2,22}, {4,34}, {14,44}, {1,16}, {6,38}, {9,36}, {14,43}, {5,26}, {4,18}, {11,19}, {11,45}, {3,28}, {8,20}, {12,24}, {7,27}, {8,46}, {14,35}, {13,37}, {3,41}, {7,24}, {5,15}, {14,46}, {7,33}, {6,37}, {13,34}, {7,35}, {13,39}, {11,43}, {2,30}, {13,45}, {2,18}, {7,19}, {6,35}, {9,21}, {3,36}, {4,39}, {7,40}, {7,42}, {14,27}, {8,29}, {12,18}, {1,36}, {7,18}, {10,16} }; // ET46.12 // Bipartite(14,32) Valencies [16,7] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 176160768 EdgePairs[46][12]:={ {2,44}, {10,24}, {5,17}, {13,32}, {4,27}, {2,46}, {12,29}, {7,15}, {11,35}, {5,34}, {4,26}, {4,16}, {12,45}, {6,17}, {2,23}, {5,38}, {8,28}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {10,23}, {1,40}, {10,26}, {14,38}, {12,39}, {10,33}, {3,35}, {9,43}, {3,37}, {2,26}, {7,34}, {1,21}, {12,35}, {7,36}, {8,25}, {10,44}, {2,28}, {1,30}, {5,32}, {9,35}, {14,28}, {8,44}, {12,37}, {13,29}, {13,16}, {2,42}, {10,22}, {8,16}, {2,45}, {6,21}, {11,38}, {3,46}, {6,40}, {2,34}, {1,17}, {5,22}, {8,19}, {10,38}, {7,20}, {9,27}, {12,20}, {12,36}, {4,41}, {8,41}, {9,19}, {2,37}, {12,44}, {8,45}, {14,30}, {14,40}, {7,39}, {4,42}, {9,41}, {5,25}, {2,39}, {7,32}, {11,15}, {1,31}, {11,22}, {10,28}, {11,31}, {14,24}, {6,30}, {4,33}, {4,21}, {13,22}, {6,18}, {10,40}, {12,43}, {2,16}, {13,31}, {3,32}, {9,25}, {7,16}, {8,36}, {6,33}, {2,32}, {5,18}, {1,23}, {11,23}, {13,43}, {6,24}, {11,29}, {5,30}, {6,44}, {7,17}, {6,46}, {11,30}, {5,46}, {13,23}, {12,28}, {8,22}, {14,42}, {8,35}, {10,42}, {9,20}, {14,41}, {3,27}, {4,28}, {1,33}, {4,43}, {3,29}, {1,43}, {13,36}, {5,42}, {9,22}, {7,31}, {5,41}, {4,36}, {12,27}, {9,40}, {8,32}, {1,42}, {3,19}, {1,24}, {12,23}, {14,22}, {5,31}, {11,24}, {11,39}, {12,19}, {12,40}, {1,39}, {3,21}, {6,19}, {1,46}, {11,46}, {13,15}, {6,41}, {1,15}, {6,28}, {10,39}, {13,27}, {13,42}, {1,37}, {14,25}, {3,16}, {4,37}, {13,26}, {14,45}, {7,23}, {2,21}, {3,30}, {5,33}, {8,34}, {10,17}, {2,29}, {8,38}, {1,26}, {14,44}, {10,36}, {10,34}, {9,17}, {10,18}, {6,25}, {11,40}, {9,33}, {9,36}, {6,34}, {14,43}, {5,26}, {8,18}, {13,38}, {9,38}, {11,19}, {4,25}, {4,20}, {11,45}, {8,20}, {12,24}, {3,41}, {3,31}, {9,24}, {10,20}, {5,15}, {14,46}, {7,33}, {6,37}, {11,34}, {7,35}, {13,39}, {9,15}, {2,30}, {13,45}, {7,37}, {13,20}, {2,18}, {9,31}, {7,19}, {4,17}, {6,35}, {4,44}, {7,21}, {14,27}, {8,29}, {4,32}, {11,18}, {12,21}, {14,29}, {14,26}, {7,18}, {5,16} }; // ET46.13 // Bipartite(10,36) Valencies [18,5] // Diameter 3 Girth 4 // Twin-free Non-VT Non-AT // Automorphism group of order 720 EdgePairs[46][13]:={ {2,44}, {1,11}, {5,17}, {10,25}, {2,33}, {6,16}, {4,27}, {5,34}, {4,24}, {8,12}, {4,26}, {3,22}, {4,16}, {4,30}, {6,17}, {8,43}, {1,13}, {5,38}, {9,45}, {8,28}, {1,32}, {3,13}, {3,25}, {3,15}, {10,23}, {7,44}, {1,40}, {9,44}, {7,22}, {4,31}, {10,33}, {5,20}, {3,37}, {9,43}, {2,26}, {8,39}, {1,21}, {8,25}, {10,44}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {8,15}, {9,35}, {8,44}, {4,23}, {8,27}, {10,15}, {6,22}, {6,29}, {6,21}, {3,34}, {7,12}, {2,25}, {6,40}, {2,34}, {10,38}, {1,18}, {7,11}, {7,20}, {9,32}, {9,26}, {9,27}, {5,11}, {4,41}, {9,19}, {8,14}, {9,41}, {2,39}, {7,32}, {3,12}, {10,41}, {4,45}, {10,28}, {2,35}, {1,22}, {6,43}, {4,33}, {10,29}, {3,20}, {9,34}, {9,42}, {7,30}, {8,17}, {2,16}, {3,39}, {6,33}, {5,18}, {1,23}, {6,24}, {7,17}, {5,24}, {9,37}, {5,46}, {8,13}, {8,22}, {10,42}, {4,15}, {4,13}, {7,14}, {3,27}, {10,46}, {4,28}, {1,33}, {10,45}, {3,29}, {1,43}, {4,46}, {5,28}, {8,26}, {7,31}, {6,15}, {10,43}, {5,12}, {9,40}, {8,32}, {8,21}, {1,42}, {3,19}, {5,31}, {8,23}, {5,36}, {1,25}, {6,19}, {1,46}, {7,29}, {6,14}, {1,37}, {3,16}, {4,37}, {10,35}, {7,23}, {6,36}, {2,21}, {3,30}, {10,17}, {2,29}, {6,45}, {8,38}, {1,26}, {10,36}, {4,14}, {10,18}, {8,24}, {2,40}, {2,31}, {3,42}, {9,39}, {9,38}, {3,38}, {4,11}, {4,20}, {5,13}, {7,27}, {7,45}, {3,41}, {2,12}, {9,24}, {9,46}, {10,20}, {6,39}, {6,37}, {5,19}, {5,21}, {2,30}, {5,35}, {2,18}, {9,31}, {1,34}, {7,19}, {6,35}, {3,36}, {7,40}, {7,42}, {1,36}, {7,18}, {5,16} }; // ET46.14 // Bipartite(10,36) Valencies [18,5] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 8358844170240000000 EdgePairs[46][14]:={ {2,44}, {1,11}, {2,24}, {1,20}, {5,17}, {9,28}, {6,32}, {4,27}, {2,46}, {7,15}, {4,24}, {8,12}, {3,22}, {3,40}, {4,30}, {8,30}, {8,43}, {1,13}, {5,38}, {9,45}, {8,42}, {8,28}, {4,29}, {1,32}, {3,13}, {3,43}, {3,25}, {10,23}, {9,44}, {1,19}, {10,33}, {3,35}, {5,20}, {3,37}, {2,26}, {7,36}, {8,25}, {2,28}, {2,14}, {5,32}, {4,23}, {8,31}, {2,42}, {10,15}, {10,22}, {3,17}, {8,16}, {6,21}, {3,34}, {7,12}, {3,46}, {6,31}, {1,38}, {2,34}, {1,17}, {2,36}, {8,19}, {9,32}, {9,26}, {9,27}, {5,11}, {1,44}, {4,41}, {5,29}, {2,38}, {7,39}, {4,42}, {1,31}, {10,41}, {4,45}, {7,13}, {9,14}, {7,43}, {7,25}, {10,28}, {6,43}, {4,33}, {5,23}, {4,21}, {10,29}, {9,34}, {10,21}, {2,20}, {10,40}, {1,29}, {7,30}, {2,16}, {4,35}, {8,36}, {6,33}, {2,32}, {5,18}, {1,23}, {5,30}, {6,44}, {5,24}, {8,13}, {8,22}, {5,14}, {9,20}, {4,15}, {3,11}, {10,46}, {10,45}, {3,29}, {1,43}, {8,37}, {5,42}, {9,22}, {7,31}, {6,15}, {5,41}, {4,36}, {5,12}, {9,40}, {3,19}, {6,27}, {5,44}, {6,26}, {8,40}, {3,23}, {5,36}, {1,25}, {6,19}, {6,14}, {10,11}, {10,39}, {1,35}, {1,37}, {3,16}, {10,35}, {8,34}, {10,17}, {6,45}, {10,27}, {1,26}, {2,22}, {10,34}, {8,24}, {6,25}, {6,38}, {2,40}, {9,33}, {5,26}, {8,18}, {4,18}, {9,39}, {9,38}, {4,11}, {4,12}, {3,28}, {7,27}, {7,45}, {8,46}, {1,41}, {3,41}, {7,24}, {3,31}, {2,12}, {1,14}, {9,46}, {6,39}, {7,33}, {6,37}, {6,20}, {2,30}, {9,15}, {6,13}, {7,37}, {5,35}, {2,18}, {7,19}, {4,17}, {9,16}, {9,21}, {4,39}, {7,42}, {7,21}, {7,18}, {10,16} }; // ET46.15 // Bipartite(10,36) Valencies [18,5] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 261213880320 EdgePairs[46][15]:={ {2,44}, {1,11}, {5,17}, {10,24}, {9,28}, {2,33}, {6,16}, {6,32}, {7,15}, {5,34}, {3,22}, {4,16}, {8,43}, {5,38}, {9,45}, {7,38}, {4,29}, {3,43}, {7,41}, {1,40}, {2,15}, {2,19}, {1,19}, {2,27}, {3,35}, {2,26}, {1,21}, {8,25}, {10,44}, {2,14}, {1,30}, {9,35}, {8,44}, {4,23}, {8,31}, {9,11}, {10,15}, {10,22}, {3,18}, {2,45}, {6,21}, {3,34}, {2,25}, {3,46}, {6,40}, {6,31}, {5,22}, {4,22}, {8,19}, {9,29}, {1,18}, {3,14}, {5,29}, {4,41}, {2,38}, {2,37}, {8,14}, {7,39}, {9,41}, {2,39}, {1,31}, {3,12}, {10,41}, {7,13}, {7,25}, {10,28}, {6,12}, {6,43}, {10,29}, {2,13}, {9,42}, {2,20}, {10,40}, {7,30}, {4,35}, {9,25}, {7,26}, {1,12}, {6,33}, {2,32}, {5,18}, {1,23}, {6,24}, {5,30}, {6,44}, {7,17}, {8,11}, {5,24}, {9,37}, {5,46}, {8,13}, {1,45}, {8,22}, {8,35}, {5,14}, {1,28}, {4,13}, {3,11}, {7,14}, {10,46}, {4,28}, {1,33}, {10,12}, {1,43}, {3,26}, {4,46}, {8,37}, {8,26}, {5,42}, {6,15}, {5,41}, {9,13}, {5,12}, {9,40}, {8,32}, {1,42}, {3,19}, {1,24}, {6,27}, {3,23}, {8,23}, {10,32}, {5,36}, {6,19}, {7,29}, {6,28}, {9,30}, {10,39}, {1,35}, {5,39}, {4,37}, {4,40}, {6,36}, {2,21}, {3,30}, {8,34}, {9,18}, {10,17}, {3,24}, {6,45}, {8,38}, {10,27}, {4,34}, {1,16}, {10,36}, {10,34}, {9,17}, {2,31}, {9,33}, {5,27}, {5,26}, {3,42}, {4,25}, {3,38}, {4,11}, {4,20}, {8,20}, {7,27}, {7,45}, {8,46}, {3,31}, {10,20}, {6,39}, {5,15}, {7,33}, {6,20}, {7,37}, {2,43}, {4,17}, {9,21}, {9,16}, {3,36}, {7,42}, {9,23}, {4,44}, {7,21}, {4,32}, {1,36}, {7,18}, {10,16} }; // ET46.16 // Bipartite(6,40) Valencies [20,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4161629115065460326400000000 EdgePairs[46][16]:={ {1,15}, {6,39}, {5,14}, {3,15}, {1,43}, {4,42}, {6,10}, {6,18}, {4,14}, {1,11}, {3,29}, {6,14}, {5,30}, {5,42}, {4,8}, {3,7}, {1,31}, {6,23}, {1,40}, {2,20}, {4,40}, {5,34}, {4,16}, {2,37}, {5,41}, {2,33}, {1,44}, {6,7}, {4,44}, {1,32}, {3,45}, {5,13}, {2,28}, {3,31}, {6,34}, {5,26}, {4,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {4,12}, {5,37}, {3,41}, {6,43}, {3,11}, {5,33}, {4,20}, {6,11}, {2,41}, {4,46}, {1,36}, {3,13}, {2,16}, {6,46}, {2,32}, {1,16}, {2,36}, {2,17}, {4,28}, {2,13}, {1,12}, {3,9}, {3,23}, {5,29}, {3,27}, {4,30}, {6,15}, {6,26}, {1,19}, {2,40}, {4,36}, {2,9}, {1,35}, {2,44}, {4,38}, {2,24}, {6,31}, {5,22}, {6,19}, {5,38}, {3,35}, {1,23}, {5,46}, {2,21}, {1,7}, {5,45}, {6,30}, {1,39}, {6,38}, {2,12}, {4,22}, {5,17}, {3,21}, {4,32}, {6,42}, {3,39}, {2,8}, {1,20}, {1,27}, {4,18}, {5,10}, {3,25}, {2,25}, {1,28}, {3,17}, {3,37}, {6,35}, {5,18}, {3,43}, {4,34}, {6,27}, {3,33}, {1,8}, {5,25}, {4,10}, {4,24}, {1,24}, {2,45} }; // ET46.17 // Bipartite(6,40) Valencies [20,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 2063912140800000000 EdgePairs[46][17]:={ {1,15}, {4,35}, {5,32}, {3,15}, {2,38}, {6,10}, {6,18}, {4,14}, {2,22}, {6,14}, {1,31}, {4,27}, {3,7}, {5,35}, {1,40}, {2,20}, {1,25}, {6,13}, {5,24}, {1,9}, {2,33}, {6,32}, {4,44}, {1,32}, {6,40}, {5,7}, {5,13}, {2,28}, {6,45}, {3,31}, {6,34}, {2,18}, {6,22}, {5,21}, {3,19}, {4,12}, {5,37}, {3,41}, {1,34}, {2,14}, {5,23}, {3,11}, {4,37}, {2,10}, {4,20}, {2,41}, {1,10}, {4,46}, {1,17}, {6,46}, {1,16}, {6,21}, {2,36}, {2,17}, {4,28}, {3,9}, {4,29}, {4,43}, {5,43}, {5,19}, {5,15}, {6,8}, {3,23}, {4,45}, {6,37}, {5,29}, {2,42}, {3,27}, {2,34}, {4,30}, {6,26}, {4,36}, {4,21}, {2,9}, {1,26}, {2,44}, {6,29}, {4,38}, {4,11}, {3,35}, {1,23}, {5,27}, {1,7}, {5,45}, {6,30}, {2,46}, {5,8}, {1,39}, {6,38}, {2,12}, {4,22}, {3,28}, {5,31}, {3,12}, {1,42}, {6,16}, {1,41}, {3,44}, {6,42}, {3,39}, {5,11}, {3,25}, {2,26}, {3,20}, {1,33}, {2,25}, {3,36}, {3,17}, {6,24}, {3,43}, {3,33}, {1,8}, {5,16}, {5,39}, {4,13}, {2,30}, {1,18}, {4,19}, {5,40}, {1,24} }; // ET46.18 // Bipartite(6,40) Valencies [20,3] // Diameter 3 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3804202857922560 EdgePairs[46][18]:={ {4,35}, {5,32}, {6,39}, {2,38}, {4,42}, {6,18}, {1,11}, {3,29}, {6,14}, {5,30}, {5,42}, {6,36}, {4,8}, {4,27}, {3,7}, {1,31}, {2,11}, {5,35}, {1,46}, {1,40}, {2,20}, {3,32}, {1,9}, {2,33}, {6,25}, {5,13}, {2,28}, {3,34}, {6,45}, {6,34}, {2,18}, {6,9}, {5,26}, {3,19}, {1,29}, {4,12}, {2,14}, {5,23}, {5,33}, {4,37}, {2,10}, {2,41}, {2,31}, {2,23}, {1,10}, {4,7}, {1,36}, {1,17}, {3,13}, {6,46}, {1,16}, {4,28}, {3,14}, {2,13}, {3,9}, {3,22}, {5,43}, {5,15}, {6,8}, {3,23}, {4,45}, {4,31}, {3,27}, {2,34}, {6,15}, {6,26}, {1,19}, {2,40}, {4,21}, {4,17}, {4,15}, {4,25}, {1,26}, {2,44}, {6,29}, {4,38}, {2,24}, {4,11}, {3,42}, {5,22}, {6,19}, {2,43}, {5,46}, {2,21}, {1,7}, {5,45}, {1,39}, {6,38}, {5,20}, {4,22}, {5,36}, {3,24}, {3,12}, {6,16}, {1,41}, {3,44}, {4,32}, {3,39}, {2,8}, {1,37}, {1,20}, {1,27}, {4,18}, {5,10}, {5,12}, {3,17}, {3,37}, {6,24}, {6,35}, {3,43}, {6,44}, {4,41}, {3,33}, {1,30}, {5,16}, {2,30}, {1,21}, {5,25}, {5,40}, {6,28} }; // ET46.19 // Bipartite(6,40) Valencies [20,3] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 754974720 EdgePairs[46][19]:={ {4,35}, {5,32}, {6,39}, {6,12}, {5,14}, {3,15}, {2,38}, {4,42}, {6,10}, {6,18}, {4,14}, {1,11}, {6,36}, {4,8}, {3,7}, {1,31}, {3,46}, {6,17}, {2,11}, {1,40}, {5,34}, {1,25}, {4,16}, {2,37}, {5,24}, {3,32}, {5,41}, {6,32}, {6,25}, {1,44}, {6,7}, {3,30}, {6,40}, {3,10}, {2,28}, {6,45}, {3,31}, {2,18}, {2,15}, {5,26}, {5,9}, {6,22}, {5,21}, {2,29}, {3,19}, {3,41}, {1,34}, {5,23}, {3,11}, {4,37}, {2,10}, {2,31}, {4,39}, {3,13}, {1,22}, {4,33}, {2,17}, {4,28}, {4,29}, {4,43}, {5,43}, {3,23}, {6,37}, {5,29}, {3,27}, {4,36}, {4,17}, {2,35}, {4,15}, {2,9}, {2,44}, {2,24}, {6,19}, {5,38}, {3,35}, {5,46}, {1,7}, {6,30}, {2,46}, {6,38}, {5,20}, {4,22}, {5,36}, {3,26}, {3,12}, {1,42}, {6,16}, {6,20}, {3,21}, {1,14}, {1,41}, {6,42}, {3,39}, {2,8}, {1,20}, {1,27}, {1,13}, {2,26}, {1,33}, {5,12}, {2,25}, {1,28}, {4,9}, {5,18}, {3,43}, {4,34}, {6,27}, {5,44}, {1,45}, {3,33}, {4,23}, {1,8}, {5,16}, {4,13}, {1,21}, {2,30}, {4,19}, {5,40}, {1,24}, {2,45} }; // ET46.20 // Bipartite(4,42) Valencies [21,2] // Diameter 4 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 393363863113826304000000 EdgePairs[46][20]:={ {2,11}, {2,14}, {4,8}, {4,9}, {2,44}, {4,39}, {2,26}, {3,12}, {1,46}, {2,32}, {2,30}, {1,29}, {2,29}, {4,44}, {4,34}, {2,24}, {1,37}, {1,40}, {1,10}, {1,43}, {4,10}, {3,21}, {3,42}, {3,27}, {4,40}, {3,33}, {2,6}, {2,36}, {3,37}, {1,31}, {4,16}, {3,9}, {3,24}, {2,12}, {4,32}, {4,33}, {1,7}, {1,16}, {3,7}, {2,20}, {3,15}, {4,45}, {4,38}, {2,38}, {2,18}, {3,25}, {4,27}, {4,21}, {4,20}, {3,19}, {3,30}, {2,5}, {3,18}, {3,31}, {1,5}, {4,15}, {4,28}, {1,17}, {4,22}, {3,6}, {3,45}, {3,39}, {2,42}, {1,28}, {2,17}, {3,13}, {2,23}, {1,13}, {2,35}, {1,19}, {2,41}, {4,26}, {1,41}, {1,22}, {2,8}, {4,14}, {1,34}, {1,35}, {1,23}, {4,46}, {1,11}, {1,25}, {3,36}, {3,43} }; // ET46.21 // Bipartite(23,23) Valencies [22,22] // Diameter 3 Girth 4 // Twin-free VT AT // Automorphism group of order 51704033477769953280000 EdgePairs[46][21]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {20,26}, {3,29}, {16,28}, {20,33}, {4,26}, {20,25}, {19,41}, {22,37}, {14,29}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {19,37}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {6,28}, {5,43}, {22,25}, {2,30}, {14,25}, {10,27}, {1,41}, {4,30}, {21,35}, {20,42}, {2,38}, {8,24}, {23,45}, {12,27}, {6,34}, {4,38}, {11,39}, {21,31}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {22,28}, {18,37}, {15,45}, {20,29}, {10,42}, {14,40}, {9,41}, {17,43}, {21,46}, {17,45}, {23,34}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {19,40}, {16,26}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {21,30}, {21,44}, {23,33}, {20,44}, {5,45}, {21,42}, {4,41}, {8,39}, {22,32}, {7,34}, {22,45}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {23,24}, {18,35}, {15,24}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {5,46}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {20,39}, {5,33}, {4,39}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {22,41}, {18,26}, {4,45}, {22,26}, {2,28}, {20,43}, {1,27}, {9,25}, {4,44}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {23,39}, {10,43}, {21,25}, {5,29}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {22,46}, {8,34}, {9,29}, {23,46}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {22,38}, {19,32}, {7,37}, {21,45}, {1,28}, {3,43}, {3,36}, {14,36}, {7,42}, {17,46}, {6,43}, {23,26}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {23,32}, {7,36}, {9,39}, {22,24}, {13,26}, {14,37}, {10,46}, {22,33}, {11,24}, {7,43}, {20,31}, {11,45}, {10,28}, {9,44}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {18,44}, {21,29}, {23,28}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {16,29}, {8,41}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {4,40}, {23,38}, {16,36}, {1,39}, {18,43}, {6,45}, {7,40}, {17,37}, {18,25}, {21,27}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {21,43}, {15,29}, {20,38}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {7,46}, {19,28}, {20,37}, {11,33}, {1,34}, {7,25}, {22,40}, {13,37}, {8,27}, {6,46}, {19,43}, {16,27}, {23,44}, {14,46}, {9,30}, {5,40}, {3,46}, {22,36}, {22,30}, {18,30}, {1,40}, {10,26}, {17,31}, {8,29}, {15,44}, {23,41}, {19,36}, {9,34}, {15,25}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {6,32}, {15,31}, {10,35}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {16,40}, {9,33}, {20,35}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {13,31}, {23,40}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {10,34}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {20,34}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {2,29}, {20,30}, {14,44}, {19,27}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {2,46}, {3,39}, {10,41}, {12,34}, {23,35}, {15,41}, {19,45}, {16,44}, {23,31}, {17,41}, {11,30}, {8,43}, {7,39}, {10,44}, {1,33}, {12,30}, {6,33}, {2,32}, {19,26}, {22,34}, {9,36}, {10,40}, {6,27}, {21,41}, {12,40}, {17,40}, {7,45}, {20,41}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {16,32}, {9,32}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {16,45}, {22,35}, {5,39}, {12,43}, {19,34}, {10,45}, {23,37}, {23,42}, {3,40}, {20,46}, {23,27}, {22,42}, {12,36}, {22,44}, {21,39}, {3,33}, {1,24}, {19,25}, {15,26}, {18,41}, {21,28}, {23,36}, {16,38}, {22,43}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {13,45}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.22 // Bipartite(23,23) Valencies [23,23] // Diameter 2 Girth 4 // Has twins VT AT // Automorphism group of order 1336653538935178044929642368586691379200000000 EdgePairs[46][22]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {20,26}, {3,29}, {16,28}, {20,33}, {4,26}, {20,25}, {19,41}, {22,37}, {14,29}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {19,37}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {6,28}, {5,43}, {12,32}, {22,25}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {20,42}, {2,38}, {8,24}, {23,45}, {12,27}, {6,34}, {4,38}, {11,39}, {21,31}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {22,28}, {18,37}, {15,45}, {20,29}, {10,42}, {14,40}, {9,41}, {17,43}, {21,46}, {17,45}, {23,34}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {19,40}, {16,26}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {21,30}, {21,44}, {23,33}, {20,44}, {5,45}, {21,42}, {4,41}, {8,39}, {22,32}, {7,34}, {22,45}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {23,24}, {18,35}, {15,24}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {5,46}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {20,39}, {5,33}, {4,39}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {22,41}, {18,26}, {4,45}, {22,26}, {2,28}, {20,43}, {1,27}, {9,25}, {4,44}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {23,39}, {10,43}, {5,29}, {21,25}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {19,44}, {22,46}, {8,34}, {9,29}, {23,46}, {4,33}, {15,40}, {18,34}, {21,34}, {1,44}, {10,31}, {22,38}, {19,32}, 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{15,44}, {23,41}, {19,36}, {9,34}, {15,25}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {16,40}, {9,33}, {20,35}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {13,31}, {23,40}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {20,34}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {2,29}, {20,30}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {23,35}, {15,41}, {19,45}, {16,44}, {23,31}, {17,41}, {11,30}, {8,43}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {6,33}, {2,32}, {19,26}, {22,34}, {9,36}, {10,40}, {6,27}, {12,40}, {21,41}, {17,40}, {7,45}, {20,41}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {16,32}, {9,32}, {18,32}, {21,32}, {23,30}, {21,26}, {22,31}, {16,45}, {22,35}, {5,39}, {12,43}, {19,34}, {10,45}, {23,37}, {23,42}, {3,40}, {20,46}, {23,27}, {22,42}, {12,36}, {22,44}, {21,39}, {3,33}, {1,24}, {19,25}, {15,26}, {18,41}, {23,43}, {21,28}, {23,36}, {16,38}, {22,43}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.23 // Bipartite(22,24) Valencies [24,22] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 697384455096614632137204714045230284800000000 EdgePairs[46][23]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {20,26}, {3,29}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {22,37}, {14,29}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {19,37}, {17,29}, {8,26}, {10,29}, {15,33}, {6,28}, {5,43}, {12,32}, {22,25}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {8,24}, {2,38}, {20,42}, {12,27}, {6,34}, {4,38}, {11,39}, {21,31}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {22,28}, {18,37}, {15,45}, {20,29}, {10,42}, {14,40}, {9,41}, {17,43}, {21,46}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {19,40}, {16,26}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {21,44}, {20,44}, {5,45}, {21,42}, {4,41}, {8,39}, {22,32}, {7,34}, {22,45}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {5,46}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {22,41}, {18,26}, {14,23}, {4,45}, {22,26}, {2,28}, {1,27}, {20,43}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {5,29}, {21,25}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {19,44}, {22,46}, {8,34}, {9,29}, {4,33}, {15,40}, {18,34}, {21,34}, {1,44}, {10,31}, {22,38}, {13,23}, {19,32}, {7,37}, {21,45}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {17,46}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {7,36}, {9,39}, {22,24}, {13,26}, {14,37}, {10,46}, {22,33}, {11,24}, {7,43}, {11,45}, {8,33}, {20,31}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {21,29}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {4,40}, {16,36}, {1,39}, {18,43}, {6,45}, {7,40}, {17,37}, {18,25}, {21,27}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {21,23}, {21,43}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {7,46}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {22,40}, {13,37}, {8,27}, {5,30}, {6,46}, {19,43}, {16,27}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {22,36}, {22,30}, {18,30}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {15,44}, {19,36}, {9,34}, {15,25}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {8,42}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {12,23}, {13,31}, {5,31}, {22,23}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {20,34}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {20,30}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {19,45}, {16,44}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {22,34}, {9,36}, {10,40}, {6,27}, {12,40}, {21,41}, {17,40}, {7,45}, {8,46}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {16,32}, {9,32}, {18,32}, {21,32}, {21,26}, {22,31}, {16,45}, {22,35}, {5,39}, {12,43}, {19,34}, {10,45}, {3,40}, {20,46}, {22,42}, {12,36}, {22,44}, {21,39}, {3,33}, {1,24}, {19,25}, {15,26}, {18,41}, {21,28}, {16,38}, {22,43}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.24 // Bipartite(21,25) Valencies [25,21] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 792482335337062081974096265960488960000000000 EdgePairs[46][24]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {3,29}, {20,26}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {14,29}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {20,22}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {8,24}, {2,38}, {20,42}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {21,31}, {16,33}, {7,26}, {19,38}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {10,22}, {18,37}, {15,45}, {20,29}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {21,46}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {19,40}, {16,26}, {3,22}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {21,44}, {20,44}, {5,45}, {21,42}, {4,41}, {9,22}, {8,39}, {7,34}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {5,46}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {18,26}, {14,23}, {4,45}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {1,29}, {2,34}, {21,22}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {5,29}, {21,25}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {21,45}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {17,46}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {20,31}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {21,29}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {4,40}, {16,36}, {1,39}, {18,43}, {6,45}, {7,40}, {17,37}, {18,25}, {21,27}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {21,23}, {21,43}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {19,43}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {19,36}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {8,42}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {20,34}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {20,30}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {16,44}, {19,45}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {9,36}, {10,40}, {6,27}, {12,40}, {21,41}, {17,40}, {7,45}, {8,46}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {21,32}, {21,26}, {16,45}, {5,39}, {12,43}, {19,34}, {10,45}, {3,40}, {20,46}, {12,36}, {21,39}, {3,33}, {1,24}, {19,25}, {15,26}, {18,41}, {21,28}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {21,38}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.25 // Bipartite(20,26) Valencies [26,20] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 981168605655410196729833472141557760000000000 EdgePairs[46][25]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {3,29}, {20,26}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {14,29}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {8,36}, {9,21}, {13,43}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {20,22}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {20,42}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {10,22}, {18,37}, {15,45}, {20,29}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {17,42}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {20,44}, {5,45}, {4,41}, {9,22}, {8,39}, {7,34}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {5,46}, {18,42}, {19,21}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {8,21}, {18,26}, {14,23}, {4,45}, {18,21}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {5,29}, {9,28}, {20,40}, {19,24}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {17,46}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {20,31}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {4,40}, {16,36}, {1,39}, {6,45}, {18,43}, {7,40}, {17,37}, {18,25}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {19,43}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {19,36}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {8,42}, {20,21}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {20,34}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {20,24}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {20,30}, {14,21}, {14,44}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {16,44}, {7,21}, {19,45}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {7,45}, {8,46}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {19,34}, {10,45}, {3,40}, {20,46}, {12,36}, {10,21}, {3,33}, {1,24}, {19,25}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {20,36}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.26 // Bipartite(19,27) Valencies [27,19] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1324577617634803765585275187391102976000000000 EdgePairs[46][26]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {3,29}, {16,28}, {4,26}, {19,41}, {14,29}, {2,20}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {4,28}, {8,36}, {9,21}, {8,20}, {13,43}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {8,44}, {18,28}, {4,34}, {13,29}, {10,22}, {18,37}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {17,42}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {18,35}, {1,26}, {9,27}, {18,31}, {1,25}, {5,46}, {18,42}, {19,21}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {4,45}, {18,21}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {18,20}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {3,20}, {5,29}, {9,28}, {19,24}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,20}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {14,36}, {7,42}, {17,46}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {4,40}, {16,36}, {1,39}, {6,45}, {18,43}, {7,40}, {17,37}, {18,25}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {7,25}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {19,43}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {19,36}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {4,20}, {16,44}, {7,21}, {19,45}, {17,41}, {11,30}, {8,43}, {2,23}, {19,20}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {7,45}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {19,34}, {10,45}, {7,20}, {3,40}, {12,36}, {10,21}, {3,33}, {1,24}, {19,25}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {2,35}, {17,33}, {10,32}, {16,24}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.27 // Bipartite(18,28) Valencies [28,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1952009120724973970336195012997414912000000000 EdgePairs[46][27]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {3,29}, {16,28}, {4,26}, {14,29}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {4,28}, {8,36}, {9,21}, {8,20}, {13,43}, {17,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {18,28}, {4,34}, {17,19}, {13,29}, {10,22}, {18,37}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {11,29}, {14,27}, {17,42}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {18,35}, {1,26}, {9,27}, {18,31}, {1,25}, {5,46}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {18,26}, {4,45}, {18,21}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {18,20}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {7,37}, {1,28}, {3,43}, {3,36}, {14,36}, {7,42}, {17,46}, {6,43}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {18,19}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {6,45}, {18,43}, {7,40}, {17,37}, {14,19}, {18,25}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {14,20}, {11,33}, {1,34}, {7,25}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {3,34}, {18,39}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {16,44}, {7,21}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {7,45}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {10,45}, {7,20}, {3,40}, {16,19}, {12,36}, {10,21}, {3,33}, {1,24}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {2,19}, {17,30}, {5,24}, {7,33}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.28 // Bipartite(17,29) Valencies [29,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 3144903583390235841097203076495835136000000000 EdgePairs[46][28]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {9,18}, {3,29}, {16,28}, {4,26}, {14,29}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {5,18}, {17,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {4,34}, {17,19}, {13,29}, {10,22}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {17,18}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {17,42}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {1,26}, {9,27}, {1,25}, {5,46}, {15,34}, {12,44}, {16,42}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {4,45}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,18}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {7,37}, {1,28}, {14,18}, {3,43}, {3,36}, {14,36}, {7,42}, {17,46}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {6,45}, {7,40}, {17,37}, {14,19}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {14,20}, {11,33}, {1,34}, {7,25}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {4,27}, {14,24}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {15,18}, {17,34}, {12,26}, {1,45}, {10,30}, {6,18}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {7,21}, {16,44}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {7,45}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {14,45}, {16,18}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {10,45}, {7,20}, {3,40}, {16,19}, {12,36}, {7,18}, {10,21}, {3,33}, {1,24}, {17,21}, {4,18}, {15,26}, {2,18}, {16,38}, {12,37}, {2,19}, {17,30}, {5,24}, {7,33}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {4,19}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.29 // Bipartite(16,30) Valencies [30,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5549829853041592660759770134992650240000000000 EdgePairs[46][29]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {15,17}, {4,46}, {10,17}, {3,29}, {9,18}, {16,28}, {4,26}, {14,29}, {2,20}, {2,26}, {16,17}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {5,18}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {4,34}, {13,29}, {10,22}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {15,20}, {14,33}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {1,26}, {9,27}, {1,25}, {5,46}, {15,34}, {12,44}, {16,42}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {6,39}, {2,44}, {2,45}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {4,45}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,18}, {9,17}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {7,37}, {1,28}, {14,18}, {3,43}, {1,17}, {3,36}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {12,17}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {6,45}, {7,40}, {14,19}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {14,20}, {11,33}, {1,34}, {7,25}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {8,17}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {8,29}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {2,33}, {6,32}, {15,31}, {10,35}, {4,27}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {6,17}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {11,17}, {15,18}, {12,26}, {1,45}, {10,30}, {6,18}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {7,21}, {16,44}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {7,45}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {6,38}, {2,17}, {11,40}, {13,42}, {14,45}, {16,18}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {10,45}, {7,20}, {3,40}, {16,19}, {12,36}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {15,26}, {2,18}, {16,38}, {12,37}, {2,19}, {5,24}, {7,33}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {10,32}, {16,24}, {4,19}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.30 // Bipartite(15,31) Valencies [31,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 10752795340268085780222054636548259840000000000 EdgePairs[46][30]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {15,17}, {4,46}, {10,17}, {3,29}, {9,18}, {4,26}, {14,29}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {15,16}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {5,18}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {5,43}, {14,16}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {2,21}, {7,26}, {11,27}, {8,44}, {4,34}, {13,29}, {10,22}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {15,20}, {14,33}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {3,22}, {6,19}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {10,23}, {15,24}, {1,26}, {9,27}, {1,25}, {5,46}, {10,16}, {12,44}, {15,34}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {7,16}, {1,22}, {6,24}, {6,39}, {2,44}, {2,45}, {1,42}, {8,21}, {9,20}, {14,23}, {4,45}, {3,16}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {14,35}, {15,27}, {12,41}, {5,42}, {11,32}, {3,31}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,18}, {9,17}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {5,16}, {7,37}, {1,28}, {14,18}, {3,43}, {1,17}, {3,36}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {12,17}, {9,42}, {9,19}, {13,35}, {13,32}, {10,24}, {2,25}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {15,30}, {3,19}, {4,40}, {2,16}, {1,39}, {6,45}, {7,40}, {14,19}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {14,20}, {11,33}, {1,34}, {11,16}, {7,25}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {14,46}, {9,30}, {5,40}, {3,46}, {8,17}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {8,29}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {13,28}, {2,33}, {6,32}, {15,31}, {10,35}, {4,27}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {6,17}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {15,19}, {9,33}, {8,16}, {8,42}, {8,32}, {7,38}, {14,30}, {15,38}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {11,17}, {15,18}, {4,16}, {12,26}, {1,45}, {10,30}, {6,18}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {6,16}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {7,21}, {12,16}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {6,27}, {12,40}, {7,45}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {6,38}, {2,17}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {9,16}, {9,32}, {5,39}, {12,43}, {1,21}, {6,21}, {10,45}, {7,20}, {3,40}, {12,36}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {15,26}, {2,18}, {12,37}, {1,16}, {2,19}, {5,24}, {7,33}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {10,32}, {4,19}, {13,16}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.31 // Bipartite(14,32) Valencies [32,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 22939296725905249664473716557969620992000000000 EdgePairs[46][31]:={ {13,25}, {3,42}, {13,40}, {6,36}, {11,42}, {4,46}, {9,18}, {3,29}, {10,17}, {4,26}, {14,29}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {13,43}, {5,18}, {14,15}, {8,26}, {10,29}, {7,17}, {13,22}, {6,28}, {5,43}, {14,16}, {12,32}, {2,30}, {14,25}, {7,15}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {2,21}, {7,26}, {11,27}, {8,44}, {4,34}, {13,29}, {10,22}, {12,22}, {14,40}, {10,42}, {9,41}, {14,33}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {13,15}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {3,22}, {6,19}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {2,36}, {12,38}, {11,44}, {13,33}, {10,23}, {1,26}, {9,27}, {1,25}, {5,46}, {10,16}, {12,44}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {7,16}, {1,22}, {6,24}, {6,39}, {2,44}, {2,45}, {1,42}, {8,21}, {9,20}, {14,23}, {4,45}, {3,16}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {9,17}, {10,18}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {1,44}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {7,37}, {1,28}, {14,18}, {3,43}, {1,17}, {3,36}, {14,36}, {7,42}, {6,43}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {12,17}, {9,42}, {9,19}, {13,35}, {13,32}, {10,24}, {2,25}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {10,36}, {12,20}, {8,41}, {13,46}, {2,40}, {9,43}, {3,19}, {4,40}, {2,16}, {1,39}, {6,45}, {7,40}, {14,19}, {10,37}, {6,44}, {2,42}, {9,46}, {7,35}, {4,42}, {14,41}, {4,15}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {12,15}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {14,20}, {11,33}, {1,34}, {11,16}, {7,25}, {13,37}, {8,27}, {5,30}, {6,46}, {14,46}, {9,30}, {5,40}, {3,46}, {8,17}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {8,29}, {7,22}, {9,34}, {6,22}, {5,19}, {13,28}, {2,33}, {6,32}, {10,35}, {4,27}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {1,19}, {5,41}, {13,41}, {6,17}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {9,33}, {8,16}, {8,42}, {8,32}, {7,38}, {14,30}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {8,15}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {11,17}, {4,16}, {12,26}, {1,45}, {10,30}, {6,18}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {6,16}, {7,44}, {11,46}, {4,31}, {2,15}, {3,41}, {10,33}, {10,39}, {13,34}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {2,46}, {3,39}, {10,41}, {11,15}, {6,26}, {12,34}, {8,19}, {4,20}, {7,21}, {12,16}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {6,27}, {12,40}, {7,45}, {8,46}, {14,38}, {6,30}, {11,25}, {6,38}, {2,17}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {9,16}, {9,32}, {5,39}, {12,43}, {1,21}, {9,15}, {6,21}, {10,45}, {7,20}, {3,40}, {12,36}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {2,18}, {12,37}, {1,16}, {2,19}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {7,19}, {2,35}, {10,32}, {4,19}, {13,16}, {10,15}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET46.32 // Bipartite(13,33) Valencies [33,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 54071199425348088494830903315214106624000000000 EdgePairs[46][32]:={ {13,21}, {6,38}, {11,40}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {5,45}, {3,26}, {12,22}, {8,26}, {13,37}, {1,40}, {13,39}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {2,46}, {13,43}, {13,27}, {6,14}, {13,40}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {9,18}, {2,34}, {10,17}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,30}, {9,33}, {12,46}, {1,17}, {4,16}, {7,45}, {8,46}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {12,26}, {13,30}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {13,24}, {2,15}, {12,23}, {5,37}, {13,20}, {13,42}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {6,46}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {13,26}, {6,24}, {2,29}, {13,16}, {5,34}, {1,38}, {1,26}, {13,19}, {3,17}, {2,36}, {13,41}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {9,46}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {11,22}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {13,17}, {7,19}, {4,32}, {2,44}, {1,30}, {13,18}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {10,46}, {11,33}, {13,25}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {7,46}, {8,45}, {3,29}, {12,17}, {13,36}, {1,41}, {2,23}, {4,45}, {10,19}, {9,22}, {12,41}, {9,19}, {3,44}, {11,44}, {13,45}, {3,25}, {11,34}, {7,35}, {11,46}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {13,22}, {1,25}, {6,19}, {2,20}, {9,16}, {4,17}, {13,31}, {5,39}, {9,30}, {3,32}, {7,28}, {6,45}, {12,18}, {2,16}, {8,34}, {13,29}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {13,38}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {13,14}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {12,14}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {9,23}, {7,21}, {8,36}, {13,44}, {8,27}, {2,45}, {5,46}, {3,33}, {13,32}, {1,45}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {4,46}, {8,43}, {2,31}, {11,45}, {1,33}, {12,36}, {3,45}, {3,14}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {13,34}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {13,35}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {13,33}, {1,15}, {13,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {13,23}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {13,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,25}, {10,23}, {9,43}, {1,46}, {4,19}, {8,39}, {3,37}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {13,46}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {3,46}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET46.33 // Bipartite(12,34) Valencies [34,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 141416983112448846832634670209021509632000000000 EdgePairs[46][33]:={ {6,38}, {11,40}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {5,45}, {3,26}, {12,22}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {2,46}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {10,17}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {12,46}, {1,17}, {4,16}, {7,45}, {8,46}, {4,13}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {1,13}, {12,26}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {6,46}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {9,46}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {10,46}, {11,33}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {7,46}, {8,45}, {3,29}, {12,17}, {1,41}, {2,23}, {10,13}, {4,45}, {10,19}, {9,22}, {12,41}, {3,44}, {9,19}, {11,44}, {3,25}, {11,34}, {7,35}, {11,13}, {11,46}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {3,32}, {7,28}, {6,45}, {12,18}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {12,14}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {2,45}, {5,46}, {3,33}, {1,45}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {4,46}, {8,43}, {2,31}, {11,45}, {1,33}, {12,36}, {3,45}, {3,14}, {5,26}, {12,44}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {12,39}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {1,46}, {4,19}, {8,39}, {3,37}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {3,46}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET46.34 // Bipartite(11,35) Valencies [35,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 412466200744642469928517788109646069760000000000 EdgePairs[46][34]:={ {6,38}, {11,40}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {5,45}, {3,26}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {2,46}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {7,45}, {8,46}, {4,13}, {8,37}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {6,46}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {9,46}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {10,46}, {11,33}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {7,46}, {8,45}, {3,29}, {1,41}, {2,23}, {10,13}, {4,45}, {10,19}, {9,22}, {3,44}, {9,19}, {11,44}, {3,25}, {11,34}, {7,35}, {11,13}, {11,46}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {6,45}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {2,45}, {5,46}, {3,33}, {1,45}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {4,46}, {8,43}, {2,31}, {11,45}, {1,33}, {3,45}, {3,14}, {5,26}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {11,19}, {8,33}, {4,12}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {1,46}, {4,19}, {8,39}, {3,37}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {11,26}, {3,46}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET46.35 // Bipartite(10,36) Valencies [36,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1349889384255193537947876397449750773760000000000 EdgePairs[46][35]:={ {6,38}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {5,43}, {5,45}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {4,37}, {4,40}, {8,31}, {2,46}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {1,12}, {10,42}, {6,29}, {9,11}, {1,20}, {3,18}, {8,16}, {2,34}, {9,18}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {7,45}, {8,46}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {6,46}, {10,35}, {6,44}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {9,46}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {10,46}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {7,46}, {8,45}, {3,29}, {1,41}, {2,23}, {10,13}, {4,45}, {10,19}, {9,22}, {4,11}, {3,44}, {9,19}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {2,45}, {5,46}, {3,33}, {2,11}, {1,45}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {4,46}, {8,43}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {1,46}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {3,46}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET46.36 // Bipartite(9,37) Valencies [37,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4994590721744216090407142670564077862912000000000 EdgePairs[46][36]:={ {6,38}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {4,28}, {5,43}, {9,10}, {5,45}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {4,37}, {4,40}, {8,31}, {2,46}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {9,11}, {1,20}, {3,18}, {2,34}, {8,16}, {9,18}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {7,45}, {8,46}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {2,10}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {6,46}, {6,44}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {1,18}, {3,38}, {8,19}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {9,46}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {9,38}, {4,10}, {9,26}, {5,14}, {7,46}, {8,45}, {3,29}, {1,41}, {2,23}, {4,45}, {9,22}, {4,11}, {3,44}, {9,19}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {9,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {2,45}, {8,27}, {5,46}, {3,33}, {2,11}, {1,45}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {4,46}, {8,43}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {4,12}, {8,14}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {5,10}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {9,43}, {1,46}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {8,25}, {2,32}, {6,33}, {2,14}, {3,46}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET46.37 // Bipartite(8,38) Valencies [38,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 21088271936253356826163491275714995421184000000000 EdgePairs[46][37]:={ {6,38}, {6,25}, {5,38}, {5,22}, {4,28}, {5,43}, {5,45}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {6,9}, {4,37}, {4,40}, {8,31}, {2,46}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {1,20}, {3,18}, {2,34}, {8,16}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {7,45}, {8,46}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {8,9}, {2,10}, {3,9}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {1,36}, {6,18}, {1,29}, {6,46}, {6,44}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {1,43}, {8,42}, {4,22}, {1,18}, {3,38}, {8,19}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {4,9}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {4,41}, {8,41}, {4,10}, {5,14}, {7,46}, {8,45}, {3,29}, {1,41}, {2,23}, {4,45}, {4,11}, {3,44}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {5,39}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {8,34}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {7,29}, {2,28}, {8,29}, {7,21}, {8,36}, {2,45}, {8,27}, {5,46}, {3,33}, {2,11}, {1,45}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {4,46}, {8,11}, {8,43}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {5,9}, {8,33}, {4,12}, {7,10}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {7,38}, {5,42}, {2,38}, {7,9}, {5,10}, {7,44}, {8,28}, {7,43}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {1,46}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {5,36}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {8,25}, {2,9}, {2,32}, {6,33}, {2,14}, {3,46}, {5,33}, {5,30}, {6,40} }; // ET46.38 // Bipartite(7,39) Valencies [39,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 102805325689235114527547019969110602678272000000000 EdgePairs[46][38]:={ {6,38}, {6,25}, {5,38}, {5,22}, {3,8}, {4,28}, {5,43}, {5,45}, {3,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {3,35}, {3,19}, {5,15}, {1,19}, {3,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {6,9}, {4,37}, {4,40}, {2,46}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {1,20}, {3,18}, {2,34}, {2,25}, {4,24}, {4,43}, {4,30}, {1,17}, {1,9}, {4,16}, {7,45}, {1,10}, {4,13}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {2,10}, {3,9}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {1,36}, {6,18}, {1,29}, {6,46}, {6,44}, {4,23}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {6,34}, {1,43}, {4,22}, {1,18}, {3,38}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {2,8}, {5,35}, {4,9}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {6,36}, {3,30}, {3,16}, {2,24}, {3,24}, {6,16}, {7,12}, {4,41}, {4,10}, {5,14}, {7,46}, {3,29}, {1,41}, {2,23}, {4,45}, {4,11}, {3,44}, {3,25}, {6,8}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {7,8}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {5,39}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {5,8}, {4,15}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {7,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {7,29}, {2,28}, {7,21}, {2,45}, {5,46}, {3,33}, {2,11}, {1,45}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {4,46}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {2,37}, {4,42}, {4,8}, {5,29}, {4,25}, {3,28}, {7,31}, {5,9}, {1,8}, {4,12}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {7,38}, {5,42}, {2,38}, {7,9}, {5,10}, {7,44}, {7,43}, {4,20}, {1,27}, {5,44}, {5,13}, {5,25}, {1,46}, {4,19}, {3,37}, {3,12}, {7,13}, {5,36}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {2,9}, {2,32}, {6,33}, {2,14}, {3,46}, {5,33}, {5,30}, {6,40} }; // ET46.39 // Bipartite(6,40) Valencies [40,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 587459003938486368728840114109203443875840000000000 EdgePairs[46][39]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {2,46}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {2,45}, {4,38}, {6,21}, {3,34}, {2,25}, {5,40}, {3,46}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {1,44}, {4,41}, {2,10}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {6,8}, {5,25}, {2,39}, {1,31}, {3,12}, {4,45}, {2,35}, {1,22}, {3,44}, {6,12}, {6,30}, {6,43}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {6,44}, {6,46}, {5,24}, {5,7}, {5,46}, {1,45}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {3,26}, {4,46}, {5,28}, {5,42}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {5,44}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {6,19}, {1,46}, {6,9}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {6,42}, {4,40}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {6,45}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {6,25}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {5,13}, {1,41}, {5,45}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {5,19}, {6,20}, {2,30}, {5,21}, {6,13}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {6,35}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36}, {5,16} }; // ET46.40 // Bipartite(5,41) Valencies [41,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4014303193579656852980407446412890199818240000000000 EdgePairs[46][40]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {2,46}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {2,42}, {3,18}, {3,17}, {3,7}, {2,45}, {4,38}, {3,34}, {2,25}, {5,40}, {3,46}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {1,44}, {4,41}, {2,10}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {5,25}, {2,39}, {1,31}, {3,12}, {4,45}, {2,35}, {1,22}, {3,44}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {5,46}, {1,45}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {1,43}, {3,26}, {4,46}, {5,28}, {5,42}, {2,17}, {4,36}, {5,41}, {4,6}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {5,44}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {1,46}, {1,15}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,40}, {2,31}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {5,13}, {1,41}, {5,45}, {5,6}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {5,19}, {2,30}, {5,21}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36}, {5,16} }; // ET46.41 // Bipartite(4,42) Valencies [42,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 33720146826069117565035422549868277678473216000000000 EdgePairs[46][41]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {2,33}, {4,27}, {2,46}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {2,28}, {2,14}, {1,30}, {4,23}, {3,5}, {2,42}, {3,18}, {3,17}, {3,7}, {2,45}, {4,38}, {3,34}, {2,25}, {3,46}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {1,18}, {3,14}, {4,8}, {1,5}, {2,5}, {1,44}, {4,41}, {2,10}, {2,38}, {2,37}, {4,42}, {2,39}, {1,31}, {3,12}, {4,45}, {2,35}, {1,22}, {3,44}, {4,33}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {1,23}, {2,6}, {1,45}, {1,9}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {1,43}, {3,26}, {4,46}, {2,17}, {4,36}, {4,6}, {1,42}, {3,19}, {4,9}, {1,24}, {3,23}, {1,39}, {3,21}, {2,7}, {1,25}, {1,46}, {1,15}, {2,11}, {4,5}, {1,35}, {1,37}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {2,40}, {2,31}, {3,42}, {4,18}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {1,41}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {2,30}, {2,18}, {1,34}, {2,43}, {4,17}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36} }; // ET46.42 // Bipartite(3,43) Valencies [43,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 362491578380243013824130792411083985043587072000000000 EdgePairs[46][42]:={ {1,15}, {3,15}, {1,43}, {2,38}, {1,11}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {3,46}, {2,11}, {1,46}, {1,40}, {2,20}, {1,25}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {1,5}, {1,44}, {3,30}, {1,32}, {3,45}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {2,41}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {2,13}, {3,14}, {1,12}, {3,9}, {3,22}, {3,23}, {2,42}, {2,34}, {3,27}, {1,19}, {2,40}, {2,35}, {2,9}, {1,4}, {3,5}, {1,35}, {1,26}, {2,44}, {2,4}, {2,24}, {3,42}, {2,27}, {3,4}, {2,43}, {3,35}, {1,23}, {2,21}, {1,7}, {2,46}, {1,39}, {2,39}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {1,42}, {2,6}, {3,21}, {1,14}, {1,41}, {3,44}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {1,13}, {3,16}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {2,25}, {3,6}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,43}, {1,45}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24}, {2,45} }; // ET46.43 // Bipartite(2,44) Valencies [44,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 5316543149576897536087251622029231780639277056000000000 EdgePairs[46][43]:={ {1,15}, {1,43}, {2,38}, {1,11}, {2,22}, {1,31}, {2,11}, {1,46}, {1,40}, {2,3}, {2,20}, {1,25}, {2,37}, {1,38}, {1,9}, {2,33}, {1,5}, {1,44}, {1,32}, {2,28}, {2,19}, {2,18}, {2,15}, {2,29}, {1,29}, {1,34}, {2,14}, {1,3}, {2,10}, {2,41}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {2,16}, {1,22}, {2,32}, {1,16}, {2,36}, {2,17}, {2,13}, {1,12}, {2,42}, {2,34}, {1,19}, {2,40}, {2,35}, {2,9}, {1,4}, {1,35}, {1,26}, {2,44}, {2,4}, {2,24}, {2,27}, {2,43}, {1,23}, {2,21}, {1,7}, {2,46}, {1,39}, {2,39}, {2,12}, {1,42}, {2,6}, {1,14}, {1,41}, {2,8}, {1,37}, {1,20}, {1,27}, {1,13}, {2,26}, {1,33}, {2,25}, {1,28}, {2,7}, {1,45}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24}, {2,45} }; // ET46.44 // Non-bipartite Valency 44 // Diameter 2 Girth 3 // Has twins VT AT // Automorphism group of order 216862434431944426122117120000 EdgePairs[46][44]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {37,43}, {13,18}, {2,6}, {32,33}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {18,45}, {5,44}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {8,44}, {14,37}, {36,39}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {29,46}, {19,27}, {28,43}, {32,34}, {7,12}, {31,33}, {21,34}, {4,10}, {3,19}, {1,15}, {5,8}, {10,30}, {24,44}, {40,44}, {9,28}, {42,46}, {25,31}, {2,23}, {16,36}, {7,26}, {7,42}, {30,31}, {21,45}, {21,31}, {13,44}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {25,33}, {34,35}, {38,43}, {9,46}, {3,27}, {29,39}, {25,32}, {25,45}, {44,45}, {5,13}, {4,45}, {36,46}, {15,33}, {21,33}, {22,27}, {30,34}, {17,36}, {10,35}, {13,40}, {11,15}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {13,41}, {22,37}, {12,26}, {15,34}, {18,41}, {7,16}, {12,16}, {14,19}, {9,43}, {3,38}, {13,24}, {11,30}, {30,32}, {40,45}, {6,42}, {4,21}, {12,42}, {29,36}, {30,33}, {14,43}, {20,34}, {23,29}, {1,33}, {4,25}, {2,42}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, {36,42}, {1,30}, {23,42}, {14,27}, {11,35}, {2,29}, {16,39}, {15,31}, {10,21}, {17,23}, {10,45}, {12,19}, {3,7}, {10,25}, {6,17}, {32,35}, {20,33}, {2,17}, {29,42}, {33,35}, {36,37}, {20,32}, {18,40}, {11,33}, {18,44}, {28,46}, {19,22}, {16,26}, {3,22}, {5,24}, {11,32}, {22,43}, {1,5}, {28,37}, {11,20}, {26,27}, {24,41}, {17,28}, {1,8}, {11,24}, {1,35}, {9,17}, {10,18}, {19,38}, {8,15}, {5,20}, {14,16}, {3,12}, {11,45}, {3,26}, {28,29}, {11,31}, {16,22}, {27,43}, {12,39}, {6,36}, {5,15}, {20,30}, {2,36}, {4,18}, {35,41}, {22,38}, {26,39}, {8,11}, {22,46}, {15,35}, {30,41}, {14,38}, {5,41}, {39,43}, {12,27}, {11,13}, {15,30}, {3,43}, {19,43}, {7,19}, {37,46}, {1,45}, {14,46}, {11,34}, {8,32}, {7,39}, {22,39}, {19,26}, {8,33}, {8,20}, {5,31}, {20,35}, {16,19}, {30,45}, {1,13}, {26,38}, {9,23}, {7,14}, {34,41}, {13,15}, {5,34}, {9,29}, {13,35}, {14,26}, {23,28}, {7,27}, {2,9}, {10,40}, {29,37}, {38,39}, {13,30}, {6,9}, {17,42}, {35,45}, {13,20}, {16,27}, {37,42}, {23,36}, {8,41}, {5,32}, {5,33}, {8,31}, {19,46}, {17,37}, {5,11}, {3,16}, {20,24}, {7,22}, {22,26}, {12,14}, {12,22}, {20,45}, {3,46}, {7,38}, {13,34}, {28,36}, {15,45}, {9,36}, {4,44}, {31,41}, {8,34}, {26,43}, {15,24}, {10,19}, {1,24}, {20,41}, {12,38}, {27,39}, {32,41}, {31,37}, {14,39}, {31,45}, {34,37}, {2,13}, {5,30}, {33,41}, {24,30}, {6,13}, {27,46}, {5,35}, {24,35}, {8,17}, {1,9}, {18,25}, {4,40}, {2,37}, {12,18}, {6,37}, {25,44}, {16,46}, {9,15}, {3,10}, {21,40}, {16,43}, {13,45}, {18,21}, {8,30}, {21,44}, {10,44}, {13,31}, {2,28}, {25,40}, {22,25}, {15,28}, {6,28}, {14,21}, {7,18}, {11,41}, {34,45}, {14,25}, {5,17}, {24,33}, {20,28}, {13,32}, {13,33}, {35,37}, {10,27}, {9,11}, {43,46}, {24,32}, {16,18}, {32,37}, {33,37}, {19,39}, {1,41}, {3,39}, {5,29}, {33,45}, {8,35}, {28,42}, {15,41}, {6,24}, {24,31}, {32,45}, {9,32}, {2,5}, {2,24}, {4,19}, {9,33}, {9,20}, {18,26}, {8,29}, {24,45}, {4,14}, {21,43}, {7,43}, {12,43}, {30,37}, {8,23}, {5,45}, {3,21}, {5,36}, {12,46}, {23,37}, {4,27}, {25,43}, {2,8}, {6,8}, {24,29}, {9,42}, {13,17}, {3,25}, {26,44}, {1,37}, {13,23}, {12,40}, {36,41}, {1,28}, {8,45}, {7,46}, {38,46}, {13,42}, {16,38}, {25,27}, {9,31}, {21,27}, {4,38}, {8,9}, {28,32}, {24,34}, {10,14}, {13,29}, {4,22}, {4,7}, {10,22}, {10,12}, {24,42}, {26,40}, {17,24}, {28,33}, {21,38}, {15,37}, {7,44}, {2,41}, {8,36}, {23,41}, {39,44}, {9,34}, {15,17}, {10,38}, {6,41}, {34,36}, {11,28}, {39,46}, {13,36}, {18,19}, {28,34}, {19,25}, {25,38}, {19,21}, {41,45}, {20,37}, {6,11}, {38,40}, {5,23}, {12,44}, {11,23}, {35,42}, {31,36}, {2,11}, {9,30}, {29,41}, {38,44}, {7,40}, {20,29}, {33,36}, 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// Automorphism group of order 119622220865480194561963161495657715064383733760000000000 EdgePairs[46][45]:={ {1,26}, {1,14}, {1,44}, {1,24}, {1,46}, {1,29}, {1,30}, {1,32}, {1,37}, {1,33}, {1,40}, {1,10}, {1,2}, {1,43}, {1,39}, {1,36}, {1,6}, {1,45}, {1,4}, {1,20}, {1,12}, {1,31}, {1,38}, {1,7}, {1,15}, {1,16}, {1,21}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {1,28}, {1,42}, {1,8}, {1,13}, {1,19}, {1,9}, {1,41}, {1,22}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25} }; // ET46.46 // Non-bipartite Valency 45 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 5502622159812088949850305428800254892961651752960000000000 EdgePairs[46][46]:={ {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {37,43}, {13,18}, {2,6}, {32,33}, {10,34}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {18,45}, {5,44}, {15,21}, {24,40}, {26,42}, 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{33,38}, {32,38}, {21,36}, {30,43}, {29,44}, {1,19}, {5,43}, {40,46}, {26,30}, {19,41}, {11,14}, {12,35}, {14,35}, {7,45}, {8,46}, {19,32}, {36,40}, {19,33}, {3,34}, {3,31}, {11,19}, {24,39}, {13,46}, {19,20}, {8,16}, {13,26}, {1,39}, {4,37}, {1,14}, {8,43}, {14,15}, {34,43}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {25,28}, {8,26}, {30,38}, {3,32}, {10,42}, {44,46}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {12,45}, {5,46}, {24,26}, {40,42}, {8,10}, {1,22}, {14,34}, {27,33}, {17,19}, {7,24}, {9,12}, {29,40}, {11,27}, {26,41}, {27,32}, {35,38}, {22,23}, {4,5}, {32,43}, {10,37}, {22,30}, {27,34}, {31,43}, {33,43}, {42,43}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {11,46}, {26,45}, {22,35}, {20,43}, {32,40}, {16,41}, {33,40}, {15,18}, {2,14}, {17,44}, {3,35}, {26,28}, {27,31}, {13,39}, {6,14}, {11,43}, {14,31}, {4,8}, {17,27}, {24,25}, {7,9}, {13,21}, {27,29}, {5,10}, {39,45}, {23,44}, {3,17}, {12,28}, {34,44}, {14,45}, {36,38}, {19,35}, {21,24}, {1,18}, {6,44}, {22,31}, {6,22}, {31,44}, {14,32}, {22,33}, {2,44}, {5,39}, {25,37}, {41,46}, {13,25}, {14,33}, {2,22}, {2,3}, {3,29}, {22,32}, {8,39}, {19,30}, {1,43}, {15,43}, {7,41}, {21,41}, {22,45}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {18,42}, {7,37}, {38,42}, {9,16}, {3,36}, {2,40}, {33,44}, {11,38}, {12,41}, {4,13}, {6,40}, {31,40}, {32,44}, {14,17}, {5,25}, {36,43}, {25,41}, {5,21}, {3,45}, {20,40}, {18,32}, {7,28}, {14,23}, {35,44}, {20,44}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {22,42}, {30,44}, {1,46}, {1,4}, {14,29}, {18,34}, {30,46}, {15,46}, {19,23}, {18,31}, {15,40}, {14,42}, {26,37}, {1,44}, {2,19}, {23,43}, {6,19}, {4,24}, {12,37}, {17,22}, {27,28}, {14,36}, {35,46}, {2,43}, {27,36}, {6,43}, {26,29}, {8,18}, {19,45}, {8,21}, {10,15}, {12,17}, {30,40}, {29,43}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {15,44}, {43,45}, {17,38}, {6,27}, {16,37}, {37,39}, {32,46}, {19,28}, {18,35}, {2,27}, {33,46}, {20,46}, {1,10}, {4,20}, {23,46}, {27,45}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {2,46}, {3,9}, {23,38}, {7,29}, {20,21}, {6,46}, {31,46}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {38,45}, {7,17}, {10,11}, {17,43}, {20,25}, {4,41}, {41,44}, {3,42}, {3,28}, {9,27}, {37,38}, {11,25}, {16,17}, {11,44}, {11,21}, {19,42}, {34,46}, {23,39}, {10,41}, {12,29}, {22,28}, {17,46}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // Total number of connected ET graphs of order 46 is 46 // ******************************************************************************************** // Order 47 // ET47.1 // Non-bipartite Valency 2 // Diameter 23 Girth 47 // Twin-free VT AT // Automorphism group of order 94 EdgePairs[47][1]:={ {27,42}, {12,27}, {13,28}, {5,37}, {21,36}, {31,46}, {4,36}, {15,47}, {1,33}, {20,35}, {8,23}, {23,38}, {16,31}, {18,33}, {30,45}, {12,44}, {29,44}, {26,41}, {5,20}, {8,40}, {9,24}, {1,16}, {15,30}, {11,43}, {6,38}, {22,37}, {14,46}, {6,21}, {3,18}, {9,41}, {7,22}, {32,47}, {24,39}, {10,42}, {2,17}, {17,32}, {7,39}, {2,34}, {11,26}, {14,29}, {28,43}, {10,25}, {25,40}, {4,19}, {13,45}, {19,34}, {3,35} }; // ET47.2 // Bipartite(23,24) Valencies [24,23] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 16039842467222136539155708423040296550400000000 EdgePairs[47][2]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {20,26}, {3,29}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {22,37}, {14,29}, {7,47}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {14,47}, {8,31}, {12,42}, {7,24}, {3,47}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {19,37}, {17,29}, {23,29}, {8,26}, {10,29}, {15,33}, {6,28}, {5,43}, {12,32}, {22,25}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {8,24}, {2,38}, {20,42}, {23,45}, {12,27}, {6,34}, {4,38}, {11,39}, {21,31}, {16,33}, {19,38}, {7,26}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {22,28}, {18,37}, {15,45}, {20,29}, {10,42}, {14,40}, {9,41}, {17,43}, {21,46}, {17,45}, {23,34}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {5,47}, {17,42}, {11,47}, {20,28}, {10,25}, {12,35}, {11,36}, {19,40}, {16,26}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {21,30}, {21,44}, {23,33}, {20,44}, {5,45}, {21,42}, {4,41}, {8,39}, {22,32}, {7,34}, {22,45}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {23,24}, {18,35}, {15,24}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {5,46}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {20,39}, {5,33}, {4,39}, {6,24}, {22,47}, {16,43}, {8,47}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {22,41}, {18,26}, {4,45}, {22,26}, {2,28}, {1,27}, {20,43}, {9,25}, {4,44}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {23,39}, {10,43}, {5,29}, {21,25}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {19,44}, {22,46}, {8,34}, {9,29}, {23,46}, {4,33}, {15,40}, {18,34}, {21,34}, {1,44}, {10,31}, {22,38}, {19,32}, {7,37}, {21,45}, {1,28}, {3,43}, {3,36}, {14,36}, {7,42}, {17,46}, {6,43}, {23,26}, {12,47}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {23,32}, {7,36}, {9,39}, {22,24}, {13,26}, {14,37}, {10,46}, {22,33}, {11,24}, {7,43}, {11,45}, {8,33}, {20,31}, {10,28}, {9,44}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {18,44}, {21,29}, {23,28}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {4,40}, {23,38}, {16,36}, {1,39}, {18,43}, {6,45}, {7,40}, {17,37}, {18,25}, {21,27}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {21,43}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {7,46}, {6,47}, {19,28}, {20,37}, {11,33}, {1,34}, {7,25}, {4,47}, {22,40}, {13,37}, {8,27}, {5,30}, {6,46}, {19,43}, {16,27}, {23,44}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {22,36}, {22,30}, {18,30}, {1,40}, {10,26}, {17,31}, {8,29}, {15,44}, {23,41}, {19,36}, {9,34}, {15,25}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {9,47}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {16,40}, {1,47}, {9,33}, {8,42}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {13,31}, {23,40}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {1,46}, {10,34}, {21,47}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {20,34}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {19,47}, {13,34}, {20,24}, {23,25}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {2,29}, {20,30}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {23,35}, {15,41}, {19,45}, {16,44}, {23,31}, {17,41}, {11,30}, {8,43}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {6,33}, {2,32}, {19,26}, {22,34}, {9,36}, {10,40}, {18,47}, {6,27}, {12,40}, {21,41}, {17,40}, {7,45}, {8,46}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {16,32}, {9,32}, {18,32}, {21,32}, {23,30}, {21,26}, {20,47}, {22,31}, {16,45}, {22,35}, {5,39}, {12,43}, {19,34}, {13,47}, {10,45}, {23,37}, {23,42}, {3,40}, {20,46}, {23,27}, {22,42}, {12,36}, {22,44}, {21,39}, {3,33}, {23,47}, {1,24}, {19,25}, {15,26}, {18,41}, {23,43}, {21,28}, {23,36}, {16,38}, {22,43}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {16,47}, {20,36}, {15,47}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {2,35}, {17,33}, {10,32}, {16,24}, {17,47}, {21,38}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.3 // Bipartite(22,25) Valencies [25,22] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 17434611377415365803430117851130757120000000000 EdgePairs[47][3]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {3,29}, {20,26}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {22,37}, {14,29}, {7,47}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {14,47}, {8,31}, {12,42}, {7,24}, {3,47}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {6,28}, {5,43}, {12,32}, {22,25}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {8,24}, {2,38}, {20,42}, {12,27}, {6,34}, {4,38}, {11,39}, {21,31}, {16,33}, {7,26}, {19,38}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {22,28}, {18,37}, {15,45}, {20,29}, {10,42}, {14,40}, {9,41}, {17,43}, {21,46}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {22,29}, {11,29}, {14,27}, {5,47}, {17,42}, {11,47}, {20,28}, {10,25}, {12,35}, {11,36}, {19,40}, {16,26}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {21,44}, {20,44}, {5,45}, {21,42}, {4,41}, {8,39}, {22,32}, {7,34}, {22,45}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {22,27}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {5,46}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {6,24}, {22,47}, {16,43}, {8,47}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {22,41}, {18,26}, {14,23}, {4,45}, {22,26}, {2,28}, {1,27}, {20,43}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {10,43}, {5,29}, {21,25}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {19,44}, {22,46}, {8,34}, {9,29}, {4,33}, {15,40}, {18,34}, {21,34}, {1,44}, {10,31}, {22,38}, {13,23}, {19,32}, {7,37}, {21,45}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {17,46}, {6,43}, {12,47}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {7,36}, {9,39}, {22,24}, {13,26}, {14,37}, {10,46}, {22,33}, {11,24}, {7,43}, {11,45}, {8,33}, {20,31}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {21,29}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {4,40}, {16,36}, {1,39}, {18,43}, {6,45}, {7,40}, {17,37}, {18,25}, {21,27}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {21,23}, {21,43}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {7,46}, {6,47}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {4,47}, {22,40}, {13,37}, {8,27}, {5,30}, {6,46}, {16,27}, {19,43}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {22,36}, {22,30}, {18,30}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {15,44}, {9,34}, {19,36}, {15,25}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {9,47}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {11,23}, {16,40}, {1,47}, {9,33}, {8,42}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {22,39}, {17,24}, {12,23}, {13,31}, {5,31}, {22,23}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {1,46}, {10,34}, {21,47}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {20,34}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {19,47}, {13,34}, {20,24}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {20,30}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {16,44}, {19,45}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {22,34}, {9,36}, {10,40}, {18,47}, {6,27}, {12,40}, {21,41}, {17,40}, {7,45}, {8,46}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {16,32}, {9,32}, {18,32}, {21,32}, {21,26}, {20,47}, {22,31}, {16,45}, {22,35}, {5,39}, {12,43}, {19,34}, {13,47}, {10,45}, {3,40}, {20,46}, {22,42}, {12,36}, {22,44}, {21,39}, {3,33}, {1,24}, {19,25}, {15,26}, {18,41}, {21,28}, {16,38}, {22,43}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {16,47}, {20,36}, {15,47}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {2,35}, {17,33}, {10,32}, {16,24}, {17,47}, {21,38}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.4 // Bipartite(21,26) Valencies [26,21] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 20604540718763614131326502914972712960000000000 EdgePairs[47][4]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {3,29}, {20,26}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {14,29}, {7,47}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {14,47}, {8,31}, {12,42}, {7,24}, {3,47}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {18,38}, {2,24}, {1,32}, {20,27}, {4,28}, {8,36}, {13,43}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {20,22}, {3,25}, {10,27}, {1,41}, {4,30}, {21,35}, {8,24}, {2,38}, {20,42}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {21,31}, {16,33}, {7,26}, {19,38}, {11,27}, {18,28}, {8,44}, {4,34}, {13,29}, {10,22}, {18,37}, {15,45}, {20,29}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {21,46}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {5,47}, {17,42}, {11,47}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {19,40}, {16,26}, {3,22}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {21,30}, {21,44}, {20,44}, {5,45}, {21,42}, {4,41}, {9,22}, {8,39}, {7,34}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {18,35}, {10,23}, {15,24}, {20,32}, {1,26}, {18,31}, {9,27}, {1,25}, {5,46}, {18,42}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {8,47}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {18,26}, {14,23}, {4,45}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {21,36}, {7,31}, {12,33}, {5,38}, {1,37}, {21,37}, {1,29}, {2,34}, {21,22}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {10,43}, {5,29}, {21,25}, {9,28}, {20,40}, {19,24}, {16,35}, {21,40}, {5,28}, {8,30}, {14,32}, {9,37}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {21,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {21,45}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {17,46}, {6,43}, {12,47}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {20,31}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {21,29}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {4,40}, {16,36}, {1,39}, {6,45}, {18,43}, {7,40}, {17,37}, {18,25}, {21,27}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {21,23}, {21,43}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {6,47}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {4,47}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {19,43}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {19,36}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {9,47}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {3,38}, {2,43}, {14,34}, {13,44}, {11,23}, {16,40}, {1,47}, {9,33}, {8,42}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {21,33}, {17,38}, {1,46}, {10,34}, {21,47}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {20,34}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {19,47}, {13,34}, {20,24}, {18,24}, {21,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {20,30}, {14,44}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {16,44}, {19,45}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {9,36}, {10,40}, {18,47}, {6,27}, {12,40}, {21,41}, {17,40}, {7,45}, {8,46}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {21,32}, {21,26}, {20,47}, {16,45}, {5,39}, {12,43}, {19,34}, {13,47}, {10,45}, {3,40}, {20,46}, {12,36}, {21,39}, {3,33}, {1,24}, {19,25}, {15,26}, {18,41}, {21,28}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {16,47}, {20,36}, {15,47}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {2,35}, {17,33}, {10,32}, {16,24}, {17,47}, {21,38}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.5 // Bipartite(20,27) Valencies [27,20] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 26491552352696075311705503747822059520000000000 EdgePairs[47][5]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {3,29}, {20,26}, {16,28}, {4,26}, {20,33}, {20,25}, {19,41}, {14,29}, {7,47}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {14,47}, {8,31}, {12,42}, {7,24}, {3,47}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {20,27}, {4,28}, {8,36}, {9,21}, {13,43}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {20,22}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {20,42}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {8,44}, {18,28}, {4,34}, {13,29}, {10,22}, {18,37}, {15,45}, {20,29}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {5,47}, {17,42}, {11,47}, {20,28}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {20,44}, {5,45}, {4,41}, {9,22}, {8,39}, {7,34}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {18,35}, {20,32}, {1,26}, {9,27}, {18,31}, {1,25}, {5,46}, {18,42}, {19,21}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {20,39}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {8,47}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {8,21}, {14,23}, {18,26}, {4,45}, {18,21}, {2,28}, {1,27}, {20,43}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {10,43}, {5,29}, {9,28}, {20,40}, {19,24}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {20,23}, {14,36}, {7,42}, {17,46}, {6,43}, {12,47}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {20,31}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {4,40}, {16,36}, {1,39}, {6,45}, {18,43}, {7,40}, {17,37}, {18,25}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {20,38}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {6,47}, {19,28}, {20,37}, {11,33}, {1,34}, {19,23}, {7,25}, {4,47}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {19,43}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {17,31}, {8,29}, {7,22}, {15,44}, {9,34}, {19,36}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {17,35}, {6,32}, {15,31}, {10,35}, {9,47}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {1,47}, {9,33}, {8,42}, {20,21}, {20,35}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {20,34}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {19,47}, {13,34}, {20,24}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {20,30}, {14,21}, {14,44}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {16,44}, {7,21}, {19,45}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {9,36}, {10,40}, {16,21}, {18,47}, {6,27}, {12,40}, {17,40}, {7,45}, {8,46}, {20,41}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {20,47}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {19,34}, {13,47}, {10,45}, {3,40}, {20,46}, {12,36}, {10,21}, {3,33}, {1,24}, {19,25}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {16,47}, {20,36}, {15,47}, {20,45}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {2,35}, {17,33}, {10,32}, {16,24}, {17,47}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.6 // Bipartite(19,28) Valencies [28,19] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 37088173293774505436387705246950883328000000000 EdgePairs[47][6]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {3,29}, {16,28}, {4,26}, {19,41}, {14,29}, {7,47}, {2,20}, {2,26}, {19,22}, {8,28}, {5,32}, {4,24}, {8,37}, {14,47}, {8,31}, {12,42}, {7,24}, {3,47}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {4,28}, {8,36}, {9,21}, {8,20}, {13,43}, {17,29}, {19,37}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {19,38}, {11,27}, {8,44}, {18,28}, {4,34}, {13,29}, {10,22}, {18,37}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {19,30}, {11,29}, {14,27}, {5,47}, {17,42}, {11,47}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {19,40}, {16,26}, {3,22}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {18,35}, {1,26}, {9,27}, {18,31}, {1,25}, {5,46}, {18,42}, {19,21}, {16,42}, {12,44}, {15,34}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {16,43}, {8,47}, {6,39}, {2,44}, {2,45}, {19,35}, {1,42}, {16,34}, {19,31}, {8,21}, {9,20}, {14,23}, {18,26}, {4,45}, {18,21}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {18,20}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {10,43}, {3,20}, {5,29}, {9,28}, {19,24}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,20}, {17,26}, {11,41}, {19,44}, {8,34}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {19,32}, {7,37}, {1,28}, {3,43}, {3,36}, {14,36}, {7,42}, {17,46}, {6,43}, {12,47}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {4,40}, {16,36}, {1,39}, {6,45}, {18,43}, {7,40}, {17,37}, {18,25}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {6,47}, {14,20}, {19,28}, {11,33}, {1,34}, {19,23}, {7,25}, {4,47}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {19,43}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {15,44}, {9,34}, {19,36}, {15,25}, {6,22}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {9,47}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {19,39}, {2,27}, {15,35}, {5,41}, {13,41}, {19,33}, {19,29}, {3,34}, {18,39}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {1,47}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {19,42}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {19,47}, {13,34}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {19,27}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {4,20}, {16,44}, {7,21}, {19,45}, {17,41}, {11,30}, {8,43}, {2,23}, {19,20}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {19,26}, {4,23}, {9,36}, {10,40}, {16,21}, {18,47}, {6,27}, {12,40}, {17,40}, {7,45}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {19,46}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {19,34}, {13,47}, {10,45}, {7,20}, {3,40}, {12,36}, {10,21}, {3,33}, {1,24}, {19,25}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {17,30}, {5,24}, {7,33}, {12,31}, {16,47}, {15,47}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {2,35}, {17,33}, {10,32}, {16,24}, {17,47}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.7 // Bipartite(18,29) Valencies [29,18] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 56608264501024245139749655376925032448000000000 EdgePairs[47][7]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {3,29}, {16,28}, {4,26}, {14,29}, {7,47}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {14,47}, {8,31}, {12,42}, {7,24}, {3,47}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {18,38}, {1,32}, {4,28}, {8,36}, {9,21}, {8,20}, {13,43}, {17,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {18,28}, {4,34}, {17,19}, {13,29}, {10,22}, {18,37}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {18,29}, {11,29}, {14,27}, {5,47}, {17,42}, {11,47}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {18,27}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {18,35}, {1,26}, {9,27}, {18,31}, {1,25}, {5,46}, {18,42}, {15,34}, {12,44}, {16,42}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {8,47}, {16,43}, {6,39}, {2,44}, {2,45}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {18,26}, {4,45}, {18,21}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {18,20}, {7,31}, {12,33}, {5,38}, {1,37}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {18,34}, {1,44}, {10,31}, {13,23}, {7,37}, {1,28}, {3,43}, {3,36}, {14,36}, {7,42}, {17,46}, {6,43}, {12,47}, {18,22}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {18,44}, {3,28}, {9,35}, {12,24}, {18,19}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {6,45}, {18,43}, {7,40}, {17,37}, {14,19}, {18,25}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {18,23}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {6,47}, {14,20}, {11,33}, {1,34}, {7,25}, {4,47}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {18,30}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {9,47}, {4,27}, {18,36}, {14,24}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {3,34}, {18,39}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {1,47}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {5,31}, {4,25}, {10,38}, {3,30}, {18,33}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {17,34}, {12,26}, {18,46}, {1,45}, {10,30}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {18,24}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {18,40}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {18,45}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {7,21}, {16,44}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {18,47}, {6,27}, {12,40}, {17,40}, {7,45}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {18,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {13,47}, {10,45}, {7,20}, {3,40}, {16,19}, {12,36}, {10,21}, {3,33}, {1,24}, {17,21}, {15,26}, {18,41}, {16,38}, {12,37}, {2,19}, {17,30}, {5,24}, {7,33}, {12,31}, {16,47}, {15,47}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {17,47}, {4,19}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.8 // Bipartite(17,30) Valencies [30,17] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 94347107501707075232916092294875054080000000000 EdgePairs[47][8]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {4,46}, {9,18}, {3,29}, {16,28}, {4,26}, {14,29}, {7,47}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {14,47}, {8,31}, {12,42}, {7,24}, {3,47}, {11,34}, {13,27}, {12,25}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {5,18}, {17,29}, {8,26}, {10,29}, {15,33}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {17,22}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {4,34}, {17,19}, {13,29}, {10,22}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {17,43}, {15,20}, {17,18}, {17,45}, {14,33}, {17,25}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {5,47}, {17,42}, {11,47}, {10,25}, {12,35}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {17,32}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {15,24}, {10,23}, {1,26}, {9,27}, {1,25}, {5,46}, {15,34}, {12,44}, {16,42}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {8,47}, {16,43}, {6,39}, {2,44}, {2,45}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {4,45}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {15,27}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {10,18}, {10,20}, {17,26}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {7,37}, {1,28}, {14,18}, {3,43}, {3,36}, {14,36}, {7,42}, {17,46}, {6,43}, {12,47}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {17,28}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {17,36}, {17,23}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {6,45}, {7,40}, {17,37}, {14,19}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {6,47}, {14,20}, {11,33}, {1,34}, {7,25}, {4,47}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {4,22}, {1,40}, {6,23}, {10,26}, {17,20}, {1,23}, {8,29}, {17,31}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {17,44}, {2,33}, {6,32}, {17,35}, {15,31}, {10,35}, {9,47}, {4,27}, {14,24}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {1,47}, {15,19}, {9,33}, {8,42}, {15,38}, {7,38}, {14,30}, {8,32}, {17,24}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {17,38}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {15,18}, {17,34}, {12,26}, {1,45}, {10,30}, {6,18}, {17,39}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {7,21}, {16,44}, {17,41}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {17,40}, {7,45}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {17,27}, {6,38}, {11,40}, {13,42}, {14,45}, {16,18}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {13,47}, {10,45}, {7,20}, {3,40}, {16,19}, {12,36}, {7,18}, {10,21}, {3,33}, {1,24}, {17,21}, {4,18}, {15,26}, {2,18}, {16,38}, {12,37}, {2,19}, {17,30}, {5,24}, {7,33}, {12,31}, {16,47}, {15,47}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {7,19}, {2,35}, {17,33}, {10,32}, {16,24}, {17,47}, {4,19}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.9 // Bipartite(16,31) Valencies [31,16] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 172044725444289372483552874184772157440000000000 EdgePairs[47][9]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {15,17}, {4,46}, {10,17}, {3,29}, {9,18}, {16,28}, {4,26}, {14,29}, {7,47}, {2,20}, {2,26}, {16,17}, {8,28}, {5,32}, {4,24}, {8,37}, {14,47}, {8,31}, {12,42}, {7,24}, {3,47}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {5,18}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {2,21}, {16,33}, {7,26}, {11,27}, {8,44}, {4,34}, {13,29}, {10,22}, {15,45}, {12,22}, {14,40}, {10,42}, {9,41}, {15,20}, {14,33}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {5,47}, {11,47}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {16,26}, {3,22}, {6,19}, {5,23}, {16,20}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {16,23}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {10,23}, {15,24}, {1,26}, {9,27}, {1,25}, {5,46}, {12,44}, {15,34}, {16,42}, {16,30}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {1,22}, {6,24}, {8,47}, {16,43}, {6,39}, {2,44}, {2,45}, {1,42}, {16,34}, {8,21}, {9,20}, {14,23}, {4,45}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {14,35}, {15,27}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {16,35}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {9,17}, {10,18}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {7,37}, {1,28}, {14,18}, {3,43}, {1,17}, {3,36}, {14,36}, {7,42}, {6,43}, {12,47}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {5,21}, {7,36}, {9,39}, {13,26}, {14,37}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {12,17}, {9,42}, {9,19}, {13,35}, {16,37}, {13,32}, {10,24}, {2,25}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {16,29}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {16,46}, {15,30}, {3,19}, {4,40}, {16,36}, {1,39}, {6,45}, {7,40}, {14,19}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {16,22}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {6,47}, {14,20}, {11,33}, {1,34}, {7,25}, {4,47}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {16,27}, {14,46}, {9,30}, {5,40}, {3,46}, {16,31}, {8,17}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {8,29}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {16,41}, {13,28}, {16,25}, {2,33}, {6,32}, {15,31}, {10,35}, {9,47}, {4,27}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {6,17}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {16,40}, {1,47}, {15,19}, {9,33}, {8,42}, {8,32}, {7,38}, {14,30}, {15,38}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {11,17}, {15,18}, {12,26}, {1,45}, {10,30}, {6,18}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {16,39}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {7,21}, {16,44}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {16,21}, {6,27}, {12,40}, {7,45}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {6,38}, {2,17}, {11,40}, {13,42}, {14,45}, {16,18}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {16,32}, {9,32}, {16,45}, {5,39}, {12,43}, {1,21}, {6,21}, {13,47}, {10,45}, {7,20}, {3,40}, {16,19}, {12,36}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {15,26}, {2,18}, {16,38}, {12,37}, {2,19}, {5,24}, {7,33}, {12,31}, {16,47}, {15,47}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {7,19}, {2,35}, {10,32}, {16,24}, {4,19}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.10 // Bipartite(15,32) Valencies [32,15] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 344089450888578744967105748369544314880000000000 EdgePairs[47][10]:={ {13,25}, {3,42}, {15,28}, {13,40}, {6,36}, {11,42}, {15,17}, {4,46}, {9,18}, {3,29}, {10,17}, {4,26}, {14,29}, {7,47}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {14,47}, {8,31}, {12,42}, {7,24}, {3,47}, {15,16}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {13,43}, {5,18}, {8,26}, {10,29}, {15,33}, {7,17}, {13,22}, {6,28}, {5,43}, {14,16}, {12,32}, {2,30}, {14,25}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {2,21}, {7,26}, {11,27}, {8,44}, {4,34}, {13,29}, {10,22}, {15,45}, {12,22}, {10,42}, {14,40}, {9,41}, {15,20}, {14,33}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {5,47}, {11,47}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {3,22}, {6,19}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {15,43}, {2,36}, {12,38}, {11,44}, {13,33}, {10,23}, {15,24}, {1,26}, {9,27}, {1,25}, {5,46}, {10,16}, {12,44}, {15,34}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {7,16}, {1,22}, {6,24}, {8,47}, {6,39}, {2,44}, {2,45}, {1,42}, {8,21}, {9,20}, {14,23}, {4,45}, {3,16}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {14,35}, {15,27}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {9,17}, {10,18}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {15,40}, {1,44}, {10,31}, {3,18}, {13,23}, {5,16}, {7,37}, {1,28}, {14,18}, {3,43}, {1,17}, {3,36}, {7,42}, {14,36}, {6,43}, {12,47}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {5,21}, {7,36}, {9,39}, {13,26}, {10,46}, {14,37}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {15,23}, {12,17}, {9,42}, {9,19}, {13,35}, {13,32}, {10,24}, {2,25}, {3,28}, {9,35}, {12,24}, {14,28}, {12,45}, {15,36}, {10,36}, {12,20}, {8,41}, {15,42}, {13,46}, {2,40}, {9,43}, {15,30}, {3,19}, {4,40}, {2,16}, {1,39}, {6,45}, {7,40}, {14,19}, {10,37}, {6,44}, {2,42}, {9,46}, {15,37}, {7,35}, {4,42}, {15,29}, {14,41}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {15,46}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {9,40}, {14,31}, {8,45}, {7,46}, {8,22}, {6,47}, {14,20}, {11,33}, {1,34}, {11,16}, {7,25}, {4,47}, {13,37}, {8,27}, {5,30}, {6,46}, {15,22}, {14,46}, {9,30}, {5,40}, {3,46}, {8,17}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {8,29}, {7,22}, {15,44}, {9,34}, {15,25}, {6,22}, {5,19}, {13,28}, {2,33}, {6,32}, {15,31}, {10,35}, {9,47}, {4,27}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {15,35}, {1,19}, {5,41}, {13,41}, {6,17}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {1,47}, {15,19}, {9,33}, {8,16}, {8,42}, {8,32}, {7,38}, {14,30}, {15,38}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {11,17}, {15,18}, {4,16}, {12,26}, {1,45}, {10,30}, {6,18}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {6,16}, {7,44}, {11,46}, {4,31}, {3,41}, {15,39}, {10,33}, {10,39}, {13,34}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {2,46}, {3,39}, {10,41}, {6,26}, {12,34}, {15,41}, {8,19}, {4,20}, {7,21}, {12,16}, {11,30}, {8,43}, {2,23}, {7,39}, {15,21}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {6,27}, {12,40}, {7,45}, {8,46}, {15,32}, {14,38}, {6,30}, {11,25}, {6,38}, {2,17}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {9,16}, {9,32}, {5,39}, {12,43}, {1,21}, {6,21}, {13,47}, {10,45}, {7,20}, {3,40}, {12,36}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {15,26}, {2,18}, {12,37}, {1,16}, {2,19}, {5,24}, {7,33}, {12,31}, {15,47}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {7,19}, {2,35}, {10,32}, {4,19}, {13,16}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.11 // Bipartite(14,33) Valencies [33,14] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 756996791954873238927632646412997492736000000000 EdgePairs[47][11]:={ {13,25}, {3,42}, {13,40}, {6,36}, {11,42}, {4,46}, {9,18}, {3,29}, {10,17}, {4,26}, {14,29}, {7,47}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {14,47}, {8,31}, {12,42}, {7,24}, {3,47}, {11,34}, {13,27}, {12,25}, {3,17}, {14,17}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {13,43}, {5,18}, {14,15}, {8,26}, {10,29}, {7,17}, {13,22}, {6,28}, {5,43}, {14,16}, {12,32}, {2,30}, {14,25}, {7,15}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {2,21}, {7,26}, {11,27}, {8,44}, {4,34}, {13,29}, {10,22}, {12,22}, {10,42}, {14,40}, {9,41}, {14,33}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {14,27}, {5,47}, {13,15}, {11,47}, {10,25}, {12,35}, {13,17}, {11,36}, {14,22}, {11,21}, {3,22}, {6,19}, {5,23}, {2,37}, {14,43}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {2,36}, {12,38}, {11,44}, {13,33}, {10,23}, {1,26}, {9,27}, {1,25}, {5,46}, {10,16}, {12,44}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {7,16}, {1,22}, {6,24}, {8,47}, {6,39}, {2,44}, {2,45}, {1,42}, {8,21}, {9,20}, {14,23}, {4,45}, {3,16}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {14,35}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {5,28}, {12,18}, {8,30}, {4,21}, {14,32}, {9,37}, {12,21}, {9,17}, {10,18}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {1,44}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {7,37}, {1,28}, {14,18}, {3,43}, {1,17}, {3,36}, {7,42}, {14,36}, {6,43}, {12,47}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {5,21}, {7,36}, {9,39}, {13,26}, {10,46}, {14,37}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {12,17}, {9,42}, {9,19}, {13,35}, {13,32}, {10,24}, {2,25}, {3,28}, {9,35}, {12,24}, {12,45}, {14,28}, {10,36}, {12,20}, {8,41}, {13,46}, {2,40}, {9,43}, {3,19}, {4,40}, {2,16}, {1,39}, {6,45}, {7,40}, {14,19}, {10,37}, {6,44}, {2,42}, {9,46}, {7,35}, {4,42}, {14,41}, {4,15}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {3,35}, {14,26}, {12,15}, {9,40}, {8,22}, {8,45}, {7,46}, {14,31}, {6,47}, {14,20}, {11,33}, {1,34}, {11,16}, {7,25}, {4,47}, {13,37}, {8,27}, {5,30}, {6,46}, {14,46}, {9,30}, {5,40}, {3,46}, {8,17}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {8,29}, {7,22}, {9,34}, {6,22}, {5,19}, {13,28}, {2,33}, {6,32}, {10,35}, {9,47}, {4,27}, {14,24}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {1,19}, {5,41}, {13,41}, {6,17}, {3,34}, {13,20}, {13,21}, {2,43}, {3,38}, {14,34}, {13,44}, {11,23}, {1,47}, {9,33}, {8,16}, {8,42}, {8,32}, {7,38}, {14,30}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {8,15}, {1,46}, {10,34}, {11,28}, {6,25}, {13,39}, {11,43}, {11,17}, {4,16}, {12,26}, {1,45}, {10,30}, {6,18}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {6,16}, {7,44}, {11,46}, {4,31}, {2,15}, {3,41}, {10,33}, {10,39}, {13,34}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {14,21}, {14,44}, {3,21}, {1,36}, {13,30}, {9,24}, {14,39}, {9,45}, {14,42}, {6,20}, {2,46}, {3,39}, {10,41}, {11,15}, {6,26}, {12,34}, {8,19}, {4,20}, {7,21}, {12,16}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {4,23}, {9,36}, {10,40}, {6,27}, {12,40}, {7,45}, {8,46}, {14,38}, {6,30}, {11,25}, {6,38}, {2,17}, {11,40}, {13,42}, {14,45}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {9,16}, {9,32}, {5,39}, {12,43}, {1,21}, {9,15}, {6,21}, {13,47}, {10,45}, {7,20}, {3,40}, {12,36}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {2,18}, {12,37}, {1,16}, {2,19}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {7,19}, {2,35}, {10,32}, {4,19}, {13,16}, {10,15}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.12 // Bipartite(13,34) Valencies [34,13] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1838420780461835008824250712717279625216000000000 EdgePairs[47][12]:={ {13,25}, {3,42}, {13,40}, {6,36}, {11,42}, {4,46}, {9,18}, {3,29}, {10,17}, {4,26}, {7,47}, {2,20}, {2,26}, {8,28}, {5,32}, {4,24}, {8,37}, {8,31}, {12,42}, {7,24}, {3,47}, {11,34}, {13,27}, {12,25}, {3,17}, {2,39}, {7,28}, {2,24}, {1,32}, {4,28}, {8,36}, {9,21}, {1,18}, {8,20}, {3,15}, {13,43}, {5,18}, {8,26}, {10,29}, {7,17}, {13,22}, {6,28}, {5,43}, {12,32}, {2,30}, {7,15}, {3,25}, {10,27}, {1,41}, {4,30}, {8,24}, {2,38}, {12,27}, {6,34}, {4,38}, {11,39}, {2,21}, {7,26}, {11,27}, {8,44}, {4,34}, {13,29}, {10,22}, {12,22}, {10,42}, {9,41}, {11,35}, {3,27}, {3,32}, {11,31}, {11,37}, {8,38}, {11,29}, {5,47}, {13,15}, {11,47}, {10,25}, {12,35}, {13,17}, {11,36}, {11,21}, {3,22}, {6,19}, {5,23}, {2,37}, {7,30}, {5,25}, {5,26}, {6,31}, {8,40}, {2,41}, {1,31}, {6,35}, {3,14}, {5,45}, {4,41}, {9,22}, {5,20}, {8,39}, {7,34}, {1,20}, {2,36}, {7,14}, {12,38}, {11,44}, {13,33}, {10,23}, {1,26}, {9,27}, {1,25}, {5,46}, {10,16}, {6,14}, {12,44}, {8,35}, {11,38}, {5,27}, {6,40}, {9,31}, {7,23}, {5,33}, {4,39}, {7,16}, {1,22}, {6,24}, {8,47}, {6,39}, {2,44}, {2,45}, {10,14}, {1,42}, {8,21}, {9,20}, {4,45}, {3,16}, {2,28}, {1,27}, {5,22}, {9,25}, {3,23}, {4,44}, {5,36}, {9,26}, {12,39}, {7,31}, {12,33}, {5,38}, {1,37}, {13,18}, {1,29}, {2,34}, {10,19}, {12,19}, {12,41}, {5,42}, {11,32}, {3,31}, {2,47}, {11,18}, {10,43}, {3,20}, {5,29}, {9,28}, {11,19}, {5,28}, {12,18}, {8,30}, {4,21}, {9,37}, {12,21}, {9,17}, {10,18}, {1,14}, {10,20}, {11,41}, {8,34}, {13,19}, {9,29}, {2,22}, {4,33}, {1,44}, {10,31}, {3,18}, {13,23}, {5,15}, {5,16}, {7,37}, {1,28}, {3,43}, {1,17}, {3,36}, {9,14}, {7,42}, {6,43}, {12,47}, {7,29}, {6,37}, {12,28}, {3,37}, {1,35}, {5,21}, {7,36}, {9,39}, {13,26}, {10,46}, {11,24}, {7,43}, {11,45}, {8,33}, {10,28}, {9,44}, {12,17}, {9,42}, {9,19}, {13,35}, {13,32}, {10,24}, {2,25}, {3,28}, {2,14}, {9,35}, {12,24}, {12,45}, {10,36}, {12,20}, {8,41}, {13,46}, {2,40}, {9,43}, {3,19}, {4,40}, {2,16}, {1,39}, {6,45}, {7,40}, {10,37}, {6,44}, {2,42}, {9,46}, {7,35}, {4,42}, {4,15}, {4,29}, {8,25}, {5,34}, {1,30}, {1,43}, {3,26}, {13,36}, {9,23}, {3,35}, {12,15}, {9,40}, {8,22}, {8,45}, {7,46}, {6,47}, {11,33}, {1,34}, {11,16}, {7,25}, {4,47}, {13,37}, {8,27}, {5,30}, {6,46}, {9,30}, {5,40}, {3,46}, {8,17}, {4,22}, {1,40}, {6,23}, {10,26}, {1,23}, {8,29}, {7,22}, {9,34}, {6,22}, {5,19}, {13,28}, {2,33}, {6,32}, {10,35}, {9,47}, {4,27}, {4,17}, {3,24}, {7,27}, {4,32}, {2,27}, {1,19}, {5,41}, {13,41}, {6,17}, {3,34}, {11,14}, {13,20}, {13,21}, {2,43}, {3,38}, {13,44}, {11,23}, {1,47}, {9,33}, {8,16}, {8,42}, {8,32}, {7,38}, {12,23}, {13,31}, {8,18}, {5,31}, {4,25}, {10,38}, {3,30}, {8,15}, {1,46}, {10,34}, {4,14}, {11,28}, {6,25}, {13,39}, {11,43}, {11,17}, {4,16}, {12,26}, {1,45}, {10,30}, {6,18}, {6,42}, {11,20}, {7,32}, {13,38}, {11,26}, {13,24}, {6,16}, {7,44}, {11,46}, {4,31}, {2,15}, {3,41}, {10,33}, {10,39}, {13,34}, {8,14}, {1,38}, {5,37}, {7,41}, {3,44}, {8,23}, {2,29}, {3,21}, {1,36}, {13,30}, {9,24}, {9,45}, {6,20}, {2,46}, {3,39}, {10,41}, {11,15}, {6,26}, {12,34}, {8,19}, {4,20}, {7,21}, {12,16}, {11,30}, {8,43}, {2,23}, {7,39}, {9,38}, {10,44}, {1,33}, {12,30}, {2,32}, {6,33}, {12,14}, {4,23}, {9,36}, {10,40}, {6,27}, {12,40}, {7,45}, {8,46}, {6,30}, {11,25}, {6,38}, {2,17}, {11,40}, {13,42}, {5,14}, {5,44}, {5,35}, {3,45}, {4,43}, {11,22}, {9,16}, {9,32}, {5,39}, {12,43}, {1,21}, {13,14}, {6,21}, {9,15}, {13,47}, {10,45}, {7,20}, {3,40}, {12,36}, {7,18}, {10,21}, {3,33}, {5,17}, {1,24}, {4,18}, {2,18}, {12,37}, {1,16}, {2,19}, {5,24}, {6,15}, {7,33}, {1,15}, {12,31}, {13,45}, {4,37}, {12,29}, {4,35}, {10,47}, {7,19}, {2,35}, {10,32}, {4,19}, {13,16}, {10,15}, {6,41}, {12,46}, {4,36}, {6,29}, {2,31} }; // ET47.13 // Bipartite(12,35) Valencies [35,12] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4949594408935709639142213457315752837120000000000 EdgePairs[47][13]:={ {6,38}, {11,40}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {5,45}, {3,26}, {12,22}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {8,40}, {6,15}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {12,16}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {2,46}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {10,47}, {8,16}, {2,34}, {9,18}, {10,17}, {12,28}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {12,46}, {1,17}, {4,16}, {7,45}, {8,46}, {4,13}, {8,37}, {12,20}, {5,41}, {7,41}, {12,38}, {1,13}, {12,26}, {7,27}, {12,42}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {12,31}, {12,40}, {10,20}, {1,24}, {2,15}, {12,23}, {5,37}, {12,13}, {9,35}, {1,36}, {6,18}, {1,29}, {12,37}, {6,46}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {9,47}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {9,46}, {3,47}, {1,42}, {7,32}, {12,24}, {1,31}, {3,31}, {12,27}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {12,15}, {8,15}, {11,21}, {12,47}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {1,47}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {10,46}, {11,33}, {8,24}, {8,47}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {7,46}, {8,45}, {3,29}, {12,17}, {1,41}, {2,23}, {10,13}, {4,45}, {10,19}, {9,22}, {12,41}, {3,44}, {4,47}, {9,19}, {11,44}, {3,25}, {11,34}, {7,35}, {11,13}, {11,46}, {2,43}, {2,27}, {12,30}, {6,30}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {3,32}, {7,28}, {6,45}, {12,18}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {12,45}, {6,22}, {4,34}, {10,25}, {12,29}, {6,31}, {11,32}, {12,25}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {12,43}, {5,20}, {2,26}, {10,40}, {12,14}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {2,45}, {5,46}, {6,47}, {3,33}, {1,45}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {11,47}, {4,46}, {8,43}, {2,31}, {11,45}, {1,33}, {12,36}, {3,45}, {3,14}, {5,26}, {12,44}, {7,47}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {12,33}, {11,19}, {8,33}, {5,47}, {12,39}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {12,34}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {11,37}, {2,47}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {12,32}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {1,46}, {4,19}, {8,39}, {3,37}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {12,35}, {6,35}, {12,19}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {12,21}, {2,14}, {11,26}, {3,46}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET47.14 // Bipartite(11,36) Valencies [36,11] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 14848783226807128917426640371947258511360000000000 EdgePairs[47][14]:={ {6,38}, {11,40}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {11,25}, {5,43}, {5,45}, {3,26}, {8,26}, {1,40}, {11,43}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {11,15}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {11,14}, {7,30}, {8,31}, {4,40}, {4,37}, {2,46}, {6,14}, {2,33}, {6,32}, {4,38}, {11,29}, {11,35}, {1,12}, {10,42}, {11,17}, {6,29}, {11,27}, {1,20}, {3,18}, {10,47}, {8,16}, {2,34}, {9,18}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {7,45}, {8,46}, {4,13}, {8,37}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {11,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {6,46}, {10,35}, {6,44}, {4,23}, {11,18}, {8,38}, {9,47}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {9,46}, {3,47}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {11,22}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {11,42}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,15}, {11,21}, {6,36}, {8,17}, {10,16}, {11,36}, {3,30}, {3,16}, {1,47}, {2,24}, {11,23}, {3,24}, {10,36}, {11,16}, {10,38}, {6,16}, {10,46}, {11,33}, {7,12}, {8,24}, {8,47}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {7,46}, {8,45}, {3,29}, {1,41}, {2,23}, {10,13}, {4,45}, {10,19}, {9,22}, {3,44}, {4,47}, {9,19}, {11,44}, {3,25}, {11,34}, {7,35}, {11,13}, {11,46}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {11,24}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {6,45}, {2,16}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {11,32}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {8,27}, {2,45}, {5,46}, {6,47}, {3,33}, {1,45}, {10,15}, {11,30}, {9,28}, {3,34}, {2,21}, {4,27}, {5,24}, {2,22}, {11,47}, {4,46}, {8,43}, {2,31}, {11,45}, {1,33}, {3,45}, {3,14}, {5,26}, {7,47}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {11,19}, {8,33}, {5,47}, {4,12}, {8,14}, {11,31}, {3,15}, {11,41}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {11,12}, {7,26}, {7,18}, {11,37}, {2,47}, {11,28}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {11,20}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {1,46}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {8,25}, {2,42}, {2,32}, {6,33}, {2,14}, {11,26}, {3,46}, {5,33}, {5,30}, {11,38}, {9,37}, {6,40} }; // ET47.15 // Bipartite(10,37) Valencies [37,10] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 49945907217442160904071426705640778629120000000000 EdgePairs[47][15]:={ {6,38}, {10,37}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {10,18}, {4,28}, {5,43}, {5,45}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {10,33}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {10,39}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {4,37}, {4,40}, {8,31}, {2,46}, {6,14}, {10,11}, {2,33}, {6,32}, {4,38}, {1,12}, {10,42}, {6,29}, {9,11}, {1,20}, {3,18}, {10,47}, {8,16}, {2,34}, {9,18}, {10,17}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {7,45}, {8,46}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {7,27}, {6,39}, {2,17}, {10,26}, {7,33}, {10,20}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {6,46}, {10,35}, {6,44}, {4,23}, {8,38}, {9,47}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {8,19}, {3,38}, {1,18}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {2,39}, {4,18}, {8,18}, {9,46}, {3,47}, {1,42}, {10,12}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,15}, {6,36}, {8,17}, {10,16}, {3,30}, {3,16}, {1,47}, {2,24}, {3,24}, {10,36}, {10,38}, {6,16}, {10,46}, {7,12}, {8,24}, {8,47}, {4,41}, {8,41}, {9,38}, {9,26}, {5,14}, {7,46}, {8,45}, {3,29}, {1,41}, {2,23}, {10,13}, {4,45}, {10,19}, {9,22}, {4,11}, {3,44}, {4,47}, {9,19}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {10,31}, {10,44}, {10,29}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {10,22}, {10,30}, {7,23}, {6,22}, {4,34}, {10,25}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {10,28}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {10,40}, {9,21}, {10,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {2,45}, {8,27}, {5,46}, {6,47}, {3,33}, {2,11}, {1,45}, {10,15}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {8,11}, {4,46}, {8,43}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {7,47}, {2,37}, {4,42}, {5,29}, {4,25}, {10,41}, {3,28}, {7,31}, {8,33}, {5,47}, {4,12}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {2,47}, {7,16}, {5,16}, {1,23}, {5,18}, {10,24}, {10,27}, {10,34}, {5,17}, {3,40}, {7,17}, {8,35}, {10,45}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {10,43}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {10,23}, {9,43}, {1,46}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {10,14}, {10,32}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {8,25}, {2,32}, {6,33}, {2,14}, {3,46}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET47.16 // Bipartite(9,38) Valencies [38,9] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 189794447426280211435471421481434958790656000000000 EdgePairs[47][16]:={ {6,38}, {6,25}, {9,32}, {5,38}, {5,22}, {9,17}, {4,28}, {5,43}, {9,10}, {5,45}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {4,37}, {4,40}, {8,31}, {2,46}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {9,11}, {1,20}, {3,18}, {2,34}, {8,16}, {9,18}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {9,33}, {8,12}, {1,17}, {4,16}, {7,45}, {8,46}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {2,10}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {9,35}, {1,36}, {6,18}, {1,29}, {6,46}, {6,44}, {4,23}, {8,38}, {9,47}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {9,36}, {1,43}, {9,29}, {9,39}, {8,42}, {9,20}, {4,22}, {1,18}, {3,38}, {8,19}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {9,46}, {3,47}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {9,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {1,47}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {8,47}, {4,41}, {8,41}, {9,38}, {4,10}, {9,26}, {5,14}, {7,46}, {8,45}, {3,29}, {1,41}, {2,23}, {4,45}, {9,22}, {4,11}, {3,44}, {4,47}, {9,19}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {9,31}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {9,16}, {5,39}, {9,30}, {9,12}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {8,34}, {9,25}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {9,41}, {6,23}, {7,39}, {3,41}, {4,36}, {4,29}, {1,32}, {9,44}, {6,43}, {6,37}, {8,32}, {7,24}, {9,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {9,21}, {7,29}, {2,28}, {8,29}, {7,21}, {9,23}, {8,36}, {2,45}, {8,27}, {5,46}, {6,47}, {3,33}, {2,11}, {1,45}, {9,28}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {4,46}, {8,11}, {8,43}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {7,47}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {8,33}, {5,47}, {4,12}, {7,10}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {9,15}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {2,47}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {9,45}, {4,26}, {1,28}, {3,27}, {7,20}, {9,27}, {7,38}, {5,42}, {2,38}, {5,10}, {7,44}, {8,28}, {7,43}, {9,40}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {9,43}, {1,46}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {9,14}, {9,42}, {5,36}, {9,34}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {8,25}, {2,32}, {6,33}, {2,14}, {3,46}, {5,33}, {5,30}, {9,37}, {6,40} }; // ET47.17 // Bipartite(8,39) Valencies [39,8] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 822442605513880916220376159752884821426176000000000 EdgePairs[47][17]:={ {6,38}, {6,25}, {5,38}, {5,22}, {4,28}, {5,43}, {5,45}, {3,26}, {8,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {8,40}, {3,35}, {8,21}, {3,19}, {5,15}, {1,19}, {3,23}, {8,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {6,9}, {4,37}, {4,40}, {8,31}, {2,46}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {1,20}, {3,18}, {2,34}, {8,16}, {2,25}, {4,24}, {4,43}, {4,30}, {8,13}, {8,30}, {8,12}, {1,17}, {1,9}, {4,16}, {7,45}, {8,46}, {1,10}, {4,13}, {8,37}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {8,9}, {2,10}, {3,9}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {1,36}, {6,18}, {1,29}, {6,46}, {6,44}, {4,23}, {8,38}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {8,22}, {6,34}, {1,43}, {8,42}, {4,22}, {1,18}, {3,38}, {8,19}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {8,18}, {3,47}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {5,35}, {4,9}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {8,10}, {8,15}, {6,36}, {8,17}, {3,30}, {3,16}, {1,47}, {2,24}, {3,24}, {6,16}, {7,12}, {8,24}, {8,47}, {4,41}, {8,41}, {4,10}, {5,14}, {7,46}, {8,45}, {3,29}, {1,41}, {2,23}, {4,45}, {4,11}, {3,44}, {4,47}, {3,25}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {5,39}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {8,34}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {4,15}, {6,23}, {3,41}, {7,39}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {8,32}, {7,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {7,29}, {2,28}, {8,29}, {7,21}, {8,36}, {2,45}, {8,27}, {5,46}, {6,47}, {3,33}, {2,11}, {1,45}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {4,46}, {8,11}, {8,43}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {7,47}, {2,37}, {4,42}, {5,29}, {4,25}, {3,28}, {7,31}, {5,9}, {8,33}, {5,47}, {4,12}, {7,10}, {8,14}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {8,44}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {2,47}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {8,35}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {7,38}, {5,42}, {2,38}, {7,9}, {5,10}, {7,44}, {8,28}, {7,43}, {4,20}, {8,20}, {1,27}, {5,44}, {5,13}, {5,25}, {1,46}, {4,19}, {3,37}, {8,39}, {3,12}, {7,13}, {5,36}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {8,25}, {2,9}, {2,32}, {6,33}, {2,14}, {3,46}, {5,33}, {5,30}, {6,40} }; // ET47.18 // Bipartite(7,40) Valencies [40,7] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 4112213027569404581101880798764424107130880000000000 EdgePairs[47][18]:={ {6,38}, {6,25}, {5,38}, {5,22}, {3,8}, {4,28}, {5,43}, {5,45}, {3,26}, {5,11}, {1,40}, {2,35}, {4,31}, {6,15}, {3,35}, {3,19}, {5,15}, {1,19}, {3,23}, {3,20}, {2,18}, {1,21}, {3,21}, {3,39}, {5,32}, {1,35}, {7,30}, {6,9}, {4,37}, {4,40}, {2,46}, {6,14}, {2,33}, {6,32}, {4,38}, {1,12}, {6,29}, {1,20}, {3,18}, {2,34}, {2,25}, {4,24}, {4,43}, {4,30}, {1,17}, {1,9}, {4,16}, {7,45}, {1,10}, {4,13}, {7,11}, {5,41}, {7,41}, {1,13}, {3,10}, {7,27}, {2,10}, {3,9}, {6,39}, {2,17}, {7,33}, {1,24}, {2,15}, {5,37}, {1,36}, {6,18}, {1,29}, {6,46}, {6,44}, {4,23}, {6,24}, {2,29}, {5,34}, {1,38}, {1,26}, {3,17}, {2,36}, {7,15}, {6,34}, {1,43}, {4,22}, {1,18}, {3,38}, {5,27}, {7,14}, {3,43}, {6,17}, {5,28}, {6,10}, {2,39}, {4,18}, {3,47}, {1,42}, {7,32}, {1,31}, {3,31}, {3,13}, {1,39}, {7,37}, {5,12}, {6,27}, {2,30}, {2,8}, {5,35}, {4,9}, {3,36}, {6,12}, {4,21}, {7,19}, {4,32}, {2,44}, {1,30}, {2,13}, {6,36}, {3,30}, {3,16}, {1,47}, {2,24}, {3,24}, {6,16}, {7,12}, {4,41}, {4,10}, {5,14}, {7,46}, {3,29}, {1,41}, {2,23}, {4,45}, {4,11}, {3,44}, {4,47}, {3,25}, {6,8}, {7,35}, {2,43}, {2,27}, {6,30}, {2,12}, {4,33}, {1,22}, {7,34}, {5,19}, {7,8}, {6,13}, {1,25}, {6,19}, {2,20}, {4,17}, {5,39}, {3,32}, {7,28}, {6,45}, {2,16}, {6,11}, {5,40}, {7,23}, {6,22}, {4,34}, {6,31}, {1,16}, {3,42}, {3,22}, {1,44}, {4,14}, {5,8}, {4,15}, {6,23}, {3,41}, {7,39}, {4,36}, {4,29}, {1,32}, {6,43}, {6,37}, {7,24}, {5,31}, {2,19}, {6,20}, {4,44}, {7,40}, {2,41}, {5,23}, {5,20}, {2,26}, {7,29}, {2,28}, {7,21}, {2,45}, {5,46}, {6,47}, {3,33}, {2,11}, {1,45}, {3,34}, {2,21}, {1,11}, {4,27}, {5,24}, {2,22}, {4,46}, {2,31}, {1,33}, {3,45}, {3,14}, {5,26}, {3,11}, {7,47}, {2,37}, {4,42}, {4,8}, {5,29}, {4,25}, {3,28}, {7,31}, {5,9}, {5,47}, {1,8}, {4,12}, {7,10}, {3,15}, {7,25}, {7,22}, {1,14}, {6,26}, {1,34}, {5,21}, {7,42}, {6,41}, {6,28}, {6,42}, {4,35}, {1,15}, {7,26}, {7,18}, {2,47}, {7,16}, {5,16}, {1,23}, {5,18}, {5,17}, {3,40}, {7,17}, {2,40}, {6,21}, {4,26}, {1,28}, {3,27}, {7,20}, {5,42}, {7,38}, {2,38}, {7,9}, {5,10}, {7,44}, {7,43}, {4,20}, {1,27}, {5,44}, {5,13}, {5,25}, {1,46}, {4,19}, {3,37}, {3,12}, {7,13}, {5,36}, {4,39}, {7,36}, {6,35}, {1,37}, {2,42}, {2,9}, {2,32}, {6,33}, {2,14}, {3,46}, {5,33}, {5,30}, {6,40} }; // ET47.19 // Bipartite(6,41) Valencies [41,6] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 24085819161477941117882444678477341198909440000000000 EdgePairs[47][19]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {6,16}, {6,32}, {4,27}, {2,46}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {6,17}, {2,23}, {1,13}, {5,38}, {3,9}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,47}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {6,7}, {2,28}, {2,14}, {1,30}, {5,32}, {6,11}, {4,23}, {2,42}, {6,22}, {3,18}, {3,17}, {6,29}, {3,7}, {2,45}, {4,38}, {6,21}, {6,47}, {3,34}, {2,25}, {5,40}, {3,46}, {6,31}, {6,40}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {1,44}, {4,41}, {2,10}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {6,8}, {5,25}, {2,39}, {1,31}, {3,12}, {4,45}, {2,35}, {1,22}, {3,44}, {6,12}, {4,47}, {6,30}, {6,43}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {6,18}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {6,33}, {5,18}, {1,23}, {6,24}, {5,30}, {6,44}, {6,46}, {5,24}, {5,7}, {5,46}, {1,45}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {6,23}, {1,43}, {3,26}, {4,46}, {5,28}, {5,42}, {6,15}, {2,17}, {4,36}, {5,41}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {6,27}, {5,44}, {6,26}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {6,19}, {1,46}, {6,9}, {6,41}, {1,15}, {6,28}, {6,14}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {6,42}, {4,40}, {2,21}, {6,36}, {3,30}, {5,33}, {3,24}, {2,29}, {6,45}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,47}, {6,25}, {1,47}, {6,38}, {2,40}, {2,31}, {6,34}, {6,10}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {5,13}, {1,41}, {5,45}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {5,15}, {6,39}, {6,37}, {3,47}, {5,19}, {6,20}, {2,30}, {5,21}, {6,13}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {6,35}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36}, {5,16} }; // ET47.20 // Bipartite(5,42) Valencies [42,5] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 168600734130345587825177112749341388392366080000000000 EdgePairs[47][20]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {5,17}, {2,33}, {4,27}, {2,46}, {5,34}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {5,38}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {5,47}, {5,20}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {2,28}, {2,14}, {1,30}, {5,32}, {4,23}, {2,42}, {3,18}, {3,17}, {3,7}, {2,45}, {4,38}, {3,34}, {2,25}, {5,40}, {3,46}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {5,22}, {1,18}, {3,14}, {4,8}, {5,11}, {1,44}, {4,41}, {2,10}, {5,29}, {2,38}, {2,37}, {5,43}, {4,42}, {5,25}, {2,39}, {1,31}, {3,12}, {4,45}, {2,35}, {1,22}, {3,44}, {4,47}, {4,33}, {4,21}, {5,23}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {5,18}, {1,23}, {5,30}, {2,6}, {5,24}, {5,7}, {5,46}, {1,45}, {1,9}, {5,14}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {1,43}, {3,26}, {4,46}, {5,28}, {5,42}, {2,17}, {4,36}, {5,41}, {4,6}, {5,12}, {1,42}, {3,19}, {4,9}, {1,24}, {5,31}, {5,44}, {3,23}, {1,39}, {3,21}, {5,36}, {2,7}, {1,25}, {1,46}, {1,15}, {2,11}, {1,35}, {1,37}, {5,39}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {5,33}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {5,8}, {2,47}, {1,47}, {2,40}, {2,31}, {5,10}, {5,27}, {5,26}, {3,42}, {4,18}, {5,9}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {5,13}, {1,41}, {5,45}, {5,6}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {5,15}, {3,47}, {5,19}, {2,30}, {5,21}, {2,18}, {5,35}, {1,34}, {5,37}, {2,43}, {4,17}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36}, {5,16} }; // ET47.21 // Bipartite(4,43) Valencies [43,4] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 1449966313520972055296523169644335940174348288000000000 EdgePairs[47][21]:={ {2,44}, {1,11}, {3,33}, {2,24}, {1,20}, {2,33}, {4,27}, {2,46}, {4,24}, {4,26}, {3,22}, {3,8}, {3,40}, {4,16}, {1,10}, {4,30}, {2,23}, {1,13}, {3,9}, {3,6}, {4,29}, {1,32}, {3,13}, {3,45}, {1,27}, {3,43}, {3,25}, {3,15}, {1,40}, {2,15}, {4,19}, {4,31}, {2,19}, {1,19}, {2,27}, {3,35}, {3,37}, {2,26}, {1,21}, {2,9}, {2,41}, {2,28}, {2,14}, {1,30}, {4,23}, {3,5}, {2,42}, {3,18}, {3,17}, {3,7}, {2,45}, {4,38}, {3,34}, {2,25}, {3,46}, {1,38}, {4,10}, {2,34}, {1,17}, {2,36}, {1,7}, {4,22}, {1,18}, {3,14}, {4,8}, {1,5}, {2,5}, {1,44}, {4,41}, {2,10}, {2,38}, {2,37}, {4,42}, {2,39}, {1,31}, {3,12}, {4,45}, {2,35}, {1,22}, {3,44}, {4,47}, {4,33}, {4,21}, {3,20}, {2,13}, {2,20}, {1,29}, {2,16}, {3,39}, {3,32}, {4,35}, {2,32}, {1,12}, {1,23}, {2,6}, {1,45}, {1,9}, {4,15}, {4,13}, {1,28}, {3,11}, {3,27}, {4,7}, {4,28}, {1,33}, {4,43}, {3,29}, {3,10}, {1,43}, {3,26}, {4,46}, {2,17}, {4,36}, {4,6}, {1,42}, {3,19}, {4,9}, {1,24}, {3,23}, {1,39}, {3,21}, {2,7}, {1,25}, {1,46}, {1,15}, {2,11}, {4,5}, {1,35}, {1,37}, {3,16}, {4,37}, {4,40}, {2,21}, {3,30}, {3,24}, {2,29}, {1,26}, {2,22}, {4,34}, {1,16}, {4,14}, {2,47}, {1,47}, {2,40}, {2,31}, {3,42}, {4,18}, {4,25}, {3,38}, {1,8}, {4,11}, {4,12}, {4,20}, {3,28}, {1,41}, {3,41}, {3,31}, {2,12}, {1,14}, {2,8}, {1,6}, {3,47}, {2,30}, {2,18}, {1,34}, {2,43}, {4,17}, {3,36}, {4,39}, {4,44}, {4,32}, {1,36} }; // ET47.22 // Bipartite(3,44) Valencies [44,3] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 15949629448730692608261754866087695341917831168000000000 EdgePairs[47][22]:={ {1,15}, {3,15}, {1,43}, {2,38}, {1,11}, {2,22}, {3,29}, {3,38}, {1,31}, {3,7}, {3,46}, {2,11}, {1,46}, {1,40}, {2,20}, {1,25}, {2,47}, {2,37}, {3,32}, {1,38}, {1,9}, {2,33}, {1,5}, {1,44}, {3,30}, {1,32}, {3,45}, {3,10}, {2,28}, {3,34}, {3,31}, {2,19}, {2,18}, {2,15}, {2,29}, {3,19}, {1,29}, {3,18}, {3,41}, {1,34}, {2,14}, {3,11}, {2,10}, {2,41}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {3,13}, {2,16}, {1,22}, {2,32}, {1,16}, {3,40}, {2,36}, {2,17}, {2,13}, {3,14}, {1,12}, {3,9}, {3,22}, {3,23}, {2,42}, {2,34}, {3,27}, {1,19}, {2,40}, {2,35}, {3,47}, {2,9}, {1,4}, {3,5}, {1,35}, {1,26}, {2,44}, {2,4}, {2,24}, {3,42}, {2,27}, {3,4}, {2,43}, {3,35}, {1,23}, {2,21}, {1,7}, {2,46}, {1,39}, {2,39}, {2,12}, {3,28}, {3,26}, {3,24}, {3,12}, {1,42}, {2,6}, {3,21}, {1,14}, {1,41}, {3,44}, {2,8}, {3,39}, {1,37}, {1,20}, {1,27}, {1,13}, {3,16}, {3,25}, {2,26}, {3,8}, {3,20}, {1,33}, {2,25}, {3,6}, {1,28}, {3,36}, {3,17}, {3,37}, {2,7}, {3,43}, {1,47}, {1,45}, {3,33}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24}, {2,45} }; // ET47.23 // Bipartite(2,45) Valencies [45,2] // Diameter 2 Girth 4 // Has twins Non-VT Non-AT // Automorphism group of order 239244441730960389123926322991315430128767467520000000000 EdgePairs[47][23]:={ {1,15}, {1,43}, {2,38}, {1,11}, {2,22}, {1,31}, {2,11}, {1,46}, {1,40}, {2,3}, {2,20}, {1,25}, {2,47}, {2,37}, {1,38}, {1,9}, {2,33}, {1,5}, {1,44}, {1,32}, {2,28}, {2,19}, {2,18}, {2,15}, {2,29}, {1,29}, {1,34}, {2,14}, {1,3}, {2,10}, {2,41}, {2,31}, {2,23}, {1,10}, {1,36}, {1,17}, {2,16}, {1,22}, {2,32}, {1,16}, {2,36}, {2,17}, {2,13}, {1,12}, {2,42}, {2,34}, {1,19}, {2,40}, {2,35}, {2,9}, {1,4}, {1,35}, {1,26}, {2,44}, {2,4}, {2,24}, {2,27}, {2,43}, {1,23}, {2,21}, {1,7}, {2,46}, {1,39}, {2,39}, {2,12}, {1,42}, {2,6}, {1,14}, {1,41}, {2,8}, {1,37}, {1,20}, {1,27}, {1,13}, {2,26}, {1,33}, {2,25}, {1,28}, {2,7}, {1,47}, {1,45}, {1,8}, {1,30}, {2,30}, {1,21}, {1,6}, {1,18}, {2,5}, {1,24}, {2,45} }; // ET47.24 // Bipartite(1,46) Valencies [46,1] // Diameter 2 No cycles // Has twins Non-VT Non-AT // Automorphism group of order 5502622159812088949850305428800254892961651752960000000000 EdgePairs[47][24]:={ {1,26}, {1,47}, {1,14}, {1,44}, {1,24}, {1,46}, {1,29}, {1,30}, {1,32}, {1,37}, {1,33}, {1,40}, {1,10}, {1,2}, {1,43}, {1,39}, {1,36}, {1,6}, {1,45}, {1,4}, {1,20}, {1,12}, {1,31}, {1,38}, {1,7}, {1,15}, {1,16}, {1,21}, {1,3}, {1,18}, {1,5}, {1,27}, {1,17}, {1,28}, {1,42}, {1,8}, {1,13}, {1,19}, {1,9}, {1,41}, {1,22}, {1,34}, {1,35}, {1,23}, {1,11}, {1,25} }; // ET47.25 // Non-bipartite Valency 46 // Diameter 1 Girth 3 // Twin-free VT AT // Automorphism group of order 258623241511168180642964355153611979969197632389120000000000 EdgePairs[47][25]:={ {15,47}, {8,40}, {7,36}, {22,36}, {6,12}, {9,22}, {1,47}, {21,30}, {18,24}, {2,12}, {19,37}, {40,41}, {37,43}, {13,18}, {2,6}, {32,33}, {10,34}, {30,47}, {12,36}, {1,25}, {4,33}, {14,28}, {4,32}, {10,31}, {28,38}, {16,29}, {2,26}, {25,30}, {21,25}, {9,14}, {6,26}, {4,30}, {16,42}, {23,26}, {7,23}, {25,35}, {21,35}, {30,35}, {18,45}, {5,44}, {35,47}, {15,21}, {24,40}, {26,42}, {5,40}, {4,35}, {6,39}, {8,44}, {14,37}, {36,39}, {33,47}, {9,38}, {27,37}, {2,39}, {15,25}, {1,20}, {31,34}, {29,46}, {20,47}, {32,47}, {19,27}, {28,43}, {32,34}, {7,12}, {31,33}, {21,34}, {24,47}, {4,10}, {33,34}, {3,19}, {1,15}, {5,8}, {10,30}, {24,44}, {31,32}, {40,44}, {31,47}, {9,28}, {42,46}, {25,31}, {2,23}, {16,36}, {7,26}, {7,42}, {30,31}, {21,45}, {21,31}, {13,44}, {3,14}, {17,39}, {1,31}, {6,23}, {31,35}, {21,32}, {17,29}, {25,34}, {15,20}, {8,47}, {25,33}, {34,35}, {38,43}, {9,46}, {3,27}, {29,39}, {25,32}, {25,45}, {44,45}, {5,13}, {4,45}, {36,46}, {15,33}, {21,33}, {22,27}, {30,34}, {13,47}, {17,36}, {10,35}, {13,40}, {11,15}, {14,22}, {15,32}, {8,24}, {1,11}, {1,34}, {13,41}, {34,47}, {22,37}, {12,26}, {15,34}, {18,41}, {7,16}, {12,16}, {14,19}, {9,43}, {3,38}, {13,24}, {11,30}, {30,32}, {40,45}, {6,42}, {4,21}, {12,42}, {29,36}, {30,33}, {14,43}, {20,34}, {23,29}, {1,33}, {4,25}, {2,42}, {1,32}, {9,37}, {27,38}, {20,31}, {6,29}, {8,13}, {36,42}, {1,30}, {23,42}, {14,27}, {11,35}, {2,29}, {16,39}, {15,31}, {10,21}, {17,23}, {10,45}, {12,19}, {3,7}, {10,25}, {6,17}, {32,35}, {20,33}, {2,17}, {29,42}, {33,35}, {36,37}, {20,32}, {18,40}, {11,33}, {18,44}, {28,46}, {5,47}, {19,22}, {16,26}, {3,22}, {5,24}, {11,32}, {22,43}, {1,5}, {28,37}, {11,20}, {26,27}, {24,41}, {17,28}, {1,8}, {11,24}, {1,35}, {9,17}, {10,18}, {19,38}, {8,15}, {5,20}, {14,16}, {3,12}, {11,45}, {3,26}, {28,29}, {11,31}, {16,22}, {27,43}, {12,39}, {6,36}, {5,15}, {20,30}, {2,36}, {4,18}, {35,41}, {22,38}, {26,39}, {8,11}, {22,46}, {15,35}, {30,41}, {14,38}, {5,41}, {39,43}, {12,27}, {11,13}, {15,30}, {3,43}, {19,43}, {7,19}, {41,47}, {37,46}, {1,45}, {14,46}, {11,34}, {8,32}, {7,39}, {22,39}, {19,26}, {8,33}, {8,20}, {5,31}, {20,35}, {16,19}, {30,45}, {1,13}, {26,38}, {9,23}, {7,14}, {34,41}, {13,15}, {5,34}, {9,29}, {13,35}, {14,26}, {23,28}, {7,27}, {2,9}, {10,40}, {29,37}, {38,39}, {13,30}, {6,9}, {17,42}, {18,47}, {35,45}, {13,20}, {16,27}, {37,42}, {23,36}, {8,41}, {5,32}, {5,33}, {8,31}, {19,46}, {17,37}, {5,11}, {3,16}, {20,24}, {7,22}, {22,26}, {12,14}, {12,22}, {20,45}, {3,46}, {7,38}, {13,34}, {28,36}, {23,24}, {15,45}, {9,36}, {3,4}, {4,44}, {31,41}, {8,34}, {26,43}, {15,24}, {10,19}, {1,24}, {41,42}, {20,41}, {12,38}, {27,39}, {32,41}, {31,37}, {14,39}, {31,45}, {34,37}, {2,13}, {5,30}, {33,41}, {24,30}, {6,13}, {27,46}, {5,35}, {8,17}, {24,35}, {1,9}, {18,25}, {4,40}, {2,37}, {12,18}, {6,37}, {25,44}, {16,46}, {9,15}, {3,10}, {21,40}, {16,43}, {13,45}, {18,21}, {8,30}, {21,44}, {10,44}, {13,31}, {2,28}, {25,40}, {22,25}, {15,28}, {6,28}, {14,21}, {7,18}, {11,41}, {21,22}, {34,45}, {14,25}, {5,17}, {24,33}, {20,28}, {13,32}, {13,33}, {35,37}, {10,27}, {9,11}, {43,46}, {24,32}, {16,18}, {32,37}, {33,37}, {19,39}, {1,41}, {3,39}, {5,29}, {33,45}, {40,47}, {8,35}, {28,42}, {15,41}, {6,24}, {24,31}, {32,45}, {9,32}, {39,40}, {2,5}, {2,24}, {4,19}, {5,6}, {9,33}, {9,20}, {18,26}, {8,29}, {24,45}, {10,47}, {4,14}, {21,43}, {7,43}, {12,43}, {30,37}, {8,23}, {5,45}, {3,21}, {5,36}, {12,46}, {4,27}, {23,37}, {25,43}, {2,8}, {6,8}, {25,47}, {24,29}, {9,42}, {13,17}, {44,47}, {3,25}, {26,44}, {1,37}, {13,23}, {12,40}, {21,47}, {36,41}, {1,28}, {8,45}, {7,46}, {38,46}, {13,42}, {16,38}, {25,27}, {9,31}, {21,27}, {4,38}, {8,9}, {4,47}, {28,32}, {24,34}, {10,14}, {13,29}, {4,22}, {4,7}, {10,22}, {10,12}, {24,42}, {26,40}, {17,24}, {28,33}, {21,38}, {15,37}, {7,44}, {46,47}, {2,41}, {8,36}, {23,41}, {39,44}, {9,34}, {15,17}, {10,38}, {6,41}, {34,36}, {11,28}, {39,46}, {13,36}, {18,19}, {28,34}, {19,25}, {25,38}, {19,21}, {41,45}, {20,37}, {6,11}, {38,40}, {5,23}, {12,44}, {11,23}, {35,42}, {31,36}, {2,11}, {9,30}, {29,41}, {38,44}, {7,40}, {20,29}, {16,47}, {33,36}, {32,36}, {28,31}, {30,42}, {26,46}, {18,27}, {1,6}, {11,37}, {1,2}, {5,9}, {4,26}, {4,12}, {2,30}, {3,18}, {7,10}, {1,29}, {6,30}, {9,35}, {1,17}, {8,28}, {5,42}, {43,44}, {18,39}, {10,43}, {16,44}, {21,26}, {17,41}, {4,43}, {35,36}, {12,47}, {5,28}, {2,35}, {17,33}, {25,26}, {10,26}, {17,20}, {16,40}, {6,35}, {15,29}, {17,32}, {25,46}, {8,42}, {24,28}, {28,35}, {10,46}, {27,40}, {16,25}, {11,17}, {25,39}, {16,21}, {5,37}, {40,43}, {24,36}, {9,24}, {21,39}, {21,46}, {30,36}, {6,20}, {2,20}, {1,36}, {14,18}, {10,16}, {4,16}, {34,42}, {4,46}, {7,25}, {20,23}, {15,36}, {17,34}, {28,30}, {31,42}, {6,15}, {9,45}, {7,21}, {7,47}, {3,5}, {19,40}, {18,22}, {29,31}, {8,37}, {37,41}, {12,25}, {22,24}, {2,15}, {13,14}, {20,36}, {6,31}, {27,44}, {41,43}, {9,13}, {1,7}, {1,23}, {6,45}, {12,21}, {23,30}, {29,34}, {15,23}, {17,31}, {2,45}, {2,31}, {13,28}, {9,18}, {20,26}, {10,17}, {11,29}, {19,44}, {12,15}, {39,47}, {3,40}, {3,44}, {11,42}, {11,16}, {2,34}, {8,19}, {37,44}, {22,40}, {20,42}, {13,37}, {33,42}, {6,34}, {2,21}, {23,35}, {18,28}, {29,33}, {32,42}, {28,41}, {29,35}, {21,23}, {23,25}, {29,32}, {23,32}, {37,45}, {6,21}, {1,12}, {2,32}, {6,33}, {5,19}, {18,38}, {22,47}, {23,33}, {7,20}, {4,29}, {1,42}, {3,8}, {10,39}, {6,25}, {4,17}, {7,31}, {12,33}, {2,25}, {17,35}, {6,32}, {2,33}, {4,6}, {26,47}, {7,15}, {12,32}, {2,4}, {22,44}, {1,26}, {28,45}, {14,44}, {15,26}, {12,20}, {11,12}, {38,41}, {11,36}, {5,14}, {29,30}, {5,27}, {8,27}, {15,42}, {15,16}, {3,13}, {17,30}, {30,39}, {24,37}, {18,46}, {4,39}, {23,31}, {18,43}, {25,29}, {28,40}, {35,39}, {23,45}, {16,35}, {14,47}, {24,27}, {18,37}, {13,19}, {4,36}, {10,29}, {21,42}, {14,41}, {13,22}, {13,43}, {14,40}, {37,40}, {9,41}, {7,11}, {19,47}, {26,34}, {7,34}, {23,34}, {10,23}, {33,39}, {14,24}, {21,29}, {8,22}, {32,39}, {2,10}, {5,38}, {6,10}, {9,40}, {25,42}, {1,16}, {28,44}, {10,36}, {16,30}, {12,34}, {7,33}, {12,31}, {15,19}, {42,45}, {7,32}, {13,27}, {11,39}, {19,24}, {5,7}, {7,30}, {26,31}, {9,10}, {17,18}, {29,45}, {24,43}, {31,39}, {8,14}, {4,23}, {8,12}, {5,22}, {3,47}, {22,41}, {7,35}, {17,25}, {1,3}, {9,44}, {34,39}, {3,24}, {8,38}, {27,47}, {17,45}, {17,21}, {15,27}, {3,20}, {5,12}, {26,32}, {4,9}, {26,33}, {11,22}, {16,20}, {20,39}, {11,26}, {27,41}, {34,38}, {7,8}, {45,46}, {5,26}, {16,32}, {24,46}, {39,41}, {13,16}, {31,38}, {16,33}, {13,38}, {16,31}, {20,27}, {16,24}, {3,15}, {26,35}, {36,44}, {43,47}, {10,28}, {16,34}, {12,30}, {25,36}, {20,38}, {3,41}, {15,39}, {18,29}, {4,42}, {35,43}, {16,45}, {42,44}, {24,38}, {36,45}, {33,38}, {32,38}, {21,36}, {30,43}, {29,44}, {1,19}, {5,43}, {9,47}, {40,46}, {26,30}, {19,41}, {11,14}, {12,35}, {14,35}, {7,45}, {8,46}, {19,32}, {36,40}, {19,33}, {3,34}, {3,31}, {11,19}, {24,39}, {13,46}, {19,20}, {8,16}, {13,26}, {1,39}, {4,37}, {1,14}, {8,43}, {14,15}, {34,43}, {14,30}, {4,28}, {7,13}, {19,34}, {1,27}, {25,28}, {8,26}, {30,38}, {38,47}, {3,32}, {10,42}, {44,46}, {1,38}, {20,22}, {18,36}, {18,23}, {5,16}, {12,24}, {14,20}, {2,18}, {3,33}, {21,28}, {12,13}, {17,40}, {3,11}, {6,18}, {15,22}, {12,45}, {5,46}, {24,26}, {40,42}, {8,10}, {1,22}, {14,34}, {27,33}, {17,19}, {7,24}, {9,12}, {29,40}, {11,27}, {26,41}, {27,32}, {35,38}, {22,23}, {4,5}, {32,43}, {10,37}, {22,30}, {27,34}, {31,43}, {33,43}, {42,43}, {9,21}, {23,40}, {9,25}, {19,31}, {3,30}, {15,38}, {11,46}, {26,45}, {22,35}, {20,43}, {28,47}, {32,40}, {16,41}, {33,40}, {15,18}, {2,14}, {45,47}, {17,44}, {3,35}, {26,28}, {27,31}, {13,39}, {6,14}, {11,43}, {14,31}, {4,8}, {17,27}, {24,25}, {7,9}, {6,47}, {13,21}, {27,29}, {5,10}, {39,45}, {23,47}, {23,44}, {3,17}, {12,28}, {2,47}, {34,44}, {14,45}, {36,38}, {19,35}, {21,24}, {1,18}, {6,44}, {22,31}, {6,22}, {31,44}, {14,32}, {22,33}, {2,44}, {5,39}, {25,37}, {41,46}, {13,25}, {14,33}, {2,22}, {2,3}, {3,29}, {22,32}, {8,39}, {37,47}, {19,30}, {1,43}, {15,43}, {7,41}, {21,41}, {22,45}, {27,35}, {19,29}, {3,6}, {11,18}, {21,37}, {34,40}, {18,42}, {7,37}, {38,42}, {9,16}, {3,36}, {2,40}, {33,44}, {11,38}, {12,41}, {4,13}, {6,40}, {31,40}, {32,44}, {14,17}, {5,25}, {36,43}, {25,41}, {5,21}, {3,45}, {20,40}, {18,32}, {7,28}, {14,23}, {35,44}, {20,44}, {19,36}, {10,13}, {18,33}, {23,27}, {22,29}, {18,20}, {9,26}, {17,47}, {22,34}, {27,30}, {10,24}, {29,38}, {16,28}, {22,42}, {30,44}, {1,46}, {1,4}, {14,29}, {18,34}, {30,46}, {15,46}, {19,23}, {18,31}, {15,40}, {14,42}, {26,37}, {1,44}, {2,19}, {23,43}, {6,19}, {11,47}, {4,24}, {12,37}, {17,22}, {27,28}, {14,36}, {35,46}, {2,43}, {27,36}, {6,43}, {26,29}, {8,18}, {19,45}, {8,21}, {10,15}, {12,17}, {30,40}, {29,43}, {8,25}, {3,23}, {1,40}, {28,39}, {9,19}, {15,44}, {43,45}, {17,38}, {6,27}, {16,37}, {29,47}, {37,39}, {32,46}, {19,28}, {18,35}, {2,27}, {42,47}, {33,46}, {20,46}, {1,10}, {4,20}, {23,46}, {27,45}, {2,16}, {27,42}, {6,38}, {35,40}, {6,16}, {11,40}, {2,38}, {2,46}, {3,9}, {23,38}, {7,29}, {20,21}, {6,46}, {31,46}, {6,7}, {18,30}, {10,32}, {4,31}, {16,23}, {2,7}, {4,15}, {10,33}, {10,20}, {17,26}, {39,42}, {5,18}, {9,39}, {38,45}, {7,17}, {10,11}, {17,43}, {20,25}, {4,41}, {41,44}, {3,42}, {3,28}, {9,27}, {37,38}, {11,25}, {16,17}, {11,44}, {11,21}, {36,47}, {19,42}, {34,46}, {23,39}, {10,41}, {12,29}, {22,28}, {17,46}, {26,36}, {4,11}, {3,37}, {4,34}, {12,23}, {1,21} }; // Total number of connected ET graphs of order 47 is 25 // ******************************************************************************************** // Total number of connected ET graphs listed above = 1894 // 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