Below is a complete list of all connected symmetric (arc-transitive) graphs of order 2 to 47, together with some information about their automorphism groups. This list was constructed from the database of all transitive groups of degree up to 47, available in Magma. Note that for any particular order (2 to 47), the graphs are not necessarily in the same order as in the list I created for orders 2 to 30 in April 2014. In this one, they are ordered by valency, and by order of the automorphism group (for each given valency). The graphs in this list are specified by their edge-sets. Another copy of this list is available with graphs specified by the neighbours of each vertex. Marston Conder December 2021 ................................................................... Symmetric connected graphs of order 2 Symmetric graph 1 of order 2 Valency 1 Diameter 1 Automorphism group of order 2 Number of arcs = 2 Number of 2-arcs = 0 2-arc-transitive true Edge-set { {1,2} } ................................................................... Symmetric connected graphs of order 3 Symmetric graph 1 of order 3 Valency 2 Diameter 1 Girth 3 Automorphism group of order 6 Number of arcs = 6 Number of 2-arcs = 6 2-arc-transitive true Edge-set { {1,2}, {2,3}, {1,3} } ................................................................... Symmetric connected graphs of order 4 Symmetric graph 1 of order 4 Valency 2 Diameter 2 Girth 4 Automorphism group of order 8 Number of arcs = 8 Number of 2-arcs = 8 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {1,4} } Symmetric graph 2 of order 4 Valency 3 Diameter 1 Girth 3 Automorphism group of order 24 Number of arcs = 12 Number of 2-arcs = 24 2-arc-transitive true Edge-set { {1,2}, {2,3}, {1,3}, {2,4}, {3,4}, {1,4} } ................................................................... Symmetric connected graphs of order 5 Symmetric graph 1 of order 5 Valency 2 Diameter 2 Girth 5 Automorphism group of order 10 Number of arcs = 10 Number of 2-arcs = 10 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {1,5} } Symmetric graph 2 of order 5 Valency 4 Diameter 1 Girth 3 Automorphism group of order 120 Number of arcs = 20 Number of 2-arcs = 60 2-arc-transitive true Edge-set { {1,2}, {2,3}, {2,4}, {3,4}, {1,4}, {3,5}, {4,5}, {1,3}, {2,5}, {1,5} } ................................................................... Symmetric connected graphs of order 6 Symmetric graph 1 of order 6 Valency 2 Diameter 3 Girth 6 Automorphism group of order 12 Number of arcs = 12 Number of 2-arcs = 12 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {1,6} } Symmetric graph 2 of order 6 Valency 3 Diameter 2 Girth 4 Automorphism group of order 72 Number of arcs = 18 Number of 2-arcs = 36 2-arc-transitive true Edge-set { {1,2}, {1,4}, {4,5}, {1,6}, {5,6}, {3,4}, {2,5}, {2,3}, {3,6} } Symmetric graph 3 of order 6 Valency 4 Diameter 2 Girth 3 Automorphism group of order 48 Number of arcs = 24 Number of 2-arcs = 72 2-arc-transitive false Edge-set { {1,2}, {4,5}, {3,4}, {1,6}, {1,3}, {5,6}, {4,6}, {2,3}, {3,5}, {2,6}, {1,5}, {2,4} } Symmetric graph 4 of order 6 Valency 5 Diameter 1 Girth 3 Automorphism group of order 720 Number of arcs = 30 Number of 2-arcs = 120 2-arc-transitive true Edge-set { {1,2}, {2,3}, {2,4}, {3,4}, {3,6}, {4,6}, {1,3}, {1,4}, {3,5}, {1,6}, {1,5}, {2,6}, {4,5}, {2,5}, {5,6} } ................................................................... Symmetric connected graphs of order 7 Symmetric graph 1 of order 7 Valency 2 Diameter 3 Girth 7 Automorphism group of order 14 Number of arcs = 14 Number of 2-arcs = 14 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {1,7} } Symmetric graph 2 of order 7 Valency 6 Diameter 1 Girth 3 Automorphism group of order 5040 Number of arcs = 42 Number of 2-arcs = 210 2-arc-transitive true Edge-set { {1,2}, {2,3}, {2,4}, {3,4}, {4,6}, {3,5}, {1,4}, {4,5}, {1,6}, {5,7}, {1,5}, {3,6}, {2,5}, {5,6}, {1,3}, {2,7}, {3,7}, {2,6}, {4,7}, {6,7}, {1,7} } ................................................................... Symmetric connected graphs of order 8 Symmetric graph 1 of order 8 Valency 2 Diameter 4 Girth 8 Automorphism group of order 16 Number of arcs = 16 Number of 2-arcs = 16 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {1,8} } Symmetric graph 2 of order 8 Valency 3 Diameter 3 Girth 4 Automorphism group of order 48 Number of arcs = 24 Number of 2-arcs = 48 2-arc-transitive true Edge-set { {1,4}, {5,8}, {3,6}, {2,6}, {2,7}, {4,8}, {1,5}, {3,7}, {3,5}, {6,8}, {2,4}, {1,7} } Symmetric graph 3 of order 8 Valency 4 Diameter 2 Girth 4 Automorphism group of order 1152 Number of arcs = 32 Number of 2-arcs = 96 2-arc-transitive true Edge-set { {1,2}, {2,3}, {2,5}, {3,4}, {2,7}, {3,6}, {4,5}, {4,7}, {3,8}, {6,7}, {5,6}, {1,4}, {5,8}, {7,8}, {1,6}, {1,8} } Symmetric graph 4 of order 8 Valency 6 Diameter 2 Girth 3 Automorphism group of order 384 Number of arcs = 48 Number of 2-arcs = 240 2-arc-transitive false Edge-set { {1,2}, {3,4}, {2,3}, {5,6}, {5,8}, {4,5}, {2,8}, {7,8}, {6,7}, {2,7}, {1,7}, {5,7}, {2,4}, {1,4}, {1,8}, {4,6}, {1,3}, {4,7}, {2,5}, {3,6}, {3,5}, {6,8}, {3,8}, {1,6} } Symmetric graph 5 of order 8 Valency 7 Diameter 1 Girth 3 Automorphism group of order 40320 Number of arcs = 56 Number of 2-arcs = 336 2-arc-transitive true Edge-set { {1,2}, {3,8}, {5,6}, {2,6}, {4,7}, {4,8}, {3,7}, {3,6}, {1,5}, {5,8}, {1,4}, {2,7}, {3,4}, {7,8}, {2,5}, {1,6}, {4,5}, {1,8}, {6,7}, {2,3}, {5,7}, {2,8}, {1,3}, {4,6}, {1,7}, {6,8}, {2,4}, {3,5} } ................................................................... Symmetric connected graphs of order 9 Symmetric graph 1 of order 9 Valency 2 Diameter 4 Girth 9 Automorphism group of order 18 Number of arcs = 18 Number of 2-arcs = 18 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {1,9} } Symmetric graph 2 of order 9 Valency 4 Diameter 2 Girth 3 Automorphism group of order 72 Number of arcs = 36 Number of 2-arcs = 108 2-arc-transitive false Edge-set { {1,3}, {2,4}, {2,3}, {4,6}, {5,9}, {1,5}, {5,7}, {4,9}, {5,6}, {7,9}, {3,8}, {4,8}, {1,8}, {3,7}, {8,9}, {2,6}, {2,7}, {1,6} } Symmetric graph 3 of order 9 Valency 6 Diameter 2 Girth 3 Automorphism group of order 1296 Number of arcs = 54 Number of 2-arcs = 270 2-arc-transitive false Edge-set { {1,2}, {4,8}, {2,3}, {5,7}, {5,9}, {3,8}, {3,4}, {6,8}, {2,9}, {1,6}, {3,5}, {4,9}, {3,7}, {4,5}, {5,6}, {7,9}, {8,9}, {1,3}, {4,6}, {2,7}, {1,5}, {2,6}, {6,7}, {1,9}, {1,8}, {2,4}, {7,8} } Symmetric graph 4 of order 9 Valency 8 Diameter 1 Girth 3 Automorphism group of order 362880 Number of arcs = 72 Number of 2-arcs = 504 2-arc-transitive true Edge-set { {1,2}, {2,9}, {4,5}, {4,8}, {3,6}, {1,9}, {3,5}, {4,9}, {3,9}, {7,8}, {1,6}, {4,7}, {5,6}, {2,7}, {5,7}, {6,9}, {3,4}, {8,9}, {6,8}, {1,4}, {1,5}, {3,7}, {7,9}, {5,9}, {2,3}, {5,8}, {2,6}, {1,7}, {1,3}, {6,7}, {2,4}, {3,8}, {1,8}, {2,5}, {4,6}, {2,8} } ................................................................... Symmetric connected graphs of order 10 Symmetric graph 1 of order 10 Valency 2 Diameter 5 Girth 10 Automorphism group of order 20 Number of arcs = 20 Number of 2-arcs = 20 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {1,10} } Symmetric graph 2 of order 10 Valency 3 Diameter 2 Girth 5 Automorphism group of order 120 Number of arcs = 30 Number of 2-arcs = 60 2-arc-transitive true Edge-set { {1,3}, {3,5}, {4,9}, {5,7}, {4,10}, {1,6}, {7,9}, {6,10}, {2,6}, {3,8}, {1,9}, {2,8}, {4,8}, {2,7}, {5,10} } Symmetric graph 3 of order 10 Valency 4 Diameter 3 Girth 4 Automorphism group of order 240 Number of arcs = 40 Number of 2-arcs = 120 2-arc-transitive true Edge-set { {1,2}, {3,4}, {2,9}, {5,6}, {3,6}, {1,4}, {8,9}, {7,8}, {7,10}, {5,8}, {6,7}, {2,3}, {1,10}, {1,8}, {9,10}, {4,5}, {4,7}, {6,9}, {2,5}, {3,10} } Symmetric graph 4 of order 10 Valency 4 Diameter 2 Girth 4 Automorphism group of order 320 Number of arcs = 40 Number of 2-arcs = 120 2-arc-transitive false Edge-set { {1,2}, {1,7}, {3,4}, {3,9}, {5,6}, {1,5}, {6,10}, {7,8}, {1,10}, {3,7}, {2,8}, {9,10}, {2,3}, {5,9}, {4,10}, {4,5}, {2,6}, {6,7}, {4,8}, {8,9} } Symmetric graph 5 of order 10 Valency 5 Diameter 2 Girth 4 Automorphism group of order 28800 Number of arcs = 50 Number of 2-arcs = 200 2-arc-transitive true Edge-set { {1,2}, {1,4}, {6,7}, {1,6}, {6,9}, {7,8}, {1,8}, {8,9}, {7,10}, {2,3}, {1,10}, {3,6}, {9,10}, {3,4}, {2,7}, {2,5}, {5,6}, {3,8}, {2,9}, {4,5}, {4,7}, {5,8}, {3,10}, {4,9}, {5,10} } Symmetric graph 6 of order 10 Valency 6 Diameter 2 Girth 3 Automorphism group of order 120 Number of arcs = 60 Number of 2-arcs = 300 2-arc-transitive false Edge-set { {1,2}, {3,4}, {2,9}, {5,6}, {1,4}, {7,8}, {7,10}, {3,6}, {3,9}, {9,10}, {6,8}, {5,8}, {4,7}, {1,5}, {8,10}, {6,9}, {3,7}, {2,10}, {1,8}, {1,7}, {5,9}, {4,6}, {2,4}, {2,5}, {3,10}, {8,9}, {1,10}, {2,3}, {4,5}, {6,7} } Symmetric graph 7 of order 10 Valency 8 Diameter 2 Girth 3 Automorphism group of order 3840 Number of arcs = 80 Number of 2-arcs = 560 2-arc-transitive false Edge-set { {1,2}, {1,7}, {3,4}, {4,7}, {3,9}, {7,9}, {5,6}, {1,8}, {2,4}, {6,9}, {8,9}, {1,5}, {1,3}, {2,9}, {1,9}, {6,10}, {7,8}, {2,5}, {3,10}, {6,7}, {4,6}, {4,8}, {2,3}, {1,10}, {3,6}, {3,7}, {5,7}, {3,5}, {1,4}, {2,8}, {2,10}, {9,10}, {7,10}, {4,5}, {2,6}, {6,8}, {5,8}, {5,9}, {4,10}, {8,10} } Symmetric graph 8 of order 10 Valency 9 Diameter 1 Girth 3 Automorphism group of order 3628800 Number of arcs = 90 Number of 2-arcs = 720 2-arc-transitive true Edge-set { {1,2}, {2,10}, {3,6}, {1,10}, {6,10}, {1,9}, {4,7}, {3,10}, {2,9}, {1,7}, {6,9}, {3,9}, {5,8}, {4,5}, {1,4}, {9,10}, {2,8}, {3,4}, {2,4}, {7,9}, {4,9}, {7,8}, {3,5}, {2,5}, {2,7}, {6,7}, {1,5}, {3,7}, {5,10}, {5,6}, {8,9}, {4,10}, {5,9}, {7,10}, {6,8}, {3,8}, {1,8}, {8,10}, {4,6}, {2,3}, {4,8}, {1,3}, {2,6}, {1,6}, {5,7} } ................................................................... Symmetric connected graphs of order 11 Symmetric graph 1 of order 11 Valency 2 Diameter 5 Girth 11 Automorphism group of order 22 Number of arcs = 22 Number of 2-arcs = 22 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {1,11} } Symmetric graph 2 of order 11 Valency 10 Diameter 1 Girth 3 Automorphism group of order 39916800 Number of arcs = 110 Number of 2-arcs = 990 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,6}, {3,4}, {6,9}, {4,7}, {7,9}, {4,5}, {1,9}, {7,10}, {5,7}, {5,8}, {1,10}, {8,10}, {5,10}, {5,6}, {1,4}, {2,10}, {3,5}, {8,11}, {6,8}, {4,10}, {2,4}, {2,11}, {3,8}, {9,11}, {2,8}, {6,11}, {4,8}, {6,7}, {2,5}, {1,3}, {3,11}, {4,6}, {4,9}, {2,7}, {5,11}, {1,8}, {1,6}, {2,9}, {3,9}, {2,6}, {1,7}, {7,11}, {5,9}, {7,8}, {1,5}, {6,10}, {4,11}, {3,7}, {3,10}, {10,11}, {8,9}, {1,11}, {9,10} } ................................................................... Symmetric connected graphs of order 12 Symmetric graph 1 of order 12 Valency 2 Diameter 6 Girth 12 Automorphism group of order 24 Number of arcs = 24 Number of 2-arcs = 24 2-arc-transitive true Edge-set { {1,2}, {4,5}, {5,6}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {1,12}, {2,3}, {3,4}, {6,7} } Symmetric graph 2 of order 12 Valency 4 Diameter 3 Girth 3 Automorphism group of order 48 Number of arcs = 48 Number of 2-arcs = 144 2-arc-transitive false Edge-set { {1,2}, {4,9}, {9,11}, {7,11}, {3,5}, {7,8}, {6,10}, {5,10}, {6,7}, {2,6}, {3,10}, {8,12}, {2,12}, {1,5}, {1,12}, {4,8}, {6,8}, {1,9}, {4,12}, {4,11}, {3,11}, {3,7}, {5,9}, {2,10} } Symmetric graph 3 of order 12 Valency 4 Diameter 3 Girth 4 Automorphism group of order 768 Number of arcs = 48 Number of 2-arcs = 144 2-arc-transitive false Edge-set { {1,2}, {1,8}, {5,6}, {3,12}, {5,12}, {9,12}, {6,11}, {9,10}, {4,7}, {11,12}, {4,9}, {1,4}, {3,10}, {7,10}, {3,4}, {8,11}, {1,10}, {5,8}, {2,7}, {2,11}, {7,8}, {2,5}, {3,6}, {6,9} } Symmetric graph 4 of order 12 Valency 5 Diameter 3 Girth 3 Automorphism group of order 120 Number of arcs = 60 Number of 2-arcs = 240 2-arc-transitive false Edge-set { {1,2}, {3,4}, {7,11}, {5,6}, {6,12}, {9,11}, {5,9}, {7,8}, {1,8}, {2,8}, {8,10}, {1,11}, {2,5}, {1,7}, {9,12}, {3,9}, {3,12}, {3,11}, {4,12}, {3,7}, {10,12}, {5,11}, {4,7}, {2,10}, {1,5}, {2,6}, {6,10}, {6,9}, {4,10}, {4,8} } Symmetric graph 5 of order 12 Valency 5 Diameter 3 Girth 4 Automorphism group of order 1440 Number of arcs = 60 Number of 2-arcs = 240 2-arc-transitive true Edge-set { {1,2}, {1,4}, {7,10}, {1,6}, {5,10}, {2,9}, {1,8}, {10,11}, {2,7}, {4,11}, {7,8}, {1,10}, {9,10}, {2,3}, {4,9}, {3,6}, {5,6}, {2,11}, {4,5}, {7,12}, {6,11}, {5,8}, {11,12}, {3,4}, {6,7}, {9,12}, {3,8}, {3,12}, {5,12}, {8,9} } Symmetric graph 6 of order 12 Valency 6 Diameter 2 Girth 3 Automorphism group of order 144 Number of arcs = 72 Number of 2-arcs = 360 2-arc-transitive false Edge-set { {1,2}, {1,8}, {5,7}, {5,6}, {1,11}, {7,8}, {5,12}, {5,10}, {10,11}, {9,11}, {9,10}, {2,7}, {3,5}, {8,10}, {11,12}, {4,9}, {4,5}, {2,9}, {2,4}, {2,3}, {1,3}, {6,11}, {7,9}, {4,11}, {2,12}, {3,4}, {8,9}, {1,6}, {6,8}, {6,7}, {3,10}, {3,8}, {4,6}, {1,12}, {10,12}, {7,12} } Symmetric graph 7 of order 12 Valency 6 Diameter 2 Girth 4 Automorphism group of order 1036800 Number of arcs = 72 Number of 2-arcs = 360 2-arc-transitive true Edge-set { {1,2}, {1,10}, {4,5}, {1,6}, {1,4}, {5,8}, {7,8}, {4,9}, {1,8}, {4,7}, {5,12}, {8,11}, {7,12}, {10,11}, {8,9}, {1,12}, {4,11}, {7,10}, {3,8}, {11,12}, {2,11}, {3,10}, {6,11}, {9,12}, {3,4}, {2,7}, {6,7}, {3,12}, {2,3}, {2,5}, {3,6}, {2,9}, {5,10}, {9,10}, {5,6}, {6,9} } Symmetric graph 8 of order 12 Valency 8 Diameter 2 Girth 3 Automorphism group of order 82944 Number of arcs = 96 Number of 2-arcs = 672 2-arc-transitive false Edge-set { {1,2}, {4,9}, {9,11}, {7,11}, {4,5}, {3,5}, {7,8}, {6,10}, {1,3}, {5,10}, {6,7}, {2,6}, {3,8}, {8,10}, {3,10}, {8,12}, {2,9}, {2,12}, {1,5}, {10,11}, {7,12}, {1,12}, {4,8}, {2,7}, {6,8}, {1,9}, {10,12}, {5,12}, {4,12}, {7,9}, {6,11}, {4,11}, {3,11}, {5,6}, {2,4}, {3,7}, {4,6}, {1,11}, {5,9}, {11,12}, {3,4}, {1,6}, {2,10}, {1,8}, {8,9}, {9,10}, {2,3}, {5,7} } Symmetric graph 9 of order 12 Valency 9 Diameter 2 Girth 3 Automorphism group of order 31104 Number of arcs = 108 Number of 2-arcs = 864 2-arc-transitive false Edge-set { {1,2}, {1,6}, {5,10}, {1,3}, {1,7}, {1,10}, {5,6}, {7,9}, {2,5}, {5,11}, {3,5}, {1,4}, {6,7}, {1,11}, {1,8}, {2,7}, {5,7}, {9,11}, {8,9}, {2,3}, {5,12}, {10,11}, {4,5}, {6,11}, {5,8}, {4,7}, {7,8}, {2,9}, {1,12}, {7,10}, {3,8}, {2,11}, {3,9}, {9,12}, {3,10}, {4,9}, {6,9}, {3,4}, {11,12}, {4,11}, {7,12}, {9,10}, {8,11}, {2,8}, {2,4}, {6,8}, {4,6}, {3,6}, {3,12}, {10,12}, {2,12}, {4,10}, {8,10}, {6,12} } Symmetric graph 10 of order 12 Valency 10 Diameter 2 Girth 3 Automorphism group of order 46080 Number of arcs = 120 Number of 2-arcs = 1080 2-arc-transitive false Edge-set { {1,2}, {3,12}, {1,4}, {1,3}, {5,12}, {2,12}, {1,6}, {3,6}, {1,5}, {7,12}, {2,7}, {4,12}, {1,8}, {3,5}, {5,8}, {1,7}, {3,7}, {9,12}, {2,4}, {4,9}, {6,12}, {2,6}, {1,10}, {3,11}, {5,7}, {7,10}, {7,11}, {1,9}, {3,4}, {5,9}, {11,12}, {2,10}, {4,6}, {6,11}, {6,10}, {8,12}, {2,5}, {4,8}, {3,8}, {7,9}, {4,7}, {2,9}, {3,9}, {1,11}, {3,10}, {5,6}, {6,8}, {2,8}, {10,12}, {2,11}, {5,10}, {9,11}, {4,10}, {6,9}, {4,11}, {5,11}, {7,8}, {8,10}, {9,10}, {8,11} } Symmetric graph 11 of order 12 Valency 11 Diameter 1 Girth 3 Automorphism group of order 479001600 Number of arcs = 132 Number of 2-arcs = 1320 2-arc-transitive true Edge-set { {1,2}, {2,3}, {5,10}, {3,4}, {5,7}, {6,12}, {4,5}, {7,8}, {6,8}, {1,7}, {9,11}, {5,6}, {2,8}, {8,9}, {7,9}, {4,9}, {3,10}, {10,11}, {6,7}, {2,9}, {3,9}, {9,10}, {4,6}, {8,10}, {3,6}, {4,12}, {11,12}, {1,12}, {4,10}, {10,12}, {1,6}, {9,12}, {1,4}, {4,7}, {1,5}, {8,11}, {1,11}, {5,12}, {1,8}, {2,7}, {1,10}, {6,11}, {2,5}, {5,8}, {3,8}, {2,6}, {2,10}, {2,11}, {3,5}, {2,12}, {7,11}, {6,9}, {2,4}, {3,7}, {5,9}, {3,12}, {3,11}, {1,3}, {5,11}, {7,10}, {4,8}, {6,10}, {4,11}, {7,12}, {8,12}, {1,9} } ................................................................... Symmetric connected graphs of order 13 Symmetric graph 1 of order 13 Valency 2 Diameter 6 Girth 13 Automorphism group of order 26 Number of arcs = 26 Number of 2-arcs = 26 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {1,13} } Symmetric graph 2 of order 13 Valency 4 Diameter 2 Girth 4 Automorphism group of order 52 Number of arcs = 52 Number of 2-arcs = 156 2-arc-transitive false Edge-set { {1,2}, {2,3}, {5,10}, {3,4}, {2,10}, {6,11}, {11,12}, {4,5}, {2,7}, {3,11}, {10,11}, {7,12}, {12,13}, {3,8}, {5,6}, {9,10}, {4,12}, {8,13}, {8,9}, {1,13}, {4,9}, {6,7}, {5,13}, {7,8}, {1,9}, {1,6} } Symmetric graph 3 of order 13 Valency 6 Diameter 2 Girth 3 Automorphism group of order 78 Number of arcs = 78 Number of 2-arcs = 390 2-arc-transitive false Edge-set { {1,2}, {2,3}, {3,6}, {3,4}, {6,9}, {4,7}, {5,9}, {4,5}, {9,12}, {7,10}, {1,5}, {5,8}, {8,12}, {6,10}, {5,6}, {2,12}, {10,13}, {1,10}, {8,11}, {4,8}, {2,6}, {2,11}, {9,13}, {10,11}, {7,11}, {6,7}, {2,5}, {3,13}, {1,11}, {4,13}, {11,12}, {3,7}, {3,12}, {1,13}, {7,8}, {1,4}, {12,13}, {8,9}, {9,10} } Symmetric graph 4 of order 13 Valency 12 Diameter 1 Girth 3 Automorphism group of order 6227020800 Number of arcs = 156 Number of 2-arcs = 1716 2-arc-transitive true Edge-set { {1,2}, {2,3}, {2,4}, {3,4}, {4,6}, {3,5}, {4,8}, {4,5}, {6,8}, {5,7}, {8,12}, {6,10}, {5,9}, {3,8}, {5,6}, {8,10}, {7,9}, {3,12}, {1,10}, {9,13}, {3,11}, {7,11}, {7,12}, {5,10}, {4,9}, {3,6}, {6,7}, {10,12}, {9,11}, {3,7}, {1,5}, {4,13}, {6,11}, {2,11}, {2,7}, {5,13}, {4,12}, {6,9}, {1,9}, {8,13}, {1,11}, {7,10}, {5,8}, {4,7}, {6,12}, {7,8}, {1,12}, {11,13}, {1,6}, {2,6}, {2,10}, {9,12}, {1,4}, {10,13}, {8,11}, {5,12}, {2,5}, {3,13}, {2,12}, {2,9}, {1,7}, {3,10}, {1,8}, {7,13}, {11,12}, {8,9}, {1,3}, {2,13}, {5,11}, {2,8}, {3,9}, {6,13}, {10,11}, {4,10}, {4,11}, {1,13}, {12,13}, {9,10} } ................................................................... Symmetric connected graphs of order 14 Symmetric graph 1 of order 14 Valency 2 Diameter 7 Girth 14 Automorphism group of order 28 Number of arcs = 28 Number of 2-arcs = 28 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {1,14} } Symmetric graph 2 of order 14 Valency 3 Diameter 3 Girth 6 Automorphism group of order 336 Number of arcs = 42 Number of 2-arcs = 84 2-arc-transitive true Edge-set { {1,2}, {3,4}, {4,9}, {5,6}, {8,13}, {6,11}, {8,11}, {3,12}, {7,8}, {1,10}, {2,5}, {1,12}, {10,13}, {5,14}, {9,10}, {2,7}, {13,14}, {6,9}, {4,7}, {3,14}, {11,12} } Symmetric graph 3 of order 14 Valency 4 Diameter 3 Girth 4 Automorphism group of order 336 Number of arcs = 56 Number of 2-arcs = 168 2-arc-transitive true Edge-set { {1,2}, {4,13}, {4,9}, {1,4}, {8,9}, {6,11}, {5,8}, {2,5}, {6,7}, {8,11}, {2,11}, {6,13}, {7,10}, {1,12}, {9,12}, {3,10}, {2,3}, {8,13}, {3,4}, {7,12}, {13,14}, {9,10}, {5,12}, {3,14}, {1,6}, {7,14}, {10,11}, {5,14} } Symmetric graph 4 of order 14 Valency 4 Diameter 3 Girth 4 Automorphism group of order 1792 Number of arcs = 56 Number of 2-arcs = 168 2-arc-transitive false Edge-set { {1,2}, {3,4}, {4,10}, {5,6}, {6,12}, {12,13}, {7,8}, {5,13}, {8,14}, {1,14}, {9,10}, {1,7}, {2,10}, {2,3}, {3,9}, {11,12}, {4,12}, {4,5}, {5,11}, {13,14}, {6,14}, {6,7}, {7,13}, {2,8}, {8,9}, {1,9}, {10,11}, {3,11} } Symmetric graph 5 of order 14 Valency 6 Diameter 3 Girth 4 Automorphism group of order 10080 Number of arcs = 84 Number of 2-arcs = 420 2-arc-transitive true Edge-set { {1,2}, {3,4}, {4,9}, {8,9}, {5,6}, {8,13}, {10,11}, {6,11}, {8,11}, {2,11}, {7,8}, {3,12}, {12,13}, {1,10}, {2,5}, {1,6}, {1,12}, {4,13}, {10,13}, {1,4}, {9,10}, {2,7}, {1,14}, {5,14}, {5,10}, {6,9}, {3,8}, {4,7}, {9,12}, {3,14}, {5,8}, {3,6}, {11,12}, {2,3}, {9,14}, {7,12}, {2,13}, {11,14}, {13,14}, {7,10}, {4,5}, {6,7} } Symmetric graph 6 of order 14 Valency 7 Diameter 2 Girth 4 Automorphism group of order 50803200 Number of arcs = 98 Number of 2-arcs = 588 2-arc-transitive true Edge-set { {1,2}, {1,4}, {8,9}, {1,6}, {8,11}, {9,10}, {1,8}, {8,13}, {10,11}, {9,12}, {2,3}, {1,10}, {10,13}, {11,12}, {3,4}, {9,14}, {2,5}, {1,12}, {3,8}, {12,13}, {3,6}, {11,14}, {4,5}, {2,9}, {2,7}, {1,14}, {5,8}, {3,10}, {13,14}, {5,6}, {2,11}, {4,7}, {4,9}, {7,8}, {5,10}, {3,12}, {2,13}, {6,7}, {4,11}, {6,9}, {7,10}, {5,12}, {3,14}, {4,13}, {6,11}, {7,12}, {5,14}, {6,13}, {7,14} } Symmetric graph 7 of order 14 Valency 12 Diameter 2 Girth 3 Automorphism group of order 645120 Number of arcs = 168 Number of 2-arcs = 1848 2-arc-transitive false Edge-set { {1,2}, {3,4}, {4,9}, {8,13}, {5,6}, {10,12}, {6,11}, {8,11}, {6,12}, {1,10}, {2,5}, {7,8}, {3,12}, {9,11}, {12,14}, {6,10}, {1,12}, {5,9}, {10,13}, {1,5}, {8,14}, {6,9}, {3,8}, {4,7}, {11,13}, {9,10}, {2,7}, {1,7}, {5,14}, {4,10}, {1,11}, {2,14}, {10,14}, {4,14}, {8,12}, {3,9}, {3,14}, {4,8}, {7,11}, {3,11}, {2,3}, {3,7}, {2,10}, {1,14}, {11,12}, {5,10}, {2,13}, {7,12}, {1,13}, {3,6}, {7,13}, {7,9}, {11,14}, {6,8}, {3,13}, {1,9}, {5,8}, {2,4}, {13,14}, {2,12}, {6,14}, {2,6}, {1,4}, {5,11}, {2,8}, {9,13}, {5,7}, {5,13}, {4,5}, {4,13}, {7,10}, {4,12}, {4,6}, {9,14}, {1,3}, {12,13}, {6,7}, {8,10}, {8,9}, {3,5}, {2,11}, {1,6}, {9,12}, {10,11} } Symmetric graph 8 of order 14 Valency 13 Diameter 1 Girth 3 Automorphism group of order 87178291200 Number of arcs = 182 Number of 2-arcs = 2184 2-arc-transitive true Edge-set { {1,2}, {2,3}, {4,8}, {6,12}, {3,4}, {8,12}, {4,6}, {5,9}, {3,6}, {3,8}, {7,14}, {9,11}, {4,5}, {3,12}, {9,14}, {6,9}, {1,8}, {5,7}, {3,11}, {6,10}, {7,10}, {5,10}, {4,7}, {11,12}, {2,4}, {4,9}, {2,14}, {11,13}, {10,12}, {5,6}, {3,7}, {3,5}, {4,14}, {9,12}, {1,4}, {1,10}, {10,14}, {10,13}, {10,11}, {2,10}, {2,9}, {6,8}, {2,7}, {5,11}, {4,12}, {5,12}, {7,11}, {1,11}, {8,11}, {6,11}, {1,7}, {5,8}, {12,14}, {3,10}, {1,3}, {8,14}, {6,13}, {12,13}, {5,13}, {11,14}, {1,9}, {6,7}, {2,5}, {2,12}, {4,11}, {7,12}, {1,5}, {3,14}, {3,13}, {9,10}, {2,11}, {1,14}, {9,13}, {1,13}, {7,9}, {8,10}, {2,8}, {5,14}, {3,9}, {6,14}, {7,8}, {1,12}, {8,13}, {7,13}, {13,14}, {4,10}, {8,9}, {1,6}, {2,6}, {4,13}, {2,13} } ................................................................... Symmetric connected graphs of order 15 Symmetric graph 1 of order 15 Valency 2 Diameter 7 Girth 15 Automorphism group of order 30 Number of arcs = 30 Number of 2-arcs = 30 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {1,15} } Symmetric graph 2 of order 15 Valency 4 Diameter 3 Girth 4 Automorphism group of order 60 Number of arcs = 60 Number of 2-arcs = 180 2-arc-transitive false Edge-set { {1,2}, {2,3}, {4,8}, {3,4}, {8,12}, {5,9}, {4,5}, {1,12}, {9,13}, {6,10}, {5,6}, {1,5}, {2,13}, {10,14}, {6,7}, {7,11}, {9,10}, {2,6}, {3,14}, {7,8}, {11,15}, {10,11}, {13,14}, {3,7}, {8,9}, {4,15}, {11,12}, {14,15}, {12,13}, {1,15} } Symmetric graph 3 of order 15 Valency 4 Diameter 3 Girth 3 Automorphism group of order 120 Number of arcs = 60 Number of 2-arcs = 180 2-arc-transitive false Edge-set { {1,2}, {9,15}, {4,5}, {7,10}, {6,15}, {5,11}, {8,10}, {3,12}, {1,11}, {2,7}, {6,9}, {11,13}, {3,8}, {3,4}, {6,14}, {7,14}, {9,13}, {12,15}, {2,10}, {8,13}, {4,14}, {5,14}, {1,12}, {6,7}, {3,15}, {1,5}, {4,8}, {2,12}, {10,13}, {9,11} } Symmetric graph 4 of order 15 Valency 6 Diameter 2 Girth 3 Automorphism group of order 720 Number of arcs = 90 Number of 2-arcs = 450 2-arc-transitive false Edge-set { {1,3}, {9,14}, {5,6}, {1,10}, {8,14}, {2,11}, {3,9}, {5,10}, {1,4}, {13,15}, {7,11}, {10,14}, {6,8}, {3,11}, {5,9}, {5,15}, {7,8}, {4,12}, {12,13}, {2,4}, {13,14}, {6,11}, {10,11}, {1,8}, {2,9}, {7,15}, {12,14}, {2,13}, {3,13}, {4,9}, {10,15}, {7,12}, {1,6}, {8,15}, {6,12}, {3,7}, {4,10}, {3,5}, {4,7}, {2,6}, {11,14}, {5,12}, {2,15}, {1,13}, {8,9} } Symmetric graph 5 of order 15 Valency 6 Diameter 2 Girth 4 Automorphism group of order 77760 Number of arcs = 90 Number of 2-arcs = 450 2-arc-transitive false Edge-set { {1,2}, {2,6}, {4,5}, {2,11}, {5,9}, {5,14}, {7,8}, {8,12}, {2,8}, {10,11}, {11,15}, {5,11}, {1,10}, {13,14}, {1,15}, {3,14}, {1,5}, {8,14}, {6,10}, {4,13}, {9,13}, {6,15}, {3,4}, {3,9}, {5,6}, {4,8}, {8,9}, {1,7}, {1,12}, {6,7}, {6,12}, {7,11}, {11,12}, {4,10}, {4,15}, {9,10}, {9,15}, {10,14}, {14,15}, {7,13}, {3,7}, {12,13}, {3,12}, {2,13}, {2,3} } Symmetric graph 6 of order 15 Valency 8 Diameter 2 Girth 3 Automorphism group of order 720 Number of arcs = 120 Number of 2-arcs = 840 2-arc-transitive false Edge-set { {1,2}, {2,3}, {4,8}, {2,4}, {3,4}, {8,12}, {4,6}, {5,9}, {1,8}, {3,5}, {4,5}, {1,12}, {6,8}, {9,13}, {1,9}, {5,7}, {6,10}, {5,6}, {3,10}, {2,9}, {5,12}, {1,5}, {8,10}, {2,13}, {7,9}, {10,14}, {6,7}, {3,11}, {2,10}, {5,13}, {7,11}, {9,10}, {10,12}, {4,11}, {6,13}, {2,6}, {9,11}, {3,14}, {7,8}, {11,15}, {10,11}, {12,14}, {4,12}, {6,14}, {13,14}, {7,14}, {11,13}, {1,14}, {11,12}, {3,7}, {8,9}, {4,15}, {14,15}, {7,15}, {13,15}, {1,3}, {12,13}, {8,15}, {2,15}, {1,15} } Symmetric graph 7 of order 15 Valency 8 Diameter 2 Girth 3 Automorphism group of order 720 Number of arcs = 120 Number of 2-arcs = 840 2-arc-transitive false Edge-set { {1,2}, {9,15}, {4,5}, {4,6}, {7,10}, {6,15}, {5,8}, {5,11}, {8,10}, {1,15}, {2,5}, {9,10}, {3,12}, {1,11}, {3,10}, {2,7}, {6,9}, {4,11}, {2,8}, {11,13}, {3,8}, {11,15}, {3,4}, {7,9}, {6,14}, {7,14}, {7,13}, {9,13}, {3,14}, {1,7}, {12,15}, {3,6}, {2,10}, {5,13}, {4,15}, {8,13}, {11,12}, {4,14}, {5,14}, {10,12}, {2,14}, {1,12}, {8,12}, {1,14}, {9,12}, {6,7}, {3,15}, {1,5}, {6,10}, {8,11}, {5,7}, {4,8}, {2,12}, {6,13}, {10,13}, {14,15}, {4,13}, {1,9}, {9,11}, {2,3} } Symmetric graph 8 of order 15 Valency 10 Diameter 2 Girth 3 Automorphism group of order 10368000 Number of arcs = 150 Number of 2-arcs = 1350 2-arc-transitive false Edge-set { {1,2}, {5,13}, {6,7}, {8,10}, {3,10}, {4,6}, {11,12}, {7,11}, {13,15}, {3,7}, {8,15}, {1,6}, {9,11}, {12,14}, {4,14}, {1,12}, {10,15}, {3,5}, {3,4}, {8,12}, {11,15}, {6,13}, {6,11}, {9,14}, {1,14}, {2,12}, {2,4}, {4,9}, {12,13}, {2,6}, {7,15}, {5,15}, {3,8}, {1,3}, {8,9}, {2,13}, {14,15}, {1,5}, {6,10}, {3,11}, {6,14}, {1,11}, {2,9}, {5,12}, {2,7}, {7,9}, {1,9}, {10,12}, {2,3}, {5,6}, {4,15}, {5,10}, {8,13}, {3,13}, {6,8}, {13,14}, {2,15}, {4,5}, {3,14}, {1,8}, {4,11}, {5,9}, {7,14}, {2,10}, {7,12}, {9,13}, {7,8}, {10,11}, {1,15}, {11,13}, {5,7}, {9,10}, {4,8}, {10,14}, {4,12} } Symmetric graph 9 of order 15 Valency 12 Diameter 2 Girth 3 Automorphism group of order 933120 Number of arcs = 180 Number of 2-arcs = 1980 2-arc-transitive false Edge-set { {1,2}, {9,15}, {4,5}, {2,15}, {7,10}, {6,15}, {1,10}, {5,11}, {8,10}, {5,6}, {7,15}, {1,15}, {3,12}, {1,11}, {7,8}, {2,7}, {6,9}, {1,4}, {3,9}, {2,8}, {11,13}, {3,8}, {6,11}, {3,4}, {8,9}, {2,11}, {4,6}, {7,12}, {1,7}, {7,9}, {6,14}, {7,14}, {3,13}, {9,13}, {4,12}, {12,15}, {2,10}, {4,10}, {5,9}, {2,5}, {10,14}, {3,10}, {4,15}, {8,13}, {11,14}, {4,14}, {2,13}, {4,11}, {5,14}, {3,5}, {9,10}, {13,15}, {11,15}, {6,12}, {7,13}, {9,12}, {10,12}, {1,12}, {8,14}, {3,14}, {5,13}, {6,7}, {1,13}, {3,15}, {1,5}, {8,15}, {5,8}, {10,11}, {6,10}, {1,3}, {8,12}, {5,7}, {4,8}, {2,12}, {9,14}, {11,12}, {10,13}, {5,12}, {14,15}, {3,6}, {1,14}, {2,6}, {4,13}, {8,11}, {9,11}, {4,7}, {2,14}, {1,9}, {2,3}, {6,13} } Symmetric graph 10 of order 15 Valency 14 Diameter 1 Girth 3 Automorphism group of order 1307674368000 Number of arcs = 210 Number of 2-arcs = 2730 2-arc-transitive true Edge-set { {1,2}, {9,15}, {2,3}, {7,10}, {8,15}, {14,15}, {1,3}, {3,12}, {5,9}, {4,7}, {10,15}, {1,7}, {13,15}, {9,14}, {6,14}, {1,14}, {10,11}, {6,8}, {5,12}, {4,5}, {3,7}, {9,12}, {2,5}, {7,8}, {12,15}, {1,10}, {8,13}, {7,13}, {1,9}, {2,13}, {3,13}, {9,11}, {2,4}, {6,11}, {5,11}, {4,6}, {12,14}, {1,5}, {6,10}, {8,14}, {11,15}, {3,6}, {4,12}, {5,10}, {6,7}, {3,9}, {2,9}, {4,8}, {10,12}, {8,12}, {9,10}, {2,8}, {1,12}, {10,13}, {8,11}, {5,15}, {3,4}, {7,11}, {11,13}, {1,6}, {13,14}, {2,6}, {7,9}, {1,4}, {2,14}, {5,6}, {4,14}, {3,11}, {6,9}, {2,12}, {5,7}, {10,14}, {1,8}, {3,8}, {4,10}, {3,10}, {8,9}, {4,15}, {4,13}, {6,15}, {5,14}, {12,13}, {11,12}, {2,7}, {2,15}, {5,8}, {1,15}, {2,11}, {1,11}, {2,10}, {3,14}, {9,13}, {4,9}, {3,5}, {8,10}, {7,15}, {6,13}, {11,14}, {3,15}, {4,11}, {1,13}, {7,12}, {7,14}, {5,13}, {6,12} } ................................................................... Symmetric connected graphs of order 16 Symmetric graph 1 of order 16 Valency 2 Diameter 8 Girth 16 Automorphism group of order 32 Number of arcs = 32 Number of 2-arcs = 32 2-arc-transitive true Edge-set { {1,3}, {7,10}, {14,16}, {4,6}, {9,12}, {1,15}, {5,7}, {11,14}, {2,4}, {8,9}, {13,15}, {3,5}, {10,11}, {2,16}, {6,8}, {12,13} } Symmetric graph 2 of order 16 Valency 3 Diameter 4 Girth 6 Automorphism group of order 96 Number of arcs = 48 Number of 2-arcs = 96 2-arc-transitive true Edge-set { {1,7}, {4,13}, {1,14}, {6,9}, {2,13}, {5,14}, {3,12}, {6,13}, {2,10}, {5,11}, {8,16}, {10,15}, {1,9}, {6,12}, {11,16}, {2,8}, {4,7}, {3,14}, {9,16}, {12,15}, {5,10}, {3,8}, {7,15}, {4,11} } Symmetric graph 3 of order 16 Valency 4 Diameter 4 Girth 4 Automorphism group of order 384 Number of arcs = 64 Number of 2-arcs = 192 2-arc-transitive true Edge-set { {1,3}, {7,10}, {13,15}, {6,15}, {6,11}, {4,13}, {2,4}, {12,13}, {4,9}, {1,12}, {8,9}, {2,16}, {14,16}, {2,7}, {9,16}, {5,16}, {7,13}, {5,12}, {8,14}, {3,14}, {6,8}, {11,14}, {3,5}, {3,10}, {4,6}, {2,11}, {1,15}, {9,12}, {1,8}, {10,11}, {10,15}, {5,7} } Symmetric graph 4 of order 16 Valency 4 Diameter 4 Girth 4 Automorphism group of order 4096 Number of arcs = 64 Number of 2-arcs = 192 2-arc-transitive false Edge-set { {1,9}, {5,12}, {6,12}, {8,16}, {7,16}, {8,15}, {7,15}, {4,9}, {3,9}, {4,10}, {3,10}, {5,13}, {6,13}, {5,14}, {6,14}, {2,16}, {1,16}, {2,15}, {1,15}, {4,11}, {3,11}, {4,12}, {3,12}, {7,13}, {8,13}, {7,14}, {8,14}, {2,10}, {1,10}, {2,9}, {6,11}, {5,11} } Symmetric graph 5 of order 16 Valency 5 Diameter 2 Girth 4 Automorphism group of order 1920 Number of arcs = 80 Number of 2-arcs = 320 2-arc-transitive true Edge-set { {1,2}, {9,15}, {3,16}, {7,13}, {8,14}, {6,16}, {5,14}, {6,12}, {2,8}, {10,16}, {1,7}, {8,12}, {4,15}, {1,10}, {2,9}, {3,9}, {11,16}, {1,11}, {5,15}, {9,13}, {3,7}, {11,15}, {3,8}, {6,13}, {4,16}, {7,12}, {4,14}, {13,14}, {5,6}, {2,6}, {4,7}, {10,14}, {1,5}, {12,15}, {10,12}, {9,10}, {3,5}, {8,11}, {11,13}, {2,4} } Symmetric graph 6 of order 16 Valency 6 Diameter 2 Girth 3 Automorphism group of order 192 Number of arcs = 96 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,5}, {9,14}, {2,16}, {2,6}, {6,9}, {8,10}, {4,12}, {10,13}, {4,14}, {2,13}, {6,14}, {1,15}, {8,15}, {3,12}, {8,11}, {6,12}, {1,9}, {5,10}, {4,11}, {6,13}, {7,9}, {2,10}, {7,15}, {10,15}, {3,11}, {3,5}, {4,15}, {3,13}, {5,14}, {2,9}, {1,14}, {8,16}, {1,7}, {5,13}, {11,14}, {1,10}, {4,8}, {7,16}, {3,7}, {3,16}, {7,12}, {5,11}, {9,16}, {4,6}, {12,15}, {11,16}, {2,8}, {12,13} } Symmetric graph 7 of order 16 Valency 6 Diameter 2 Girth 3 Automorphism group of order 1152 Number of arcs = 96 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,5}, {8,9}, {3,11}, {12,15}, {4,7}, {2,14}, {1,13}, {6,16}, {6,10}, {4,10}, {5,15}, {8,14}, {3,7}, {12,16}, {2,12}, {9,13}, {2,6}, {4,13}, {6,11}, {11,15}, {5,12}, {7,10}, {2,10}, {1,16}, {8,16}, {3,14}, {7,15}, {1,9}, {6,14}, {4,12}, {9,14}, {11,16}, {10,13}, {2,5}, {3,8}, {8,12}, {3,15}, {5,9}, {1,6}, {4,16}, {7,13}, {1,11}, {7,11}, {3,9}, {4,8}, {10,14}, {2,15}, {5,13} } Symmetric graph 8 of order 16 Valency 6 Diameter 3 Girth 4 Automorphism group of order 12288 Number of arcs = 96 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,7}, {4,11}, {3,7}, {2,13}, {5,12}, {4,14}, {3,11}, {6,12}, {8,16}, {1,10}, {6,9}, {5,13}, {12,15}, {2,14}, {5,11}, {1,9}, {6,10}, {3,8}, {11,15}, {9,16}, {2,10}, {6,13}, {8,15}, {5,9}, {11,16}, {2,7}, {9,15}, {3,14}, {1,8}, {10,16}, {4,13}, {2,9}, {2,8}, {5,14}, {4,12}, {7,16}, {4,7}, {1,14}, {12,16}, {3,12}, {4,8}, {5,10}, {1,13}, {7,15}, {6,14}, {6,11}, {3,13}, {10,15} } Symmetric graph 9 of order 16 Valency 7 Diameter 3 Girth 4 Automorphism group of order 80640 Number of arcs = 112 Number of 2-arcs = 672 2-arc-transitive true Edge-set { {1,4}, {10,11}, {5,10}, {11,16}, {1,13}, {7,11}, {4,8}, {3,16}, {10,14}, {4,15}, {1,16}, {2,5}, {8,12}, {3,6}, {1,6}, {11,13}, {4,5}, {8,10}, {3,10}, {9,13}, {7,9}, {2,15}, {12,14}, {6,8}, {14,16}, {5,7}, {2,11}, {1,12}, {6,11}, {4,9}, {13,15}, {2,8}, {3,13}, {1,7}, {9,16}, {10,15}, {4,14}, {8,16}, {5,12}, {2,9}, {6,14}, {1,10}, {3,12}, {4,11}, {5,13}, {2,3}, {7,15}, {9,12}, {8,13}, {6,15}, {5,16}, {7,14}, {6,9}, {12,15}, {2,14}, {3,7} } Symmetric graph 10 of order 16 Valency 8 Diameter 2 Girth 4 Automorphism group of order 3251404800 Number of arcs = 128 Number of 2-arcs = 896 2-arc-transitive true Edge-set { {1,3}, {9,11}, {8,13}, {9,15}, {6,15}, {1,8}, {3,5}, {6,11}, {8,14}, {11,14}, {3,13}, {5,15}, {8,10}, {9,12}, {1,11}, {2,3}, {4,5}, {2,15}, {1,4}, {3,9}, {10,11}, {12,14}, {5,7}, {6,16}, {2,8}, {13,15}, {1,15}, {9,16}, {7,10}, {10,12}, {14,16}, {7,13}, {10,15}, {6,8}, {8,9}, {1,7}, {2,16}, {2,4}, {4,10}, {6,12}, {11,13}, {3,14}, {5,16}, {14,15}, {6,7}, {2,7}, {2,12}, {4,13}, {3,6}, {5,11}, {7,14}, {5,8}, {13,16}, {10,16}, {2,11}, {4,9}, {12,13}, {4,14}, {3,10}, {1,12}, {4,6}, {5,12}, {1,16}, {7,9} } Symmetric graph 11 of order 16 Valency 9 Diameter 2 Girth 3 Automorphism group of order 1152 Number of arcs = 144 Number of 2-arcs = 1152 2-arc-transitive false Edge-set { {1,6}, {9,16}, {8,13}, {2,8}, {1,11}, {4,10}, {7,9}, {10,13}, {7,16}, {2,13}, {5,14}, {4,15}, {8,11}, {4,5}, {4,9}, {2,11}, {6,11}, {4,13}, {1,12}, {5,12}, {3,14}, {10,15}, {7,10}, {2,7}, {12,14}, {5,15}, {8,14}, {1,15}, {7,13}, {2,16}, {4,14}, {9,15}, {6,16}, {3,13}, {6,12}, {3,5}, {5,11}, {4,6}, {11,13}, {3,12}, {5,10}, {1,10}, {7,12}, {3,16}, {4,11}, {6,9}, {11,16}, {1,14}, {12,15}, {3,8}, {2,9}, {9,14}, {2,5}, {8,15}, {4,7}, {6,15}, {5,16}, {3,6}, {2,15}, {11,14}, {7,14}, {8,9}, {1,8}, {1,16}, {12,13}, {3,10}, {3,9}, {8,10}, {2,12}, {10,16}, {1,7}, {6,13} } Symmetric graph 12 of order 16 Valency 10 Diameter 2 Girth 3 Automorphism group of order 1920 Number of arcs = 160 Number of 2-arcs = 1440 2-arc-transitive false Edge-set { {1,2}, {3,9}, {2,10}, {13,14}, {4,6}, {7,9}, {10,12}, {6,12}, {5,13}, {2,15}, {3,7}, {4,15}, {1,7}, {1,12}, {1,3}, {6,8}, {11,13}, {9,11}, {9,10}, {5,14}, {6,15}, {11,15}, {3,5}, {3,14}, {2,6}, {3,8}, {6,16}, {13,16}, {4,16}, {7,13}, {4,12}, {8,12}, {5,11}, {2,11}, {11,16}, {9,16}, {8,14}, {6,11}, {12,14}, {5,6}, {2,9}, {3,10}, {10,14}, {2,4}, {7,14}, {13,15}, {1,15}, {1,10}, {1,8}, {8,16}, {10,16}, {14,16}, {4,13}, {4,14}, {5,8}, {2,16}, {3,16}, {1,5}, {2,8}, {3,11}, {9,13}, {4,10}, {7,12}, {5,12}, {9,15}, {7,10}, {5,15}, {2,12}, {4,7}, {12,15}, {5,7}, {8,10}, {8,11}, {4,9}, {6,14}, {6,13}, {7,15}, {1,11}, {1,9}, {3,13} } Symmetric graph 13 of order 16 Valency 12 Diameter 2 Girth 3 Automorphism group of order 7962624 Number of arcs = 192 Number of 2-arcs = 2112 2-arc-transitive false Edge-set { {1,5}, {4,13}, {2,12}, {6,15}, {11,15}, {9,16}, {6,10}, {4,14}, {5,12}, {8,14}, {8,11}, {5,16}, {1,10}, {4,7}, {7,15}, {11,13}, {4,9}, {2,6}, {2,7}, {1,13}, {1,8}, {4,8}, {2,16}, {10,13}, {7,12}, {3,15}, {3,11}, {3,5}, {3,14}, {6,12}, {8,15}, {5,11}, {1,16}, {4,10}, {3,16}, {3,10}, {6,13}, {12,15}, {2,13}, {1,12}, {2,15}, {1,11}, {8,16}, {10,16}, {3,9}, {3,6}, {5,14}, {9,14}, {12,14}, {8,9}, {2,9}, {7,14}, {9,13}, {1,9}, {4,6}, {2,5}, {1,14}, {4,12}, {2,8}, {8,13}, {12,16}, {10,15}, {7,11}, {10,14}, {7,9}, {1,6}, {4,15}, {5,9}, {6,14}, {6,16}, {12,13}, {8,12}, {8,10}, {7,16}, {11,14}, {5,13}, {2,11}, {11,16}, {5,10}, {3,7}, {3,13}, {6,11}, {5,15}, {1,15}, {4,11}, {4,16}, {2,10}, {7,13}, {9,15}, {3,12}, {3,8}, {7,10}, {1,7}, {6,9}, {4,5}, {2,14} } Symmetric graph 14 of order 16 Valency 14 Diameter 2 Girth 3 Automorphism group of order 10321920 Number of arcs = 224 Number of 2-arcs = 2912 2-arc-transitive false Edge-set { {1,3}, {1,6}, {4,5}, {1,9}, {5,15}, {5,10}, {3,16}, {5,13}, {10,11}, {10,16}, {4,10}, {14,16}, {6,12}, {4,9}, {10,13}, {12,16}, {4,7}, {8,14}, {4,12}, {9,14}, {3,14}, {12,14}, {9,11}, {8,9}, {7,15}, {3,5}, {3,13}, {4,13}, {8,12}, {7,9}, {2,3}, {1,11}, {5,8}, {3,7}, {11,13}, {6,14}, {4,11}, {7,11}, {8,13}, {1,13}, {11,15}, {2,10}, {6,10}, {4,16}, {6,13}, {3,12}, {8,16}, {1,7}, {3,15}, {2,13}, {2,6}, {4,6}, {1,16}, {6,15}, {2,4}, {7,13}, {5,7}, {3,8}, {2,8}, {13,16}, {1,12}, {5,12}, {8,10}, {14,15}, {3,9}, {9,13}, {12,15}, {6,8}, {1,15}, {2,5}, {6,11}, {2,9}, {5,9}, {10,15}, {3,6}, {13,15}, {2,12}, {2,16}, {6,16}, {1,4}, {12,13}, {9,12}, {1,8}, {7,16}, {1,14}, {11,14}, {8,11}, {7,10}, {9,16}, {8,15}, {3,10}, {10,14}, {6,9}, {4,15}, {10,12}, {6,7}, {9,15}, {1,5}, {7,12}, {5,11}, {7,14}, {2,14}, {11,16}, {1,10}, {4,14}, {4,8}, {2,15}, {3,11}, {5,16}, {2,7}, {2,11}, {5,14} } Symmetric graph 15 of order 16 Valency 15 Diameter 1 Girth 3 Automorphism group of order 20922789888000 Number of arcs = 240 Number of 2-arcs = 3360 2-arc-transitive true Edge-set { {1,2}, {6,15}, {3,16}, {10,13}, {7,14}, {9,16}, {5,14}, {11,12}, {7,16}, {1,8}, {4,12}, {4,15}, {3,8}, {11,16}, {1,6}, {2,3}, {5,13}, {2,10}, {1,9}, {2,9}, {8,16}, {1,10}, {6,13}, {9,15}, {4,5}, {14,15}, {3,11}, {6,7}, {7,15}, {1,16}, {6,14}, {7,12}, {7,10}, {8,14}, {2,4}, {10,12}, {8,9}, {11,13}, {10,11}, {6,16}, {12,13}, {11,14}, {6,11}, {1,12}, {2,15}, {3,5}, {3,14}, {1,7}, {5,8}, {13,16}, {8,12}, {10,15}, {8,13}, {3,6}, {4,9}, {9,12}, {1,4}, {5,16}, {1,3}, {9,13}, {10,14}, {1,5}, {2,7}, {3,7}, {2,6}, {4,16}, {6,9}, {2,16}, {5,7}, {12,14}, {11,15}, {4,6}, {9,11}, {13,15}, {7,13}, {7,8}, {15,16}, {4,11}, {3,12}, {8,10}, {2,13}, {5,10}, {5,11}, {6,12}, {1,11}, {10,16}, {1,14}, {2,8}, {3,9}, {5,15}, {4,14}, {4,8}, {4,10}, {3,13}, {6,8}, {14,16}, {1,15}, {7,9}, {2,12}, {5,9}, {2,14}, {1,13}, {12,16}, {6,10}, {7,11}, {3,15}, {4,7}, {12,15}, {5,6}, {13,14}, {8,11}, {9,10}, {2,11}, {3,10}, {4,13}, {5,12}, {8,15}, {9,14}, {2,5}, {3,4} } ................................................................... Symmetric connected graphs of order 17 Symmetric graph 1 of order 17 Valency 2 Diameter 8 Girth 17 Automorphism group of order 34 Number of arcs = 34 Number of 2-arcs = 34 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {15,16}, {16,17}, {1,17} } Symmetric graph 2 of order 17 Valency 4 Diameter 3 Girth 4 Automorphism group of order 68 Number of arcs = 68 Number of 2-arcs = 204 2-arc-transitive false Edge-set { {1,2}, {2,3}, {1,14}, {3,4}, {10,14}, {2,15}, {1,17}, {4,5}, {6,10}, {11,15}, {16,17}, {3,16}, {13,14}, {1,5}, {5,6}, {2,6}, {7,11}, {15,16}, {12,16}, {12,13}, {5,9}, {4,17}, {9,10}, {14,15}, {6,7}, {3,7}, {8,12}, {11,12}, {9,13}, {13,17}, {8,9}, {4,8}, {10,11}, {7,8} } Symmetric graph 3 of order 17 Valency 8 Diameter 2 Girth 3 Automorphism group of order 136 Number of arcs = 136 Number of 2-arcs = 952 2-arc-transitive false Edge-set { {1,2}, {2,3}, {1,10}, {3,4}, {2,10}, {2,11}, {1,14}, {4,5}, {3,11}, {10,14}, {3,12}, {6,10}, {2,15}, {1,16}, {5,6}, {4,12}, {2,6}, {11,15}, {14,16}, {4,13}, {7,11}, {12,14}, {3,16}, {8,10}, {2,17}, {1,17}, {6,7}, {5,13}, {3,7}, {10,12}, {12,16}, {6,8}, {15,17}, {16,17}, {5,14}, {8,12}, {4,6}, {13,15}, {15,16}, {4,17}, {9,11}, {13,14}, {1,3}, {9,10}, {1,9}, {7,8}, {6,14}, {4,8}, {2,4}, {11,13}, {14,15}, {13,17}, {7,9}, {12,13}, {8,9}, {9,17}, {6,15}, {9,13}, {5,7}, {11,12}, {8,17}, {1,5}, {7,16}, {10,11}, {7,15}, {5,9}, {3,5}, {8,16} } Symmetric graph 4 of order 17 Valency 16 Diameter 1 Girth 3 Automorphism group of order 355687428096000 Number of arcs = 272 Number of 2-arcs = 4080 2-arc-transitive true Edge-set { {1,2}, {2,3}, {1,4}, {3,4}, {4,7}, {2,5}, {1,10}, {4,5}, {7,10}, {5,8}, {2,10}, {3,6}, {4,13}, {2,11}, {1,11}, {5,6}, {10,13}, {8,11}, {6,9}, {5,13}, {3,11}, {4,11}, {7,16}, {5,14}, {3,10}, {3,12}, {4,14}, {2,12}, {1,14}, {6,7}, {13,16}, {11,14}, {9,12}, {8,16}, {6,14}, {3,13}, {4,12}, {7,14}, {5,12}, {10,14}, {8,17}, {6,15}, {6,13}, {7,11}, {7,17}, {5,15}, {6,10}, {4,17}, {2,15}, {1,6}, {7,8}, {2,16}, {14,17}, {12,15}, {9,17}, {7,15}, {6,16}, {3,7}, {10,17}, {8,15}, {2,6}, {13,17}, {11,15}, {6,11}, {1,9}, {9,16}, {3,16}, {8,12}, {2,14}, {1,8}, {9,13}, {11,16}, {1,5}, {10,15}, {4,9}, {2,7}, {1,16}, {8,9}, {3,17}, {1,15}, {2,9}, {12,16}, {4,8}, {5,9}, {4,16}, {3,15}, {9,14}, {7,12}, {14,16}, {5,17}, {4,6}, {3,8}, {12,17}, {12,14}, {1,13}, {9,11}, {5,10}, {8,10}, {2,4}, {2,17}, {1,12}, {9,10}, {8,13}, {10,12}, {7,9}, {6,8}, {15,17}, {6,12}, {13,15}, {5,7}, {10,16}, {6,17}, {1,3}, {8,14}, {11,13}, {5,11}, {3,5}, {4,10}, {4,15}, {2,13}, {1,17}, {10,11}, {11,17}, {2,8}, {5,16}, {9,15}, {7,13}, {16,17}, {3,9}, {11,12}, {1,7}, {15,16}, {3,14}, {13,14}, {14,15}, {12,13} } ................................................................... Symmetric connected graphs of order 18 Symmetric graph 1 of order 18 Valency 2 Diameter 9 Girth 18 Automorphism group of order 36 Number of arcs = 36 Number of 2-arcs = 36 2-arc-transitive true Edge-set { {1,4}, {15,18}, {11,13}, {8,10}, {3,5}, {1,17}, {14,15}, {9,11}, {6,8}, {2,3}, {16,17}, {12,14}, {7,9}, {4,6}, {2,18}, {13,16}, {10,12}, {5,7} } Symmetric graph 2 of order 18 Valency 3 Diameter 4 Girth 6 Automorphism group of order 216 Number of arcs = 54 Number of 2-arcs = 108 2-arc-transitive true Edge-set { {1,4}, {15,18}, {2,10}, {9,10}, {4,14}, {3,17}, {8,12}, {3,6}, {8,17}, {11,15}, {2,5}, {7,16}, {9,18}, {13,16}, {3,11}, {4,7}, {14,17}, {1,12}, {5,8}, {6,9}, {6,13}, {2,16}, {7,11}, {5,15}, {1,18}, {12,13}, {10,14} } Symmetric graph 3 of order 18 Valency 4 Diameter 3 Girth 4 Automorphism group of order 144 Number of arcs = 72 Number of 2-arcs = 216 2-arc-transitive false Edge-set { {1,5}, {3,8}, {15,17}, {10,18}, {4,14}, {1,12}, {8,12}, {2,6}, {2,11}, {10,13}, {3,13}, {5,15}, {4,5}, {4,7}, {16,18}, {6,16}, {2,9}, {9,14}, {8,17}, {13,17}, {9,17}, {7,11}, {7,18}, {1,16}, {1,10}, {4,12}, {9,12}, {3,6}, {3,11}, {7,15}, {2,15}, {5,13}, {14,18}, {6,14}, {8,16}, {10,11} } Symmetric graph 4 of order 18 Valency 4 Diameter 4 Girth 4 Automorphism group of order 9216 Number of arcs = 72 Number of 2-arcs = 216 2-arc-transitive false Edge-set { {1,7}, {7,16}, {2,17}, {6,16}, {2,8}, {1,8}, {9,18}, {6,11}, {8,16}, {8,15}, {1,18}, {7,15}, {1,17}, {2,18}, {3,10}, {11,14}, {5,16}, {6,15}, {5,15}, {2,7}, {10,17}, {9,17}, {10,18}, {4,14}, {3,14}, {5,12}, {6,12}, {5,11}, {4,9}, {3,9}, {4,10}, {12,13}, {12,14}, {11,13}, {3,13}, {4,13} } Symmetric graph 5 of order 18 Valency 6 Diameter 3 Girth 4 Automorphism group of order 216 Number of arcs = 108 Number of 2-arcs = 540 2-arc-transitive false Edge-set { {1,4}, {8,10}, {6,13}, {14,18}, {3,18}, {3,12}, {11,15}, {9,12}, {4,7}, {5,9}, {7,17}, {2,5}, {2,16}, {1,10}, {15,17}, {10,13}, {13,17}, {14,16}, {8,17}, {9,11}, {4,14}, {8,18}, {3,6}, {2,6}, {3,11}, {8,11}, {1,5}, {7,12}, {6,14}, {15,16}, {1,16}, {12,13}, {9,18}, {5,15}, {4,15}, {7,16}, {1,18}, {2,17}, {1,12}, {12,15}, {7,10}, {5,8}, {6,7}, {3,17}, {2,11}, {9,16}, {10,14}, {2,10}, {5,13}, {4,8}, {6,9}, {13,18}, {11,14}, {3,4} } Symmetric graph 6 of order 18 Valency 6 Diameter 3 Girth 4 Automorphism group of order 559872 Number of arcs = 108 Number of 2-arcs = 540 2-arc-transitive false Edge-set { {1,4}, {1,17}, {3,12}, {15,17}, {3,13}, {2,10}, {7,11}, {13,15}, {5,13}, {2,11}, {11,16}, {7,18}, {4,18}, {5,9}, {8,9}, {11,13}, {5,16}, {4,11}, {1,16}, {9,18}, {4,8}, {9,14}, {6,8}, {12,14}, {10,17}, {9,11}, {8,16}, {4,14}, {1,6}, {1,9}, {8,12}, {14,17}, {3,6}, {10,12}, {7,15}, {13,18}, {8,17}, {6,14}, {6,10}, {1,12}, {12,15}, {3,17}, {2,3}, {7,10}, {14,16}, {6,15}, {10,13}, {2,15}, {3,7}, {2,18}, {5,7}, {2,5}, {16,18}, {4,5} } Symmetric graph 7 of order 18 Valency 8 Diameter 2 Girth 3 Automorphism group of order 36864 Number of arcs = 144 Number of 2-arcs = 1008 2-arc-transitive false Edge-set { {1,7}, {8,17}, {3,18}, {2,18}, {12,17}, {1,10}, {5,11}, {4,11}, {2,15}, {12,16}, {8,13}, {3,14}, {11,16}, {1,15}, {9,16}, {6,15}, {6,7}, {4,9}, {5,15}, {10,16}, {4,10}, {5,7}, {5,16}, {10,15}, {6,8}, {3,9}, {5,14}, {10,13}, {6,12}, {2,9}, {9,14}, {6,13}, {6,11}, {1,9}, {5,13}, {10,14}, {9,13}, {6,14}, {11,17}, {1,18}, {12,18}, {2,17}, {3,13}, {8,14}, {12,15}, {2,16}, {7,14}, {4,13}, {4,14}, {7,13}, {3,12}, {2,8}, {3,11}, {1,8}, {4,12}, {2,7}, {3,10}, {5,8}, {4,18}, {7,17}, {4,17}, {7,18}, {3,17}, {8,18}, {9,15}, {6,16}, {11,18}, {1,17}, {2,10}, {5,12}, {1,16}, {11,15} } Symmetric graph 8 of order 18 Valency 8 Diameter 3 Girth 4 Automorphism group of order 725760 Number of arcs = 144 Number of 2-arcs = 1008 2-arc-transitive true Edge-set { {1,4}, {8,10}, {12,17}, {14,15}, {2,8}, {6,18}, {3,5}, {10,16}, {7,14}, {2,11}, {5,11}, {6,13}, {9,12}, {14,18}, {3,15}, {8,15}, {1,13}, {1,10}, {7,17}, {4,11}, {4,14}, {9,13}, {16,18}, {3,7}, {1,5}, {6,10}, {4,9}, {2,16}, {8,12}, {10,17}, {4,17}, {7,9}, {6,15}, {1,18}, {12,14}, {11,15}, {8,13}, {2,3}, {5,8}, {5,17}, {13,16}, {1,7}, {6,12}, {3,10}, {4,16}, {2,14}, {2,9}, {11,18}, {5,14}, {9,15}, {1,12}, {3,13}, {8,18}, {15,17}, {10,11}, {7,16}, {7,11}, {4,6}, {10,14}, {3,12}, {9,18}, {2,6}, {5,16}, {4,8}, {1,15}, {13,17}, {3,18}, {6,7}, {11,13}, {2,17}, {12,16}, {5,9} } Symmetric graph 9 of order 18 Valency 9 Diameter 2 Girth 4 Automorphism group of order 263363788800 Number of arcs = 162 Number of 2-arcs = 1296 2-arc-transitive true Edge-set { {1,10}, {4,13}, {8,14}, {8,17}, {2,18}, {9,11}, {3,12}, {2,11}, {5,12}, {3,14}, {6,15}, {9,10}, {7,13}, {5,14}, {9,15}, {6,18}, {7,16}, {3,13}, {1,17}, {4,12}, {8,10}, {9,18}, {3,16}, {7,12}, {6,17}, {4,11}, {8,15}, {2,13}, {7,18}, {8,12}, {6,10}, {1,15}, {7,11}, {2,16}, {5,17}, {1,12}, {2,15}, {3,10}, {6,11}, {4,16}, {1,14}, {5,10}, {4,15}, {5,16}, {6,13}, {7,14}, {8,13}, {9,17}, {4,18}, {9,13}, {8,16}, {7,17}, {1,18}, {2,17}, {3,11}, {8,11}, {2,12}, {3,17}, {2,10}, {1,11}, {5,11}, {6,14}, {2,14}, {5,15}, {9,12}, {7,15}, {5,13}, {4,14}, {9,14}, {5,18}, {9,16}, {3,15}, {1,16}, {6,12}, {7,10}, {8,18}, {3,18}, {6,16}, {4,10}, {1,13}, {4,17} } Symmetric graph 10 of order 18 Valency 10 Diameter 2 Girth 3 Automorphism group of order 4320 Number of arcs = 180 Number of 2-arcs = 1620 2-arc-transitive false Edge-set { {1,4}, {15,18}, {2,18}, {2,5}, {6,8}, {5,13}, {6,16}, {13,16}, {3,16}, {7,17}, {1,11}, {3,9}, {6,17}, {3,6}, {4,9}, {6,14}, {4,17}, {5,10}, {10,15}, {8,14}, {12,17}, {1,5}, {14,17}, {1,17}, {8,18}, {2,12}, {1,7}, {4,18}, {12,16}, {3,14}, {7,11}, {4,11}, {15,16}, {3,18}, {5,7}, {4,15}, {5,18}, {6,11}, {11,13}, {9,15}, {10,18}, {2,6}, {4,13}, {1,14}, {9,10}, {2,15}, {4,8}, {5,14}, {9,16}, {3,10}, {2,8}, {5,16}, {10,17}, {1,15}, {8,12}, {5,12}, {13,17}, {1,16}, {2,9}, {7,18}, {12,14}, {2,13}, {8,16}, {2,11}, {3,7}, {4,12}, {7,13}, {11,16}, {3,4}, {3,13}, {5,9}, {6,15}, {8,13}, {6,10}, {6,7}, {10,13}, {9,14}, {11,18}, {14,18}, {2,17}, {9,17}, {3,12}, {1,8}, {9,11}, {1,10}, {7,12}, {11,14}, {7,15}, {8,10}, {12,15} } Symmetric graph 11 of order 18 Valency 12 Diameter 2 Girth 3 Automorphism group of order 2239488000 Number of arcs = 216 Number of 2-arcs = 2376 2-arc-transitive false Edge-set { {1,7}, {2,17}, {2,13}, {9,18}, {7,14}, {12,18}, {9,14}, {4,10}, {4,8}, {2,11}, {2,10}, {6,10}, {6,8}, {4,11}, {3,14}, {3,15}, {1,14}, {1,15}, {5,18}, {5,14}, {3,18}, {3,17}, {1,17}, {5,15}, {11,13}, {10,16}, {7,13}, {11,16}, {11,17}, {10,13}, {7,17}, {8,18}, {10,18}, {8,16}, {9,13}, {7,16}, {9,17}, {11,18}, {5,12}, {5,9}, {3,8}, {3,12}, {2,12}, {2,9}, {5,8}, {5,7}, {3,9}, {2,7}, {1,10}, {1,8}, {3,10}, {1,12}, {4,12}, {4,9}, {2,8}, {4,7}, {5,10}, {6,16}, {6,18}, {4,16}, {4,18}, {1,13}, {1,16}, {6,13}, {6,14}, {4,14}, {1,18}, {2,16}, {2,18}, {4,13}, {2,14}, {3,13}, {3,16}, {6,17}, {6,15}, {4,15}, {2,15}, {8,15}, {12,17}, {10,15}, {8,17}, {8,14}, {12,15}, {10,14}, {12,13}, {11,15}, {10,17}, {11,14}, {8,13}, {12,14}, {9,15}, {9,16}, {12,16}, {7,15}, {7,18}, {1,11}, {6,9}, {6,7}, {3,7}, {3,11}, {1,9}, {6,11}, {6,12}, {5,11}, {5,17}, {5,13}, {4,17}, {5,16} } Symmetric graph 12 of order 18 Valency 15 Diameter 2 Girth 3 Automorphism group of order 33592320 Number of arcs = 270 Number of 2-arcs = 3780 2-arc-transitive false Edge-set { {1,4}, {3,15}, {11,14}, {1,10}, {2,5}, {8,10}, {12,17}, {4,10}, {7,18}, {5,16}, {3,12}, {11,17}, {1,13}, {12,15}, {2,11}, {12,16}, {5,17}, {4,15}, {7,11}, {3,16}, {6,8}, {14,17}, {8,18}, {9,14}, {9,13}, {2,15}, {2,7}, {10,16}, {6,12}, {7,10}, {3,18}, {5,8}, {3,6}, {9,11}, {10,18}, {5,11}, {8,16}, {6,17}, {12,18}, {2,16}, {6,7}, {7,13}, {2,8}, {5,15}, {8,14}, {1,17}, {4,18}, {5,14}, {2,9}, {2,10}, {7,12}, {14,16}, {5,13}, {4,7}, {3,7}, {1,5}, {9,15}, {4,17}, {13,16}, {6,9}, {13,18}, {8,12}, {1,18}, {4,12}, {9,12}, {2,17}, {4,14}, {2,14}, {10,13}, {10,17}, {6,18}, {4,9}, {15,18}, {9,16}, {7,15}, {7,14}, {3,13}, {3,8}, {8,11}, {1,16}, {1,9}, {2,12}, {14,18}, {4,13}, {3,14}, {5,12}, {11,15}, {8,15}, {4,16}, {5,7}, {15,16}, {3,11}, {1,14}, {11,13}, {1,12}, {4,11}, {11,18}, {6,14}, {7,16}, {6,13}, {2,18}, {12,14}, {13,17}, {1,8}, {9,18}, {11,16}, {6,15}, {1,11}, {9,10}, {1,6}, {6,16}, {1,7}, {9,17}, {3,17}, {4,8}, {3,9}, {15,17}, {2,6}, {5,18}, {5,10}, {6,11}, {2,4}, {5,9}, {7,17}, {3,4}, {6,10}, {10,15}, {8,17}, {8,13}, {3,10}, {2,13}, {10,14}, {1,15}, {12,13}, {3,5} } Symmetric graph 13 of order 18 Valency 16 Diameter 2 Girth 3 Automorphism group of order 185794560 Number of arcs = 288 Number of 2-arcs = 4320 2-arc-transitive false Edge-set { {1,3}, {13,15}, {3,8}, {8,9}, {2,5}, {1,15}, {8,18}, {1,4}, {9,18}, {14,18}, {4,13}, {9,13}, {3,5}, {1,12}, {12,18}, {13,16}, {3,7}, {4,12}, {9,12}, {7,12}, {8,16}, {2,7}, {4,8}, {2,9}, {15,18}, {8,13}, {6,13}, {3,16}, {6,12}, {12,16}, {8,10}, {2,6}, {2,15}, {8,17}, {6,16}, {7,16}, {4,6}, {9,16}, {16,17}, {1,10}, {6,18}, {2,14}, {4,17}, {1,16}, {7,18}, {4,14}, {4,9}, {5,12}, {1,8}, {2,18}, {10,15}, {6,8}, {6,17}, {14,16}, {6,10}, {10,18}, {14,17}, {9,14}, {4,5}, {1,11}, {11,18}, {10,17}, {6,14}, {2,10}, {7,14}, {4,10}, {6,9}, {10,11}, {6,11}, {3,13}, {3,10}, {12,17}, {12,14}, {11,16}, {7,11}, {10,13}, {3,6}, {2,12}, {1,7}, {4,16}, {7,9}, {1,13}, {3,18}, {3,9}, {5,10}, {1,17}, {11,17}, {11,14}, {7,10}, {1,6}, {3,17}, {10,14}, {3,12}, {10,12}, {4,7}, {1,9}, {16,18}, {7,13}, {5,13}, {3,15}, {12,15}, {3,11}, {7,17}, {1,14}, {3,14}, {5,17}, {14,15}, {8,15}, {2,8}, {6,7}, {6,15}, {15,17}, {8,14}, {2,13}, {10,16}, {2,4}, {9,17}, {2,3}, {8,12}, {4,15}, {11,13}, {5,11}, {11,15}, {5,7}, {13,17}, {8,11}, {2,16}, {2,17}, {9,15}, {5,8}, {5,16}, {5,15}, {2,11}, {7,15}, {1,5}, {5,18}, {4,18}, {5,14}, {9,11}, {1,18}, {4,11}, {5,9}, {13,18}, {12,13} } Symmetric graph 14 of order 18 Valency 17 Diameter 1 Girth 3 Automorphism group of order 6402373705728000 Number of arcs = 306 Number of 2-arcs = 4896 2-arc-transitive true Edge-set { {1,2}, {5,6}, {8,16}, {13,15}, {3,15}, {4,8}, {1,11}, {9,12}, {7,9}, {9,16}, {2,9}, {4,10}, {6,11}, {1,5}, {8,14}, {2,11}, {10,13}, {2,18}, {10,17}, {2,8}, {1,10}, {2,6}, {10,16}, {7,10}, {6,18}, {1,13}, {3,14}, {5,15}, {8,15}, {3,4}, {4,11}, {1,6}, {14,16}, {7,12}, {7,18}, {6,17}, {12,16}, {7,14}, {5,18}, {4,6}, {11,16}, {5,7}, {8,18}, {6,13}, {3,16}, {7,8}, {1,18}, {17,18}, {13,17}, {3,12}, {5,12}, {2,4}, {9,15}, {4,9}, {9,11}, {6,14}, {5,13}, {3,8}, {1,4}, {11,18}, {12,17}, {13,14}, {3,5}, {8,11}, {3,18}, {4,17}, {15,17}, {12,15}, {3,6}, {1,8}, {1,14}, {15,18}, {11,12}, {12,13}, {3,7}, {4,18}, {11,17}, {5,17}, {8,12}, {14,17}, {12,14}, {2,13}, {11,15}, {6,10}, {6,16}, {9,10}, {2,10}, {10,14}, {3,13}, {7,15}, {4,16}, {5,10}, {6,8}, {1,17}, {11,14}, {4,7}, {15,16}, {2,15}, {16,17}, {2,12}, {9,14}, {5,9}, {9,13}, {13,16}, {2,3}, {4,5}, {9,17}, {7,13}, {16,18}, {2,17}, {6,12}, {5,14}, {14,15}, {11,13}, {3,11}, {4,13}, {7,16}, {1,9}, {8,13}, {1,3}, {2,7}, {10,18}, {6,7}, {9,18}, {8,10}, {5,8}, {4,14}, {8,9}, {6,9}, {10,15}, {1,7}, {2,16}, {6,15}, {2,14}, {12,18}, {7,17}, {8,17}, {1,12}, {5,16}, {4,15}, {3,9}, {1,16}, {10,12}, {2,5}, {4,12}, {7,11}, {13,18}, {3,17}, {3,10}, {10,11}, {14,18}, {5,11}, {1,15} } ................................................................... Symmetric connected graphs of order 19 Symmetric graph 1 of order 19 Valency 2 Diameter 9 Girth 19 Automorphism group of order 38 Number of arcs = 38 Number of 2-arcs = 38 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {15,16}, {16,17}, {17,18}, {18,19}, {1,19} } Symmetric graph 2 of order 19 Valency 6 Diameter 2 Girth 3 Automorphism group of order 114 Number of arcs = 114 Number of 2-arcs = 570 2-arc-transitive false Edge-set { {1,2}, {2,3}, {1,8}, {3,4}, {8,15}, {2,9}, {1,12}, {4,5}, {3,15}, {9,16}, {4,12}, {3,10}, {8,19}, {2,13}, {5,6}, {4,16}, {4,15}, {10,17}, {11,19}, {5,13}, {4,11}, {7,15}, {1,9}, {12,13}, {3,14}, {8,9}, {6,7}, {5,17}, {3,11}, {5,16}, {11,18}, {7,18}, {13,14}, {6,14}, {9,10}, {5,12}, {8,16}, {2,10}, {1,19}, {15,16}, {12,19}, {7,8}, {6,18}, {10,18}, {14,15}, {6,17}, {10,11}, {16,17}, {7,19}, {6,13}, {9,17}, {11,12}, {1,13}, {17,18}, {7,14}, {18,19}, {2,14} } Symmetric graph 3 of order 19 Valency 18 Diameter 1 Girth 3 Automorphism group of order 121645100408832000 Number of arcs = 342 Number of 2-arcs = 5814 2-arc-transitive true Edge-set { {1,2}, {2,3}, {1,5}, {3,4}, {5,9}, {2,6}, {1,17}, {4,5}, {9,13}, {6,10}, {14,17}, {3,7}, {2,5}, {2,18}, {1,8}, {5,6}, {13,17}, {10,14}, {11,14}, {7,11}, {15,18}, {8,15}, {4,8}, {6,9}, {3,6}, {5,17}, {3,19}, {5,12}, {2,9}, {1,10}, {6,7}, {2,17}, {14,18}, {8,11}, {11,15}, {12,15}, {3,15}, {8,12}, {16,19}, {12,19}, {9,16}, {10,19}, {10,13}, {7,10}, {2,14}, {4,7}, {6,18}, {8,17}, {1,4}, {6,13}, {7,17}, {3,10}, {5,14}, {2,11}, {1,18}, {7,8}, {3,18}, {5,8}, {15,19}, {9,12}, {12,16}, {13,16}, {7,19}, {4,16}, {9,19}, {1,13}, {7,16}, {10,17}, {4,14}, {1,11}, {16,18}, {11,18}, {5,15}, {2,12}, {9,18}, {8,10}, {7,14}, {8,18}, {6,8}, {4,11}, {6,15}, {15,17}, {3,12}, {3,5}, {2,19}, {1,12}, {8,9}, {4,19}, {1,16}, {6,16}, {4,13}, {14,16}, {4,6}, {13,15}, {1,3}, {17,19}, {4,12}, {3,13}, {5,7}, {12,14}, {9,11}, {10,18}, {10,12}, {7,9}, {2,10}, {8,19}, {9,17}, {5,16}, {2,13}, {1,7}, {9,10}, {2,4}, {11,13}, {4,15}, {11,19}, {1,9}, {8,16}, {5,13}, {7,13}, {6,17}, {7,15}, {3,14}, {12,18}, {7,18}, {6,14}, {3,11}, {5,18}, {10,16}, {8,14}, {4,17}, {5,11}, {2,8}, {1,6}, {10,11}, {13,19}, {3,16}, {1,14}, {4,10}, {11,17}, {6,11}, {6,19}, {9,15}, {7,12}, {6,12}, {2,15}, {3,9}, {12,17}, {4,18}, {10,15}, {8,13}, {3,17}, {5,10}, {2,7}, {11,12}, {11,16}, {4,9}, {1,15}, {13,18}, {3,8}, {2,16}, {14,19}, {5,19}, {9,14}, {12,13}, {18,19}, {17,18}, {13,14}, {1,19}, {15,16}, {16,17}, {14,15} } ................................................................... Symmetric connected graphs of order 20 Symmetric graph 1 of order 20 Valency 2 Diameter 10 Girth 20 Automorphism group of order 40 Number of arcs = 40 Number of 2-arcs = 40 2-arc-transitive true Edge-set { {1,3}, {4,5}, {12,14}, {6,7}, {13,15}, {2,4}, {8,10}, {16,17}, {3,6}, {11,13}, {9,11}, {18,19}, {5,8}, {14,16}, {1,20}, {7,9}, {15,18}, {10,12}, {17,20}, {2,19} } Symmetric graph 2 of order 20 Valency 3 Diameter 5 Girth 5 Automorphism group of order 120 Number of arcs = 60 Number of 2-arcs = 120 2-arc-transitive true Edge-set { {1,5}, {6,9}, {7,17}, {10,14}, {8,20}, {1,11}, {13,18}, {11,19}, {3,12}, {6,16}, {14,17}, {2,17}, {2,12}, {4,16}, {8,15}, {4,13}, {10,19}, {1,18}, {5,15}, {7,19}, {3,15}, {12,20}, {2,6}, {9,20}, {7,16}, {4,11}, {5,10}, {9,13}, {8,18}, {3,14} } Symmetric graph 3 of order 20 Valency 3 Diameter 5 Girth 6 Automorphism group of order 240 Number of arcs = 60 Number of 2-arcs = 120 2-arc-transitive true Edge-set { {1,6}, {1,12}, {5,10}, {3,12}, {10,19}, {2,17}, {3,15}, {8,19}, {14,17}, {11,20}, {9,14}, {5,15}, {8,16}, {7,20}, {4,13}, {7,18}, {2,5}, {6,16}, {6,9}, {10,13}, {4,11}, {2,11}, {1,18}, {8,17}, {4,16}, {9,20}, {12,19}, {3,14}, {7,15}, {13,18} } Symmetric graph 4 of order 20 Valency 4 Diameter 4 Girth 4 Automorphism group of order 80 Number of arcs = 80 Number of 2-arcs = 240 2-arc-transitive false Edge-set { {1,3}, {1,15}, {17,20}, {15,17}, {12,17}, {3,9}, {13,16}, {3,17}, {12,13}, {3,6}, {7,13}, {1,19}, {6,20}, {11,18}, {9,11}, {13,20}, {6,11}, {7,9}, {1,7}, {2,20}, {11,14}, {10,15}, {2,16}, {4,5}, {8,14}, {5,19}, {6,8}, {9,16}, {5,7}, {2,8}, {14,19}, {14,15}, {16,18}, {5,12}, {8,10}, {4,10}, {2,4}, {18,19}, {4,18}, {10,12} } Symmetric graph 5 of order 20 Valency 4 Diameter 4 Girth 4 Automorphism group of order 320 Number of arcs = 80 Number of 2-arcs = 240 2-arc-transitive false Edge-set { {1,3}, {2,14}, {6,7}, {5,18}, {5,7}, {10,12}, {6,18}, {1,9}, {9,12}, {11,19}, {14,15}, {1,10}, {2,20}, {6,13}, {11,20}, {13,15}, {3,16}, {18,19}, {2,19}, {6,14}, {4,5}, {10,17}, {4,16}, {17,19}, {7,20}, {10,18}, {3,5}, {8,9}, {8,20}, {2,3}, {7,9}, {4,12}, {1,14}, {11,13}, {4,11}, {12,13}, {8,15}, {16,17}, {8,16}, {15,17} } Symmetric graph 6 of order 20 Valency 4 Diameter 5 Girth 4 Automorphism group of order 20480 Number of arcs = 80 Number of 2-arcs = 240 2-arc-transitive false Edge-set { {1,3}, {14,15}, {3,5}, {2,4}, {16,17}, {12,14}, {5,8}, {13,16}, {4,6}, {1,20}, {18,20}, {10,12}, {8,10}, {15,18}, {11,13}, {6,7}, {18,19}, {1,19}, {7,10}, {10,11}, {2,19}, {17,19}, {9,11}, {7,9}, {15,17}, {2,3}, {5,7}, {11,14}, {17,20}, {2,20}, {8,9}, {9,12}, {14,16}, {4,5}, {16,18}, {1,4}, {6,8}, {12,13}, {13,15}, {3,6} } Symmetric graph 7 of order 20 Valency 6 Diameter 3 Girth 4 Automorphism group of order 240 Number of arcs = 120 Number of 2-arcs = 600 2-arc-transitive false Edge-set { {1,6}, {8,9}, {12,15}, {10,16}, {13,20}, {14,19}, {2,17}, {13,18}, {1,19}, {2,20}, {4,5}, {3,17}, {3,6}, {8,11}, {1,20}, {4,7}, {3,8}, {6,12}, {2,5}, {5,11}, {9,16}, {8,10}, {7,9}, {10,15}, {2,8}, {5,12}, {6,11}, {9,14}, {7,10}, {10,13}, {15,17}, {11,16}, {16,18}, {13,19}, {14,20}, {2,19}, {5,10}, {11,13}, {12,14}, {16,17}, {9,15}, {15,18}, {3,20}, {4,19}, {1,18}, {1,7}, {4,6}, {3,5}, {12,13}, {16,19}, {15,20}, {4,18}, {14,17}, {1,8}, {2,7}, {6,9}, {7,12}, {4,17}, {3,18}, {11,14} } Symmetric graph 8 of order 20 Valency 6 Diameter 3 Girth 3 Automorphism group of order 240 Number of arcs = 120 Number of 2-arcs = 600 2-arc-transitive false Edge-set { {1,4}, {6,7}, {3,17}, {10,11}, {5,8}, {1,8}, {13,16}, {14,19}, {9,12}, {6,12}, {6,17}, {17,19}, {12,15}, {4,18}, {14,15}, {13,20}, {10,15}, {8,13}, {1,10}, {15,20}, {2,7}, {2,3}, {18,20}, {11,16}, {16,19}, {12,17}, {6,13}, {3,20}, {9,16}, {5,11}, {5,18}, {2,9}, {4,19}, {1,15}, {1,13}, {10,17}, {8,12}, {3,8}, {4,9}, {7,14}, {5,14}, {4,7}, {3,10}, {6,20}, {16,17}, {1,19}, {4,6}, {11,18}, {9,18}, {7,11}, {3,5}, {8,9}, {7,10}, {2,16}, {2,14}, {2,20}, {12,14}, {11,13}, {5,19}, {15,18} } Symmetric graph 9 of order 20 Valency 6 Diameter 3 Girth 4 Automorphism group of order 240 Number of arcs = 120 Number of 2-arcs = 600 2-arc-transitive false Edge-set { {1,4}, {12,16}, {7,10}, {3,6}, {15,19}, {10,17}, {1,15}, {5,8}, {5,14}, {17,20}, {1,14}, {5,12}, {10,16}, {2,9}, {2,7}, {6,17}, {13,20}, {11,14}, {7,12}, {2,3}, {6,19}, {11,18}, {10,11}, {4,9}, {1,20}, {8,13}, {4,7}, {3,10}, {4,19}, {11,15}, {8,9}, {4,17}, {16,18}, {12,13}, {3,18}, {15,17}, {1,8}, {14,16}, {4,5}, {16,20}, {9,18}, {7,14}, {13,15}, {3,8}, {18,19}, {5,20}, {9,12}, {6,7}, {2,16}, {6,13}, {2,13}, {9,15}, {14,19}, {6,11}, {2,19}, {1,10}, {5,18}, {8,11}, {12,17}, {3,20} } Symmetric graph 10 of order 20 Valency 6 Diameter 3 Girth 3 Automorphism group of order 240 Number of arcs = 120 Number of 2-arcs = 600 2-arc-transitive false Edge-set { {1,4}, {2,3}, {6,7}, {5,8}, {8,14}, {10,12}, {7,13}, {9,11}, {11,18}, {14,15}, {12,17}, {13,16}, {12,16}, {1,16}, {6,17}, {18,20}, {11,15}, {2,15}, {5,18}, {17,19}, {15,19}, {3,18}, {6,19}, {2,10}, {16,20}, {4,17}, {5,20}, {1,9}, {3,20}, {1,8}, {14,19}, {3,10}, {4,9}, {5,14}, {4,19}, {2,7}, {13,20}, {6,13}, {1,20}, {4,8}, {3,7}, {6,11}, {9,18}, {2,19}, {5,12}, {10,17}, {4,6}, {7,11}, {8,12}, {12,14}, {10,16}, {1,13}, {3,5}, {11,13}, {9,15}, {2,14}, {7,10}, {15,18}, {8,9}, {16,17} } Symmetric graph 11 of order 20 Valency 6 Diameter 2 Girth 4 Automorphism group of order 122880 Number of arcs = 120 Number of 2-arcs = 600 2-arc-transitive false Edge-set { {1,5}, {3,13}, {6,9}, {8,17}, {9,14}, {10,14}, {8,15}, {1,12}, {14,18}, {6,10}, {13,18}, {12,20}, {3,12}, {6,15}, {6,16}, {2,18}, {10,13}, {5,16}, {2,17}, {12,19}, {3,15}, {14,17}, {10,20}, {10,19}, {4,16}, {2,5}, {5,10}, {13,17}, {9,19}, {4,15}, {1,17}, {8,20}, {1,18}, {4,13}, {7,19}, {5,9}, {9,13}, {5,15}, {9,20}, {4,14}, {7,20}, {1,6}, {8,19}, {3,16}, {2,6}, {7,17}, {4,11}, {3,14}, {7,18}, {3,11}, {4,12}, {7,15}, {1,11}, {2,11}, {7,16}, {8,18}, {8,16}, {2,12}, {11,20}, {11,19} } Symmetric graph 12 of order 20 Valency 8 Diameter 3 Girth 4 Automorphism group of order 245760 Number of arcs = 160 Number of 2-arcs = 1120 2-arc-transitive false Edge-set { {1,3}, {2,8}, {15,17}, {7,10}, {2,16}, {5,19}, {9,12}, {4,9}, {1,4}, {6,7}, {10,16}, {14,15}, {13,19}, {3,17}, {3,6}, {3,18}, {1,8}, {15,18}, {9,16}, {1,20}, {4,6}, {4,10}, {5,12}, {8,9}, {11,14}, {7,13}, {2,19}, {12,17}, {17,20}, {2,20}, {11,17}, {8,10}, {2,15}, {5,20}, {9,11}, {3,10}, {8,13}, {1,16}, {18,20}, {4,18}, {6,19}, {2,3}, {12,18}, {5,8}, {1,7}, {7,14}, {13,16}, {17,19}, {6,12}, {12,14}, {14,16}, {18,19}, {2,4}, {5,7}, {13,15}, {14,19}, {3,5}, {4,17}, {10,11}, {2,7}, {6,8}, {10,15}, {13,20}, {11,18}, {16,17}, {6,11}, {1,15}, {12,13}, {6,20}, {14,20}, {11,13}, {16,18}, {9,15}, {1,19}, {5,11}, {7,9}, {4,5}, {10,12}, {8,14}, {3,9} } Symmetric graph 13 of order 20 Valency 8 Diameter 2 Girth 4 Automorphism group of order 79626240 Number of arcs = 160 Number of 2-arcs = 1120 2-arc-transitive false Edge-set { {1,5}, {2,6}, {6,9}, {5,10}, {5,20}, {10,13}, {6,19}, {9,14}, {4,9}, {4,19}, {14,17}, {3,10}, {3,20}, {13,18}, {13,20}, {8,13}, {3,8}, {3,17}, {2,18}, {14,19}, {7,14}, {4,7}, {4,18}, {1,17}, {4,17}, {4,8}, {11,17}, {8,14}, {7,11}, {2,7}, {1,18}, {3,18}, {3,7}, {12,18}, {7,13}, {8,12}, {1,8}, {2,17}, {13,17}, {2,8}, {8,11}, {12,17}, {2,16}, {11,18}, {7,12}, {12,16}, {1,7}, {5,12}, {1,6}, {14,18}, {1,15}, {11,15}, {6,11}, {2,5}, {5,11}, {11,16}, {2,15}, {1,16}, {12,15}, {15,20}, {6,12}, {9,15}, {6,10}, {16,19}, {10,16}, {5,9}, {9,16}, {16,20}, {5,19}, {6,20}, {15,19}, {10,15}, {13,19}, {10,14}, {14,20}, {9,13}, {4,20}, {3,9}, {4,10}, {3,19} } Symmetric graph 14 of order 20 Valency 9 Diameter 3 Girth 3 Automorphism group of order 1440 Number of arcs = 180 Number of 2-arcs = 1440 2-arc-transitive false Edge-set { {1,3}, {17,19}, {5,15}, {6,12}, {4,8}, {2,13}, {14,18}, {13,20}, {8,18}, {11,16}, {10,20}, {2,6}, {9,11}, {5,10}, {2,7}, {8,11}, {3,11}, {4,14}, {7,10}, {1,20}, {6,13}, {4,16}, {9,19}, {2,15}, {10,14}, {7,20}, {11,19}, {4,17}, {15,19}, {9,18}, {1,16}, {7,15}, {10,12}, {5,19}, {5,7}, {1,10}, {16,17}, {6,16}, {8,9}, {6,18}, {9,15}, {7,12}, {4,6}, {8,19}, {12,18}, {3,9}, {14,19}, {5,17}, {7,13}, {3,15}, {8,14}, {12,14}, {1,14}, {13,17}, {8,16}, {1,11}, {3,13}, {13,16}, {3,7}, {12,20}, {1,18}, {6,8}, {3,20}, {6,9}, {1,8}, {2,12}, {15,18}, {1,5}, {2,4}, {11,17}, {4,19}, {10,17}, {2,17}, {7,17}, {12,15}, {3,5}, {11,13}, {9,13}, {5,11}, {6,20}, {3,18}, {2,19}, {5,14}, {18,20}, {4,12}, {4,10}, {14,15}, {10,16}, {2,9}, {16,20} } Symmetric graph 15 of order 20 Valency 9 Diameter 3 Girth 4 Automorphism group of order 7257600 Number of arcs = 180 Number of 2-arcs = 1440 2-arc-transitive true Edge-set { {1,3}, {3,6}, {7,18}, {3,16}, {7,10}, {2,9}, {1,19}, {3,17}, {7,12}, {9,19}, {16,19}, {5,20}, {15,17}, {6,12}, {14,18}, {2,7}, {8,9}, {6,19}, {12,20}, {14,15}, {12,17}, {12,14}, {11,15}, {9,13}, {1,18}, {2,11}, {8,16}, {6,10}, {2,14}, {5,9}, {17,19}, {10,20}, {15,20}, {12,16}, {10,14}, {8,11}, {6,13}, {3,11}, {1,8}, {2,6}, {8,14}, {5,11}, {13,20}, {4,15}, {5,7}, {5,17}, {10,17}, {10,16}, {5,14}, {9,15}, {1,12}, {11,19}, {13,16}, {11,18}, {11,13}, {8,17}, {14,19}, {4,10}, {3,7}, {18,20}, {5,16}, {3,20}, {7,15}, {4,13}, {4,18}, {1,15}, {2,16}, {3,9}, {6,8}, {6,18}, {13,17}, {4,12}, {1,5}, {7,13}, {4,5}, {1,10}, {2,20}, {3,14}, {4,19}, {7,19}, {1,13}, {9,12}, {9,18}, {4,8}, {2,4}, {6,15}, {16,18}, {8,20}, {10,11}, {2,17} } Symmetric graph 16 of order 20 Valency 10 Diameter 2 Girth 4 Automorphism group of order 26336378880000 Number of arcs = 200 Number of 2-arcs = 1800 2-arc-transitive true Edge-set { {1,3}, {12,14}, {9,19}, {2,4}, {1,8}, {10,19}, {15,17}, {11,13}, {10,20}, {12,17}, {3,9}, {15,18}, {6,7}, {6,11}, {2,7}, {9,20}, {16,18}, {6,8}, {14,19}, {17,19}, {5,11}, {4,13}, {1,16}, {7,13}, {11,18}, {4,10}, {16,17}, {5,8}, {5,12}, {3,13}, {1,15}, {7,10}, {6,15}, {7,14}, {2,20}, {9,12}, {3,18}, {5,7}, {13,20}, {18,20}, {6,12}, {3,14}, {2,15}, {8,14}, {2,19}, {9,11}, {4,18}, {6,16}, {1,4}, {10,16}, {8,17}, {5,19}, {4,14}, {2,16}, {8,9}, {5,16}, {8,13}, {1,19}, {10,11}, {4,17}, {10,15}, {7,17}, {5,20}, {12,13}, {12,18}, {3,6}, {14,15}, {1,20}, {10,12}, {3,17}, {5,15}, {2,3}, {9,15}, {7,18}, {6,20}, {4,6}, {14,16}, {2,8}, {13,19}, {1,11}, {9,16}, {8,18}, {6,19}, {11,14}, {11,17}, {4,5}, {13,16}, {1,12}, {3,10}, {7,9}, {3,5}, {13,15}, {1,7}, {14,20}, {2,12}, {18,19}, {2,11}, {4,9}, {8,10}, {17,20} } Symmetric graph 17 of order 20 Valency 12 Diameter 2 Girth 3 Automorphism group of order 2880 Number of arcs = 240 Number of 2-arcs = 2640 2-arc-transitive false Edge-set { {1,6}, {2,11}, {11,17}, {12,15}, {3,20}, {8,9}, {5,16}, {14,20}, {3,8}, {5,19}, {8,17}, {6,16}, {4,13}, {2,12}, {13,18}, {9,18}, {7,18}, {7,10}, {5,10}, {14,19}, {7,13}, {2,13}, {4,18}, {4,9}, {12,18}, {10,13}, {10,16}, {4,19}, {9,14}, {3,18}, {10,19}, {5,11}, {14,17}, {10,15}, {3,14}, {3,17}, {6,9}, {6,15}, {1,15}, {15,18}, {1,7}, {7,20}, {1,20}, {9,20}, {12,19}, {5,20}, {8,11}, {7,16}, {4,17}, {6,12}, {15,20}, {3,9}, {3,6}, {9,15}, {3,16}, {1,10}, {1,18}, {7,14}, {15,17}, {6,20}, {6,19}, {5,15}, {5,14}, {2,8}, {1,16}, {4,10}, {4,7}, {4,15}, {1,12}, {13,20}, {16,19}, {4,5}, {10,20}, {8,19}, {3,13}, {1,8}, {12,13}, {4,14}, {3,12}, {13,19}, {11,18}, {7,17}, {7,12}, {16,17}, {11,16}, {8,15}, {11,20}, {2,20}, {2,7}, {4,6}, {6,17}, {2,19}, {8,18}, {5,12}, {2,9}, {1,14}, {3,10}, {8,13}, {2,16}, {4,11}, {12,17}, {12,14}, {2,15}, {1,11}, {8,14}, {1,19}, {11,13}, {2,17}, {8,10}, {2,5}, {11,14}, {6,11}, {6,13}, {9,16}, {10,17}, {9,19}, {16,18}, {5,18}, {7,9}, {3,5} } Symmetric graph 18 of order 20 Valency 12 Diameter 2 Girth 3 Automorphism group of order 122880 Number of arcs = 240 Number of 2-arcs = 2640 2-arc-transitive false Edge-set { {1,3}, {8,11}, {13,18}, {13,19}, {12,20}, {1,9}, {6,15}, {9,16}, {9,15}, {14,15}, {10,11}, {11,18}, {7,13}, {4,6}, {1,4}, {5,18}, {2,7}, {6,18}, {1,7}, {6,10}, {1,16}, {13,17}, {8,12}, {1,13}, {6,12}, {9,20}, {15,19}, {4,7}, {4,17}, {7,11}, {3,6}, {14,19}, {11,20}, {4,8}, {5,11}, {2,13}, {2,9}, {5,15}, {9,11}, {13,15}, {4,14}, {4,11}, {15,18}, {7,10}, {6,16}, {7,20}, {17,19}, {5,17}, {13,20}, {12,19}, {4,18}, {10,16}, {10,12}, {7,19}, {17,20}, {3,13}, {3,12}, {9,12}, {12,18}, {7,14}, {7,12}, {6,9}, {1,15}, {16,17}, {12,17}, {1,6}, {8,19}, {4,5}, {2,4}, {15,20}, {10,19}, {2,16}, {5,9}, {2,3}, {3,5}, {10,15}, {14,16}, {6,17}, {2,8}, {14,17}, {16,20}, {9,19}, {2,15}, {5,10}, {8,9}, {8,14}, {14,18}, {1,14}, {6,11}, {10,20}, {16,19}, {14,20}, {11,19}, {2,5}, {2,14}, {4,13}, {3,7}, {3,17}, {1,10}, {5,12}, {3,18}, {3,8}, {1,8}, {2,10}, {5,16}, {16,18}, {7,9}, {18,19}, {13,16}, {4,12}, {15,17}, {8,10}, {3,14}, {8,20}, {11,17}, {8,13}, {3,11}, {18,20}, {1,5}, {2,6} } Symmetric graph 19 of order 20 Valency 15 Diameter 2 Girth 3 Automorphism group of order 4976640000 Number of arcs = 300 Number of 2-arcs = 4200 2-arc-transitive false Edge-set { {1,6}, {10,20}, {2,15}, {9,12}, {1,20}, {5,19}, {10,11}, {2,8}, {5,7}, {12,20}, {15,20}, {13,16}, {14,19}, {1,9}, {7,19}, {4,11}, {6,16}, {3,14}, {2,12}, {7,20}, {5,12}, {3,11}, {8,16}, {4,13}, {9,19}, {8,20}, {5,15}, {6,13}, {3,19}, {1,17}, {2,16}, {4,18}, {2,19}, {7,11}, {6,12}, {3,20}, {7,14}, {1,18}, {4,16}, {3,17}, {8,13}, {7,12}, {4,20}, {5,16}, {10,14}, {3,10}, {13,18}, {12,19}, {15,17}, {11,19}, {11,16}, {14,17}, {13,19}, {3,6}, {2,10}, {2,7}, {12,18}, {4,6}, {3,9}, {14,20}, {15,18}, {11,17}, {12,17}, {3,7}, {4,8}, {2,6}, {13,20}, {14,16}, {4,9}, {9,18}, {1,12}, {8,18}, {2,13}, {10,17}, {1,13}, {6,19}, {1,11}, {4,15}, {9,17}, {3,13}, {8,19}, {10,18}, {2,14}, {7,18}, {4,12}, {9,20}, {5,14}, {1,15}, {6,17}, {7,17}, {6,18}, {3,12}, {10,19}, {2,11}, {9,16}, {8,17}, {5,13}, {8,14}, {5,18}, {2,20}, {7,15}, {8,11}, {9,15}, {8,15}, {10,13}, {6,15}, {5,17}, {3,18}, {8,12}, {7,13}, {4,19}, {9,14}, {9,11}, {6,14}, {2,17}, {5,20}, {10,15}, {2,18}, {9,13}, {1,19}, {6,11}, {4,17}, {3,16}, {4,7}, {14,18}, {11,20}, {5,6}, {1,7}, {5,8}, {5,10}, {4,10}, {1,8}, {15,16}, {3,8}, {13,17}, {5,9}, {2,9}, {15,19}, {12,16}, {1,10}, {11,18}, {4,14}, {6,20}, {10,16}, {3,15}, {7,16}, {1,14}, {5,11}, {10,12}, {1,16} } Symmetric graph 20 of order 20 Valency 16 Diameter 2 Girth 3 Automorphism group of order 955514880 Number of arcs = 320 Number of 2-arcs = 4800 2-arc-transitive false Edge-set { {1,3}, {5,20}, {6,11}, {3,12}, {7,19}, {9,11}, {2,20}, {5,10}, {1,6}, {4,7}, {3,8}, {9,13}, {2,18}, {3,19}, {7,12}, {12,14}, {17,19}, {11,20}, {6,7}, {3,5}, {5,8}, {4,6}, {13,15}, {16,18}, {4,5}, {6,8}, {7,10}, {10,16}, {1,15}, {4,18}, {8,13}, {3,9}, {2,7}, {7,11}, {3,20}, {5,12}, {6,19}, {8,12}, {4,19}, {2,15}, {9,16}, {1,17}, {10,14}, {6,12}, {5,19}, {8,11}, {4,20}, {7,14}, {3,17}, {1,14}, {10,17}, {6,17}, {5,14}, {8,15}, {4,16}, {5,13}, {6,18}, {7,9}, {2,3}, {10,12}, {1,19}, {4,11}, {8,20}, {8,10}, {1,4}, {2,19}, {9,12}, {1,13}, {10,18}, {18,20}, {11,13}, {14,16}, {15,17}, {10,11}, {1,20}, {4,12}, {8,19}, {8,9}, {2,4}, {3,6}, {5,7}, {7,16}, {3,15}, {5,18}, {6,13}, {16,20}, {11,15}, {14,18}, {13,17}, {11,18}, {13,20}, {12,16}, {15,19}, {2,8}, {4,9}, {12,15}, {16,19}, {11,17}, {14,20}, {7,13}, {3,18}, {6,9}, {2,5}, {8,14}, {4,17}, {6,20}, {5,11}, {10,13}, {1,18}, {15,20}, {11,16}, {14,17}, {9,15}, {2,16}, {1,16}, {10,15}, {9,14}, {2,17}, {6,10}, {1,5}, {4,8}, {1,7}, {3,10}, {12,17}, {14,19}, {2,9}, {16,17}, {14,15}, {15,18}, {13,16}, {9,17}, {2,14}, {1,10}, {2,10}, {1,9}, {9,18}, {2,13}, {3,16}, {7,15}, {5,17}, {6,14}, {12,19}, {8,16}, {4,15}, {3,11}, {7,20}, {17,20}, {11,14}, {18,19}, {12,13}, {12,20}, {11,19}, {13,19}, {12,18}, {13,18}, {4,10}, {1,8}, {2,6}, {5,9}, {3,7} } Symmetric graph 21 of order 20 Valency 18 Diameter 2 Girth 3 Automorphism group of order 3715891200 Number of arcs = 360 Number of 2-arcs = 6120 2-arc-transitive false Edge-set { {1,3}, {11,17}, {7,15}, {15,20}, {10,18}, {3,10}, {2,6}, {5,10}, {2,13}, {7,19}, {3,9}, {7,11}, {3,7}, {13,18}, {16,20}, {7,14}, {3,19}, {2,18}, {12,16}, {3,6}, {6,14}, {8,11}, {4,7}, {3,15}, {6,18}, {3,11}, {6,7}, {2,19}, {9,12}, {5,9}, {1,13}, {6,11}, {18,19}, {9,16}, {1,17}, {11,13}, {7,20}, {11,20}, {4,15}, {5,18}, {3,12}, {6,8}, {10,11}, {2,7}, {13,19}, {9,20}, {11,15}, {7,18}, {3,13}, {6,20}, {14,16}, {8,16}, {4,17}, {8,14}, {4,19}, {2,17}, {12,15}, {13,15}, {18,20}, {6,19}, {9,14}, {8,9}, {1,4}, {17,20}, {10,15}, {2,15}, {12,18}, {3,5}, {6,13}, {5,15}, {10,12}, {2,8}, {14,19}, {9,19}, {11,16}, {7,17}, {4,13}, {5,20}, {3,18}, {6,16}, {12,14}, {5,8}, {6,9}, {2,11}, {7,12}, {5,13}, {13,20}, {1,9}, {1,11}, {4,9}, {1,5}, {12,20}, {8,10}, {5,11}, {6,12}, {10,16}, {2,10}, {2,12}, {5,19}, {9,13}, {14,20}, {1,8}, {4,11}, {4,8}, {4,5}, {12,17}, {8,15}, {10,13}, {7,10}, {2,3}, {2,16}, {16,19}, {9,17}, {11,14}, {10,14}, {7,16}, {3,17}, {4,18}, {5,16}, {1,6}, {4,14}, {9,15}, {1,18}, {3,20}, {6,10}, {8,12}, {5,14}, {11,19}, {7,9}, {1,20}, {1,16}, {8,13}, {4,20}, {15,18}, {16,18}, {3,16}, {6,17}, {2,14}, {12,19}, {2,5}, {12,13}, {8,17}, {15,17}, {14,17}, {15,19}, {13,17}, {14,15}, {13,16}, {16,17}, {4,12}, {8,18}, {8,19}, {10,17}, {4,10}, {11,18}, {9,18}, {1,14}, {8,20}, {1,15}, {1,7}, {1,19}, {1,12}, {2,4}, {17,19}, {7,13}, {4,16}, {5,17}, {6,15}, {14,18}, {3,8}, {4,6}, {5,12}, {10,19}, {2,9}, {9,11}, {10,20}, {2,20}, {1,10}, {5,7}, {3,14} } Symmetric graph 22 of order 20 Valency 19 Diameter 1 Girth 3 Automorphism group of order 2432902008176640000 Number of arcs = 380 Number of 2-arcs = 6840 2-arc-transitive true Edge-set { {1,2}, {9,13}, {10,13}, {7,16}, {2,15}, {15,16}, {2,3}, {6,11}, {13,18}, {10,12}, {2,18}, {11,12}, {11,13}, {1,10}, {5,12}, {8,9}, {10,16}, {2,4}, {15,19}, {3,7}, {4,10}, {5,19}, {7,8}, {5,16}, {2,8}, {9,15}, {3,13}, {3,19}, {7,18}, {7,20}, {14,15}, {3,11}, {8,13}, {10,20}, {6,18}, {1,11}, {1,6}, {8,15}, {3,20}, {3,6}, {5,18}, {1,20}, {6,14}, {11,18}, {13,20}, {10,14}, {12,15}, {11,16}, {1,5}, {4,6}, {1,4}, {6,19}, {14,18}, {12,17}, {5,11}, {1,8}, {16,20}, {2,14}, {4,15}, {4,9}, {5,9}, {9,12}, {18,20}, {12,14}, {4,11}, {1,19}, {1,9}, {3,10}, {4,18}, {13,19}, {9,17}, {5,10}, {4,8}, {4,16}, {2,19}, {3,17}, {18,19}, {7,12}, {2,5}, {8,11}, {3,9}, {8,12}, {9,20}, {6,12}, {4,17}, {17,19}, {3,5}, {8,18}, {13,14}, {11,19}, {10,17}, {12,20}, {15,20}, {15,18}, {7,19}, {7,15}, {4,19}, {14,19}, {7,17}, {5,8}, {8,20}, {6,9}, {5,13}, {7,9}, {13,15}, {11,15}, {1,3}, {8,10}, {4,20}, {6,16}, {3,15}, {3,18}, {14,20}, {11,20}, {6,13}, {11,17}, {1,16}, {6,10}, {4,5}, {6,7}, {10,18}, {5,20}, {8,14}, {7,11}, {1,15}, {19,20}, {7,14}, {4,7}, {12,19}, {8,17}, {6,17}, {1,18}, {4,14}, {14,16}, {2,17}, {5,6}, {15,17}, {3,16}, {4,12}, {6,8}, {5,17}, {1,17}, {1,7}, {6,15}, {16,18}, {2,12}, {9,11}, {1,13}, {3,14}, {1,12}, {10,11}, {8,19}, {12,16}, {2,9}, {8,16}, {3,8}, {10,15}, {3,4}, {14,17}, {9,18}, {12,13}, {1,14}, {6,20}, {5,7}, {17,20}, {9,16}, {9,10}, {4,13}, {13,17}, {3,12}, {17,18}, {2,11}, {9,14}, {13,16}, {12,18}, {2,10}, {7,10}, {2,13}, {11,14}, {9,19}, {7,13}, {5,15}, {5,14}, {2,20}, {16,17}, {16,19}, {2,7}, {2,16}, {10,19}, {2,6} } ................................................................... Symmetric connected graphs of order 21 Symmetric graph 1 of order 21 Valency 2 Diameter 10 Girth 21 Automorphism group of order 42 Number of arcs = 42 Number of 2-arcs = 42 2-arc-transitive true Edge-set { {1,5}, {2,6}, {4,7}, {3,4}, {5,8}, {9,11}, {6,9}, {7,12}, {10,15}, {8,10}, {11,13}, {14,18}, {12,14}, {15,16}, {17,21}, {13,17}, {18,19}, {2,20}, {16,20}, {3,21}, {1,19} } Symmetric graph 2 of order 21 Valency 4 Diameter 3 Girth 4 Automorphism group of order 84 Number of arcs = 84 Number of 2-arcs = 252 2-arc-transitive false Edge-set { {1,5}, {12,15}, {3,21}, {2,21}, {12,13}, {9,11}, {2,6}, {9,10}, {1,6}, {10,13}, {17,20}, {15,16}, {1,19}, {17,19}, {14,16}, {3,19}, {10,14}, {4,8}, {5,8}, {7,12}, {3,4}, {4,7}, {7,11}, {2,4}, {11,14}, {18,20}, {18,21}, {13,17}, {2,20}, {14,18}, {15,17}, {1,20}, {11,15}, {5,9}, {6,9}, {8,10}, {8,12}, {3,5}, {16,21}, {16,19}, {13,18}, {6,7} } Symmetric graph 3 of order 21 Valency 4 Diameter 3 Girth 3 Automorphism group of order 336 Number of arcs = 84 Number of 2-arcs = 252 2-arc-transitive false Edge-set { {1,5}, {4,7}, {9,18}, {8,11}, {4,17}, {10,19}, {5,10}, {12,14}, {6,15}, {8,21}, {11,17}, {1,13}, {14,21}, {7,13}, {14,18}, {15,16}, {3,16}, {3,12}, {6,20}, {11,15}, {2,9}, {1,20}, {2,4}, {16,19}, {1,10}, {18,20}, {7,12}, {3,15}, {5,8}, {9,19}, {8,17}, {12,21}, {4,13}, {9,14}, {2,19}, {6,18}, {3,7}, {5,21}, {6,11}, {13,20}, {2,17}, {10,16} } Symmetric graph 4 of order 21 Valency 6 Diameter 3 Girth 3 Automorphism group of order 126 Number of arcs = 126 Number of 2-arcs = 630 2-arc-transitive false Edge-set { {1,5}, {3,16}, {6,15}, {6,18}, {12,14}, {1,19}, {4,19}, {4,11}, {14,21}, {9,21}, {10,16}, {1,15}, {2,10}, {2,13}, {5,8}, {12,21}, {3,21}, {7,12}, {16,19}, {15,19}, {15,17}, {7,13}, {17,20}, {13,20}, {3,9}, {12,18}, {3,14}, {8,14}, {9,17}, {6,10}, {1,12}, {10,19}, {8,20}, {11,20}, {2,20}, {7,18}, {14,16}, {5,14}, {9,11}, {18,21}, {4,7}, {9,15}, {10,15}, {1,7}, {2,18}, {11,13}, {2,8}, {11,17}, {6,21}, {8,16}, {5,12}, {3,11}, {5,17}, {7,19}, {13,18}, {4,13}, {8,10}, {3,4}, {6,9}, {1,17}, {5,20}, {4,16}, {2,6} } Symmetric graph 5 of order 21 Valency 6 Diameter 3 Girth 4 Automorphism group of order 3919104 Number of arcs = 126 Number of 2-arcs = 630 2-arc-transitive false Edge-set { {1,4}, {13,17}, {15,16}, {6,8}, {5,9}, {5,7}, {4,8}, {16,20}, {18,19}, {17,21}, {18,21}, {17,20}, {16,19}, {7,11}, {8,11}, {9,12}, {7,12}, {8,10}, {9,10}, {7,10}, {9,11}, {8,12}, {2,21}, {3,20}, {2,20}, {3,19}, {1,21}, {3,21}, {1,20}, {2,19}, {1,19}, {10,14}, {10,13}, {11,15}, {11,14}, {11,13}, {12,15}, {12,14}, {10,15}, {12,13}, {2,6}, {1,6}, {2,5}, {3,4}, {2,4}, {3,6}, {3,5}, {1,5}, {14,16}, {13,18}, {13,16}, {15,18}, {14,18}, {15,17}, {14,17}, {4,7}, {6,9}, {6,7}, {5,8}, {4,9}, {16,21}, {18,20}, {17,19} } Symmetric graph 6 of order 21 Valency 8 Diameter 2 Girth 3 Automorphism group of order 336 Number of arcs = 168 Number of 2-arcs = 1176 2-arc-transitive false Edge-set { {1,5}, {3,4}, {5,9}, {6,8}, {3,18}, {9,12}, {2,16}, {7,11}, {6,21}, {12,18}, {12,13}, {4,20}, {11,17}, {10,15}, {2,21}, {3,7}, {13,21}, {12,14}, {13,17}, {1,19}, {2,8}, {15,19}, {14,16}, {5,17}, {6,10}, {14,21}, {3,17}, {13,18}, {7,14}, {17,19}, {6,16}, {4,11}, {15,20}, {1,16}, {8,13}, {18,20}, {9,19}, {2,10}, {5,7}, {6,19}, {9,14}, {17,21}, {10,18}, {7,20}, {1,11}, {8,15}, {4,8}, {5,20}, {1,12}, {4,14}, {9,10}, {2,20}, {1,7}, {7,21}, {3,19}, {5,15}, {15,16}, {11,16}, {8,11}, {2,9}, {4,12}, {5,13}, {1,13}, {8,18}, {2,4}, {4,17}, {5,10}, {3,10}, {1,6}, {3,15}, {9,16}, {16,20}, {11,15}, {6,18}, {3,14}, {9,17}, {11,21}, {8,19}, {6,14}, {12,20}, {7,18}, {12,19}, {2,13}, {10,21} } Symmetric graph 7 of order 21 Valency 8 Diameter 2 Girth 3 Automorphism group of order 336 Number of arcs = 168 Number of 2-arcs = 1176 2-arc-transitive false Edge-set { {1,8}, {4,16}, {5,11}, {8,20}, {3,11}, {9,15}, {16,19}, {2,11}, {6,15}, {15,18}, {12,16}, {1,20}, {6,11}, {4,15}, {2,15}, {7,16}, {16,21}, {8,12}, {13,20}, {4,19}, {2,5}, {7,15}, {1,15}, {8,16}, {8,17}, {10,20}, {8,21}, {3,20}, {11,13}, {14,19}, {2,17}, {3,6}, {4,9}, {15,17}, {10,16}, {5,16}, {11,20}, {11,19}, {10,19}, {2,14}, {5,19}, {2,6}, {11,14}, {1,18}, {6,7}, {8,10}, {14,20}, {3,8}, {9,20}, {1,14}, {6,13}, {4,18}, {1,9}, {4,7}, {5,21}, {7,10}, {13,19}, {2,18}, {18,19}, {2,12}, {4,13}, {5,18}, {7,17}, {5,12}, {1,17}, {3,21}, {3,9}, {10,17}, {10,14}, {6,9}, {4,21}, {1,21}, {6,12}, {9,21}, {3,12}, {9,13}, {10,13}, {14,18}, {7,12}, {3,5}, {7,13}, {18,21}, {12,17}, {14,17} } Symmetric graph 8 of order 21 Valency 10 Diameter 2 Girth 3 Automorphism group of order 5040 Number of arcs = 210 Number of 2-arcs = 1890 2-arc-transitive false Edge-set { {1,2}, {7,8}, {12,13}, {12,15}, {16,17}, {12,14}, {3,16}, {16,18}, {19,20}, {3,18}, {9,19}, {17,18}, {4,19}, {20,21}, {5,21}, {3,17}, {4,9}, {11,20}, {14,21}, {4,20}, {6,20}, {10,21}, {19,21}, {5,6}, {6,11}, {9,20}, {10,14}, {2,5}, {13,19}, {6,18}, {6,21}, {5,10}, {1,5}, {6,15}, {4,5}, {1,11}, {11,21}, {5,14}, {9,13}, {15,18}, {2,4}, {8,11}, {15,20}, {17,21}, {5,17}, {1,4}, {5,19}, {1,6}, {11,15}, {7,11}, {1,3}, {4,6}, {10,11}, {1,10}, {2,7}, {10,19}, {2,6}, {4,13}, {11,18}, {14,17}, {3,4}, {8,10}, {2,13}, {3,5}, {16,19}, {4,16}, {7,10}, {1,7}, {2,3}, {2,12}, {7,9}, {9,10}, {2,15}, {1,9}, {7,15}, {8,12}, {15,21}, {1,8}, {10,17}, {13,16}, {18,20}, {3,6}, {8,9}, {13,15}, {8,17}, {9,11}, {7,12}, {8,16}, {14,15}, {2,14}, {3,8}, {7,14}, {3,12}, {14,19}, {7,13}, {9,16}, {17,19}, {13,14}, {13,20}, {12,16}, {8,18}, {12,18}, {18,21}, {12,17}, {16,20} } Symmetric graph 9 of order 21 Valency 10 Diameter 2 Girth 3 Automorphism group of order 5040 Number of arcs = 210 Number of 2-arcs = 1890 2-arc-transitive false Edge-set { {1,12}, {7,16}, {7,18}, {12,19}, {7,17}, {4,12}, {12,20}, {16,21}, {6,12}, {10,16}, {12,21}, {5,16}, {18,19}, {6,19}, {5,12}, {1,16}, {9,18}, {15,19}, {6,16}, {4,18}, {11,19}, {17,20}, {4,21}, {5,20}, {1,21}, {11,16}, {1,18}, {7,19}, {11,17}, {4,14}, {14,20}, {3,21}, {5,18}, {1,19}, {6,17}, {4,10}, {10,20}, {2,21}, {6,10}, {5,11}, {6,7}, {10,18}, {2,19}, {1,17}, {4,7}, {7,20}, {2,20}, {6,13}, {13,21}, {3,19}, {6,9}, {4,17}, {4,11}, {1,20}, {7,21}, {10,15}, {9,21}, {5,15}, {6,8}, {5,9}, {1,15}, {2,11}, {5,7}, {9,17}, {4,15}, {8,21}, {10,12}, {5,8}, {3,20}, {1,14}, {2,10}, {9,14}, {3,15}, {6,14}, {3,11}, {1,13}, {11,14}, {3,7}, {2,8}, {11,12}, {3,10}, {8,19}, {9,12}, {15,16}, {4,8}, {11,13}, {2,9}, {8,15}, {14,18}, {3,14}, {3,9}, {5,13}, {10,13}, {2,18}, {8,13}, {2,16}, {9,15}, {8,20}, {14,16}, {2,17}, {8,14}, {3,13}, {13,17}, {15,17}, {13,18} } Symmetric graph 10 of order 21 Valency 12 Diameter 2 Girth 3 Automorphism group of order 30240 Number of arcs = 252 Number of 2-arcs = 2772 2-arc-transitive false Edge-set { {1,4}, {10,13}, {12,16}, {2,5}, {9,13}, {4,19}, {8,20}, {11,14}, {10,17}, {2,8}, {2,13}, {6,16}, {7,18}, {3,6}, {7,14}, {5,20}, {9,21}, {1,10}, {2,14}, {12,19}, {18,20}, {3,19}, {12,15}, {11,18}, {3,9}, {3,14}, {4,17}, {8,16}, {5,13}, {9,12}, {10,14}, {6,8}, {18,21}, {15,17}, {6,11}, {8,15}, {6,21}, {7,19}, {2,11}, {3,15}, {10,20}, {16,21}, {1,20}, {13,17}, {4,8}, {3,5}, {9,14}, {7,12}, {1,18}, {5,19}, {15,21}, {6,12}, {1,7}, {1,15}, {5,18}, {9,17}, {6,14}, {7,10}, {11,15}, {4,9}, {16,19}, {13,18}, {4,12}, {2,20}, {13,21}, {1,16}, {11,17}, {3,8}, {6,17}, {5,15}, {8,18}, {3,12}, {1,13}, {11,21}, {17,19}, {2,21}, {14,18}, {5,9}, {1,6}, {7,15}, {8,10}, {2,16}, {6,20}, {13,19}, {4,10}, {12,20}, {7,21}, {1,11}, {1,19}, {4,15}, {8,11}, {12,13}, {5,7}, {17,20}, {14,16}, {5,10}, {3,21}, {14,19}, {2,17}, {12,18}, {1,9}, {4,18}, {6,13}, {9,16}, {15,16}, {6,7}, {2,4}, {8,13}, {9,11}, {3,17}, {4,21}, {14,20}, {5,11}, {10,21}, {8,19}, {2,12}, {15,20}, {3,18}, {10,16}, {2,7}, {5,16}, {4,14}, {7,17}, {11,19}, {9,20}, {3,10} } Symmetric graph 11 of order 21 Valency 14 Diameter 2 Girth 3 Automorphism group of order 768144384000 Number of arcs = 294 Number of 2-arcs = 3822 2-arc-transitive false Edge-set { {1,8}, {2,17}, {6,20}, {14,16}, {13,19}, {11,19}, {10,15}, {5,14}, {7,12}, {4,11}, {5,12}, {2,11}, {4,9}, {1,20}, {5,16}, {6,18}, {3,21}, {5,21}, {3,16}, {2,19}, {7,17}, {11,17}, {10,20}, {8,20}, {12,15}, {9,18}, {9,16}, {8,15}, {14,18}, {12,16}, {13,21}, {2,13}, {1,10}, {6,10}, {6,9}, {3,8}, {3,13}, {7,14}, {2,9}, {6,8}, {1,13}, {3,14}, {7,10}, {7,16}, {4,19}, {4,17}, {1,15}, {3,19}, {7,15}, {2,15}, {4,18}, {1,18}, {7,19}, {6,15}, {4,20}, {5,18}, {1,21}, {8,18}, {14,21}, {12,21}, {13,17}, {9,17}, {11,18}, {8,21}, {8,19}, {12,17}, {12,20}, {12,18}, {11,21}, {9,19}, {10,17}, {13,20}, {9,20}, {6,12}, {5,9}, {3,9}, {4,13}, {7,13}, {5,13}, {2,12}, {2,10}, {6,11}, {6,14}, {3,10}, {6,13}, {3,12}, {5,10}, {7,11}, {4,14}, {4,10}, {3,11}, {6,19}, {3,15}, {3,20}, {7,18}, {7,21}, {4,21}, {7,20}, {4,16}, {6,16}, {1,19}, {5,19}, {5,15}, {4,15}, {3,18}, {1,16}, {2,21}, {5,17}, {1,17}, {2,18}, {12,19}, {11,15}, {9,15}, {10,18}, {13,18}, {9,21}, {10,21}, {14,17}, {14,15}, {11,20}, {11,16}, {8,16}, {8,17}, {13,15}, {14,20}, {10,16}, {13,16}, {2,8}, {7,8}, {1,12}, {4,12}, {7,9}, {1,9}, {1,14}, {5,8}, {5,11}, {2,14}, {4,8}, {1,11}, {2,16}, {6,21}, {6,17}, {3,17}, {5,20}, {2,20}, {14,19}, {10,19} } Symmetric graph 12 of order 21 Valency 18 Diameter 2 Girth 3 Automorphism group of order 1410877440 Number of arcs = 378 Number of 2-arcs = 6426 2-arc-transitive false Edge-set { {1,4}, {7,14}, {13,17}, {10,20}, {6,20}, {12,17}, {5,7}, {3,10}, {1,13}, {10,16}, {6,17}, {2,7}, {15,20}, {18,20}, {4,9}, {3,15}, {7,12}, {5,13}, {4,16}, {3,9}, {7,16}, {8,20}, {14,20}, {1,11}, {4,10}, {1,18}, {8,10}, {14,21}, {17,21}, {9,11}, {4,15}, {2,20}, {12,15}, {5,18}, {14,16}, {9,17}, {9,21}, {15,21}, {16,20}, {9,20}, {1,19}, {10,19}, {1,10}, {6,10}, {4,14}, {3,17}, {7,18}, {8,13}, {4,19}, {3,19}, {6,12}, {5,21}, {1,21}, {11,14}, {4,17}, {1,8}, {10,14}, {6,11}, {2,4}, {15,18}, {8,18}, {6,9}, {7,21}, {3,21}, {12,21}, {3,11}, {4,12}, {1,16}, {9,10}, {10,21}, {11,13}, {4,7}, {3,13}, {4,13}, {3,16}, {7,15}, {12,19}, {5,19}, {2,14}, {11,17}, {2,9}, {11,15}, {6,13}, {2,16}, {12,18}, {3,7}, {12,13}, {5,10}, {1,6}, {14,17}, {7,17}, {7,19}, {13,19}, {3,6}, {8,14}, {11,18}, {4,8}, {18,19}, {8,19}, {13,21}, {16,21}, {3,20}, {12,20}, {2,12}, {5,9}, {1,15}, {6,14}, {2,17}, {9,13}, {4,21}, {3,4}, {3,12}, {5,12}, {1,5}, {17,20}, {9,12}, {5,15}, {12,14}, {5,17}, {9,16}, {9,15}, {11,20}, {4,20}, {2,6}, {2,11}, {2,15}, {1,7}, {8,21}, {5,11}, {5,16}, {8,16}, {9,14}, {6,18}, {2,8}, {2,5}, {3,18}, {7,13}, {13,16}, {10,17}, {6,7}, {7,20}, {15,16}, {6,19}, {14,19}, {17,19}, {2,18}, {8,11}, {2,19}, {11,19}, {1,9}, {10,15}, {2,10}, {6,8}, {18,21}, {7,11}, {10,13}, {6,16}, {8,17}, {3,14}, {15,17}, {6,15}, {13,18}, {1,17}, {7,10}, {6,21}, {2,21}, {4,18}, {11,21}, {1,14}, {5,8}, {13,20}, {9,18}, {16,19}, {9,19}, {8,15}, {14,18}, {5,20}, {12,16}, {1,20}, {11,16}, {2,13}, {4,11}, {8,12}, {3,5}, {3,8}, {1,12}, {15,19}, {10,18}, {5,14} } Symmetric graph 13 of order 21 Valency 20 Diameter 1 Girth 3 Automorphism group of order 51090942171709440000 Number of arcs = 420 Number of 2-arcs = 7980 2-arc-transitive true Edge-set { {1,2}, {1,14}, {7,8}, {1,18}, {7,18}, {2,12}, {12,13}, {1,20}, {4,7}, {12,20}, {4,12}, {13,14}, {8,16}, {13,19}, {16,17}, {1,8}, {5,7}, {12,21}, {10,12}, {8,13}, {5,16}, {13,21}, {10,16}, {18,19}, {17,18}, {2,6}, {3,19}, {17,21}, {6,15}, {19,20}, {7,13}, {11,12}, {13,17}, {6,16}, {4,13}, {15,16}, {2,19}, {6,11}, {11,19}, {17,19}, {6,17}, {4,6}, {15,19}, {3,20}, {4,21}, {15,20}, {4,20}, {9,14}, {3,7}, {9,21}, {15,17}, {6,20}, {9,10}, {1,3}, {3,8}, {5,21}, {12,19}, {12,17}, {13,16}, {2,16}, {17,20}, {6,9}, {1,19}, {19,21}, {10,17}, {6,10}, {3,14}, {8,21}, {9,16}, {3,16}, {2,21}, {3,15}, {20,21}, {9,15}, {1,10}, {3,10}, {3,21}, {5,9}, {8,10}, {3,5}, {5,10}, {5,18}, {14,18}, {7,12}, {9,12}, {5,17}, {6,14}, {10,15}, {8,9}, {1,5}, {4,5}, {14,15}, {1,7}, {7,9}, {2,7}, {9,13}, {11,17}, {3,13}, {16,21}, {13,15}, {16,20}, {6,19}, {8,19}, {8,15}, {5,20}, {7,21}, {3,17}, {6,21}, {4,15}, {4,9}, {1,15}, {9,18}, {2,17}, {6,13}, {5,6}, {14,19}, {6,7}, {9,19}, {14,17}, {6,8}, {7,10}, {3,9}, {8,17}, {1,4}, {7,15}, {7,17}, {5,11}, {11,14}, {2,4}, {7,11}, {9,11}, {4,11}, {11,15}, {11,20}, {18,20}, {4,18}, {12,16}, {5,13}, {14,16}, {4,10}, {2,5}, {1,11}, {11,21}, {10,11}, {10,18}, {3,18}, {1,12}, {5,12}, {12,14}, {8,12}, {5,19}, {2,20}, {7,19}, {9,17}, {10,19}, {1,21}, {2,3}, {2,10}, {8,11}, {6,12}, {9,20}, {1,6}, {10,21}, {10,14}, {4,14}, {8,20}, {1,17}, {18,21}, {14,21}, {15,18}, {2,9}, {1,13}, {12,15}, {2,15}, {13,20}, {3,12}, {11,16}, {2,11}, {16,18}, {2,18}, {2,14}, {16,19}, {6,18}, {1,16}, {4,16}, {7,20}, {7,16}, {11,13}, {13,18}, {2,13}, {3,11}, {8,14}, {5,8}, {5,15}, {14,20}, {3,4}, {15,21}, {7,14}, {5,14}, {1,9}, {4,17}, {2,8}, {10,20}, {10,13}, {4,19}, {4,8}, {8,18}, {3,6}, {12,18}, {11,18} } ................................................................... Symmetric connected graphs of order 22 Symmetric graph 1 of order 22 Valency 2 Diameter 11 Girth 22 Automorphism group of order 44 Number of arcs = 44 Number of 2-arcs = 44 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {15,16}, {16,17}, {17,18}, {18,19}, {19,20}, {20,21}, {21,22}, {1,22} } Symmetric graph 2 of order 22 Valency 4 Diameter 5 Girth 4 Automorphism group of order 45056 Number of arcs = 88 Number of 2-arcs = 264 2-arc-transitive false Edge-set { {1,3}, {4,5}, {11,14}, {6,7}, {13,16}, {13,15}, {1,21}, {8,9}, {15,17}, {16,18}, {2,4}, {16,17}, {2,3}, {1,4}, {10,11}, {18,20}, {17,20}, {3,5}, {18,19}, {4,6}, {3,6}, {12,13}, {12,14}, {11,13}, {19,21}, {20,21}, {5,7}, {14,16}, {19,22}, {6,8}, {5,8}, {14,15}, {2,22}, {1,22}, {2,21}, {8,10}, {7,10}, {7,9}, {15,18}, {9,12}, {9,11}, {10,12}, {17,19}, {20,22} } Symmetric graph 3 of order 22 Valency 5 Diameter 3 Girth 4 Automorphism group of order 1320 Number of arcs = 110 Number of 2-arcs = 440 2-arc-transitive true Edge-set { {1,3}, {3,8}, {4,6}, {8,16}, {6,10}, {7,12}, {5,7}, {10,16}, {10,18}, {12,19}, {2,15}, {9,13}, {11,15}, {8,9}, {10,19}, {12,18}, {13,19}, {2,17}, {13,22}, {4,9}, {3,17}, {6,20}, {1,9}, {14,17}, {16,20}, {10,11}, {17,19}, {12,22}, {2,13}, {6,17}, {15,22}, {4,14}, {3,20}, {6,21}, {7,20}, {5,11}, {8,14}, {7,21}, {4,11}, {5,14}, {18,21}, {1,19}, {12,14}, {20,22}, {2,21}, {3,15}, {9,21}, {5,16}, {8,18}, {1,7}, {15,18}, {1,11}, {4,22}, {2,5}, {13,16} } Symmetric graph 4 of order 22 Valency 6 Diameter 3 Girth 4 Automorphism group of order 1320 Number of arcs = 132 Number of 2-arcs = 660 2-arc-transitive true Edge-set { {1,12}, {3,14}, {11,14}, {9,15}, {8,15}, {7,15}, {8,13}, {1,19}, {1,22}, {6,19}, {1,18}, {5,19}, {6,20}, {4,18}, {3,13}, {6,14}, {3,18}, {7,14}, {6,17}, {3,22}, {2,14}, {2,13}, {6,21}, {8,12}, {10,17}, {10,22}, {2,19}, {9,20}, {4,15}, {8,17}, {9,22}, {2,15}, {5,15}, {8,21}, {9,17}, {9,18}, {8,16}, {4,20}, {4,16}, {3,17}, {11,18}, {11,21}, {7,20}, {4,13}, {6,16}, {10,19}, {7,22}, {4,19}, {1,16}, {1,21}, {2,22}, {5,18}, {10,12}, {9,21}, {7,16}, {5,12}, {10,20}, {5,17}, {11,13}, {7,12}, {10,13}, {5,14}, {3,16}, {2,21}, {11,20}, {11,12} } Symmetric graph 5 of order 22 Valency 10 Diameter 3 Girth 4 Automorphism group of order 79833600 Number of arcs = 220 Number of 2-arcs = 1980 2-arc-transitive true Edge-set { {1,4}, {16,17}, {11,22}, {7,9}, {3,16}, {4,13}, {2,17}, {1,22}, {8,19}, {7,18}, {16,21}, {5,17}, {6,22}, {9,15}, {3,12}, {13,16}, {2,11}, {12,21}, {13,20}, {10,22}, {4,19}, {7,14}, {1,16}, {9,19}, {3,9}, {2,10}, {1,8}, {8,15}, {3,18}, {18,21}, {5,7}, {6,16}, {4,15}, {12,17}, {3,14}, {1,18}, {5,11}, {6,14}, {2,13}, {2,7}, {13,22}, {5,19}, {7,16}, {11,16}, {1,12}, {8,13}, {8,21}, {2,15}, {7,12}, {11,20}, {15,20}, {10,18}, {4,21}, {10,14}, {19,22}, {7,20}, {10,16}, {8,17}, {15,22}, {6,18}, {5,21}, {4,11}, {9,17}, {6,20}, {5,10}, {5,15}, {6,12}, {12,19}, {5,13}, {2,6}, {9,13}, {7,22}, {16,19}, {4,7}, {11,18}, {14,21}, {1,20}, {12,15}, {3,22}, {18,19}, {14,17}, {8,11}, {14,15}, {12,13}, {14,19}, {9,21}, {3,20}, {10,20}, {4,10}, {1,9}, {4,17}, {17,22}, {3,8}, {2,19}, {13,18}, {6,9}, {10,12}, {1,5}, {6,8}, {11,14}, {15,18}, {2,21}, {3,5}, {17,20}, {1,14}, {2,3}, {20,21}, {4,6}, {8,10}, {9,11} } Symmetric graph 6 of order 22 Valency 11 Diameter 2 Girth 4 Automorphism group of order 3186701844480000 Number of arcs = 242 Number of 2-arcs = 2420 2-arc-transitive true Edge-set { {1,12}, {7,14}, {1,14}, {6,12}, {6,14}, {7,16}, {1,16}, {6,16}, {11,12}, {11,14}, {11,16}, {7,18}, {1,18}, {6,18}, {11,18}, {5,12}, {5,14}, {5,16}, {5,18}, {7,20}, {1,20}, {6,20}, {11,20}, {5,20}, {10,12}, {10,14}, {10,16}, {10,18}, {10,20}, {7,22}, {1,22}, {6,22}, {11,22}, {5,22}, {10,22}, {4,12}, {4,14}, {4,16}, {4,18}, {4,20}, {4,22}, {7,13}, {1,13}, {6,13}, {11,13}, {5,13}, {10,13}, {4,13}, {9,12}, {9,14}, {9,16}, {9,18}, {9,20}, {9,22}, {9,13}, {7,15}, {1,15}, {6,15}, {11,15}, {5,15}, {10,15}, {4,15}, {9,15}, {3,12}, {3,14}, {3,16}, {3,18}, {3,20}, {3,22}, {3,13}, {3,15}, {7,17}, {1,17}, {6,17}, {11,17}, {5,17}, {10,17}, {4,17}, {9,17}, {3,17}, {8,12}, {8,14}, {8,16}, {8,18}, {8,20}, {8,22}, {8,13}, {8,15}, {8,17}, {7,19}, {1,19}, {6,19}, {11,19}, {5,19}, {10,19}, {4,19}, {9,19}, {3,19}, {8,19}, {2,12}, {2,14}, {2,16}, {2,18}, {2,20}, {2,22}, {2,13}, {2,15}, {2,17}, {2,19}, {7,21}, {1,21}, {6,21}, {11,21}, {5,21}, {10,21}, {4,21}, {9,21}, {3,21}, {8,21}, {2,21}, {7,12} } Symmetric graph 7 of order 22 Valency 20 Diameter 2 Girth 3 Automorphism group of order 81749606400 Number of arcs = 440 Number of 2-arcs = 8360 2-arc-transitive false Edge-set { {1,3}, {19,22}, {11,19}, {2,15}, {14,22}, {2,13}, {3,14}, {4,21}, {10,12}, {9,15}, {1,22}, {10,21}, {2,12}, {9,19}, {1,19}, {16,20}, {20,21}, {7,14}, {4,8}, {7,10}, {15,22}, {11,22}, {7,16}, {8,21}, {14,21}, {4,12}, {2,8}, {2,22}, {11,14}, {9,13}, {1,16}, {13,21}, {6,9}, {1,5}, {5,20}, {6,20}, {6,7}, {5,8}, {4,15}, {10,22}, {13,15}, {3,22}, {3,6}, {5,9}, {5,16}, {6,21}, {9,16}, {1,21}, {14,20}, {4,20}, {5,21}, {6,12}, {15,21}, {12,22}, {8,10}, {2,7}, {9,11}, {10,16}, {2,21}, {8,11}, {7,18}, {11,17}, {1,12}, {13,17}, {1,11}, {13,18}, {6,11}, {5,18}, {5,12}, {6,17}, {10,20}, {7,15}, {8,22}, {4,10}, {2,10}, {15,19}, {18,19}, {8,12}, {7,17}, {3,12}, {9,17}, {11,16}, {18,21}, {3,8}, {7,9}, {16,22}, {11,21}, {1,9}, {1,13}, {1,20}, {13,20}, {12,16}, {17,21}, {4,18}, {4,16}, {14,15}, {4,22}, {5,7}, {6,8}, {8,13}, {3,7}, {8,9}, {16,21}, {12,21}, {5,13}, {6,18}, {5,15}, {3,16}, {4,11}, {10,17}, {2,16}, {13,22}, {3,11}, {10,18}, {11,13}, {3,18}, {12,18}, {15,17}, {12,14}, {4,17}, {16,18}, {1,7}, {4,6}, {5,10}, {6,22}, {7,20}, {8,20}, {7,21}, {2,4}, {10,14}, {2,18}, {5,14}, {14,19}, {4,19}, {8,17}, {3,13}, {3,9}, {5,19}, {6,19}, {3,15}, {9,22}, {13,16}, {3,21}, {7,11}, {2,11}, {1,10}, {4,9}, {16,17}, {18,20}, {15,20}, {3,20}, {9,20}, {20,22}, {5,17}, {5,11}, {2,6}, {9,21}, {14,16}, {2,17}, {11,18}, {15,18}, {3,19}, {8,16}, {9,12}, {10,15}, {13,19}, {8,15}, {10,13}, {2,3}, {14,18}, {9,14}, {1,4}, {17,20}, {11,20}, {7,12}, {11,15}, {18,22}, {1,6}, {6,13}, {6,16}, {12,20}, {1,8}, {12,15}, {1,17}, {2,9}, {1,14}, {2,20}, {10,19}, {2,19}, {8,19}, {7,19}, {14,17}, {7,22}, {3,10}, {16,19}, {19,21}, {3,5}, {3,17}, {1,18}, {7,13}, {1,15}, {12,17}, {12,13}, {8,14}, {4,7}, {2,14}, {4,5}, {6,10}, {12,19}, {9,18}, {6,14}, {4,13}, {10,11}, {5,22}, {4,14}, {17,22}, {2,5}, {6,15}, {17,19}, {8,18} } Symmetric graph 8 of order 22 Valency 21 Diameter 1 Girth 3 Automorphism group of order 1124000727777607680000 Number of arcs = 462 Number of 2-arcs = 9240 2-arc-transitive true Edge-set { {1,2}, {2,17}, {5,17}, {2,9}, {12,17}, {9,10}, {10,12}, {2,5}, {17,18}, {9,19}, {2,12}, {5,22}, {1,18}, {19,22}, {2,10}, {10,17}, {6,9}, {12,21}, {5,11}, {6,18}, {2,19}, {8,10}, {10,14}, {6,17}, {5,21}, {8,11}, {6,14}, {2,22}, {1,17}, {9,22}, {1,12}, {4,5}, {16,18}, {16,19}, {10,11}, {4,6}, {16,21}, {2,11}, {1,22}, {1,4}, {3,22}, {1,20}, {4,9}, {12,16}, {10,16}, {1,14}, {4,11}, {3,4}, {16,20}, {2,8}, {14,17}, {9,17}, {5,12}, {5,8}, {14,18}, {17,19}, {10,21}, {3,10}, {6,13}, {19,21}, {11,13}, {6,19}, {14,22}, {1,11}, {4,21}, {3,16}, {13,16}, {2,14}, {11,17}, {8,17}, {5,14}, {17,21}, {3,5}, {8,20}, {8,14}, {15,17}, {3,18}, {13,19}, {13,22}, {1,19}, {3,17}, {5,20}, {14,21}, {3,11}, {20,21}, {3,8}, {13,15}, {4,17}, {3,9}, {12,20}, {5,9}, {12,18}, {10,19}, {1,10}, {4,10}, {3,6}, {9,11}, {6,12}, {16,22}, {1,9}, {20,22}, {1,8}, {4,7}, {11,16}, {7,14}, {6,16}, {14,20}, {13,20}, {8,19}, {7,13}, {2,3}, {17,20}, {9,14}, {11,12}, {4,12}, {10,20}, {9,16}, {9,12}, {1,15}, {4,22}, {1,3}, {4,20}, {12,15}, {6,20}, {8,21}, {7,11}, {7,8}, {13,14}, {5,6}, {9,20}, {8,12}, {10,15}, {10,22}, {15,16}, {4,8}, {7,12}, {9,21}, {3,12}, {8,18}, {15,19}, {5,10}, {10,18}, {2,21}, {11,22}, {1,6}, {17,22}, {1,5}, {21,22}, {8,16}, {11,18}, {4,19}, {2,16}, {8,13}, {14,19}, {5,18}, {8,15}, {18,21}, {3,7}, {11,19}, {7,20}, {4,13}, {3,15}, {7,15}, {7,18}, {2,20}, {9,15}, {12,22}, {18,20}, {15,22}, {5,13}, {18,19}, {5,19}, {2,18}, {5,15}, {3,14}, {15,21}, {12,19}, {2,15}, {4,15}, {1,16}, {18,22}, {2,4}, {8,22}, {12,13}, {1,21}, {2,7}, {5,16}, {9,18}, {19,20}, {6,15}, {6,22}, {11,14}, {8,9}, {12,14}, {1,13}, {11,21}, {2,13}, {1,7}, {6,10}, {6,11}, {15,18}, {7,22}, {7,21}, {3,13}, {14,15}, {7,10}, {10,13}, {6,21}, {2,6}, {3,20}, {13,17}, {6,8}, {4,14}, {7,19}, {16,17}, {7,17}, {11,15}, {14,16}, {11,20}, {4,18}, {3,19}, {5,7}, {7,9}, {15,20}, {4,16}, {3,21}, {6,7}, {9,13}, {13,21}, {7,16}, {13,18} } ................................................................... Symmetric connected graphs of order 23 Symmetric graph 1 of order 23 Valency 2 Diameter 11 Girth 23 Automorphism group of order 46 Number of arcs = 46 Number of 2-arcs = 46 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {15,16}, {16,17}, {17,18}, {18,19}, {19,20}, {20,21}, {21,22}, {22,23}, {1,23} } Symmetric graph 2 of order 23 Valency 22 Diameter 1 Girth 3 Automorphism group of order 25852016738884976640000 Number of arcs = 506 Number of 2-arcs = 10626 2-arc-transitive true Edge-set { {1,2}, {2,3}, {1,3}, {3,4}, {3,5}, {2,4}, {1,5}, {4,5}, {5,7}, {4,6}, {5,9}, {3,7}, {2,6}, {1,9}, {5,6}, {7,9}, {6,8}, {9,13}, {7,11}, {6,10}, {9,17}, {4,8}, {5,13}, {3,11}, {2,10}, {1,17}, {6,7}, {9,11}, {8,10}, {13,17}, {11,15}, {10,14}, {2,17}, {8,12}, {13,21}, {11,19}, {10,18}, {10,17}, {7,15}, {6,14}, {2,9}, {4,12}, {5,21}, {3,19}, {2,18}, {1,10}, {7,8}, {11,13}, {10,12}, {17,21}, {15,19}, {14,18}, {12,16}, {6,21}, {4,19}, {3,18}, {3,10}, {15,23}, {14,22}, {12,20}, {14,21}, {12,19}, {11,18}, {10,19}, {8,16}, {6,13}, {4,11}, {3,17}, {7,23}, {6,22}, {9,18}, {4,20}, {5,14}, {3,12}, {2,11}, {1,19}, {8,9}, {13,15}, {12,14}, {2,21}, {19,23}, {18,22}, {16,20}, {8,23}, {7,22}, {5,20}, {7,14}, {5,12}, {5,19}, {1,16}, {16,23}, {15,22}, {4,18}, {13,20}, {14,23}, {12,21}, {11,20}, {14,19}, {8,15}, {7,21}, {5,10}, {1,8}, {13,22}, {12,17}, {7,16}, {6,15}, {4,9}, {4,13}, {5,23}, {3,21}, {2,20}, {1,14}, {9,10}, {15,17}, {14,16}, {4,23}, {3,22}, {1,20}, {9,16}, {9,23}, {6,20}, {9,14}, {8,22}, {7,12}, {2,16}, {1,15}, {4,22}, {18,23}, {16,21}, {15,20}, {4,14}, {13,18}, {6,11}, {9,19}, {10,23}, {8,17}, {8,13}, {7,17}, {2,7}, {1,6}, {9,22}, {5,18}, {3,16}, {2,15}, {1,4}, {10,11}, {17,19}, {16,18}, {17,22}, {11,16}, {10,15}, {4,17}, {13,23}, {3,8}, {7,20}, {12,22}, {8,18}, {6,16}, {5,15}, {4,7}, {2,12}, {11,21}, {10,20}, {14,17}, {1,11}, {19,22}, {10,13}, {3,13}, {17,20}, {6,19}, {9,12}, {5,8}, {3,6}, {2,5}, {1,7}, {11,12}, {19,21}, {18,20}, {8,21}, {7,10}, {2,22}, {13,16}, {20,23}, {12,15}, {8,11}, {6,9}, {7,13}, {3,23}, {18,21}, {16,19}, {15,18}, {4,10}, {1,21}, {14,20}, {11,14}, {2,19}, {10,16}, {17,23}, {9,15}, {5,11}, {3,9}, {2,8}, {1,13}, {12,13}, {21,23}, {20,22}, {13,19}, {3,20}, {16,22}, {6,23}, {15,21}, {11,17}, {8,14}, {2,13}, {5,22}, {12,18}, {6,12}, {7,19}, {1,18}, {4,16}, {4,21}, {3,14}, {8,19}, {10,22}, {6,17}, {9,21}, {5,17}, {3,15}, {2,14}, {13,14}, {2,23}, {1,22}, {5,16}, {8,20}, {11,22}, {6,18}, {10,21}, {4,15}, {9,20}, {12,23}, {11,23}, {1,12}, {7,18}, {14,15}, {19,20}, {17,18}, {15,16}, {20,21}, {18,19}, {16,17}, {22,23}, {21,22}, {1,23} } ................................................................... Symmetric connected graphs of order 24 Symmetric graph 1 of order 24 Valency 2 Diameter 12 Girth 24 Automorphism group of order 48 Number of arcs = 48 Number of 2-arcs = 48 2-arc-transitive true Edge-set { {1,3}, {15,18}, {19,21}, {6,8}, {10,11}, {13,16}, {2,24}, {3,5}, {8,9}, {18,20}, {21,23}, {2,4}, {11,14}, {16,17}, {20,22}, {5,7}, {9,12}, {14,15}, {1,23}, {4,6}, {7,10}, {17,19}, {22,24}, {12,13} } Symmetric graph 2 of order 24 Valency 3 Diameter 4 Girth 6 Automorphism group of order 144 Number of arcs = 72 Number of 2-arcs = 144 2-arc-transitive true Edge-set { {1,10}, {6,10}, {13,22}, {10,23}, {17,22}, {3,20}, {12,22}, {3,14}, {5,16}, {8,14}, {3,12}, {5,21}, {4,18}, {7,21}, {5,12}, {14,23}, {7,18}, {15,24}, {9,17}, {18,23}, {1,21}, {9,15}, {2,19}, {2,11}, {6,19}, {1,15}, {6,17}, {7,13}, {8,19}, {4,11}, {2,13}, {9,20}, {11,24}, {16,24}, {4,20}, {8,16} } Symmetric graph 3 of order 24 Valency 4 Diameter 4 Girth 3 Automorphism group of order 96 Number of arcs = 96 Number of 2-arcs = 288 2-arc-transitive false Edge-set { {1,3}, {3,23}, {12,20}, {1,23}, {4,20}, {7,16}, {5,10}, {4,12}, {16,24}, {5,19}, {10,17}, {12,14}, {13,21}, {7,24}, {10,19}, {2,17}, {14,15}, {6,21}, {13,16}, {7,22}, {7,18}, {2,10}, {12,15}, {6,13}, {11,16}, {18,22}, {17,21}, {1,18}, {8,23}, {15,23}, {11,13}, {8,17}, {1,9}, {8,15}, {6,20}, {3,19}, {4,24}, {2,4}, {8,21}, {9,18}, {9,20}, {3,11}, {2,24}, {5,22}, {11,19}, {6,9}, {5,14}, {14,22} } Symmetric graph 4 of order 24 Valency 4 Diameter 3 Girth 5 Automorphism group of order 96 Number of arcs = 96 Number of 2-arcs = 288 2-arc-transitive false Edge-set { {1,4}, {3,24}, {12,19}, {2,23}, {3,20}, {7,15}, {6,10}, {4,11}, {16,23}, {5,20}, {10,18}, {12,13}, {13,22}, {8,24}, {9,19}, {1,17}, {14,16}, {5,21}, {13,15}, {7,21}, {8,18}, {2,9}, {11,15}, {6,14}, {12,16}, {17,22}, {18,21}, {2,18}, {7,23}, {15,24}, {11,14}, {7,17}, {1,10}, {8,16}, {6,19}, {4,19}, {4,23}, {2,3}, {8,22}, {9,17}, {10,20}, {3,12}, {1,24}, {6,22}, {11,20}, {5,9}, {5,13}, {14,21} } Symmetric graph 5 of order 24 Valency 4 Diameter 4 Girth 4 Automorphism group of order 96 Number of arcs = 96 Number of 2-arcs = 288 2-arc-transitive false Edge-set { {1,3}, {4,17}, {2,24}, {1,15}, {8,18}, {22,23}, {16,17}, {14,24}, {6,16}, {7,22}, {19,21}, {13,15}, {5,8}, {11,22}, {4,13}, {5,19}, {12,21}, {18,20}, {12,14}, {3,6}, {20,22}, {10,19}, {1,12}, {3,18}, {9,20}, {2,11}, {9,11}, {2,4}, {17,19}, {10,12}, {9,24}, {2,16}, {7,17}, {10,23}, {7,10}, {1,23}, {15,18}, {8,9}, {13,23}, {5,15}, {8,21}, {21,24}, {14,16}, {6,7}, {3,14}, {6,20}, {11,13}, {4,5} } Symmetric graph 6 of order 24 Valency 4 Diameter 4 Girth 4 Automorphism group of order 96 Number of arcs = 96 Number of 2-arcs = 288 2-arc-transitive false Edge-set { {1,3}, {12,22}, {14,23}, {13,15}, {15,18}, {2,24}, {2,4}, {9,23}, {1,11}, {9,19}, {11,21}, {3,13}, {13,24}, {4,5}, {12,14}, {14,16}, {5,8}, {16,17}, {22,23}, {1,23}, {7,21}, {10,24}, {2,15}, {2,12}, {7,18}, {10,20}, {4,18}, {4,14}, {17,19}, {3,6}, {9,11}, {11,13}, {19,21}, {6,7}, {21,24}, {5,20}, {8,22}, {5,16}, {1,16}, {8,17}, {3,17}, {7,10}, {18,20}, {10,12}, {20,22}, {6,19}, {6,15}, {8,9} } Symmetric graph 7 of order 24 Valency 4 Diameter 4 Girth 4 Automorphism group of order 768 Number of arcs = 96 Number of 2-arcs = 288 2-arc-transitive false Edge-set { {1,3}, {6,8}, {17,24}, {12,14}, {8,12}, {2,10}, {4,22}, {19,23}, {1,9}, {14,23}, {9,12}, {5,16}, {7,18}, {13,18}, {3,16}, {6,15}, {20,24}, {1,19}, {15,23}, {9,20}, {11,21}, {5,7}, {9,13}, {2,21}, {8,21}, {5,17}, {12,22}, {2,4}, {4,15}, {3,6}, {16,24}, {1,22}, {15,20}, {10,14}, {11,13}, {7,11}, {2,20}, {14,17}, {10,11}, {7,22}, {18,23}, {6,18}, {8,17}, {4,5}, {13,24}, {16,19}, {10,19}, {3,21} } Symmetric graph 8 of order 24 Valency 4 Diameter 6 Girth 4 Automorphism group of order 98304 Number of arcs = 96 Number of 2-arcs = 288 2-arc-transitive false Edge-set { {1,13}, {3,14}, {4,14}, {10,20}, {4,16}, {3,16}, {9,21}, {4,15}, {3,15}, {9,22}, {10,21}, {6,15}, {5,15}, {11,22}, {6,16}, {5,16}, {11,21}, {12,22}, {12,21}, {5,17}, {6,17}, {12,24}, {5,18}, {6,18}, {12,23}, {11,24}, {11,23}, {8,18}, {7,18}, {1,23}, {8,17}, {7,17}, {1,24}, {2,23}, {2,24}, {7,19}, {8,19}, {2,14}, {7,20}, {8,20}, {2,13}, {1,14}, {9,20}, {4,13}, {10,19}, {9,19}, {3,13}, {10,22} } Symmetric graph 9 of order 24 Valency 5 Diameter 4 Girth 4 Automorphism group of order 480 Number of arcs = 120 Number of 2-arcs = 480 2-arc-transitive true Edge-set { {1,3}, {1,17}, {1,11}, {3,15}, {1,7}, {3,19}, {9,17}, {1,5}, {3,13}, {16,17}, {11,14}, {5,15}, {3,9}, {17,21}, {10,11}, {15,18}, {7,22}, {8,19}, {14,17}, {11,19}, {15,23}, {7,13}, {6,19}, {9,12}, {5,20}, {13,24}, {6,16}, {11,22}, {8,15}, {7,16}, {9,23}, {5,21}, {4,16}, {8,14}, {21,24}, {4,10}, {10,18}, {7,20}, {19,24}, {6,9}, {5,10}, {13,18}, {14,23}, {2,18}, {6,22}, {22,23}, {2,6}, {12,13}, {16,24}, {4,14}, {12,21}, {8,21}, {2,12}, {4,20}, {10,24}, {20,23}, {2,4}, {18,22}, {2,8}, {12,20} } Symmetric graph 10 of order 24 Valency 6 Diameter 3 Girth 3 Automorphism group of order 144 Number of arcs = 144 Number of 2-arcs = 720 2-arc-transitive false Edge-set { {1,3}, {9,13}, {11,16}, {20,21}, {9,24}, {15,17}, {5,19}, {2,4}, {4,17}, {21,23}, {13,24}, {5,16}, {6,8}, {1,12}, {10,14}, {12,15}, {5,10}, {8,12}, {4,24}, {14,17}, {20,23}, {1,5}, {7,11}, {2,21}, {13,18}, {16,20}, {19,22}, {10,23}, {16,18}, {6,20}, {12,22}, {1,23}, {7,18}, {12,13}, {8,10}, {2,24}, {4,14}, {1,16}, {8,17}, {7,9}, {2,15}, {4,5}, {3,18}, {22,24}, {14,23}, {6,15}, {5,7}, {2,11}, {18,20}, {14,16}, {7,22}, {9,20}, {13,15}, {10,19}, {10,12}, {8,21}, {6,9}, {3,23}, {19,24}, {2,6}, {1,22}, {15,19}, {4,7}, {3,8}, {18,22}, {17,21}, {11,21}, {11,14}, {3,13}, {3,6}, {17,19}, {9,11} } Symmetric graph 11 of order 24 Valency 6 Diameter 3 Girth 4 Automorphism group of order 288 Number of arcs = 144 Number of 2-arcs = 720 2-arc-transitive false Edge-set { {1,4}, {7,11}, {12,14}, {16,18}, {21,24}, {6,15}, {18,22}, {3,7}, {9,13}, {1,15}, {2,22}, {8,10}, {4,14}, {2,3}, {8,18}, {13,24}, {5,19}, {17,20}, {2,11}, {8,12}, {19,23}, {6,7}, {14,18}, {11,13}, {4,17}, {3,23}, {5,9}, {15,17}, {4,6}, {12,16}, {11,21}, {22,23}, {10,24}, {5,16}, {3,18}, {17,21}, {13,16}, {19,21}, {9,20}, {4,8}, {7,22}, {10,14}, {1,21}, {2,16}, {15,19}, {7,9}, {3,13}, {1,5}, {7,17}, {6,20}, {14,23}, {2,24}, {18,19}, {1,12}, {5,8}, {20,24}, {13,17}, {9,12}, {4,24}, {6,10}, {11,15}, {3,5}, {12,22}, {9,23}, {20,22}, {14,15}, {10,19}, {8,21}, {16,20}, {2,6}, {1,23}, {10,11} } Symmetric graph 12 of order 24 Valency 6 Diameter 3 Girth 4 Automorphism group of order 1152 Number of arcs = 144 Number of 2-arcs = 720 2-arc-transitive false Edge-set { {1,10}, {3,19}, {1,21}, {2,17}, {5,20}, {3,16}, {4,21}, {19,23}, {18,22}, {6,12}, {2,12}, {20,22}, {16,24}, {4,11}, {8,17}, {5,15}, {7,11}, {14,24}, {21,23}, {3,10}, {7,18}, {6,14}, {9,12}, {13,22}, {20,24}, {2,11}, {6,10}, {18,23}, {15,22}, {8,12}, {9,14}, {7,13}, {8,16}, {4,15}, {2,19}, {1,20}, {5,11}, {17,24}, {14,23}, {7,10}, {9,18}, {6,13}, {8,11}, {15,24}, {7,15}, {8,14}, {6,21}, {3,18}, {4,14}, {7,16}, {5,13}, {9,17}, {1,17}, {5,19}, {9,10}, {13,23}, {6,20}, {2,18}, {9,15}, {8,13}, {16,23}, {4,10}, {5,12}, {17,22}, {4,19}, {1,16}, {1,11}, {19,24}, {21,22}, {3,12}, {3,20}, {2,21} } Symmetric graph 13 of order 24 Valency 6 Diameter 3 Girth 4 Automorphism group of order 1152 Number of arcs = 144 Number of 2-arcs = 720 2-arc-transitive false Edge-set { {1,6}, {10,21}, {3,12}, {2,8}, {8,13}, {4,12}, {9,16}, {9,23}, {2,10}, {19,23}, {2,17}, {4,11}, {11,16}, {1,18}, {15,18}, {5,15}, {2,9}, {10,13}, {6,16}, {5,24}, {9,14}, {3,11}, {11,14}, {3,18}, {14,18}, {12,23}, {13,17}, {20,23}, {17,22}, {1,20}, {1,9}, {10,15}, {2,19}, {18,21}, {5,22}, {1,7}, {15,19}, {3,20}, {14,19}, {12,13}, {13,20}, {4,6}, {5,16}, {17,21}, {6,15}, {7,14}, {6,21}, {12,22}, {1,10}, {12,15}, {10,24}, {8,23}, {7,22}, {16,17}, {20,24}, {9,22}, {16,20}, {19,24}, {4,19}, {11,21}, {18,22}, {8,14}, {8,21}, {3,8}, {4,7}, {4,17}, {2,5}, {7,13}, {6,23}, {7,24}, {11,24}, {3,5} } Symmetric graph 14 of order 24 Valency 6 Diameter 4 Girth 4 Automorphism group of order 26873856 Number of arcs = 144 Number of 2-arcs = 720 2-arc-transitive false Edge-set { {1,3}, {10,15}, {3,17}, {22,24}, {1,15}, {7,10}, {3,10}, {6,20}, {6,24}, {15,22}, {15,17}, {14,24}, {1,7}, {10,24}, {2,4}, {14,20}, {4,6}, {20,22}, {6,15}, {7,22}, {6,11}, {14,15}, {7,17}, {1,24}, {9,16}, {4,18}, {2,11}, {4,9}, {4,14}, {2,20}, {4,22}, {6,7}, {11,14}, {11,22}, {7,14}, {17,24}, {21,23}, {2,16}, {8,9}, {16,18}, {11,18}, {9,23}, {9,11}, {18,20}, {9,20}, {5,19}, {5,23}, {16,21}, {13,23}, {2,8}, {8,21}, {8,18}, {2,23}, {18,23}, {13,19}, {3,5}, {19,21}, {5,16}, {5,12}, {13,16}, {5,8}, {8,13}, {1,12}, {3,13}, {1,19}, {3,21}, {12,13}, {12,21}, {12,17}, {10,12}, {17,19}, {10,19} } Symmetric graph 15 of order 24 Valency 7 Diameter 3 Girth 3 Automorphism group of order 336 Number of arcs = 168 Number of 2-arcs = 1008 2-arc-transitive false Edge-set { {1,4}, {7,17}, {4,8}, {3,12}, {10,23}, {10,17}, {4,24}, {9,13}, {7,15}, {6,14}, {13,20}, {3,14}, {10,13}, {4,17}, {4,21}, {11,22}, {1,22}, {12,24}, {3,23}, {16,23}, {2,6}, {20,22}, {1,16}, {9,23}, {2,7}, {14,22}, {1,13}, {3,17}, {4,10}, {17,21}, {5,15}, {14,19}, {5,7}, {8,19}, {4,13}, {15,21}, {6,9}, {7,20}, {12,20}, {8,16}, {5,20}, {16,19}, {8,12}, {6,11}, {5,23}, {2,19}, {7,22}, {1,8}, {3,9}, {7,10}, {14,17}, {3,21}, {18,24}, {3,5}, {19,23}, {2,18}, {12,18}, {10,19}, {17,22}, {21,24}, {11,16}, {6,22}, {15,16}, {2,10}, {18,20}, {5,16}, {15,24}, {6,18}, {9,18}, {5,12}, {8,24}, {9,11}, {12,14}, {13,23}, {9,21}, {11,21}, {6,19}, {11,15}, {13,18}, {2,15}, {2,24}, {8,14}, {1,20}, {1,11} } Symmetric graph 16 of order 24 Valency 8 Diameter 3 Girth 3 Automorphism group of order 384 Number of arcs = 192 Number of 2-arcs = 1344 2-arc-transitive false Edge-set { {1,7}, {4,10}, {8,22}, {2,7}, {11,19}, {9,18}, {2,21}, {3,10}, {7,22}, {11,15}, {15,23}, {8,20}, {5,20}, {3,17}, {12,19}, {10,18}, {2,22}, {11,21}, {4,15}, {6,21}, {9,16}, {21,24}, {16,23}, {14,24}, {1,19}, {6,12}, {12,15}, {7,20}, {5,19}, {3,18}, {11,17}, {1,15}, {4,11}, {17,24}, {1,13}, {3,20}, {5,17}, {1,9}, {6,22}, {5,14}, {8,23}, {12,24}, {13,16}, {12,21}, {4,16}, {10,16}, {22,24}, {14,23}, {1,20}, {5,12}, {6,15}, {4,21}, {4,8}, {2,11}, {6,9}, {4,13}, {8,17}, {1,16}, {19,23}, {6,14}, {18,24}, {2,13}, {14,18}, {10,21}, {13,22}, {12,17}, {3,11}, {3,19}, {5,18}, {2,9}, {8,24}, {12,23}, {14,16}, {2,17}, {1,11}, {7,15}, {13,20}, {9,19}, {4,22}, {3,8}, {10,23}, {13,18}, {5,9}, {3,13}, {7,17}, {14,20}, {6,16}, {20,23}, {9,21}, {14,22}, {6,7}, {8,15}, {2,18}, {10,19}, {10,24}, {5,7} } Symmetric graph 17 of order 24 Valency 8 Diameter 3 Girth 3 Automorphism group of order 1152 Number of arcs = 192 Number of 2-arcs = 1344 2-arc-transitive false Edge-set { {1,3}, {2,11}, {6,15}, {12,15}, {7,16}, {4,20}, {11,13}, {16,20}, {8,11}, {19,24}, {12,21}, {1,5}, {4,5}, {15,18}, {7,10}, {5,19}, {4,12}, {15,23}, {7,22}, {6,21}, {13,16}, {8,23}, {3,11}, {14,15}, {5,14}, {9,20}, {11,19}, {7,24}, {17,21}, {3,6}, {3,14}, {1,16}, {5,8}, {20,22}, {14,24}, {21,24}, {4,13}, {13,23}, {18,19}, {10,12}, {22,23}, {2,22}, {2,15}, {6,7}, {17,20}, {9,11}, {3,17}, {9,14}, {4,18}, {3,7}, {1,21}, {10,13}, {20,23}, {2,4}, {6,13}, {2,17}, {6,9}, {3,23}, {14,22}, {4,24}, {1,9}, {13,21}, {1,23}, {1,18}, {5,10}, {18,22}, {2,10}, {3,19}, {8,17}, {2,24}, {12,14}, {16,24}, {12,20}, {11,16}, {8,15}, {7,18}, {6,20}, {9,18}, {10,17}, {5,22}, {1,12}, {5,16}, {4,8}, {13,18}, {2,6}, {14,17}, {9,24}, {10,23}, {11,22}, {15,19}, {7,12}, {16,17}, {8,9}, {19,21}, {10,19}, {8,21} } Symmetric graph 18 of order 24 Valency 8 Diameter 3 Girth 3 Automorphism group of order 1152 Number of arcs = 192 Number of 2-arcs = 1344 2-arc-transitive false Edge-set { {1,4}, {1,11}, {5,15}, {11,15}, {7,15}, {3,20}, {11,14}, {15,20}, {7,11}, {20,24}, {11,21}, {2,5}, {4,6}, {15,17}, {7,9}, {5,20}, {4,11}, {15,24}, {7,21}, {5,21}, {13,15}, {7,23}, {3,12}, {14,16}, {5,13}, {10,20}, {11,20}, {8,24}, {18,21}, {3,5}, {4,14}, {1,15}, {5,7}, {20,21}, {13,24}, {21,23}, {3,13}, {14,23}, {18,20}, {10,11}, {22,24}, {2,21}, {2,16}, {6,8}, {17,19}, {9,12}, {3,18}, {10,14}, {4,17}, {4,7}, {1,22}, {9,13}, {19,23}, {2,3}, {6,14}, {1,17}, {5,9}, {3,24}, {14,21}, {4,23}, {1,10}, {13,22}, {2,23}, {2,18}, {6,10}, {17,22}, {2,9}, {4,19}, {7,17}, {1,24}, {12,13}, {16,23}, {12,19}, {12,16}, {8,16}, {8,18}, {6,19}, {9,17}, {10,18}, {6,22}, {2,12}, {6,16}, {3,8}, {14,18}, {1,6}, {13,17}, {9,23}, {10,24}, {12,22}, {16,19}, {8,12}, {16,18}, {8,10}, {19,22}, {9,19}, {8,22} } Symmetric graph 19 of order 24 Valency 8 Diameter 3 Girth 3 Automorphism group of order 196608 Number of arcs = 192 Number of 2-arcs = 1344 2-arc-transitive false Edge-set { {1,9}, {15,18}, {8,17}, {2,24}, {4,14}, {1,12}, {13,20}, {5,16}, {11,18}, {14,19}, {2,21}, {15,21}, {5,17}, {7,20}, {10,23}, {3,23}, {2,22}, {6,14}, {8,19}, {2,10}, {4,16}, {4,24}, {4,15}, {1,10}, {13,23}, {7,11}, {9,19}, {6,17}, {7,12}, {6,13}, {12,22}, {3,16}, {16,18}, {8,12}, {10,20}, {16,17}, {7,18}, {14,23}, {3,21}, {5,14}, {11,21}, {14,24}, {4,21}, {15,17}, {7,17}, {6,20}, {11,22}, {6,19}, {8,18}, {8,10}, {13,24}, {5,19}, {9,20}, {1,24}, {3,22}, {2,23}, {3,14}, {12,21}, {5,20}, {7,9}, {1,23}, {3,13}, {2,11}, {2,12}, {4,13}, {15,22}, {10,19}, {4,22}, {6,15}, {1,11}, {13,19}, {9,24}, {6,16}, {8,9}, {10,24}, {14,20}, {12,17}, {5,15}, {11,17}, {16,22}, {12,18}, {7,10}, {9,23}, {1,22}, {6,18}, {16,21}, {5,18}, {1,21}, {3,24}, {8,20}, {8,11}, {7,19}, {2,9}, {5,13}, {4,23}, {3,15} } Symmetric graph 20 of order 24 Valency 8 Diameter 3 Girth 4 Automorphism group of order 2293235712 Number of arcs = 192 Number of 2-arcs = 1344 2-arc-transitive false Edge-set { {1,13}, {6,22}, {1,24}, {10,16}, {6,24}, {12,24}, {9,20}, {4,20}, {12,16}, {7,24}, {12,21}, {8,19}, {4,16}, {8,14}, {7,20}, {4,21}, {12,17}, {7,14}, {9,21}, {11,15}, {7,18}, {4,14}, {11,21}, {2,18}, {8,17}, {9,14}, {5,21}, {2,17}, {10,14}, {9,19}, {3,22}, {6,17}, {2,14}, {9,22}, {5,17}, {6,23}, {11,18}, {5,18}, {10,21}, {2,19}, {9,15}, {5,23}, {2,20}, {10,15}, {7,19}, {3,13}, {10,13}, {1,18}, {5,16}, {2,23}, {10,19}, {5,15}, {1,23}, {11,16}, {6,15}, {7,23}, {3,19}, {8,23}, {3,20}, {12,15}, {7,17}, {1,20}, {4,15}, {11,23}, {3,15}, {11,24}, {8,20}, {4,22}, {1,19}, {3,16}, {12,23}, {11,17}, {7,13}, {8,13}, {3,21}, {12,18}, {6,16}, {8,24}, {4,19}, {3,14}, {11,22}, {12,22}, {8,18}, {4,13}, {5,22}, {1,17}, {9,13}, {6,21}, {2,13}, {10,22}, {6,18}, {1,14}, {5,24}, {9,16}, {10,20}, {2,24} } Symmetric graph 21 of order 24 Valency 9 Diameter 3 Girth 4 Automorphism group of order 80621568 Number of arcs = 216 Number of 2-arcs = 1728 2-arc-transitive false Edge-set { {1,13}, {9,16}, {4,19}, {5,19}, {11,16}, {3,13}, {3,22}, {3,23}, {10,19}, {11,13}, {8,16}, {4,21}, {8,23}, {9,21}, {8,24}, {7,21}, {12,13}, {3,15}, {10,16}, {4,13}, {11,18}, {2,22}, {4,24}, {7,18}, {5,15}, {2,16}, {4,22}, {8,18}, {6,15}, {2,17}, {4,14}, {6,21}, {12,19}, {11,15}, {3,16}, {10,21}, {10,13}, {7,23}, {9,20}, {8,22}, {10,17}, {1,18}, {6,23}, {7,19}, {11,20}, {9,22}, {10,18}, {2,18}, {6,24}, {7,20}, {12,20}, {3,17}, {5,22}, {2,15}, {2,24}, {3,14}, {6,13}, {8,19}, {11,21}, {12,15}, {12,16}, {4,15}, {7,17}, {5,14}, {1,16}, {4,23}, {9,18}, {7,24}, {10,14}, {5,23}, {12,21}, {10,15}, {10,20}, {6,14}, {1,17}, {11,14}, {1,14}, {8,20}, {1,23}, {9,23}, {6,20}, {7,22}, {8,17}, {5,21}, {3,18}, {2,13}, {11,19}, {6,22}, {12,17}, {9,19}, {3,24}, {1,24}, {2,14}, {12,18}, {12,14}, {1,15}, {5,24}, {5,13}, {9,17}, {9,24}, {7,16}, {4,20}, {2,23}, {8,21}, {5,20}, {11,17}, {6,19}, {1,22} } Symmetric graph 22 of order 24 Valency 10 Diameter 3 Girth 3 Automorphism group of order 491520 Number of arcs = 240 Number of 2-arcs = 2160 2-arc-transitive false Edge-set { {1,3}, {4,20}, {8,23}, {8,19}, {18,24}, {5,14}, {9,21}, {7,14}, {17,21}, {6,17}, {3,10}, {1,22}, {1,13}, {9,12}, {15,19}, {13,22}, {9,18}, {4,15}, {18,21}, {2,4}, {11,20}, {20,23}, {4,10}, {8,16}, {8,14}, {12,23}, {11,19}, {7,16}, {2,10}, {14,16}, {12,17}, {3,19}, {16,19}, {6,24}, {9,17}, {3,15}, {7,24}, {8,24}, {12,18}, {5,8}, {20,24}, {14,15}, {5,21}, {1,14}, {13,21}, {5,23}, {9,11}, {13,15}, {5,22}, {3,11}, {7,20}, {1,15}, {5,13}, {18,23}, {4,11}, {17,23}, {7,15}, {5,17}, {6,21}, {4,19}, {16,20}, {6,23}, {6,13}, {10,22}, {6,14}, {10,21}, {14,22}, {1,21}, {6,8}, {10,18}, {1,16}, {9,22}, {1,4}, {8,13}, {2,9}, {1,9}, {12,24}, {12,19}, {2,16}, {18,22}, {4,16}, {2,22}, {3,9}, {19,24}, {5,18}, {4,9}, {13,16}, {6,22}, {2,15}, {7,19}, {17,24}, {8,15}, {2,21}, {2,14}, {10,11}, {2,13}, {15,20}, {1,10}, {14,21}, {11,17}, {3,20}, {10,12}, {3,12}, {4,12}, {7,23}, {5,7}, {10,17}, {3,16}, {5,24}, {12,20}, {19,23}, {6,7}, {17,22}, {7,13}, {6,18}, {11,24}, {2,3}, {8,20}, {11,23}, {11,18} } Symmetric graph 23 of order 24 Valency 10 Diameter 3 Girth 4 Automorphism group of order 5898240 Number of arcs = 240 Number of 2-arcs = 2160 2-arc-transitive false Edge-set { {1,3}, {8,9}, {10,23}, {4,18}, {2,20}, {3,14}, {10,15}, {17,24}, {6,7}, {9,11}, {6,23}, {1,16}, {13,16}, {17,19}, {14,19}, {4,22}, {2,12}, {2,8}, {5,15}, {5,16}, {7,18}, {5,11}, {21,24}, {7,21}, {9,20}, {1,20}, {13,15}, {15,17}, {20,22}, {12,13}, {13,24}, {19,22}, {4,6}, {6,8}, {8,10}, {1,12}, {16,18}, {8,21}, {12,21}, {4,5}, {5,23}, {10,19}, {14,24}, {18,19}, {14,20}, {3,18}, {10,11}, {2,15}, {18,24}, {11,22}, {10,20}, {3,13}, {3,5}, {1,7}, {11,13}, {7,17}, {6,11}, {9,15}, {17,23}, {3,22}, {9,16}, {4,17}, {22,23}, {3,6}, {1,8}, {9,12}, {13,23}, {8,17}, {12,22}, {5,12}, {16,17}, {12,14}, {1,4}, {2,16}, {14,16}, {9,23}, {21,23}, {2,4}, {10,16}, {14,23}, {3,21}, {9,19}, {8,18}, {4,21}, {2,11}, {18,20}, {11,21}, {20,21}, {15,18}, {10,24}, {2,7}, {6,15}, {4,14}, {2,3}, {7,10}, {9,24}, {1,15}, {11,14}, {17,20}, {22,24}, {7,22}, {6,24}, {8,22}, {1,19}, {7,9}, {3,17}, {4,13}, {6,12}, {6,16}, {19,21}, {13,19}, {18,23}, {5,8}, {2,19}, {10,12}, {5,24}, {14,15}, {5,7}, {13,20}, {1,11} } Symmetric graph 24 of order 24 Valency 11 Diameter 3 Girth 4 Automorphism group of order 958003200 Number of arcs = 264 Number of 2-arcs = 2640 2-arc-transitive true Edge-set { {1,4}, {4,17}, {12,14}, {12,17}, {6,14}, {13,24}, {2,24}, {12,24}, {6,24}, {13,16}, {2,16}, {7,14}, {1,9}, {3,7}, {9,11}, {7,24}, {9,24}, {7,16}, {9,16}, {9,14}, {3,9}, {4,11}, {13,22}, {2,17}, {12,19}, {18,22}, {13,17}, {1,23}, {19,23}, {7,22}, {9,17}, {1,7}, {9,19}, {9,22}, {4,19}, {1,13}, {2,19}, {1,18}, {13,19}, {17,23}, {14,23}, {14,20}, {1,21}, {3,12}, {6,11}, {11,20}, {5,21}, {1,6}, {4,8}, {10,12}, {6,8}, {7,10}, {20,22}, {17,21}, {1,12}, {6,19}, {4,22}, {7,19}, {1,20}, {19,21}, {6,17}, {4,14}, {3,6}, {7,11}, {5,12}, {8,12}, {6,10}, {8,13}, {2,10}, {5,13}, {2,8}, {12,22}, {18,24}, {16,23}, {5,23}, {8,23}, {15,19}, {15,22}, {4,16}, {12,16}, {14,18}, {20,24}, {16,21}, {16,18}, {2,22}, {17,20}, {5,20}, {8,21}, {6,22}, {4,24}, {6,16}, {14,21}, {7,17}, {4,5}, {2,14}, {22,23}, {15,24}, {21,24}, {16,20}, {2,3}, {14,15}, {1,15}, {3,21}, {11,18}, {5,9}, {8,9}, {4,10}, {8,15}, {10,15}, {10,18}, {10,20}, {11,13}, {2,5}, {5,7}, {3,20}, {11,21}, {5,15}, {15,17}, {3,13}, {2,11}, {8,20}, {10,21}, {3,18}, {10,13}, {18,19}, {11,23}, {3,15}, {11,15}, {5,18}, {3,23}, {8,18}, {10,23} } Symmetric graph 25 of order 24 Valency 12 Diameter 2 Girth 3 Automorphism group of order 589824 Number of arcs = 288 Number of 2-arcs = 3168 2-arc-transitive false Edge-set { {1,9}, {14,18}, {2,18}, {3,19}, {7,10}, {3,13}, {10,17}, {12,22}, {16,17}, {1,24}, {9,20}, {8,22}, {4,17}, {5,21}, {6,15}, {4,23}, {4,9}, {8,14}, {2,11}, {5,15}, {15,23}, {4,10}, {9,21}, {6,11}, {16,20}, {12,24}, {13,21}, {10,18}, {2,21}, {15,19}, {7,23}, {13,22}, {5,17}, {11,24}, {3,20}, {7,24}, {1,21}, {6,18}, {2,16}, {5,19}, {2,23}, {4,11}, {8,21}, {6,14}, {6,20}, {8,16}, {3,17}, {1,10}, {6,13}, {3,12}, {7,16}, {13,24}, {5,20}, {8,15}, {5,14}, {2,9}, {11,22}, {14,24}, {16,18}, {10,19}, {13,23}, {1,11}, {12,20}, {7,13}, {13,17}, {10,22}, {16,23}, {12,19}, {7,19}, {2,12}, {11,19}, {9,22}, {14,17}, {1,18}, {8,19}, {6,22}, {4,24}, {8,20}, {11,20}, {15,24}, {3,23}, {7,20}, {13,18}, {2,17}, {5,22}, {7,14}, {1,17}, {1,12}, {8,13}, {14,22}, {5,18}, {8,24}, {4,20}, {8,9}, {1,15}, {4,13}, {6,12}, {1,16}, {6,17}, {1,22}, {5,12}, {2,15}, {4,19}, {7,9}, {3,14}, {12,23}, {8,10}, {14,21}, {11,23}, {2,22}, {5,11}, {9,17}, {15,20}, {16,19}, {4,14}, {9,18}, {8,23}, {7,15}, {3,11}, {10,20}, {14,23}, {2,10}, {11,21}, {15,18}, {3,18}, {12,21}, {6,19}, {4,18}, {4,12}, {9,19}, {2,24}, {7,22}, {7,21}, {15,17}, {1,23}, {5,13}, {16,24}, {3,24}, {5,16}, {3,10}, {3,9}, {6,21}, {6,16}, {10,21} } Symmetric graph 26 of order 24 Valency 12 Diameter 2 Girth 4 Automorphism group of order 458885065605120000 Number of arcs = 288 Number of 2-arcs = 3168 2-arc-transitive true Edge-set { {1,13}, {11,16}, {8,17}, {2,14}, {6,24}, {10,19}, {11,20}, {12,15}, {7,18}, {4,21}, {2,21}, {9,14}, {2,17}, {10,24}, {5,23}, {9,20}, {12,19}, {4,15}, {12,23}, {4,18}, {8,15}, {7,13}, {11,18}, {7,21}, {3,22}, {1,22}, {10,13}, {1,18}, {9,23}, {5,13}, {5,15}, {1,23}, {5,20}, {9,16}, {8,19}, {2,20}, {12,24}, {4,19}, {3,16}, {11,24}, {3,17}, {7,16}, {8,14}, {12,17}, {8,22}, {3,13}, {5,22}, {11,22}, {1,17}, {10,22}, {6,13}, {10,18}, {1,21}, {2,23}, {5,18}, {9,15}, {6,14}, {6,16}, {2,24}, {6,19}, {10,15}, {7,20}, {1,19}, {11,23}, {3,20}, {8,16}, {3,24}, {11,19}, {11,17}, {7,24}, {3,14}, {4,16}, {8,21}, {12,14}, {4,17}, {12,22}, {8,13}, {4,14}, {6,21}, {12,21}, {2,18}, {9,21}, {5,14}, {9,17}, {2,22}, {1,24}, {6,17}, {10,16}, {10,14}, {6,20}, {2,16}, {9,24}, {2,19}, {6,15}, {10,23}, {4,20}, {1,15}, {7,23}, {5,19}, {11,15}, {3,23}, {8,20}, {7,15}, {4,23}, {12,20}, {12,18}, {8,23}, {4,13}, {3,15}, {7,22}, {11,13}, {3,18}, {11,21}, {7,14}, {10,21}, {6,18}, {2,13}, {9,18}, {5,21}, {1,14}, {5,17}, {9,22}, {5,24}, {6,22}, {1,16}, {10,17}, {10,20}, {9,13}, {1,20}, {5,16}, {3,19}, {8,24}, {12,16}, {4,24}, {7,19}, {8,18}, {12,13}, {4,22}, {7,17}, {3,21}, {11,14}, {6,23}, {2,15}, {9,19} } Symmetric graph 27 of order 24 Valency 14 Diameter 2 Girth 3 Automorphism group of order 241920 Number of arcs = 336 Number of 2-arcs = 4368 2-arc-transitive false Edge-set { {1,4}, {4,13}, {6,24}, {9,13}, {6,18}, {2,15}, {5,13}, {9,17}, {18,21}, {11,15}, {5,11}, {5,8}, {17,22}, {9,14}, {4,18}, {10,17}, {10,21}, {11,20}, {2,11}, {8,23}, {7,17}, {14,23}, {4,7}, {14,16}, {4,20}, {3,10}, {10,14}, {16,21}, {11,13}, {6,11}, {10,22}, {9,10}, {20,22}, {2,9}, {19,23}, {1,7}, {5,23}, {7,22}, {1,16}, {15,20}, {10,18}, {10,19}, {15,16}, {13,18}, {6,19}, {7,12}, {12,16}, {13,19}, {1,6}, {6,22}, {9,23}, {9,16}, {12,20}, {2,12}, {7,18}, {15,23}, {5,7}, {3,22}, {9,21}, {3,19}, {1,14}, {5,17}, {21,22}, {1,21}, {3,15}, {19,24}, {4,15}, {3,18}, {14,19}, {4,12}, {12,24}, {8,19}, {1,17}, {11,22}, {9,11}, {3,9}, {8,12}, {12,17}, {11,18}, {15,21}, {3,5}, {18,24}, {5,24}, {5,14}, {12,21}, {1,8}, {8,22}, {11,19}, {15,17}, {14,18}, {4,19}, {3,6}, {17,20}, {2,21}, {6,21}, {3,23}, {16,24}, {4,10}, {3,20}, {2,14}, {2,24}, {6,8}, {17,23}, {3,13}, {8,13}, {6,17}, {11,23}, {7,21}, {3,16}, {13,24}, {10,24}, {7,14}, {21,23}, {8,20}, {8,10}, {7,11}, {2,17}, {6,14}, {4,23}, {4,16}, {20,24}, {2,8}, {14,20}, {3,7}, {11,16}, {13,21}, {6,15}, {1,10}, {5,20}, {2,22}, {2,5}, {12,13}, {13,22}, {6,9}, {1,23}, {16,22}, {10,15}, {18,23}, {18,20}, {5,10}, {7,15}, {2,19}, {6,12}, {12,23}, {16,19}, {1,20}, {9,20}, {7,19}, {5,16}, {1,13}, {2,18}, {8,15}, {4,22}, {9,24}, {14,22}, {8,18}, {5,21}, {15,24}, {3,12}, {12,14}, {1,11}, {4,9}, {17,19}, {1,24}, {8,16}, {2,4}, {13,17}, {7,24} } Symmetric graph 28 of order 24 Valency 15 Diameter 2 Girth 3 Automorphism group of order 17280 Number of arcs = 360 Number of 2-arcs = 5040 2-arc-transitive false Edge-set { {1,6}, {4,14}, {5,19}, {12,13}, {1,20}, {2,7}, {7,10}, {10,17}, {3,24}, {5,14}, {12,19}, {3,16}, {6,17}, {3,20}, {6,21}, {6,20}, {11,21}, {15,21}, {16,18}, {2,12}, {1,7}, {7,17}, {10,24}, {9,15}, {4,18}, {4,6}, {5,11}, {5,15}, {12,18}, {4,22}, {4,5}, {5,12}, {19,22}, {15,22}, {11,22}, {2,15}, {8,9}, {4,9}, {16,17}, {17,24}, {3,14}, {6,19}, {3,6}, {6,11}, {20,21}, {16,21}, {11,18}, {2,23}, {8,13}, {9,20}, {4,13}, {5,20}, {2,19}, {7,22}, {2,11}, {8,17}, {9,24}, {13,24}, {13,20}, {2,13}, {7,20}, {2,17}, {7,24}, {10,13}, {11,24}, {19,24}, {13,22}, {11,16}, {1,18}, {8,23}, {13,18}, {20,23}, {6,9}, {4,11}, {12,15}, {4,7}, {5,10}, {4,15}, {5,18}, {4,19}, {5,22}, {9,22}, {8,19}, {16,23}, {14,17}, {1,10}, {3,8}, {12,23}, {2,5}, {7,12}, {7,16}, {6,13}, {16,19}, {17,22}, {8,11}, {18,21}, {10,21}, {3,12}, {10,16}, {3,17}, {3,5}, {6,12}, {6,16}, {11,17}, {3,21}, {10,20}, {19,21}, {16,22}, {7,21}, {3,13}, {9,19}, {8,14}, {1,23}, {8,10}, {3,9}, {5,23}, {12,14}, {13,19}, {20,22}, {2,24}, {2,20}, {11,13}, {2,8}, {7,9}, {7,13}, {18,24}, {13,23}, {9,23}, {1,11}, {14,20}, {1,15}, {8,18}, {17,23}, {14,24}, {2,16}, {6,24}, {4,10}, {1,19}, {8,22}, {15,17}, {4,21}, {6,15}, {7,18}, {4,17}, {5,24}, {15,18}, {12,21}, {10,15}, {3,22}, {3,18}, {10,23}, {1,12}, {1,8}, {14,23}, {14,19}, {8,21}, {18,23}, {7,14}, {12,17}, {1,24}, {3,10}, {5,16}, {10,19}, {1,16}, {6,23}, {9,16}, {11,14}, {15,20}, {11,20}, {2,21}, {2,9}, {15,24}, {8,15}, {9,18}, {14,21}, {1,14}, {1,22}, {9,14}, {4,23}, {12,22} } Symmetric graph 29 of order 24 Valency 16 Diameter 2 Girth 3 Automorphism group of order 393289924608000 Number of arcs = 384 Number of 2-arcs = 5760 2-arc-transitive false Edge-set { {1,9}, {8,16}, {11,23}, {2,10}, {15,18}, {13,23}, {5,20}, {7,15}, {12,24}, {9,17}, {1,17}, {12,23}, {5,22}, {3,20}, {7,14}, {16,17}, {14,24}, {6,19}, {16,18}, {2,23}, {8,18}, {2,11}, {14,23}, {5,19}, {3,21}, {3,14}, {6,20}, {7,10}, {1,11}, {16,21}, {10,18}, {2,18}, {11,24}, {6,21}, {4,19}, {8,13}, {10,17}, {1,18}, {7,23}, {5,12}, {2,17}, {1,15}, {7,13}, {12,20}, {5,21}, {3,19}, {8,14}, {6,22}, {4,10}, {6,11}, {10,21}, {4,20}, {16,24}, {11,20}, {10,22}, {4,18}, {15,17}, {1,24}, {7,17}, {1,12}, {13,24}, {4,22}, {4,13}, {8,9}, {2,12}, {15,22}, {2,24}, {8,17}, {1,23}, {5,16}, {14,19}, {7,18}, {11,17}, {16,22}, {14,20}, {7,19}, {3,22}, {4,14}, {8,10}, {15,21}, {4,21}, {3,13}, {5,15}, {9,24}, {13,20}, {4,24}, {7,9}, {10,24}, {6,18}, {7,20}, {3,24}, {5,17}, {9,18}, {8,24}, {2,16}, {11,19}, {3,9}, {9,22}, {15,23}, {12,19}, {9,21}, {3,17}, {7,24}, {6,12}, {2,15}, {8,23}, {5,11}, {3,10}, {14,18}, {8,21}, {1,16}, {13,18}, {2,20}, {3,18}, {7,21}, {1,19}, {15,24}, {4,17}, {4,9}, {14,17}, {6,23}, {7,22}, {5,24}, {6,9}, {16,23}, {6,24}, {1,13}, {1,20}, {7,16}, {6,10}, {2,14}, {6,15}, {12,18}, {13,19}, {8,20}, {6,16}, {10,23}, {3,23}, {9,23}, {8,19}, {4,23}, {12,17}, {1,21}, {2,22}, {4,15}, {11,18}, {1,22}, {7,12}, {6,17}, {1,10}, {4,16}, {8,11}, {5,18}, {2,9}, {2,21}, {5,13}, {3,16}, {6,14}, {6,13}, {8,12}, {11,22}, {7,11}, {12,21}, {13,17}, {8,22}, {5,10}, {5,23}, {2,19}, {8,15}, {5,9}, {4,11}, {3,12}, {3,11}, {1,14}, {16,19}, {2,13}, {15,20}, {4,12}, {14,22}, {13,21}, {13,22}, {15,19}, {16,20}, {3,15}, {5,14}, {9,20}, {10,19}, {10,20}, {11,21}, {12,22}, {9,19}, {14,21} } Symmetric graph 30 of order 24 Valency 18 Diameter 2 Girth 3 Automorphism group of order 6449725440000 Number of arcs = 432 Number of 2-arcs = 7344 2-arc-transitive false Edge-set { {1,3}, {13,15}, {19,21}, {10,20}, {9,15}, {2,7}, {5,17}, {8,22}, {6,12}, {20,21}, {11,15}, {4,14}, {7,20}, {5,18}, {8,18}, {17,24}, {2,14}, {2,8}, {6,17}, {20,23}, {9,16}, {10,22}, {4,8}, {6,7}, {6,18}, {1,4}, {3,6}, {5,11}, {3,24}, {9,14}, {3,14}, {8,20}, {2,3}, {8,12}, {6,23}, {11,16}, {1,22}, {12,18}, {3,16}, {4,17}, {2,4}, {13,16}, {19,22}, {15,17}, {2,21}, {18,23}, {1,13}, {21,24}, {9,21}, {10,11}, {10,21}, {3,8}, {6,8}, {14,15}, {8,14}, {12,17}, {2,23}, {19,23}, {18,19}, {6,24}, {15,19}, {16,21}, {5,16}, {3,22}, {14,16}, {20,22}, {10,19}, {1,7}, {5,20}, {3,15}, {17,20}, {4,23}, {10,13}, {9,19}, {2,11}, {11,17}, {22,23}, {12,13}, {2,22}, {8,21}, {3,17}, {9,20}, {10,15}, {3,9}, {8,10}, {5,24}, {12,14}, {7,12}, {5,23}, {4,5}, {2,24}, {5,15}, {2,19}, {16,17}, {1,16}, {1,15}, {18,21}, {10,16}, {1,8}, {7,22}, {5,12}, {4,13}, {7,19}, {1,6}, {15,20}, {15,21}, {5,8}, {12,16}, {9,12}, {7,21}, {14,23}, {13,20}, {3,13}, {1,12}, {10,24}, {1,14}, {18,20}, {8,17}, {3,21}, {6,11}, {12,15}, {11,21}, {11,18}, {1,24}, {9,24}, {10,14}, {4,24}, {7,14}, {1,23}, {16,18}, {11,14}, {20,24}, {5,19}, {13,19}, {16,19}, {2,6}, {8,19}, {7,18}, {18,24}, {9,22}, {4,7}, {5,7}, {13,17}, {6,15}, {2,20}, {3,18}, {19,24}, {7,17}, {10,23}, {6,9}, {13,24}, {14,19}, {11,22}, {12,24}, {9,13}, {4,6}, {3,5}, {2,15}, {17,21}, {17,23}, {2,13}, {11,13}, {11,24}, {10,12}, {22,24}, {4,9}, {7,10}, {6,19}, {4,16}, {9,23}, {8,11}, {1,5}, {5,9}, {14,17}, {3,7}, {1,21}, {4,18}, {5,10}, {6,20}, {4,21}, {7,11}, {12,22}, {12,23}, {7,9}, {13,18}, {14,24}, {9,11}, {15,18}, {14,20}, {2,5}, {3,23}, {11,23}, {1,11}, {4,22}, {16,22}, {12,21}, {8,13}, {1,19}, {3,10}, {4,15}, {17,19}, {6,16}, {18,22}, {2,16}, {17,22}, {7,13}, {14,18}, {6,10}, {21,23}, {8,9}, {1,20}, {13,23}, {15,22}, {16,20}, {4,10}, {2,12} } Symmetric graph 31 of order 24 Valency 20 Diameter 2 Girth 3 Automorphism group of order 137594142720 Number of arcs = 480 Number of 2-arcs = 9120 2-arc-transitive false Edge-set { {1,3}, {11,15}, {5,15}, {6,24}, {10,12}, {6,17}, {4,10}, {13,18}, {3,18}, {20,23}, {11,21}, {3,7}, {16,20}, {6,21}, {2,4}, {8,14}, {4,15}, {5,8}, {17,24}, {10,24}, {1,12}, {15,21}, {5,19}, {9,24}, {10,18}, {12,16}, {6,16}, {1,22}, {13,20}, {6,10}, {17,22}, {4,20}, {3,13}, {7,18}, {18,21}, {11,23}, {1,10}, {7,17}, {4,23}, {13,19}, {18,22}, {8,21}, {5,23}, {9,11}, {5,18}, {3,9}, {2,15}, {2,8}, {14,24}, {18,20}, {3,21}, {2,7}, {8,16}, {5,14}, {4,21}, {8,19}, {1,8}, {12,17}, {11,20}, {7,19}, {14,16}, {14,23}, {4,9}, {10,22}, {1,20}, {14,17}, {4,17}, {19,24}, {12,22}, {4,8}, {15,19}, {5,22}, {6,12}, {10,16}, {1,13}, {8,24}, {10,15}, {1,5}, {12,21}, {16,19}, {9,20}, {1,17}, {4,13}, {1,6}, {7,22}, {11,22}, {15,20}, {3,23}, {7,11}, {12,24}, {7,21}, {19,23}, {9,13}, {1,14}, {13,17}, {6,22}, {2,21}, {8,11}, {15,24}, {7,13}, {3,16}, {6,7}, {18,23}, {9,23}, {2,11}, {16,22}, {6,20}, {10,23}, {9,17}, {3,11}, {5,20}, {9,21}, {14,15}, {13,22}, {10,21}, {11,17}, {1,11}, {5,7}, {22,24}, {7,15}, {2,16}, {6,14}, {11,18}, {3,15}, {2,19}, {2,12}, {6,8}, {5,17}, {21,24}, {12,19}, {13,23}, {1,19}, {7,14}, {17,23}, {14,22}, {13,15}, {2,3}, {9,18}, {1,16}, {12,20}, {6,13}, {14,19}, {5,9}, {3,19}, {4,14}, {8,17}, {2,9}, {8,18}, {3,24}, {14,20}, {17,21}, {5,12}, {4,24}, {10,19}, {10,13}, {2,14}, {10,20}, {1,21}, {7,12}, {11,24}, {12,15}, {4,19}, {2,18}, {9,16}, {1,18}, {8,12}, {6,15}, {5,10}, {16,23}, {12,23}, {11,16}, {3,20}, {3,17}, {4,7}, {7,23}, {15,23}, {3,14}, {1,9}, {2,13}, {2,6}, {10,14}, {5,16}, {8,22}, {5,11}, {9,15}, {8,23}, {1,7}, {17,19}, {4,22}, {3,22}, {7,20}, {8,20}, {13,24}, {3,10}, {4,11}, {13,16}, {6,18}, {21,23}, {2,20}, {14,21}, {10,11}, {1,15}, {11,19}, {12,18}, {6,23}, {7,16}, {4,12}, {9,22}, {8,15}, {22,23}, {17,20}, {5,24}, {9,12}, {16,21}, {6,19}, {10,17}, {5,13}, {15,22}, {13,21}, {2,5}, {20,24}, {14,18}, {5,21}, {16,24}, {9,14}, {4,18}, {3,8}, {6,11}, {7,24}, {9,19}, {2,22}, {2,17}, {6,9}, {2,10}, {4,16}, {8,13}, {18,24}, {1,4}, {3,12}, {18,19} } Symmetric graph 32 of order 24 Valency 21 Diameter 2 Girth 3 Automorphism group of order 67722117120 Number of arcs = 504 Number of 2-arcs = 10080 2-arc-transitive false Edge-set { {1,4}, {3,22}, {8,20}, {2,11}, {3,7}, {8,13}, {6,17}, {9,10}, {2,7}, {5,7}, {8,18}, {6,23}, {19,24}, {13,19}, {6,9}, {4,12}, {1,7}, {5,9}, {7,23}, {5,21}, {6,14}, {12,24}, {1,19}, {10,15}, {2,16}, {15,18}, {16,23}, {9,24}, {4,19}, {5,22}, {11,20}, {5,8}, {9,23}, {4,21}, {7,12}, {1,5}, {14,23}, {18,21}, {16,24}, {5,10}, {3,15}, {8,16}, {12,22}, {1,21}, {9,15}, {17,20}, {14,22}, {12,21}, {1,15}, {2,4}, {15,22}, {16,20}, {11,23}, {3,21}, {4,13}, {10,17}, {8,23}, {6,21}, {9,12}, {18,20}, {5,11}, {3,23}, {8,21}, {12,16}, {1,24}, {14,20}, {14,18}, {10,21}, {2,15}, {2,17}, {7,22}, {6,15}, {3,11}, {3,14}, {9,17}, {4,22}, {13,17}, {11,16}, {3,24}, {5,14}, {11,18}, {3,17}, {8,22}, {1,22}, {9,20}, {11,17}, {13,21}, {15,17}, {1,10}, {2,14}, {7,18}, {18,22}, {20,23}, {6,19}, {12,13}, {8,12}, {1,6}, {14,24}, {18,19}, {4,11}, {13,20}, {14,17}, {4,23}, {2,12}, {8,14}, {6,18}, {11,15}, {3,10}, {2,8}, {13,16}, {17,24}, {12,18}, {1,17}, {9,22}, {9,13}, {7,11}, {3,5}, {19,22}, {7,10}, {7,24}, {9,19}, {11,22}, {3,20}, {13,23}, {2,10}, {21,24}, {4,20}, {10,14}, {2,19}, {7,13}, {8,11}, {3,6}, {3,8}, {4,17}, {10,13}, {18,23}, {17,19}, {13,22}, {1,16}, {7,20}, {15,24}, {16,19}, {5,18}, {6,11}, {8,19}, {10,16}, {2,24}, {15,20}, {14,16}, {10,20}, {13,18}, {17,23}, {13,24}, {1,20}, {9,11}, {6,24}, {20,24}, {14,19}, {10,22}, {2,6}, {1,8}, {15,23}, {10,19}, {2,13}, {5,20}, {11,14}, {3,19}, {3,4}, {9,18}, {4,7}, {2,23}, {7,21}, {3,16}, {6,7}, {5,12}, {2,5}, {4,16}, {7,17}, {1,23}, {2,18}, {6,16}, {9,16}, {5,23}, {4,8}, {6,10}, {7,19}, {12,23}, {12,20}, {1,14}, {15,19}, {8,15}, {5,17}, {2,22}, {15,21}, {15,16}, {14,21}, {4,24}, {12,15}, {2,9}, {17,22}, {16,21}, {6,13}, {12,17}, {12,19}, {1,13}, {10,18}, {3,13}, {8,17}, {4,9}, {4,10}, {10,24}, {3,12}, {6,8}, {1,18}, {17,21}, {7,16}, {4,14}, {1,12}, {1,9}, {7,14}, {2,21}, {7,15}, {5,19}, {11,21}, {9,21}, {21,22}, {5,13}, {9,14}, {4,15}, {6,20}, {5,16}, {1,11}, {8,24}, {16,22}, {6,22}, {19,23}, {3,9}, {18,24}, {2,20}, {11,19}, {11,13}, {5,15}, {3,18}, {12,14}, {5,24}, {4,18}, {21,23}, {20,22}, {8,10}, {11,24}, {10,23}, {6,12} } Symmetric graph 33 of order 24 Valency 22 Diameter 2 Girth 3 Automorphism group of order 1961990553600 Number of arcs = 528 Number of 2-arcs = 11088 2-arc-transitive false Edge-set { {1,3}, {9,11}, {17,20}, {16,23}, {1,7}, {4,6}, {11,13}, {14,22}, {21,23}, {11,20}, {6,20}, {1,10}, {9,18}, {16,17}, {7,18}, {4,15}, {8,22}, {16,21}, {4,16}, {1,11}, {1,4}, {11,24}, {8,20}, {5,23}, {7,14}, {6,14}, {13,23}, {5,20}, {10,13}, {18,24}, {7,19}, {5,15}, {8,14}, {10,14}, {18,23}, {11,16}, {1,20}, {10,11}, {18,20}, {1,22}, {4,19}, {5,11}, {2,22}, {10,21}, {1,18}, {4,9}, {17,22}, {3,21}, {2,4}, {17,24}, {3,8}, {5,21}, {3,20}, {6,12}, {2,13}, {10,24}, {18,19}, {4,5}, {4,8}, {5,22}, {14,21}, {14,16}, {1,23}, {4,11}, {16,24}, {1,8}, {11,14}, {7,11}, {15,20}, {3,10}, {12,18}, {2,16}, {7,12}, {15,19}, {8,24}, {8,16}, {14,20}, {10,23}, {6,7}, {13,15}, {8,9}, {10,12}, {6,21}, {13,22}, {9,19}, {5,17}, {2,8}, {10,16}, {11,17}, {1,15}, {2,9}, {12,17}, {3,19}, {21,24}, {3,5}, {12,14}, {2,10}, {10,18}, {10,19}, {5,18}, {2,7}, {10,15}, {8,18}, {14,18}, {4,23}, {11,22}, {20,21}, {22,23}, {11,19}, {16,18}, {16,20}, {1,6}, {4,13}, {9,24}, {8,17}, {2,14}, {19,23}, {2,6}, {3,13}, {12,24}, {19,21}, {14,19}, {4,18}, {22,24}, {8,21}, {6,9}, {13,17}, {3,24}, {5,7}, {15,24}, {9,16}, {7,17}, {3,15}, {3,23}, {12,19}, {5,19}, {14,24}, {8,23}, {6,16}, {1,13}, {20,24}, {12,23}, {6,15}, {3,9}, {16,22}, {10,17}, {15,18}, {8,19}, {5,24}, {8,12}, {2,5}, {12,20}, {6,19}, {13,24}, {5,14}, {4,14}, {10,22}, {18,21}, {7,16}, {7,22}, {15,21}, {3,16}, {1,12}, {14,23}, {11,23}, {9,20}, {3,18}, {5,13}, {3,22}, {12,21}, {9,17}, {3,17}, {12,16}, {4,12}, {5,10}, {7,21}, {15,22}, {5,16}, {7,9}, {6,17}, {9,21}, {2,20}, {6,10}, {13,21}, {7,23}, {6,13}, {9,13}, {9,22}, {17,21}, {2,12}, {2,3}, {4,22}, {19,22}, {1,14}, {9,23}, {4,21}, {2,21}, {15,23}, {6,24}, {8,13}, {5,12}, {2,11}, {9,12}, {2,18}, {4,10}, {7,24}, {8,15}, {5,8}, {6,23}, {7,20}, {9,14}, {17,23}, {11,15}, {18,22}, {1,21}, {5,9}, {14,17}, {2,17}, {15,17}, {7,13}, {14,15}, {2,23}, {2,24}, {8,10}, {20,23}, {1,24}, {20,22}, {1,17}, {3,7}, {7,15}, {6,8}, {13,16}, {12,15}, {2,19}, {17,19}, {7,10}, {11,18}, {4,20}, {16,19}, {2,15}, {1,19}, {6,22}, {13,19}, {6,11}, {4,7}, {8,11}, {6,18}, {3,6}, {13,18}, {4,24}, {12,22}, {19,24}, {11,21}, {13,20}, {3,12}, {12,13}, {3,14}, {3,11}, {9,15}, {1,16}, {1,9}, {10,20}, {1,5}, {4,17} } Symmetric graph 34 of order 24 Valency 23 Diameter 1 Girth 3 Automorphism group of order 620448401733239439360000 Number of arcs = 552 Number of 2-arcs = 12144 2-arc-transitive true Edge-set { {1,2}, {3,4}, {11,24}, {5,20}, {16,19}, {9,22}, {3,14}, {16,23}, {4,10}, {11,19}, {7,15}, {17,21}, {5,9}, {5,14}, {16,18}, {11,15}, {7,23}, {13,20}, {19,20}, {9,19}, {14,15}, {2,12}, {8,17}, {6,18}, {1,13}, {16,21}, {9,10}, {14,16}, {10,18}, {10,11}, {7,21}, {9,12}, {14,17}, {2,15}, {8,23}, {4,6}, {19,23}, {4,15}, {19,21}, {9,15}, {12,14}, {17,18}, {3,24}, {11,22}, {1,6}, {2,13}, {8,10}, {12,21}, {4,7}, {6,24}, {11,18}, {1,7}, {13,21}, {9,20}, {11,14}, {7,18}, {10,13}, {20,21}, {9,13}, {14,20}, {2,18}, {1,8}, {21,24}, {6,14}, {13,18}, {3,12}, {11,17}, {1,15}, {2,23}, {8,20}, {12,19}, {15,19}, {15,23}, {12,20}, {17,19}, {18,19}, {9,17}, {14,24}, {18,22}, {6,10}, {5,22}, {3,16}, {4,8}, {12,24}, {3,7}, {6,11}, {2,20}, {18,24}, {1,22}, {8,19}, {8,22}, {14,21}, {2,4}, {8,24}, {21,23}, {4,9}, {9,14}, {14,18}, {2,10}, {8,21}, {7,13}, {6,20}, {18,23}, {1,4}, {6,9}, {14,23}, {4,18}, {3,10}, {11,21}, {2,24}, {1,3}, {8,14}, {12,18}, {7,10}, {6,21}, {5,24}, {16,22}, {13,14}, {4,12}, {17,24}, {3,15}, {11,23}, {1,23}, {19,24}, {15,22}, {15,17}, {12,15}, {17,23}, {23,24}, {4,22}, {6,19}, {13,15}, {10,19}, {15,21}, {14,22}, {3,18}, {10,17}, {5,21}, {8,13}, {16,17}, {5,10}, {5,11}, {7,16}, {1,20}, {2,19}, {22,24}, {3,22}, {2,5}, {8,16}, {8,9}, {3,23}, {4,11}, {10,22}, {3,21}, {4,17}, {1,19}, {1,17}, {1,18}, {3,20}, {2,3}, {15,18}, {9,18}, {10,14}, {18,21}, {3,13}, {11,20}, {2,7}, {6,8}, {10,15}, {4,20}, {10,20}, {5,13}, {16,20}, {1,14}, {3,11}, {4,5}, {16,24}, {10,24}, {21,22}, {8,18}, {1,12}, {5,7}, {7,14}, {20,24}, {19,22}, {6,22}, {5,12}, {12,17}, {5,17}, {6,12}, {13,17}, {17,22}, {6,15}, {13,23}, {17,20}, {5,19}, {7,12}, {6,17}, {13,19}, {15,20}, {5,18}, {6,13}, {1,10}, {2,6}, {13,16}, {9,16}, {2,11}, {7,8}, {4,23}, {4,24}, {3,19}, {3,5}, {5,16}, {1,11}, {1,21}, {2,9}, {5,15}, {14,19}, {1,16}, {4,19}, {15,24}, {13,24}, {5,23}, {4,16}, {11,16}, {10,12}, {10,21}, {9,21}, {18,20}, {6,16}, {9,23}, {4,14}, {8,11}, {12,13}, {20,23}, {13,22}, {1,5}, {2,21}, {2,16}, {2,14}, {22,23}, {12,22}, {6,7}, {8,12}, {6,23}, {4,13}, {7,19}, {12,23}, {10,16}, {3,8}, {11,12}, {7,11}, {7,9}, {3,9}, {2,8}, {20,22}, {15,16}, {1,24}, {9,11}, {12,16}, {7,24}, {3,17}, {7,22}, {3,6}, {10,23}, {1,9}, {4,21}, {7,17}, {5,6}, {2,22}, {8,15}, {7,20}, {11,13}, {9,24}, {2,17}, {5,8} } ................................................................... Symmetric connected graphs of order 25 Symmetric graph 1 of order 25 Valency 2 Diameter 12 Girth 25 Automorphism group of order 50 Number of arcs = 50 Number of 2-arcs = 50 2-arc-transitive true Edge-set { {1,6}, {10,15}, {14,17}, {16,21}, {5,25}, {4,9}, {8,13}, {12,20}, {19,24}, {3,23}, {2,7}, {6,11}, {15,18}, {17,22}, {1,21}, {5,10}, {9,14}, {13,16}, {20,25}, {4,24}, {3,8}, {7,12}, {11,19}, {18,23}, {2,22} } Symmetric graph 2 of order 25 Valency 4 Diameter 3 Girth 4 Automorphism group of order 100 Number of arcs = 100 Number of 2-arcs = 300 2-arc-transitive false Edge-set { {1,6}, {12,21}, {8,14}, {2,7}, {3,18}, {6,25}, {14,23}, {7,13}, {11,19}, {5,21}, {8,19}, {1,16}, {9,23}, {10,16}, {4,25}, {2,15}, {15,18}, {16,25}, {12,20}, {1,22}, {20,24}, {5,13}, {5,20}, {19,23}, {7,18}, {3,24}, {4,12}, {14,17}, {9,15}, {15,24}, {7,21}, {3,11}, {6,17}, {8,22}, {5,10}, {3,8}, {2,23}, {10,11}, {17,21}, {11,25}, {6,12}, {1,14}, {13,16}, {10,24}, {4,9}, {2,17}, {18,22}, {4,19}, {9,20}, {13,22} } Symmetric graph 3 of order 25 Valency 4 Diameter 4 Girth 4 Automorphism group of order 200 Number of arcs = 100 Number of 2-arcs = 300 2-arc-transitive false Edge-set { {1,6}, {11,20}, {4,7}, {17,24}, {12,18}, {5,10}, {3,24}, {15,19}, {20,25}, {3,6}, {9,15}, {16,23}, {1,25}, {11,17}, {4,9}, {10,14}, {2,23}, {14,18}, {7,11}, {19,24}, {2,10}, {3,22}, {8,14}, {20,22}, {6,12}, {5,24}, {15,16}, {3,8}, {17,22}, {9,13}, {1,22}, {13,17}, {4,25}, {6,15}, {18,23}, {1,9}, {13,19}, {2,21}, {7,13}, {19,21}, {18,25}, {10,11}, {4,23}, {14,20}, {2,7}, {5,8}, {16,21}, {8,12}, {5,21}, {12,16} } Symmetric graph 4 of order 25 Valency 6 Diameter 3 Girth 3 Automorphism group of order 300 Number of arcs = 150 Number of 2-arcs = 750 2-arc-transitive false Edge-set { {1,2}, {1,6}, {2,3}, {1,25}, {2,7}, {6,11}, {3,4}, {2,21}, {5,6}, {3,8}, {19,25}, {7,12}, {11,16}, {4,5}, {6,7}, {3,22}, {21,25}, {1,7}, {10,11}, {4,9}, {20,21}, {5,24}, {8,13}, {13,19}, {12,17}, {16,21}, {1,5}, {5,25}, {7,8}, {11,12}, {4,23}, {21,22}, {2,8}, {19,20}, {6,12}, {15,16}, {5,10}, {16,22}, {4,10}, {9,14}, {14,20}, {18,24}, {13,18}, {7,13}, {17,22}, {1,21}, {8,9}, {19,24}, {12,13}, {16,17}, {22,23}, {6,10}, {3,9}, {16,20}, {24,25}, {13,14}, {11,17}, {17,23}, {9,15}, {10,15}, {14,19}, {8,14}, {12,18}, {18,23}, {2,22}, {9,10}, {20,25}, {4,24}, {17,18}, {23,24}, {11,15}, {14,15}, {18,19}, {15,20}, {3,23} } Symmetric graph 5 of order 25 Valency 8 Diameter 3 Girth 4 Automorphism group of order 1200 Number of arcs = 200 Number of 2-arcs = 1400 2-arc-transitive false Edge-set { {1,6}, {4,20}, {2,19}, {18,21}, {5,22}, {16,25}, {3,21}, {8,24}, {15,25}, {9,19}, {1,11}, {7,22}, {14,23}, {8,17}, {4,15}, {13,16}, {7,15}, {10,14}, {2,25}, {17,21}, {11,20}, {2,6}, {5,9}, {9,12}, {1,23}, {16,24}, {15,18}, {5,10}, {13,22}, {8,23}, {5,15}, {10,20}, {3,14}, {9,18}, {7,16}, {15,24}, {11,21}, {6,22}, {4,16}, {3,19}, {1,17}, {2,12}, {7,17}, {13,23}, {10,25}, {1,18}, {9,13}, {8,11}, {1,10}, {12,16}, {15,19}, {18,22}, {14,17}, {4,9}, {2,24}, {17,25}, {20,23}, {6,15}, {10,13}, {11,19}, {5,23}, {4,21}, {3,7}, {20,24}, {8,12}, {14,18}, {2,13}, {6,16}, {3,20}, {2,18}, {12,22}, {7,23}, {10,21}, {9,24}, {11,25}, {5,17}, {3,13}, {14,24}, {10,19}, {8,18}, {6,21}, {1,12}, {9,25}, {3,8}, {4,22}, {19,23}, {3,25}, {7,11}, {12,20}, {13,17}, {6,14}, {1,24}, {4,8}, {2,7}, {5,11}, {12,21}, {4,14}, {6,20}, {5,16}, {19,22} } Symmetric graph 6 of order 25 Valency 8 Diameter 2 Girth 3 Automorphism group of order 28800 Number of arcs = 200 Number of 2-arcs = 1400 2-arc-transitive false Edge-set { {1,2}, {7,9}, {7,12}, {23,24}, {11,21}, {14,24}, {11,15}, {16,18}, {18,23}, {12,17}, {8,10}, {13,18}, {23,25}, {12,15}, {5,10}, {9,19}, {1,16}, {18,19}, {4,14}, {14,15}, {21,25}, {1,11}, {19,20}, {16,20}, {3,18}, {5,15}, {10,25}, {3,23}, {21,24}, {2,7}, {1,3}, {19,24}, {8,13}, {22,25}, {13,15}, {5,25}, {17,20}, {3,8}, {7,10}, {3,5}, {4,24}, {2,5}, {4,9}, {1,6}, {17,19}, {10,15}, {20,25}, {6,16}, {17,18}, {8,23}, {9,24}, {11,12}, {6,7}, {7,17}, {3,13}, {5,20}, {10,20}, {2,3}, {4,5}, {6,21}, {16,17}, {24,25}, {6,10}, {2,17}, {8,18}, {22,23}, {9,10}, {2,12}, {21,22}, {7,22}, {3,4}, {15,25}, {1,5}, {2,22}, {6,9}, {1,4}, {14,19}, {16,21}, {21,23}, {12,14}, {22,24}, {6,11}, {11,14}, {2,4}, {17,22}, {6,8}, {9,14}, {18,20}, {1,21}, {16,19}, {11,13}, {15,20}, {12,13}, {7,8}, {8,9}, {13,14}, {13,23}, {12,22}, {4,19}, {11,16} } Symmetric graph 7 of order 25 Valency 10 Diameter 2 Girth 4 Automorphism group of order 248832000000 Number of arcs = 250 Number of 2-arcs = 2250 2-arc-transitive false Edge-set { {1,6}, {19,25}, {10,12}, {10,14}, {2,23}, {3,24}, {11,17}, {5,24}, {11,19}, {12,20}, {5,6}, {13,16}, {1,7}, {2,8}, {16,21}, {13,18}, {1,9}, {2,10}, {16,23}, {3,6}, {17,24}, {18,25}, {9,12}, {4,7}, {19,21}, {10,13}, {20,22}, {6,14}, {7,15}, {3,25}, {4,9}, {18,22}, {19,23}, {10,15}, {20,24}, {6,11}, {7,12}, {5,25}, {16,25}, {8,13}, {1,21}, {9,14}, {2,22}, {3,23}, {15,17}, {17,21}, {4,24}, {11,18}, {12,19}, {13,20}, {14,16}, {2,7}, {17,23}, {8,15}, {9,11}, {4,22}, {5,23}, {1,24}, {11,20}, {6,13}, {2,25}, {12,16}, {3,21}, {13,17}, {14,18}, {2,9}, {7,14}, {15,19}, {3,10}, {4,6}, {5,7}, {1,8}, {20,21}, {16,22}, {18,24}, {8,12}, {5,21}, {1,22}, {14,20}, {15,16}, {4,8}, {12,18}, {5,9}, {13,19}, {1,10}, {2,6}, {16,24}, {4,25}, {3,7}, {17,25}, {18,21}, {19,22}, {20,23}, {6,15}, {7,11}, {9,13}, {3,22}, {14,17}, {15,18}, {3,9}, {4,10}, {19,24}, {20,25}, {17,22}, {8,14}, {18,23}, {9,15}, {10,11}, {6,12}, {7,13}, {1,25}, {2,21}, {4,23}, {11,16}, {5,8}, {8,11}, {1,23}, {2,24}, {4,21}, {5,22}, {14,19}, {15,20}, {12,17}, {5,10}, {3,8} } Symmetric graph 8 of order 25 Valency 12 Diameter 2 Girth 3 Automorphism group of order 600 Number of arcs = 300 Number of 2-arcs = 3300 2-arc-transitive false Edge-set { {1,2}, {4,14}, {4,19}, {9,15}, {3,9}, {18,24}, {22,25}, {5,24}, {22,24}, {16,18}, {6,8}, {1,21}, {16,19}, {6,9}, {16,21}, {12,15}, {18,23}, {12,17}, {2,7}, {4,11}, {12,14}, {3,23}, {17,22}, {7,12}, {11,23}, {20,25}, {10,15}, {6,18}, {11,16}, {8,20}, {2,14}, {4,17}, {9,10}, {15,20}, {5,10}, {6,24}, {6,11}, {8,21}, {2,20}, {10,17}, {6,10}, {8,13}, {1,13}, {7,25}, {15,22}, {17,18}, {10,23}, {13,25}, {12,13}, {1,19}, {14,15}, {8,9}, {23,24}, {7,22}, {13,18}, {7,19}, {9,22}, {16,17}, {11,12}, {13,14}, {7,8}, {22,23}, {7,17}, {5,12}, {4,5}, {21,25}, {11,15}, {8,18}, {6,7}, {1,5}, {16,20}, {5,20}, {3,4}, {18,19}, {15,25}, {24,25}, {12,22}, {6,16}, {6,21}, {2,21}, {5,18}, {14,21}, {2,3}, {21,22}, {8,23}, {10,20}, {19,20}, {5,15}, {2,12}, {11,21}, {2,8}, {3,16}, {9,19}, {1,11}, {10,25}, {12,18}, {2,17}, {13,23}, {3,13}, {13,19}, {9,24}, {3,18}, {1,25}, {1,16}, {20,21}, {17,23}, {11,17}, {1,7}, {11,14}, {3,15}, {14,24}, {6,12}, {7,13}, {19,25}, {14,20}, {10,11}, {3,22}, {4,10}, {15,16}, {18,20}, {8,14}, {5,6}, {3,5}, {16,22}, {1,4}, {4,23}, {11,13}, {8,10}, {2,4}, {17,19}, {17,20}, {2,5}, {1,3}, {13,15}, {7,10}, {21,24}, {7,9}, {23,25}, {19,24}, {21,23}, {4,9}, {9,14}, {3,8}, {14,19}, {4,24}, {5,25}, {2,22}, {1,6}, {12,24}, {9,16} } Symmetric graph 9 of order 25 Valency 16 Diameter 2 Girth 3 Automorphism group of order 28800 Number of arcs = 400 Number of 2-arcs = 6000 2-arc-transitive false Edge-set { {1,2}, {12,17}, {10,21}, {19,20}, {16,24}, {8,11}, {18,20}, {5,10}, {1,17}, {1,15}, {15,25}, {14,23}, {7,22}, {10,25}, {1,8}, {7,8}, {12,20}, {21,24}, {9,12}, {21,23}, {6,9}, {9,23}, {4,21}, {11,14}, {16,18}, {2,13}, {6,8}, {9,20}, {12,23}, {21,22}, {18,23}, {13,22}, {10,19}, {1,16}, {1,11}, {18,25}, {3,19}, {6,16}, {11,21}, {11,18}, {3,13}, {4,6}, {3,21}, {6,11}, {2,11}, {3,18}, {4,14}, {7,14}, {8,15}, {17,24}, {13,23}, {4,22}, {3,10}, {1,6}, {19,21}, {11,16}, {2,18}, {21,25}, {2,5}, {5,8}, {17,20}, {12,15}, {15,21}, {12,14}, {7,21}, {6,25}, {8,9}, {5,22}, {17,19}, {13,15}, {4,15}, {7,18}, {14,25}, {22,24}, {5,19}, {3,4}, {11,22}, {18,19}, {13,14}, {4,7}, {14,17}, {7,10}, {22,25}, {8,19}, {2,4}, {3,14}, {4,18}, {22,23}, {1,20}, {24,25}, {5,11}, {2,16}, {2,3}, {8,22}, {12,13}, {17,18}, {14,15}, {7,15}, {17,25}, {8,10}, {9,18}, {7,17}, {10,12}, {7,23}, {12,22}, {10,20}, {1,24}, {9,19}, {16,23}, {9,11}, {4,19}, {14,16}, {13,18}, {6,13}, {4,9}, {3,23}, {6,22}, {7,16}, {2,12}, {5,20}, {9,24}, {5,23}, {2,9}, {8,13}, {9,14}, {2,25}, {5,7}, {2,22}, {2,7}, {5,25}, {8,17}, {4,24}, {5,14}, {4,20}, {14,24}, {8,18}, {13,20}, {17,22}, {2,17}, {14,19}, {3,8}, {16,21}, {1,21}, {9,25}, {7,12}, {15,17}, {10,15}, {19,24}, {5,16}, {20,25}, {8,24}, {6,20}, {8,23}, {20,22}, {3,25}, {13,24}, {16,20}, {18,21}, {11,13}, {16,19}, {1,12}, {3,5}, {6,17}, {11,15}, {6,7}, {3,17}, {4,5}, {3,6}, {11,19}, {13,16}, {15,18}, {10,16}, {1,3}, {11,12}, {6,10}, {23,24}, {6,14}, {9,10}, {16,17}, {2,10}, {10,13}, {20,23}, {1,4}, {23,25}, {10,24}, {1,5}, {2,24}, {19,22}, {1,9}, {1,23}, {11,25}, {5,15}, {12,19}, {4,13}, {3,12}, {15,24}, {15,20}, {6,21}, {12,21}, {7,9} } Symmetric graph 10 of order 25 Valency 20 Diameter 2 Girth 3 Automorphism group of order 2985984000000 Number of arcs = 500 Number of 2-arcs = 9500 2-arc-transitive false Edge-set { {1,6}, {3,8}, {8,15}, {1,18}, {5,10}, {10,12}, {4,16}, {5,21}, {12,20}, {4,14}, {8,20}, {8,21}, {18,21}, {2,7}, {7,14}, {2,19}, {2,23}, {14,17}, {2,12}, {6,18}, {6,24}, {20,23}, {6,19}, {17,23}, {12,24}, {6,25}, {15,20}, {5,17}, {12,23}, {4,24}, {5,14}, {4,6}, {14,20}, {2,21}, {6,21}, {4,9}, {9,11}, {4,25}, {11,19}, {5,15}, {9,16}, {9,22}, {17,25}, {9,17}, {19,25}, {15,22}, {9,23}, {12,17}, {3,20}, {15,21}, {1,21}, {3,12}, {1,8}, {11,17}, {4,23}, {9,24}, {3,16}, {1,25}, {8,12}, {3,13}, {1,15}, {1,7}, {17,21}, {14,24}, {7,19}, {7,25}, {19,22}, {11,23}, {4,17}, {9,12}, {6,12}, {5,6}, {15,19}, {3,6}, {6,15}, {1,20}, {19,23}, {15,24}, {9,14}, {2,9}, {6,17}, {3,14}, {2,15}, {6,13}, {1,22}, {13,16}, {7,20}, {16,22}, {13,25}, {7,21}, {14,19}, {13,24}, {3,23}, {3,10}, {13,19}, {7,22}, {1,19}, {3,22}, {10,14}, {1,11}, {4,13}, {3,9}, {12,22}, {10,17}, {10,23}, {16,24}, {14,21}, {2,20}, {6,14}, {8,14}, {2,8}, {12,16}, {5,8}, {4,18}, {16,25}, {13,22}, {6,11}, {9,20}, {1,12}, {5,13}, {10,18}, {10,24}, {16,23}, {8,13}, {7,18}, {5,23}, {4,12}, {11,16}, {14,18}, {4,8}, {8,11}, {5,18}, {2,25}, {6,22}, {12,25}, {5,19}, {11,22}, {5,25}, {5,7}, {15,16}, {10,25}, {9,13}, {20,22}, {1,23}, {13,17}, {15,17}, {3,7}, {7,15}, {16,21}, {14,25}, {10,15}, {1,16}, {3,21}, {1,14}, {8,17}, {8,23}, {18,24}, {4,22}, {9,25}, {12,21}, {5,20}, {3,15}, {1,9}, {3,17}, {3,19}, {15,25}, {10,19}, {9,21}, {3,24}, {15,18}, {5,24}, {7,11}, {2,11}, {10,11}, {4,10}, {2,10}, {2,16}, {18,22}, {11,25}, {4,15}, {3,11}, {8,16}, {8,22}, {18,25}, {10,16}, {13,18}, {11,20}, {1,10}, {10,13}, {15,23}, {2,22}, {12,18}, {17,24}, {3,25}, {12,19}, {5,9}, {18,23}, {7,12}, {4,19}, {6,20}, {20,21}, {1,24}, {7,23}, {3,18}, {1,13}, {1,17}, {13,23}, {7,24}, {11,18}, {4,11}, {4,20}, {11,21}, {4,7}, {9,19}, {6,23}, {20,25}, {19,21}, {5,22}, {7,17}, {7,16}, {7,13}, {20,24}, {14,23}, {2,13}, {9,18}, {19,24}, {14,22}, {5,16}, {4,21}, {2,24}, {2,14}, {8,18}, {8,24}, {6,16}, {8,25}, {8,19}, {5,11}, {10,20}, {2,17}, {10,21}, {14,16}, {10,22}, {13,21}, {2,6}, {13,20}, {2,18}, {17,22}, {9,15}, {5,12}, {11,24} } Symmetric graph 11 of order 25 Valency 24 Diameter 1 Girth 3 Automorphism group of order 15511210043330985984000000 Number of arcs = 600 Number of 2-arcs = 13800 2-arc-transitive true Edge-set { {1,2}, {17,25}, {11,25}, {1,10}, {13,24}, {10,11}, {12,13}, {21,25}, {5,25}, {5,13}, {19,22}, {11,21}, {5,12}, {5,8}, {3,19}, {2,10}, {4,13}, {3,10}, {9,13}, {3,5}, {9,19}, {20,24}, {1,20}, {2,11}, {4,12}, {3,8}, {3,9}, {3,7}, {9,23}, {14,20}, {17,21}, {5,11}, {5,6}, {18,19}, {14,21}, {2,5}, {4,5}, {14,19}, {3,14}, {2,9}, {4,20}, {1,14}, {17,22}, {12,25}, {11,17}, {11,12}, {6,8}, {3,18}, {7,14}, {2,23}, {4,14}, {2,14}, {14,15}, {2,7}, {4,16}, {6,14}, {12,22}, {10,17}, {4,24}, {3,11}, {9,12}, {9,16}, {20,23}, {1,15}, {2,22}, {4,10}, {3,17}, {9,11}, {3,6}, {9,18}, {20,22}, {14,22}, {4,17}, {11,14}, {6,12}, {17,18}, {22,25}, {10,25}, {1,24}, {8,10}, {3,13}, {1,11}, {12,24}, {8,11}, {3,12}, {7,18}, {16,23}, {14,23}, {2,15}, {15,22}, {7,10}, {16,17}, {6,11}, {6,22}, {10,18}, {10,21}, {15,17}, {7,11}, {6,9}, {8,18}, {18,22}, {10,16}, {8,24}, {3,20}, {1,21}, {5,24}, {6,13}, {2,12}, {4,8}, {4,9}, {8,14}, {12,16}, {6,17}, {19,25}, {17,24}, {11,20}, {6,21}, {5,18}, {2,24}, {4,11}, {12,14}, {14,18}, {2,16}, {4,23}, {17,20}, {22,24}, {10,20}, {1,6}, {18,24}, {11,22}, {10,12}, {3,16}, {1,23}, {15,24}, {10,24}, {13,20}, {13,25}, {7,21}, {5,23}, {5,14}, {2,19}, {8,13}, {3,22}, {12,23}, {2,3}, {15,23}, {7,15}, {16,22}, {6,10}, {17,19}, {19,24}, {20,21}, {15,21}, {5,7}, {1,9}, {11,18}, {16,20}, {21,23}, {5,15}, {2,21}, {1,19}, {21,24}, {11,15}, {7,12}, {4,18}, {14,16}, {7,23}, {23,24}, {15,20}, {9,21}, {7,13}, {22,23}, {2,17}, {2,25}, {4,25}, {9,22}, {16,19}, {8,17}, {6,7}, {18,23}, {4,6}, {7,22}, {10,23}, {8,9}, {1,18}, {16,24}, {1,13}, {12,17}, {2,18}, {3,23}, {9,15}, {13,17}, {12,18}, {8,22}, {10,15}, {9,17}, {6,16}, {6,18}, {1,12}, {12,21}, {5,17}, {18,25}, {16,25}, {13,23}, {11,24}, {12,20}, {8,21}, {9,14}, {2,8}, {6,25}, {13,19}, {21,22}, {13,21}, {5,22}, {5,10}, {4,7}, {9,10}, {19,23}, {14,24}, {2,20}, {8,16}, {14,17}, {15,19}, {9,24}, {8,20}, {18,21}, {5,16}, {1,22}, {4,21}, {3,15}, {7,9}, {14,25}, {11,23}, {12,15}, {20,25}, {1,25}, {2,13}, {4,22}, {11,19}, {8,15}, {6,23}, {15,18}, {15,16}, {13,16}, {12,19}, {2,4}, {7,19}, {6,20}, {1,17}, {11,13}, {13,18}, {9,20}, {1,8}, {1,7}, {7,16}, {6,15}, {16,18}, {7,20}, {16,21}, {23,25}, {15,25}, {3,24}, {17,23}, {2,6}, {4,19}, {1,5}, {8,23}, {7,24}, {19,21}, {5,21}, {1,4}, {8,25}, {3,25}, {3,4}, {1,3}, {13,15}, {6,19}, {8,12}, {10,14}, {7,17}, {5,20}, {3,21}, {5,9}, {13,22}, {10,22}, {19,20}, {4,15}, {24,25}, {10,13}, {11,16}, {8,19}, {6,24}, {18,20}, {7,25}, {7,8}, {10,19}, {13,14}, {1,16}, {9,25}, {5,19} } ................................................................... Symmetric connected graphs of order 26 Symmetric graph 1 of order 26 Valency 2 Diameter 13 Girth 26 Automorphism group of order 52 Number of arcs = 52 Number of 2-arcs = 52 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {15,16}, {16,17}, {17,18}, {18,19}, {19,20}, {20,21}, {21,22}, {22,23}, {23,24}, {24,25}, {25,26}, {1,26} } Symmetric graph 2 of order 26 Valency 3 Diameter 5 Girth 6 Automorphism group of order 78 Number of arcs = 78 Number of 2-arcs = 156 2-arc-transitive false Edge-set { {1,3}, {4,5}, {7,15}, {6,7}, {16,23}, {10,17}, {6,12}, {8,10}, {6,24}, {18,25}, {11,18}, {12,20}, {13,19}, {8,14}, {21,24}, {9,12}, {5,13}, {8,26}, {17,24}, {1,19}, {20,26}, {20,22}, {14,21}, {2,21}, {15,22}, {9,16}, {23,26}, {11,14}, {3,23}, {2,9}, {5,25}, {17,19}, {4,22}, {1,7}, {2,25}, {4,10}, {13,16}, {15,18}, {3,11} } Symmetric graph 3 of order 26 Valency 4 Diameter 5 Girth 4 Automorphism group of order 104 Number of arcs = 104 Number of 2-arcs = 312 2-arc-transitive false Edge-set { {1,4}, {3,6}, {10,20}, {5,8}, {3,19}, {11,22}, {21,24}, {7,10}, {4,14}, {5,21}, {19,22}, {13,24}, {6,7}, {23,25}, {5,15}, {9,11}, {6,16}, {17,20}, {7,23}, {4,5}, {6,22}, {15,25}, {15,18}, {8,9}, {3,13}, {1,26}, {16,26}, {7,17}, {12,13}, {8,18}, {2,3}, {12,21}, {9,26}, {13,16}, {4,20}, {8,24}, {1,17}, {1,11}, {10,12}, {14,23}, {18,19}, {10,25}, {2,18}, {2,25}, {9,19}, {14,15}, {11,14}, {2,12}, {20,21}, {16,17}, {24,26}, {22,23} } Symmetric graph 4 of order 26 Valency 4 Diameter 3 Girth 6 Automorphism group of order 11232 Number of arcs = 104 Number of 2-arcs = 312 2-arc-transitive true Edge-set { {1,15}, {7,24}, {7,22}, {12,19}, {9,20}, {9,19}, {8,20}, {6,23}, {3,15}, {2,22}, {10,17}, {6,22}, {3,17}, {2,16}, {10,25}, {1,18}, {7,17}, {8,26}, {11,14}, {9,15}, {8,18}, {11,24}, {11,20}, {2,26}, {13,25}, {5,14}, {1,24}, {10,19}, {4,16}, {1,16}, {6,25}, {12,26}, {4,20}, {13,26}, {13,21}, {5,21}, {12,23}, {12,24}, {9,22}, {3,14}, {13,15}, {5,18}, {4,23}, {2,14}, {10,16}, {4,21}, {3,23}, {8,17}, {7,21}, {11,25}, {5,19}, {6,18} } Symmetric graph 5 of order 26 Valency 4 Diameter 6 Girth 4 Automorphism group of order 212992 Number of arcs = 104 Number of 2-arcs = 312 2-arc-transitive false Edge-set { {1,3}, {18,20}, {24,26}, {8,9}, {13,16}, {14,15}, {20,22}, {24,25}, {3,5}, {4,6}, {10,12}, {9,11}, {16,17}, {14,16}, {20,21}, {1,26}, {19,21}, {2,25}, {6,8}, {5,7}, {6,7}, {12,14}, {3,6}, {9,12}, {16,18}, {15,18}, {22,24}, {21,23}, {21,24}, {2,3}, {22,23}, {1,4}, {2,4}, {2,26}, {1,25}, {5,8}, {12,13}, {11,13}, {11,14}, {17,20}, {18,19}, {23,26}, {17,19}, {23,25}, {15,17}, {8,10}, {7,10}, {7,9}, {13,15}, {19,22}, {4,5}, {10,11} } Symmetric graph 6 of order 26 Valency 6 Diameter 3 Girth 4 Automorphism group of order 156 Number of arcs = 156 Number of 2-arcs = 780 2-arc-transitive false Edge-set { {1,3}, {2,7}, {2,10}, {1,19}, {9,12}, {1,26}, {4,9}, {2,4}, {10,16}, {5,25}, {3,22}, {2,22}, {10,17}, {8,25}, {1,8}, {1,9}, {18,26}, {4,5}, {13,21}, {18,19}, {7,9}, {23,26}, {4,24}, {20,21}, {11,18}, {2,20}, {10,11}, {2,25}, {3,10}, {22,24}, {17,23}, {8,13}, {16,23}, {19,25}, {3,12}, {16,22}, {17,25}, {8,15}, {6,24}, {21,23}, {9,15}, {6,26}, {4,21}, {1,21}, {9,18}, {7,26}, {24,25}, {11,20}, {11,13}, {16,18}, {5,7}, {18,24}, {17,20}, {6,11}, {14,15}, {20,26}, {3,6}, {14,22}, {8,10}, {3,23}, {19,22}, {12,17}, {15,21}, {5,23}, {13,19}, {12,19}, {15,24}, {6,14}, {15,17}, {7,14}, {4,11}, {7,16}, {6,8}, {13,16}, {12,14}, {14,20}, {5,12}, {5,13} } Symmetric graph 7 of order 26 Valency 8 Diameter 2 Girth 4 Automorphism group of order 425984 Number of arcs = 208 Number of 2-arcs = 1456 2-arc-transitive false Edge-set { {1,3}, {12,21}, {8,24}, {23,26}, {20,22}, {16,18}, {6,15}, {4,14}, {10,25}, {10,19}, {4,20}, {16,25}, {15,18}, {11,14}, {5,7}, {12,13}, {7,9}, {9,12}, {10,11}, {7,10}, {4,5}, {13,16}, {3,20}, {15,25}, {14,24}, {5,21}, {2,17}, {13,23}, {6,22}, {8,17}, {2,11}, {8,23}, {11,22}, {7,24}, {7,17}, {2,12}, {4,13}, {6,16}, {10,12}, {8,10}, {3,5}, {13,15}, {14,16}, {2,26}, {17,20}, {19,22}, {4,6}, {1,25}, {18,19}, {1,26}, {22,24}, {21,23}, {1,4}, {24,25}, {19,21}, {16,17}, {2,3}, {17,19}, {22,23}, {11,13}, {6,7}, {7,23}, {12,22}, {7,18}, {1,12}, {3,13}, {5,16}, {14,23}, {10,26}, {9,25}, {9,19}, {1,11}, {13,24}, {9,20}, {6,21}, {3,19}, {15,26}, {11,21}, {9,26}, {4,19}, {16,26}, {1,17}, {2,18}, {15,17}, {2,4}, {23,25}, {2,25}, {6,8}, {14,15}, {12,14}, {5,8}, {8,9}, {9,11}, {21,24}, {3,6}, {18,20}, {24,26}, {20,21}, {5,15}, {5,22}, {1,18}, {3,14}, {8,18}, {10,20} } Symmetric graph 8 of order 26 Valency 9 Diameter 3 Girth 4 Automorphism group of order 11232 Number of arcs = 234 Number of 2-arcs = 1872 2-arc-transitive true Edge-set { {1,14}, {8,24}, {12,22}, {12,16}, {9,25}, {9,23}, {8,15}, {11,23}, {2,15}, {13,22}, {5,17}, {3,22}, {1,17}, {7,16}, {7,25}, {3,26}, {1,19}, {7,20}, {7,26}, {9,21}, {8,21}, {10,18}, {9,17}, {10,24}, {11,22}, {11,19}, {2,20}, {13,19}, {5,20}, {4,17}, {13,24}, {6,24}, {2,19}, {10,20}, {4,19}, {13,20}, {5,22}, {5,16}, {4,25}, {1,25}, {6,14}, {10,22}, {11,17}, {12,25}, {9,14}, {9,26}, {8,19}, {6,26}, {3,19}, {10,26}, {6,21}, {3,21}, {2,18}, {10,23}, {10,14}, {11,16}, {12,21}, {12,15}, {9,18}, {6,20}, {2,25}, {3,16}, {2,21}, {10,21}, {8,23}, {11,18}, {2,23}, {13,14}, {12,18}, {8,14}, {13,23}, {5,15}, {8,22}, {12,17}, {4,22}, {13,17}, {6,16}, {3,25}, {4,15}, {13,18}, {6,17}, {3,24}, {4,18}, {4,24}, {1,20}, {8,25}, {12,14}, {11,26}, {5,23}, {7,23}, {7,15}, {1,22}, {5,26}, {2,24}, {4,26}, {5,25}, {4,14}, {1,26}, {6,19}, {3,20}, {1,23}, {6,15}, {8,16}, {1,21}, {7,18}, {9,16}, {11,15}, {11,21}, {5,24}, {7,14}, {10,15}, {9,24}, {13,16}, {3,18}, {7,19}, {12,20}, {2,17} } Symmetric graph 9 of order 26 Valency 12 Diameter 2 Girth 3 Automorphism group of order 638976 Number of arcs = 312 Number of 2-arcs = 3432 2-arc-transitive false Edge-set { {1,3}, {2,22}, {11,20}, {3,21}, {18,19}, {23,26}, {5,25}, {2,4}, {11,17}, {18,24}, {7,26}, {9,16}, {1,9}, {8,15}, {2,3}, {1,21}, {12,19}, {17,26}, {5,8}, {10,18}, {7,10}, {14,16}, {1,22}, {11,19}, {14,15}, {19,22}, {14,20}, {12,13}, {16,21}, {2,21}, {4,22}, {17,20}, {24,25}, {6,26}, {16,17}, {1,8}, {8,13}, {18,20}, {7,13}, {13,22}, {6,11}, {15,23}, {3,22}, {24,26}, {5,26}, {6,12}, {16,23}, {3,24}, {18,26}, {6,23}, {23,25}, {6,24}, {4,11}, {15,17}, {4,21}, {17,19}, {12,18}, {17,23}, {8,25}, {10,15}, {2,10}, {7,16}, {1,4}, {20,21}, {5,13}, {21,24}, {18,23}, {7,25}, {5,14}, {22,24}, {3,5}, {4,5}, {9,12}, {11,18}, {10,16}, {1,10}, {8,16}, {4,6}, {9,11}, {9,15}, {10,11}, {16,18}, {1,7}, {7,9}, {4,9}, {2,9}, {4,10}, {1,26}, {5,12}, {12,17}, {17,24}, {8,26}, {18,25}, {6,7}, {9,17}, {8,9}, {13,15}, {12,20}, {13,16}, {13,19}, {11,14}, {15,22}, {4,23}, {17,25}, {10,17}, {9,18}, {6,8}, {3,23}, {3,10}, {2,8}, {3,11}, {3,12}, {19,25}, {6,14}, {5,7}, {20,22}, {13,20}, {11,13}, {15,21}, {4,12}, {19,26}, {20,26}, {7,15}, {14,22}, {14,19}, {1,19}, {12,14}, {19,21}, {1,20}, {16,22}, {3,6}, {8,10}, {15,18}, {2,7}, {7,14}, {8,14}, {14,21}, {16,24}, {6,25}, {5,11}, {15,24}, {5,24}, {5,23}, {2,20}, {13,21}, {2,26}, {2,25}, {1,25}, {4,24}, {22,23}, {20,25}, {6,13}, {21,23}, {10,12}, {3,9}, {2,19} } Symmetric graph 10 of order 26 Valency 12 Diameter 3 Girth 4 Automorphism group of order 12454041600 Number of arcs = 312 Number of 2-arcs = 3432 2-arc-transitive true Edge-set { {1,4}, {3,5}, {4,7}, {6,8}, {8,12}, {5,9}, {7,15}, {7,10}, {11,16}, {10,14}, {16,23}, {12,20}, {9,17}, {6,15}, {9,11}, {15,19}, {13,18}, {5,24}, {2,19}, {18,26}, {5,21}, {14,22}, {14,23}, {9,20}, {7,17}, {6,11}, {12,13}, {20,24}, {17,21}, {6,13}, {1,10}, {8,25}, {12,22}, {4,21}, {3,13}, {10,25}, {8,24}, {12,17}, {2,18}, {16,26}, {2,21}, {14,20}, {9,15}, {7,13}, {11,24}, {14,15}, {1,23}, {22,25}, {1,11}, {3,11}, {4,19}, {18,23}, {1,8}, {19,26}, {16,22}, {9,23}, {3,10}, {5,25}, {4,24}, {3,17}, {2,14}, {6,20}, {1,15}, {13,25}, {22,24}, {16,17}, {2,6}, {3,26}, {10,21}, {4,16}, {5,18}, {12,26}, {20,21}, {8,19}, {7,22}, {8,9}, {2,3}, {11,14}, {4,6}, {1,26}, {23,25}, {18,22}, {18,20}, {17,19}, {5,7}, {10,12}, {14,17}, {13,16}, {15,18}, {16,20}, {3,8}, {2,24}, {7,11}, {4,25}, {21,26}, {19,23}, {10,18}, {19,22}, {9,13}, {12,15}, {2,9}, {1,5}, {6,10}, {5,14}, {8,16}, {3,22}, {15,24}, {7,26}, {17,25}, {13,21}, {11,19}, {10,19}, {21,23}, {1,20}, {6,23}, {4,12}, {3,20}, {2,12}, {5,16}, {8,18}, {6,22}, {15,25}, {9,26}, {1,17}, {13,24}, {11,21}, {13,19}, {24,26}, {4,14}, {7,23}, {8,14}, {3,23}, {5,12}, {10,16}, {11,18}, {6,26}, {20,25}, {4,9}, {1,22}, {17,24}, {15,21}, {1,13}, {2,25}, {2,7}, {2,16}, {8,21}, {12,23}, {5,19}, {10,24}, {11,25}, {14,26}, {7,20}, {4,18}, {9,22}, {6,17}, {3,15} } Symmetric graph 11 of order 26 Valency 13 Diameter 2 Girth 4 Automorphism group of order 77551576087265280000 Number of arcs = 338 Number of 2-arcs = 4056 2-arc-transitive true Edge-set { {1,14}, {6,23}, {13,15}, {13,22}, {7,14}, {1,18}, {8,23}, {5,18}, {12,23}, {6,14}, {13,19}, {6,15}, {7,24}, {12,17}, {6,22}, {13,26}, {7,18}, {13,14}, {1,23}, {1,22}, {8,14}, {2,19}, {4,26}, {11,18}, {5,22}, {12,14}, {5,23}, {6,19}, {6,18}, {13,23}, {7,15}, {12,15}, {13,24}, {1,20}, {11,25}, {5,17}, {12,21}, {6,26}, {12,22}, {13,18}, {13,17}, {7,22}, {7,23}, {8,19}, {1,26}, {8,18}, {2,23}, {9,15}, {3,21}, {10,26}, {4,17}, {11,22}, {4,18}, {5,14}, {5,26}, {12,18}, {11,23}, {12,19}, {7,19}, {1,24}, {5,15}, {6,24}, {7,20}, {8,16}, {10,20}, {4,25}, {11,16}, {5,21}, {11,17}, {12,26}, {12,25}, {6,17}, {13,21}, {7,26}, {1,19}, {2,15}, {1,17}, {8,22}, {2,14}, {9,19}, {3,24}, {2,16}, {9,21}, {3,25}, {10,17}, {3,26}, {4,22}, {4,21}, {11,26}, {10,18}, {11,14}, {4,23}, {5,19}, {1,15}, {8,20}, {11,15}, {12,24}, {13,20}, {1,16}, {2,25}, {3,20}, {10,24}, {4,16}, {10,25}, {11,21}, {11,20}, {5,25}, {12,16}, {6,21}, {13,25}, {7,17}, {8,15}, {9,24}, {1,21}, {8,26}, {2,18}, {9,23}, {3,15}, {2,20}, {9,25}, {2,21}, {3,17}, {3,16}, {10,21}, {9,26}, {10,22}, {3,18}, {4,14}, {10,23}, {11,19}, {8,24}, {4,15}, {5,24}, {6,20}, {7,16}, {8,25}, {9,20}, {10,16}, {10,15}, {4,20}, {11,24}, {5,16}, {12,20}, {6,25}, {13,16}, {7,21}, {2,24}, {1,25}, {8,17}, {2,22}, {9,14}, {3,19}, {9,16}, {8,21}, {9,17}, {2,26}, {3,22}, {9,18}, {10,14}, {3,23}, {4,19}, {10,19}, {4,24}, {5,20}, {6,16}, {7,25}, {2,17}, {9,22}, {3,14} } Symmetric graph 12 of order 26 Valency 24 Diameter 2 Girth 3 Automorphism group of order 51011754393600 Number of arcs = 624 Number of 2-arcs = 14352 2-arc-transitive false Edge-set { {1,3}, {2,23}, {4,6}, {3,26}, {5,24}, {5,7}, {23,25}, {2,6}, {8,25}, {6,21}, {8,10}, {1,26}, {1,5}, {3,7}, {22,26}, {1,9}, {7,24}, {12,22}, {9,12}, {2,25}, {2,4}, {4,8}, {21,23}, {6,10}, {2,11}, {4,11}, {4,21}, {10,25}, {14,23}, {10,11}, {11,14}, {1,24}, {3,5}, {22,24}, {5,9}, {24,26}, {5,12}, {7,12}, {3,13}, {9,24}, {5,13}, {12,26}, {1,12}, {3,20}, {15,26}, {12,13}, {9,20}, {13,15}, {4,25}, {6,23}, {6,8}, {6,11}, {8,11}, {8,14}, {10,21}, {10,14}, {19,23}, {6,16}, {11,25}, {6,19}, {8,16}, {2,14}, {2,10}, {4,14}, {15,25}, {2,17}, {10,19}, {14,16}, {11,21}, {15,19}, {16,17}, {7,26}, {5,22}, {7,9}, {7,13}, {9,22}, {9,13}, {20,22}, {9,15}, {12,24}, {12,20}, {12,15}, {5,16}, {7,18}, {9,26}, {1,13}, {7,22}, {16,22}, {9,18}, {1,20}, {3,15}, {3,12}, {20,24}, {5,15}, {1,17}, {1,18}, {3,19}, {16,20}, {15,18}, {13,24}, {17,22}, {16,18}, {18,19}, {21,25}, {8,23}, {19,21}, {10,16}, {11,23}, {11,19}, {11,16}, {11,15}, {11,17}, {4,10}, {14,25}, {14,21}, {10,15}, {14,17}, {8,18}, {17,21}, {10,20}, {2,19}, {4,16}, {8,21}, {10,23}, {18,23}, {11,20}, {15,23}, {6,17}, {6,14}, {6,15}, {8,17}, {2,18}, {4,19}, {4,20}, {13,23}, {6,22}, {18,21}, {15,17}, {17,20}, {16,25}, {18,20}, {13,17}, {3,22}, {12,16}, {12,18}, {3,9}, {13,26}, {13,22}, {9,16}, {13,18}, {13,19}, {20,26}, {1,15}, {7,20}, {15,24}, {12,17}, {19,24}, {12,14}, {12,21}, {16,24}, {5,18}, {3,17}, {9,14}, {13,21}, {17,26}, {7,19}, {5,20}, {7,15}, {7,17}, {18,22}, {9,19}, {14,24}, {5,21}, {16,26}, {5,8}, {7,23}, {17,19}, {14,18}, {20,21}, {16,19}, {10,17}, {14,20}, {19,25}, {2,16}, {8,19}, {16,23}, {11,18}, {2,21}, {2,15}, {4,17}, {4,15}, {17,25}, {10,18}, {14,19}, {4,13}, {22,25}, {14,15}, {7,10}, {18,25}, {8,20}, {10,22}, {15,21}, {20,23}, {11,13}, {11,22}, {6,7}, {8,24}, {8,9}, {3,21}, {10,26}, {19,22}, {15,20}, {7,14}, {21,24}, {13,16}, {12,19}, {1,22}, {1,16}, {3,18}, {3,16}, {18,26}, {9,17}, {13,20}, {1,7}, {3,24}, {18,24}, {5,19}, {5,17}, {1,19}, {15,22}, {8,26}, {1,23}, {10,12}, {14,22}, {9,21}, {8,12}, {12,23}, {17,24}, {3,14}, {21,26}, {4,22}, {9,25}, {9,11}, {6,24}, {12,25}, {2,12}, {8,13}, {22,23}, {4,7}, {24,25}, {10,13}, {2,8}, {4,23}, {4,18}, {17,23}, {6,20}, {6,18}, {2,20}, {16,21}, {6,25}, {20,25}, {6,13}, {8,22}, {2,13}, {8,15}, {2,9}, {2,3}, {4,26}, {7,11}, {11,24}, {3,10}, {14,26}, {7,25}, {2,24}, {5,23}, {11,26}, {1,11}, {4,5}, {1,14}, {1,10}, {3,8}, {23,26}, {5,10}, {1,25}, {5,26}, {19,26}, {5,14}, {7,21}, {7,16}, {1,21}, {9,23}, {3,11}, {3,6}, {2,5}, {4,9}, {13,25}, {6,12}, {1,4}, {3,25}, {4,12}, {6,9}, {2,26}, {2,22}, {10,24}, {2,7}, {4,24}, {1,6}, {5,11}, {1,8}, {3,23}, {5,25}, {6,26} } Symmetric graph 13 of order 26 Valency 25 Diameter 1 Girth 3 Automorphism group of order 403291461126605635584000000 Number of arcs = 650 Number of 2-arcs = 15600 2-arc-transitive true Edge-set { {1,2}, {10,21}, {6,19}, {5,16}, {12,25}, {13,23}, {22,26}, {9,12}, {1,21}, {3,18}, {9,16}, {6,7}, {13,24}, {15,19}, {4,18}, {11,16}, {5,21}, {12,19}, {1,14}, {5,8}, {4,12}, {1,11}, {23,24}, {14,22}, {6,17}, {10,24}, {13,22}, {20,26}, {2,14}, {5,17}, {8,12}, {1,15}, {5,9}, {12,21}, {13,18}, {16,26}, {21,25}, {19,23}, {9,20}, {7,21}, {2,18}, {16,17}, {8,21}, {7,17}, {10,13}, {19,25}, {18,23}, {11,23}, {2,22}, {10,25}, {18,24}, {15,26}, {3,4}, {6,23}, {9,11}, {2,21}, {18,20}, {7,16}, {21,22}, {19,20}, {4,9}, {11,21}, {5,18}, {12,16}, {6,14}, {5,24}, {12,15}, {1,4}, {3,5}, {7,13}, {13,26}, {4,26}, {3,11}, {12,14}, {10,14}, {5,6}, {11,12}, {5,20}, {7,12}, {11,24}, {6,16}, {24,25}, {3,13}, {9,26}, {7,14}, {5,13}, {7,8}, {13,15}, {10,19}, {6,18}, {3,16}, {9,25}, {14,17}, {5,10}, {15,22}, {4,20}, {8,17}, {7,23}, {4,8}, {11,15}, {6,12}, {14,26}, {12,24}, {5,19}, {12,18}, {3,26}, {2,4}, {11,17}, {9,14}, {1,16}, {23,25}, {22,23}, {9,17}, {18,22}, {16,20}, {17,19}, {1,9}, {6,24}, {14,24}, {6,15}, {4,24}, {2,15}, {4,17}, {1,8}, {8,15}, {18,25}, {16,23}, {16,25}, {9,23}, {8,18}, {15,16}, {3,21}, {14,16}, {10,15}, {12,23}, {1,22}, {3,17}, {9,10}, {1,6}, {8,24}, {4,15}, {4,11}, {14,23}, {6,9}, {21,24}, {20,24}, {6,22}, {13,16}, {25,26}, {5,22}, {1,12}, {11,25}, {2,23}, {19,22}, {2,26}, {11,20}, {2,7}, {7,24}, {13,14}, {2,20}, {8,22}, {15,20}, {16,22}, {15,25}, {4,23}, {17,18}, {10,16}, {9,13}, {21,26}, {14,18}, {2,10}, {8,11}, {4,25}, {1,19}, {3,7}, {7,19}, {2,11}, {14,19}, {12,26}, {1,3}, {11,13}, {4,21}, {11,19}, {17,23}, {10,22}, {17,25}, {10,23}, {20,22}, {2,17}, {10,17}, {6,20}, {20,21}, {7,20}, {3,14}, {1,13}, {3,12}, {4,7}, {14,20}, {5,7}, {12,22}, {1,20}, {1,5}, {1,23}, {20,25}, {7,18}, {19,21}, {18,19}, {2,8}, {4,16}, {21,23}, {17,20}, {7,10}, {15,17}, {7,25}, {11,22}, {10,12}, {17,26}, {3,10}, {1,24}, {3,15}, {9,19}, {18,21}, {16,19}, {3,8}, {9,15}, {6,13}, {13,19}, {18,26}, {4,6}, {8,26}, {17,24}, {6,25}, {10,26}, {3,6}, {3,20}, {1,18}, {3,22}, {13,17}, {11,14}, {2,5}, {1,25}, {5,15}, {14,25}, {5,23}, {8,20}, {7,15}, {2,3}, {13,21}, {19,26}, {8,14}, {8,10}, {13,25}, {23,26}, {15,18}, {8,19}, {6,8}, {15,24}, {12,17}, {8,13}, {7,11}, {2,13}, {2,9}, {10,11}, {2,6}, {2,25}, {5,26}, {24,26}, {8,23}, {6,21}, {19,24}, {8,16}, {2,24}, {3,23}, {9,24}, {14,21}, {16,18}, {3,19}, {9,21}, {3,9}, {5,14}, {10,20}, {2,12}, {1,17}, {12,13}, {11,26}, {16,24}, {3,24}, {8,25}, {17,21}, {4,13}, {5,12}, {1,26}, {4,22}, {22,24}, {14,15}, {4,5}, {17,22}, {9,22}, {6,11}, {15,23}, {3,25}, {7,9}, {1,10}, {13,20}, {7,26}, {20,23}, {7,22}, {11,18}, {2,16}, {6,10}, {4,10}, {12,20}, {1,7}, {5,25}, {10,18}, {2,19}, {5,11}, {9,18}, {16,21}, {15,21}, {4,19}, {22,25}, {8,9}, {6,26}, {4,14} } ................................................................... Symmetric connected graphs of order 27 Symmetric graph 1 of order 27 Valency 2 Diameter 13 Girth 27 Automorphism group of order 54 Number of arcs = 54 Number of 2-arcs = 54 2-arc-transitive true Edge-set { {1,4}, {6,7}, {9,10}, {12,15}, {14,17}, {16,20}, {19,24}, {23,25}, {3,27}, {2,5}, {4,8}, {7,11}, {10,13}, {15,18}, {17,21}, {20,22}, {24,26}, {1,25}, {3,6}, {5,9}, {8,12}, {11,14}, {13,16}, {18,19}, {21,23}, {22,27}, {2,26} } Symmetric graph 2 of order 27 Valency 4 Diameter 4 Girth 4 Automorphism group of order 108 Number of arcs = 108 Number of 2-arcs = 324 2-arc-transitive false Edge-set { {1,4}, {2,27}, {22,26}, {3,6}, {19,23}, {5,8}, {17,21}, {1,26}, {24,25}, {9,11}, {15,18}, {10,14}, {11,14}, {2,5}, {21,22}, {4,7}, {16,20}, {15,17}, {9,12}, {16,21}, {6,8}, {3,25}, {23,27}, {8,10}, {14,17}, {12,13}, {10,13}, {19,22}, {3,4}, {24,26}, {2,25}, {20,24}, {6,9}, {18,19}, {14,16}, {8,11}, {18,20}, {5,7}, {1,27}, {20,23}, {7,12}, {13,16}, {11,15}, {12,15}, {21,24}, {2,6}, {23,25}, {13,18}, {7,10}, {17,19}, {4,9}, {3,26}, {1,5}, {22,27} } Symmetric graph 3 of order 27 Valency 4 Diameter 4 Girth 3 Automorphism group of order 216 Number of arcs = 108 Number of 2-arcs = 324 2-arc-transitive false Edge-set { {1,7}, {8,18}, {19,27}, {4,9}, {11,20}, {3,19}, {7,22}, {4,21}, {1,13}, {3,17}, {7,26}, {8,25}, {14,19}, {2,22}, {10,18}, {24,27}, {6,17}, {10,26}, {8,21}, {9,20}, {2,20}, {3,11}, {16,25}, {14,25}, {4,15}, {11,17}, {6,24}, {6,10}, {15,21}, {2,9}, {1,16}, {13,17}, {18,26}, {5,20}, {2,12}, {12,22}, {4,23}, {6,13}, {15,24}, {9,23}, {7,16}, {21,25}, {5,18}, {12,27}, {10,24}, {1,23}, {5,8}, {14,16}, {22,26}, {13,23}, {12,19}, {5,11}, {15,27}, {3,14} } Symmetric graph 4 of order 27 Valency 6 Diameter 3 Girth 4 Automorphism group of order 324 Number of arcs = 162 Number of 2-arcs = 810 2-arc-transitive false Edge-set { {1,7}, {1,15}, {12,16}, {1,10}, {12,22}, {9,20}, {20,26}, {12,21}, {9,16}, {5,20}, {14,22}, {3,18}, {22,25}, {3,9}, {9,23}, {1,20}, {14,20}, {18,26}, {6,22}, {3,14}, {5,24}, {3,19}, {11,25}, {16,27}, {5,8}, {11,18}, {14,17}, {6,18}, {1,22}, {3,12}, {3,24}, {19,25}, {9,25}, {4,16}, {5,15}, {11,24}, {4,14}, {2,11}, {8,27}, {8,19}, {7,26}, {6,13}, {24,27}, {4,19}, {15,25}, {1,16}, {5,12}, {11,20}, {4,11}, {2,8}, {14,27}, {8,18}, {13,26}, {6,10}, {13,24}, {10,19}, {7,17}, {2,17}, {15,23}, {4,7}, {2,13}, {10,27}, {8,22}, {12,26}, {6,9}, {13,19}, {10,17}, {7,24}, {17,25}, {15,21}, {4,23}, {2,21}, {13,16}, {10,23}, {7,21}, {5,17}, {15,18}, {2,23}, {21,27}, {23,26}, {6,21} } Symmetric graph 5 of order 27 Valency 6 Diameter 3 Girth 3 Automorphism group of order 324 Number of arcs = 162 Number of 2-arcs = 810 2-arc-transitive false Edge-set { {1,7}, {1,15}, {11,17}, {1,10}, {11,23}, {8,21}, {20,26}, {11,19}, {8,17}, {5,20}, {13,23}, {3,18}, {22,25}, {2,8}, {8,24}, {1,20}, {13,21}, {18,26}, {6,22}, {2,13}, {5,24}, {3,19}, {10,27}, {16,27}, {4,7}, {12,18}, {13,18}, {6,18}, {1,22}, {2,11}, {3,24}, {19,25}, {8,27}, {4,16}, {4,14}, {12,24}, {6,13}, {7,26}, {9,19}, {9,25}, {5,15}, {15,17}, {21,27}, {24,27}, {4,19}, {14,27}, {1,16}, {4,11}, {12,20}, {6,10}, {13,26}, {9,18}, {15,25}, {5,12}, {15,22}, {6,21}, {14,24}, {7,16}, {10,21}, {23,26}, {3,9}, {6,9}, {12,26}, {9,22}, {11,25}, {5,8}, {15,20}, {2,21}, {14,19}, {7,23}, {10,16}, {4,23}, {3,14}, {17,25}, {14,16}, {7,20}, {10,22}, {2,23}, {3,12}, {5,17}, {2,17} } Symmetric graph 6 of order 27 Valency 6 Diameter 3 Girth 3 Automorphism group of order 1296 Number of arcs = 162 Number of 2-arcs = 810 2-arc-transitive false Edge-set { {1,7}, {1,15}, {11,16}, {1,10}, {11,22}, {8,20}, {19,25}, {11,21}, {8,16}, {4,19}, {13,22}, {2,17}, {24,27}, {8,23}, {3,19}, {13,20}, {17,25}, {5,24}, {4,23}, {2,21}, {12,26}, {18,26}, {6,9}, {13,17}, {5,17}, {3,24}, {2,23}, {21,27}, {7,26}, {6,18}, {6,13}, {5,15}, {3,12}, {9,25}, {8,27}, {4,14}, {14,18}, {23,26}, {6,21}, {13,26}, {3,18}, {6,10}, {5,12}, {3,9}, {15,25}, {14,27}, {4,11}, {14,23}, {10,20}, {7,18}, {9,17}, {15,24}, {12,19}, {5,8}, {3,14}, {11,25}, {10,27}, {4,7}, {14,21}, {10,18}, {7,22}, {9,24}, {15,19}, {12,17}, {16,27}, {6,22}, {1,20}, {10,24}, {7,19}, {9,21}, {15,16}, {12,23}, {4,16}, {1,22}, {20,26}, {2,11}, {1,16}, {22,25}, {5,20}, {2,8}, {2,13} } Symmetric graph 7 of order 27 Valency 6 Diameter 3 Girth 3 Automorphism group of order 1296 Number of arcs = 162 Number of 2-arcs = 810 2-arc-transitive false Edge-set { {1,7}, {4,8}, {12,17}, {9,25}, {15,18}, {10,17}, {19,26}, {9,16}, {13,18}, {22,27}, {11,17}, {20,26}, {2,19}, {7,16}, {16,25}, {14,18}, {23,27}, {3,22}, {21,26}, {2,20}, {2,7}, {5,19}, {1,10}, {8,16}, {17,25}, {1,16}, {24,27}, {3,23}, {5,8}, {6,22}, {4,11}, {2,21}, {3,7}, {5,20}, {2,10}, {1,13}, {12,20}, {18,25}, {1,17}, {9,26}, {4,16}, {12,25}, {3,24}, {6,8}, {6,23}, {5,11}, {4,14}, {15,21}, {5,21}, {3,10}, {2,13}, {10,20}, {12,23}, {1,18}, {9,27}, {4,17}, {12,26}, {15,25}, {9,19}, {6,24}, {6,11}, {5,14}, {13,21}, {15,24}, {3,13}, {11,20}, {10,23}, {4,18}, {12,27}, {15,26}, {7,19}, {9,22}, {6,14}, {14,21}, {13,24}, {11,23}, {15,27}, {8,19}, {7,22}, {14,24}, {8,22} } Symmetric graph 8 of order 27 Valency 6 Diameter 4 Girth 4 Automorphism group of order 181398528 Number of arcs = 162 Number of 2-arcs = 810 2-arc-transitive false Edge-set { {1,4}, {1,22}, {9,11}, {1,14}, {3,9}, {11,18}, {13,17}, {9,21}, {3,18}, {8,13}, {11,26}, {17,24}, {6,25}, {20,23}, {18,21}, {13,25}, {3,26}, {8,24}, {6,17}, {15,20}, {2,23}, {5,10}, {1,27}, {21,26}, {24,25}, {6,8}, {5,20}, {2,15}, {10,23}, {19,27}, {1,7}, {12,16}, {4,9}, {2,5}, {10,15}, {12,27}, {7,19}, {1,16}, {4,26}, {9,14}, {18,22}, {11,13}, {7,12}, {16,19}, {4,18}, {14,26}, {9,22}, {6,11}, {13,21}, {3,24}, {17,20}, {14,18}, {22,26}, {11,24}, {6,21}, {3,13}, {10,17}, {20,25}, {2,8}, {23,27}, {21,24}, {3,6}, {2,17}, {10,25}, {8,20}, {16,23}, {5,27}, {7,15}, {2,25}, {8,10}, {7,23}, {5,16}, {15,27}, {4,12}, {14,19}, {5,7}, {15,16}, {12,22}, {4,19}, {12,14}, {19,22} } Symmetric graph 9 of order 27 Valency 8 Diameter 2 Girth 3 Automorphism group of order 216 Number of arcs = 216 Number of 2-arcs = 1512 2-arc-transitive false Edge-set { {1,7}, {9,16}, {19,26}, {6,17}, {9,20}, {3,11}, {5,11}, {5,13}, {2,8}, {2,17}, {10,20}, {7,24}, {23,27}, {14,24}, {3,23}, {14,19}, {3,17}, {8,18}, {21,25}, {5,8}, {8,25}, {2,22}, {10,24}, {16,25}, {10,26}, {4,15}, {14,16}, {7,26}, {15,27}, {3,21}, {11,16}, {5,7}, {8,27}, {4,18}, {7,21}, {1,12}, {6,12}, {14,18}, {12,18}, {6,21}, {13,25}, {22,25}, {6,9}, {11,22}, {5,24}, {15,20}, {1,18}, {5,19}, {12,27}, {6,24}, {9,23}, {3,19}, {10,18}, {4,21}, {1,16}, {12,19}, {22,26}, {13,23}, {7,16}, {4,23}, {7,22}, {1,13}, {2,12}, {6,13}, {13,17}, {2,20}, {24,27}, {14,25}, {3,14}, {4,9}, {10,23}, {4,22}, {2,14}, {17,26}, {3,7}, {11,27}, {1,15}, {9,26}, {15,17}, {6,16}, {9,19}, {15,26}, {16,27}, {13,19}, {8,23}, {8,17}, {10,25}, {4,14}, {12,21}, {1,20}, {15,24}, {8,21}, {19,27}, {18,26}, {11,17}, {5,20}, {2,9}, {11,20}, {5,18}, {6,10}, {15,21}, {12,22}, {1,23}, {20,25}, {3,10}, {4,11}, {2,24}, {13,22} } Symmetric graph 10 of order 27 Valency 8 Diameter 2 Girth 3 Automorphism group of order 1296 Number of arcs = 216 Number of 2-arcs = 1512 2-arc-transitive false Edge-set { {1,4}, {5,9}, {5,21}, {8,13}, {2,4}, {8,10}, {4,27}, {2,14}, {3,17}, {4,9}, {5,20}, {14,16}, {3,15}, {9,19}, {5,7}, {16,20}, {6,27}, {19,24}, {9,13}, {2,5}, {8,11}, {4,25}, {1,25}, {16,22}, {3,6}, {18,19}, {12,13}, {2,26}, {8,15}, {11,25}, {22,25}, {7,19}, {6,7}, {12,23}, {12,26}, {2,13}, {2,17}, {4,8}, {4,20}, {14,18}, {3,14}, {9,21}, {11,22}, {6,19}, {23,26}, {13,17}, {8,20}, {3,18}, {18,21}, {9,14}, {21,22}, {9,11}, {12,15}, {1,26}, {7,15}, {1,6}, {17,24}, {10,13}, {17,20}, {20,24}, {3,5}, {5,25}, {16,23}, {16,19}, {2,27}, {18,22}, {11,14}, {7,12}, {6,26}, {3,25}, {19,23}, {10,26}, {23,27}, {1,13}, {2,16}, {10,22}, {11,27}, {13,18}, {8,21}, {1,18}, {6,21}, {12,24}, {15,17}, {24,25}, {11,23}, {12,25}, {6,8}, {4,19}, {22,26}, {7,20}, {7,10}, {17,21}, {20,22}, {11,15}, {7,14}, {17,23}, {10,14}, {3,27}, {5,26}, {21,23}, {18,24}, {9,12}, {15,16}, {1,15}, {10,27}, {24,27}, {1,16}, {10,24} } Symmetric graph 11 of order 27 Valency 8 Diameter 3 Girth 3 Automorphism group of order 1296 Number of arcs = 216 Number of 2-arcs = 1512 2-arc-transitive false Edge-set { {1,4}, {4,13}, {5,20}, {13,18}, {20,26}, {15,20}, {17,21}, {12,18}, {1,26}, {20,24}, {7,17}, {16,20}, {17,25}, {10,19}, {3,18}, {9,12}, {1,12}, {4,24}, {5,7}, {3,20}, {15,17}, {10,26}, {3,22}, {11,20}, {2,17}, {10,22}, {3,9}, {8,21}, {10,16}, {5,12}, {9,27}, {12,24}, {4,9}, {3,13}, {15,26}, {21,22}, {4,17}, {3,25}, {8,24}, {7,10}, {2,5}, {7,20}, {11,17}, {6,10}, {3,6}, {2,8}, {10,13}, {5,27}, {19,25}, {18,23}, {8,11}, {2,10}, {9,15}, {12,21}, {23,27}, {12,15}, {13,27}, {5,18}, {4,26}, {16,24}, {7,25}, {2,19}, {5,22}, {15,23}, {8,26}, {6,15}, {6,21}, {17,22}, {3,11}, {8,14}, {5,14}, {4,19}, {6,25}, {6,23}, {8,18}, {9,16}, {1,14}, {11,23}, {6,8}, {16,27}, {24,25}, {9,19}, {1,23}, {12,25}, {1,21}, {13,24}, {2,15}, {22,26}, {9,22}, {6,16}, {13,21}, {1,16}, {14,25}, {7,23}, {14,16}, {14,19}, {18,19}, {4,11}, {21,27}, {14,22}, {11,27}, {2,24}, {1,7}, {11,14}, {19,23}, {7,13}, {2,27}, {18,26} } Symmetric graph 12 of order 27 Valency 10 Diameter 2 Girth 3 Automorphism group of order 51840 Number of arcs = 270 Number of 2-arcs = 2430 2-arc-transitive false Edge-set { {1,2}, {2,20}, {9,16}, {20,25}, {9,10}, {6,23}, {17,24}, {1,25}, {1,10}, {6,11}, {12,17}, {16,19}, {2,3}, {7,15}, {4,14}, {1,16}, {2,11}, {12,16}, {19,27}, {2,26}, {12,15}, {14,27}, {23,26}, {11,24}, {17,20}, {9,20}, {5,22}, {13,21}, {8,13}, {2,23}, {16,24}, {20,27}, {9,26}, {12,23}, {24,27}, {21,26}, {11,18}, {6,9}, {12,22}, {13,27}, {18,22}, {3,6}, {7,27}, {4,26}, {15,25}, {10,14}, {6,25}, {10,17}, {3,18}, {8,19}, {23,25}, {7,23}, {16,20}, {3,9}, {4,24}, {21,25}, {10,18}, {6,17}, {3,27}, {7,21}, {4,18}, {15,26}, {6,19}, {2,17}, {3,12}, {14,21}, {18,23}, {3,24}, {15,19}, {17,19}, {5,21}, {18,21}, {8,9}, {5,6}, {1,22}, {1,13}, {11,13}, {1,19}, {11,15}, {12,14}, {15,20}, {7,11}, {1,3}, {5,16}, {3,21}, {10,24}, {7,8}, {4,5}, {2,14}, {17,21}, {18,20}, {5,10}, {8,24}, {5,15}, {9,22}, {6,13}, {19,26}, {9,14}, {10,13}, {22,25}, {3,15}, {7,17}, {4,20}, {22,26}, {11,14}, {8,25}, {4,6}, {18,19}, {2,8}, {16,23}, {11,16}, {22,27}, {13,26}, {12,13}, {5,27}, {4,12}, {8,18}, {5,8}, {13,20}, {10,15}, {14,25}, {24,25}, {8,12}, {4,7}, {14,19}, {17,22}, {1,4}, {1,7}, {2,5}, {24,26}, {7,9}, {23,27}, {10,23}, {11,22}, {16,21} } Symmetric graph 13 of order 27 Valency 12 Diameter 2 Girth 3 Automorphism group of order 1296 Number of arcs = 324 Number of 2-arcs = 3564 2-arc-transitive false Edge-set { {1,7}, {3,16}, {11,27}, {1,15}, {12,20}, {21,25}, {2,9}, {3,23}, {4,11}, {8,20}, {1,22}, {7,27}, {8,24}, {2,17}, {10,25}, {1,11}, {12,16}, {6,21}, {2,14}, {8,18}, {22,26}, {3,12}, {11,17}, {16,25}, {9,27}, {10,18}, {18,26}, {10,19}, {19,27}, {3,8}, {3,21}, {2,11}, {15,20}, {1,20}, {4,7}, {15,24}, {2,24}, {5,10}, {13,18}, {21,26}, {12,26}, {7,17}, {1,12}, {14,21}, {2,19}, {15,27}, {17,25}, {9,25}, {13,19}, {13,26}, {7,21}, {9,19}, {9,23}, {1,18}, {12,24}, {2,21}, {2,10}, {8,23}, {4,22}, {11,22}, {6,16}, {14,27}, {10,23}, {4,18}, {5,19}, {3,13}, {13,22}, {7,26}, {7,24}, {20,26}, {14,16}, {3,20}, {5,24}, {23,25}, {4,9}, {8,19}, {17,27}, {8,25}, {9,22}, {6,23}, {6,7}, {7,16}, {24,27}, {9,17}, {11,21}, {10,20}, {2,7}, {10,24}, {3,10}, {11,18}, {16,26}, {6,12}, {14,17}, {12,21}, {4,15}, {24,25}, {5,9}, {11,19}, {6,13}, {13,23}, {12,22}, {6,17}, {10,16}, {18,27}, {8,26}, {7,22}, {5,20}, {1,8}, {8,16}, {14,25}, {9,18}, {23,26}, {12,17}, {15,16}, {4,16}, {20,27}, {19,25}, {3,22}, {2,16}, {10,27}, {3,18}, {1,19}, {13,21}, {15,26}, {7,20}, {4,20}, {14,24}, {1,24}, {4,14}, {5,17}, {13,25}, {9,21}, {2,23}, {6,15}, {1,17}, {15,19}, {5,8}, {11,26}, {15,18}, {13,17}, {14,20}, {15,23}, {2,15}, {3,9}, {1,13}, {11,23}, {6,24}, {22,27}, {6,8}, {14,22}, {5,18}, {5,14}, {4,23}, {3,14}, {4,21}, {6,19}, {5,22}, {4,10}, {12,25}, {6,11}, {5,13}, {5,12} } Symmetric graph 14 of order 27 Valency 12 Diameter 2 Girth 3 Automorphism group of order 1296 Number of arcs = 324 Number of 2-arcs = 3564 2-arc-transitive false Edge-set { {1,5}, {2,17}, {8,18}, {11,19}, {1,9}, {20,22}, {7,19}, {10,18}, {3,15}, {17,23}, {18,25}, {9,12}, {6,14}, {18,26}, {15,16}, {16,22}, {12,19}, {4,14}, {20,27}, {3,19}, {22,27}, {13,19}, {13,23}, {21,25}, {2,26}, {21,22}, {4,19}, {4,25}, {10,20}, {9,25}, {10,14}, {13,18}, {15,21}, {1,8}, {12,24}, {6,22}, {14,18}, {15,27}, {9,24}, {14,22}, {7,18}, {11,15}, {3,7}, {5,11}, {13,24}, {11,21}, {4,9}, {9,15}, {14,24}, {15,17}, {8,27}, {13,17}, {12,16}, {6,12}, {23,27}, {13,25}, {1,16}, {2,12}, {7,22}, {4,15}, {20,24}, {17,20}, {6,13}, {21,23}, {5,9}, {14,26}, {1,22}, {2,19}, {4,24}, {6,23}, {23,25}, {2,14}, {22,26}, {16,19}, {4,10}, {3,20}, {16,27}, {2,10}, {3,8}, {6,7}, {11,23}, {10,15}, {3,24}, {8,23}, {17,25}, {4,23}, {20,25}, {1,6}, {2,23}, {1,20}, {1,11}, {10,21}, {5,13}, {21,26}, {5,22}, {7,27}, {11,13}, {9,21}, {9,26}, {14,16}, {4,8}, {5,7}, {11,26}, {5,24}, {8,25}, {1,21}, {2,4}, {9,17}, {11,18}, {6,8}, {3,5}, {5,26}, {3,27}, {2,9}, {8,16}, {12,17}, {12,14}, {6,27}, {24,25}, {10,22}, {11,16}, {14,20}, {16,26}, {3,10}, {4,16}, {12,20}, {19,27}, {1,13}, {5,17}, {12,27}, {3,11}, {6,18}, {10,17}, {3,18}, {2,7}, {8,11}, {8,14}, {24,26}, {7,10}, {15,23}, {1,25}, {8,20}, {7,17}, {3,4}, {2,6}, {7,13}, {18,24}, {19,23}, {5,20}, {7,26}, {2,21}, {9,16}, {10,25}, {1,12}, {12,13}, {6,21}, {15,22}, {19,26}, {17,27}, {5,15}, {18,21}, {19,24} } Symmetric graph 15 of order 27 Valency 12 Diameter 2 Girth 3 Automorphism group of order 725594112 Number of arcs = 324 Number of 2-arcs = 3564 2-arc-transitive false Edge-set { {1,7}, {1,18}, {4,8}, {10,18}, {4,16}, {10,25}, {9,25}, {13,16}, {7,21}, {11,16}, {21,25}, {17,25}, {13,26}, {1,11}, {7,17}, {8,24}, {14,17}, {24,26}, {8,19}, {12,17}, {19,26}, {1,19}, {7,27}, {2,14}, {4,12}, {10,19}, {9,18}, {8,18}, {18,27}, {9,22}, {15,18}, {22,27}, {2,22}, {9,20}, {2,16}, {20,27}, {11,26}, {2,20}, {2,8}, {4,20}, {2,10}, {3,8}, {5,15}, {11,22}, {13,20}, {11,21}, {11,20}, {2,21}, {7,16}, {9,16}, {16,25}, {3,16}, {7,23}, {5,17}, {23,25}, {14,27}, {3,23}, {5,9}, {5,23}, {5,11}, {3,17}, {12,27}, {3,21}, {3,9}, {2,12}, {5,21}, {3,11}, {3,13}, {6,9}, {12,16}, {14,23}, {14,19}, {12,23}, {5,19}, {12,24}, {14,21}, {3,24}, {12,19}, {12,21}, {3,19}, {8,17}, {18,26}, {17,26}, {8,25}, {1,17}, {7,26}, {6,17}, {12,26}, {6,18}, {15,25}, {1,24}, {6,7}, {3,15}, {6,24}, {6,12}, {6,14}, {3,10}, {6,19}, {1,12}, {5,10}, {1,14}, {15,17}, {8,20}, {10,17}, {20,26}, {15,22}, {15,24}, {6,22}, {15,20}, {10,24}, {6,20}, {10,22}, {15,19}, {1,22}, {10,20}, {1,20}, {16,27}, {9,26}, {2,18}, {8,27}, {1,9}, {4,18}, {10,27}, {15,27}, {1,13}, {4,22}, {4,10}, {6,13}, {4,15}, {6,11}, {2,15}, {9,23}, {13,18}, {23,27}, {9,21}, {11,18}, {21,27}, {13,23}, {13,22}, {4,23}, {13,21}, {4,21}, {11,23}, {2,23}, {2,7}, {5,16}, {11,25}, {4,7}, {13,25}, {4,14}, {5,13}, {7,24}, {14,16}, {24,25}, {7,19}, {19,25}, {14,24}, {5,24}, {5,8}, {14,26}, {8,22}, {22,26} } Symmetric graph 16 of order 27 Valency 16 Diameter 2 Girth 3 Automorphism group of order 51840 Number of arcs = 432 Number of 2-arcs = 6480 2-arc-transitive false Edge-set { {1,5}, {4,15}, {5,21}, {13,16}, {20,25}, {15,19}, {18,21}, {11,18}, {2,26}, {20,22}, {9,17}, {16,21}, {16,25}, {12,19}, {1,18}, {7,12}, {1,11}, {6,24}, {6,7}, {2,20}, {13,17}, {10,27}, {3,24}, {11,19}, {2,18}, {11,22}, {2,9}, {9,21}, {12,16}, {4,12}, {9,26}, {12,22}, {4,7}, {5,11}, {3,14}, {14,26}, {19,22}, {6,20}, {6,17}, {10,18}, {3,26}, {8,23}, {8,10}, {3,5}, {7,21}, {11,16}, {6,12}, {1,6}, {2,7}, {11,13}, {6,27}, {19,27}, {18,24}, {9,11}, {2,12}, {9,13}, {12,20}, {24,27}, {7,24}, {12,13}, {13,26}, {7,15}, {11,21}, {5,17}, {4,27}, {17,24}, {7,27}, {2,21}, {14,20}, {17,19}, {10,14}, {3,19}, {8,12}, {1,10}, {5,24}, {1,25}, {14,23}, {8,25}, {10,23}, {5,15}, {4,21}, {19,26}, {18,22}, {7,11}, {2,11}, {9,14}, {4,14}, {5,19}, {6,26}, {6,22}, {7,18}, {11,26}, {8,19}, {21,23}, {8,16}, {3,12}, {1,15}, {11,24}, {6,9}, {18,27}, {24,26}, {9,20}, {12,17}, {3,23}, {8,15}, {15,22}, {9,18}, {12,26}, {7,26}, {16,26}, {22,25}, {7,19}, {10,15}, {3,21}, {13,23}, {8,20}, {3,10}, {3,15}, {23,26}, {8,22}, {6,19}, {6,18}, {17,20}, {17,27}, {10,21}, {3,16}, {8,17}, {4,16}, {9,25}, {12,23}, {4,8}, {5,10}, {15,21}, {4,22}, {5,9}, {1,17}, {14,27}, {9,23}, {1,8}, {15,16}, {21,25}, {13,19}, {18,20}, {21,24}, {7,16}, {1,13}, {6,11}, {20,27}, {14,24}, {2,14}, {1,22}, {16,23}, {1,19}, {14,18}, {11,25}, {2,23}, {5,25}, {3,7}, {11,15}, {19,24}, {9,10}, {23,25}, {2,16}, {13,25}, {12,27}, {1,24}, {9,24}, {7,22}, {2,22}, {21,26}, {16,22}, {10,25}, {4,18}, {17,23}, {5,8}, {4,10}, {5,16}, {4,25}, {7,14}, {2,25}, {14,21}, {16,19}, {12,14}, {10,20}, {3,17}, {3,8}, {2,4}, {22,27}, {1,9}, {20,23}, {18,25}, {2,13}, {13,20}, {15,27}, {8,27}, {1,27}, {5,23}, {15,18}, {5,26}, {5,13}, {6,14}, {10,24}, {2,6}, {3,4}, {3,27}, {15,24}, {13,22}, {6,13}, {1,20}, {15,25}, {8,13}, {17,26}, {10,17}, {4,23}, {14,17}, {4,20} } Symmetric graph 17 of order 27 Valency 16 Diameter 2 Girth 3 Automorphism group of order 2177280 Number of arcs = 432 Number of 2-arcs = 6480 2-arc-transitive false Edge-set { {1,5}, {3,5}, {19,25}, {3,4}, {21,25}, {14,26}, {13,17}, {2,4}, {21,27}, {13,26}, {13,16}, {3,14}, {7,20}, {2,10}, {2,6}, {20,27}, {13,25}, {15,16}, {2,14}, {9,20}, {2,12}, {4,21}, {3,21}, {9,18}, {6,23}, {20,24}, {1,6}, {20,26}, {15,25}, {15,18}, {2,13}, {9,19}, {1,12}, {6,21}, {3,20}, {8,18}, {6,22}, {20,23}, {16,27}, {4,13}, {16,21}, {8,11}, {4,26}, {10,15}, {5,18}, {19,26}, {15,27}, {14,18}, {1,13}, {8,19}, {1,11}, {6,20}, {2,20}, {8,17}, {5,22}, {19,23}, {16,26}, {4,15}, {18,21}, {7,11}, {6,26}, {12,15}, {4,18}, {9,25}, {2,27}, {9,13}, {12,16}, {17,24}, {7,22}, {14,27}, {1,24}, {3,8}, {11,25}, {14,17}, {1,15}, {8,21}, {3,11}, {5,20}, {2,19}, {7,17}, {5,24}, {19,22}, {18,26}, {6,15}, {18,20}, {7,10}, {6,25}, {12,14}, {4,17}, {9,27}, {1,27}, {8,13}, {11,16}, {16,24}, {9,22}, {1,23}, {2,8}, {11,27}, {15,20}, {12,23}, {5,10}, {6,9}, {3,15}, {5,19}, {7,21}, {24,26}, {13,22}, {3,10}, {1,19}, {7,16}, {4,24}, {21,22}, {18,25}, {6,14}, {17,20}, {9,10}, {5,25}, {11,14}, {6,17}, {8,27}, {1,26}, {8,15}, {11,18}, {16,23}, {9,24}, {3,23}, {2,7}, {10,27}, {15,19}, {12,22}, {5,12}, {6,8}, {4,19}, {24,25}, {15,22}, {1,18}, {4,23}, {8,26}, {1,21}, {17,25}, {9,16}, {5,14}, {11,20}, {21,24}, {17,19}, {9,12}, {5,27}, {11,13}, {6,16}, {3,26}, {7,15}, {10,18}, {18,23}, {8,24}, {3,22}, {1,7}, {10,26}, {14,19}, {11,22}, {4,12}, {5,8}, {23,25}, {15,24}, {1,17}, {7,26}, {17,27}, {5,13}, {11,19}, {4,27}, {7,14}, {16,19}, {10,13}, {8,12}, {3,25}, {18,22}, {5,16}, {10,17}, {8,23}, {2,22}, {1,9}, {12,26}, {14,21}, {11,24}, {4,11}, {5,7}, {23,27}, {14,24}, {3,17}, {7,25}, {10,19}, {9,14}, {2,25}, {17,22}, {3,9}, {12,17}, {2,24}, {7,23}, {13,21}, {6,11}, {12,25}, {10,24}, {4,7}, {22,27}, {14,23}, {3,16}, {10,21}, {13,20}, {6,10}, {10,23}, {4,9}, {2,16}, {22,26}, {13,23}, {12,21}, {2,18}, {12,20} } Symmetric graph 18 of order 27 Valency 18 Diameter 2 Girth 3 Automorphism group of order 286708355039232000 Number of arcs = 486 Number of 2-arcs = 8262 2-arc-transitive false Edge-set { {1,7}, {1,9}, {11,17}, {1,8}, {11,16}, {10,20}, {20,26}, {11,18}, {10,19}, {20,25}, {12,23}, {2,19}, {23,26}, {2,8}, {10,21}, {20,27}, {12,22}, {1,19}, {23,25}, {2,7}, {5,21}, {2,22}, {1,12}, {17,26}, {5,8}, {12,18}, {12,24}, {3,19}, {23,27}, {2,9}, {4,21}, {1,22}, {1,11}, {17,25}, {5,7}, {12,17}, {5,24}, {3,13}, {2,16}, {4,12}, {11,21}, {8,26}, {13,18}, {21,27}, {6,21}, {3,22}, {1,10}, {17,27}, {5,9}, {12,16}, {4,24}, {3,15}, {1,16}, {4,11}, {11,20}, {7,26}, {13,17}, {21,26}, {5,18}, {6,13}, {10,24}, {12,25}, {15,21}, {3,20}, {8,18}, {24,27}, {3,9}, {6,24}, {3,14}, {3,16}, {4,10}, {11,19}, {9,26}, {13,16}, {21,25}, {4,18}, {6,15}, {10,23}, {11,25}, {15,20}, {2,20}, {8,17}, {24,26}, {3,8}, {13,27}, {14,24}, {6,19}, {7,21}, {3,23}, {2,10}, {18,27}, {6,9}, {10,16}, {6,18}, {6,14}, {10,22}, {10,25}, {15,19}, {1,20}, {8,16}, {24,25}, {3,7}, {15,27}, {14,23}, {5,19}, {7,20}, {2,23}, {2,12}, {18,26}, {6,8}, {10,18}, {9,24}, {6,22}, {1,14}, {3,17}, {5,10}, {12,19}, {9,27}, {14,16}, {19,25}, {14,27}, {14,22}, {4,19}, {7,19}, {1,23}, {2,11}, {18,25}, {6,7}, {10,17}, {9,23}, {5,22}, {1,13}, {2,17}, {5,12}, {12,21}, {8,27}, {14,18}, {19,27}, {6,16}, {4,14}, {11,22}, {10,26}, {13,19}, {1,21}, {9,16}, {22,25}, {9,22}, {4,22}, {1,15}, {1,17}, {5,11}, {12,20}, {7,27}, {14,17}, {19,26}, {5,16}, {4,13}, {11,24}, {12,26}, {13,21}, {3,21}, {9,18}, {22,27}, {14,25}, {15,22}, {4,20}, {8,19}, {1,24}, {3,11}, {16,25}, {4,7}, {4,16}, {4,15}, {11,23}, {11,26}, {13,20}, {2,21}, {9,17}, {22,26}, {13,25}, {15,24}, {6,20}, {8,21}, {3,24}, {3,10}, {16,27}, {4,9}, {7,22}, {4,23}, {2,15}, {1,18}, {6,11}, {7,25}, {15,17}, {15,25}, {15,23}, {5,20}, {8,20}, {2,24}, {3,12}, {16,26}, {4,8}, {7,24}, {6,23}, {2,14}, {3,18}, {6,10}, {9,25}, {15,16}, {4,17}, {5,15}, {11,27}, {14,20}, {7,17}, {7,23}, {5,23}, {2,13}, {2,18}, {6,12}, {8,25}, {15,18}, {6,17}, {5,14}, {10,27}, {14,19}, {7,16}, {15,26}, {13,23}, {9,20}, {5,17}, {5,13}, {12,27}, {14,21}, {7,18}, {14,26}, {13,22}, {9,19}, {8,23}, {13,26}, {13,24}, {9,21}, {8,22}, {8,24} } Symmetric graph 19 of order 27 Valency 24 Diameter 2 Girth 3 Automorphism group of order 3656994324480 Number of arcs = 648 Number of 2-arcs = 14904 2-arc-transitive false Edge-set { {1,4}, {4,27}, {3,26}, {22,27}, {3,21}, {6,24}, {20,25}, {3,22}, {18,21}, {6,18}, {4,25}, {2,26}, {2,17}, {17,23}, {6,19}, {3,6}, {18,25}, {7,18}, {4,9}, {7,26}, {2,9}, {23,27}, {3,19}, {5,24}, {20,27}, {5,9}, {8,27}, {1,9}, {8,16}, {16,26}, {2,5}, {6,26}, {2,25}, {7,23}, {9,19}, {7,11}, {9,13}, {10,27}, {3,15}, {11,24}, {13,20}, {5,10}, {15,27}, {1,22}, {16,21}, {6,16}, {5,25}, {1,17}, {17,22}, {6,21}, {10,25}, {1,15}, {12,22}, {14,21}, {4,10}, {15,26}, {8,12}, {7,14}, {8,24}, {7,20}, {1,27}, {24,26}, {2,20}, {5,23}, {19,27}, {1,11}, {13,16}, {10,16}, {5,15}, {11,20}, {12,13}, {10,15}, {15,24}, {19,22}, {11,21}, {6,14}, {23,25}, {12,17}, {15,17}, {19,25}, {14,22}, {21,23}, {3,4}, {18,26}, {8,18}, {4,7}, {8,26}, {2,7}, {1,19}, {3,9}, {2,4}, {19,23}, {11,19}, {4,14}, {23,26}, {10,18}, {13,18}, {4,22}, {3,11}, {14,24}, {20,23}, {12,21}, {10,14}, {11,13}, {13,22}, {2,12}, {14,17}, {11,17}, {6,13}, {21,26}, {2,24}, {17,20}, {5,17}, {6,27}, {1,25}, {1,16}, {16,22}, {5,21}, {4,20}, {12,26}, {8,15}, {7,24}, {8,19}, {14,25}, {1,23}, {6,12}, {15,21}, {10,24}, {14,19}, {11,23}, {2,14}, {3,16}, {5,18}, {18,20}, {4,12}, {13,26}, {2,22}, {16,19}, {9,21}, {8,10}, {9,14}, {8,23}, {16,23}, {5,19}, {3,13}, {18,22}, {1,18}, {4,16}, {3,25}, {9,20}, {7,12}, {11,27}, {12,24}, {14,20}, {5,11}, {13,27}, {5,26}, {6,10}, {15,25}, {5,27}, {3,27}, {5,16}, {16,20}, {5,12}, {1,24}, {7,19}, {9,11}, {7,15}, {9,24}, {3,18}, {6,20}, {12,25}, {2,13}, {13,19}, {11,22}, {15,20}, {18,24}, {8,22}, {17,27}, {9,17}, {6,8}, {9,25}, {1,8}, {22,26}, {2,21}, {4,23}, {19,26}, {4,8}, {3,8}, {21,24}, {10,20}, {12,14}, {14,23}, {2,11}, {13,17}, {12,16}, {5,14}, {13,23}, {2,10}, {14,18}, {2,19}, {5,22}, {1,20}, {5,13}, {7,25}, {7,17}, {6,9}, {21,27}, {3,10}, {20,24}, {3,5}, {18,27}, {5,7}, {4,15}, {12,19}, {11,14}, {10,13}, {15,22}, {1,12}, {14,16}, {7,16}, {16,25}, {1,5}, {6,15}, {24,25}, {3,7}, {9,18}, {9,26}, {6,23}, {10,17}, {20,22}, {6,22}, {22,25}, {1,21}, {21,25}, {8,25}, {1,7}, {8,17}, {6,7}, {1,10}, {17,26}, {11,16}, {12,15}, {2,6}, {10,19}, {24,27}, {15,16}, {3,20}, {12,18}, {3,12}, {9,22}, {8,21}, {9,10}, {10,23}, {15,19}, {14,26}, {3,24}, {16,24}, {5,20}, {12,27}, {3,14}, {2,18}, {4,17}, {17,19}, {6,11}, {13,21}, {10,22}, {1,13}, {9,15}, {7,10}, {13,25}, {7,13}, {8,13}, {10,26}, {2,15}, {4,21}, {11,25}, {6,17}, {6,25}, {7,22}, {14,27}, {3,23}, {18,23}, {8,11}, {1,26}, {2,23}, {2,16}, {3,17}, {18,19}, {4,18}, {4,26}, {4,19}, {12,23}, {4,11}, {9,12}, {8,14}, {11,26}, {8,20}, {2,27}, {17,21}, {7,21}, {15,18}, {11,15}, {13,24}, {17,25}, {2,8}, {1,6}, {21,22}, {10,21}, {9,27}, {9,16}, {5,8}, {20,26}, {4,24}, {11,18}, {15,23}, {19,24}, {12,20}, {16,27}, {7,27}, {4,13}, {9,23}, {17,24}, {1,14} } Symmetric graph 20 of order 27 Valency 26 Diameter 1 Girth 3 Automorphism group of order 10888869450418352160768000000 Number of arcs = 702 Number of 2-arcs = 17550 2-arc-transitive true Edge-set { {1,2}, {1,26}, {10,11}, {1,9}, {8,10}, {2,27}, {19,20}, {1,23}, {10,18}, {2,7}, {17,19}, {22,26}, {9,11}, {3,25}, {1,17}, {5,10}, {2,24}, {19,27}, {12,26}, {11,16}, {3,8}, {9,19}, {4,8}, {23,27}, {18,20}, {11,15}, {7,12}, {1,8}, {10,26}, {2,18}, {14,19}, {6,26}, {6,11}, {3,22}, {9,13}, {8,21}, {10,27}, {20,25}, {7,15}, {12,17}, {3,23}, {1,18}, {7,20}, {13,17}, {17,22}, {5,9}, {24,25}, {5,27}, {20,24}, {12,13}, {16,21}, {1,7}, {10,17}, {2,9}, {8,19}, {24,26}, {11,27}, {3,16}, {4,9}, {8,15}, {4,27}, {15,20}, {15,19}, {4,12}, {21,23}, {18,22}, {7,14}, {3,17}, {2,22}, {11,25}, {5,12}, {16,24}, {8,13}, {21,26}, {15,17}, {1,24}, {12,25}, {2,16}, {4,26}, {18,23}, {14,18}, {6,7}, {9,14}, {6,25}, {2,6}, {13,21}, {21,22}, {10,14}, {1,12}, {10,16}, {2,8}, {19,26}, {23,26}, {11,18}, {3,7}, {6,9}, {6,8}, {22,27}, {9,20}, {10,15}, {20,23}, {13,18}, {5,7}, {17,24}, {20,22}, {5,25}, {3,5}, {13,20}, {14,17}, {19,24}, {12,16}, {16,23}, {4,11}, {14,21}, {6,10}, {7,21}, {5,8}, {1,6}, {11,13}, {15,16}, {3,4}, {19,23}, {1,13}, {10,21}, {2,10}, {19,25}, {7,26}, {11,17}, {3,9}, {9,17}, {24,27}, {20,27}, {12,15}, {4,23}, {15,18}, {4,7}, {19,22}, {23,25}, {2,5}, {17,25}, {21,24}, {12,18}, {14,16}, {2,4}, {12,14}, {21,25}, {8,16}, {3,6}, {10,13}, {7,18}, {1,4}, {21,27}, {1,5}, {1,21}, {10,22}, {2,14}, {3,19}, {2,26}, {11,19}, {3,11}, {9,12}, {8,27}, {20,26}, {15,23}, {8,23}, {18,26}, {6,22}, {22,25}, {5,13}, {17,20}, {5,24}, {12,20}, {13,16}, {11,14}, {8,11}, {6,14}, {13,24}, {7,10}, {4,15}, {2,21}, {12,24}, {16,27}, {1,20}, {14,22}, {1,14}, {3,10}, {2,19}, {4,19}, {16,26}, {11,23}, {3,15}, {9,26}, {3,27}, {15,27}, {13,23}, {18,21}, {7,22}, {9,25}, {5,17}, {7,17}, {9,24}, {8,25}, {6,18}, {13,25}, {7,27}, {4,16}, {6,21}, {2,12}, {16,19}, {5,20}, {14,26}, {6,13}, {1,25}, {1,16}, {10,23}, {2,15}, {12,19}, {3,26}, {1,11}, {3,20}, {9,10}, {17,27}, {5,15}, {9,23}, {8,18}, {15,22}, {5,22}, {17,21}, {14,24}, {8,12}, {6,23}, {7,11}, {4,24}, {11,21}, {12,22}, {9,16}, {10,20}, {4,14}, {13,26}, {18,25}, {4,21}, {1,10}, {10,25}, {2,17}, {5,19}, {5,26}, {11,24}, {3,13}, {9,15}, {1,27}, {15,25}, {2,23}, {18,19}, {8,22}, {5,18}, {17,23}, {7,24}, {8,14}, {6,16}, {7,13}, {4,17}, {12,27}, {16,20}, {6,20}, {14,27}, {13,19}, {2,25}, {9,21}, {14,20}, {10,19}, {2,11}, {7,19}, {8,26}, {11,26}, {3,18}, {9,18}, {6,27}, {15,21}, {5,23}, {18,24}, {1,22}, {5,11}, {17,26}, {3,24}, {8,17}, {6,12}, {7,16}, {4,10}, {12,21}, {16,22}, {8,20}, {13,22}, {4,25}, {3,21}, {14,23}, {16,25}, {2,3}, {1,19}, {26,27}, {11,20}, {3,12}, {7,9}, {9,27}, {15,24}, {23,24}, {18,27}, {4,22}, {5,14}, {17,18}, {6,24}, {8,9}, {6,15}, {7,8}, {4,13}, {10,12}, {2,20}, {13,14}, {7,25}, {19,21}, {14,15}, {16,17}, {15,26}, {11,12}, {1,3}, {9,22}, {25,27}, {13,15}, {12,23}, {16,18}, {22,23}, {5,6}, {6,17}, {22,24}, {8,24}, {4,6}, {7,23}, {4,5}, {20,21}, {2,13}, {25,26}, {3,14}, {5,16}, {13,27}, {1,15}, {4,18}, {11,22}, {5,21}, {10,24}, {6,19}, {4,20}, {14,25} } ................................................................... Symmetric connected graphs of order 28 Symmetric graph 1 of order 28 Valency 2 Diameter 14 Girth 28 Automorphism group of order 56 Number of arcs = 56 Number of 2-arcs = 56 2-arc-transitive true Edge-set { {1,3}, {20,21}, {10,12}, {1,28}, {17,20}, {7,10}, {26,28}, {15,17}, {6,7}, {24,26}, {13,15}, {4,6}, {22,24}, {11,13}, {2,4}, {19,22}, {9,11}, {2,27}, {18,19}, {8,9}, {25,27}, {16,18}, {5,8}, {23,25}, {14,16}, {3,5}, {21,23}, {12,14} } Symmetric graph 2 of order 28 Valency 3 Diameter 4 Girth 7 Automorphism group of order 336 Number of arcs = 84 Number of 2-arcs = 168 2-arc-transitive true Edge-set { {1,6}, {10,13}, {14,26}, {1,28}, {4,10}, {17,26}, {13,18}, {5,14}, {1,15}, {17,24}, {6,18}, {22,28}, {4,17}, {9,26}, {13,27}, {2,14}, {7,24}, {18,21}, {10,22}, {5,22}, {15,24}, {6,9}, {20,28}, {4,8}, {7,12}, {21,25}, {7,27}, {2,21}, {5,19}, {11,15}, {2,12}, {11,25}, {12,20}, {8,25}, {9,23}, {3,27}, {3,19}, {11,19}, {16,20}, {8,16}, {16,23}, {3,23} } Symmetric graph 3 of order 28 Valency 4 Diameter 4 Girth 6 Automorphism group of order 672 Number of arcs = 112 Number of 2-arcs = 336 2-arc-transitive true Edge-set { {1,17}, {14,20}, {14,18}, {21,28}, {3,27}, {19,21}, {13,27}, {9,23}, {12,22}, {2,24}, {9,27}, {4,12}, {22,24}, {7,15}, {16,23}, {10,25}, {6,11}, {8,13}, {15,17}, {15,24}, {21,23}, {1,25}, {6,20}, {8,10}, {11,15}, {7,9}, {5,7}, {8,16}, {16,18}, {4,26}, {5,25}, {10,28}, {7,14}, {6,8}, {12,16}, {2,18}, {4,28}, {3,25}, {10,24}, {6,26}, {3,11}, {9,26}, {5,12}, {5,19}, {1,20}, {3,18}, {2,26}, {11,21}, {13,19}, {13,17}, {1,23}, {20,22}, {2,19}, {4,17}, {14,28}, {22,27} } Symmetric graph 4 of order 28 Valency 4 Diameter 4 Girth 4 Automorphism group of order 1792 Number of arcs = 112 Number of 2-arcs = 336 2-arc-transitive false Edge-set { {1,3}, {1,4}, {5,7}, {5,8}, {8,19}, {9,11}, {7,19}, {9,12}, {12,23}, {24,26}, {14,16}, {11,23}, {24,25}, {14,15}, {10,25}, {15,28}, {1,27}, {16,28}, {18,20}, {10,26}, {2,27}, {18,19}, {2,13}, {4,19}, {1,13}, {3,5}, {4,20}, {6,17}, {22,24}, {3,6}, {5,17}, {22,23}, {8,23}, {7,9}, {8,24}, {10,21}, {9,21}, {26,27}, {7,10}, {26,28}, {12,28}, {11,14}, {12,27}, {13,25}, {14,25}, {11,13}, {4,15}, {16,18}, {3,15}, {2,17}, {2,18}, {16,17}, {20,22}, {6,21}, {6,22}, {20,21} } Symmetric graph 5 of order 28 Valency 4 Diameter 7 Girth 4 Automorphism group of order 458752 Number of arcs = 112 Number of 2-arcs = 336 2-arc-transitive false Edge-set { {1,15}, {6,20}, {8,19}, {9,23}, {11,23}, {12,24}, {12,25}, {13,27}, {2,28}, {1,27}, {2,15}, {1,16}, {4,16}, {4,17}, {6,17}, {5,18}, {5,20}, {6,19}, {8,20}, {7,19}, {7,21}, {7,22}, {10,21}, {9,22}, {10,23}, {9,24}, {11,24}, {12,23}, {11,25}, {12,26}, {14,26}, {11,26}, {13,26}, {14,25}, {14,27}, {13,28}, {2,27}, {1,28}, {2,16}, {4,15}, {3,16}, {3,18}, {3,15}, {3,17}, {4,18}, {6,18}, {5,17}, {5,19}, {7,20}, {8,21}, {8,22}, {10,22}, {9,21}, {10,24}, {13,25}, {14,28} } Symmetric graph 6 of order 28 Valency 6 Diameter 4 Girth 4 Automorphism group of order 168 Number of arcs = 168 Number of 2-arcs = 840 2-arc-transitive false Edge-set { {1,3}, {2,7}, {23,26}, {8,17}, {1,24}, {19,26}, {17,20}, {15,18}, {2,11}, {7,25}, {18,23}, {10,19}, {13,20}, {9,15}, {11,14}, {16,21}, {10,12}, {6,8}, {5,24}, {1,19}, {16,26}, {12,17}, {3,13}, {9,27}, {8,14}, {11,21}, {4,10}, {6,28}, {5,7}, {3,22}, {5,12}, {3,6}, {2,27}, {24,25}, {18,28}, {7,10}, {13,23}, {19,22}, {9,20}, {5,15}, {6,11}, {8,26}, {4,21}, {1,12}, {3,25}, {22,27}, {17,24}, {1,28}, {2,4}, {2,23}, {26,27}, {21,24}, {20,25}, {18,19}, {13,16}, {12,22}, {9,11}, {4,14}, {10,28}, {6,23}, {5,27}, {2,20}, {15,25}, {11,18}, {7,13}, {22,23}, {1,8}, {14,19}, {20,21}, {10,16}, {12,13}, {8,9}, {4,5}, {6,16}, {17,27}, {14,24}, {21,28}, {4,26}, {16,17}, {7,18}, {3,9}, {14,15}, {25,28}, {15,22} } Symmetric graph 7 of order 28 Valency 6 Diameter 3 Girth 3 Automorphism group of order 168 Number of arcs = 168 Number of 2-arcs = 840 2-arc-transitive false Edge-set { {1,5}, {5,15}, {11,28}, {1,15}, {4,28}, {21,28}, {16,24}, {4,11}, {6,28}, {9,24}, {19,28}, {7,24}, {3,20}, {6,21}, {9,16}, {13,28}, {24,25}, {20,24}, {14,20}, {5,27}, {8,9}, {12,17}, {13,19}, {7,25}, {3,24}, {20,27}, {5,22}, {9,20}, {5,17}, {2,9}, {2,17}, {15,26}, {10,23}, {14,27}, {22,27}, {8,20}, {5,12}, {9,26}, {17,21}, {15,17}, {10,15}, {7,10}, {10,19}, {1,25}, {4,23}, {18,22}, {8,14}, {2,26}, {2,21}, {17,26}, {15,23}, {7,19}, {1,10}, {4,19}, {1,22}, {4,14}, {14,22}, {11,22}, {6,18}, {2,16}, {10,25}, {19,23}, {1,18}, {4,8}, {11,14}, {6,11}, {2,6}, {6,16}, {12,13}, {18,25}, {3,7}, {11,18}, {13,21}, {16,25}, {7,13}, {3,13}, {12,27}, {12,21}, {16,18}, {3,27}, {3,12}, {23,26}, {8,26}, {8,23} } Symmetric graph 8 of order 28 Valency 6 Diameter 3 Girth 4 Automorphism group of order 336 Number of arcs = 168 Number of 2-arcs = 840 2-arc-transitive false Edge-set { {1,6}, {9,16}, {23,26}, {17,23}, {3,5}, {2,8}, {16,18}, {2,25}, {11,16}, {10,13}, {24,27}, {12,15}, {22,25}, {23,28}, {5,10}, {5,12}, {19,22}, {18,23}, {4,5}, {20,21}, {2,7}, {3,6}, {13,20}, {1,8}, {14,19}, {16,17}, {2,27}, {13,19}, {1,27}, {4,26}, {12,14}, {2,28}, {10,16}, {11,13}, {21,27}, {9,15}, {22,28}, {24,26}, {7,9}, {23,25}, {6,12}, {5,11}, {20,22}, {21,26}, {7,12}, {6,9}, {20,23}, {8,11}, {18,21}, {19,24}, {17,22}, {2,5}, {4,7}, {15,20}, {3,8}, {14,17}, {13,18}, {3,28}, {16,19}, {1,26}, {4,27}, {9,14}, {15,18}, {1,28}, {3,26}, {4,25}, {10,15}, {12,13}, {11,14}, {22,27}, {21,28}, {8,9}, {24,25}, {6,11}, {7,10}, {17,24}, {8,10}, {18,24}, {19,21}, {1,7}, {4,6}, {14,20}, {15,17}, {3,25} } Symmetric graph 9 of order 28 Valency 6 Diameter 3 Girth 3 Automorphism group of order 336 Number of arcs = 168 Number of 2-arcs = 840 2-arc-transitive false Edge-set { {1,9}, {4,13}, {9,14}, {15,28}, {4,26}, {18,27}, {2,5}, {15,17}, {6,13}, {20,22}, {8,17}, {24,27}, {2,18}, {10,28}, {6,21}, {19,22}, {11,24}, {7,20}, {8,21}, {14,22}, {1,18}, {5,10}, {24,26}, {6,23}, {3,7}, {12,21}, {19,25}, {5,11}, {6,26}, {1,22}, {13,22}, {14,17}, {7,17}, {8,10}, {23,26}, {12,16}, {16,25}, {19,23}, {3,9}, {12,28}, {10,17}, {6,28}, {4,22}, {12,24}, {18,25}, {1,11}, {10,27}, {2,25}, {3,11}, {8,23}, {20,23}, {4,16}, {9,16}, {1,24}, {10,18}, {5,26}, {6,15}, {2,7}, {11,21}, {3,13}, {12,14}, {1,20}, {14,19}, {7,15}, {3,16}, {8,11}, {23,27}, {15,25}, {4,25}, {7,13}, {14,21}, {9,17}, {2,26}, {3,5}, {16,28}, {13,21}, {12,27}, {8,20}, {19,27}, {15,19}, {4,24}, {9,18}, {5,28}, {2,20} } Symmetric graph 10 of order 28 Valency 6 Diameter 3 Girth 3 Automorphism group of order 336 Number of arcs = 168 Number of 2-arcs = 840 2-arc-transitive false Edge-set { {1,14}, {2,13}, {9,27}, {1,24}, {8,20}, {6,17}, {21,23}, {2,21}, {19,27}, {7,18}, {15,26}, {10,22}, {13,28}, {19,24}, {18,20}, {17,28}, {4,23}, {11,23}, {3,12}, {5,26}, {2,8}, {21,28}, {4,19}, {11,18}, {1,15}, {10,14}, {7,11}, {4,27}, {7,24}, {3,25}, {5,16}, {15,20}, {20,26}, {14,19}, {2,18}, {9,28}, {4,11}, {12,27}, {5,13}, {6,9}, {14,24}, {9,17}, {16,25}, {5,22}, {12,15}, {10,25}, {8,18}, {3,15}, {4,9}, {11,24}, {1,20}, {6,14}, {3,17}, {16,23}, {8,25}, {6,22}, {13,21}, {9,19}, {6,10}, {12,16}, {17,25}, {3,8}, {1,26}, {5,12}, {11,21}, {4,21}, {15,27}, {13,22}, {7,10}, {7,16}, {22,26}, {1,19}, {6,28}, {10,16}, {7,25}, {2,20}, {3,27}, {18,24}, {8,17}, {12,23}, {5,23}, {2,28}, {14,22}, {13,26} } Symmetric graph 11 of order 28 Valency 6 Diameter 3 Girth 4 Automorphism group of order 5505024 Number of arcs = 168 Number of 2-arcs = 840 2-arc-transitive false Edge-set { {1,3}, {8,13}, {3,9}, {15,25}, {1,20}, {4,13}, {3,13}, {22,24}, {22,23}, {6,8}, {9,12}, {14,15}, {1,4}, {13,15}, {11,18}, {6,27}, {11,17}, {6,28}, {19,25}, {20,25}, {4,10}, {16,22}, {2,23}, {8,14}, {4,9}, {15,22}, {1,23}, {9,28}, {7,18}, {1,19}, {16,25}, {9,27}, {7,17}, {2,19}, {5,24}, {11,22}, {6,24}, {12,22}, {3,14}, {4,14}, {11,21}, {10,28}, {2,20}, {6,23}, {8,17}, {2,4}, {26,28}, {18,19}, {5,8}, {9,11}, {21,24}, {13,16}, {26,27}, {17,19}, {5,7}, {10,11}, {18,20}, {6,7}, {25,27}, {2,3}, {14,16}, {10,12}, {25,28}, {17,20}, {7,14}, {15,21}, {5,28}, {20,26}, {7,13}, {12,18}, {5,27}, {1,24}, {16,21}, {19,26}, {3,10}, {2,24}, {12,17}, {16,26}, {5,23}, {15,26}, {12,21}, {8,18}, {10,27}, {21,23} } Symmetric graph 12 of order 28 Valency 8 Diameter 3 Girth 4 Automorphism group of order 5505024 Number of arcs = 224 Number of 2-arcs = 1568 2-arc-transitive false Edge-set { {1,3}, {2,24}, {5,28}, {13,27}, {14,28}, {4,21}, {6,27}, {12,22}, {11,21}, {17,23}, {6,8}, {3,22}, {7,18}, {7,25}, {8,17}, {8,26}, {14,23}, {11,13}, {3,9}, {18,24}, {5,7}, {10,24}, {12,25}, {10,15}, {9,23}, {11,26}, {9,16}, {4,5}, {11,14}, {12,26}, {9,24}, {5,20}, {13,24}, {12,14}, {4,10}, {3,10}, {13,19}, {15,25}, {17,19}, {4,9}, {14,20}, {16,26}, {18,20}, {4,6}, {5,8}, {7,26}, {16,25}, {13,20}, {14,19}, {2,4}, {3,6}, {12,13}, {11,25}, {10,23}, {6,19}, {5,19}, {6,20}, {1,12}, {15,17}, {20,21}, {1,23}, {2,11}, {16,18}, {19,22}, {13,23}, {10,16}, {15,18}, {2,12}, {1,11}, {3,5}, {6,7}, {8,25}, {15,26}, {1,4}, {2,3}, {2,7}, {25,28}, {15,21}, {2,8}, {1,8}, {26,27}, {16,22}, {1,7}, {18,19}, {15,22}, {17,24}, {25,27}, {26,28}, {14,24}, {9,15}, {16,17}, {2,23}, {6,28}, {1,24}, {5,27}, {10,27}, {9,27}, {9,28}, {10,28}, {20,22}, {7,17}, {3,21}, {16,21}, {17,20}, {18,23}, {14,27}, {13,28}, {4,22}, {19,21}, {12,21}, {8,18}, {11,22} } Symmetric graph 13 of order 28 Valency 8 Diameter 3 Girth 4 Automorphism group of order 64210599936 Number of arcs = 224 Number of 2-arcs = 1568 2-arc-transitive false Edge-set { {1,3}, {5,7}, {15,18}, {9,12}, {5,22}, {19,22}, {14,16}, {10,11}, {9,25}, {23,25}, {7,19}, {18,20}, {2,14}, {13,15}, {1,14}, {10,26}, {1,28}, {24,26}, {12,23}, {22,24}, {3,20}, {6,18}, {17,19}, {1,13}, {5,18}, {14,15}, {2,13}, {4,5}, {15,28}, {2,27}, {16,28}, {11,24}, {25,27}, {7,23}, {7,24}, {10,22}, {3,6}, {21,23}, {4,19}, {5,17}, {9,22}, {3,5}, {18,19}, {6,17}, {13,16}, {8,9}, {16,27}, {4,20}, {2,28}, {15,27}, {26,27}, {12,28}, {12,27}, {22,23}, {13,25}, {7,9}, {7,10}, {26,28}, {8,24}, {8,23}, {9,21}, {14,25}, {3,19}, {10,21}, {4,6}, {17,20}, {11,14}, {1,27}, {2,3}, {4,16}, {11,28}, {3,16}, {11,27}, {25,28}, {1,17}, {13,26}, {12,14}, {12,13}, {2,4}, {21,24}, {14,26}, {8,10}, {1,18}, {6,7}, {16,18}, {8,20}, {2,17}, {4,15}, {7,20}, {2,18}, {3,15}, {1,4}, {5,21}, {16,17}, {11,13}, {6,8}, {10,12}, {6,22}, {20,22}, {20,21}, {6,21}, {8,19}, {12,24}, {5,8}, {15,17}, {9,26}, {9,11}, {10,25}, {24,25}, {11,23}, {19,21}, {23,26} } Symmetric graph 14 of order 28 Valency 9 Diameter 2 Girth 3 Automorphism group of order 504 Number of arcs = 252 Number of 2-arcs = 2016 2-arc-transitive false Edge-set { {1,2}, {19,21}, {26,28}, {8,27}, {4,17}, {17,18}, {15,26}, {22,27}, {4,16}, {12,25}, {13,16}, {10,12}, {17,25}, {8,19}, {14,15}, {5,22}, {4,6}, {13,25}, {9,10}, {7,18}, {6,11}, {13,14}, {9,24}, {1,7}, {10,16}, {12,18}, {8,26}, {17,27}, {23,25}, {8,9}, {3,14}, {5,6}, {4,5}, {10,11}, {14,18}, {24,28}, {1,3}, {13,20}, {2,23}, {11,23}, {9,14}, {7,28}, {3,20}, {20,21}, {11,28}, {6,24}, {1,13}, {9,13}, {7,10}, {17,26}, {19,27}, {15,16}, {12,22}, {15,18}, {3,27}, {3,5}, {6,23}, {3,4}, {6,25}, {22,24}, {13,23}, {2,21}, {1,11}, {14,16}, {12,19}, {2,15}, {23,28}, {3,9}, {18,20}, {11,21}, {16,24}, {1,27}, {18,22}, {5,7}, {20,23}, {14,28}, {20,24}, {16,17}, {8,15}, {17,22}, {8,13}, {8,10}, {2,3}, {5,12}, {15,23}, {2,4}, {24,25}, {5,10}, {18,23}, {7,14}, {5,20}, {11,12}, {4,26}, {21,22}, {2,28}, {7,17}, {19,25}, {15,21}, {3,24}, {6,7}, {22,28}, {1,12}, {9,21}, {16,20}, {6,16}, {12,13}, {25,26}, {11,26}, {14,27}, {24,26}, {2,19}, {4,19}, {1,6}, {10,15}, {9,11}, {9,22}, {2,7}, {18,19}, {21,26}, {25,27}, {4,8}, {5,21}, {27,28}, {10,17}, {19,20}, {1,8} } Symmetric graph 15 of order 28 Valency 12 Diameter 2 Girth 3 Automorphism group of order 1344 Number of arcs = 336 Number of 2-arcs = 3696 2-arc-transitive false Edge-set { {1,5}, {1,9}, {20,27}, {8,9}, {8,27}, {16,18}, {10,22}, {3,8}, {8,17}, {3,16}, {10,17}, {17,24}, {2,23}, {7,26}, {5,13}, {3,12}, {17,28}, {3,20}, {12,24}, {2,28}, {7,20}, {5,24}, {20,25}, {14,24}, {10,28}, {15,25}, {4,14}, {9,19}, {1,22}, {1,20}, {5,12}, {6,28}, {13,20}, {12,18}, {22,28}, {5,25}, {6,14}, {10,13}, {12,25}, {4,18}, {19,22}, {1,25}, {14,20}, {15,18}, {11,22}, {23,25}, {7,13}, {15,21}, {3,11}, {11,23}, {4,26}, {8,19}, {8,21}, {9,26}, {13,27}, {9,18}, {22,27}, {6,20}, {2,13}, {18,22}, {5,17}, {6,23}, {13,26}, {12,13}, {1,15}, {11,20}, {7,22}, {5,15}, {6,11}, {11,17}, {23,26}, {19,26}, {13,21}, {9,15}, {11,27}, {18,23}, {4,22}, {17,21}, {3,23}, {6,26}, {15,28}, {11,15}, {1,19}, {21,27}, {6,12}, {7,28}, {7,15}, {11,14}, {3,19}, {3,27}, {16,17}, {8,14}, {16,22}, {1,10}, {8,23}, {16,26}, {2,18}, {17,26}, {13,23}, {20,24}, {14,22}, {5,22}, {1,6}, {9,21}, {6,18}, {13,19}, {1,21}, {2,6}, {7,18}, {7,24}, {14,28}, {14,19}, {1,16}, {6,16}, {7,10}, {15,23}, {11,26}, {16,24}, {12,28}, {2,14}, {6,21}, {3,7}, {16,27}, {10,16}, {2,5}, {4,13}, {12,19}, {4,21}, {4,7}, {21,28}, {12,16}, {2,24}, {4,17}, {24,26}, {7,9}, {5,27}, {3,28}, {15,17}, {2,9}, {9,24}, {18,25}, {1,26}, {18,27}, {8,16}, {2,17}, {9,27}, {2,10}, {19,23}, {4,25}, {4,12}, {2,27}, {5,19}, {3,15}, {24,25}, {10,23}, {19,28}, {4,11}, {10,25}, {14,25}, {9,14}, {4,8}, {10,20}, {20,21}, {3,24}, {8,10}, {8,25}, {5,11}, {12,21} } Symmetric graph 16 of order 28 Valency 12 Diameter 2 Girth 3 Automorphism group of order 40320 Number of arcs = 336 Number of 2-arcs = 3696 2-arc-transitive false Edge-set { {1,7}, {4,9}, {19,27}, {8,11}, {8,26}, {16,19}, {10,21}, {3,6}, {7,17}, {3,14}, {9,17}, {19,24}, {2,21}, {7,27}, {5,16}, {2,12}, {18,28}, {4,20}, {12,23}, {4,28}, {8,20}, {8,24}, {19,25}, {14,21}, {10,27}, {16,25}, {4,16}, {10,19}, {1,24}, {2,20}, {5,10}, {6,25}, {13,17}, {11,18}, {22,26}, {5,28}, {6,15}, {11,13}, {12,26}, {3,18}, {17,22}, {3,25}, {14,17}, {15,19}, {11,21}, {23,27}, {7,16}, {15,24}, {2,11}, {11,24}, {2,26}, {7,19}, {5,21}, {9,25}, {14,27}, {10,18}, {22,25}, {5,20}, {2,15}, {20,22}, {6,17}, {7,23}, {14,26}, {9,13}, {1,13}, {12,20}, {6,22}, {5,14}, {6,9}, {12,17}, {23,28}, {20,26}, {13,24}, {12,15}, {11,28}, {20,23}, {4,24}, {19,21}, {3,21}, {6,27}, {16,28}, {10,15}, {2,19}, {21,25}, {6,10}, {7,25}, {7,14}, {10,14}, {4,19}, {1,27}, {16,20}, {8,15}, {16,23}, {4,10}, {5,23}, {15,26}, {1,18}, {18,26}, {13,22}, {18,24}, {14,23}, {8,22}, {1,8}, {9,22}, {5,18}, {13,18}, {1,23}, {2,8}, {8,18}, {6,24}, {13,28}, {14,18}, {1,14}, {6,13}, {7,12}, {15,22}, {11,25}, {16,21}, {12,27}, {2,16}, {7,21}, {3,5}, {15,27}, {11,16}, {2,7}, {4,15}, {11,19}, {4,23}, {4,5}, {21,26}, {9,16}, {2,22}, {3,17}, {24,28}, {7,11}, {5,26}, {1,28}, {15,20}, {3,9}, {9,23}, {17,25}, {3,26}, {17,27}, {8,13}, {1,17}, {9,28}, {3,10}, {17,23}, {2,25}, {1,12}, {4,27}, {6,19}, {3,13}, {24,27}, {10,24}, {20,28}, {1,11}, {10,26}, {13,25}, {12,14}, {4,6}, {9,20}, {18,21}, {3,22}, {8,12}, {8,28}, {5,9}, {12,22} } Symmetric graph 17 of order 28 Valency 12 Diameter 3 Girth 4 Automorphism group of order 165150720 Number of arcs = 336 Number of 2-arcs = 3696 2-arc-transitive false Edge-set { {1,15}, {10,27}, {11,27}, {5,15}, {4,18}, {5,20}, {4,25}, {10,22}, {11,15}, {13,17}, {6,21}, {4,22}, {13,15}, {2,17}, {10,21}, {8,15}, {7,18}, {10,20}, {11,25}, {14,24}, {5,19}, {7,21}, {8,16}, {8,17}, {10,24}, {11,19}, {14,28}, {5,28}, {7,15}, {8,18}, {10,26}, {11,24}, {13,25}, {6,23}, {4,15}, {13,18}, {2,20}, {10,25}, {12,23}, {3,22}, {14,15}, {7,25}, {8,23}, {9,26}, {12,24}, {14,26}, {5,24}, {12,15}, {2,18}, {3,20}, {14,25}, {6,22}, {3,15}, {11,23}, {13,26}, {6,24}, {9,18}, {12,20}, {2,25}, {2,24}, {10,19}, {11,21}, {1,16}, {10,17}, {13,24}, {6,19}, {4,28}, {13,28}, {2,15}, {10,18}, {1,26}, {7,22}, {10,23}, {11,20}, {11,26}, {1,24}, {9,17}, {12,19}, {2,26}, {1,23}, {9,20}, {12,22}, {6,28}, {13,22}, {2,23}, {8,21}, {7,16}, {11,22}, {1,25}, {9,19}, {12,21}, {2,16}, {13,16}, {6,17}, {4,19}, {2,28}, {10,28}, {12,28}, {14,18}, {7,20}, {8,25}, {9,27}, {12,27}, {5,18}, {2,19}, {3,21}, {14,16}, {3,19}, {11,28}, {6,18}, {1,27}, {7,23}, {1,18}, {4,20}, {1,20}, {9,25}, {2,27}, {5,17}, {1,28}, {9,28}, {4,16}, {8,19}, {7,26}, {3,16}, {8,24}, {7,19}, {8,20}, {14,17}, {8,26}, {9,24}, {14,21}, {5,16}, {3,17}, {3,28}, {6,15}, {3,18}, {3,26}, {13,23}, {6,20}, {4,17}, {4,26}, {8,22}, {9,23}, {14,22}, {3,25}, {13,21}, {6,16}, {5,27}, {4,27}, {13,27}, {6,27}, {3,27}, {12,26}, {14,23}, {12,16}, {9,22}, {5,22}, {11,16}, {1,19}, {4,21}, {5,21}, {1,17}, {9,21}, {7,24}, {7,17}, {12,25}, {14,27}, {5,23} } Symmetric graph 18 of order 28 Valency 13 Diameter 3 Girth 3 Automorphism group of order 2184 Number of arcs = 364 Number of 2-arcs = 4368 2-arc-transitive false Edge-set { {1,3}, {14,20}, {7,26}, {1,9}, {9,22}, {15,26}, {5,11}, {14,17}, {2,26}, {11,17}, {2,23}, {15,23}, {5,7}, {15,28}, {9,28}, {9,13}, {13,15}, {11,25}, {5,28}, {13,22}, {3,25}, {22,23}, {3,17}, {3,23}, {17,20}, {2,20}, {10,17}, {2,10}, {10,23}, {5,16}, {12,15}, {3,7}, {20,28}, {10,11}, {16,20}, {7,12}, {11,22}, {7,13}, {20,22}, {1,28}, {1,13}, {22,25}, {18,28}, {13,18}, {1,25}, {18,22}, {7,24}, {6,23}, {16,17}, {20,26}, {5,18}, {1,15}, {1,24}, {6,26}, {10,26}, {5,10}, {1,11}, {3,14}, {10,14}, {11,16}, {12,23}, {3,27}, {10,27}, {14,16}, {12,26}, {11,27}, {14,23}, {21,26}, {4,5}, {8,22}, {24,28}, {7,27}, {14,28}, {17,26}, {14,21}, {4,26}, {8,15}, {15,18}, {7,18}, {5,14}, {9,20}, {7,9}, {9,18}, {5,24}, {6,22}, {3,16}, {4,20}, {7,19}, {4,18}, {1,19}, {9,24}, {6,15}, {15,19}, {3,9}, {11,24}, {8,28}, {3,21}, {5,19}, {11,13}, {9,12}, {8,11}, {23,25}, {6,17}, {23,27}, {26,27}, {1,17}, {2,22}, {2,5}, {17,27}, {2,14}, {7,21}, {4,28}, {20,24}, {5,21}, {19,27}, {8,14}, {17,21}, {2,4}, {8,23}, {2,7}, {4,15}, {6,20}, {12,20}, {21,28}, {10,15}, {2,16}, {5,25}, {16,22}, {3,12}, {13,27}, {4,22}, {3,19}, {11,19}, {13,26}, {25,28}, {13,19}, {9,25}, {8,20}, {1,21}, {19,21}, {6,9}, {12,28}, {13,24}, {8,25}, {3,6}, {19,23}, {8,17}, {1,8}, {22,27}, {1,6}, {18,23}, {18,25}, {7,16}, {4,10}, {10,19}, {15,21}, {10,21}, {2,12}, {12,14}, {24,26}, {21,24}, {2,27}, {16,25}, {6,12}, {6,13}, {14,25}, {4,11}, {16,27}, {18,19}, {2,18}, {17,24}, {12,18}, {9,16}, {12,21}, {4,24}, {4,13}, {19,25}, {16,24}, {6,8}, {8,10}, {6,27}, {4,8} } Symmetric graph 19 of order 28 Valency 13 Diameter 3 Girth 4 Automorphism group of order 174356582400 Number of arcs = 364 Number of 2-arcs = 4368 2-arc-transitive true Edge-set { {1,4}, {3,5}, {21,24}, {4,7}, {2,23}, {21,25}, {12,19}, {2,3}, {14,24}, {6,22}, {20,22}, {23,25}, {12,16}, {13,28}, {5,18}, {4,6}, {22,23}, {17,21}, {3,19}, {8,26}, {1,11}, {26,27}, {6,11}, {16,20}, {13,15}, {8,18}, {10,18}, {4,28}, {7,11}, {2,9}, {3,8}, {1,24}, {22,26}, {11,20}, {12,25}, {10,12}, {5,23}, {5,14}, {9,24}, {15,27}, {8,14}, {1,17}, {6,8}, {16,18}, {9,13}, {9,25}, {3,10}, {24,28}, {2,14}, {14,17}, {6,19}, {13,23}, {5,21}, {19,21}, {24,26}, {11,15}, {14,27}, {6,17}, {13,20}, {18,25}, {7,22}, {2,20}, {7,17}, {19,26}, {9,16}, {7,27}, {3,13}, {5,12}, {10,21}, {1,8}, {1,13}, {8,9}, {18,19}, {4,26}, {19,23}, {16,26}, {4,20}, {19,28}, {3,22}, {12,17}, {8,28}, {1,5}, {18,22}, {7,25}, {2,12}, {25,28}, {15,19}, {14,16}, {9,17}, {3,27}, {8,12}, {1,10}, {18,27}, {11,23}, {2,26}, {11,14}, {6,27}, {10,14}, {5,15}, {4,18}, {4,23}, {7,13}, {2,18}, {20,25}, {13,21}, {4,21}, {1,19}, {13,26}, {11,28}, {5,9}, {3,24}, {15,24}, {22,28}, {5,20}, {8,15}, {6,24}, {10,28}, {5,28}, {12,13}, {5,7}, {2,21}, {11,26}, {9,11}, {6,13}, {10,23}, {16,28}, {15,17}, {10,26}, {4,9}, {23,27}, {13,18}, {9,27}, {14,22}, {17,20}, {15,22}, {3,17}, {1,27}, {3,25}, {7,16}, {2,7}, {3,11}, {20,24}, {4,14}, {9,22}, {6,16}, {4,12}, {12,24}, {18,24}, {4,15}, {17,28}, {7,19}, {16,21}, {2,6}, {1,16}, {8,21}, {10,20}, {7,10}, {2,28}, {6,25}, {12,22}, {14,19}, {17,26}, {10,15}, {15,25}, {20,27}, {11,18}, {9,19}, {12,27}, {6,10}, {21,27}, {16,23}, {2,15}, {17,23}, {11,21}, {3,16}, {7,24}, {1,22}, {1,25}, {14,25}, {8,23}, {5,26}, {8,20} } Symmetric graph 20 of order 28 Valency 14 Diameter 2 Girth 4 Automorphism group of order 15200108913103994880000 Number of arcs = 392 Number of 2-arcs = 5096 2-arc-transitive true Edge-set { {1,3}, {2,23}, {9,27}, {1,15}, {2,28}, {10,20}, {5,8}, {2,8}, {22,27}, {1,19}, {6,28}, {9,11}, {7,25}, {3,14}, {1,28}, {14,28}, {20,21}, {5,19}, {2,12}, {26,27}, {4,6}, {3,10}, {8,18}, {13,23}, {9,12}, {2,19}, {6,27}, {13,19}, {6,12}, {11,22}, {20,25}, {3,26}, {1,4}, {17,28}, {5,24}, {4,10}, {9,23}, {7,9}, {14,15}, {2,11}, {8,17}, {1,12}, {26,28}, {5,20}, {4,5}, {12,14}, {11,26}, {4,17}, {3,21}, {18,19}, {23,25}, {9,24}, {2,24}, {10,27}, {6,16}, {7,10}, {10,15}, {8,13}, {12,22}, {18,28}, {14,16}, {2,4}, {17,27}, {19,25}, {6,24}, {6,11}, {3,25}, {4,13}, {12,17}, {18,24}, {10,16}, {22,23}, {9,20}, {15,26}, {1,8}, {1,16}, {5,7}, {4,21}, {7,13}, {8,9}, {7,22}, {11,14}, {17,19}, {6,15}, {12,21}, {1,24}, {10,28}, {18,20}, {5,16}, {12,26}, {23,26}, {3,5}, {4,18}, {14,24}, {10,11}, {16,17}, {7,21}, {15,21}, {8,25}, {22,24}, {14,27}, {2,7}, {21,27}, {3,13}, {11,13}, {8,14}, {12,18}, {16,26}, {4,22}, {17,20}, {2,16}, {1,27}, {9,19}, {6,7}, {11,17}, {15,25}, {4,25}, {17,24}, {6,23}, {3,9}, {13,16}, {7,18}, {16,21}, {13,20}, {8,22}, {20,22}, {14,23}, {5,12}, {13,28}, {11,18}, {15,17}, {21,24}, {10,19}, {16,25}, {1,7}, {21,28}, {2,20}, {5,27}, {10,12}, {8,26}, {3,18}, {16,18}, {24,26}, {10,23}, {5,15}, {7,14}, {11,21}, {13,15}, {11,25}, {14,19}, {3,17}, {15,18}, {16,22}, {1,20}, {7,26}, {21,23}, {2,27}, {13,27}, {19,22}, {6,20}, {1,11}, {25,28}, {4,9}, {7,17}, {17,23}, {9,15}, {6,8}, {3,22}, {12,13}, {18,23}, {9,16}, {15,22}, {19,21}, {25,27}, {13,24}, {5,28}, {14,20}, {5,11}, {19,26}, {2,3}, {18,27}, {10,24}, {8,10}, {4,14}, {2,15}, {8,21}, {20,26}, {5,23}, {6,19}, {3,6}, {12,25}, {1,23}, {9,28}, {22,28}, {24,25}, {4,26} } Symmetric graph 21 of order 28 Valency 15 Diameter 2 Girth 3 Automorphism group of order 40320 Number of arcs = 420 Number of 2-arcs = 5880 2-arc-transitive false Edge-set { {1,14}, {13,15}, {2,26}, {12,14}, {18,20}, {5,10}, {10,17}, {2,13}, {2,11}, {9,27}, {4,14}, {17,23}, {24,27}, {1,17}, {8,27}, {10,14}, {17,20}, {10,16}, {5,19}, {13,24}, {2,28}, {1,26}, {8,25}, {6,20}, {13,19}, {1,15}, {8,26}, {8,20}, {16,19}, {13,17}, {2,27}, {1,27}, {4,8}, {11,17}, {15,27}, {23,28}, {7,24}, {6,14}, {13,20}, {3,10}, {9,17}, {5,15}, {10,26}, {8,21}, {16,22}, {4,27}, {4,12}, {14,28}, {7,20}, {12,15}, {18,26}, {5,8}, {4,16}, {11,28}, {7,15}, {10,20}, {17,19}, {15,20}, {19,26}, {8,24}, {16,28}, {1,16}, {8,23}, {12,20}, {18,19}, {3,26}, {9,25}, {6,19}, {13,21}, {4,13}, {2,12}, {14,27}, {4,20}, {17,25}, {6,27}, {1,18}, {12,23}, {18,24}, {5,17}, {10,27}, {7,8}, {11,22}, {3,15}, {20,24}, {19,28}, {2,24}, {3,13}, {2,9}, {19,27}, {4,21}, {11,18}, {5,9}, {16,24}, {11,24}, {15,28}, {3,16}, {9,23}, {12,19}, {18,21}, {17,27}, {1,28}, {12,27}, {4,18}, {5,28}, {7,10}, {6,8}, {13,16}, {3,11}, {9,15}, {11,15}, {15,26}, {16,25}, {4,11}, {9,28}, {7,14}, {5,25}, {6,10}, {5,22}, {4,28}, {7,12}, {1,20}, {14,24}, {20,28}, {2,10}, {2,19}, {1,21}, {8,22}, {14,26}, {11,25}, {6,9}, {13,14}, {1,23}, {8,19}, {16,21}, {3,23}, {12,25}, {6,18}, {3,28}, {7,9}, {14,25}, {10,18}, {7,19}, {9,16}, {14,23}, {18,23}, {5,24}, {6,11}, {6,16}, {13,23}, {3,12}, {9,18}, {6,15}, {7,11}, {9,26}, {2,20}, {11,19}, {9,24}, {21,27}, {12,16}, {11,14}, {6,23}, {12,18}, {5,18}, {5,12}, {11,21}, {15,22}, {3,18}, {2,21}, {21,23}, {22,24}, {4,17}, {22,23}, {3,24}, {4,26}, {6,13}, {3,27}, {4,9}, {10,28}, {7,17}, {5,13}, {25,26}, {8,28}, {7,16}, {6,25}, {3,25}, {5,21}, {2,22}, {7,21}, {13,26}, {2,25}, {20,25}, {5,14}, {7,23}, {1,19}, {2,23}, {12,22}, {7,26}, {1,25}, {6,22}, {1,24}, {22,26}, {3,17}, {10,22}, {3,8}, {15,21}, {21,25}, {10,21}, {17,22}, {4,22}, {1,22} } Symmetric graph 22 of order 28 Valency 18 Diameter 2 Girth 3 Automorphism group of order 120960 Number of arcs = 504 Number of 2-arcs = 8568 2-arc-transitive false Edge-set { {1,6}, {21,28}, {6,28}, {13,19}, {12,19}, {19,28}, {6,19}, {5,10}, {1,24}, {3,10}, {1,15}, {10,19}, {1,19}, {10,28}, {4,25}, {8,14}, {15,21}, {11,28}, {4,22}, {14,25}, {6,21}, {4,10}, {1,14}, {10,21}, {1,28}, {4,19}, {14,19}, {17,23}, {20,27}, {8,27}, {7,22}, {6,13}, {12,21}, {2,19}, {16,23}, {10,27}, {8,17}, {20,22}, {13,28}, {6,12}, {4,23}, {14,27}, {8,21}, {22,28}, {4,13}, {12,14}, {19,21}, {10,23}, {1,27}, {8,10}, {1,22}, {9,14}, {4,9}, {11,18}, {3,17}, {18,27}, {7,17}, {16,26}, {5,28}, {6,24}, {3,13}, {12,15}, {10,24}, {1,26}, {7,14}, {9,23}, {4,18}, {14,17}, {9,27}, {4,7}, {11,16}, {5,19}, {19,24}, {3,28}, {6,15}, {14,23}, {8,18}, {17,22}, {13,27}, {7,12}, {16,19}, {5,23}, {24,27}, {3,8}, {15,22}, {10,13}, {1,12}, {4,14}, {18,21}, {17,28}, {4,27}, {16,21}, {1,8}, {16,22}, {1,23}, {16,27}, {2,12}, {2,13}, {9,22}, {12,18}, {2,17}, {9,26}, {4,5}, {7,20}, {18,23}, {19,25}, {8,19}, {15,28}, {6,11}, {5,22}, {24,25}, {3,6}, {4,15}, {11,14}, {20,21}, {18,28}, {8,26}, {9,16}, {12,23}, {2,27}, {8,9}, {1,18}, {16,17}, {23,26}, {5,27}, {2,7}, {13,23}, {10,25}, {10,15}, {1,11}, {19,22}, {12,27}, {5,18}, {17,24}, {3,26}, {5,15}, {7,10}, {15,18}, {11,17}, {22,27}, {7,25}, {6,16}, {14,24}, {3,21}, {8,23}, {12,13}, {9,19}, {17,27}, {7,13}, {21,27}, {7,28}, {7,16}, {14,21}, {9,28}, {7,18}, {3,24}, {15,26}, {5,24}, {24,26}, {1,16}, {10,16}, {3,12}, {2,15}, {9,24}, {4,26}, {1,20}, {16,18}, {23,25}, {11,26}, {3,5}, {2,9}, {10,17}, {1,7}, {2,28}, {16,25}, {15,17}, {11,20}, {6,25}, {6,23}, {2,8}, {13,22}, {11,13}, {3,14}, {9,15}, {18,24}, {17,26}, {7,9}, {14,20}, {9,18}, {18,25}, {5,26}, {5,14}, {4,17}, {4,6}, {2,21}, {1,10}, {3,18}, {12,25}, {4,11}, {5,20}, {8,15}, {11,22}, {15,24}, {13,18}, {12,17}, {19,26}, {7,26}, {8,13}, {12,22}, {12,26}, {2,5}, {11,25}, {6,20}, {15,25}, {8,11}, {15,20}, {7,21}, {23,28}, {3,22}, {21,26}, {20,23}, {11,21}, {2,23}, {9,20}, {2,20}, {22,25}, {8,25}, {6,9}, {4,21}, {2,11}, {14,28}, {5,16}, {13,24}, {8,22}, {2,16}, {20,25}, {6,27}, {2,25}, {5,12}, {2,24}, {3,9}, {10,20}, {20,26}, {7,24}, {3,16}, {3,20}, {13,20}, {6,17}, {13,26}, {11,24}, {3,25}, {5,11} } Symmetric graph 23 of order 28 Valency 21 Diameter 2 Girth 3 Automorphism group of order 15485790781440000 Number of arcs = 588 Number of 2-arcs = 11760 2-arc-transitive false Edge-set { {1,8}, {5,15}, {15,26}, {1,28}, {6,20}, {11,28}, {6,14}, {5,14}, {11,15}, {7,25}, {2,16}, {14,16}, {7,17}, {16,23}, {1,17}, {20,23}, {16,28}, {6,28}, {6,13}, {12,19}, {4,26}, {1,18}, {17,26}, {1,23}, {6,24}, {3,19}, {10,26}, {5,24}, {3,15}, {10,25}, {2,8}, {14,26}, {1,11}, {7,14}, {11,16}, {7,19}, {16,27}, {21,27}, {7,24}, {2,11}, {14,17}, {5,22}, {11,24}, {3,14}, {5,10}, {8,15}, {7,8}, {10,16}, {3,27}, {7,21}, {11,18}, {14,25}, {10,20}, {3,28}, {6,21}, {13,18}, {12,25}, {4,15}, {18,26}, {11,17}, {14,23}, {5,16}, {15,28}, {6,17}, {19,23}, {16,26}, {6,27}, {9,26}, {1,9}, {9,23}, {4,9}, {6,8}, {10,19}, {4,16}, {18,28}, {17,24}, {3,23}, {1,12}, {13,20}, {8,16}, {10,28}, {3,17}, {21,23}, {20,25}, {6,26}, {6,15}, {19,26}, {1,25}, {3,9}, {9,21}, {6,23}, {4,19}, {16,22}, {5,28}, {13,17}, {12,23}, {18,25}, {2,25}, {11,21}, {7,23}, {19,22}, {5,27}, {13,21}, {12,24}, {2,28}, {11,22}, {16,24}, {10,17}, {8,23}, {1,26}, {1,20}, {14,28}, {6,11}, {3,16}, {10,27}, {11,26}, {1,14}, {7,9}, {9,16}, {11,20}, {14,22}, {5,20}, {15,22}, {8,22}, {2,20}, {17,22}, {7,15}, {18,27}, {2,26}, {5,11}, {8,24}, {3,10}, {8,21}, {5,21}, {15,24}, {19,25}, {2,27}, {14,18}, {11,25}, {3,24}, {3,21}, {10,23}, {4,8}, {13,25}, {2,12}, {7,11}, {7,28}, {6,16}, {11,27}, {5,13}, {12,15}, {3,20}, {21,22}, {4,22}, {7,10}, {12,26}, {1,13}, {19,24}, {10,21}, {13,22}, {5,12}, {4,13}, {12,18}, {4,28}, {6,10}, {8,19}, {12,27}, {7,13}, {9,20}, {4,27}, {10,24}, {4,14}, {12,16}, {13,28}, {8,26}, {1,10}, {18,24}, {3,25}, {10,15}, {14,15}, {5,25}, {2,15}, {11,23}, {7,16}, {3,26}, {1,21}, {9,18}, {9,25}, {5,17}, {15,23}, {20,26}, {1,22}, {16,25}, {12,17}, {13,23}, {12,28}, {13,26}, {4,25}, {2,18}, {3,13}, {6,19}, {9,22}, {5,9}, {4,11}, {1,16}, {20,28}, {3,18}, {21,25}, {4,20}, {8,28}, {13,27}, {7,12}, {5,23}, {13,16}, {3,8}, {4,21}, {10,18}, {8,25}, {13,19}, {19,28}, {11,19}, {7,26}, {9,28}, {1,19}, {20,27}, {21,28}, {2,21}, {6,18}, {14,24}, {5,19}, {15,27}, {8,27}, {18,23}, {20,24}, {2,19}, {17,27}, {2,14}, {7,18}, {9,24}, {19,27}, {2,22}, {2,9}, {9,17}, {8,18}, {2,17}, {17,23}, {21,26}, {1,24}, {14,19}, {5,18}, {15,25}, {12,21}, {6,25}, {17,28}, {12,20}, {3,11}, {14,21}, {20,22}, {12,22}, {13,15}, {21,24}, {14,27}, {2,13}, {7,27}, {5,26}, {1,15}, {3,22}, {4,12}, {9,19}, {9,27}, {8,20}, {1,27}, {2,23}, {4,17}, {18,22}, {14,20}, {4,23}, {4,18}, {7,22}, {8,17}, {7,20}, {6,9}, {9,15}, {10,22}, {5,8}, {2,10}, {6,22}, {4,24}, {6,12}, {2,24}, {13,24}, {4,10}, {3,12}, {17,25} } Symmetric graph 24 of order 28 Valency 24 Diameter 2 Girth 3 Automorphism group of order 23115815976960 Number of arcs = 672 Number of 2-arcs = 15456 2-arc-transitive false Edge-set { {1,5}, {1,16}, {1,22}, {1,19}, {6,22}, {1,10}, {10,22}, {22,27}, {10,13}, {2,10}, {1,28}, {20,22}, {10,28}, {10,20}, {10,24}, {10,15}, {17,28}, {8,20}, {4,28}, {20,21}, {16,22}, {7,10}, {22,28}, {16,20}, {7,28}, {20,28}, {12,28}, {11,20}, {18,28}, {5,20}, {16,26}, {7,15}, {3,28}, {3,22}, {16,24}, {7,11}, {9,28}, {10,19}, {6,10}, {14,28}, {4,20}, {10,16}, {7,19}, {6,28}, {14,22}, {4,16}, {7,22}, {16,28}, {16,18}, {7,25}, {8,22}, {16,25}, {7,16}, {19,23}, {6,13}, {14,18}, {4,5}, {2,22}, {16,23}, {10,23}, {12,19}, {6,11}, {14,25}, {4,17}, {22,26}, {16,19}, {5,28}, {20,27}, {13,28}, {2,20}, {3,7}, {24,28}, {19,28}, {6,20}, {5,14}, {4,27}, {13,22}, {2,16}, {3,19}, {6,24}, {10,14}, {4,10}, {19,22}, {6,16}, {8,19}, {6,25}, {14,21}, {4,14}, {3,10}, {19,21}, {6,14}, {14,19}, {4,6}, {5,9}, {12,27}, {13,17}, {2,8}, {3,16}, {1,24}, {10,21}, {9,19}, {6,12}, {12,20}, {5,27}, {18,27}, {13,25}, {2,17}, {7,14}, {3,6}, {24,26}, {5,19}, {6,27}, {7,24}, {15,28}, {17,22}, {8,16}, {4,7}, {21,28}, {2,14}, {4,23}, {12,22}, {11,16}, {5,22}, {16,27}, {7,13}, {2,28}, {1,7}, {3,24}, {15,24}, {10,17}, {8,10}, {4,19}, {6,21}, {2,5}, {23,27}, {12,13}, {2,11}, {7,20}, {20,24}, {5,10}, {10,27}, {13,19}, {2,6}, {5,15}, {3,27}, {13,21}, {7,9}, {3,20}, {20,23}, {5,11}, {9,27}, {13,20}, {2,7}, {7,27}, {3,13}, {2,24}, {24,27}, {15,18}, {6,17}, {8,26}, {4,15}, {3,21}, {2,19}, {6,23}, {1,12}, {11,22}, {11,28}, {9,20}, {5,26}, {19,27}, {13,27}, {2,18}, {1,15}, {8,24}, {15,25}, {17,21}, {8,14}, {21,26}, {14,20}, {2,13}, {2,23}, {12,23}, {11,13}, {5,16}, {1,27}, {13,24}, {2,15}, {12,14}, {4,11}, {18,22}, {10,26}, {15,19}, {3,14}, {4,24}, {9,16}, {7,21}, {3,9}, {12,24}, {10,18}, {19,25}, {19,24}, {6,15}, {14,17}, {4,8}, {4,22}, {16,21}, {1,14}, {2,12}, {11,23}, {12,18}, {20,26}, {3,5}, {2,9}, {1,21}, {9,24}, {12,15}, {17,27}, {8,18}, {4,25}, {7,12}, {1,20}, {15,20}, {5,17}, {8,27}, {4,13}, {2,21}, {15,23}, {11,17}, {8,9}, {14,26}, {23,28}, {1,17}, {7,17}, {8,28}, {4,21}, {14,24}, {8,23}, {4,12}, {11,21}, {11,15}, {5,25}, {2,26}, {3,18}, {5,24}, {9,23}, {21,27}, {9,13}, {10,25}, {22,25}, {16,17}, {7,26}, {1,13}, {15,27}, {17,24}, {8,15}, {21,25}, {1,18}, {3,11}, {18,21}, {9,26}, {8,21}, {4,9}, {12,21}, {17,25}, {8,17}, {1,6}, {15,22}, {12,17}, {8,11}, {4,18}, {5,21}, {7,18}, {3,25}, {5,18}, {7,23}, {3,12}, {11,24}, {19,26}, {6,19}, {11,14}, {11,18}, {20,25}, {14,27}, {5,12}, {11,27}, {13,18}, {3,15}, {11,19}, {6,9}, {9,25}, {18,25}, {1,23}, {4,26}, {1,11}, {9,22}, {12,26}, {15,26}, {1,26}, {3,17}, {9,21}, {9,18}, {17,26}, {12,16}, {9,15}, {18,24}, {11,25}, {9,17}, {23,25}, {6,26}, {14,23}, {11,26}, {9,14}, {1,8}, {2,25}, {17,23}, {23,26}, {3,26}, {18,26}, {3,8}, {24,25}, {1,9}, {1,25}, {2,27}, {18,23}, {12,25}, {5,23}, {5,13}, {8,25}, {15,17}, {13,26}, {3,23}, {6,18}, {8,12}, {13,23}, {15,21}, {8,13} } Symmetric graph 25 of order 28 Valency 26 Diameter 2 Girth 3 Automorphism group of order 1428329123020800 Number of arcs = 728 Number of 2-arcs = 18200 2-arc-transitive false Edge-set { {1,3}, {12,22}, {5,28}, {6,20}, {10,17}, {7,13}, {8,26}, {8,28}, {7,16}, {2,24}, {2,19}, {10,25}, {13,21}, {16,26}, {11,22}, {13,26}, {22,26}, {18,25}, {4,21}, {3,21}, {23,27}, {21,27}, {15,27}, {15,24}, {12,19}, {5,10}, {13,18}, {16,18}, {4,11}, {6,19}, {9,17}, {10,16}, {11,13}, {6,16}, {11,17}, {1,15}, {1,12}, {5,11}, {6,18}, {5,12}, {5,18}, {4,14}, {24,25}, {5,14}, {14,17}, {3,25}, {3,17}, {3,23}, {20,27}, {10,15}, {7,24}, {8,19}, {1,10}, {1,13}, {1,18}, {1,4}, {11,19}, {6,9}, {8,27}, {7,15}, {2,23}, {2,20}, {18,24}, {4,19}, {10,19}, {9,13}, {8,18}, {4,7}, {2,9}, {17,22}, {3,28}, {20,22}, {10,28}, {7,19}, {8,9}, {1,8}, {1,7}, {7,20}, {8,10}, {9,11}, {6,14}, {3,15}, {12,23}, {7,9}, {8,14}, {2,14}, {12,15}, {2,12}, {2,5}, {4,12}, {5,24}, {14,28}, {16,25}, {17,24}, {3,19}, {21,23}, {26,27}, {15,22}, {22,24}, {19,28}, {10,22}, {13,28}, {1,22}, {1,28}, {6,28}, {19,27}, {9,15}, {8,23}, {14,26}, {22,25}, {17,25}, {24,27}, {21,28}, {16,27}, {1,23}, {11,27}, {6,15}, {15,19}, {10,23}, {13,20}, {1,26}, {11,25}, {6,21}, {2,6}, {2,17}, {12,13}, {5,26}, {16,17}, {13,24}, {19,26}, {25,27}, {15,21}, {23,26}, {22,28}, {25,28}, {16,21}, {24,26}, {19,22}, {19,23}, {9,20}, {7,14}, {12,17}, {3,5}, {4,20}, {10,24}, {23,25}, {20,21}, {9,26}, {14,22}, {9,21}, {14,27}, {17,20}, {3,10}, {10,27}, {7,21}, {11,20}, {6,10}, {3,7}, {15,18}, {2,3}, {12,27}, {5,15}, {4,5}, {14,16}, {6,17}, {3,6}, {17,23}, {13,27}, {15,26}, {6,24}, {17,19}, {10,13}, {6,22}, {17,28}, {13,22}, {26,28}, {8,13}, {7,26}, {15,25}, {3,20}, {4,26}, {9,16}, {11,14}, {2,15}, {3,14}, {5,13}, {18,26}, {14,18}, {4,25}, {4,22}, {24,28}, {14,19}, {9,25}, {8,17}, {17,27}, {4,24}, {19,24}, {13,16}, {16,22}, {11,28}, {9,12}, {5,8}, {7,18}, {8,21}, {7,27}, {2,21}, {2,27}, {10,20}, {8,11}, {2,18}, {2,4}, {13,23}, {11,15}, {14,15}, {12,25}, {5,17}, {3,18}, {4,16}, {11,24}, {6,13}, {17,26}, {13,15}, {12,26}, {4,18}, {3,16}, {11,23}, {6,27}, {15,17}, {4,27}, {23,28}, {16,20}, {14,21}, {2,10}, {7,12}, {3,24}, {4,15}, {12,24}, {16,23}, {5,23}, {18,20}, {9,14}, {14,25}, {2,28}, {2,16}, {5,19}, {14,24}, {19,25}, {5,25}, {18,21}, {8,24}, {5,21}, {1,17}, {12,21}, {5,27}, {14,20}, {7,17}, {3,8}, {7,11}, {6,8}, {9,18}, {2,8}, {2,7}, {8,12}, {5,7}, {10,14}, {13,25}, {3,11}, {7,23}, {13,19}, {2,13}, {2,26}, {13,17}, {11,26}, {10,26}, {11,21}, {3,12}, {12,28}, {5,16}, {11,16}, {6,11}, {18,23}, {9,19}, {17,21}, {3,27}, {7,10}, {1,16}, {1,11}, {1,9}, {1,14}, {6,12}, {3,13}, {9,27}, {15,23}, {12,20}, {2,22}, {2,25}, {6,23}, {10,18}, {4,13}, {4,17}, {20,23}, {8,22}, {1,25}, {1,21}, {18,22}, {21,25}, {18,27}, {16,19}, {9,22}, {1,27}, {4,10}, {3,9}, {15,20}, {10,12}, {1,5}, {11,18}, {4,6}, {9,23}, {2,11}, {10,11}, {1,6}, {12,18}, {9,24}, {7,25}, {6,25}, {18,28}, {5,9}, {21,24}, {20,25}, {10,21}, {12,14}, {8,15}, {14,23}, {3,26}, {22,23}, {5,20}, {8,25}, {9,28}, {5,22}, {7,22}, {1,20}, {21,26}, {22,27}, {20,26}, {16,24}, {4,8}, {18,19}, {4,9}, {1,24}, {19,21}, {4,28}, {20,28}, {8,20}, {1,19}, {6,26}, {20,24}, {6,7}, {4,23}, {7,28}, {15,28}, {12,16}, {3,22}, {8,16}, {16,28} } Symmetric graph 26 of order 28 Valency 27 Diameter 1 Girth 3 Automorphism group of order 304888344611713860501504000000 Number of arcs = 756 Number of 2-arcs = 19656 2-arc-transitive true Edge-set { {1,2}, {12,16}, {14,21}, {23,26}, {17,24}, {10,21}, {4,15}, {6,11}, {26,28}, {8,9}, {8,10}, {5,21}, {2,4}, {22,27}, {12,19}, {4,14}, {7,13}, {6,19}, {5,28}, {15,25}, {16,22}, {5,15}, {2,16}, {13,21}, {4,9}, {14,19}, {7,24}, {23,27}, {1,26}, {11,17}, {10,22}, {15,19}, {3,28}, {1,25}, {1,4}, {7,11}, {13,19}, {5,9}, {18,27}, {12,20}, {7,23}, {23,24}, {13,27}, {9,12}, {16,23}, {14,24}, {3,21}, {22,25}, {19,22}, {1,10}, {11,15}, {9,28}, {8,25}, {11,24}, {26,27}, {6,12}, {21,28}, {8,14}, {10,13}, {5,7}, {2,23}, {1,27}, {11,12}, {2,19}, {5,6}, {12,18}, {20,21}, {12,22}, {19,21}, {14,28}, {13,25}, {1,3}, {1,11}, {9,22}, {20,24}, {3,27}, {17,26}, {17,18}, {11,28}, {25,26}, {9,11}, {8,26}, {3,24}, {17,22}, {11,23}, {24,26}, {9,10}, {8,15}, {2,21}, {4,6}, {7,18}, {20,23}, {1,7}, {5,12}, {14,27}, {12,13}, {19,25}, {5,22}, {15,18}, {16,20}, {9,14}, {8,13}, {6,24}, {27,28}, {4,26}, {7,17}, {4,5}, {10,15}, {15,16}, {3,5}, {13,28}, {9,25}, {11,16}, {14,26}, {12,24}, {21,27}, {13,17}, {1,16}, {11,14}, {4,13}, {7,9}, {20,26}, {3,17}, {17,21}, {4,18}, {7,26}, {17,23}, {1,21}, {4,11}, {10,19}, {3,18}, {1,20}, {2,12}, {6,21}, {12,14}, {7,25}, {22,23}, {9,17}, {8,18}, {2,24}, {6,27}, {6,8}, {10,28}, {8,20}, {3,10}, {5,13}, {6,18}, {20,28}, {14,25}, {13,22}, {6,15}, {16,28}, {2,9}, {7,8}, {10,23}, {13,26}, {6,9}, {8,28}, {5,25}, {2,22}, {15,27}, {16,21}, {4,22}, {7,19}, {3,25}, {18,26}, {12,28}, {21,25}, {10,24}, {3,26}, {1,17}, {1,18}, {11,20}, {9,23}, {20,27}, {3,12}, {18,24}, {10,25}, {15,22}, {3,15}, {19,24}, {5,27}, {6,22}, {19,28}, {9,19}, {2,13}, {3,19}, {1,5}, {18,25}, {20,22}, {14,23}, {13,24}, {6,10}, {15,28}, {9,26}, {8,17}, {21,24}, {4,27}, {3,8}, {12,23}, {10,14}, {13,15}, {3,22}, {1,19}, {25,28}, {6,17}, {18,28}, {2,8}, {8,21}, {4,10}, {6,28}, {8,11}, {10,26}, {12,21}, {4,21}, {14,22}, {2,11}, {2,20}, {3,6}, {12,17}, {18,21}, {16,26}, {14,17}, {4,7}, {15,17}, {20,25}, {15,20}, {3,16}, {9,16}, {4,24}, {7,27}, {7,16}, {5,19}, {2,5}, {16,18}, {2,6}, {3,13}, {1,9}, {4,20}, {3,7}, {17,19}, {5,18}, {10,18}, {1,23}, {7,12}, {19,23}, {5,24}, {16,25}, {5,11}, {2,26}, {1,28}, {4,25}, {7,22}, {5,16}, {13,18}, {9,20}, {24,27}, {12,27}, {21,23}, {11,25}, {2,18}, {6,20}, {19,26}, {5,17}, {8,12}, {22,26}, {2,27}, {9,27}, {11,22}, {1,14}, {9,21}, {18,20}, {3,20}, {18,23}, {10,11}, {15,26}, {3,9}, {1,8}, {2,7}, {19,27}, {6,25}, {22,28}, {10,16}, {4,8}, {22,24}, {2,15}, {6,16}, {11,26}, {5,10}, {1,12}, {6,23}, {11,21}, {18,19}, {5,20}, {7,10}, {19,20}, {14,16}, {15,21}, {4,16}, {4,19}, {14,15}, {13,16}, {2,28}, {21,26}, {4,17}, {21,22}, {15,23}, {13,14}, {16,17}, {14,18}, {6,7}, {10,17}, {3,4}, {24,28}, {8,27}, {10,12}, {17,27}, {23,25}, {8,19}, {25,27}, {23,28}, {24,25}, {1,13}, {7,14}, {2,3}, {1,6}, {12,25}, {13,20}, {17,25}, {9,13}, {18,22}, {7,28}, {13,23}, {9,24}, {3,14}, {16,24}, {17,20}, {2,17}, {5,14}, {2,25}, {12,15}, {1,24}, {11,27}, {7,20}, {5,23}, {16,19}, {8,23}, {16,27}, {4,23}, {6,14}, {12,26}, {3,11}, {9,18}, {11,18}, {15,24}, {4,12}, {1,22}, {11,19}, {10,27}, {3,23}, {4,28}, {8,22}, {7,21}, {1,15}, {10,20}, {5,8}, {2,10}, {5,26}, {8,24}, {8,16}, {9,15}, {14,20}, {17,28}, {11,13}, {7,15}, {6,26}, {2,14}, {6,13} } ................................................................... Symmetric connected graphs of order 29 Symmetric graph 1 of order 29 Valency 2 Diameter 14 Girth 29 Automorphism group of order 58 Number of arcs = 58 Number of 2-arcs = 58 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,7}, {4,7}, {4,24}, {8,24}, {8,14}, {5,14}, {5,12}, {12,25}, {25,27}, {9,27}, {9,20}, {15,20}, {15,29}, {6,29}, {6,23}, {13,23}, {11,13}, {11,26}, {19,26}, {19,28}, {22,28}, {10,22}, {10,18}, {18,21}, {17,21}, {16,17}, {1,16} } Symmetric graph 2 of order 29 Valency 4 Diameter 4 Girth 4 Automorphism group of order 116 Number of arcs = 116 Number of 2-arcs = 348 2-arc-transitive false Edge-set { {1,2}, {1,9}, {2,3}, {1,16}, {2,20}, {9,10}, {3,7}, {1,23}, {9,27}, {3,15}, {16,17}, {18,20}, {10,14}, {4,7}, {2,13}, {6,16}, {9,20}, {10,22}, {7,29}, {23,24}, {25,27}, {15,21}, {17,21}, {5,18}, {11,14}, {4,24}, {3,11}, {13,23}, {16,27}, {15,20}, {17,29}, {10,18}, {8,14}, {4,6}, {8,13}, {22,28}, {24,28}, {12,25}, {12,21}, {18,21}, {5,26}, {8,24}, {7,26}, {11,13}, {6,23}, {22,27}, {15,29}, {17,25}, {5,14}, {8,22}, {4,19}, {19,28}, {25,28}, {5,12}, {12,19}, {11,26}, {6,29}, {19,26} } Symmetric graph 3 of order 29 Valency 14 Diameter 2 Girth 3 Automorphism group of order 406 Number of arcs = 406 Number of 2-arcs = 5278 2-arc-transitive false Edge-set { {1,2}, {1,6}, {2,3}, {1,10}, {2,23}, {6,7}, {3,7}, {1,14}, {2,18}, {6,27}, {3,13}, {10,11}, {4,23}, {7,11}, {4,7}, {1,18}, {2,5}, {6,22}, {3,21}, {3,10}, {9,23}, {7,17}, {14,15}, {18,26}, {8,27}, {13,24}, {11,15}, {4,26}, {8,11}, {4,24}, {1,22}, {2,21}, {6,9}, {3,12}, {10,26}, {10,23}, {7,25}, {7,14}, {7,18}, {13,27}, {13,20}, {11,21}, {4,16}, {18,19}, {5,29}, {2,22}, {19,21}, {9,14}, {17,28}, {15,19}, {26,29}, {2,8}, {19,24}, {12,15}, {14,26}, {8,28}, {8,24}, {1,26}, {2,10}, {6,25}, {3,17}, {10,13}, {20,23}, {7,16}, {2,14}, {14,27}, {13,18}, {11,29}, {4,27}, {11,18}, {4,5}, {11,22}, {4,21}, {9,11}, {17,24}, {15,25}, {17,26}, {8,20}, {1,24}, {22,23}, {21,28}, {5,9}, {6,12}, {6,26}, {23,25}, {5,20}, {16,22}, {19,23}, {28,29}, {6,19}, {3,14}, {23,28}, {16,19}, {25,29}, {5,19}, {4,12}, {14,22}, {12,28}, {8,14}, {2,19}, {6,14}, {3,18}, {10,29}, {23,27}, {7,21}, {14,17}, {24,27}, {13,15}, {11,20}, {1,4}, {6,18}, {3,5}, {17,22}, {5,15}, {3,8}, {9,24}, {15,22}, {21,26}, {8,9}, {12,24}, {15,26}, {8,25}, {20,26}, {8,16}, {19,29}, {27,29}, {1,28}, {26,27}, {4,25}, {9,13}, {12,20}, {10,16}, {13,28}, {5,7}, {13,22}, {24,25}, {5,10}, {22,25}, {12,18}, {5,14}, {6,23}, {3,28}, {10,18}, {5,23}, {7,22}, {3,27}, {11,25}, {4,17}, {18,21}, {5,16}, {17,19}, {15,24}, {1,8}, {2,24}, {10,22}, {21,23}, {7,9}, {7,12}, {9,19}, {12,29}, {19,26}, {2,25}, {12,13}, {14,20}, {16,28}, {6,28}, {8,29}, {13,17}, {16,24}, {10,27}, {21,25}, {9,18}, {5,12}, {13,23}, {9,27}, {11,26}, {4,10}, {15,29}, {8,21}, {17,21}, {9,20}, {1,12}, {19,28}, {25,27}, {11,13}, {4,20}, {11,16}, {20,28}, {6,29}, {16,17}, {18,24}, {17,27}, {20,21}, {9,16}, {12,25}, {2,15}, {15,20}, {1,16}, {22,28}, {3,29}, {15,17}, {1,20}, {16,29} } Symmetric graph 4 of order 29 Valency 28 Diameter 1 Girth 3 Automorphism group of order 8841761993739701954543616000000 Number of arcs = 812 Number of 2-arcs = 21924 2-arc-transitive true Edge-set { {1,2}, {1,3}, {2,3}, {1,4}, {2,7}, {3,4}, {3,7}, {1,5}, {2,24}, {3,8}, {4,5}, {7,24}, {4,8}, {4,7}, {1,6}, {2,12}, {3,25}, {4,9}, {7,14}, {5,6}, {12,24}, {8,25}, {5,9}, {14,24}, {5,8}, {4,24}, {1,7}, {2,23}, {3,13}, {4,26}, {7,27}, {5,10}, {20,24}, {8,15}, {6,7}, {12,23}, {13,25}, {9,26}, {14,27}, {6,10}, {12,20}, {15,25}, {6,9}, {12,14}, {5,25}, {8,24}, {1,8}, {2,4}, {3,24}, {4,14}, {7,11}, {5,27}, {19,24}, {8,28}, {6,11}, {12,18}, {21,25}, {9,16}, {14,29}, {7,8}, {4,23}, {13,24}, {14,26}, {11,27}, {10,27}, {19,20}, {15,28}, {18,23}, {13,21}, {16,26}, {27,29}, {7,10}, {20,23}, {13,15}, {6,26}, {12,27}, {9,25}, {8,14}, {1,9}, {2,14}, {3,5}, {4,25}, {5,15}, {5,24}, {8,12}, {6,28}, {9,12}, {20,25}, {9,29}, {14,22}, {7,12}, {23,26}, {13,19}, {22,26}, {17,27}, {10,17}, {1,20}, {2,15}, {8,9}, {14,25}, {8,11}, {15,27}, {5,19}, {12,28}, {11,28}, {9,18}, {20,21}, {16,29}, {22,29}, {11,17}, {1,19}, {2,28}, {4,18}, {21,24}, {14,16}, {11,29}, {19,23}, {13,28}, {10,26}, {20,27}, {9,15}, {5,14}, {1,10}, {2,20}, {3,15}, {4,6}, {5,26}, {24,27}, {6,16}, {12,29}, {6,25}, {9,13}, {7,29}, {22,23}, {10,13}, {21,26}, {2,10}, {6,20}, {15,23}, {8,13}, {14,20}, {23,27}, {10,19}, {18,28}, {11,18}, {16,18}, {1,21}, {3,16}, {3,29}, {9,10}, {15,26}, {16,28}, {13,29}, {22,25}, {21,22}, {15,17}, {2,17}, {3,22}, {8,17}, {11,22}, {18,19}, {21,28}, {10,16}, {20,29}, {6,15}, {5,12}, {1,11}, {2,18}, {3,21}, {4,16}, {5,7}, {23,24}, {6,27}, {12,19}, {25,28}, {7,17}, {1,23}, {2,13}, {7,26}, {10,14}, {11,20}, {2,8}, {11,14}, {22,27}, {17,19}, {3,11}, {3,18}, {7,21}, {16,24}, {9,14}, {15,21}, {24,28}, {19,29}, {1,22}, {4,17}, {10,11}, {18,20}, {16,27}, {17,29}, {17,22}, {1,18}, {2,21}, {7,16}, {23,29}, {6,13}, {12,25}, {1,12}, {2,26}, {3,19}, {4,22}, {5,17}, {1,24}, {6,8}, {4,12}, {24,25}, {7,28}, {9,23}, {13,20}, {26,29}, {8,18}, {3,14}, {8,27}, {4,19}, {11,15}, {5,18}, {12,21}, {3,9}, {12,15}, {23,28}, {8,22}, {17,25}, {10,15}, {5,20}, {16,22}, {25,29}, {11,12}, {18,26}, {19,21}, {17,28}, {3,17}, {11,23}, {13,26}, {25,27}, {1,13}, {2,25}, {3,27}, {4,20}, {5,23}, {10,24}, {6,18}, {12,16}, {1,25}, {7,9}, {14,23}, {5,13}, {25,26}, {8,29}, {14,21}, {2,27}, {6,19}, {9,19}, {4,15}, {9,28}, {13,22}, {4,10}, {7,20}, {13,16}, {24,29}, {11,16}, {18,29}, {6,21}, {17,23}, {12,13}, {19,27}, {20,22}, {11,19}, {26,28}, {9,27}, {1,14}, {2,11}, {3,26}, {4,28}, {5,21}, {15,24}, {6,24}, {11,25}, {7,19}, {21,23}, {13,17}, {1,26}, {8,10}, {6,14}, {26,27}, {2,9}, {15,22}, {3,28}, {10,20}, {20,28}, {5,16}, {10,29}, {5,11}, {18,24}, {8,21}, {14,17}, {12,17}, {2,19}, {7,22}, {13,14}, {19,22}, {10,28}, {9,20}, {1,15}, {2,5}, {3,12}, {4,27}, {5,29}, {22,24}, {6,22}, {16,25}, {7,25}, {8,23}, {12,26}, {8,20}, {14,18}, {1,27}, {9,11}, {7,15}, {27,28}, {3,10}, {3,20}, {16,23}, {4,29}, {11,21}, {15,18}, {21,29}, {6,17}, {6,12}, {19,25}, {9,22}, {13,18}, {14,15}, {18,22}, {10,21}, {15,20}, {1,16}, {2,29}, {3,6}, {4,13}, {5,28}, {9,24}, {2,6}, {23,25}, {7,23}, {10,23}, {17,26}, {8,26}, {13,27}, {9,21}, {15,19}, {1,28}, {10,12}, {20,26}, {8,16}, {28,29}, {4,11}, {7,18}, {4,21}, {17,24}, {12,22}, {16,19}, {2,22}, {7,13}, {14,19}, {15,16}, {17,18}, {16,21}, {15,29}, {1,17}, {11,24}, {6,29}, {10,25}, {3,23}, {24,26}, {18,27}, {14,28}, {10,22}, {17,20}, {16,20}, {1,29}, {11,13}, {18,25}, {21,27}, {9,17}, {8,19}, {5,22}, {13,23}, {16,17}, {2,16}, {6,23}, {11,26}, {19,28}, {10,18}, {18,21}, {17,21}, {19,26}, {22,28} } ................................................................... Symmetric connected graphs of order 30 Symmetric graph 1 of order 30 Valency 2 Diameter 15 Girth 30 Automorphism group of order 60 Number of arcs = 60 Number of 2-arcs = 60 2-arc-transitive true Edge-set { {1,4}, {1,29}, {27,29}, {25,27}, {24,25}, {22,24}, {20,22}, {17,20}, {15,17}, {14,15}, {12,14}, {10,12}, {7,10}, {6,7}, {3,6}, {2,3}, {2,30}, {28,30}, {26,28}, {23,26}, {21,23}, {19,21}, {18,19}, {16,18}, {13,16}, {11,13}, {9,11}, {8,9}, {5,8}, {4,5} } Symmetric graph 2 of order 30 Valency 3 Diameter 4 Girth 8 Automorphism group of order 1440 Number of arcs = 90 Number of 2-arcs = 180 2-arc-transitive true Edge-set { {1,22}, {1,30}, {10,28}, {1,23}, {5,28}, {6,29}, {15,28}, {5,29}, {6,24}, {3,27}, {2,18}, {12,29}, {6,23}, {5,27}, {2,24}, {3,19}, {13,18}, {11,17}, {7,25}, {9,27}, {2,20}, {3,22}, {15,18}, {11,24}, {7,19}, {13,22}, {10,17}, {14,17}, {4,25}, {12,26}, {14,21}, {9,21}, {11,19}, {7,16}, {10,30}, {12,25}, {13,26}, {4,30}, {8,21}, {9,20}, {4,20}, {14,26}, {8,23}, {15,16}, {8,16} } Symmetric graph 3 of order 30 Valency 4 Diameter 5 Girth 4 Automorphism group of order 120 Number of arcs = 120 Number of 2-arcs = 360 2-arc-transitive false Edge-set { {1,3}, {2,10}, {8,29}, {1,30}, {23,25}, {21,23}, {2,24}, {22,29}, {5,28}, {19,28}, {27,30}, {20,21}, {15,18}, {13,15}, {11,13}, {16,24}, {14,22}, {12,19}, {3,25}, {18,25}, {10,18}, {26,27}, {17,20}, {9,11}, {8,10}, {5,8}, {3,5}, {7,16}, {6,14}, {4,12}, {1,23}, {15,23}, {8,15}, {24,26}, {16,17}, {7,9}, {2,29}, {28,29}, {25,28}, {7,30}, {6,27}, {4,26}, {21,30}, {13,21}, {5,13}, {22,24}, {14,16}, {6,7}, {19,22}, {18,19}, {20,27}, {17,26}, {11,20}, {3,11}, {12,14}, {4,6}, {10,12}, {9,17}, {1,9}, {2,4} } Symmetric graph 4 of order 30 Valency 4 Diameter 5 Girth 3 Automorphism group of order 120 Number of arcs = 120 Number of 2-arcs = 360 2-arc-transitive false Edge-set { {1,4}, {2,12}, {13,20}, {6,11}, {14,27}, {23,25}, {5,10}, {5,7}, {2,28}, {17,26}, {6,22}, {13,15}, {23,29}, {8,22}, {3,8}, {1,18}, {11,18}, {14,21}, {9,16}, {16,24}, {7,29}, {20,25}, {13,28}, {25,29}, {4,29}, {12,17}, {17,19}, {10,12}, {15,28}, {26,30}, {19,21}, {14,19}, {8,30}, {3,28}, {18,25}, {15,23}, {10,23}, {5,21}, {6,9}, {16,27}, {9,24}, {4,27}, {18,20}, {7,21}, {24,26}, {24,30}, {9,11}, {10,15}, {13,22}, {1,11}, {2,3}, {3,30}, {2,17}, {20,22}, {14,16}, {4,7}, {5,12}, {1,27}, {19,26}, {6,8} } Symmetric graph 5 of order 30 Valency 4 Diameter 4 Girth 4 Automorphism group of order 120 Number of arcs = 120 Number of 2-arcs = 360 2-arc-transitive false Edge-set { {1,4}, {11,30}, {1,17}, {6,13}, {12,16}, {11,18}, {7,17}, {24,28}, {5,22}, {14,22}, {10,15}, {13,17}, {8,16}, {18,25}, {4,7}, {19,25}, {8,23}, {6,24}, {8,27}, {21,24}, {20,21}, {9,29}, {18,28}, {7,22}, {22,26}, {3,10}, {15,17}, {25,30}, {13,27}, {3,26}, {3,20}, {4,24}, {5,19}, {2,26}, {19,23}, {7,9}, {14,23}, {8,25}, {20,29}, {2,29}, {18,21}, {6,15}, {12,27}, {2,28}, {16,29}, {2,14}, {4,30}, {1,19}, {10,23}, {13,20}, {3,27}, {15,26}, {5,9}, {11,14}, {5,12}, {1,12}, {10,11}, {6,30}, {9,28}, {16,21} } Symmetric graph 6 of order 30 Valency 4 Diameter 3 Girth 5 Automorphism group of order 120 Number of arcs = 120 Number of 2-arcs = 360 2-arc-transitive false Edge-set { {1,3}, {16,25}, {13,19}, {11,30}, {8,9}, {18,21}, {12,28}, {2,4}, {24,29}, {8,28}, {21,26}, {6,23}, {5,16}, {1,10}, {18,30}, {15,26}, {14,20}, {3,19}, {4,23}, {10,28}, {6,29}, {7,16}, {11,13}, {2,9}, {19,25}, {5,24}, {12,29}, {7,10}, {17,22}, {11,27}, {18,25}, {13,28}, {20,26}, {3,14}, {1,23}, {9,22}, {2,21}, {8,15}, {23,30}, {7,27}, {22,25}, {6,15}, {17,29}, {5,8}, {10,21}, {12,18}, {16,20}, {4,20}, {3,24}, {9,27}, {5,30}, {12,14}, {6,7}, {11,17}, {17,26}, {14,27}, {4,13}, {2,24}, {1,22}, {15,19} } Symmetric graph 7 of order 30 Valency 4 Diameter 3 Girth 5 Automorphism group of order 240 Number of arcs = 120 Number of 2-arcs = 360 2-arc-transitive false Edge-set { {1,9}, {12,21}, {3,13}, {6,30}, {11,27}, {1,25}, {5,19}, {7,27}, {2,26}, {5,17}, {22,28}, {12,15}, {13,23}, {8,24}, {3,17}, {18,22}, {11,16}, {14,24}, {8,9}, {1,16}, {18,29}, {6,20}, {13,25}, {5,29}, {4,14}, {17,30}, {16,19}, {10,29}, {8,28}, {14,26}, {4,21}, {12,19}, {8,13}, {10,28}, {15,25}, {7,23}, {2,10}, {5,23}, {9,27}, {16,26}, {19,24}, {4,25}, {4,18}, {17,21}, {6,24}, {2,30}, {11,20}, {15,20}, {11,22}, {1,29}, {3,22}, {9,30}, {2,15}, {20,23}, {7,14}, {7,10}, {12,28}, {21,27}, {3,26}, {6,18} } Symmetric graph 8 of order 30 Valency 4 Diameter 5 Girth 3 Automorphism group of order 240 Number of arcs = 120 Number of 2-arcs = 360 2-arc-transitive false Edge-set { {1,5}, {2,7}, {22,29}, {5,8}, {27,30}, {19,28}, {23,26}, {2,6}, {22,28}, {16,27}, {12,25}, {4,15}, {11,19}, {23,30}, {4,14}, {1,8}, {21,30}, {15,19}, {11,23}, {13,16}, {7,12}, {18,24}, {3,16}, {10,14}, {4,17}, {14,25}, {10,25}, {6,7}, {28,29}, {20,27}, {24,25}, {8,19}, {17,30}, {14,15}, {13,26}, {5,18}, {9,13}, {10,21}, {1,10}, {3,5}, {12,24}, {3,18}, {21,27}, {15,28}, {11,26}, {12,20}, {24,29}, {3,13}, {4,6}, {2,22}, {9,22}, {6,17}, {18,29}, {2,9}, {16,20}, {8,11}, {17,23}, {9,26}, {1,21}, {7,20} } Symmetric graph 9 of order 30 Valency 4 Diameter 4 Girth 6 Automorphism group of order 720 Number of arcs = 120 Number of 2-arcs = 360 2-arc-transitive true Edge-set { {1,4}, {7,10}, {4,18}, {13,16}, {16,29}, {10,24}, {18,25}, {20,21}, {11,27}, {5,21}, {11,19}, {8,29}, {2,24}, {22,25}, {26,27}, {5,14}, {9,14}, {15,19}, {3,8}, {2,28}, {22,23}, {28,30}, {9,12}, {15,17}, {3,6}, {7,23}, {6,20}, {13,30}, {12,26}, {1,17}, {7,16}, {1,10}, {20,27}, {13,21}, {4,26}, {11,16}, {4,29}, {5,10}, {24,27}, {18,21}, {11,14}, {18,19}, {2,29}, {5,8}, {24,25}, {14,28}, {9,25}, {3,19}, {2,15}, {8,22}, {6,28}, {22,30}, {9,17}, {3,12}, {15,23}, {1,6}, {20,23}, {26,30}, {13,17}, {7,12} } Symmetric graph 10 of order 30 Valency 4 Diameter 7 Girth 4 Automorphism group of order 983040 Number of arcs = 120 Number of 2-arcs = 360 2-arc-transitive false Edge-set { {1,11}, {20,21}, {2,12}, {1,29}, {19,21}, {19,22}, {10,20}, {2,29}, {1,30}, {2,30}, {20,22}, {17,29}, {9,19}, {10,19}, {9,20}, {10,28}, {18,29}, {18,30}, {17,30}, {7,17}, {9,28}, {10,27}, {9,27}, {15,28}, {8,18}, {7,18}, {8,17}, {7,25}, {16,28}, {16,27}, {15,27}, {5,15}, {8,25}, {7,26}, {8,26}, {14,25}, {6,16}, {5,16}, {6,15}, {5,23}, {13,25}, {13,26}, {14,26}, {4,14}, {6,23}, {5,24}, {6,24}, {11,23}, {3,13}, {4,13}, {3,14}, {4,21}, {12,23}, {12,24}, {11,24}, {3,21}, {4,22}, {3,22}, {1,12}, {2,11} } Symmetric graph 11 of order 30 Valency 6 Diameter 3 Girth 4 Automorphism group of order 720 Number of arcs = 180 Number of 2-arcs = 900 2-arc-transitive false Edge-set { {1,7}, {7,15}, {3,8}, {15,30}, {3,27}, {9,13}, {18,30}, {11,27}, {9,24}, {14,28}, {2,25}, {2,18}, {11,23}, {6,24}, {14,19}, {2,16}, {16,29}, {12,26}, {8,22}, {2,8}, {9,23}, {6,21}, {19,27}, {6,16}, {12,29}, {19,26}, {3,17}, {10,24}, {4,23}, {13,20}, {1,17}, {8,13}, {1,9}, {14,21}, {12,24}, {15,19}, {4,17}, {10,28}, {12,23}, {7,22}, {5,19}, {21,25}, {4,18}, {20,25}, {13,28}, {1,25}, {7,14}, {11,29}, {21,26}, {4,19}, {16,28}, {12,30}, {4,22}, {5,16}, {4,21}, {18,28}, {15,20}, {11,22}, {13,21}, {10,22}, {12,25}, {15,29}, {3,26}, {6,17}, {10,30}, {3,16}, {11,28}, {5,24}, {11,25}, {20,27}, {6,20}, {17,30}, {5,20}, {17,29}, {10,27}, {1,27}, {6,22}, {5,18}, {3,9}, {7,24}, {13,30}, {1,18}, {10,26}, {8,15}, {2,26}, {5,23}, {9,14}, {2,7}, {8,23}, {14,29} } Symmetric graph 12 of order 30 Valency 6 Diameter 3 Girth 4 Automorphism group of order 1440 Number of arcs = 180 Number of 2-arcs = 900 2-arc-transitive false Edge-set { {1,7}, {5,11}, {6,26}, {19,30}, {2,14}, {12,13}, {15,29}, {21,30}, {9,29}, {24,28}, {8,25}, {7,20}, {16,30}, {9,23}, {17,29}, {11,24}, {3,23}, {23,27}, {14,18}, {5,16}, {11,22}, {1,10}, {6,27}, {10,24}, {17,28}, {19,27}, {3,13}, {22,23}, {7,27}, {5,28}, {14,19}, {3,28}, {4,27}, {1,13}, {13,17}, {10,26}, {22,25}, {8,21}, {1,16}, {11,15}, {10,30}, {5,18}, {12,19}, {4,26}, {2,24}, {12,23}, {18,27}, {20,28}, {4,14}, {21,24}, {18,22}, {3,25}, {1,23}, {6,17}, {18,30}, {21,26}, {9,25}, {8,28}, {4,24}, {1,18}, {2,17}, {5,25}, {7,26}, {7,22}, {13,20}, {4,15}, {12,16}, {7,15}, {9,19}, {20,29}, {6,9}, {2,15}, {14,25}, {17,21}, {2,8}, {11,14}, {10,20}, {12,21}, {13,26}, {2,9}, {22,29}, {3,16}, {5,10}, {6,15}, {11,20}, {6,12}, {8,16}, {3,29}, {8,19}, {4,30} } Symmetric graph 13 of order 30 Valency 6 Diameter 5 Girth 4 Automorphism group of order 1209323520 Number of arcs = 180 Number of 2-arcs = 900 2-arc-transitive false Edge-set { {1,16}, {2,18}, {1,30}, {3,17}, {3,28}, {2,29}, {13,30}, {14,29}, {15,28}, {13,26}, {15,27}, {14,25}, {11,26}, {12,25}, {10,27}, {11,22}, {10,23}, {12,24}, {7,22}, {8,24}, {9,23}, {7,19}, {9,20}, {8,21}, {5,19}, {6,21}, {4,20}, {5,18}, {4,16}, {6,17}, {3,18}, {1,17}, {2,16}, {3,29}, {2,30}, {1,28}, {15,29}, {13,28}, {14,30}, {15,25}, {14,26}, {13,27}, {10,25}, {11,27}, {12,26}, {10,24}, {12,22}, {11,23}, {9,24}, {7,23}, {8,22}, {9,21}, {8,19}, {7,20}, {4,21}, {5,20}, {6,19}, {4,17}, {6,18}, {5,16}, {2,17}, {3,16}, {1,18}, {2,28}, {1,29}, {3,30}, {14,28}, {15,30}, {13,29}, {14,27}, {13,25}, {15,26}, {12,27}, {10,26}, {11,25}, {12,23}, {11,24}, {10,22}, {8,23}, {9,22}, {7,24}, {8,20}, {7,21}, {9,19}, {6,20}, {4,19}, {5,21}, {6,16}, {5,17}, {4,18} } Symmetric graph 14 of order 30 Valency 7 Diameter 3 Girth 4 Automorphism group of order 40320 Number of arcs = 210 Number of 2-arcs = 1260 2-arc-transitive true Edge-set { {1,16}, {15,18}, {9,18}, {11,23}, {3,24}, {6,23}, {3,26}, {5,27}, {6,21}, {3,28}, {4,29}, {2,27}, {6,28}, {3,21}, {14,29}, {10,20}, {7,25}, {2,30}, {15,28}, {3,19}, {5,29}, {1,29}, {13,30}, {8,20}, {7,19}, {2,19}, {5,28}, {3,30}, {15,29}, {13,20}, {14,25}, {8,27}, {9,22}, {12,22}, {8,17}, {11,19}, {5,24}, {10,29}, {13,25}, {13,18}, {12,17}, {11,17}, {8,16}, {9,26}, {10,22}, {8,26}, {10,19}, {5,25}, {3,17}, {11,29}, {13,24}, {12,25}, {4,22}, {12,20}, {7,16}, {6,16}, {2,26}, {2,23}, {5,26}, {10,21}, {10,28}, {4,25}, {13,27}, {12,23}, {7,24}, {1,23}, {1,21}, {9,16}, {14,26}, {14,16}, {13,21}, {10,27}, {12,28}, {4,17}, {7,22}, {8,23}, {2,18}, {9,28}, {8,21}, {14,19}, {6,19}, {14,30}, {15,27}, {1,22}, {12,30}, {7,17}, {7,27}, {6,18}, {15,30}, {4,21}, {14,20}, {4,18}, {9,20}, {15,17}, {5,23}, {1,24}, {1,30}, {2,22}, {15,16}, {4,26}, {11,20}, {9,24}, {11,24}, {6,25}, {11,18} } Symmetric graph 15 of order 30 Valency 8 Diameter 3 Girth 4 Automorphism group of order 1440 Number of arcs = 240 Number of 2-arcs = 1680 2-arc-transitive false Edge-set { {1,3}, {1,6}, {3,5}, {1,9}, {3,7}, {6,10}, {5,8}, {1,18}, {3,11}, {6,14}, {5,9}, {9,17}, {7,12}, {10,13}, {8,10}, {3,19}, {6,21}, {5,13}, {9,25}, {7,16}, {10,18}, {8,11}, {4,18}, {11,20}, {14,22}, {9,14}, {17,26}, {12,15}, {13,17}, {10,12}, {6,7}, {5,22}, {9,11}, {7,23}, {10,26}, {8,15}, {18,19}, {11,28}, {14,30}, {3,17}, {12,19}, {13,21}, {6,19}, {8,21}, {12,25}, {16,24}, {18,25}, {11,16}, {4,20}, {20,27}, {22,29}, {14,18}, {4,26}, {15,20}, {17,22}, {12,14}, {7,9}, {8,24}, {18,21}, {11,13}, {14,16}, {17,20}, {12,27}, {13,29}, {19,22}, {21,23}, {25,28}, {1,16}, {4,6}, {5,20}, {7,22}, {11,26}, {15,23}, {10,23}, {14,28}, {15,30}, {19,28}, {21,30}, {2,24}, {3,25}, {16,19}, {6,27}, {8,29}, {4,12}, {20,24}, {22,25}, {13,15}, {19,23}, {21,26}, {25,30}, {16,17}, {4,8}, {20,21}, {22,24}, {26,27}, {2,15}, {23,25}, {28,29}, {1,30}, {9,24}, {13,27}, {16,29}, {1,23}, {5,28}, {7,30}, {2,10}, {24,28}, {26,29}, {15,18}, {23,27}, {1,28}, {4,30}, {24,26}, {27,30}, {2,29}, {2,17}, {2,27}, {3,29}, {2,4}, {2,5} } Symmetric graph 16 of order 30 Valency 8 Diameter 3 Girth 3 Automorphism group of order 1440 Number of arcs = 240 Number of 2-arcs = 1680 2-arc-transitive false Edge-set { {1,3}, {7,9}, {2,29}, {5,11}, {17,27}, {8,28}, {26,30}, {2,17}, {15,22}, {16,21}, {10,12}, {6,15}, {11,28}, {23,27}, {4,25}, {8,21}, {10,30}, {14,19}, {8,23}, {13,20}, {7,24}, {12,18}, {16,18}, {1,14}, {15,17}, {11,15}, {16,30}, {12,14}, {10,24}, {6,20}, {24,28}, {12,27}, {18,25}, {5,19}, {6,30}, {14,28}, {3,26}, {5,29}, {13,27}, {18,22}, {9,16}, {13,22}, {7,25}, {14,21}, {8,10}, {14,17}, {8,15}, {5,16}, {12,29}, {13,18}, {20,21}, {15,29}, {11,13}, {12,16}, {22,24}, {3,9}, {2,4}, {19,22}, {1,27}, {21,25}, {15,25}, {9,23}, {2,28}, {22,26}, {16,26}, {6,12}, {7,17}, {19,26}, {6,23}, {5,24}, {3,27}, {20,25}, {18,28}, {5,10}, {6,14}, {2,13}, {7,22}, {6,9}, {3,20}, {20,24}, {8,26}, {17,26}, {7,16}, {19,29}, {13,23}, {9,11}, {1,30}, {4,19}, {19,23}, {3,24}, {14,24}, {3,8}, {11,30}, {4,23}, {4,7}, {1,18}, {5,21}, {10,27}, {2,12}, {1,25}, {1,11}, {17,21}, {2,20}, {3,29}, {4,28}, {21,23}, {4,10}, {5,13}, {7,27}, {11,17}, {25,29}, {1,19}, {4,30}, {9,29}, {8,18}, {20,30}, {9,28}, {2,26}, {10,15}, {6,22} } Symmetric graph 17 of order 30 Valency 8 Diameter 3 Girth 3 Automorphism group of order 1440 Number of arcs = 240 Number of 2-arcs = 1680 2-arc-transitive false Edge-set { {1,3}, {2,9}, {9,26}, {10,28}, {8,25}, {5,28}, {6,8}, {13,27}, {7,22}, {6,11}, {5,29}, {13,17}, {1,22}, {11,18}, {2,29}, {3,14}, {15,21}, {7,12}, {11,30}, {18,19}, {2,24}, {17,25}, {1,17}, {3,16}, {15,19}, {7,9}, {11,26}, {20,24}, {10,25}, {2,4}, {9,16}, {8,30}, {12,28}, {12,20}, {23,30}, {19,26}, {18,24}, {15,23}, {3,20}, {10,21}, {13,25}, {6,16}, {5,19}, {9,27}, {3,28}, {6,24}, {21,24}, {4,13}, {6,27}, {5,7}, {1,10}, {28,29}, {8,27}, {18,29}, {13,20}, {22,23}, {4,23}, {22,26}, {14,18}, {5,23}, {3,6}, {22,30}, {14,28}, {4,9}, {5,15}, {2,27}, {17,23}, {8,21}, {2,13}, {9,22}, {18,21}, {12,13}, {10,15}, {2,21}, {12,17}, {1,30}, {7,26}, {17,22}, {11,14}, {21,29}, {15,25}, {17,20}, {3,24}, {4,15}, {10,14}, {16,20}, {1,14}, {2,18}, {16,22}, {1,28}, {8,10}, {17,30}, {21,25}, {14,19}, {8,11}, {12,29}, {3,10}, {7,28}, {8,15}, {27,30}, {12,25}, {19,23}, {18,26}, {5,12}, {6,30}, {7,16}, {11,19}, {4,19}, {16,24}, {9,13}, {4,27}, {24,29}, {16,26}, {20,25}, {7,29}, {11,27}, {14,26}, {6,20}, {1,23}, {4,5} } Symmetric graph 18 of order 30 Valency 8 Diameter 3 Girth 4 Automorphism group of order 40320 Number of arcs = 240 Number of 2-arcs = 1680 2-arc-transitive true Edge-set { {1,4}, {6,9}, {14,23}, {2,13}, {4,26}, {4,20}, {7,17}, {3,10}, {13,18}, {6,16}, {6,23}, {6,30}, {22,23}, {8,22}, {9,12}, {5,14}, {3,24}, {3,7}, {11,18}, {2,17}, {26,29}, {2,20}, {7,26}, {2,11}, {19,26}, {20,25}, {7,16}, {21,25}, {10,16}, {13,27}, {17,25}, {5,19}, {8,24}, {5,22}, {9,24}, {7,28}, {8,10}, {12,13}, {12,16}, {6,20}, {10,30}, {13,22}, {16,22}, {10,28}, {16,29}, {6,21}, {15,30}, {17,22}, {9,29}, {15,26}, {5,15}, {14,17}, {3,29}, {18,28}, {8,15}, {5,12}, {1,29}, {19,21}, {1,25}, {16,25}, {13,19}, {4,8}, {9,27}, {14,21}, {3,27}, {1,18}, {17,27}, {2,30}, {22,26}, {11,14}, {3,19}, {3,25}, {16,18}, {12,17}, {20,29}, {2,26}, {19,30}, {8,25}, {25,30}, {20,24}, {7,23}, {11,27}, {18,21}, {1,27}, {14,20}, {15,21}, {9,15}, {15,17}, {5,29}, {10,23}, {13,24}, {4,28}, {5,24}, {24,28}, {7,9}, {12,28}, {10,11}, {21,24}, {11,29}, {8,27}, {1,12}, {12,30}, {20,22}, {6,13}, {5,10}, {11,15}, {2,28}, {14,28}, {4,30}, {18,26}, {8,18}, {23,27}, {1,19}, {19,23}, {4,9}, {2,3}, {1,14}, {4,23}, {6,11}, {7,21} } Symmetric graph 19 of order 30 Valency 8 Diameter 3 Girth 4 Automorphism group of order 1966080 Number of arcs = 240 Number of 2-arcs = 1680 2-arc-transitive false Edge-set { {1,11}, {4,14}, {13,29}, {5,16}, {11,28}, {15,21}, {9,27}, {8,17}, {19,25}, {14,29}, {1,29}, {18,24}, {8,26}, {2,30}, {2,15}, {10,19}, {18,23}, {12,28}, {3,22}, {16,21}, {9,28}, {4,21}, {9,13}, {20,26}, {6,24}, {10,27}, {4,18}, {10,14}, {3,18}, {14,26}, {1,12}, {16,22}, {20,25}, {5,24}, {1,30}, {6,23}, {7,12}, {17,24}, {8,25}, {2,29}, {1,15}, {8,11}, {15,27}, {11,27}, {7,26}, {6,20}, {2,16}, {5,20}, {11,24}, {1,16}, {16,28}, {12,24}, {16,27}, {4,28}, {4,13}, {13,30}, {17,23}, {7,25}, {3,21}, {6,19}, {4,22}, {10,13}, {17,30}, {19,26}, {10,28}, {9,14}, {13,26}, {18,29}, {18,30}, {2,26}, {14,30}, {4,17}, {7,11}, {20,21}, {3,17}, {14,25}, {19,21}, {6,29}, {13,25}, {17,29}, {1,25}, {6,30}, {2,25}, {5,29}, {5,15}, {15,22}, {5,23}, {8,12}, {20,22}, {19,22}, {10,23}, {12,27}, {15,28}, {4,27}, {9,24}, {10,24}, {3,27}, {5,19}, {11,23}, {8,21}, {12,23}, {3,28}, {8,22}, {7,21}, {9,20}, {9,23}, {3,13}, {7,22}, {10,20}, {3,14}, {9,19}, {8,18}, {1,26}, {5,30}, {2,11}, {6,15}, {6,16}, {2,12}, {7,18}, {7,17} } Symmetric graph 20 of order 30 Valency 8 Diameter 3 Girth 3 Automorphism group of order 3932160 Number of arcs = 240 Number of 2-arcs = 1680 2-arc-transitive false Edge-set { {1,3}, {5,28}, {14,21}, {22,25}, {7,24}, {20,29}, {12,17}, {11,30}, {15,18}, {9,14}, {16,24}, {2,17}, {2,6}, {4,10}, {7,20}, {12,26}, {4,9}, {9,29}, {3,13}, {6,26}, {13,23}, {8,27}, {14,24}, {20,28}, {1,16}, {7,27}, {22,26}, {7,16}, {5,26}, {19,28}, {11,21}, {16,23}, {10,19}, {13,21}, {8,19}, {9,20}, {12,29}, {22,24}, {7,28}, {4,5}, {8,20}, {12,30}, {16,18}, {4,14}, {12,25}, {22,23}, {18,29}, {9,30}, {8,23}, {25,27}, {19,29}, {11,17}, {19,27}, {26,28}, {16,17}, {1,5}, {14,22}, {13,24}, {15,17}, {1,6}, {1,4}, {20,27}, {12,22}, {1,15}, {10,30}, {18,30}, {7,15}, {10,13}, {19,30}, {8,15}, {5,27}, {2,18}, {2,3}, {21,23}, {2,4}, {3,9}, {5,25}, {20,30}, {12,18}, {9,19}, {11,29}, {3,10}, {14,23}, {21,24}, {8,28}, {17,30}, {1,18}, {3,5}, {10,14}, {6,25}, {4,6}, {3,14}, {10,20}, {11,25}, {15,23}, {6,27}, {21,25}, {8,24}, {4,13}, {6,28}, {10,29}, {13,22}, {21,26}, {15,24}, {1,17}, {7,23}, {26,27}, {2,5}, {17,29}, {7,19}, {2,15}, {3,6}, {25,28}, {11,26}, {12,21}, {11,18}, {9,13}, {11,22}, {8,16}, {2,16} } Symmetric graph 21 of order 30 Valency 9 Diameter 2 Girth 4 Automorphism group of order 7255941120 Number of arcs = 270 Number of 2-arcs = 2160 2-arc-transitive false Edge-set { {1,7}, {6,28}, {7,20}, {9,24}, {13,25}, {13,28}, {3,30}, {12,27}, {24,27}, {5,22}, {14,19}, {10,17}, {5,18}, {3,10}, {5,24}, {22,27}, {15,25}, {16,21}, {7,19}, {5,16}, {17,19}, {3,7}, {1,10}, {12,26}, {6,29}, {14,20}, {2,11}, {15,28}, {11,27}, {15,21}, {5,28}, {6,16}, {17,20}, {11,17}, {4,18}, {9,23}, {1,30}, {24,26}, {13,29}, {10,18}, {14,26}, {2,29}, {7,24}, {13,27}, {9,20}, {11,25}, {13,21}, {18,21}, {10,16}, {8,19}, {2,30}, {6,22}, {3,11}, {4,24}, {23,27}, {16,19}, {12,17}, {4,30}, {4,23}, {3,28}, {10,27}, {13,30}, {1,9}, {12,18}, {14,27}, {2,28}, {2,12}, {16,20}, {15,29}, {3,8}, {4,22}, {14,21}, {22,25}, {2,10}, {5,23}, {15,20}, {17,21}, {8,22}, {2,8}, {23,26}, {13,19}, {5,17}, {14,28}, {6,30}, {10,25}, {5,30}, {4,17}, {13,20}, {1,11}, {5,29}, {1,8}, {22,26}, {14,25}, {1,12}, {4,16}, {2,7}, {13,26}, {1,29}, {4,29}, {8,21}, {15,27}, {7,21}, {24,25}, {9,22}, {12,16}, {6,17}, {7,22}, {10,26}, {1,28}, {6,18}, {7,23}, {8,20}, {12,25}, {18,20}, {11,26}, {4,28}, {6,23}, {8,23}, {15,26}, {14,29}, {3,12}, {6,24}, {11,18}, {9,21}, {11,16}, {9,19}, {8,24}, {2,9}, {23,25}, {15,30}, {18,19}, {3,9}, {14,30}, {3,29}, {15,19} } Symmetric graph 22 of order 30 Valency 10 Diameter 3 Girth 4 Automorphism group of order 7200 Number of arcs = 300 Number of 2-arcs = 2700 2-arc-transitive false Edge-set { {1,6}, {7,25}, {1,20}, {14,21}, {2,12}, {2,7}, {7,20}, {15,18}, {13,26}, {8,16}, {16,29}, {8,21}, {2,16}, {2,21}, {5,19}, {10,27}, {17,30}, {23,30}, {3,22}, {3,8}, {3,28}, {15,22}, {3,13}, {8,15}, {13,16}, {6,19}, {24,26}, {5,24}, {4,29}, {9,22}, {12,29}, {9,11}, {14,17}, {3,17}, {9,27}, {17,25}, {11,19}, {14,27}, {9,17}, {19,22}, {3,27}, {8,30}, {1,25}, {13,30}, {11,23}, {6,13}, {10,28}, {18,21}, {4,14}, {16,28}, {21,29}, {20,23}, {4,28}, {4,18}, {9,26}, {4,9}, {23,26}, {4,24}, {9,12}, {6,28}, {18,26}, {4,23}, {1,11}, {6,14}, {17,24}, {22,29}, {7,14}, {12,20}, {17,29}, {22,30}, {15,28}, {1,30}, {24,27}, {5,25}, {5,15}, {10,13}, {10,18}, {8,25}, {13,21}, {7,15}, {18,25}, {5,10}, {10,23}, {12,30}, {15,23}, {11,18}, {16,23}, {25,27}, {5,30}, {10,12}, {20,28}, {1,26}, {4,13}, {11,28}, {2,26}, {7,29}, {9,21}, {11,29}, {14,22}, {19,27}, {20,22}, {11,24}, {12,19}, {3,12}, {15,17}, {19,21}, {2,27}, {5,14}, {6,24}, {12,24}, {15,27}, {5,20}, {14,26}, {6,29}, {16,24}, {5,29}, {7,30}, {10,17}, {18,30}, {20,27}, {25,28}, {21,28}, {2,11}, {13,20}, {1,16}, {9,16}, {4,19}, {1,15}, {8,26}, {6,18}, {19,26}, {13,25}, {2,6}, {7,19}, {1,21}, {8,11}, {2,22}, {5,9}, {10,22}, {7,24}, {12,25}, {8,20}, {2,17}, {3,7}, {3,23}, {4,8}, {1,10}, {6,23}, {14,16}, {3,18} } Symmetric graph 23 of order 30 Valency 10 Diameter 3 Girth 4 Automorphism group of order 35831808000000 Number of arcs = 300 Number of 2-arcs = 2700 2-arc-transitive false Edge-set { {1,3}, {1,10}, {18,25}, {1,15}, {18,19}, {12,25}, {22,24}, {1,21}, {13,18}, {12,19}, {22,30}, {6,25}, {24,28}, {18,28}, {8,16}, {1,27}, {7,18}, {12,13}, {6,22}, {6,19}, {28,30}, {8,9}, {25,30}, {4,24}, {4,18}, {2,16}, {4,12}, {2,22}, {8,22}, {11,14}, {1,18}, {7,12}, {12,22}, {6,13}, {6,28}, {4,8}, {19,30}, {4,30}, {2,9}, {11,20}, {24,25}, {9,24}, {9,18}, {16,26}, {9,12}, {22,26}, {14,17}, {6,9}, {26,28}, {2,28}, {8,17}, {8,28}, {8,11}, {5,14}, {5,27}, {1,12}, {18,22}, {6,7}, {12,28}, {13,30}, {4,6}, {2,4}, {11,26}, {19,24}, {9,30}, {9,26}, {17,20}, {5,20}, {27,29}, {16,24}, {16,18}, {16,20}, {12,16}, {20,22}, {14,23}, {6,16}, {20,28}, {8,23}, {5,21}, {16,30}, {4,20}, {4,26}, {2,23}, {2,17}, {11,21}, {2,11}, {5,8}, {11,27}, {14,29}, {3,5}, {3,29}, {1,6}, {7,30}, {13,24}, {17,26}, {5,26}, {23,27}, {9,20}, {20,23}, {21,29}, {20,29}, {3,23}, {14,16}, {14,22}, {14,28}, {8,29}, {5,15}, {4,14}, {2,29}, {11,15}, {3,7}, {9,14}, {26,29}, {23,26}, {15,17}, {17,21}, {7,27}, {2,5}, {17,27}, {3,11}, {5,10}, {10,29}, {3,25}, {10,23}, {10,25}, {1,30}, {7,24}, {21,23}, {3,17}, {15,29}, {7,10}, {10,17}, {15,25}, {10,11}, {3,13}, {13,27}, {15,23}, {13,21}, {7,21}, {25,27}, {3,19}, {10,19}, {15,19}, {1,24}, {7,15}, {21,25}, {10,13}, {19,21}, {19,27}, {13,15} } Symmetric graph 24 of order 30 Valency 12 Diameter 2 Girth 3 Automorphism group of order 720 Number of arcs = 360 Number of 2-arcs = 3960 2-arc-transitive false Edge-set { {1,5}, {7,26}, {5,8}, {15,23}, {3,14}, {13,26}, {21,30}, {18,27}, {9,29}, {23,28}, {14,25}, {11,18}, {11,21}, {2,24}, {14,17}, {2,10}, {16,21}, {12,18}, {22,29}, {2,6}, {23,30}, {6,11}, {8,19}, {9,16}, {1,29}, {22,26}, {3,11}, {21,24}, {2,4}, {17,20}, {10,17}, {8,27}, {6,9}, {18,21}, {6,27}, {6,30}, {12,13}, {1,19}, {7,17}, {8,10}, {20,23}, {7,30}, {11,19}, {8,25}, {4,9}, {1,10}, {20,22}, {13,24}, {1,15}, {14,27}, {2,11}, {21,23}, {24,27}, {6,15}, {4,28}, {25,28}, {7,12}, {3,22}, {5,13}, {10,21}, {18,20}, {15,18}, {6,12}, {19,30}, {13,22}, {1,13}, {5,7}, {8,29}, {10,20}, {19,28}, {16,25}, {24,29}, {15,26}, {6,8}, {9,30}, {19,24}, {15,16}, {27,30}, {4,12}, {16,22}, {4,15}, {3,28}, {9,20}, {26,28}, {5,25}, {5,11}, {21,29}, {2,30}, {23,27}, {4,27}, {6,28}, {20,28}, {17,25}, {7,28}, {3,5}, {13,17}, {5,10}, {20,29}, {12,16}, {12,19}, {17,19}, {10,16}, {13,27}, {1,6}, {14,18}, {16,19}, {3,30}, {18,24}, {11,15}, {4,25}, {3,20}, {17,24}, {25,30}, {10,14}, {2,20}, {16,23}, {12,14}, {6,26}, {5,30}, {11,17}, {8,18}, {9,11}, {24,25}, {16,27}, {12,20}, {1,22}, {3,12}, {9,26}, {1,28}, {22,25}, {5,26}, {5,29}, {3,4}, {24,28}, {1,12}, {19,22}, {15,25}, {7,27}, {2,29}, {23,26}, {9,18}, {7,11}, {2,19}, {4,13}, {9,10}, {7,20}, {18,22}, {11,13}, {26,29}, {3,21}, {4,29}, {6,14}, {18,26}, {22,30}, {2,13}, {1,23}, {13,16}, {3,24}, {15,24}, {4,10}, {8,17}, {14,23}, {2,14}, {7,16}, {8,12}, {5,14}, {17,26}, {9,25}, {4,7}, {8,28}, {3,15}, {2,23}, {9,19}, {10,15}, {17,23}, {7,21}, {27,29}, {14,22}, {8,21}, {1,21} } Symmetric graph 25 of order 30 Valency 12 Diameter 3 Girth 4 Automorphism group of order 1440 Number of arcs = 360 Number of 2-arcs = 3960 2-arc-transitive false Edge-set { {1,16}, {1,26}, {8,28}, {1,20}, {4,28}, {13,29}, {6,16}, {3,28}, {8,29}, {6,27}, {4,27}, {2,30}, {3,26}, {8,18}, {10,29}, {6,17}, {13,27}, {2,16}, {11,18}, {11,27}, {7,23}, {5,22}, {10,20}, {4,17}, {13,25}, {2,29}, {3,24}, {12,18}, {11,30}, {7,26}, {8,22}, {11,25}, {11,28}, {11,26}, {14,22}, {15,21}, {5,30}, {10,24}, {3,29}, {8,24}, {12,27}, {4,21}, {9,30}, {7,27}, {2,22}, {10,19}, {13,17}, {9,25}, {11,23}, {5,26}, {14,20}, {13,30}, {10,16}, {11,21}, {9,26}, {11,29}, {6,26}, {11,20}, {4,26}, {10,25}, {5,23}, {5,24}, {6,19}, {10,27}, {2,17}, {13,19}, {13,16}, {9,28}, {15,23}, {5,19}, {14,28}, {7,30}, {10,22}, {14,29}, {4,24}, {12,30}, {9,19}, {11,22}, {15,26}, {5,20}, {3,25}, {4,23}, {15,20}, {4,19}, {2,26}, {3,20}, {4,18}, {11,16}, {8,20}, {6,21}, {9,29}, {15,24}, {13,24}, {3,17}, {14,18}, {6,28}, {7,24}, {12,22}, {14,30}, {8,30}, {15,29}, {5,17}, {14,24}, {6,25}, {14,23}, {5,21}, {6,30}, {2,27}, {2,25}, {8,19}, {9,23}, {15,17}, {14,19}, {10,26}, {12,20}, {5,16}, {10,21}, {9,17}, {15,27}, {12,16}, {3,23}, {8,17}, {14,27}, {7,20}, {4,22}, {8,25}, {1,27}, {8,26}, {3,16}, {3,18}, {7,18}, {2,19}, {12,19}, {13,23}, {12,17}, {1,25}, {6,18}, {13,21}, {2,23}, {5,25}, {12,24}, {3,21}, {9,18}, {15,25}, {5,18}, {7,28}, {7,21}, {9,22}, {14,16}, {15,22}, {15,19}, {12,23}, {14,25}, {6,20}, {4,29}, {9,16}, {7,29}, {12,28}, {2,28}, {1,28}, {13,20}, {4,16}, {1,17}, {1,21}, {7,17}, {15,30}, {9,24}, {1,18}, {7,22}, {10,18}, {1,19}, {12,21}, {1,24}, {10,23}, {2,21}, {8,27}, {6,22}, {1,29}, {3,30}, {13,28} } Symmetric graph 26 of order 30 Valency 12 Diameter 2 Girth 3 Automorphism group of order 23592960 Number of arcs = 360 Number of 2-arcs = 3960 2-arc-transitive false Edge-set { {1,7}, {5,13}, {3,19}, {25,29}, {3,16}, {1,11}, {28,30}, {17,23}, {1,10}, {5,12}, {7,19}, {22,24}, {9,22}, {15,27}, {5,18}, {6,19}, {8,29}, {13,16}, {3,11}, {21,23}, {14,16}, {5,14}, {20,26}, {9,21}, {28,29}, {2,16}, {11,30}, {14,30}, {4,23}, {10,25}, {3,12}, {13,15}, {8,19}, {10,26}, {1,8}, {26,29}, {12,18}, {17,24}, {25,30}, {22,23}, {10,20}, {12,29}, {7,24}, {24,26}, {4,22}, {2,15}, {18,28}, {6,17}, {7,20}, {9,25}, {4,11}, {18,27}, {6,18}, {4,19}, {27,30}, {18,23}, {10,11}, {8,28}, {16,27}, {14,15}, {15,18}, {6,12}, {8,23}, {13,21}, {21,27}, {16,18}, {2,14}, {6,20}, {9,20}, {22,28}, {2,9}, {17,28}, {5,17}, {4,12}, {2,7}, {21,28}, {2,10}, {4,16}, {2,11}, {21,24}, {10,22}, {15,28}, {6,7}, {14,25}, {19,26}, {10,21}, {8,20}, {9,26}, {9,28}, {8,30}, {14,22}, {4,15}, {13,25}, {10,19}, {10,28}, {6,8}, {12,30}, {15,17}, {23,25}, {5,20}, {22,27}, {1,9}, {27,29}, {2,8}, {6,13}, {3,20}, {24,25}, {13,22}, {6,14}, {20,25}, {2,13}, {3,30}, {17,26}, {11,18}, {18,24}, {17,27}, {17,25}, {5,22}, {14,29}, {4,24}, {14,26}, {4,20}, {7,28}, {6,11}, {18,25}, {6,22}, {4,30}, {11,29}, {8,24}, {9,27}, {1,15}, {23,26}, {14,21}, {5,19}, {26,30}, {3,15}, {1,12}, {16,17}, {7,23}, {12,17}, {3,29}, {1,24}, {10,12}, {16,28}, {1,23}, {4,21}, {8,27}, {18,26}, {2,12}, {3,22}, {7,30}, {2,23}, {4,29}, {2,24}, {5,21}, {9,19}, {13,26}, {1,16}, {5,11}, {10,27}, {9,11}, {16,19}, {19,25}, {15,19}, {3,23}, {1,14}, {13,29}, {3,24}, {15,20}, {6,21}, {16,20}, {7,27}, {7,29}, {5,7}, {11,17}, {5,8}, {3,21}, {9,12}, {13,30}, {1,13} } Symmetric graph 27 of order 30 Valency 12 Diameter 3 Girth 4 Automorphism group of order 14511882240 Number of arcs = 360 Number of 2-arcs = 3960 2-arc-transitive false Edge-set { {1,16}, {11,20}, {12,25}, {6,16}, {4,30}, {9,17}, {5,20}, {11,28}, {15,25}, {2,29}, {13,23}, {10,24}, {3,26}, {6,30}, {14,30}, {4,24}, {9,27}, {9,20}, {3,21}, {10,22}, {14,25}, {7,18}, {13,18}, {8,19}, {11,21}, {2,28}, {15,23}, {2,26}, {8,23}, {13,29}, {13,16}, {7,24}, {3,19}, {6,24}, {3,30}, {5,19}, {15,18}, {6,17}, {9,26}, {8,20}, {12,22}, {1,27}, {7,27}, {4,23}, {5,16}, {4,28}, {1,21}, {14,27}, {9,18}, {8,21}, {10,21}, {14,23}, {2,18}, {3,25}, {7,22}, {11,25}, {7,25}, {13,22}, {4,19}, {11,29}, {13,28}, {15,16}, {2,19}, {11,23}, {14,29}, {12,27}, {10,28}, {15,26}, {8,24}, {6,23}, {2,30}, {15,17}, {5,17}, {7,20}, {12,19}, {1,19}, {11,30}, {1,29}, {13,24}, {12,28}, {7,26}, {12,24}, {3,27}, {5,23}, {5,18}, {6,28}, {14,26}, {8,18}, {12,21}, {10,27}, {9,19}, {15,22}, {1,17}, {9,16}, {4,20}, {9,22}, {1,20}, {7,17}, {4,29}, {3,16}, {4,22}, {1,25}, {11,27}, {9,25}, {4,21}, {10,29}, {14,16}, {4,18}, {8,22}, {1,18}, {8,27}, {9,21}, {2,16}, {14,28}, {2,21}, {10,23}, {10,30}, {6,22}, {1,30}, {4,17}, {5,29}, {12,29}, {3,20}, {13,25}, {7,16}, {5,24}, {13,17}, {7,19}, {11,19}, {14,18}, {12,30}, {1,28}, {15,24}, {8,26}, {12,23}, {2,27}, {5,28}, {6,19}, {3,29}, {15,27}, {10,20}, {12,26}, {11,24}, {6,29}, {13,30}, {3,17}, {6,20}, {1,26}, {15,29}, {12,20}, {9,24}, {3,18}, {11,26}, {8,25}, {13,27}, {2,17}, {7,23}, {3,28}, {10,25}, {5,21}, {6,18}, {15,28}, {2,20}, {13,26}, {14,22}, {5,22}, {11,22}, {4,16}, {14,17}, {7,21}, {10,19}, {14,24}, {8,17}, {2,25}, {15,30}, {5,30}, {8,16}, {9,23}, {10,26}, {6,21} } Symmetric graph 28 of order 30 Valency 12 Diameter 2 Girth 4 Automorphism group of order 1934917632000000 Number of arcs = 360 Number of 2-arcs = 3960 2-arc-transitive false Edge-set { {1,7}, {11,28}, {1,12}, {23,26}, {9,26}, {11,25}, {1,10}, {15,21}, {22,29}, {21,30}, {7,29}, {22,26}, {9,30}, {11,29}, {1,8}, {4,14}, {15,20}, {13,19}, {19,28}, {14,20}, {20,27}, {12,28}, {13,21}, {19,29}, {20,30}, {7,27}, {19,26}, {9,28}, {11,27}, {1,11}, {4,17}, {15,23}, {2,18}, {13,24}, {18,23}, {24,26}, {1,17}, {14,23}, {17,24}, {23,25}, {10,26}, {2,14}, {13,20}, {18,19}, {24,28}, {17,20}, {23,27}, {12,25}, {18,21}, {24,29}, {23,30}, {7,26}, {9,25}, {11,26}, {1,9}, {6,7}, {4,15}, {15,22}, {5,12}, {2,16}, {5,15}, {18,22}, {16,21}, {21,29}, {6,11}, {1,15}, {14,22}, {6,16}, {17,21}, {22,30}, {8,29}, {2,17}, {13,23}, {5,18}, {18,24}, {16,23}, {21,26}, {6,17}, {17,23}, {15,24}, {22,25}, {10,30}, {5,14}, {18,20}, {16,19}, {21,28}, {22,27}, {12,29}, {7,30}, {9,29}, {11,30}, {6,12}, {4,7}, {4,13}, {15,19}, {10,25}, {5,10}, {3,12}, {4,10}, {5,13}, {3,14}, {16,20}, {14,19}, {20,28}, {6,9}, {4,11}, {1,13}, {3,9}, {6,14}, {19,27}, {2,15}, {13,22}, {5,16}, {3,15}, {16,22}, {14,21}, {20,29}, {6,15}, {17,22}, {4,16}, {19,30}, {8,27}, {5,17}, {3,18}, {16,24}, {20,26}, {19,25}, {10,28}, {12,27}, {7,28}, {9,27}, {6,10}, {4,12}, {2,7}, {4,18}, {8,30}, {10,29}, {5,8}, {8,25}, {3,10}, {4,8}, {2,10}, {3,17}, {1,18}, {14,24}, {4,9}, {2,11}, {3,7}, {24,25}, {2,13}, {3,13}, {1,14}, {17,19}, {23,28}, {6,13}, {24,27}, {3,16}, {23,29}, {24,30}, {8,26}, {12,26}, {7,25}, {6,8}, {2,12}, {5,7}, {8,28}, {10,27}, {5,11}, {3,8}, {2,8}, {1,16}, {2,9}, {6,18}, {21,25}, {22,28}, {21,27}, {12,30}, {5,9}, {3,11}, {20,25} } Symmetric graph 29 of order 30 Valency 14 Diameter 3 Girth 4 Automorphism group of order 2615348736000 Number of arcs = 420 Number of 2-arcs = 5460 2-arc-transitive true Edge-set { {1,4}, {12,22}, {13,27}, {1,16}, {3,20}, {13,30}, {16,26}, {22,24}, {21,27}, {11,18}, {14,29}, {6,30}, {16,24}, {20,24}, {7,21}, {3,11}, {2,13}, {4,26}, {7,15}, {17,19}, {5,29}, {15,23}, {6,27}, {10,24}, {4,24}, {11,21}, {4,18}, {11,29}, {2,26}, {11,15}, {14,19}, {21,30}, {16,28}, {12,20}, {7,13}, {23,26}, {1,22}, {8,17}, {18,30}, {5,28}, {9,23}, {3,23}, {10,26}, {4,9}, {6,11}, {4,12}, {11,13}, {2,15}, {4,19}, {7,12}, {13,17}, {5,15}, {19,23}, {20,21}, {7,28}, {19,22}, {17,29}, {15,30}, {2,6}, {14,24}, {21,25}, {16,18}, {20,29}, {26,30}, {3,27}, {8,25}, {2,18}, {6,7}, {17,24}, {14,28}, {9,25}, {3,10}, {5,12}, {12,14}, {9,20}, {10,12}, {5,13}, {15,27}, {10,19}, {12,16}, {13,20}, {16,19}, {21,23}, {22,28}, {12,17}, {1,20}, {8,30}, {23,28}, {9,22}, {3,17}, {12,30}, {4,29}, {14,26}, {1,25}, {1,17}, {3,30}, {5,8}, {18,23}, {6,23}, {10,28}, {2,19}, {4,8}, {7,24}, {17,21}, {5,18}, {23,29}, {6,20}, {19,25}, {2,8}, {17,28}, {26,27}, {1,10}, {15,25}, {9,11}, {6,14}, {16,29}, {15,20}, {10,18}, {9,16}, {28,30}, {13,23}, {22,26}, {9,17}, {2,3}, {1,14}, {3,25}, {8,16}, {18,20}, {18,22}, {27,29}, {6,25}, {2,24}, {3,14}, {12,25}, {3,5}, {8,11}, {14,18}, {6,16}, {8,27}, {8,22}, {18,27}, {25,28}, {2,9}, {3,7}, {9,14}, {1,11}, {12,23}, {10,29}, {2,28}, {8,14}, {18,25}, {7,26}, {10,15}, {5,19}, {5,24}, {22,29}, {7,9}, {6,17}, {5,21}, {24,25}, {8,10}, {11,19}, {2,21}, {7,18}, {1,7}, {19,27}, {4,21}, {11,28}, {14,15}, {8,20}, {7,29}, {15,17}, {24,27}, {10,21}, {13,25}, {17,26}, {11,26}, {15,22}, {3,16}, {5,9}, {14,21}, {25,29}, {7,19}, {20,26}, {6,22}, {9,30}, {4,28}, {1,5}, {19,30}, {1,27}, {2,12}, {4,13}, {2,29}, {5,26}, {1,23}, {8,23}, {4,6}, {3,22}, {11,24}, {4,15}, {1,30}, {6,10}, {9,27}, {24,30}, {13,22}, {16,21}, {20,28}, {13,16}, {12,27}, {10,13} } Symmetric graph 30 of order 30 Valency 15 Diameter 2 Girth 4 Automorphism group of order 3420024505448398848000000 Number of arcs = 450 Number of 2-arcs = 6300 2-arc-transitive true Edge-set { {1,16}, {10,24}, {11,25}, {5,30}, {2,21}, {6,16}, {6,20}, {14,19}, {7,29}, {15,27}, {15,24}, {11,28}, {13,28}, {7,26}, {14,23}, {8,18}, {4,22}, {8,30}, {2,22}, {9,20}, {9,24}, {2,17}, {5,18}, {3,23}, {12,17}, {1,30}, {3,19}, {7,17}, {1,27}, {13,16}, {2,16}, {11,22}, {10,27}, {12,29}, {3,26}, {10,19}, {7,25}, {12,26}, {14,26}, {10,18}, {4,25}, {11,24}, {11,27}, {6,28}, {1,20}, {4,21}, {8,19}, {5,26}, {14,21}, {6,18}, {4,17}, {5,19}, {5,23}, {12,21}, {6,30}, {2,20}, {4,20}, {15,20}, {9,28}, {13,25}, {15,30}, {14,17}, {5,29}, {15,23}, {12,28}, {13,22}, {10,30}, {14,29}, {3,29}, {15,19}, {7,28}, {13,27}, {13,30}, {8,27}, {9,16}, {6,24}, {7,22}, {10,23}, {8,29}, {3,22}, {9,19}, {1,24}, {7,21}, {8,23}, {8,26}, {14,22}, {9,18}, {4,24}, {7,24}, {3,18}, {11,16}, {2,28}, {1,18}, {3,21}, {8,17}, {1,26}, {14,16}, {2,25}, {15,18}, {3,17}, {5,17}, {1,23}, {12,16}, {2,30}, {2,18}, {12,23}, {11,20}, {9,27}, {12,25}, {15,26}, {10,17}, {5,25}, {11,23}, {6,27}, {12,22}, {10,26}, {10,29}, {3,25}, {11,19}, {7,27}, {12,27}, {4,29}, {13,20}, {4,16}, {6,19}, {5,22}, {10,21}, {6,29}, {3,20}, {4,28}, {1,19}, {5,21}, {8,21}, {6,26}, {14,20}, {4,18}, {4,19}, {13,21}, {13,24}, {11,30}, {14,28}, {1,29}, {15,21}, {8,28}, {13,26}, {9,30}, {14,25}, {15,29}, {15,17}, {5,28}, {13,23}, {12,30}, {14,30}, {9,25}, {2,24}, {7,20}, {9,23}, {8,25}, {15,22}, {9,17}, {5,24}, {7,16}, {6,23}, {8,22}, {10,22}, {9,29}, {3,24}, {7,19}, {7,23}, {2,27}, {13,18}, {3,16}, {6,17}, {1,22}, {10,16}, {2,29}, {11,18}, {3,28}, {1,17}, {1,21}, {8,16}, {2,26}, {14,18}, {4,27}, {12,24}, {11,26}, {10,28}, {1,25}, {11,21}, {12,20}, {9,26}, {10,25}, {15,25}, {11,17}, {5,27}, {4,30}, {2,19}, {5,20}, {9,21}, {6,25}, {13,19}, {5,16}, {6,21}, {6,22}, {10,20}, {7,30}, {14,27}, {13,29}, {15,16}, {14,24}, {11,29}, {15,28}, {1,28}, {7,18}, {4,23}, {8,24}, {2,23}, {8,20}, {9,22}, {12,18}, {3,30}, {3,27}, {13,17}, {12,19}, {4,26} } Symmetric graph 31 of order 30 Valency 16 Diameter 2 Girth 3 Automorphism group of order 23592960 Number of arcs = 480 Number of 2-arcs = 7200 2-arc-transitive false Edge-set { {1,11}, {2,21}, {20,22}, {1,15}, {1,19}, {16,26}, {2,30}, {2,23}, {20,25}, {2,25}, {20,29}, {17,24}, {6,26}, {1,20}, {9,19}, {4,19}, {18,26}, {5,30}, {1,18}, {5,19}, {19,26}, {10,30}, {12,30}, {3,28}, {3,17}, {6,13}, {2,26}, {20,30}, {6,25}, {18,29}, {7,25}, {11,29}, {17,29}, {6,27}, {4,20}, {9,14}, {2,29}, {20,27}, {4,25}, {14,29}, {17,25}, {6,29}, {5,20}, {9,17}, {9,21}, {8,13}, {8,12}, {8,30}, {12,28}, {3,27}, {13,23}, {1,17}, {6,19}, {20,26}, {9,30}, {3,18}, {5,13}, {19,29}, {10,27}, {10,18}, {5,15}, {19,21}, {10,22}, {19,30}, {10,28}, {3,14}, {7,13}, {7,26}, {11,30}, {6,28}, {18,24}, {10,19}, {14,26}, {7,30}, {7,18}, {5,11}, {19,28}, {10,24}, {18,30}, {5,28}, {3,19}, {10,13}, {4,26}, {14,30}, {6,30}, {18,28}, {6,15}, {9,27}, {16,23}, {9,22}, {16,21}, {9,20}, {9,16}, {13,22}, {8,21}, {8,14}, {7,12}, {11,27}, {4,23}, {20,28}, {3,25}, {13,29}, {17,26}, {6,20}, {9,18}, {8,29}, {12,27}, {4,27}, {14,23}, {19,25}, {10,29}, {5,14}, {7,17}, {5,29}, {17,27}, {14,25}, {15,25}, {1,29}, {5,16}, {2,17}, {9,29}, {8,17}, {8,28}, {12,24}, {15,23}, {10,17}, {20,21}, {3,13}, {12,29}, {5,25}, {17,28}, {6,24}, {10,20}, {9,15}, {15,27}, {4,21}, {14,22}, {13,25}, {5,12}, {4,13}, {8,25}, {5,27}, {17,23}, {6,11}, {9,24}, {3,20}, {9,13}, {8,27}, {3,23}, {6,14}, {11,24}, {6,16}, {2,18}, {15,24}, {1,26}, {16,27}, {1,16}, {9,28}, {16,24}, {15,21}, {14,21}, {7,22}, {7,11}, {4,11}, {13,26}, {8,18}, {19,27}, {10,23}, {17,30}, {3,26}, {13,30}, {18,27}, {10,16}, {7,21}, {7,14}, {11,28}, {4,24}, {18,25}, {4,28}, {14,24}, {15,28}, {10,14}, {7,28}, {5,24}, {18,23}, {2,19}, {1,30}, {16,28}, {8,16}, {12,22}, {3,21}, {11,23}, {15,26}, {12,23}, {19,22}, {10,21}, {4,18}, {3,12}, {5,26}, {6,23}, {7,15}, {2,24}, {5,23}, {4,22}, {7,27}, {4,14}, {6,12}, {8,26}, {7,16}, {8,11}, {4,12}, {13,24}, {12,21}, {3,22}, {3,24}, {1,25}, {1,24}, {2,15}, {15,22}, {11,22}, {7,29}, {4,17}, {9,23}, {10,15}, {13,21}, {8,22}, {3,11}, {8,15}, {2,20}, {16,22}, {1,12}, {11,21}, {16,25}, {2,11}, {1,21}, {2,12}, {1,23}, {2,22}, {2,16}, {1,22} } Symmetric graph 32 of order 30 Valency 16 Diameter 2 Girth 3 Automorphism group of order 23592960 Number of arcs = 480 Number of 2-arcs = 7200 2-arc-transitive false Edge-set { {1,7}, {3,10}, {24,29}, {21,28}, {22,28}, {5,15}, {23,29}, {1,18}, {23,30}, {2,18}, {6,13}, {7,19}, {22,27}, {6,15}, {3,18}, {12,24}, {21,27}, {6,16}, {4,18}, {12,23}, {9,20}, {10,26}, {4,29}, {24,30}, {2,17}, {5,13}, {7,20}, {12,21}, {11,28}, {5,25}, {1,17}, {5,14}, {8,20}, {12,22}, {11,27}, {6,25}, {8,25}, {3,27}, {13,28}, {2,22}, {15,22}, {5,16}, {4,17}, {11,23}, {9,19}, {10,25}, {3,29}, {11,29}, {1,25}, {18,26}, {6,19}, {14,19}, {3,17}, {11,24}, {10,19}, {9,25}, {3,30}, {11,30}, {2,25}, {17,26}, {5,19}, {14,20}, {14,30}, {1,24}, {17,21}, {15,23}, {9,18}, {4,30}, {2,23}, {13,30}, {2,7}, {6,14}, {8,19}, {11,22}, {12,27}, {6,26}, {8,26}, {4,27}, {14,28}, {1,22}, {15,21}, {15,26}, {3,19}, {14,24}, {18,20}, {12,13}, {5,26}, {4,20}, {16,26}, {4,10}, {11,21}, {12,28}, {7,26}, {4,28}, {14,27}, {1,21}, {16,21}, {4,19}, {14,23}, {17,20}, {11,13}, {16,25}, {10,16}, {3,28}, {5,24}, {17,29}, {1,11}, {13,27}, {6,7}, {8,18}, {2,21}, {16,22}, {6,23}, {9,16}, {10,20}, {9,26}, {12,30}, {2,26}, {17,25}, {5,20}, {13,20}, {2,24}, {17,22}, {16,23}, {10,18}, {13,29}, {7,13}, {1,26}, {4,21}, {16,28}, {5,10}, {18,25}, {3,12}, {11,15}, {6,20}, {13,19}, {3,22}, {8,13}, {12,29}, {18,22}, {16,24}, {10,17}, {14,29}, {1,8}, {4,22}, {16,27}, {6,10}, {3,11}, {12,15}, {8,14}, {7,14}, {8,28}, {1,23}, {18,21}, {6,28}, {24,26}, {15,24}, {9,17}, {20,29}, {2,8}, {5,27}, {8,27}, {7,25}, {13,23}, {17,19}, {11,14}, {15,25}, {3,9}, {5,23}, {17,30}, {2,11}, {6,8}, {7,18}, {9,15}, {10,15}, {9,29}, {3,20}, {13,24}, {2,29}, {19,28}, {18,19}, {12,14}, {21,25}, {4,9}, {1,30}, {9,30}, {18,30}, {2,12}, {5,8}, {7,17}, {2,30}, {8,17}, {5,7}, {20,28}, {1,12}, {21,26}, {10,30}, {10,29}, {9,23}, {6,24}, {18,29}, {22,25}, {3,15}, {9,24}, {15,27}, {6,9}, {4,11}, {12,16}, {6,27}, {11,16}, {4,12}, {23,26}, {5,9}, {20,30}, {7,27}, {7,28}, {8,22}, {3,21}, {15,28}, {19,29}, {1,14}, {8,21}, {23,25}, {19,30}, {24,25}, {1,13}, {7,21}, {7,22}, {5,28}, {2,14}, {20,27}, {22,26}, {19,27}, {3,16}, {10,24}, {10,23}, {1,29}, {4,15}, {4,16}, {2,13} } Symmetric graph 33 of order 30 Valency 18 Diameter 2 Girth 3 Automorphism group of order 21772800 Number of arcs = 540 Number of 2-arcs = 9180 2-arc-transitive false Edge-set { {1,4}, {4,9}, {17,24}, {9,24}, {21,24}, {11,30}, {9,27}, {24,30}, {9,21}, {13,30}, {9,14}, {3,21}, {1,28}, {11,21}, {3,30}, {1,9}, {13,24}, {14,21}, {3,26}, {24,27}, {5,21}, {6,13}, {14,16}, {2,17}, {13,21}, {14,28}, {3,6}, {1,16}, {4,24}, {17,21}, {26,30}, {13,27}, {5,14}, {6,16}, {10,16}, {17,30}, {9,11}, {7,13}, {14,22}, {8,26}, {4,23}, {10,27}, {5,26}, {5,11}, {18,27}, {13,26}, {4,14}, {1,27}, {2,5}, {6,8}, {16,23}, {4,10}, {17,26}, {9,30}, {11,13}, {14,27}, {3,16}, {1,10}, {4,11}, {7,27}, {5,22}, {8,10}, {23,26}, {10,20}, {3,11}, {21,28}, {22,26}, {4,19}, {27,28}, {5,7}, {9,29}, {8,24}, {17,20}, {7,16}, {10,22}, {7,21}, {22,28}, {12,17}, {11,25}, {16,26}, {5,24}, {4,17}, {11,17}, {18,22}, {8,23}, {20,23}, {10,29}, {9,20}, {11,16}, {3,24}, {1,21}, {21,26}, {4,28}, {17,27}, {6,10}, {4,20}, {24,28}, {17,22}, {11,19}, {7,28}, {7,22}, {20,30}, {16,29}, {15,20}, {6,21}, {16,28}, {1,13}, {2,14}, {7,10}, {15,24}, {1,17}, {2,11}, {19,22}, {2,24}, {23,30}, {11,15}, {19,26}, {20,28}, {7,30}, {13,22}, {14,19}, {2,7}, {27,29}, {18,21}, {12,28}, {10,26}, {9,22}, {7,25}, {23,29}, {8,20}, {15,29}, {8,13}, {2,20}, {10,21}, {26,28}, {6,30}, {9,16}, {4,13}, {14,17}, {13,16}, {10,14}, {11,27}, {9,15}, {1,30}, {2,9}, {11,28}, {15,28}, {1,22}, {2,19}, {7,19}, {3,15}, {2,10}, {15,25}, {14,23}, {2,26}, {4,26}, {5,27}, {5,18}, {20,22}, {19,30}, {25,30}, {6,9}, {18,28}, {7,15}, {5,30}, {9,18}, {3,29}, {1,8}, {21,25}, {6,28}, {10,15}, {1,15}, {2,13}, {3,22}, {1,19}, {4,7}, {5,15}, {18,19}, {12,13}, {14,25}, {2,29}, {16,20}, {10,30}, {12,19}, {3,8}, {15,23}, {13,20}, {2,25}, {13,18}, {14,30}, {1,23}, {10,24}, {9,26}, {20,27}, {24,25}, {3,4}, {2,28}, {1,25}, {2,6}, {7,17}, {15,18}, {15,19}, {6,25}, {5,20}, {18,30}, {18,25}, {6,12}, {5,8}, {5,16}, {10,18}, {11,22}, {7,12}, {22,25}, {3,14}, {3,18}, {1,12}, {21,23}, {6,19}, {3,7}, {12,24}, {12,14}, {2,23}, {20,25}, {4,25}, {6,17}, {4,18}, {15,17}, {19,24}, {6,22}, {4,29}, {5,12}, {3,20}, {6,23}, {25,29}, {15,26}, {12,18}, {12,26}, {3,27}, {1,5}, {8,17}, {16,24}, {9,12}, {2,18}, {18,23}, {19,27}, {12,25}, {6,15}, {8,18}, {12,23}, {3,12}, {8,19}, {7,23}, {12,20}, {19,29}, {6,27}, {16,25}, {17,29}, {13,29}, {8,14}, {16,19}, {5,29}, {8,11}, {23,27}, {8,28}, {22,29}, {8,29}, {11,23}, {21,29}, {12,29}, {8,25} } Symmetric graph 34 of order 30 Valency 18 Diameter 2 Girth 3 Automorphism group of order 7255941120 Number of arcs = 540 Number of 2-arcs = 9180 2-arc-transitive false Edge-set { {1,4}, {6,8}, {20,26}, {9,29}, {8,25}, {11,13}, {23,30}, {9,15}, {12,29}, {18,27}, {16,28}, {2,22}, {14,23}, {26,30}, {17,23}, {15,18}, {10,19}, {5,12}, {20,24}, {21,22}, {2,25}, {11,22}, {4,14}, {2,21}, {10,23}, {19,26}, {15,16}, {3,17}, {7,17}, {3,13}, {1,24}, {1,14}, {4,12}, {6,21}, {1,18}, {16,22}, {2,16}, {11,15}, {3,4}, {11,29}, {5,21}, {21,28}, {7,10}, {5,27}, {19,28}, {3,6}, {6,25}, {20,30}, {8,17}, {18,26}, {9,14}, {6,19}, {12,20}, {1,20}, {4,20}, {11,21}, {16,29}, {5,8}, {18,23}, {7,14}, {2,27}, {14,24}, {2,13}, {15,24}, {5,9}, {19,25}, {9,12}, {13,22}, {21,29}, {8,10}, {11,19}, {25,30}, {9,30}, {3,25}, {13,17}, {6,13}, {8,13}, {1,26}, {14,18}, {20,23}, {7,29}, {8,27}, {2,19}, {12,23}, {25,28}, {7,30}, {4,10}, {24,30}, {4,27}, {3,26}, {24,29}, {9,27}, {12,15}, {17,30}, {9,18}, {1,27}, {22,28}, {2,15}, {3,16}, {12,22}, {6,14}, {22,30}, {21,27}, {10,28}, {27,29}, {8,28}, {6,11}, {12,30}, {1,23}, {23,28}, {7,15}, {10,29}, {4,15}, {3,21}, {2,17}, {12,24}, {8,16}, {17,26}, {3,22}, {5,26}, {5,11}, {4,19}, {3,23}, {10,30}, {18,29}, {10,14}, {19,30}, {6,10}, {5,20}, {4,26}, {1,17}, {18,22}, {9,25}, {1,22}, {14,22}, {2,5}, {16,24}, {5,15}, {16,25}, {17,22}, {2,6}, {2,24}, {13,23}, {26,28}, {16,23}, {15,17}, {8,26}, {26,29}, {5,14}, {4,21}, {10,21}, {18,24}, {20,29}, {8,11}, {1,5}, {19,22}, {7,11}, {7,18}, {16,27}, {8,15}, {19,23}, {14,17}, {15,22}, {3,14}, {9,16}, {17,25}, {7,13}, {10,20}, {1,19}, {6,9}, {1,6}, {20,22}, {1,25}, {4,7}, {3,20}, {11,24}, {7,26}, {1,21}, {10,22}, {4,9}, {21,25}, {21,24}, {4,13}, {2,20}, {11,23}, {21,26}, {4,8}, {7,25}, {27,30}, {8,14}, {2,26}, {14,16}, {3,19}, {1,15}, {6,7}, {20,27}, {18,28}, {7,16}, {7,12}, {8,29}, {22,29}, {5,25}, {9,11}, {12,21}, {27,28}, {7,28}, {13,16}, {6,15}, {20,25}, {1,13}, {6,12}, {6,20}, {5,13}, {3,18}, {11,28}, {1,16}, {8,30}, {9,26}, {12,14}, {2,18}, {11,14}, {2,4}, {12,28}, {25,29}, {4,11}, {11,30}, {6,26}, {9,28}, {10,13}, {19,24}, {12,13}, {20,28}, {17,28}, {23,29}, {6,27}, {18,30}, {10,24}, {24,28}, {9,17}, {18,25}, {9,13}, {7,27}, {5,19}, {12,19}, {11,20}, {16,30}, {17,24}, {13,18}, {8,18}, {16,26}, {4,25}, {3,15}, {3,24}, {17,27}, {13,24}, {2,23}, {15,23}, {9,10}, {21,30}, {5,7}, {3,27}, {19,27}, {19,29}, {8,12}, {3,5}, {5,10}, {21,23}, {2,14}, {10,15}, {17,29} } Symmetric graph 35 of order 30 Valency 20 Diameter 2 Girth 3 Automorphism group of order 86400 Number of arcs = 600 Number of 2-arcs = 11400 2-arc-transitive false Edge-set { {1,7}, {9,16}, {1,22}, {4,20}, {4,27}, {9,26}, {6,22}, {2,10}, {24,28}, {10,11}, {11,24}, {14,20}, {4,12}, {19,26}, {2,6}, {6,17}, {3,21}, {13,30}, {9,15}, {17,24}, {3,17}, {24,30}, {9,17}, {2,25}, {19,28}, {10,21}, {16,24}, {5,14}, {12,29}, {6,19}, {2,21}, {1,19}, {2,26}, {8,29}, {7,25}, {12,23}, {13,20}, {20,22}, {4,18}, {1,30}, {1,8}, {25,26}, {12,30}, {9,13}, {1,20}, {4,26}, {6,27}, {8,21}, {5,13}, {15,29}, {17,29}, {3,7}, {4,30}, {9,27}, {19,23}, {15,21}, {14,16}, {5,19}, {2,29}, {6,29}, {7,21}, {5,9}, {22,29}, {6,14}, {12,21}, {15,18}, {16,27}, {21,28}, {10,16}, {2,23}, {20,28}, {6,28}, {3,10}, {9,12}, {13,22}, {9,18}, {5,22}, {14,27}, {8,12}, {13,16}, {20,23}, {2,9}, {22,28}, {10,14}, {12,24}, {11,19}, {2,11}, {18,29}, {5,7}, {7,23}, {15,22}, {14,18}, {1,15}, {14,26}, {8,16}, {1,25}, {10,12}, {13,24}, {11,20}, {4,11}, {5,28}, {10,29}, {7,18}, {4,25}, {19,27}, {23,29}, {6,15}, {14,21}, {15,19}, {2,14}, {16,29}, {7,20}, {4,23}, {15,26}, {19,25}, {2,19}, {21,29}, {7,16}, {3,22}, {18,30}, {11,27}, {13,29}, {7,15}, {4,17}, {3,27}, {2,13}, {15,28}, {13,19}, {2,15}, {8,17}, {3,25}, {20,21}, {4,16}, {23,26}, {6,20}, {3,20}, {7,26}, {6,23}, {11,25}, {18,21}, {5,16}, {20,27}, {2,28}, {10,28}, {4,21}, {13,26}, {17,25}, {3,19}, {21,30}, {5,24}, {6,24}, {17,21}, {3,15}, {14,30}, {1,23}, {16,28}, {1,10}, {22,26}, {6,18}, {19,30}, {9,22}, {18,22}, {14,25}, {12,19}, {5,27}, {8,22}, {3,16}, {23,30}, {9,20}, {2,24}, {17,28}, {10,24}, {7,13}, {15,23}, {15,17}, {3,14}, {10,27}, {8,24}, {5,11}, {11,29}, {19,22}, {2,18}, {25,29}, {7,19}, {6,25}, {19,21}, {4,15}, {2,16}, {1,28}, {14,22}, {12,18}, {5,6}, {7,14}, {1,27}, {8,26}, {3,12}, {11,17}, {16,22}, {1,18}, {24,26}, {8,11}, {5,23}, {20,29}, {5,26}, {8,27}, {8,25}, {7,28}, {4,10}, {24,27}, {14,28}, {2,8}, {25,28}, {1,12}, {3,29}, {7,30}, {4,7}, {23,27}, {11,28}, {6,13}, {13,17}, {7,24}, {14,23}, {12,20}, {5,8}, {9,23}, {1,29}, {18,25}, {12,25}, {9,28}, {10,22}, {4,13}, {15,27}, {6,12}, {2,30}, {5,12}, {20,26}, {4,6}, {3,26}, {6,30}, {25,27}, {8,19}, {5,21}, {7,11}, {11,23}, {18,26}, {4,8}, {12,28}, {10,13}, {2,20}, {4,28}, {9,21}, {1,13}, {17,30}, {3,9}, {16,23}, {10,18}, {3,11}, {17,23}, {15,24}, {14,17}, {3,6}, {8,14}, {5,29}, {7,29}, {18,24}, {21,27}, {16,30}, {16,25}, {9,11}, {11,22}, {1,24}, {17,26}, {22,30}, {5,17}, {10,23}, {11,18}, {18,27}, {10,17}, {3,24}, {11,30}, {13,25}, {13,27}, {8,15}, {12,16}, {1,9}, {10,19}, {8,30}, {20,24}, {13,21}, {5,18}, {1,17}, {15,16}, {8,20}, {3,30}, {10,26}, {1,14}, {9,30}, {12,26}, {9,25}, {4,22} } Symmetric graph 36 of order 30 Valency 20 Diameter 2 Girth 3 Automorphism group of order 286708355039232000000 Number of arcs = 600 Number of 2-arcs = 11400 2-arc-transitive false Edge-set { {1,11}, {11,27}, {7,18}, {1,27}, {18,25}, {18,24}, {3,13}, {7,25}, {10,24}, {13,23}, {7,24}, {13,21}, {13,30}, {9,19}, {10,18}, {3,23}, {7,20}, {5,21}, {8,30}, {19,22}, {3,21}, {5,30}, {19,29}, {3,30}, {19,27}, {19,26}, {6,15}, {20,24}, {5,13}, {8,13}, {9,22}, {3,16}, {5,16}, {1,29}, {3,17}, {4,27}, {6,26}, {15,30}, {9,29}, {4,26}, {15,28}, {9,27}, {1,26}, {15,25}, {9,26}, {15,24}, {15,22}, {2,12}, {16,21}, {16,30}, {1,19}, {17,30}, {4,19}, {6,19}, {6,30}, {9,11}, {4,11}, {7,28}, {9,14}, {1,14}, {10,25}, {9,15}, {2,24}, {3,22}, {12,27}, {6,28}, {2,22}, {12,26}, {6,25}, {10,22}, {12,23}, {6,24}, {7,22}, {12,21}, {6,22}, {12,30}, {12,28}, {8,17}, {11,29}, {11,26}, {7,15}, {14,27}, {14,26}, {10,15}, {15,26}, {2,15}, {3,15}, {2,27}, {6,18}, {2,18}, {3,26}, {6,20}, {10,20}, {5,23}, {6,12}, {7,12}, {8,21}, {6,13}, {9,30}, {1,28}, {17,25}, {2,26}, {9,28}, {17,24}, {2,23}, {8,28}, {17,22}, {2,21}, {5,28}, {17,29}, {2,30}, {3,28}, {17,27}, {2,28}, {17,26}, {17,23}, {4,14}, {18,28}, {18,22}, {3,12}, {20,25}, {20,22}, {5,12}, {12,24}, {12,22}, {8,12}, {13,22}, {9,12}, {1,12}, {8,25}, {2,13}, {9,13}, {9,24}, {2,16}, {8,16}, {1,22}, {2,17}, {5,17}, {4,29}, {2,19}, {3,19}, {6,27}, {2,11}, {7,26}, {10,23}, {14,23}, {8,24}, {7,23}, {14,21}, {8,22}, {6,23}, {14,30}, {8,29}, {4,23}, {14,28}, {8,27}, {1,23}, {14,25}, {8,26}, {9,23}, {14,24}, {8,23}, {14,22}, {14,29}, {13,26}, {13,28}, {9,17}, {16,23}, {16,28}, {1,17}, {17,21}, {17,28}, {4,17}, {19,30}, {19,28}, {6,17}, {11,28}, {7,17}, {10,17}, {8,19}, {7,19}, {6,21}, {8,11}, {6,11}, {7,30}, {8,14}, {10,28}, {8,15}, {1,15}, {2,25}, {8,18}, {9,18}, {3,24}, {8,20}, {5,22}, {4,21}, {5,29}, {20,29}, {4,30}, {3,29}, {20,27}, {4,28}, {2,29}, {20,26}, {4,25}, {10,29}, {20,23}, {4,24}, {7,29}, {20,21}, {4,22}, {6,29}, {20,30}, {20,28}, {19,24}, {19,23}, {6,14}, {11,22}, {11,23}, {7,14}, {10,14}, {15,27}, {15,23}, {2,14}, {18,26}, {18,23}, {3,14}, {5,14}, {4,15}, {5,15}, {4,18}, {3,18}, {3,27}, {4,20}, {2,20}, {5,26}, {4,12}, {10,12}, {4,13}, {7,13}, {9,21}, {4,16}, {6,16}, {1,30}, {10,27}, {1,25}, {16,25}, {10,26}, {9,25}, {16,24}, {16,22}, {10,21}, {5,25}, {16,29}, {10,30}, {3,25}, {16,27}, {16,26}, {15,21}, {15,29}, {18,30}, {18,29}, {3,20}, {5,20}, {12,25}, {12,29}, {13,24}, {13,29}, {9,20}, {1,20}, {10,13}, {1,13}, {10,16}, {9,16}, {1,24}, {10,19}, {5,19}, {10,11}, {3,11}, {7,27}, {5,24}, {7,21}, {11,21}, {11,30}, {5,27}, {1,21}, {11,25}, {11,24}, {13,27}, {13,25}, {1,16}, {19,21}, {19,25}, {7,16}, {5,11}, {7,11}, {5,18}, {1,18}, {18,27}, {18,21} } Symmetric graph 37 of order 30 Valency 24 Diameter 2 Girth 3 Automorphism group of order 23219011584000000 Number of arcs = 720 Number of 2-arcs = 16560 2-arc-transitive false Edge-set { {1,7}, {2,21}, {18,29}, {1,15}, {17,24}, {9,27}, {5,12}, {2,7}, {3,18}, {10,18}, {6,19}, {24,25}, {9,25}, {6,20}, {16,27}, {1,21}, {17,29}, {4,9}, {5,14}, {9,23}, {5,26}, {5,13}, {15,21}, {18,30}, {8,19}, {24,30}, {8,25}, {15,22}, {2,15}, {18,24}, {10,27}, {6,12}, {3,24}, {13,25}, {1,16}, {20,25}, {6,29}, {7,16}, {6,11}, {2,16}, {7,15}, {9,28}, {5,11}, {13,22}, {21,30}, {18,28}, {11,19}, {22,30}, {8,30}, {3,23}, {3,17}, {9,18}, {5,19}, {23,25}, {9,26}, {5,20}, {15,27}, {4,18}, {14,19}, {11,30}, {2,8}, {14,30}, {8,22}, {5,27}, {12,15}, {8,21}, {4,29}, {15,28}, {1,8}, {4,17}, {7,21}, {3,29}, {24,26}, {10,25}, {16,28}, {11,16}, {2,23}, {11,24}, {5,10}, {13,19}, {21,28}, {11,23}, {22,28}, {14,20}, {4,10}, {6,14}, {9,24}, {5,25}, {6,13}, {16,21}, {17,30}, {8,20}, {24,29}, {7,25}, {16,22}, {3,9}, {12,13}, {19,28}, {11,28}, {1,22}, {12,28}, {1,11}, {23,30}, {6,25}, {9,16}, {7,20}, {3,27}, {7,26}, {3,10}, {2,22}, {4,27}, {12,14}, {7,19}, {8,26}, {4,28}, {1,17}, {17,20}, {18,19}, {6,23}, {16,26}, {11,13}, {15,26}, {10,24}, {17,19}, {20,28}, {10,23}, {13,26}, {19,25}, {6,30}, {8,16}, {8,15}, {4,24}, {10,28}, {14,22}, {18,27}, {12,19}, {8,29}, {4,23}, {14,25}, {11,20}, {2,27}, {10,21}, {19,26}, {18,23}, {20,26}, {2,19}, {17,28}, {5,30}, {8,24}, {4,25}, {14,21}, {22,29}, {9,14}, {21,29}, {7,29}, {14,26}, {17,23}, {3,25}, {9,13}, {12,20}, {1,27}, {13,21}, {7,30}, {3,26}, {10,13}, {2,10}, {6,18}, {10,14}, {6,22}, {5,21}, {5,17}, {15,20}, {4,7}, {2,28}, {3,7}, {6,21}, {10,22}, {11,29}, {13,30}, {5,28}, {11,15}, {4,30}, {7,22}, {3,30}, {23,26}, {10,26}, {12,16}, {1,23}, {5,9}, {13,20}, {21,27}, {22,27}, {12,30}, {1,25}, {9,17}, {15,23}, {13,29}, {14,29}, {1,13}, {17,21}, {6,10}, {6,28}, {18,22}, {19,30}, {8,13}, {1,24}, {12,23}, {12,24}, {12,29}, {10,17}, {8,14}, {2,25}, {2,24}, {7,14}, {2,26}, {17,26}, {5,15}, {1,26}, {5,16}, {6,15}, {16,24}, {6,16}, {3,22}, {3,21}, {4,21}, {15,24}, {16,23}, {19,27}, {2,11}, {6,26}, {10,16}, {3,28}, {23,29}, {11,14}, {2,17}, {18,20}, {6,24}, {16,25}, {15,25}, {11,27}, {2,30}, {8,18}, {7,17}, {3,20}, {2,12}, {12,27}, {1,12}, {2,18}, {10,15}, {5,23}, {13,28}, {11,21}, {11,22}, {20,27}, {12,22}, {1,30}, {8,17}, {1,18}, {12,21}, {1,29}, {10,29}, {6,7}, {3,16}, {2,29}, {7,18}, {6,8}, {4,16}, {5,7}, {3,15}, {4,19}, {5,8}, {4,15}, {14,23}, {14,24}, {13,24}, {3,19}, {4,20}, {9,21}, {1,19}, {5,29}, {8,23}, {4,26}, {17,27}, {1,28}, {1,10}, {6,17}, {5,22}, {5,18}, {15,19}, {4,8}, {3,8}, {11,17}, {9,22}, {4,14}, {1,20}, {2,20}, {1,9}, {7,23}, {16,20}, {11,26}, {24,28}, {16,19}, {23,28}, {23,27}, {11,18}, {2,9}, {24,27}, {12,18}, {12,26}, {15,29}, {12,17}, {15,30}, {4,13}, {16,29}, {3,14}, {3,13}, {16,30}, {2,13}, {18,21}, {6,27}, {17,22}, {20,30}, {7,13}, {6,9}, {18,26}, {4,22}, {10,19}, {3,12}, {2,14}, {1,14}, {18,25}, {20,29}, {19,29}, {7,28}, {10,20}, {17,25}, {9,20}, {9,19}, {7,27}, {3,11}, {8,27}, {4,12}, {4,11}, {8,28}, {9,15}, {5,24}, {14,28}, {9,29}, {13,23}, {21,26}, {14,27}, {9,30}, {13,27}, {22,26}, {10,30}, {22,25}, {21,25}, {7,24}, {12,25}, {11,25} } Symmetric graph 38 of order 30 Valency 25 Diameter 2 Girth 3 Automorphism group of order 2149908480000000 Number of arcs = 750 Number of 2-arcs = 18000 2-arc-transitive false Edge-set { {1,6}, {11,16}, {12,26}, {4,20}, {2,26}, {16,23}, {7,13}, {3,14}, {15,26}, {11,23}, {6,25}, {4,7}, {3,17}, {17,29}, {4,14}, {15,18}, {5,26}, {19,23}, {1,25}, {7,20}, {16,24}, {10,26}, {13,17}, {14,29}, {10,14}, {5,15}, {10,30}, {5,24}, {4,13}, {14,18}, {5,9}, {1,19}, {13,23}, {8,25}, {2,7}, {11,24}, {10,12}, {7,17}, {3,29}, {6,22}, {4,6}, {20,26}, {23,28}, {3,10}, {5,17}, {4,30}, {18,24}, {18,28}, {5,12}, {13,19}, {20,28}, {21,28}, {12,22}, {6,13}, {3,13}, {14,17}, {4,9}, {1,18}, {12,19}, {13,30}, {8,11}, {2,12}, {3,25}, {10,27}, {15,17}, {11,29}, {1,22}, {6,20}, {2,20}, {16,28}, {10,17}, {5,29}, {14,30}, {15,24}, {8,26}, {13,16}, {14,26}, {7,26}, {3,23}, {25,27}, {7,22}, {14,20}, {15,28}, {5,13}, {13,28}, {14,21}, {9,22}, {9,27}, {3,8}, {2,17}, {7,27}, {3,22}, {21,27}, {2,23}, {8,16}, {3,16}, {17,26}, {4,10}, {5,18}, {9,11}, {1,12}, {2,8}, {2,16}, {3,28}, {17,21}, {20,27}, {2,15}, {14,24}, {10,15}, {20,29}, {25,28}, {5,10}, {5,19}, {1,30}, {20,24}, {8,12}, {7,16}, {3,26}, {7,15}, {3,11}, {6,27}, {4,22}, {10,20}, {5,28}, {12,30}, {13,24}, {4,28}, {18,21}, {5,22}, {6,19}, {18,26}, {23,27}, {3,6}, {4,17}, {4,26}, {18,23}, {23,29}, {14,25}, {24,29}, {10,25}, {17,23}, {8,29}, {3,18}, {5,27}, {19,22}, {3,12}, {3,27}, {17,22}, {4,21}, {9,18}, {8,30}, {19,29}, {25,30}, {15,27}, {5,11}, {25,29}, {14,23}, {8,15}, {21,29}, {9,25}, {15,25}, {7,11}, {6,18}, {4,27}, {6,14}, {4,15}, {5,23}, {13,20}, {14,28}, {9,12}, {1,13}, {20,30}, {2,11}, {12,16}, {11,27}, {6,15}, {4,11}, {14,27}, {15,22}, {10,21}, {7,29}, {11,19}, {5,20}, {19,28}, {7,30}, {3,24}, {24,27}, {10,22}, {12,20}, {2,13}, {11,28}, {12,21}, {2,18}, {16,27}, {6,17}, {4,29}, {15,23}, {1,14}, {15,20}, {16,29}, {25,26}, {8,14}, {12,27}, {13,22}, {2,28}, {16,21}, {13,27}, {14,22}, {9,21}, {1,9}, {12,23}, {8,13}, {9,26}, {1,23}, {7,25}, {14,16}, {10,13}, {5,14}, {13,26}, {1,7}, {7,24}, {4,24}, {10,18}, {22,30}, {6,24}, {10,28}, {5,7}, {18,30}, {9,14}, {1,15}, {12,29}, {13,25}, {8,23}, {2,14}, {15,16}, {10,23}, {5,8}, {13,21}, {9,19}, {2,24}, {24,28}, {19,25}, {24,30}, {10,24}, {4,25}, {7,18}, {19,27}, {21,30}, {9,24}, {19,24}, {10,19}, {1,17}, {9,16}, {1,26}, {13,29}, {4,16}, {14,19}, {12,25}, {3,7}, {18,22}, {2,19}, {16,30}, {12,17}, {7,28}, {3,21}, {11,20}, {2,6}, {1,29}, {20,25}, {5,16}, {19,26}, {18,25}, {8,19}, {20,21}, {9,28}, {17,30}, {1,8}, {7,12}, {8,27}, {2,22}, {17,28}, {22,29}, {20,23}, {8,28}, {3,15}, {11,17}, {1,27}, {20,22}, {2,21}, {9,15}, {1,11}, {6,29}, {10,16}, {5,25}, {7,19}, {12,18}, {3,19}, {6,30}, {24,26}, {4,18}, {18,27}, {2,29}, {16,25}, {8,17}, {11,22}, {6,21}, {17,25}, {4,23}, {8,18}, {19,21}, {9,30}, {2,25}, {17,27}, {23,30}, {11,25}, {17,24}, {10,29}, {3,20}, {4,12}, {13,18}, {9,20}, {1,28}, {8,21}, {16,22}, {6,26}, {22,28}, {1,21}, {4,19}, {2,30}, {11,18}, {5,6}, {9,17}, {6,11}, {22,27}, {8,24}, {2,10}, {6,28}, {8,22}, {8,20}, {10,11}, {11,26}, {3,30}, {4,8}, {15,29}, {9,23}, {11,30}, {12,24}, {6,12}, {1,10}, {2,27}, {7,21}, {3,9}, {5,21}, {18,29}, {15,19}, {7,23}, {15,21}, {19,30}, {2,9}, {1,16}, {21,26}, {22,26}, {6,23}, {9,13}, {9,29}, {15,30}, {7,14}, {1,24}, {16,26}, {23,26}, {11,21}, {1,20}, {5,30}, {6,16}, {12,28} } Symmetric graph 39 of order 30 Valency 27 Diameter 2 Girth 3 Automorphism group of order 219419659468800 Number of arcs = 810 Number of 2-arcs = 21060 2-arc-transitive false Edge-set { {1,4}, {5,9}, {6,20}, {8,21}, {4,22}, {7,10}, {1,5}, {12,20}, {2,24}, {9,18}, {6,9}, {1,19}, {23,30}, {5,8}, {4,20}, {3,10}, {1,28}, {6,16}, {21,30}, {14,22}, {7,21}, {5,22}, {5,11}, {3,20}, {17,25}, {7,12}, {8,20}, {4,24}, {9,10}, {1,6}, {19,30}, {5,26}, {11,20}, {7,28}, {5,13}, {12,25}, {2,12}, {18,24}, {9,17}, {12,19}, {2,23}, {8,18}, {4,9}, {2,8}, {4,29}, {4,10}, {13,29}, {15,26}, {3,19}, {23,28}, {10,20}, {1,24}, {9,16}, {6,8}, {1,21}, {22,30}, {5,7}, {5,20}, {11,25}, {3,12}, {8,14}, {4,27}, {2,10}, {1,29}, {19,26}, {11,23}, {8,22}, {4,18}, {3,13}, {26,28}, {3,6}, {21,28}, {16,30}, {21,29}, {15,22}, {3,11}, {3,28}, {6,17}, {20,30}, {14,24}, {9,21}, {6,22}, {21,24}, {9,27}, {6,10}, {1,9}, {6,30}, {22,27}, {10,18}, {14,23}, {16,27}, {4,11}, {17,26}, {7,11}, {1,10}, {1,30}, {5,16}, {13,22}, {7,20}, {5,24}, {5,12}, {2,20}, {18,25}, {9,12}, {8,19}, {4,23}, {8,10}, {2,13}, {26,29}, {3,4}, {19,28}, {20,24}, {17,24}, {9,15}, {6,25}, {5,27}, {11,14}, {3,27}, {2,17}, {7,29}, {18,20}, {9,24}, {9,30}, {6,14}, {18,19}, {14,26}, {11,27}, {4,7}, {5,19}, {12,26}, {2,11}, {25,28}, {12,13}, {12,27}, {18,23}, {2,4}, {19,29}, {4,26}, {11,19}, {5,15}, {10,25}, {1,12}, {16,24}, {8,17}, {12,21}, {2,22}, {7,18}, {12,16}, {15,21}, {22,25}, {1,7}, {5,30}, {5,21}, {20,22}, {7,25}, {15,18}, {9,25}, {14,30}, {7,17}, {15,28}, {13,25}, {2,9}, {6,29}, {14,29}, {15,27}, {2,19}, {23,29}, {5,25}, {8,28}, {4,13}, {18,22}, {10,19}, {1,23}, {8,16}, {4,8}, {3,8}, {4,28}, {13,30}, {3,21}, {22,28}, {3,24}, {6,7}, {1,20}, {24,30}, {18,21}, {14,27}, {10,27}, {6,19}, {11,26}, {10,16}, {1,8}, {16,29}, {8,15}, {21,23}, {16,22}, {7,13}, {4,25}, {17,29}, {4,15}, {19,25}, {19,27}, {10,23}, {10,30}, {1,14}, {16,21}, {21,25}, {12,22}, {7,24}, {5,17}, {11,30}, {3,14}, {17,27}, {2,15}, {25,29}, {9,19}, {6,23}, {8,11}, {27,28}, {2,6}, {13,26}, {3,22}, {18,28}, {3,15}, {17,30}, {7,14}, {6,21}, {9,14}, {6,27}, {3,29}, {8,23}, {4,16}, {1,13}, {26,30}, {3,5}, {20,28}, {16,28}, {8,13}, {20,29}, {15,24}, {2,28}, {6,18}, {13,28}, {12,23}, {2,16}, {13,18}, {9,26}, {20,23}, {8,25}, {4,12}, {8,12}, {13,19}, {23,26}, {14,16}, {13,21}, {22,26}, {24,25}, {12,17}, {15,23}, {11,16}, {18,26}, {21,22}, {7,27}, {5,10}, {24,27}, {10,17}, {16,25}, {6,11}, {20,26}, {11,24}, {9,22}, {18,30}, {1,11}, {3,30}, {13,24}, {9,20}, {6,24}, {19,24}, {12,18}, {9,11}, {7,19}, {5,23}, {12,30}, {2,14}, {1,15}, {25,30}, {27,29}, {10,13}, {2,7}, {9,13}, {19,22}, {6,26}, {10,15}, {9,23}, {11,13}, {3,26}, {11,15}, {3,25}, {1,17}, {7,30}, {1,25}, {17,20}, {12,28}, {2,26}, {3,18}, {9,28}, {16,19}, {8,29}, {2,25}, {12,29}, {17,19}, {15,29}, {15,25}, {13,27}, {10,26}, {11,21}, {24,29}, {18,27}, {12,15}, {17,23}, {2,5}, {17,22}, {7,15}, {6,13}, {14,25}, {4,19}, {16,23}, {5,14}, {11,18}, {3,17}, {6,28}, {14,18}, {14,21}, {13,20}, {24,26}, {3,9}, {24,28}, {11,22}, {14,17}, {13,17}, {2,18}, {13,16}, {8,26}, {7,16}, {15,19}, {23,25}, {4,30}, {15,16}, {15,30}, {5,29}, {10,14}, {1,27}, {12,14}, {10,21}, {1,22}, {14,28}, {2,21}, {22,29}, {3,23}, {17,21}, {16,20}, {7,22}, {18,29}, {4,14}, {15,20}, {10,29}, {11,28}, {21,27}, {14,19}, {21,26}, {20,27}, {10,24}, {10,28}, {11,29}, {23,27}, {13,23}, {16,26}, {27,30}, {2,29}, {4,21}, {19,23}, {5,18}, {17,28}, {8,24}, {4,17}, {2,30}, {7,26}, {12,24}, {10,22}, {1,18}, {8,27}, {9,29}, {15,17}, {14,20}, {3,16}, {6,12}, {20,25}, {11,17}, {1,16}, {2,27}, {8,30}, {1,26}, {3,7}, {6,15}, {5,28}, {7,23} } Symmetric graph 40 of order 30 Valency 28 Diameter 2 Girth 3 Automorphism group of order 42849873690624000 Number of arcs = 840 Number of 2-arcs = 22680 2-arc-transitive false Edge-set { {1,3}, {1,8}, {16,18}, {1,30}, {13,16}, {23,26}, {9,26}, {1,14}, {5,16}, {20,26}, {9,12}, {3,6}, {4,20}, {6,28}, {20,29}, {1,19}, {11,16}, {10,26}, {2,9}, {6,17}, {20,24}, {21,28}, {27,29}, {8,9}, {1,18}, {7,17}, {17,24}, {1,22}, {13,17}, {6,24}, {16,23}, {22,26}, {9,28}, {6,27}, {20,30}, {2,28}, {15,29}, {9,24}, {1,25}, {4,17}, {3,24}, {12,16}, {8,22}, {11,13}, {6,21}, {28,30}, {13,29}, {1,23}, {16,26}, {24,29}, {14,25}, {4,24}, {3,25}, {1,15}, {7,16}, {12,25}, {4,9}, {3,26}, {6,15}, {7,20}, {12,28}, {22,29}, {9,11}, {1,21}, {14,17}, {5,24}, {2,12}, {15,22}, {13,25}, {6,10}, {4,28}, {3,29}, {1,5}, {16,19}, {7,24}, {17,25}, {4,8}, {3,18}, {21,26}, {9,27}, {15,30}, {7,13}, {20,22}, {9,16}, {12,14}, {5,22}, {13,20}, {6,12}, {4,16}, {6,26}, {9,20}, {4,13}, {5,19}, {11,19}, {4,7}, {3,17}, {5,8}, {18,19}, {10,16}, {26,29}, {9,14}, {5,21}, {19,27}, {7,28}, {17,29}, {6,8}, {18,20}, {9,25}, {1,10}, {14,24}, {12,21}, {22,27}, {13,15}, {6,7}, {22,28}, {28,29}, {1,16}, {8,16}, {19,24}, {11,25}, {4,10}, {2,3}, {2,21}, {15,27}, {15,25}, {7,10}, {5,20}, {12,19}, {7,12}, {17,22}, {8,13}, {6,18}, {2,16}, {18,26}, {9,23}, {4,29}, {3,14}, {19,25}, {7,30}, {8,23}, {6,16}, {8,20}, {11,28}, {21,29}, {5,10}, {15,17}, {26,28}, {9,29}, {19,21}, {11,27}, {10,15}, {2,7}, {17,20}, {12,24}, {9,21}, {1,27}, {7,26}, {9,17}, {6,9}, {1,20}, {17,28}, {12,17}, {10,18}, {2,23}, {18,22}, {23,28}, {7,29}, {8,24}, {18,25}, {10,30}, {2,13}, {18,23}, {26,27}, {9,30}, {6,13}, {6,20}, {19,28}, {11,29}, {2,8}, {11,18}, {21,23}, {12,29}, {14,22}, {13,24}, {6,25}, {1,13}, {17,23}, {24,26}, {5,28}, {19,29}, {16,30}, {4,19}, {3,11}, {16,21}, {8,27}, {11,15}, {7,21}, {20,25}, {10,12}, {12,15}, {7,22}, {12,13}, {6,22}, {1,26}, {26,30}, {9,13}, {4,18}, {3,23}, {7,27}, {17,30}, {15,18}, {8,15}, {10,21}, {5,25}, {10,19}, {14,30}, {10,17}, {2,24}, {18,21}, {23,27}, {14,27}, {15,24}, {7,25}, {2,26}, {9,15}, {6,23}, {3,28}, {8,19}, {5,18}, {19,23}, {14,29}, {5,14}, {3,30}, {1,9}, {12,22}, {10,27}, {2,30}, {24,25}, {10,25}, {13,28}, {6,29}, {11,22}, {25,27}, {2,29}, {14,15}, {4,21}, {3,27}, {16,28}, {8,29}, {1,11}, {14,20}, {24,28}, {25,29}, {1,29}, {1,17}, {16,24}, {22,25}, {21,24}, {4,15}, {15,23}, {3,12}, {4,22}, {6,14}, {4,30}, {3,13}, {5,23}, {19,26}, {5,30}, {2,20}, {4,26}, {6,11}, {20,21}, {14,28}, {5,29}, {1,12}, {1,24}, {12,18}, {22,23}, {13,22}, {3,16}, {13,21}, {15,19}, {7,11}, {5,9}, {4,25}, {4,6}, {3,20}, {2,22}, {13,18}, {14,26}, {7,18}, {18,28}, {11,30}, {10,28}, {16,29}, {8,14}, {5,17}, {21,27}, {27,30}, {21,25}, {7,14}, {12,27}, {1,7}, {1,6}, {16,20}, {20,28}, {7,23}, {17,26}, {3,8}, {14,21}, {23,25}, {25,30}, {10,13}, {16,27}, {8,30}, {2,19}, {18,27}, {23,30}, {14,19}, {5,11}, {24,27}, {2,4}, {3,15}, {8,26}, {11,21}, {3,10}, {2,6}, {15,20}, {25,28}, {10,29}, {3,9}, {1,4}, {8,12}, {18,30}, {13,23}, {10,23}, {4,23}, {13,19}, {2,11}, {1,28}, {15,21}, {21,30}, {2,14}, {5,15}, {4,5}, {3,19}, {5,27}, {19,30}, {12,20}, {10,11}, {8,17}, {8,11}, {12,26}, {9,22}, {13,30}, {17,19}, {11,24}, {4,12}, {3,22}, {5,13}, {6,19}, {16,25}, {7,19}, {8,21}, {7,15}, {9,19}, {20,23}, {10,14}, {2,5}, {2,17}, {16,17}, {9,18}, {5,7}, {7,9}, {18,24}, {2,15}, {11,20}, {23,29}, {12,23}, {22,30}, {13,26}, {10,24}, {2,25}, {11,14}, {14,16}, {22,24}, {4,14}, {3,5}, {20,27}, {12,30}, {11,26}, {2,18}, {11,23}, {10,22}, {4,11}, {3,21}, {8,25}, {6,30}, {16,22}, {8,28}, {5,12}, {19,22}, {13,27}, {18,29}, {14,23}, {5,26}, {3,7}, {15,28}, {8,10}, {2,10}, {8,18}, {14,18}, {17,21}, {24,30}, {17,27}, {10,20}, {4,27}, {11,17}, {15,26}, {2,27} } Symmetric graph 41 of order 30 Valency 29 Diameter 1 Girth 3 Automorphism group of order 265252859812191058636308480000000 Number of arcs = 870 Number of 2-arcs = 24360 2-arc-transitive true Edge-set { {1,2}, {7,24}, {5,16}, {3,29}, {4,12}, {4,21}, {8,13}, {25,28}, {11,23}, {15,19}, {6,18}, {9,15}, {18,22}, {2,23}, {7,14}, {11,26}, {17,27}, {10,16}, {20,28}, {1,12}, {2,24}, {14,22}, {10,25}, {12,17}, {15,24}, {14,27}, {10,19}, {16,24}, {5,28}, {8,29}, {9,12}, {6,10}, {20,21}, {18,20}, {3,30}, {13,21}, {13,29}, {11,30}, {26,27}, {7,19}, {6,16}, {3,24}, {4,5}, {8,27}, {9,19}, {13,26}, {17,29}, {18,19}, {3,6}, {3,12}, {4,24}, {8,20}, {9,30}, {1,13}, {2,29}, {3,21}, {4,13}, {4,11}, {2,25}, {7,23}, {17,19}, {6,15}, {13,22}, {25,29}, {22,26}, {14,30}, {10,26}, {1,11}, {9,23}, {23,25}, {14,23}, {5,10}, {1,20}, {6,20}, {21,30}, {1,29}, {2,12}, {21,22}, {13,25}, {3,28}, {4,15}, {8,18}, {2,20}, {7,30}, {1,17}, {2,15}, {6,23}, {14,21}, {18,25}, {3,23}, {1,14}, {2,10}, {22,28}, {11,25}, {19,28}, {6,11}, {3,15}, {4,18}, {2,30}, {7,26}, {5,17}, {1,15}, {14,16}, {24,25}, {5,23}, {9,28}, {11,22}, {15,23}, {14,18}, {10,15}, {24,26}, {16,29}, {12,28}, {1,18}, {2,3}, {12,22}, {23,27}, {14,19}, {25,26}, {17,23}, {6,27}, {19,21}, {5,8}, {1,9}, {6,13}, {21,29}, {7,10}, {16,20}, {16,17}, {15,28}, {16,26}, {17,28}, {8,16}, {22,30}, {5,9}, {1,22}, {7,25}, {16,23}, {19,24}, {5,6}, {9,27}, {19,22}, {23,26}, {14,17}, {11,28}, {11,27}, {12,15}, {18,24}, {2,14}, {24,30}, {5,26}, {5,29}, {7,18}, {3,16}, {12,24}, {5,24}, {16,22}, {8,9}, {9,22}, {14,26}, {10,17}, {16,28}, {7,8}, {9,16}, {13,24}, {19,27}, {17,20}, {2,27}, {10,22}, {20,25}, {11,24}, {14,15}, {10,18}, {1,5}, {6,29}, {12,21}, {3,8}, {7,12}, {8,21}, {9,13}, {3,26}, {4,17}, {4,16}, {8,28}, {11,17}, {15,27}, {10,27}, {19,20}, {12,16}, {24,28}, {8,14}, {9,10}, {12,13}, {24,29}, {21,25}, {13,23}, {11,19}, {5,11}, {6,19}, {28,30}, {1,8}, {2,9}, {6,26}, {17,21}, {16,18}, {20,22}, {25,30}, {2,22}, {2,4}, {7,17}, {15,16}, {22,23}, {14,25}, {9,25}, {12,29}, {18,21}, {3,13}, {11,12}, {24,27}, {6,21}, {11,18}, {3,27}, {2,21}, {7,13}, {5,27}, {1,19}, {8,15}, {7,27}, {16,19}, {26,29}, {16,21}, {13,28}, {1,3}, {4,22}, {8,25}, {15,30}, {1,27}, {2,19}, {21,28}, {3,9}, {10,11}, {20,27}, {10,20}, {20,30}, {12,19}, {6,24}, {3,14}, {4,10}, {8,24}, {3,5}, {1,4}, {4,6}, {4,25}, {8,23}, {14,29}, {10,12}, {11,13}, {3,19}, {3,4}, {4,8}, {21,27}, {13,19}, {2,17}, {7,15}, {6,8}, {9,21}, {13,18}, {11,21}, {13,27}, {13,15}, {4,14}, {18,30}, {20,24}, {5,30}, {19,29}, {26,30}, {17,26}, {3,10}, {4,20}, {8,12}, {9,24}, {13,14}, {10,29}, {4,7}, {22,25}, {6,22}, {2,28}, {7,11}, {6,12}, {7,22}, {6,28}, {15,18}, {3,18}, {15,21}, {2,11}, {3,20}, {12,20}, {13,20}, {29,30}, {1,30}, {2,26}, {3,11}, {4,27}, {2,8}, {7,9}, {13,17}, {15,29}, {19,23}, {6,14}, {3,25}, {4,23}, {9,26}, {17,22}, {14,28}, {1,10}, {2,7}, {7,16}, {17,24}, {5,15}, {9,18}, {3,22}, {10,13}, {27,30}, {19,26}, {5,19}, {5,18}, {18,29}, {16,27}, {8,26}, {9,17}, {15,17}, {19,25}, {9,14}, {23,28}, {11,14}, {4,30}, {10,14}, {5,22}, {23,29}, {12,14}, {8,30}, {1,7}, {2,16}, {20,29}, {12,30}, {1,21}, {2,13}, {6,25}, {21,23}, {7,28}, {11,16}, {5,12}, {1,24}, {7,20}, {16,30}, {2,5}, {9,11}, {22,27}, {11,15}, {13,30}, {1,26}, {2,6}, {4,28}, {8,11}, {15,22}, {15,26}, {17,18}, {10,23}, {14,20}, {1,28}, {9,20}, {1,23}, {20,23}, {12,23}, {14,24}, {5,14}, {4,26}, {1,25}, {11,29}, {18,26}, {6,7}, {3,17}, {12,18}, {27,29}, {25,27}, {10,24}, {22,24}, {5,20}, {19,30}, {23,30}, {5,25}, {5,7}, {1,16}, {5,21}, {10,28}, {11,20}, {15,20}, {18,23}, {12,25}, {23,24}, {8,22}, {26,28}, {18,28}, {6,17}, {18,27}, {27,28}, {1,6}, {8,10}, {7,21}, {8,17}, {9,29}, {8,19}, {16,25}, {6,9}, {7,29}, {21,24}, {5,13}, {17,25}, {12,27}, {10,21}, {4,19}, {3,7}, {12,26}, {13,16}, {28,29}, {17,30}, {4,9}, {22,29}, {20,26}, {4,29}, {10,30}, {2,18}, {21,26}, {15,25}, {6,30} } ................................................................... Symmetric connected graphs of order 31 Symmetric graph 1 of order 31 Valency 2 Diameter 15 Girth 31 Automorphism group of order 62 Number of arcs = 62 Number of 2-arcs = 62 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {15,16}, {16,17}, {17,18}, {18,19}, {19,20}, {20,21}, {21,22}, {22,23}, {23,24}, {24,25}, {25,26}, {26,27}, {27,28}, {28,29}, {29,30}, {30,31}, {1,31} } Symmetric graph 2 of order 31 Valency 6 Diameter 3 Girth 3 Automorphism group of order 186 Number of arcs = 186 Number of 2-arcs = 930 2-arc-transitive false Edge-set { {1,2}, {2,3}, {19,25}, {3,4}, {13,19}, {20,26}, {5,10}, {4,5}, {7,13}, {14,20}, {10,15}, {21,27}, {4,30}, {6,11}, {5,6}, {1,7}, {8,14}, {15,20}, {15,21}, {4,9}, {11,16}, {22,28}, {24,29}, {5,31}, {6,7}, {7,12}, {26,27}, {1,26}, {2,8}, {20,25}, {9,15}, {9,14}, {16,21}, {16,22}, {3,29}, {7,8}, {12,17}, {27,28}, {23,29}, {18,23}, {25,30}, {11,12}, {1,6}, {1,31}, {8,13}, {20,21}, {24,30}, {2,27}, {3,9}, {14,19}, {21,26}, {10,16}, {3,8}, {8,9}, {17,22}, {28,29}, {17,23}, {23,28}, {12,13}, {13,18}, {21,22}, {18,24}, {19,24}, {16,17}, {26,31}, {2,7}, {25,26}, {25,31}, {14,15}, {4,29}, {3,28}, {4,10}, {9,10}, {22,27}, {29,30}, {11,17}, {2,28}, {13,14}, {22,23}, {12,18}, {17,18}, {15,16}, {10,11}, {1,27}, {30,31}, {19,20}, {5,30}, {5,11}, {23,24}, {6,12}, {18,19}, {24,25}, {6,31} } Symmetric graph 3 of order 31 Valency 10 Diameter 2 Girth 3 Automorphism group of order 310 Number of arcs = 310 Number of 2-arcs = 2790 2-arc-transitive false Edge-set { {1,2}, {2,3}, {1,16}, {3,4}, {1,17}, {2,17}, {8,16}, {4,5}, {2,18}, {16,24}, {3,18}, {1,24}, {9,17}, {4,8}, {5,6}, {3,19}, {1,9}, {17,25}, {8,12}, {4,19}, {2,25}, {12,16}, {10,18}, {20,24}, {5,9}, {2,4}, {6,7}, {4,20}, {2,10}, {16,20}, {18,26}, {24,28}, {9,13}, {4,6}, {5,20}, {3,26}, {1,28}, {13,17}, {6,8}, {11,19}, {21,25}, {10,12}, {6,10}, {18,20}, {3,5}, {7,8}, {5,21}, {3,11}, {1,5}, {17,21}, {8,10}, {19,27}, {25,29}, {12,14}, {10,14}, {20,22}, {5,7}, {6,21}, {4,27}, {2,29}, {14,16}, {14,18}, {22,24}, {7,9}, {12,20}, {22,26}, {26,28}, {11,13}, {7,11}, {19,21}, {9,10}, {17,18}, {8,9}, {6,22}, {4,12}, {2,6}, {16,18}, {18,22}, {24,26}, {9,11}, {20,28}, {26,30}, {28,30}, {13,15}, {11,15}, {21,23}, {10,11}, {18,19}, {7,22}, {5,28}, {3,30}, {1,30}, {15,17}, {15,19}, {23,25}, {11,12}, {19,20}, {13,21}, {23,27}, {27,29}, {13,14}, {21,22}, {25,26}, {9,24}, {7,23}, {5,13}, {3,7}, {1,3}, {17,19}, {19,23}, {25,27}, {12,13}, {20,21}, {21,29}, {27,31}, {29,31}, {14,15}, {22,23}, {26,27}, {9,25}, {8,23}, {6,29}, {4,31}, {2,31}, {15,16}, {23,24}, {27,28}, {10,25}, {14,22}, {29,30}, {11,26}, {13,28}, {8,24}, {6,14}, {16,17}, {24,25}, {28,29}, {10,26}, {22,30}, {30,31}, {11,27}, {13,29}, {7,30}, {1,31}, {12,27}, {14,29}, {15,23}, {15,30}, {7,15}, {12,28}, {14,30}, {23,31}, {15,31}, {8,31}, {16,31} } Symmetric graph 4 of order 31 Valency 30 Diameter 1 Girth 3 Automorphism group of order 8222838654177922817725562880000000 Number of arcs = 930 Number of 2-arcs = 26970 2-arc-transitive true Edge-set { {1,2}, {2,3}, {9,18}, {3,4}, {18,27}, {10,19}, {7,19}, {4,5}, {5,27}, {19,28}, {7,26}, {11,20}, {16,28}, {8,20}, {1,16}, {5,6}, {5,14}, {6,28}, {14,26}, {20,29}, {4,16}, {8,27}, {1,17}, {12,21}, {6,25}, {17,29}, {4,20}, {9,21}, {10,25}, {2,17}, {9,20}, {6,7}, {14,23}, {6,15}, {2,14}, {7,29}, {4,23}, {15,27}, {21,30}, {13,25}, {5,17}, {5,20}, {9,28}, {10,26}, {2,18}, {9,29}, {13,22}, {3,15}, {8,23}, {18,30}, {13,29}, {5,21}, {5,25}, {10,22}, {3,19}, {11,26}, {8,28}, {3,18}, {18,29}, {10,21}, {19,25}, {7,8}, {1,23}, {15,24}, {2,21}, {7,16}, {11,23}, {8,30}, {1,13}, {5,24}, {22,31}, {3,22}, {8,24}, {6,18}, {14,29}, {6,21}, {14,25}, {10,29}, {4,19}, {11,27}, {17,28}, {7,18}, {10,30}, {13,19}, {12,24}, {9,24}, {19,31}, {7,22}, {14,30}, {13,24}, {6,22}, {3,14}, {6,26}, {8,14}, {12,28}, {16,27}, {12,27}, {6,17}, {4,10}, {7,27}, {19,30}, {7,13}, {11,22}, {3,28}, {20,26}, {8,16}, {8,9}, {1,10}, {2,24}, {16,25}, {11,30}, {8,17}, {1,20}, {9,31}, {12,31}, {9,25}, {7,23}, {15,30}, {2,13}, {3,23}, {15,26}, {2,8}, {13,28}, {5,16}, {4,29}, {8,19}, {1,7}, {11,31}, {22,28}, {14,20}, {16,24}, {16,31}, {1,12}, {15,31}, {2,22}, {24,30}, {12,23}, {4,15}, {2,27}, {17,23}, {9,15}, {2,10}, {23,29}, {5,11}, {5,28}, {1,26}, {20,31}, {16,22}, {1,24}, {6,12}, {4,27}, {21,27}, {17,25}, {9,17}, {10,20}, {9,10}, {2,11}, {3,25}, {17,26}, {1,21}, {18,24}, {4,24}, {11,17}, {3,9}, {10,18}, {5,30}, {5,13}, {10,16}, {1,9}, {6,31}, {4,12}, {15,21}, {2,25}, {20,30}, {12,18}, {25,31}, {22,30}, {18,26}, {21,29}, {11,19}, {3,11}, {18,28}, {13,21}, {6,14}, {6,29}, {4,14}, {12,20}, {9,30}, {15,23}, {5,26}, {3,26}, {8,29}, {19,29}, {11,21}, {25,28}, {10,11}, {3,12}, {4,26}, {7,30}, {19,27}, {7,28}, {14,22}, {14,24}, {20,28}, {9,19}, {23,31}, {5,15}, {8,18}, {21,31}, {22,25}, {7,15}, {8,31}, {12,22}, {7,17}, {3,13}, {6,16}, {6,27}, {4,7}, {3,24}, {2,23}, {13,23}, {2,5}, {15,25}, {10,31}, {19,22}, {14,17}, {17,27}, {10,13}, {13,16}, {3,6}, {26,29}, {4,8}, {11,12}, {4,13}, {1,22}, {16,26}, {1,4}, {2,12}, {2,30}, {4,25}, {16,19}, {11,14}, {7,10}, {3,31}, {23,26}, {8,12}, {1,11}, {12,15}, {1,29}, {24,27}, {20,23}, {5,8}, {1,5}, {27,30}, {18,21}, {21,24}, {14,18}, {8,11}, {28,31}, {12,16}, {15,18}, {2,29}, {24,28}, {20,24}, {23,27}, {13,17}, {5,9}, {5,10}, {12,13}, {9,12}, {17,20}, {18,22}, {16,20}, {2,6}, {1,28}, {27,31}, {17,21}, {9,13}, {10,15}, {6,9}, {11,15}, {26,30}, {21,25}, {10,14}, {9,14}, {22,26}, {3,7}, {3,30}, {15,19}, {2,7}, {6,10}, {4,31}, {15,20}, {7,11}, {13,18}, {25,29}, {4,30}, {25,30}, {21,26}, {24,29}, {14,19}, {6,11}, {14,28}, {13,14}, {19,23}, {7,12}, {20,25}, {18,23}, {4,9}, {26,31}, {3,29}, {19,24}, {11,16}, {11,28}, {17,22}, {3,8}, {2,28}, {2,19}, {12,17}, {1,27}, {22,27}, {1,18}, {23,28}, {5,31}, {16,21}, {11,25}, {1,6}, {7,24}, {8,13}, {5,22}, {8,22}, {3,17}, {13,30}, {2,16}, {6,23}, {15,29}, {2,4}, {14,15}, {1,15}, {8,25}, {7,21}, {5,19}, {17,31}, {13,27}, {16,30}, {6,20}, {12,29}, {4,6}, {10,27}, {4,18}, {3,20}, {16,18}, {9,26}, {12,26}, {7,9}, {4,21}, {14,31}, {6,8}, {9,23}, {1,30}, {10,24}, {12,14}, {10,12}, {27,29}, {22,24}, {18,20}, {21,23}, {11,13}, {3,5}, {5,18}, {15,16}, {9,11}, {8,10}, {1,3}, {14,16}, {29,31}, {24,26}, {20,22}, {23,25}, {13,15}, {5,7}, {5,23}, {26,28}, {25,27}, {17,19}, {7,20}, {15,17}, {1,19}, {2,31}, {10,23}, {19,21}, {9,22}, {28,30}, {2,15}, {15,28}, {13,26}, {12,30}, {7,25}, {3,21}, {6,24}, {14,27}, {6,19}, {7,14}, {16,17}, {10,28}, {9,27}, {2,20}, {13,31}, {17,30}, {12,25}, {8,21}, {11,24}, {1,14}, {14,21}, {4,17}, {8,26}, {16,29}, {1,25}, {11,29}, {9,16}, {18,31}, {21,28}, {3,16}, {12,19}, {4,22}, {11,18}, {4,11}, {17,24}, {15,22}, {1,8}, {3,27}, {23,30}, {2,26}, {16,23}, {8,15}, {17,18}, {4,28}, {19,26}, {18,25}, {24,31}, {22,29}, {3,10}, {6,30}, {2,9}, {5,29}, {10,17}, {13,20}, {6,13}, {19,20}, {7,31}, {20,27}, {5,12}, {29,30}, {26,27}, {21,22}, {20,21}, {18,19}, {30,31}, {27,28}, {22,23}, {28,29}, {24,25}, {23,24}, {1,31}, {25,26} } ................................................................... Symmetric connected graphs of order 32 Symmetric graph 1 of order 32 Valency 2 Diameter 16 Girth 32 Automorphism group of order 64 Number of arcs = 64 Number of 2-arcs = 64 2-arc-transitive true Edge-set { {1,5}, {1,29}, {19,22}, {26,29}, {13,19}, {3,8}, {24,26}, {9,13}, {3,31}, {18,24}, {6,9}, {27,31}, {15,18}, {2,6}, {21,27}, {11,15}, {2,30}, {20,21}, {7,11}, {25,30}, {14,20}, {4,7}, {23,25}, {10,14}, {4,32}, {17,23}, {5,10}, {28,32}, {16,17}, {22,28}, {12,16}, {8,12} } Symmetric graph 2 of order 32 Valency 3 Diameter 5 Girth 6 Automorphism group of order 192 Number of arcs = 96 Number of 2-arcs = 192 2-arc-transitive true Edge-set { {1,9}, {13,31}, {12,25}, {11,22}, {5,32}, {9,24}, {7,30}, {4,10}, {19,29}, {21,26}, {6,14}, {7,13}, {24,25}, {17,30}, {14,27}, {15,26}, {2,18}, {3,23}, {8,20}, {11,30}, {9,32}, {7,24}, {6,17}, {1,21}, {12,20}, {3,31}, {16,23}, {8,28}, {1,29}, {10,17}, {13,21}, {6,25}, {22,28}, {5,16}, {8,15}, {23,27}, {18,31}, {2,12}, {3,11}, {20,32}, {4,19}, {16,29}, {10,28}, {5,22}, {2,27}, {15,18}, {14,19}, {4,26} } Symmetric graph 3 of order 32 Valency 4 Diameter 4 Girth 4 Automorphism group of order 128 Number of arcs = 128 Number of 2-arcs = 384 2-arc-transitive false Edge-set { {1,17}, {16,27}, {1,25}, {5,21}, {10,31}, {7,27}, {12,25}, {1,30}, {16,23}, {9,17}, {6,18}, {5,31}, {10,21}, {7,19}, {12,20}, {11,27}, {8,25}, {4,21}, {14,31}, {16,18}, {15,29}, {2,24}, {9,30}, {6,23}, {13,19}, {3,20}, {5,20}, {10,19}, {7,32}, {12,22}, {9,23}, {6,30}, {15,21}, {2,31}, {3,28}, {13,26}, {11,18}, {8,17}, {4,29}, {14,24}, {13,30}, {3,23}, {14,17}, {4,18}, {2,19}, {15,20}, {11,29}, {8,24}, {1,22}, {16,32}, {9,28}, {6,26}, {11,24}, {8,29}, {4,26}, {14,28}, {15,25}, {2,27}, {13,22}, {3,32}, {12,32}, {7,22}, {5,28}, {10,26} } Symmetric graph 4 of order 32 Valency 4 Diameter 4 Girth 4 Automorphism group of order 256 Number of arcs = 128 Number of 2-arcs = 384 2-arc-transitive false Edge-set { {1,5}, {5,10}, {17,23}, {10,14}, {9,23}, {21,27}, {1,14}, {9,32}, {13,27}, {25,31}, {7,28}, {17,32}, {13,19}, {2,31}, {28,31}, {20,30}, {13,26}, {12,32}, {19,21}, {2,24}, {4,31}, {6,20}, {13,18}, {20,32}, {3,15}, {2,29}, {16,19}, {11,14}, {24,25}, {4,7}, {6,28}, {6,18}, {8,20}, {3,24}, {2,22}, {19,23}, {3,14}, {16,18}, {4,29}, {1,15}, {28,30}, {6,26}, {8,12}, {24,27}, {9,22}, {11,23}, {3,22}, {8,18}, {4,5}, {1,7}, {17,30}, {15,27}, {9,29}, {11,16}, {11,22}, {8,10}, {5,12}, {7,26}, {17,21}, {10,16}, {12,29}, {15,26}, {21,25}, {25,30} } Symmetric graph 5 of order 32 Valency 4 Diameter 4 Girth 6 Automorphism group of order 2304 Number of arcs = 128 Number of 2-arcs = 384 2-arc-transitive true Edge-set { {1,17}, {12,22}, {9,29}, {5,29}, {8,22}, {14,32}, {13,24}, {14,27}, {13,20}, {5,25}, {8,17}, {16,19}, {15,28}, {7,20}, {6,27}, {3,19}, {3,28}, {10,20}, {11,27}, {2,27}, {2,20}, {12,25}, {9,17}, {4,18}, {4,26}, {10,26}, {11,18}, {9,24}, {12,32}, {4,24}, {4,32}, {10,31}, {11,23}, {3,30}, {3,21}, {10,21}, {11,30}, {2,29}, {2,22}, {1,23}, {1,31}, {7,32}, {6,24}, {16,29}, {15,22}, {7,23}, {6,31}, {16,23}, {15,31}, {8,30}, {5,21}, {13,30}, {14,21}, {16,26}, {15,18}, {7,28}, {6,19}, {14,17}, {13,25}, {5,18}, {8,26}, {1,25}, {9,28}, {12,19} } Symmetric graph 6 of order 32 Valency 4 Diameter 4 Girth 4 Automorphism group of order 4096 Number of arcs = 128 Number of 2-arcs = 384 2-arc-transitive false Edge-set { {1,5}, {8,28}, {19,22}, {15,25}, {23,26}, {10,21}, {13,18}, {15,27}, {11,14}, {9,29}, {6,12}, {20,23}, {4,13}, {16,18}, {19,31}, {9,14}, {1,30}, {11,29}, {27,32}, {11,22}, {2,8}, {6,20}, {17,23}, {4,16}, {3,21}, {1,31}, {19,30}, {25,32}, {10,31}, {5,9}, {7,25}, {22,27}, {2,21}, {11,24}, {3,8}, {6,17}, {3,29}, {12,31}, {28,30}, {13,26}, {24,27}, {10,16}, {5,25}, {7,9}, {17,29}, {3,32}, {2,15}, {26,30}, {14,20}, {13,28}, {12,16}, {1,24}, {4,5}, {17,32}, {7,18}, {15,20}, {2,14}, {8,12}, {7,19}, {6,28}, {18,22}, {4,24}, {10,23}, {21,26} } Symmetric graph 7 of order 32 Valency 4 Diameter 8 Girth 4 Automorphism group of order 2097152 Number of arcs = 128 Number of 2-arcs = 384 2-arc-transitive false Edge-set { {1,17}, {12,23}, {11,21}, {14,30}, {13,32}, {16,29}, {15,31}, {7,20}, {8,18}, {5,19}, {6,17}, {9,25}, {10,27}, {11,26}, {12,28}, {2,31}, {1,29}, {4,32}, {3,30}, {6,24}, {5,22}, {8,23}, {7,21}, {13,28}, {14,26}, {15,27}, {16,25}, {3,19}, {4,17}, {1,20}, {2,18}, {10,21}, {9,23}, {12,22}, {11,24}, {16,32}, {15,30}, {14,31}, {13,29}, {5,18}, {6,20}, {7,17}, {8,19}, {11,27}, {12,25}, {9,28}, {10,26}, {4,29}, {3,31}, {2,30}, {1,32}, {8,22}, {7,24}, {6,21}, {5,23}, {15,26}, {16,28}, {13,25}, {14,27}, {2,19}, {3,18}, {4,20}, {10,24}, {9,22} } Symmetric graph 8 of order 32 Valency 5 Diameter 4 Girth 5 Automorphism group of order 1920 Number of arcs = 160 Number of 2-arcs = 640 2-arc-transitive true Edge-set { {1,3}, {12,31}, {18,26}, {6,18}, {9,12}, {7,13}, {13,24}, {7,30}, {2,13}, {6,10}, {3,12}, {20,23}, {20,28}, {15,23}, {20,31}, {7,28}, {11,23}, {17,20}, {9,30}, {2,4}, {6,31}, {12,26}, {4,16}, {5,32}, {5,16}, {16,22}, {21,32}, {4,18}, {5,9}, {2,20}, {16,28}, {11,32}, {4,8}, {5,14}, {10,28}, {3,7}, {17,25}, {18,30}, {2,9}, {6,13}, {12,24}, {22,25}, {17,29}, {1,10}, {21,29}, {1,22}, {21,26}, {22,30}, {10,29}, {7,32}, {13,25}, {4,11}, {5,17}, {2,21}, {10,11}, {19,32}, {25,27}, {24,29}, {1,19}, {26,28}, {8,14}, {14,23}, {3,17}, {23,30}, {6,15}, {14,26}, {8,27}, {8,29}, {9,27}, {11,25}, {1,14}, {15,27}, {8,31}, {16,24}, {19,24}, {19,27}, {3,15}, {18,19}, {15,21}, {22,31} } Symmetric graph 9 of order 32 Valency 5 Diameter 5 Girth 4 Automorphism group of order 3840 Number of arcs = 160 Number of 2-arcs = 640 2-arc-transitive true Edge-set { {1,4}, {8,14}, {5,13}, {6,31}, {16,24}, {5,9}, {15,22}, {10,12}, {21,30}, {17,29}, {26,28}, {2,9}, {22,31}, {24,30}, {18,25}, {7,32}, {19,23}, {17,19}, {20,27}, {2,20}, {16,21}, {3,11}, {2,13}, {12,24}, {18,30}, {19,28}, {15,28}, {11,32}, {23,29}, {9,27}, {25,27}, {22,26}, {13,26}, {6,10}, {17,26}, {3,7}, {6,15}, {4,17}, {7,28}, {1,19}, {21,25}, {9,11}, {11,25}, {8,29}, {18,20}, {2,22}, {12,31}, {4,12}, {3,18}, {5,16}, {3,15}, {1,10}, {21,32}, {16,27}, {2,3}, {14,23}, {10,30}, {8,27}, {11,23}, {14,25}, {15,23}, {8,31}, {4,8}, {20,31}, {20,24}, {13,24}, {6,18}, {7,30}, {7,13}, {1,14}, {9,29}, {5,32}, {22,29}, {12,26}, {6,14}, {19,32}, {4,16}, {10,28}, {5,17}, {1,21} } Symmetric graph 10 of order 32 Valency 6 Diameter 3 Girth 3 Automorphism group of order 192 Number of arcs = 192 Number of 2-arcs = 960 2-arc-transitive false Edge-set { {1,9}, {7,12}, {3,26}, {6,14}, {8,28}, {10,21}, {16,29}, {4,16}, {6,31}, {13,23}, {11,27}, {8,30}, {4,17}, {1,17}, {1,30}, {16,19}, {14,31}, {3,31}, {5,21}, {5,24}, {13,18}, {10,27}, {9,25}, {23,30}, {12,25}, {23,26}, {12,18}, {10,26}, {1,28}, {1,19}, {4,19}, {10,19}, {14,29}, {15,30}, {17,32}, {15,32}, {22,32}, {8,24}, {4,12}, {7,22}, {3,15}, {18,31}, {6,22}, {8,15}, {21,31}, {16,21}, {6,26}, {8,21}, {12,23}, {11,26}, {12,28}, {19,26}, {9,28}, {19,30}, {6,9}, {2,18}, {2,10}, {20,25}, {2,20}, {2,13}, {20,29}, {13,32}, {22,27}, {18,28}, {2,29}, {14,24}, {2,27}, {14,17}, {16,31}, {13,30}, {17,27}, {7,16}, {6,23}, {8,11}, {21,28}, {7,23}, {3,11}, {24,25}, {4,25}, {15,20}, {5,25}, {9,20}, {3,20}, {5,13}, {24,29}, {11,24}, {11,17}, {4,32}, {1,14}, {3,18}, {5,10}, {7,27}, {7,29}, {15,22}, {9,22}, {5,32} } Symmetric graph 11 of order 32 Valency 6 Diameter 4 Girth 4 Automorphism group of order 384 Number of arcs = 192 Number of 2-arcs = 960 2-arc-transitive false Edge-set { {1,13}, {6,26}, {9,19}, {2,14}, {4,27}, {24,30}, {16,30}, {5,25}, {10,20}, {7,16}, {1,18}, {7,23}, {10,28}, {12,23}, {3,28}, {23,29}, {15,29}, {12,26}, {6,22}, {19,31}, {3,19}, {8,26}, {2,15}, {8,14}, {8,15}, {2,17}, {8,24}, {9,27}, {11,24}, {14,31}, {4,14}, {5,27}, {21,30}, {17,30}, {4,25}, {11,20}, {10,25}, {11,25}, {5,21}, {20,32}, {4,20}, {7,25}, {1,16}, {7,13}, {10,21}, {10,18}, {1,28}, {6,23}, {23,32}, {3,18}, {13,29}, {3,15}, {13,32}, {3,13}, {6,28}, {22,29}, {18,29}, {3,26}, {12,19}, {9,26}, {6,15}, {15,31}, {2,19}, {8,27}, {8,22}, {17,31}, {9,24}, {11,17}, {9,22}, {9,17}, {2,27}, {5,24}, {24,31}, {4,17}, {14,30}, {4,16}, {11,27}, {11,21}, {20,30}, {1,25}, {21,32}, {5,16}, {16,32}, {1,20}, {7,28}, {7,21}, {18,32}, {10,23}, {12,18}, {6,13}, {12,28}, {12,22}, {19,29}, {2,26}, {22,31}, {5,14} } Symmetric graph 12 of order 32 Valency 6 Diameter 4 Girth 4 Automorphism group of order 384 Number of arcs = 192 Number of 2-arcs = 960 2-arc-transitive false Edge-set { {1,13}, {3,17}, {15,32}, {11,20}, {7,14}, {2,27}, {21,29}, {10,21}, {6,27}, {4,13}, {19,31}, {18,29}, {2,16}, {8,25}, {12,23}, {8,23}, {12,25}, {15,29}, {2,17}, {3,19}, {13,32}, {9,28}, {5,22}, {1,18}, {16,30}, {14,31}, {4,20}, {5,14}, {9,20}, {22,31}, {4,28}, {2,25}, {23,29}, {11,18}, {7,16}, {3,27}, {21,32}, {24,30}, {1,26}, {12,17}, {8,15}, {10,19}, {6,13}, {4,16}, {18,31}, {10,24}, {6,26}, {7,28}, {11,22}, {19,30}, {5,25}, {9,23}, {12,21}, {8,27}, {20,29}, {2,14}, {17,32}, {3,15}, {1,19}, {13,30}, {12,28}, {8,22}, {6,23}, {10,25}, {7,21}, {11,27}, {9,26}, {5,24}, {16,31}, {4,18}, {14,29}, {2,20}, {9,17}, {5,15}, {3,26}, {24,32}, {22,30}, {1,28}, {23,31}, {4,25}, {8,13}, {12,19}, {6,16}, {10,18}, {11,24}, {7,26}, {20,32}, {3,14}, {17,30}, {1,15}, {5,28}, {9,22}, {6,21}, {10,27}, {11,26}, {7,24} } Symmetric graph 13 of order 32 Valency 6 Diameter 3 Girth 4 Automorphism group of order 384 Number of arcs = 192 Number of 2-arcs = 960 2-arc-transitive false Edge-set { {1,9}, {6,15}, {14,30}, {3,11}, {11,32}, {1,22}, {3,27}, {7,14}, {10,26}, {7,24}, {7,26}, {15,32}, {14,19}, {2,10}, {16,27}, {5,18}, {5,29}, {9,30}, {16,23}, {9,18}, {5,16}, {3,24}, {7,32}, {1,26}, {18,27}, {13,29}, {4,19}, {2,31}, {12,27}, {12,21}, {4,12}, {6,22}, {3,30}, {4,29}, {24,31}, {6,27}, {21,30}, {12,31}, {10,23}, {9,24}, {7,16}, {15,18}, {5,14}, {19,27}, {2,21}, {4,28}, {13,26}, {8,13}, {8,19}, {2,25}, {8,31}, {20,25}, {9,25}, {11,19}, {14,22}, {3,10}, {13,21}, {4,9}, {23,30}, {8,23}, {2,11}, {22,31}, {3,20}, {8,25}, {24,29}, {6,30}, {16,31}, {21,32}, {1,12}, {19,26}, {2,18}, {13,20}, {5,28}, {15,28}, {16,17}, {6,13}, {8,15}, {17,25}, {6,17}, {18,26}, {1,32}, {10,29}, {20,28}, {22,29}, {15,24}, {23,32}, {14,25}, {10,17}, {4,23}, {11,22}, {7,20}, {17,28}, {12,20}, {11,28}, {5,21}, {1,17} } Symmetric graph 14 of order 32 Valency 6 Diameter 4 Girth 3 Automorphism group of order 384 Number of arcs = 192 Number of 2-arcs = 960 2-arc-transitive false Edge-set { {1,10}, {5,15}, {14,29}, {3,12}, {12,32}, {1,21}, {4,27}, {8,14}, {10,25}, {8,24}, {7,25}, {15,31}, {14,20}, {13,19}, {2,9}, {15,27}, {5,17}, {6,29}, {10,30}, {15,23}, {9,17}, {6,16}, {3,23}, {8,32}, {1,25}, {17,27}, {2,26}, {18,28}, {13,30}, {3,19}, {2,32}, {12,28}, {12,22}, {11,21}, {4,11}, {5,22}, {3,29}, {24,32}, {6,28}, {22,30}, {11,31}, {10,24}, {7,15}, {15,17}, {6,14}, {19,28}, {2,22}, {16,18}, {5,13}, {20,27}, {3,28}, {14,26}, {10,18}, {16,24}, {7,13}, {8,20}, {19,25}, {7,31}, {20,26}, {9,26}, {12,19}, {14,21}, {4,10}, {24,30}, {7,23}, {11,20}, {1,11}, {22,32}, {8,26}, {5,30}, {23,29}, {3,9}, {16,32}, {11,27}, {1,18}, {21,31}, {2,12}, {2,17}, {5,27}, {21,29}, {4,30}, {23,31}, {16,28}, {17,26}, {6,18}, {9,23}, {8,16}, {18,25}, {1,31}, {9,29}, {7,19}, {4,24}, {13,25}, {13,22}, {4,20}, {6,21} } Symmetric graph 15 of order 32 Valency 6 Diameter 3 Girth 4 Automorphism group of order 1536 Number of arcs = 192 Number of 2-arcs = 960 2-arc-transitive false Edge-set { {1,9}, {14,30}, {8,32}, {7,18}, {16,17}, {6,21}, {19,25}, {23,27}, {4,26}, {20,26}, {2,13}, {9,22}, {22,28}, {4,25}, {3,10}, {1,12}, {9,23}, {12,30}, {2,28}, {15,19}, {14,29}, {10,30}, {8,24}, {11,24}, {4,13}, {16,31}, {5,31}, {6,32}, {8,23}, {7,29}, {6,17}, {3,15}, {11,29}, {17,25}, {8,18}, {16,18}, {7,31}, {5,17}, {11,21}, {21,25}, {11,32}, {7,21}, {13,19}, {5,20}, {13,20}, {5,24}, {20,27}, {6,22}, {19,28}, {12,21}, {23,25}, {18,26}, {22,26}, {15,31}, {2,10}, {21,27}, {5,23}, {24,26}, {2,27}, {9,32}, {7,22}, {4,9}, {10,22}, {7,19}, {3,14}, {24,28}, {1,27}, {1,14}, {1,28}, {3,25}, {3,11}, {9,29}, {4,12}, {10,23}, {12,24}, {15,20}, {5,29}, {2,11}, {1,15}, {6,30}, {8,19}, {13,30}, {8,30}, {10,31}, {3,26}, {14,18}, {16,32}, {4,16}, {13,29}, {12,31}, {17,28}, {18,27}, {15,32}, {14,17}, {2,16}, {6,20} } Symmetric graph 16 of order 32 Valency 6 Diameter 3 Girth 4 Automorphism group of order 23040 Number of arcs = 192 Number of 2-arcs = 960 2-arc-transitive true Edge-set { {1,9}, {24,30}, {6,21}, {6,13}, {12,31}, {7,20}, {3,27}, {20,25}, {3,20}, {16,31}, {15,18}, {1,17}, {7,26}, {12,21}, {14,26}, {1,21}, {1,26}, {16,27}, {15,23}, {4,28}, {3,24}, {6,29}, {10,17}, {7,13}, {7,31}, {18,27}, {10,26}, {13,19}, {7,24}, {6,27}, {10,24}, {12,27}, {9,23}, {5,28}, {24,32}, {11,22}, {2,10}, {1,31}, {14,20}, {3,11}, {3,29}, {22,29}, {17,25}, {16,17}, {7,15}, {4,12}, {9,30}, {10,29}, {13,22}, {2,25}, {6,17}, {12,20}, {3,9}, {22,31}, {9,18}, {5,30}, {21,32}, {11,19}, {4,10}, {6,15}, {8,32}, {17,28}, {23,29}, {5,22}, {16,24}, {19,26}, {14,21}, {1,11}, {8,14}, {11,28}, {14,29}, {2,18}, {13,30}, {8,25}, {20,28}, {5,14}, {18,26}, {21,30}, {8,16}, {15,28}, {4,30}, {2,32}, {2,22}, {11,32}, {8,19}, {23,31}, {13,25}, {19,27}, {4,23}, {4,19}, {8,23}, {2,12}, {5,16}, {15,32}, {9,25}, {5,18} } Symmetric graph 17 of order 32 Valency 6 Diameter 4 Girth 4 Automorphism group of order 6291456 Number of arcs = 192 Number of 2-arcs = 960 2-arc-transitive false Edge-set { {1,13}, {18,30}, {9,17}, {4,16}, {23,29}, {3,28}, {7,24}, {19,31}, {12,20}, {6,15}, {13,30}, {11,27}, {5,23}, {2,14}, {22,32}, {2,25}, {6,21}, {3,19}, {16,30}, {17,29}, {11,26}, {5,28}, {4,13}, {10,18}, {7,14}, {16,31}, {10,26}, {8,22}, {3,15}, {1,20}, {11,22}, {20,29}, {24,30}, {5,25}, {12,21}, {4,27}, {19,30}, {12,17}, {8,23}, {2,18}, {13,31}, {20,32}, {10,27}, {8,25}, {1,16}, {11,19}, {9,21}, {7,26}, {5,16}, {2,15}, {21,30}, {14,29}, {4,26}, {12,28}, {22,29}, {3,25}, {6,24}, {4,17}, {10,23}, {17,32}, {21,31}, {8,28}, {9,24}, {1,26}, {18,31}, {9,20}, {5,22}, {7,15}, {4,20}, {10,19}, {8,16}, {15,29}, {12,25}, {6,27}, {3,14}, {12,24}, {8,13}, {24,31}, {15,32}, {1,27}, {9,25}, {23,32}, {2,28}, {7,21}, {2,19}, {6,26}, {11,18}, {6,14}, {1,17}, {5,13}, {14,32}, {9,28}, {10,22}, {3,18}, {7,27}, {11,23} } Symmetric graph 18 of order 32 Valency 7 Diameter 4 Girth 4 Automorphism group of order 1344 Number of arcs = 224 Number of 2-arcs = 1344 2-arc-transitive true Edge-set { {1,6}, {1,25}, {22,28}, {1,22}, {9,22}, {6,24}, {12,14}, {14,22}, {6,14}, {14,29}, {8,25}, {16,28}, {16,19}, {20,32}, {6,19}, {14,20}, {19,25}, {20,28}, {19,29}, {3,20}, {9,25}, {17,24}, {12,18}, {9,17}, {7,18}, {10,32}, {2,8}, {7,28}, {10,19}, {8,20}, {7,9}, {10,24}, {8,12}, {9,29}, {3,7}, {3,10}, {8,23}, {5,16}, {11,16}, {6,32}, {5,29}, {11,27}, {6,26}, {13,32}, {2,30}, {2,28}, {21,25}, {24,27}, {12,26}, {9,13}, {7,30}, {10,28}, {14,27}, {26,29}, {8,13}, {16,30}, {25,32}, {3,29}, {3,27}, {23,26}, {3,13}, {23,30}, {15,25}, {17,26}, {18,27}, {15,17}, {18,31}, {15,23}, {11,31}, {2,19}, {4,21}, {2,24}, {12,21}, {5,22}, {16,21}, {27,30}, {4,26}, {13,24}, {12,30}, {19,23}, {11,20}, {21,29}, {17,30}, {4,18}, {22,32}, {2,9}, {3,23}, {11,23}, {7,21}, {10,15}, {4,15}, {18,22}, {5,10}, {6,11}, {5,17}, {15,31}, {1,31}, {4,5}, {13,18}, {4,11}, {4,32}, {7,15}, {8,31}, {2,14}, {5,27}, {13,26}, {28,31}, {1,17}, {24,31}, {20,21}, {1,12}, {1,16} } Symmetric graph 19 of order 32 Valency 8 Diameter 4 Girth 4 Automorphism group of order 43008 Number of arcs = 256 Number of 2-arcs = 1792 2-arc-transitive true Edge-set { {1,9}, {14,17}, {17,27}, {3,27}, {22,26}, {2,31}, {6,13}, {8,26}, {2,12}, {13,22}, {8,15}, {12,20}, {5,32}, {6,9}, {12,23}, {2,13}, {15,18}, {17,28}, {10,21}, {21,32}, {5,12}, {9,23}, {23,29}, {13,20}, {18,26}, {1,28}, {6,32}, {7,29}, {20,27}, {4,26}, {1,16}, {16,22}, {18,31}, {10,17}, {21,27}, {3,32}, {20,30}, {7,26}, {13,21}, {18,32}, {5,28}, {23,25}, {1,29}, {7,14}, {2,11}, {4,11}, {1,31}, {5,16}, {11,18}, {9,20}, {17,30}, {7,27}, {3,9}, {4,30}, {4,32}, {5,25}, {14,23}, {11,17}, {1,10}, {16,21}, {14,24}, {8,27}, {4,12}, {9,19}, {24,32}, {6,30}, {8,12}, {2,25}, {1,15}, {2,28}, {4,13}, {8,31}, {11,22}, {16,20}, {16,19}, {5,11}, {9,24}, {23,30}, {21,31}, {1,25}, {14,18}, {7,9}, {7,10}, {4,14}, {24,31}, {13,19}, {18,25}, {19,25}, {2,14}, {15,17}, {22,30}, {4,27}, {3,16}, {3,26}, {8,11}, {12,24}, {10,22}, {7,31}, {19,26}, {5,30}, {22,29}, {6,10}, {3,15}, {8,16}, {10,18}, {3,10}, {19,32}, {23,26}, {24,28}, {17,29}, {7,13}, {21,28}, {15,23}, {6,25}, {24,27}, {3,30}, {22,25}, {5,15}, {6,14}, {19,31}, {2,29}, {6,28}, {15,24}, {12,19}, {20,29}, {8,29}, {20,28}, {11,21} } Symmetric graph 20 of order 32 Valency 8 Diameter 4 Girth 4 Automorphism group of order 25165824 Number of arcs = 256 Number of 2-arcs = 1792 2-arc-transitive false Edge-set { {1,5}, {21,26}, {5,28}, {10,15}, {12,30}, {14,26}, {28,31}, {18,32}, {1,13}, {2,29}, {16,17}, {15,19}, {4,30}, {3,14}, {20,31}, {4,8}, {19,24}, {20,21}, {3,5}, {1,22}, {6,18}, {7,17}, {2,23}, {5,18}, {1,21}, {2,24}, {8,17}, {19,23}, {4,7}, {3,6}, {20,22}, {24,28}, {8,26}, {5,12}, {10,21}, {6,10}, {12,22}, {23,26}, {7,28}, {9,21}, {5,11}, {8,25}, {24,27}, {7,27}, {23,25}, {11,22}, {6,9}, {12,14}, {10,31}, {15,28}, {26,30}, {26,29}, {16,28}, {10,32}, {12,13}, {25,32}, {13,27}, {9,29}, {11,16}, {11,15}, {9,30}, {14,27}, {25,31}, {19,29}, {4,16}, {3,32}, {13,20}, {14,18}, {1,31}, {2,15}, {17,30}, {1,15}, {18,30}, {14,17}, {2,31}, {4,32}, {13,19}, {20,29}, {3,16}, {18,21}, {17,24}, {2,8}, {4,23}, {7,19}, {6,20}, {3,22}, {8,19}, {4,24}, {3,21}, {5,20}, {18,22}, {1,6}, {2,7}, {17,23}, {8,10}, {12,24}, {7,12}, {10,23}, {22,28}, {6,26}, {11,24}, {8,9}, {5,27}, {21,25}, {6,25}, {22,27}, {9,23}, {7,11}, {28,32}, {13,26}, {12,29}, {10,16}, {27,29}, {16,25}, {11,32}, {9,13}, {9,14}, {11,31}, {15,25}, {27,30}, {4,14}, {19,31}, {15,20}, {3,30}, {1,29}, {16,18}, {17,32}, {2,13} } Symmetric graph 21 of order 32 Valency 8 Diameter 4 Girth 4 Automorphism group of order 1761205026816 Number of arcs = 256 Number of 2-arcs = 1792 2-arc-transitive false Edge-set { {1,5}, {13,20}, {3,24}, {25,30}, {18,29}, {3,15}, {6,9}, {11,14}, {10,31}, {15,28}, {1,32}, {19,22}, {23,28}, {23,26}, {11,21}, {16,27}, {8,28}, {9,32}, {12,13}, {2,29}, {8,17}, {4,8}, {4,5}, {6,12}, {1,23}, {7,25}, {7,27}, {9,22}, {12,22}, {24,25}, {26,29}, {10,14}, {4,13}, {17,32}, {16,17}, {2,22}, {16,20}, {2,24}, {19,24}, {3,6}, {6,18}, {7,18}, {10,21}, {8,26}, {5,11}, {5,10}, {21,26}, {27,30}, {16,25}, {12,32}, {15,19}, {27,32}, {19,31}, {2,14}, {18,31}, {3,14}, {3,29}, {5,17}, {20,23}, {20,21}, {1,21}, {24,27}, {7,12}, {7,9}, {6,27}, {11,31}, {12,24}, {15,26}, {28,29}, {10,15}, {11,29}, {14,26}, {4,30}, {1,30}, {1,13}, {20,32}, {3,7}, {18,24}, {18,22}, {21,28}, {7,19}, {10,23}, {11,23}, {5,26}, {5,28}, {8,10}, {9,13}, {13,25}, {12,30}, {9,16}, {15,18}, {3,31}, {5,20}, {2,31}, {8,20}, {1,8}, {17,21}, {4,21}, {4,23}, {6,25}, {9,24}, {22,27}, {22,25}, {28,31}, {11,15}, {1,16}, {20,30}, {4,16}, {17,30}, {13,17}, {3,22}, {2,7}, {2,6}, {6,19}, {8,11}, {25,32}, {13,27}, {9,30}, {14,18}, {14,19}, {19,29}, {2,15}, {17,23}, {10,29}, {14,28}, {26,31}, {4,32}, {12,16} } Symmetric graph 22 of order 32 Valency 9 Diameter 3 Girth 3 Automorphism group of order 1152 Number of arcs = 288 Number of 2-arcs = 2304 2-arc-transitive false Edge-set { {1,11}, {10,24}, {6,26}, {16,27}, {16,30}, {8,21}, {4,22}, {17,31}, {5,11}, {19,31}, {20,29}, {8,12}, {18,30}, {4,32}, {13,24}, {10,22}, {3,26}, {4,25}, {9,20}, {8,25}, {5,31}, {14,19}, {3,18}, {1,23}, {13,27}, {11,30}, {8,17}, {2,22}, {7,18}, {1,21}, {15,26}, {9,29}, {7,20}, {3,24}, {14,25}, {10,28}, {2,14}, {24,28}, {6,15}, {1,13}, {17,27}, {5,10}, {19,26}, {20,32}, {8,13}, {23,30}, {7,14}, {24,29}, {6,12}, {22,32}, {7,9}, {2,16}, {21,28}, {14,23}, {5,28}, {2,27}, {16,18}, {12,21}, {6,27}, {1,32}, {13,17}, {16,22}, {3,30}, {9,23}, {13,20}, {8,27}, {15,19}, {7,28}, {16,20}, {9,21}, {11,23}, {7,29}, {2,29}, {12,18}, {14,28}, {15,28}, {5,17}, {11,31}, {14,31}, {12,25}, {4,17}, {6,23}, {13,32}, {2,19}, {15,29}, {13,26}, {9,27}, {1,20}, {10,32}, {11,26}, {9,31}, {12,29}, {6,19}, {5,20}, {18,28}, {2,12}, {18,32}, {3,13}, {4,10}, {24,26}, {4,14}, {21,25}, {4,15}, {23,27}, {23,25}, {22,27}, {1,15}, {17,29}, {6,9}, {3,16}, {8,10}, {22,26}, {20,25}, {3,9}, {2,31}, {14,18}, {5,25}, {3,31}, {1,30}, {1,28}, {15,17}, {15,21}, {11,17}, {12,24}, {6,32}, {4,29}, {8,30}, {11,22}, {7,26}, {4,23}, {5,24}, {7,22}, {3,21}, {2,24}, {6,18}, {12,32}, {16,25}, {8,19}, {10,30}, {19,30}, {7,11}, {5,16}, {21,31}, {10,19} } Symmetric graph 23 of order 32 Valency 9 Diameter 3 Girth 4 Automorphism group of order 2304 Number of arcs = 288 Number of 2-arcs = 2304 2-arc-transitive false Edge-set { {1,3}, {14,22}, {5,21}, {9,20}, {19,31}, {19,30}, {30,32}, {7,12}, {4,5}, {8,13}, {4,32}, {8,9}, {6,32}, {9,14}, {18,25}, {4,27}, {13,30}, {22,30}, {10,17}, {3,20}, {6,13}, {1,17}, {3,12}, {6,29}, {14,29}, {1,9}, {12,19}, {8,27}, {18,23}, {13,16}, {1,22}, {10,32}, {20,32}, {9,31}, {2,28}, {11,24}, {3,14}, {7,21}, {10,29}, {20,29}, {22,28}, {5,24}, {14,25}, {21,27}, {29,31}, {10,19}, {5,12}, {4,25}, {16,17}, {24,27}, {23,26}, {10,11}, {15,20}, {20,22}, {5,31}, {2,6}, {11,14}, {3,6}, {7,14}, {1,5}, {12,13}, {15,21}, {25,28}, {19,21}, {18,19}, {2,31}, {3,31}, {7,10}, {23,30}, {25,30}, {16,19}, {1,32}, {10,13}, {2,4}, {8,11}, {27,30}, {18,22}, {11,28}, {15,24}, {16,23}, {1,25}, {7,24}, {17,26}, {2,26}, {7,16}, {7,31}, {5,30}, {21,29}, {9,26}, {19,28}, {9,18}, {4,19}, {10,25}, {20,27}, {16,32}, {8,15}, {2,18}, {8,32}, {8,23}, {5,14}, {13,21}, {4,11}, {24,32}, {6,22}, {2,10}, {11,20}, {3,28}, {23,31}, {15,26}, {12,23}, {16,25}, {8,22}, {5,18}, {7,28}, {17,24}, {6,17}, {11,18}, {4,15}, {4,13}, {9,30}, {1,7}, {12,17}, {2,8}, {1,27}, {3,16}, {6,11}, {14,15}, {6,23}, {3,26}, {13,26}, {2,21}, {24,25}, {26,27}, {15,18}, {17,20}, {23,28}, {28,29}, {24,29}, {16,22}, {9,12}, {17,21}, {26,29}, {12,27}, {15,31} } Symmetric graph 24 of order 32 Valency 10 Diameter 3 Girth 4 Automorphism group of order 23040 Number of arcs = 320 Number of 2-arcs = 2880 2-arc-transitive true Edge-set { {1,3}, {12,30}, {3,31}, {16,24}, {12,26}, {12,32}, {5,31}, {10,21}, {8,18}, {16,19}, {9,26}, {16,31}, {6,26}, {18,32}, {1,5}, {22,29}, {8,27}, {16,27}, {21,26}, {18,20}, {2,19}, {9,30}, {21,32}, {5,18}, {17,19}, {2,9}, {8,31}, {6,16}, {18,30}, {4,23}, {11,21}, {5,27}, {13,27}, {5,21}, {13,18}, {3,19}, {9,22}, {8,25}, {26,29}, {4,20}, {2,24}, {6,22}, {1,16}, {7,26}, {15,20}, {2,29}, {4,30}, {27,32}, {17,21}, {2,18}, {8,24}, {12,16}, {9,11}, {7,32}, {3,15}, {22,25}, {1,13}, {5,14}, {13,24}, {3,18}, {1,22}, {8,14}, {20,31}, {2,4}, {21,30}, {20,27}, {10,27}, {19,23}, {11,25}, {19,32}, {10,29}, {4,8}, {4,17}, {2,21}, {19,28}, {9,28}, {23,29}, {4,11}, {11,24}, {6,13}, {3,7}, {15,22}, {8,29}, {4,16}, {16,21}, {18,26}, {2,15}, {25,30}, {28,31}, {6,28}, {12,22}, {17,31}, {14,30}, {3,24}, {1,23}, {10,14}, {8,12}, {3,21}, {23,27}, {25,32}, {5,19}, {11,29}, {4,32}, {5,25}, {13,19}, {13,29}, {7,20}, {10,25}, {26,31}, {6,20}, {11,27}, {7,11}, {15,32}, {3,29}, {4,22}, {14,20}, {2,6}, {9,23}, {11,15}, {10,15}, {14,17}, {12,28}, {18,22}, {8,19}, {9,16}, {20,24}, {10,12}, {6,32}, {6,17}, {2,14}, {5,15}, {12,23}, {26,27}, {3,12}, {22,31}, {5,9}, {7,13}, {6,10}, {1,20}, {15,23}, {11,31}, {1,10}, {14,26}, {14,23}, {25,28}, {17,25}, {13,25}, {15,28}, {17,29}, {7,30}, {7,17}, {1,17}, {9,13}, {1,30}, {14,28}, {24,28}, {7,23}, {10,24}, {7,28}, {24,30} } Symmetric graph 25 of order 32 Valency 10 Diameter 2 Girth 4 Automorphism group of order 125829120 Number of arcs = 320 Number of 2-arcs = 2880 2-arc-transitive false Edge-set { {1,5}, {12,29}, {1,18}, {6,27}, {8,12}, {7,12}, {13,18}, {1,30}, {2,15}, {6,19}, {12,27}, {6,20}, {12,28}, {7,23}, {13,20}, {7,18}, {11,22}, {17,21}, {3,30}, {2,6}, {1,6}, {12,15}, {4,30}, {2,5}, {12,16}, {16,20}, {28,32}, {4,23}, {5,20}, {7,20}, {13,28}, {5,26}, {11,30}, {8,25}, {14,29}, {28,31}, {7,26}, {2,17}, {12,30}, {2,18}, {6,22}, {12,21}, {7,25}, {11,29}, {1,17}, {6,21}, {12,22}, {4,21}, {5,22}, {10,16}, {16,32}, {25,32}, {4,29}, {4,20}, {5,28}, {2,23}, {13,29}, {1,24}, {7,11}, {14,19}, {23,27}, {24,27}, {8,19}, {9,16}, {24,28}, {8,11}, {14,17}, {6,28}, {13,17}, {26,30}, {2,30}, {6,25}, {14,20}, {23,28}, {5,27}, {14,18}, {25,30}, {2,29}, {6,26}, {25,29}, {26,29}, {9,21}, {4,22}, {10,22}, {10,23}, {27,32}, {4,32}, {5,25}, {1,16}, {11,16}, {17,32}, {8,20}, {18,31}, {11,28}, {3,24}, {15,32}, {1,15}, {15,31}, {3,19}, {10,21}, {3,22}, {16,31}, {5,19}, {11,27}, {8,24}, {2,16}, {8,23}, {7,24}, {7,17}, {14,30}, {4,24}, {1,29}, {13,19}, {14,28}, {8,17}, {13,30}, {2,24}, {14,27}, {13,27}, {10,25}, {3,29}, {26,32}, {9,26}, {10,15}, {1,23}, {18,22}, {5,21}, {10,14}, {4,19}, {9,13}, {26,31}, {17,22}, {18,21}, {3,31}, {9,25}, {9,22}, {11,15}, {15,19}, {27,31}, {11,21}, {16,19}, {15,20}, {7,19}, {25,31}, {8,18}, {3,23}, {17,31}, {9,14}, {8,26}, {10,24}, {10,13}, {18,32}, {9,24}, {3,32}, {3,20}, {10,26}, {9,15}, {3,21}, {9,23}, {4,31} } Symmetric graph 26 of order 32 Valency 12 Diameter 3 Girth 3 Automorphism group of order 1536 Number of arcs = 384 Number of 2-arcs = 4224 2-arc-transitive false Edge-set { {1,9}, {6,18}, {7,31}, {15,23}, {17,30}, {20,26}, {14,27}, {8,14}, {3,22}, {16,29}, {11,18}, {11,27}, {9,23}, {3,32}, {6,16}, {3,19}, {6,28}, {9,22}, {19,25}, {7,30}, {4,12}, {2,15}, {1,17}, {2,32}, {1,16}, {6,14}, {7,22}, {22,25}, {13,25}, {7,23}, {4,30}, {12,22}, {24,25}, {23,31}, {15,30}, {6,9}, {7,19}, {12,28}, {10,24}, {20,29}, {1,21}, {2,26}, {8,17}, {16,18}, {18,31}, {17,25}, {13,32}, {7,18}, {4,31}, {3,23}, {6,30}, {9,20}, {19,27}, {9,28}, {10,19}, {4,28}, {5,10}, {14,20}, {22,27}, {21,29}, {11,26}, {2,19}, {13,28}, {10,21}, {14,26}, {14,22}, {8,29}, {3,11}, {6,23}, {12,20}, {24,27}, {1,31}, {5,13}, {8,21}, {11,30}, {12,23}, {10,18}, {20,31}, {17,27}, {9,32}, {16,19}, {18,28}, {7,15}, {4,17}, {15,26}, {14,17}, {16,28}, {4,25}, {15,20}, {21,26}, {23,29}, {6,11}, {12,32}, {16,24}, {6,31}, {5,12}, {8,24}, {21,31}, {5,24}, {10,30}, {2,27}, {12,17}, {24,32}, {5,15}, {8,20}, {3,27}, {3,9}, {6,19}, {19,30}, {2,22}, {1,25}, {14,23}, {22,30}, {1,11}, {2,23}, {16,21}, {18,26}, {14,31}, {4,24}, {5,29}, {20,28}, {2,29}, {1,14}, {16,32}, {6,25}, {7,13}, {7,12}, {15,31}, {15,17}, {8,27}, {3,16}, {4,15}, {21,28}, {10,26}, {8,11}, {10,27}, {14,30}, {1,30}, {2,13}, {4,21}, {23,26}, {1,24}, {13,19}, {13,24}, {17,32}, {2,18}, {13,21}, {3,29}, {11,19}, {23,28}, {22,32}, {16,25}, {6,22}, {7,25}, {24,30}, {12,29}, {11,24}, {9,17}, {19,32}, {10,31}, {3,14}, {9,29}, {7,10}, {4,20}, {15,27}, {3,26}, {11,31}, {3,18}, {4,13}, {5,27}, {1,20}, {8,26}, {8,16}, {8,9}, {1,28}, {5,32}, {18,29}, {13,18}, {5,21}, {4,10}, {5,20}, {12,25}, {2,12}, {15,22}, {9,25}, {7,28}, {13,29}, {11,21}, {5,26}, {8,32}, {5,17}, {2,10} } Symmetric graph 27 of order 32 Valency 12 Diameter 3 Girth 4 Automorphism group of order 2304 Number of arcs = 384 Number of 2-arcs = 4224 2-arc-transitive false Edge-set { {1,5}, {2,12}, {16,23}, {3,21}, {18,24}, {6,17}, {7,28}, {21,26}, {8,27}, {25,29}, {11,25}, {14,31}, {9,13}, {10,13}, {5,15}, {12,26}, {10,14}, {11,15}, {16,32}, {3,9}, {9,17}, {18,31}, {4,5}, {20,22}, {6,19}, {20,24}, {6,20}, {12,19}, {8,16}, {15,21}, {12,18}, {5,20}, {19,23}, {8,17}, {17,30}, {1,7}, {1,22}, {19,21}, {22,25}, {19,31}, {27,31}, {4,29}, {4,12}, {16,22}, {27,32}, {11,26}, {14,30}, {8,28}, {25,32}, {11,28}, {14,32}, {18,30}, {10,17}, {7,15}, {5,19}, {8,26}, {21,27}, {18,29}, {12,28}, {6,26}, {28,30}, {10,25}, {15,31}, {2,31}, {2,9}, {13,23}, {2,7}, {23,27}, {5,26}, {26,30}, {7,16}, {9,27}, {26,31}, {4,30}, {4,11}, {4,32}, {3,22}, {4,21}, {18,22}, {7,17}, {7,27}, {1,11}, {15,23}, {12,17}, {2,5}, {10,15}, {16,30}, {1,9}, {27,29}, {2,29}, {24,25}, {20,31}, {9,19}, {8,13}, {12,15}, {5,14}, {3,29}, {13,21}, {10,18}, {12,14}, {13,29}, {2,10}, {16,24}, {9,20}, {4,8}, {3,31}, {4,24}, {19,24}, {6,28}, {13,24}, {6,14}, {12,16}, {15,29}, {7,13}, {14,22}, {11,19}, {2,22}, {4,23}, {17,22}, {22,26}, {9,25}, {13,31}, {9,14}, {11,13}, {2,23}, {17,23}, {21,25}, {3,12}, {8,20}, {17,29}, {3,11}, {3,32}, {3,24}, {28,31}, {19,30}, {10,20}, {6,15}, {8,18}, {5,16}, {1,32}, {24,27}, {20,29}, {18,21}, {5,18}, {20,32}, {3,6}, {7,25}, {22,28}, {19,32}, {4,10}, {15,22}, {1,31}, {25,30}, {6,25}, {11,18}, {17,21}, {7,18}, {3,8}, {6,13}, {5,27}, {23,26}, {3,7}, {4,6}, {12,27}, {20,23}, {24,28}, {9,26}, {1,21}, {10,28}, {15,32}, {1,23}, {1,30}, {1,8}, {26,29}, {2,30}, {8,14}, {10,27}, {28,32}, {16,29}, {14,21}, {9,16}, {7,19}, {11,16}, {5,25}, {1,10}, {11,20}, {2,6}, {23,28}, {2,24}, {14,24}, {13,30}, {17,32} } Symmetric graph 28 of order 32 Valency 12 Diameter 2 Girth 3 Automorphism group of order 12582912 Number of arcs = 384 Number of 2-arcs = 4224 2-arc-transitive false Edge-set { {1,9}, {14,19}, {14,20}, {1,18}, {15,25}, {2,18}, {15,26}, {7,14}, {20,32}, {23,26}, {1,10}, {7,13}, {19,32}, {23,25}, {2,10}, {9,18}, {15,23}, {2,29}, {6,26}, {3,25}, {2,27}, {13,20}, {9,17}, {16,23}, {1,29}, {6,25}, {3,26}, {1,27}, {13,19}, {7,19}, {14,32}, {3,23}, {10,27}, {13,28}, {3,19}, {2,17}, {12,26}, {1,22}, {13,32}, {8,19}, {16,26}, {14,31}, {3,24}, {9,27}, {14,28}, {3,20}, {1,17}, {12,25}, {2,22}, {8,20}, {16,25}, {18,29}, {6,15}, {3,12}, {22,27}, {8,13}, {17,31}, {7,16}, {1,12}, {22,25}, {19,31}, {2,11}, {6,14}, {20,30}, {17,29}, {6,16}, {24,25}, {2,9}, {18,30}, {5,15}, {4,12}, {22,28}, {8,14}, {18,31}, {7,15}, {2,12}, {22,26}, {20,31}, {1,11}, {6,13}, {19,30}, {24,26}, {7,28}, {3,32}, {10,17}, {12,22}, {11,22}, {6,32}, {8,30}, {16,24}, {5,31}, {9,24}, {9,23}, {14,22}, {11,20}, {1,30}, {5,25}, {13,21}, {12,19}, {15,18}, {15,17}, {4,26}, {8,28}, {3,31}, {15,24}, {1,28}, {7,27}, {4,32}, {10,18}, {11,21}, {6,31}, {7,30}, {5,32}, {10,23}, {13,22}, {11,19}, {2,30}, {5,26}, {14,21}, {12,20}, {16,17}, {4,25}, {2,28}, {9,31}, {7,23}, {12,29}, {6,22}, {13,31}, {11,30}, {6,21}, {12,30}, {15,29}, {6,17}, {4,24}, {9,28}, {16,30}, {5,18}, {4,19}, {14,27}, {6,18}, {15,30}, {2,21}, {4,20}, {5,17}, {16,29}, {11,25}, {10,32}, {8,23}, {10,31}, {7,24}, {5,22}, {4,23}, {10,28}, {7,20}, {9,32}, {11,29}, {5,21}, {13,27}, {1,21}, {11,26}, {8,24}, {5,14}, {3,9}, {23,27}, {3,11}, {17,30}, {5,16}, {21,27}, {4,11}, {23,28}, {3,10}, {8,15}, {21,28}, {24,27}, {4,9}, {18,32}, {21,25}, {17,32}, {4,10}, {5,13}, {19,29}, {21,26}, {8,16}, {24,28}, {20,29}, {16,18}, {8,27}, {12,21}, {4,31}, {8,29}, {10,24}, {7,29} } Symmetric graph 29 of order 32 Valency 12 Diameter 2 Girth 3 Automorphism group of order 75497472 Number of arcs = 384 Number of 2-arcs = 4224 2-arc-transitive false Edge-set { {1,9}, {8,31}, {20,25}, {3,19}, {11,21}, {9,23}, {6,14}, {2,10}, {5,18}, {14,26}, {3,27}, {11,31}, {2,25}, {5,29}, {24,30}, {7,32}, {19,26}, {6,16}, {8,23}, {24,29}, {13,30}, {2,18}, {15,18}, {11,27}, {7,23}, {14,19}, {6,22}, {10,23}, {12,21}, {4,20}, {12,22}, {10,24}, {5,13}, {5,28}, {24,32}, {3,11}, {2,21}, {1,10}, {21,30}, {9,29}, {7,16}, {8,19}, {16,27}, {18,26}, {15,27}, {4,11}, {2,22}, {10,29}, {5,30}, {4,24}, {11,32}, {2,26}, {14,25}, {3,28}, {6,17}, {13,25}, {4,28}, {12,32}, {1,26}, {6,30}, {23,29}, {16,23}, {12,20}, {1,12}, {18,27}, {7,14}, {8,32}, {20,26}, {14,21}, {3,9}, {22,31}, {10,25}, {22,32}, {3,10}, {5,21}, {18,28}, {15,32}, {16,24}, {8,13}, {15,31}, {17,27}, {7,13}, {4,19}, {10,26}, {6,21}, {1,17}, {12,27}, {7,24}, {13,19}, {14,30}, {2,17}, {16,18}, {5,15}, {23,30}, {14,29}, {16,17}, {12,28}, {8,24}, {13,20}, {9,24}, {11,22}, {11,28}, {2,32}, {9,25}, {6,28}, {8,25}, {20,28}, {8,15}, {4,29}, {22,30}, {3,20}, {6,13}, {3,30}, {2,31}, {18,25}, {23,32}, {4,12}, {3,23}, {8,16}, {20,27}, {12,31}, {1,32}, {21,29}, {19,27}, {7,15}, {4,30}, {22,29}, {5,17}, {13,26}, {5,14}, {3,24}, {7,20}, {15,28}, {1,22}, {10,30}, {9,30}, {7,19}, {16,28}, {6,27}, {23,31}, {2,9}, {17,25}, {3,12}, {1,21}, {6,29}, {1,25}, {4,27}, {17,26}, {12,19}, {9,17}, {21,31}, {10,17}, {13,21}, {4,9}, {6,18}, {9,18}, {11,19}, {8,14}, {11,20}, {2,12}, {17,28}, {2,11}, {21,32}, {6,15}, {19,25}, {8,20}, {14,22}, {10,18}, {13,22}, {4,10}, {13,29}, {1,18}, {16,31}, {9,26}, {5,22}, {16,32}, {15,24}, {7,31}, {15,23}, {14,20}, {15,17}, {7,25}, {7,26}, {3,29}, {1,31}, {5,16}, {5,27}, {19,28}, {24,31}, {8,26}, {4,23}, {1,11} } Symmetric graph 30 of order 32 Valency 12 Diameter 3 Girth 4 Automorphism group of order 5283615080448 Number of arcs = 384 Number of 2-arcs = 4224 2-arc-transitive false Edge-set { {1,10}, {14,24}, {8,22}, {16,25}, {1,12}, {20,31}, {15,24}, {5,9}, {5,32}, {11,24}, {3,22}, {1,27}, {14,30}, {10,25}, {6,12}, {13,22}, {7,19}, {2,22}, {19,29}, {12,25}, {4,12}, {18,31}, {15,17}, {4,24}, {22,27}, {7,16}, {1,26}, {5,14}, {8,32}, {11,21}, {3,20}, {15,31}, {2,15}, {19,28}, {13,23}, {23,31}, {15,21}, {8,28}, {13,25}, {5,11}, {3,32}, {11,17}, {3,18}, {1,30}, {9,30}, {10,29}, {6,10}, {17,25}, {12,18}, {4,31}, {15,27}, {9,19}, {5,23}, {6,24}, {22,31}, {16,22}, {1,19}, {2,20}, {24,29}, {12,32}, {4,16}, {18,27}, {14,17}, {6,30}, {10,23}, {6,21}, {3,28}, {13,28}, {15,26}, {2,11}, {11,30}, {10,32}, {6,16}, {24,28}, {5,15}, {2,32}, {12,22}, {4,19}, {2,18}, {17,29}, {12,29}, {4,10}, {18,30}, {9,17}, {7,24}, {22,26}, {7,13}, {7,26}, {8,14}, {8,25}, {14,21}, {8,20}, {5,29}, {3,9}, {1,17}, {6,27}, {11,19}, {21,25}, {12,20}, {1,31}, {15,30}, {9,31}, {23,27}, {3,29}, {5,18}, {4,30}, {9,27}, {16,29}, {7,21}, {20,26}, {14,26}, {8,11}, {21,32}, {16,20}, {17,28}, {3,15}, {2,28}, {6,31}, {12,23}, {4,21}, {7,12}, {4,26}, {2,14}, {8,29}, {9,21}, {5,20}, {3,25}, {12,28}, {10,22}, {6,19}, {2,23}, {21,29}, {11,31}, {13,18}, {23,30}, {8,18}, {7,30}, {9,26}, {13,29}, {7,10}, {19,25}, {15,19}, {1,24}, {24,32}, {16,32}, {1,16}, {20,27}, {7,17}, {4,13}, {11,27}, {3,14}, {22,30}, {6,26}, {1,13}, {18,26}, {7,27}, {8,9}, {5,25}, {19,32}, {16,23}, {14,31}, {10,28}, {10,18}, {6,17}, {3,23}, {21,28}, {1,21}, {20,30}, {11,26}, {3,11}, {17,32}, {16,18}, {24,25}, {13,32}, {14,19}, {8,15}, {13,20}, {23,26}, {2,9}, {9,24}, {6,13}, {7,31}, {2,25}, {8,23}, {5,28}, {5,22}, {4,27}, {14,27}, {10,20}, {16,28}, {4,17}, {2,29} } Symmetric graph 31 of order 32 Valency 14 Diameter 3 Girth 4 Automorphism group of order 5284823040 Number of arcs = 448 Number of 2-arcs = 5824 2-arc-transitive false Edge-set { {1,7}, {19,30}, {8,17}, {6,12}, {13,22}, {8,29}, {7,16}, {22,31}, {3,5}, {16,26}, {9,26}, {11,29}, {7,21}, {14,30}, {8,28}, {10,26}, {9,24}, {17,32}, {6,20}, {2,14}, {28,31}, {2,23}, {1,31}, {11,21}, {4,21}, {25,30}, {8,10}, {12,15}, {22,25}, {4,29}, {7,29}, {2,24}, {2,31}, {23,28}, {1,12}, {8,9}, {16,23}, {5,31}, {5,14}, {15,20}, {18,25}, {4,10}, {24,29}, {20,27}, {11,18}, {10,19}, {17,24}, {21,25}, {22,32}, {2,7}, {3,27}, {1,26}, {9,32}, {19,21}, {11,30}, {8,21}, {20,28}, {12,18}, {10,20}, {18,24}, {4,27}, {19,22}, {3,17}, {23,29}, {14,27}, {11,28}, {10,32}, {6,24}, {15,32}, {6,25}, {5,13}, {2,19}, {12,21}, {4,15}, {2,13}, {12,16}, {1,25}, {9,23}, {20,30}, {8,18}, {17,31}, {1,23}, {10,13}, {4,22}, {25,29}, {7,10}, {4,5}, {14,29}, {7,22}, {3,15}, {5,24}, {7,28}, {3,18}, {6,26}, {9,13}, {16,20}, {11,27}, {5,12}, {23,27}, {5,32}, {16,32}, {13,18}, {3,10}, {19,27}, {18,26}, {14,22}, {3,28}, {1,19}, {1,11}, {7,15}, {16,24}, {11,17}, {2,26}, {9,19}, {21,32}, {24,30}, {2,8}, {18,32}, {6,19}, {11,15}, {26,30}, {13,17}, {28,32}, {4,30}, {7,17}, {14,28}, {3,21}, {3,6}, {6,23}, {9,14}, {15,26}, {2,20}, {13,30}, {15,31}, {9,25}, {4,17}, {20,29}, {8,27}, {12,28}, {4,16}, {18,31}, {1,13}, {10,23}, {12,22}, {7,18}, {7,9}, {15,23}, {6,31}, {13,21}, {2,12}, {8,16}, {4,9}, {8,30}, {17,25}, {5,20}, {27,31}, {5,11}, {14,18}, {22,26}, {24,27}, {1,32}, {16,19}, {14,21}, {3,29}, {7,30}, {19,28}, {15,24}, {17,26}, {2,11}, {3,9}, {8,15}, {23,30}, {1,8}, {13,27}, {10,31}, {16,25}, {20,22}, {18,23}, {12,29}, {6,14}, {4,6}, {15,25}, {9,31}, {12,30}, {17,23}, {13,28}, {10,25}, {20,21}, {8,22}, {13,29}, {12,27}, {16,31}, {4,18}, {1,20}, {7,27}, {11,22}, {19,29}, {3,16}, {10,24}, {1,14}, {5,26}, {5,25}, {5,19}, {27,32}, {1,24}, {3,22}, {11,16}, {26,29}, {2,32}, {10,14}, {21,26}, {3,30}, {24,28}, {15,19}, {14,17}, {6,11}, {6,32}, {6,13}, {12,17}, {9,20}, {4,28}, {21,31}, {2,25}, {5,23} } Symmetric graph 32 of order 32 Valency 15 Diameter 3 Girth 3 Automorphism group of order 23040 Number of arcs = 480 Number of 2-arcs = 6720 2-arc-transitive false Edge-set { {1,3}, {2,30}, {12,18}, {1,17}, {11,20}, {16,21}, {2,8}, {2,22}, {1,12}, {9,15}, {7,27}, {27,32}, {13,16}, {1,25}, {4,11}, {1,28}, {11,14}, {2,16}, {8,12}, {12,31}, {15,22}, {3,26}, {3,5}, {3,19}, {5,29}, {5,32}, {16,25}, {2,24}, {12,23}, {15,29}, {7,17}, {2,4}, {6,12}, {6,15}, {7,26}, {1,32}, {11,16}, {4,8}, {16,20}, {8,30}, {28,31}, {14,15}, {23,30}, {18,24}, {18,31}, {10,30}, {18,28}, {8,18}, {19,31}, {8,19}, {29,31}, {24,32}, {16,23}, {1,14}, {9,11}, {8,10}, {15,19}, {22,26}, {1,29}, {11,17}, {7,16}, {8,32}, {7,31}, {15,32}, {23,26}, {3,24}, {2,19}, {12,29}, {25,29}, {4,17}, {9,32}, {16,27}, {17,25}, {4,20}, {6,30}, {6,31}, {15,26}, {13,17}, {10,20}, {14,21}, {2,9}, {20,21}, {4,21}, {2,6}, {21,25}, {28,30}, {10,25}, {4,28}, {18,20}, {19,30}, {14,19}, {9,29}, {13,32}, {10,16}, {12,26}, {12,15}, {7,22}, {11,25}, {10,31}, {15,28}, {23,28}, {14,24}, {2,18}, {12,19}, {1,7}, {26,32}, {3,16}, {19,25}, {4,29}, {20,26}, {3,30}, {13,23}, {10,24}, {14,30}, {9,18}, {1,10}, {11,28}, {16,18}, {19,23}, {22,29}, {3,32}, {5,16}, {22,24}, {1,23}, {17,27}, {20,32}, {7,20}, {30,32}, {23,31}, {15,24}, {5,22}, {21,27}, {6,27}, {13,26}, {11,22}, {9,27}, {13,27}, {27,29}, {11,32}, {24,27}, {6,20}, {11,24}, {21,23}, {6,17}, {9,21}, {2,27}, {10,17}, {20,28}, {6,10}, {26,28}, {19,22}, {5,19}, {8,24}, {16,31}, {8,15}, {3,14}, {7,23}, {21,30}, {4,31}, {4,13}, {6,14}, {9,26}, {1,21}, {2,11}, {8,28}, {2,26}, {3,12}, {24,29}, {18,29}, {17,19}, {9,23}, {17,30}, {5,13}, {12,21}, {4,15}, {6,7}, {21,32}, {10,13}, {10,28}, {14,28}, {9,14}, {2,13}, {10,12}, {3,22}, {1,5}, {9,19}, {3,27}, {20,29}, {13,20}, {14,31}, {3,7}, {5,23}, {24,25}, {7,14}, {5,25}, {3,18}, {7,29}, {5,9}, {7,9}, {12,27}, {13,22}, {5,11}, {4,9}, {7,11}, {4,23}, {6,24}, {14,25}, {16,30}, {25,31}, {18,26}, {3,10}, {12,13}, {1,15}, {4,25}, {4,6}, {14,18}, {18,21}, {10,22}, {17,22}, {1,20}, {5,8}, {8,13}, {15,17}, {19,27}, {13,29}, {6,21}, {6,26}, {8,21}, {22,28}, {5,18}, {25,27}, {26,30}, {22,31}, {5,28}, {17,32}, {20,24}, {11,30}, {8,25}, {2,31}, {17,23} } Symmetric graph 33 of order 32 Valency 15 Diameter 3 Girth 3 Automorphism group of order 23040 Number of arcs = 480 Number of 2-arcs = 6720 2-arc-transitive false Edge-set { {1,4}, {2,29}, {12,17}, {1,18}, {11,19}, {16,22}, {1,8}, {2,21}, {2,12}, {10,15}, {7,28}, {28,32}, {14,16}, {2,25}, {4,12}, {1,27}, {11,13}, {1,16}, {8,11}, {11,31}, {15,21}, {4,26}, {3,6}, {4,19}, {6,29}, {6,32}, {16,26}, {1,24}, {11,23}, {16,29}, {8,17}, {2,3}, {5,12}, {5,15}, {7,25}, {2,32}, {12,16}, {15,25}, {4,7}, {15,20}, {7,30}, {27,31}, {13,15}, {23,29}, {17,24}, {18,32}, {10,29}, {17,28}, {7,18}, {19,32}, {7,19}, {29,32}, {23,32}, {16,24}, {2,14}, {9,12}, {7,10}, {16,19}, {22,25}, {1,30}, {11,18}, {8,16}, {8,31}, {15,31}, {24,26}, {3,23}, {1,19}, {11,29}, {16,32}, {24,31}, {15,23}, {26,29}, {3,17}, {9,31}, {15,27}, {17,26}, {3,20}, {5,30}, {5,31}, {13,18}, {10,19}, {14,22}, {1,9}, {19,21}, {4,22}, {1,6}, {21,26}, {28,29}, {10,26}, {3,28}, {18,19}, {19,29}, {13,19}, {14,32}, {9,16}, {11,26}, {8,22}, {3,21}, {10,32}, {16,28}, {24,28}, {14,23}, {2,17}, {12,20}, {2,7}, {25,32}, {4,16}, {20,25}, {4,30}, {20,31}, {15,30}, {9,24}, {13,30}, {10,18}, {2,10}, {12,28}, {15,18}, {14,20}, {9,30}, {13,31}, {18,23}, {19,24}, {22,30}, {3,31}, {22,23}, {18,27}, {8,20}, {30,31}, {5,21}, {10,11}, {21,28}, {6,28}, {14,26}, {12,22}, {10,27}, {13,28}, {14,17}, {12,32}, {23,27}, {13,24}, {4,18}, {6,19}, {21,24}, {6,18}, {10,21}, {2,28}, {19,28}, {5,10}, {25,28}, {7,24}, {4,14}, {27,30}, {21,29}, {4,32}, {6,16}, {6,9}, {6,13}, {1,22}, {1,11}, {8,27}, {1,26}, {3,11}, {16,17}, {17,29}, {17,20}, {9,20}, {17,31}, {12,14}, {9,22}, {5,17}, {11,21}, {6,8}, {21,31}, {2,15}, {26,27}, {20,22}, {5,20}, {25,30}, {13,21}, {10,14}, {9,28}, {20,30}, {18,30}, {2,5}, {9,25}, {4,27}, {11,15}, {7,21}, {6,23}, {8,14}, {4,5}, {6,25}, {6,22}, {8,29}, {3,13}, {5,14}, {14,27}, {9,13}, {11,27}, {6,11}, {4,10}, {4,24}, {3,9}, {7,32}, {7,12}, {22,32}, {5,7}, {3,25}, {2,23}, {12,24}, {18,22}, {22,27}, {8,26}, {1,31}, {7,13}, {20,27}, {5,24}, {8,9}, {20,23}, {5,27}, {13,25}, {9,17}, {17,21}, {2,20}, {3,29}, {7,15}, {18,25}, {26,31}, {5,26}, {3,15}, {14,29}, {12,30}, {19,26}, {3,8}, {24,30}, {1,13}, {23,25}, {12,25}, {8,23}, {10,23} } Symmetric graph 34 of order 32 Valency 15 Diameter 3 Girth 4 Automorphism group of order 41845579776000 Number of arcs = 480 Number of 2-arcs = 6720 2-arc-transitive true Edge-set { {1,3}, {3,7}, {4,9}, {7,14}, {9,32}, {8,16}, {10,26}, {1,14}, {14,32}, {16,26}, {26,29}, {13,31}, {18,31}, {10,15}, {21,25}, {4,14}, {1,26}, {14,29}, {10,31}, {18,21}, {10,23}, {1,21}, {2,25}, {13,30}, {25,30}, {7,30}, {15,32}, {17,25}, {9,11}, {22,27}, {1,8}, {10,14}, {3,10}, {4,21}, {1,23}, {15,25}, {11,30}, {7,27}, {15,19}, {12,25}, {3,11}, {4,27}, {3,22}, {2,24}, {2,13}, {9,24}, {2,22}, {14,24}, {2,32}, {26,32}, {17,29}, {9,29}, {8,22}, {16,27}, {19,26}, {6,12}, {23,28}, {3,13}, {4,31}, {1,15}, {14,25}, {7,15}, {9,25}, {8,11}, {10,27}, {3,19}, {4,12}, {17,22}, {24,27}, {2,19}, {6,14}, {23,32}, {17,32}, {6,17}, {9,28}, {20,22}, {9,19}, {6,8}, {7,12}, {4,20}, {2,4}, {16,20}, {11,26}, {3,28}, {1,20}, {11,14}, {4,26}, {3,29}, {21,29}, {23,29}, {16,23}, {12,13}, {28,31}, {6,31}, {18,23}, {10,17}, {6,21}, {21,28}, {5,19}, {12,24}, {2,7}, {9,13}, {8,25}, {10,30}, {3,32}, {4,17}, {1,9}, {14,22}, {9,16}, {22,26}, {13,27}, {19,31}, {6,15}, {23,25}, {7,17}, {6,9}, {8,28}, {10,20}, {12,29}, {6,20}, {11,23}, {3,6}, {14,16}, {8,29}, {5,16}, {24,26}, {12,18}, {5,28}, {16,17}, {6,26}, {13,21}, {16,31}, {14,28}, {20,32}, {8,18}, {5,10}, {4,8}, {5,18}, {19,21}, {5,7}, {3,18}, {4,5}, {1,27}, {14,19}, {8,10}, {10,21}, {7,23}, {19,23}, {1,12}, {2,28}, {13,20}, {5,25}, {24,30}, {16,30}, {19,30}, {15,29}, {11,21}, {5,11}, {20,28}, {11,20}, {2,16}, {13,26}, {22,31}, {15,24}, {7,26}, {3,16}, {18,26}, {10,12}, {2,6}, {13,23}, {6,30}, {21,32}, {12,22}, {8,32}, {16,21}, {5,13}, {24,31}, {15,18}, {19,27}, {12,19}, {7,21}, {1,31}, {14,18}, {28,30}, {7,20}, {5,22}, {29,31}, {2,11}, {25,31}, {18,30}, {1,5}, {5,29}, {7,31}, {15,22}, {8,13}, {22,30}, {11,17}, {6,27}, {7,9}, {4,23}, {1,17}, {13,15}, {11,15}, {25,27}, {12,32}, {17,19}, {3,24}, {2,18}, {9,22}, {20,24}, {17,24}, {11,27}, {5,24}, {18,27}, {2,10}, {9,18}, {15,28}, {20,25}, {21,24}, {27,29}, {12,28}, {11,31}, {30,32}, {6,23}, {17,28}, {27,32}, {3,25}, {4,30}, {1,30}, {5,32}, {4,15}, {22,23}, {8,19}, {13,17}, {26,28}, {20,29}, {12,16}, {18,20}, {2,29}, {8,24} } Symmetric graph 35 of order 32 Valency 16 Diameter 2 Girth 4 Automorphism group of order 875526273394790105088000000 Number of arcs = 512 Number of 2-arcs = 7680 2-arc-transitive true Edge-set { {1,9}, {1,14}, {16,25}, {14,26}, {5,14}, {11,25}, {14,29}, {8,19}, {19,32}, {5,20}, {2,11}, {20,29}, {5,11}, {11,31}, {11,29}, {3,19}, {19,27}, {5,21}, {7,11}, {21,29}, {9,30}, {22,30}, {7,9}, {24,30}, {6,22}, {7,24}, {21,31}, {8,11}, {3,13}, {13,27}, {7,21}, {8,21}, {3,11}, {14,31}, {11,27}, {3,23}, {23,27}, {3,21}, {7,14}, {21,27}, {16,30}, {22,28}, {7,16}, {17,30}, {4,22}, {7,17}, {20,31}, {1,11}, {3,10}, {10,27}, {7,20}, {1,21}, {1,22}, {8,16}, {22,26}, {2,22}, {1,10}, {16,29}, {10,26}, {8,17}, {3,22}, {12,28}, {2,12}, {17,29}, {1,23}, {3,9}, {14,30}, {9,27}, {6,16}, {6,17}, {4,12}, {20,30}, {3,16}, {14,28}, {16,27}, {5,23}, {23,29}, {3,17}, {4,14}, {17,27}, {18,28}, {4,16}, {17,25}, {4,18}, {4,17}, {20,28}, {1,16}, {5,10}, {10,29}, {4,20}, {1,17}, {8,22}, {8,9}, {22,32}, {2,18}, {8,10}, {9,29}, {10,32}, {8,24}, {5,22}, {15,28}, {2,15}, {24,29}, {8,23}, {3,14}, {14,25}, {14,27}, {2,16}, {2,17}, {4,15}, {20,25}, {19,25}, {2,14}, {9,32}, {2,19}, {2,20}, {13,28}, {19,26}, {2,13}, {15,25}, {21,32}, {5,9}, {16,28}, {19,28}, {4,13}, {13,26}, {18,25}, {16,26}, {22,29}, {17,26}, {8,12}, {12,32}, {24,32}, {5,12}, {9,28}, {16,32}, {5,18}, {18,29}, {4,9}, {17,32}, {18,31}, {4,11}, {21,25}, {7,18}, {4,21}, {24,28}, {5,16}, {5,15}, {15,29}, {4,24}, {5,17}, {6,18}, {8,15}, {15,32}, {1,24}, {5,19}, {15,31}, {6,15}, {24,27}, {8,18}, {8,14}, {9,25}, {14,32}, {2,21}, {7,15}, {24,25}, {19,30}, {2,9}, {9,26}, {6,19}, {2,24}, {13,31}, {23,26}, {6,13}, {15,30}, {21,26}, {11,28}, {19,31}, {7,13}, {18,30}, {19,29}, {8,13}, {13,32}, {24,26}, {5,13}, {7,19}, {11,26}, {13,29}, {13,30}, {3,12}, {12,26}, {6,20}, {16,31}, {18,32}, {12,27}, {8,20}, {20,32}, {21,28}, {3,24}, {1,18}, {18,26}, {6,9}, {23,31}, {6,11}, {7,23}, {6,21}, {1,15}, {15,26}, {6,24}, {5,24}, {6,23}, {3,15}, {15,27}, {1,20}, {1,19}, {10,31}, {6,10}, {20,27}, {3,18}, {9,31}, {11,32}, {7,10}, {24,31}, {12,31}, {23,32}, {6,12}, {10,30}, {11,30}, {22,31}, {7,12}, {23,30}, {20,26}, {1,13}, {7,22}, {12,30}, {18,27}, {12,29}, {21,30}, {3,20}, {17,28}, {23,25}, {6,14}, {2,23}, {1,12}, {4,23}, {10,25}, {4,10}, {2,10}, {17,31}, {12,25}, {10,28}, {22,25}, {23,28}, {22,27}, {4,19}, {13,25} } Symmetric graph 36 of order 32 Valency 18 Diameter 2 Girth 3 Automorphism group of order 75497472 Number of arcs = 576 Number of 2-arcs = 9792 2-arc-transitive false Edge-set { {1,11}, {5,20}, {20,29}, {8,28}, {5,18}, {16,28}, {5,9}, {2,12}, {13,24}, {8,29}, {3,18}, {12,17}, {13,32}, {8,22}, {18,28}, {6,19}, {19,30}, {24,25}, {7,26}, {2,16}, {9,24}, {4,29}, {3,21}, {4,30}, {10,24}, {15,26}, {2,32}, {1,24}, {12,29}, {3,13}, {7,27}, {6,17}, {15,27}, {6,10}, {14,25}, {7,11}, {1,13}, {12,23}, {19,32}, {22,25}, {7,28}, {3,16}, {9,22}, {4,31}, {2,21}, {3,15}, {10,22}, {21,25}, {13,18}, {12,31}, {15,19}, {5,25}, {7,20}, {16,19}, {9,30}, {4,24}, {21,26}, {14,23}, {7,30}, {4,17}, {11,18}, {14,31}, {7,21}, {17,27}, {11,25}, {1,20}, {23,29}, {5,24}, {20,26}, {19,26}, {8,30}, {10,27}, {6,15}, {14,32}, {1,12}, {13,23}, {21,32}, {22,32}, {1,28}, {3,9}, {16,22}, {6,31}, {2,19}, {4,18}, {21,31}, {1,27}, {2,11}, {24,29}, {3,26}, {9,19}, {16,30}, {18,27}, {8,14}, {5,23}, {6,32}, {15,22}, {10,28}, {3,25}, {7,22}, {13,31}, {23,26}, {8,25}, {1,15}, {10,23}, {3,30}, {4,22}, {3,29}, {9,23}, {16,25}, {1,31}, {2,23}, {11,30}, {4,14}, {14,20}, {11,29}, {5,28}, {16,26}, {8,9}, {7,18}, {13,28}, {5,12}, {13,27}, {6,12}, {2,15}, {11,21}, {14,27}, {17,31}, {15,25}, {5,19}, {20,30}, {24,26}, {8,26}, {10,31}, {10,32}, {13,20}, {21,28}, {17,32}, {1,32}, {7,9}, {16,17}, {6,27}, {3,22}, {9,31}, {5,11}, {6,20}, {19,29}, {4,13}, {12,21}, {22,27}, {6,28}, {15,17}, {3,14}, {8,18}, {7,10}, {18,32}, {1,23}, {13,26}, {8,12}, {2,14}, {11,24}, {20,31}, {8,27}, {4,15}, {10,21}, {3,32}, {1,22}, {4,16}, {9,21}, {22,26}, {14,17}, {11,32}, {16,20}, {6,26}, {8,19}, {15,20}, {10,29}, {3,23}, {23,28}, {9,29}, {13,17}, {12,32}, {2,22}, {24,28}, {1,29}, {12,24}, {18,30}, {14,26}, {7,19}, {17,30}, {6,18}, {19,31}, {2,29}, {11,23}, {14,18}, {11,31}, {15,28}, {5,10}, {13,25}, {7,12}, {2,13}, {16,27}, {5,26}, {10,30}, {4,32}, {1,21}, {8,20}, {18,29}, {5,17}, {6,9}, {3,24}, {2,30}, {1,14}, {4,23}, {23,27}, {12,26}, {24,30}, {6,23}, {19,25}, {20,25}, {7,29}, {9,28}, {5,16}, {14,24}, {22,31}, {2,27}, {4,10}, {15,21}, {5,32}, {3,17}, {2,28}, {23,30}, {4,25}, {10,20}, {15,29}, {17,28}, {7,13}, {6,24}, {5,31}, {16,21}, {9,27}, {4,26}, {8,21}, {8,13}, {10,19}, {15,30}, {1,19}, {12,25}, {9,20}, {3,10}, {6,16}, {16,29}, {12,18}, {11,26}, {11,17}, {2,20}, {13,19}, {12,30}, {8,17}, {6,11}, {14,28}, {1,16}, {12,22}, {23,25}, {7,25}, {9,32}, {14,19}, {18,31}, {2,31}, {8,10}, {15,18}, {4,21}, {11,22}, {5,27}, {16,18}, {7,17}, {2,24}, {21,27}, {22,28}, {24,27}, {17,29}, {20,32}, {1,30}, {8,11}, {6,25}, {3,31}, {7,14}, {4,9}, {5,15} } Symmetric graph 37 of order 32 Valency 20 Diameter 2 Girth 3 Automorphism group of order 125829120 Number of arcs = 640 Number of 2-arcs = 12160 2-arc-transitive false Edge-set { {1,3}, {4,32}, {6,20}, {5,31}, {19,24}, {1,20}, {9,28}, {2,6}, {10,23}, {7,19}, {27,31}, {4,20}, {6,28}, {14,29}, {11,21}, {5,9}, {8,30}, {22,32}, {19,27}, {8,27}, {6,13}, {12,23}, {20,31}, {19,28}, {1,14}, {9,11}, {11,23}, {18,25}, {22,25}, {2,29}, {10,21}, {12,28}, {7,17}, {5,21}, {2,24}, {13,19}, {12,27}, {13,28}, {7,12}, {1,24}, {9,26}, {8,26}, {23,28}, {14,19}, {11,27}, {4,23}, {6,25}, {25,29}, {3,21}, {8,25}, {3,32}, {9,16}, {9,21}, {3,11}, {5,18}, {22,30}, {1,22}, {14,26}, {4,11}, {15,27}, {8,13}, {2,22}, {1,10}, {3,7}, {26,27}, {13,26}, {4,12}, {14,24}, {11,26}, {4,8}, {4,7}, {6,31}, {10,29}, {21,30}, {10,28}, {7,30}, {8,14}, {11,32}, {19,23}, {25,27}, {13,25}, {3,12}, {8,31}, {19,32}, {1,9}, {9,29}, {18,29}, {7,29}, {5,32}, {20,24}, {17,29}, {16,21}, {22,29}, {1,21}, {25,32}, {3,20}, {2,16}, {10,14}, {12,21}, {2,17}, {4,21}, {25,30}, {25,31}, {3,19}, {13,18}, {12,15}, {24,28}, {7,26}, {2,5}, {4,30}, {6,22}, {27,32}, {8,20}, {10,13}, {12,30}, {10,24}, {26,30}, {26,31}, {4,19}, {7,23}, {10,25}, {3,30}, {28,31}, {8,19}, {1,6}, {9,23}, {11,30}, {18,22}, {12,22}, {1,17}, {14,30}, {11,22}, {8,17}, {7,25}, {5,25}, {3,24}, {9,13}, {12,29}, {9,24}, {26,29}, {26,32}, {5,19}, {24,27}, {4,29}, {6,21}, {11,29}, {18,21}, {11,16}, {14,18}, {8,18}, {7,20}, {11,15}, {17,22}, {1,16}, {2,18}, {4,22}, {24,29}, {20,32}, {20,28}, {3,17}, {5,16}, {23,30}, {22,26}, {1,4}, {3,15}, {5,13}, {22,31}, {1,19}, {9,12}, {6,9}, {23,29}, {20,27}, {16,24}, {18,26}, {4,15}, {7,14}, {11,31}, {10,27}, {2,3}, {5,10}, {12,31}, {17,19}, {2,9}, {12,24}, {7,28}, {24,30}, {12,26}, {4,17}, {10,12}, {17,30}, {6,10}, {19,31}, {8,32}, {9,30}, {12,32}, {17,20}, {6,14}, {7,27}, {8,29}, {21,32}, {12,25}, {2,14}, {21,26}, {2,4}, {17,25}, {21,25}, {15,28}, {7,13}, {9,27}, {7,32}, {4,18}, {21,31}, {10,11}, {18,30}, {2,19}, {18,19}, {11,25}, {3,18}, {16,22}, {3,16}, {16,23}, {14,25}, {16,28}, {8,28}, {15,21}, {2,13}, {6,16}, {5,14}, {7,11}, {18,31}, {5,20}, {14,20}, {11,28}, {15,32}, {13,20}, {10,16}, {8,12}, {17,32}, {2,30}, {4,31}, {6,19}, {18,32}, {15,20}, {10,26}, {2,23}, {6,27}, {1,29}, {8,11}, {16,31}, {15,19}, {23,27}, {3,23}, {13,30}, {10,22}, {6,26}, {13,27}, {3,29}, {14,27}, {17,31}, {15,31}, {13,17}, {1,30}, {9,22}, {5,28}, {7,24}, {17,21}, {5,26}, {4,24}, {1,23}, {9,25}, {7,18}, {5,22}, {3,31}, {9,15}, {13,29}, {5,27}, {8,24}, {3,22}, {12,16}, {14,17}, {16,19}, {16,32}, {16,20}, {14,28}, {1,15}, {3,8}, {14,23}, {2,20}, {20,23}, {25,28}, {15,24}, {26,28}, {5,15}, {13,24}, {5,17}, {18,20}, {10,30}, {1,13}, {6,18}, {6,17}, {17,26}, {13,23}, {6,15}, {15,23}, {21,29}, {2,21}, {15,22}, {2,10}, {7,31}, {6,32}, {16,27}, {11,24}, {4,16}, {28,32}, {8,23}, {9,14}, {10,15}, {2,15}, {1,18}, {1,5} } Symmetric graph 38 of order 32 Valency 21 Diameter 2 Girth 3 Automorphism group of order 967680 Number of arcs = 672 Number of 2-arcs = 13440 2-arc-transitive false Edge-set { {1,5}, {19,30}, {7,27}, {6,12}, {15,24}, {2,20}, {11,26}, {16,17}, {25,31}, {21,28}, {2,17}, {7,29}, {6,21}, {1,13}, {9,29}, {8,22}, {3,23}, {4,10}, {10,13}, {3,27}, {12,19}, {8,29}, {6,23}, {9,20}, {16,26}, {17,27}, {19,25}, {24,30}, {4,7}, {9,15}, {16,32}, {18,26}, {18,28}, {25,32}, {5,20}, {14,31}, {8,30}, {14,24}, {4,30}, {2,32}, {5,11}, {6,16}, {24,31}, {9,18}, {16,28}, {17,25}, {20,25}, {7,15}, {21,32}, {1,22}, {3,9}, {2,8}, {11,23}, {4,6}, {10,24}, {12,28}, {15,17}, {20,31}, {8,26}, {15,21}, {11,22}, {3,14}, {9,22}, {3,5}, {12,22}, {4,11}, {10,14}, {7,19}, {21,27}, {10,23}, {12,18}, {15,28}, {23,28}, {1,17}, {12,31}, {8,15}, {11,29}, {6,14}, {13,19}, {27,29}, {17,22}, {3,25}, {10,28}, {13,17}, {5,15}, {22,32}, {3,22}, {3,12}, {4,8}, {10,21}, {20,21}, {2,26}, {11,27}, {14,19}, {26,30}, {7,18}, {15,32}, {5,32}, {18,29}, {6,28}, {13,25}, {20,29}, {17,31}, {8,25}, {14,28}, {17,30}, {3,16}, {8,21}, {2,23}, {7,10}, {13,21}, {1,18}, {9,28}, {2,19}, {13,26}, {23,32}, {15,26}, {18,32}, {19,32}, {5,27}, {18,31}, {13,31}, {14,23}, {1,30}, {6,20}, {24,26}, {2,27}, {11,19}, {14,25}, {20,30}, {5,16}, {22,31}, {3,21}, {2,12}, {12,20}, {7,23}, {10,16}, {18,21}, {2,28}, {9,13}, {16,29}, {17,23}, {1,25}, {6,24}, {4,24}, {2,9}, {11,16}, {18,23}, {4,32}, {5,10}, {12,30}, {8,24}, {4,23}, {19,21}, {14,18}, {26,32}, {5,18}, {5,31}, {8,28}, {14,27}, {1,29}, {6,9}, {2,13}, {1,24}, {1,12}, {22,26}, {11,21}, {2,14}, {5,9}, {16,22}, {3,17}, {12,25}, {7,9}, {16,21}, {8,10}, {13,23}, {4,18}, {8,12}, {15,23}, {18,27}, {19,28}, {25,29}, {14,20}, {24,27}, {4,19}, {5,30}, {7,22}, {3,15}, {12,32}, {6,29}, {4,9}, {11,25}, {1,21}, {14,22}, {6,11}, {13,22}, {4,13}, {23,25}, {1,20}, {7,17}, {21,25}, {1,28}, {9,17}, {2,29}, {6,13}, {24,29}, {1,10}, {7,12}, {19,22}, {10,26}, {13,18}, {27,32}, {5,19}, {6,31}, {7,16}, {21,31}, {20,26}, {3,30}, {3,29}, {20,23}, {17,28}, {28,31}, {8,17}, {15,29}, {6,32}, {5,25}, {20,22}, {11,31}, {8,14}, {27,30}, {12,16}, {15,31}, {8,20}, {6,27}, {19,24}, {5,23}, {1,11}, {9,14}, {22,27}, {10,19}, {13,27}, {3,18}, {9,30}, {28,30}, {16,30}, {7,31}, {1,26}, {19,29}, {23,29}, {1,6}, {15,19}, {8,32}, {4,16}, {10,31}, {15,20}, {3,19}, {24,25}, {4,20}, {16,18}, {2,5}, {3,6}, {12,24}, {11,17}, {15,27}, {16,25}, {10,29}, {23,26}, {4,25}, {10,20}, {7,30}, {7,21}, {4,27}, {17,24}, {14,30}, {16,20}, {26,31}, {6,26}, {18,24}, {1,14}, {5,24}, {4,22}, {2,11}, {11,14}, {6,19}, {10,17}, {3,26}, {10,27}, {1,7}, {9,21}, {9,32}, {7,25}, {3,8}, {12,23}, {3,10}, {12,13}, {8,18}, {2,16}, {7,26}, {13,29}, {11,15}, {3,31}, {20,27}, {13,30}, {1,32}, {11,18}, {2,24}, {5,22}, {12,15}, {16,24}, {9,25}, {2,21}, {4,28}, {17,32}, {8,13}, {4,31}, {7,14}, {21,30}, {19,26}, {2,31}, {8,11}, {1,15}, {5,28}, {23,30}, {6,17}, {11,30}, {14,32}, {22,28}, {22,29}, {9,26}, {9,24}, {10,32}, {5,13}, {2,7}, {4,15}, {28,29}, {12,27} } Symmetric graph 39 of order 32 Valency 24 Diameter 2 Girth 3 Automorphism group of order 63429799040778240000 Number of arcs = 768 Number of 2-arcs = 17664 2-arc-transitive false Edge-set { {1,9}, {11,17}, {13,32}, {8,21}, {5,9}, {20,28}, {11,23}, {7,26}, {16,17}, {13,30}, {3,26}, {4,19}, {5,21}, {10,32}, {22,25}, {8,23}, {5,16}, {20,30}, {22,28}, {4,14}, {3,27}, {1,16}, {7,30}, {18,28}, {14,23}, {2,31}, {1,26}, {16,23}, {16,30}, {3,30}, {4,17}, {2,26}, {8,19}, {14,19}, {12,27}, {13,25}, {16,32}, {10,30}, {17,25}, {6,19}, {5,19}, {1,12}, {24,31}, {11,32}, {22,32}, {5,23}, {23,30}, {17,28}, {8,14}, {5,27}, {12,32}, {22,31}, {4,9}, {3,12}, {10,20}, {20,31}, {11,21}, {23,28}, {18,30}, {14,17}, {8,31}, {4,15}, {3,29}, {4,16}, {11,22}, {6,27}, {2,24}, {21,28}, {9,23}, {2,28}, {1,30}, {5,30}, {1,17}, {8,26}, {9,19}, {12,26}, {16,25}, {10,23}, {2,27}, {8,24}, {13,27}, {13,22}, {10,28}, {3,18}, {4,24}, {1,21}, {7,9}, {5,26}, {1,19}, {6,17}, {5,12}, {9,27}, {24,26}, {14,24}, {15,27}, {13,29}, {16,27}, {2,21}, {8,9}, {15,25}, {20,29}, {6,12}, {7,19}, {5,17}, {1,13}, {19,31}, {11,30}, {17,32}, {17,30}, {8,11}, {5,32}, {9,32}, {22,26}, {3,13}, {10,22}, {23,31}, {16,21}, {5,18}, {1,14}, {12,25}, {6,9}, {20,25}, {11,20}, {2,20}, {18,26}, {7,13}, {6,28}, {6,14}, {1,11}, {7,32}, {10,17}, {22,30}, {4,11}, {3,32}, {8,15}, {5,29}, {16,22}, {13,20}, {6,32}, {2,22}, {2,12}, {24,25}, {15,20}, {11,18}, {23,25}, {16,20}, {7,31}, {9,17}, {13,26}, {15,21}, {4,18}, {15,22}, {10,29}, {4,10}, {3,25}, {8,16}, {4,27}, {3,24}, {21,30}, {8,28}, {8,30}, {9,21}, {9,26}, {16,28}, {13,23}, {2,32}, {8,22}, {11,28}, {2,18}, {1,24}, {1,23}, {7,16}, {6,30}, {11,19}, {10,21}, {15,17}, {3,31}, {4,21}, {3,21}, {4,31}, {6,22}, {11,25}, {15,26}, {19,29}, {15,19}, {12,29}, {8,18}, {5,14}, {2,30}, {8,17}, {14,21}, {13,28}, {9,24}, {16,29}, {2,23}, {3,20}, {15,28}, {23,29}, {12,22}, {10,31}, {6,31}, {7,21}, {5,31}, {3,23}, {10,27}, {5,13}, {20,32}, {7,15}, {7,14}, {18,29}, {14,18}, {14,27}, {13,31}, {16,26}, {14,25}, {20,27}, {6,13}, {7,17}, {19,26}, {9,30}, {17,26}, {23,26}, {16,19}, {5,20}, {12,28}, {2,9}, {21,26}, {7,12}, {6,11}, {5,11}, {1,32}, {15,30}, {17,29}, {3,9}, {1,18}, {5,15}, {24,28}, {7,27}, {7,28}, {24,27}, {2,15}, {8,29}, {21,31}, {24,32}, {4,29}, {3,15}, {22,29}, {10,18}, {6,26}, {12,30}, {17,31}, {20,26}, {2,13}, {16,18}, {1,31}, {4,28}, {8,10}, {18,27}, {24,29}, {1,10}, {7,25}, {24,30}, {1,28}, {18,25}, {14,20}, {3,28}, {4,23}, {10,24}, {10,19}, {7,29}, {6,18}, {19,25}, {12,20}, {11,24}, {23,32}, {12,21}, {4,20}, {11,29}, {5,25}, {4,32}, {3,22}, {13,17}, {8,32}, {5,22}, {1,22}, {3,16}, {4,30}, {12,17}, {7,22}, {10,25}, {9,29}, {7,11}, {16,24}, {2,19}, {10,26}, {6,25}, {12,24}, {15,31}, {1,27}, {7,24}, {14,29}, {13,24}, {2,29}, {7,18}, {15,32}, {8,27}, {5,24}, {4,22}, {11,31}, {7,23}, {6,16}, {11,27}, {14,26}, {19,27}, {9,18}, {6,20}, {6,29}, {14,32}, {21,25}, {2,17}, {11,26}, {19,32}, {6,21}, {3,19}, {4,12}, {19,28}, {2,14}, {3,14}, {5,28}, {7,10}, {21,29}, {16,31}, {14,28}, {23,27}, {8,20}, {9,28}, {2,16}, {2,11}, {14,30}, {17,27}, {5,10}, {2,10}, {8,25}, {18,31}, {13,18}, {9,25}, {6,23}, {18,32}, {14,22}, {15,24}, {6,10}, {2,25}, {12,18}, {15,23}, {21,27}, {1,25}, {9,20}, {4,25}, {15,29}, {12,23}, {8,12}, {21,32}, {9,22}, {1,15}, {4,13}, {4,26}, {12,19}, {12,31}, {13,19}, {19,30}, {1,29}, {1,20}, {9,31}, {14,31}, {6,24}, {7,20}, {13,21}, {15,18}, {3,17}, {8,13}, {22,27}, {3,10}, {3,11}, {6,15} } Symmetric graph 40 of order 32 Valency 28 Diameter 2 Girth 3 Automorphism group of order 4438236667576320 Number of arcs = 896 Number of 2-arcs = 24192 2-arc-transitive false Edge-set { {1,5}, {14,25}, {9,13}, {24,31}, {5,20}, {11,32}, {4,6}, {2,18}, {6,14}, {13,27}, {1,9}, {2,23}, {13,28}, {12,14}, {8,26}, {10,25}, {13,31}, {5,14}, {22,32}, {6,18}, {11,25}, {4,9}, {17,26}, {10,32}, {21,32}, {6,17}, {10,31}, {15,23}, {16,19}, {12,24}, {3,20}, {2,32}, {6,24}, {14,31}, {5,13}, {1,20}, {23,29}, {8,13}, {9,24}, {2,20}, {11,28}, {4,12}, {7,23}, {19,26}, {1,12}, {3,23}, {1,19}, {23,30}, {7,13}, {14,26}, {2,12}, {3,24}, {17,30}, {8,32}, {5,29}, {7,28}, {10,18}, {1,31}, {6,27}, {11,27}, {1,26}, {10,23}, {13,18}, {2,31}, {5,24}, {14,32}, {6,13}, {6,25}, {9,27}, {4,17}, {15,32}, {6,16}, {11,18}, {4,31}, {6,26}, {10,27}, {9,21}, {2,17}, {10,28}, {16,17}, {5,23}, {19,28}, {17,27}, {5,25}, {9,28}, {3,17}, {16,32}, {6,15}, {23,31}, {5,19}, {10,26}, {1,10}, {18,27}, {11,31}, {3,7}, {21,26}, {1,15}, {16,23}, {4,14}, {13,22}, {16,21}, {15,17}, {8,12}, {3,25}, {2,25}, {14,18}, {9,22}, {23,25}, {9,19}, {12,17}, {3,32}, {2,26}, {10,24}, {13,32}, {13,24}, {14,20}, {11,22}, {4,18}, {12,26}, {1,30}, {8,23}, {13,29}, {7,14}, {8,9}, {2,28}, {13,23}, {14,19}, {12,22}, {3,18}, {11,19}, {4,30}, {7,26}, {12,21}, {7,29}, {14,17}, {5,21}, {17,28}, {7,22}, {18,26}, {14,24}, {13,20}, {11,21}, {7,27}, {11,26}, {1,29}, {13,30}, {8,14}, {24,32}, {12,23}, {3,19}, {12,25}, {3,9}, {8,22}, {18,25}, {2,9}, {2,24}, {16,27}, {11,15}, {19,23}, {19,30}, {25,30}, {17,29}, {7,32}, {28,31}, {5,12}, {20,32}, {6,29}, {19,29}, {7,30}, {10,15}, {1,16}, {24,27}, {11,20}, {24,26}, {10,20}, {8,31}, {4,29}, {17,24}, {5,11}, {4,28}, {7,10}, {1,27}, {11,23}, {23,26}, {10,19}, {12,18}, {3,31}, {1,32}, {6,23}, {18,32}, {6,31}, {5,27}, {9,20}, {2,29}, {8,28}, {4,32}, {6,22}, {16,31}, {5,15}, {4,16}, {10,17}, {17,32}, {6,32}, {5,31}, {5,28}, {8,27}, {5,9}, {3,28}, {15,19}, {15,22}, {7,31}, {5,26}, {7,21}, {16,20}, {15,29}, {19,25}, {18,31}, {2,30}, {16,22}, {15,18}, {9,23}, {2,19}, {4,25}, {6,21}, {15,31}, {5,16}, {1,18}, {4,11}, {15,20}, {16,29}, {8,24}, {20,25}, {4,10}, {22,29}, {7,18}, {9,30}, {2,8}, {5,17}, {28,32}, {3,5}, {21,28}, {20,21}, {4,7}, {22,26}, {2,21}, {10,14}, {1,13}, {1,6}, {23,27}, {4,13}, {14,22}, {4,5}, {22,28}, {3,16}, {15,21}, {12,30}, {3,8}, {25,29}, {7,9}, {18,22}, {6,9}, {2,27}, {18,23}, {19,31}, {6,12}, {3,27}, {2,15}, {16,24}, {26,31}, {9,14}, {2,13}, {12,16}, {3,15}, {22,25}, {9,18}, {9,17}, {17,23}, {19,32}, {8,10}, {1,25}, {11,24}, {13,17}, {1,8}, {6,11}, {4,27}, {4,26}, {10,22}, {1,28}, {14,29}, {7,24}, {14,30}, {28,29}, {7,12}, {3,26}, {1,7}, {14,23}, {2,14}, {14,21}, {16,18}, {11,14}, {21,27}, {11,17}, {5,30}, {20,30}, {8,29}, {2,16}, {15,24}, {13,19}, {15,30}, {20,28}, {24,25}, {10,21}, {20,29}, {8,30}, {8,25}, {24,28}, {12,20}, {9,25}, {6,30}, {20,27}, {12,28}, {3,12}, {4,20}, {8,16}, {15,25}, {3,11}, {4,21}, {15,26}, {10,16}, {13,26}, {1,21}, {14,27}, {11,13}, {19,21}, {6,19}, {27,30}, {16,28}, {12,15}, {20,23}, {10,30}, {12,31}, {25,32}, {13,25}, {17,22}, {20,31}, {14,28}, {12,13}, {27,29}, {7,11}, {3,10}, {15,27}, {11,16}, {4,24}, {20,22}, {4,15}, {8,20}, {8,17}, {2,5}, {10,13}, {1,14}, {22,27}, {26,30}, {18,29}, {19,24}, {26,32}, {6,10}, {10,29}, {8,11}, {20,24}, {7,17}, {23,28}, {9,16}, {12,19}, {3,29}, {21,25}, {5,22}, {16,25}, {9,15}, {17,31}, {5,32}, {5,10}, {7,25}, {9,31}, {19,22}, {18,30}, {3,14}, {13,21}, {3,6}, {26,29}, {6,28}, {3,30}, {8,21}, {18,24}, {18,21}, {3,13}, {1,17}, {1,11}, {12,27}, {7,16}, {24,30}, {2,11}, {8,19}, {12,29}, {23,32}, {22,31}, {5,18}, {9,32}, {2,6}, {28,30}, {3,22}, {21,29}, {27,32}, {3,21}, {2,10}, {1,24}, {6,20}, {7,20}, {21,31}, {4,22}, {22,30}, {8,18}, {9,29}, {2,7}, {18,28}, {7,15}, {16,26}, {12,32}, {25,31}, {4,8}, {1,23}, {27,31}, {17,21}, {11,29}, {24,29}, {11,30}, {4,23}, {16,30}, {9,26}, {1,22}, {4,19}, {19,27}, {8,15}, {17,25}, {7,19}, {15,28}, {2,22}, {20,26}, {21,30} } Symmetric graph 41 of order 32 Valency 30 Diameter 2 Girth 3 Automorphism group of order 1371195958099968000 Number of arcs = 960 Number of 2-arcs = 27840 2-arc-transitive false Edge-set { {1,3}, {3,10}, {12,25}, {7,10}, {5,25}, {1,32}, {8,22}, {7,26}, {2,5}, {1,6}, {19,22}, {3,21}, {12,32}, {25,30}, {2,26}, {2,21}, {4,6}, {11,19}, {3,5}, {12,20}, {24,30}, {10,29}, {4,25}, {21,32}, {8,32}, {1,27}, {15,22}, {2,4}, {11,21}, {4,29}, {4,11}, {5,9}, {20,26}, {24,31}, {6,10}, {19,25}, {23,32}, {8,9}, {18,27}, {15,18}, {7,28}, {5,16}, {1,9}, {22,26}, {21,29}, {4,32}, {21,25}, {3,12}, {12,23}, {19,30}, {3,13}, {4,9}, {11,26}, {29,31}, {4,7}, {9,28}, {16,26}, {9,31}, {6,8}, {6,19}, {2,23}, {9,21}, {18,22}, {18,31}, {5,7}, {5,20}, {1,24}, {10,22}, {17,21}, {17,32}, {8,25}, {12,14}, {23,28}, {14,19}, {13,28}, {2,24}, {6,20}, {3,8}, {6,12}, {2,30}, {28,29}, {4,16}, {26,32}, {1,29}, {4,22}, {10,32}, {8,17}, {24,27}, {10,15}, {6,26}, {2,31}, {7,21}, {22,28}, {16,31}, {9,26}, {8,11}, {6,24}, {2,20}, {14,21}, {6,31}, {1,20}, {5,24}, {10,20}, {4,17}, {11,17}, {8,29}, {14,30}, {3,28}, {14,22}, {28,31}, {2,19}, {6,23}, {9,19}, {3,18}, {12,18}, {7,30}, {13,29}, {4,27}, {13,21}, {27,32}, {1,25}, {1,22}, {16,32}, {17,24}, {16,24}, {11,15}, {4,18}, {11,18}, {5,23}, {9,20}, {10,25}, {5,32}, {8,20}, {11,28}, {14,26}, {12,16}, {9,30}, {3,26}, {13,25}, {18,23}, {7,19}, {5,13}, {20,21}, {11,31}, {26,29}, {11,30}, {3,24}, {20,22}, {14,31}, {2,8}, {6,21}, {25,31}, {1,7}, {5,18}, {18,20}, {4,23}, {9,11}, {16,29}, {5,22}, {20,31}, {3,23}, {9,12}, {6,18}, {18,19}, {7,23}, {9,13}, {26,27}, {13,31}, {7,27}, {25,28}, {1,16}, {16,27}, {15,29}, {10,11}, {24,25}, {16,30}, {3,29}, {11,22}, {4,24}, {5,17}, {17,20}, {8,24}, {10,14}, {14,32}, {8,28}, {2,15}, {15,28}, {23,26}, {4,30}, {12,21}, {12,22}, {3,30}, {13,18}, {14,18}, {19,31}, {7,13}, {9,14}, {26,28}, {6,17}, {17,19}, {8,23}, {6,9}, {19,32}, {23,25}, {7,24}, {2,16}, {20,32}, {8,14}, {8,27}, {6,15}, {2,10}, {1,15}, {22,30}, {14,17}, {17,28}, {24,26}, {23,29}, {22,31}, {7,31}, {2,28}, {16,21}, {27,31}, {7,15}, {10,18}, {18,25}, {23,30}, {3,9}, {16,22}, {1,11}, {5,29}, {4,20}, {2,12}, {6,14}, {19,28}, {14,23}, {9,17}, {17,26}, {8,31}, {6,7}, {20,28}, {14,16}, {6,30}, {3,19}, {22,23}, {10,17}, {17,25}, {5,14}, {14,24}, {10,28}, {2,17}, {8,15}, {21,23}, {30,31}, {12,26}, {22,24}, {3,20}, {13,16}, {1,18}, {20,27}, {14,15}, {16,25}, {3,7}, {9,18}, {18,26}, {6,13}, {19,27}, {13,23}, {9,27}, {7,16}, {29,32}, {11,25}, {4,19}, {11,13}, {13,24}, {15,26}, {4,8}, {30,32}, {10,27}, {15,25}, {28,30}, {10,31}, {8,16}, {6,29}, {2,11}, {21,24}, {1,17}, {5,8}, {17,22}, {2,18}, {11,14}, {9,32}, {1,23}, {5,19}, {13,20}, {5,11}, {12,13}, {27,30}, {3,15}, {27,29}, {18,21}, {16,17}, {3,31}, {11,24}, {20,29}, {4,14}, {23,31}, {19,26}, {2,13}, {7,14}, {5,28}, {1,14}, {17,27}, {15,17}, {8,10}, {6,25}, {20,30}, {3,14}, {7,12}, {6,28}, {16,19}, {9,23}, {10,24}, {17,29}, {8,13}, {6,27}, {21,27}, {22,25}, {1,31}, {5,26}, {11,23}, {9,24}, {16,20}, {14,29}, {5,27}, {15,20}, {17,30}, {3,17}, {1,13}, {22,27}, {6,16}, {19,29}, {16,18}, {18,29}, {7,11}, {4,13}, {11,27}, {15,31}, {2,32}, {8,21}, {18,30}, {10,23}, {9,25}, {12,28}, {10,26}, {2,25}, {2,14}, {21,28}, {5,15}, {12,24}, {8,12}, {7,22}, {1,26}, {15,32}, {1,19}, {13,22}, {15,24}, {5,31}, {20,25}, {4,31}, {12,27}, {13,30}, {3,27}, {7,29}, {6,32}, {12,17}, {10,19}, {15,23}, {8,30}, {16,23}, {4,28}, {14,27}, {7,18}, {9,16}, {17,31}, {10,21}, {4,15}, {2,29}, {6,11}, {19,24}, {3,16}, {12,29}, {23,27}, {13,19}, {13,27}, {7,25}, {1,5}, {9,15}, {10,16}, {25,29}, {20,24}, {1,30}, {5,12}, {20,23}, {3,22}, {12,31}, {2,6}, {19,21}, {7,17}, {8,18}, {16,28}, {19,23}, {15,27}, {10,13}, {25,27}, {12,30}, {14,20}, {24,28}, {14,28}, {26,31}, {2,7}, {26,30}, {4,21}, {11,32}, {1,4}, {1,8}, {6,22}, {5,21}, {11,29}, {18,32}, {25,32}, {2,3}, {13,32}, {10,12}, {15,30}, {9,22}, {5,10}, {13,17}, {4,5}, {13,26}, {11,16}, {7,20}, {18,24}, {14,25}, {28,32}, {17,23}, {10,30}, {12,15}, {2,22}, {3,6}, {12,19}, {8,19}, {1,28}, {3,25}, {22,32}, {11,20}, {24,29}, {4,10}, {2,27}, {5,30}, {1,12}, {9,29}, {21,31}, {4,26}, {15,21}, {7,32}, {1,21}, {13,15}, {21,30}, {2,9}, {18,28}, {22,29}, {24,32}, {3,11}, {1,10}, {3,32}, {7,9}, {4,12}, {15,19}, {21,26}, {8,26} } Symmetric graph 42 of order 32 Valency 31 Diameter 1 Girth 3 Automorphism group of order 263130836933693530167218012160000000 Number of arcs = 992 Number of 2-arcs = 29760 2-arc-transitive true Edge-set { {1,2}, {1,17}, {1,9}, {2,18}, {1,5}, {2,10}, {17,25}, {1,19}, {2,6}, {17,21}, {9,13}, {18,26}, {1,10}, {2,20}, {3,17}, {9,27}, {18,22}, {5,23}, {10,14}, {25,29}, {1,21}, {2,9}, {17,26}, {4,18}, {5,14}, {10,28}, {11,25}, {19,28}, {6,24}, {7,21}, {13,31}, {26,30}, {1,27}, {2,22}, {5,17}, {9,29}, {18,25}, {7,19}, {6,13}, {21,30}, {12,26}, {10,30}, {20,27}, {3,12}, {8,22}, {23,32}, {14,32}, {15,29}, {1,14}, {2,28}, {11,17}, {9,19}, {6,18}, {5,31}, {13,25}, {10,20}, {8,20}, {3,23}, {15,27}, {22,29}, {15,21}, {14,26}, {4,11}, {16,28}, {24,31}, {7,16}, {16,30}, {1,7}, {2,13}, {17,30}, {6,9}, {12,18}, {5,10}, {3,25}, {19,32}, {6,32}, {13,23}, {21,26}, {4,26}, {4,24}, {14,24}, {11,31}, {24,27}, {16,22}, {7,29}, {8,30}, {12,32}, {8,15}, {1,20}, {2,8}, {17,23}, {9,15}, {18,29}, {3,5}, {22,25}, {19,21}, {10,16}, {20,31}, {3,16}, {23,28}, {27,29}, {7,12}, {12,14}, {8,11}, {4,15}, {1,26}, {2,19}, {4,17}, {9,28}, {18,24}, {5,24}, {25,31}, {4,6}, {11,13}, {10,27}, {20,22}, {8,21}, {26,32}, {28,30}, {14,31}, {7,22}, {1,29}, {2,25}, {10,17}, {9,18}, {3,18}, {5,30}, {12,25}, {12,19}, {6,23}, {13,32}, {14,21}, {11,26}, {4,27}, {16,29}, {15,30}, {7,32}, {11,20}, {1,31}, {2,30}, {13,17}, {9,21}, {5,25}, {15,19}, {6,29}, {13,22}, {10,22}, {3,28}, {16,23}, {7,27}, {14,18}, {8,31}, {15,24}, {16,20}, {6,26}, {1,32}, {2,32}, {15,17}, {9,23}, {5,27}, {13,19}, {10,24}, {3,31}, {11,23}, {11,21}, {8,28}, {14,20}, {7,25}, {4,32}, {12,24}, {8,26}, {3,29}, {1,16}, {2,31}, {16,17}, {9,24}, {16,18}, {5,28}, {14,19}, {6,28}, {10,23}, {12,21}, {6,27}, {12,22}, {4,30}, {7,26}, {13,20}, {4,29}, {1,8}, {2,15}, {17,32}, {8,9}, {15,18}, {5,12}, {8,25}, {19,30}, {7,10}, {3,30}, {21,28}, {22,27}, {11,22}, {3,14}, {20,29}, {23,26}, {18,31}, {1,4}, {2,7}, {17,24}, {9,16}, {4,5}, {24,25}, {19,22}, {6,11}, {4,13}, {10,15}, {20,21}, {27,30}, {11,14}, {26,31}, {28,29}, {25,32}, {1,18}, {2,3}, {17,20}, {9,12}, {18,23}, {5,8}, {18,19}, {3,6}, {12,13}, {10,11}, {21,24}, {26,27}, {14,15}, {6,7}, {29,32}, {30,31}, {13,16}, {1,25}, {2,17}, {9,26}, {5,22}, {25,28}, {4,19}, {10,25}, {22,23}, {6,21}, {12,27}, {14,29}, {7,24}, {3,20}, {16,31}, {15,32}, {8,23}, {1,13}, {2,26}, {9,17}, {5,29}, {11,19}, {13,30}, {10,18}, {13,21}, {11,28}, {3,27}, {14,22}, {7,31}, {12,20}, {8,32}, {16,24}, {4,28}, {1,23}, {2,14}, {17,29}, {5,9}, {19,31}, {6,30}, {6,10}, {15,23}, {21,25}, {23,27}, {7,11}, {20,32}, {22,26}, {4,16}, {8,12}, {18,30}, {1,28}, {2,24}, {7,17}, {9,31}, {5,19}, {10,32}, {3,15}, {3,21}, {24,28}, {13,27}, {14,28}, {6,20}, {16,26}, {11,29}, {8,18}, {4,22}, {15,25}, {1,30}, {2,27}, {12,17}, {9,20}, {5,32}, {10,19}, {16,21}, {12,30}, {14,23}, {7,30}, {3,26}, {8,29}, {6,31}, {4,25}, {11,18}, {13,24}, {1,15}, {2,29}, {14,17}, {9,22}, {5,26}, {16,19}, {10,21}, {8,27}, {15,22}, {7,28}, {15,20}, {4,31}, {3,32}, {13,18}, {6,25}, {12,23}, {1,24}, {2,16}, {17,31}, {7,9}, {5,11}, {19,29}, {8,10}, {21,27}, {4,14}, {11,24}, {20,30}, {24,26}, {18,32}, {23,25}, {3,13}, {22,28}, {1,12}, {2,23}, {8,17}, {9,32}, {5,20}, {6,19}, {6,12}, {10,31}, {4,21}, {14,27}, {7,18}, {15,26}, {12,29}, {16,25}, {13,28}, {11,30}, {1,22}, {2,11}, {17,28}, {4,9}, {5,16}, {19,26}, {3,10}, {3,22}, {21,32}, {18,27}, {7,14}, {20,25}, {24,29}, {22,31}, {8,13}, {23,30}, {6,15}, {1,11}, {2,21}, {6,17}, {9,30}, {5,18}, {8,19}, {10,29}, {16,27}, {14,25}, {7,20}, {13,26}, {12,31}, {11,32}, {4,23}, {15,28}, {3,24}, {1,6}, {2,12}, {17,27}, {3,9}, {5,15}, {19,25}, {4,10}, {21,31}, {8,14}, {7,13}, {20,26}, {23,29}, {22,32}, {6,16}, {18,28}, {24,30}, {1,3}, {2,5}, {17,22}, {9,14}, {19,24}, {10,13}, {18,21}, {27,32}, {4,7}, {20,23}, {26,29}, {28,31}, {11,16}, {3,8}, {25,30}, {12,15}, {2,4}, {17,19}, {9,11}, {5,7}, {10,12}, {21,23}, {25,27}, {14,16}, {18,20}, {26,28}, {29,31}, {30,32}, {6,8}, {13,15}, {22,24}, {17,18}, {9,10}, {5,6}, {19,20}, {21,22}, {27,28}, {13,14}, {7,8}, {25,26}, {29,30}, {31,32}, {15,16}, {3,4}, {23,24}, {11,12}, {9,25}, {5,21}, {3,19}, {10,26}, {11,27}, {14,30}, {7,23}, {4,20}, {13,29}, {15,31}, {16,32}, {8,24}, {12,28}, {6,22}, {5,13}, {19,27}, {21,29}, {6,14}, {7,15}, {20,28}, {23,31}, {24,32}, {8,16}, {4,12}, {22,30}, {3,11}, {19,23}, {27,31}, {3,7}, {20,24}, {28,32}, {12,16}, {4,8}, {11,15} } ................................................................... Symmetric connected graphs of order 33 Symmetric graph 1 of order 33 Valency 2 Diameter 16 Girth 33 Automorphism group of order 66 Number of arcs = 66 Number of 2-arcs = 66 2-arc-transitive true Edge-set { {1,4}, {30,32}, {23,27}, {17,21}, {11,14}, {6,9}, {3,31}, {26,29}, {20,22}, {13,16}, {8,10}, {2,5}, {28,33}, {24,25}, {18,19}, {12,15}, {4,7}, {1,32}, {27,30}, {21,23}, {14,17}, {9,11}, {3,6}, {29,31}, {22,26}, {16,20}, {10,13}, {5,8}, {2,33}, {25,28}, {19,24}, {15,18}, {7,12} } Symmetric graph 2 of order 33 Valency 4 Diameter 5 Girth 4 Automorphism group of order 132 Number of arcs = 132 Number of 2-arcs = 396 2-arc-transitive false Edge-set { {1,4}, {20,22}, {3,31}, {4,9}, {17,20}, {16,19}, {30,32}, {22,26}, {3,5}, {2,4}, {14,17}, {1,6}, {15,18}, {25,29}, {9,11}, {20,24}, {19,23}, {2,32}, {21,22}, {3,33}, {11,14}, {1,31}, {10,13}, {26,28}, {5,9}, {4,8}, {17,21}, {6,7}, {18,19}, {29,33}, {16,20}, {28,32}, {30,31}, {7,12}, {11,15}, {24,27}, {23,26}, {2,5}, {22,25}, {3,6}, {14,16}, {13,18}, {15,17}, {27,29}, {25,30}, {28,33}, {9,10}, {8,12}, {21,23}, {7,11}, {19,24}, {2,33}, {1,32}, {12,13}, {10,14}, {27,28}, {26,30}, {5,7}, {6,8}, {18,21}, {29,31}, {12,15}, {23,27}, {24,25}, {13,16}, {8,10} } Symmetric graph 3 of order 33 Valency 6 Diameter 5 Girth 4 Automorphism group of order 7981535232 Number of arcs = 198 Number of 2-arcs = 990 2-arc-transitive false Edge-set { {1,4}, {21,24}, {17,19}, {6,8}, {2,4}, {3,33}, {23,25}, {21,22}, {19,24}, {18,19}, {16,20}, {14,16}, {7,10}, {6,9}, {2,5}, {4,8}, {3,4}, {3,31}, {1,5}, {1,32}, {1,33}, {28,32}, {27,30}, {24,27}, {23,26}, {21,23}, {19,22}, {18,20}, {24,25}, {20,24}, {16,19}, {17,20}, {15,16}, {18,21}, {13,17}, {16,21}, {14,17}, {13,18}, {11,13}, {12,15}, {8,12}, {4,7}, {7,11}, {6,7}, {2,6}, {4,9}, {3,5}, {1,31}, {8,10}, {5,8}, {3,32}, {29,32}, {3,6}, {2,31}, {2,32}, {30,33}, {1,6}, {2,33}, {28,33}, {30,31}, {25,30}, {29,31}, {26,29}, {25,29}, {22,26}, {27,28}, {23,27}, {19,23}, {24,26}, {20,22}, {17,21}, {15,17}, {22,27}, {22,25}, {13,16}, {14,18}, {12,13}, {20,23}, {15,18}, {10,14}, {11,14}, {10,15}, {9,12}, {9,11}, {5,9}, {7,12}, {8,11}, {29,33}, {5,7}, {9,10}, {30,32}, {28,31}, {26,30}, {25,28}, {27,29}, {26,28}, {12,14}, {10,13}, {11,15} } Symmetric graph 4 of order 33 Valency 10 Diameter 3 Girth 3 Automorphism group of order 330 Number of arcs = 330 Number of 2-arcs = 2970 2-arc-transitive false Edge-set { {1,4}, {23,28}, {20,33}, {8,21}, {5,28}, {1,26}, {8,25}, {18,27}, {12,26}, {8,24}, {28,31}, {15,28}, {16,20}, {14,18}, {12,18}, {13,32}, {13,17}, {10,15}, {16,22}, {18,19}, {6,12}, {2,8}, {9,28}, {5,8}, {3,28}, {26,33}, {14,25}, {4,32}, {2,13}, {10,32}, {13,22}, {3,6}, {1,7}, {6,31}, {1,15}, {5,11}, {3,23}, {4,14}, {25,32}, {13,27}, {10,22}, {22,32}, {18,29}, {12,21}, {8,16}, {10,28}, {18,24}, {12,31}, {8,30}, {19,28}, {2,18}, {7,33}, {6,29}, {1,21}, {3,11}, {7,23}, {6,20}, {22,30}, {19,32}, {17,28}, {11,20}, {2,22}, {9,32}, {3,20}, {12,24}, {24,31}, {21,30}, {5,19}, {4,23}, {2,33}, {3,14}, {7,18}, {6,13}, {1,17}, {4,7}, {13,29}, {10,27}, {22,26}, {18,33}, {12,14}, {8,11}, {2,10}, {9,22}, {12,30}, {27,28}, {29,32}, {13,21}, {20,26}, {19,24}, {17,21}, {7,20}, {4,30}, {3,25}, {7,27}, {8,31}, {24,25}, {20,29}, {4,21}, {3,16}, {7,10}, {26,30}, {19,25}, {10,19}, {6,22}, {2,19}, {6,9}, {27,31}, {21,23}, {5,33}, {1,29}, {17,32}, {11,13}, {1,32}, {15,20}, {17,23}, {11,33}, {4,16}, {8,13}, {4,10}, {11,29}, {3,9}, {7,29}, {6,27}, {15,26}, {16,25}, {17,26}, {11,25}, {30,33}, {14,30}, {11,17}, {9,12}, {14,19}, {6,18}, {9,26}, {25,29}, {23,27}, {11,23}, {7,15}, {16,30}, {20,22}, {21,27}, {9,17}, {5,26}, {1,24}, {3,31}, {21,31}, {5,15}, {1,12}, {23,33}, {14,33}, {24,29}, {15,31}, {15,16}, {2,30}, {15,24}, {10,16}, {4,25}, {2,27}, {9,14}, {5,17}, {5,24}, {16,31}, {9,19}, {2,5}, {14,23} } Symmetric graph 5 of order 33 Valency 20 Diameter 2 Girth 3 Automorphism group of order 239500800 Number of arcs = 660 Number of 2-arcs = 12540 2-arc-transitive false Edge-set { {1,4}, {19,30}, {11,14}, {3,8}, {6,28}, {15,22}, {19,22}, {6,20}, {10,17}, {2,28}, {4,13}, {16,24}, {23,33}, {8,16}, {28,33}, {7,28}, {13,29}, {13,33}, {21,26}, {2,21}, {4,12}, {23,30}, {14,24}, {17,31}, {25,32}, {11,18}, {9,31}, {6,31}, {17,25}, {2,11}, {4,9}, {2,4}, {4,16}, {1,23}, {5,24}, {11,23}, {9,24}, {9,25}, {1,30}, {9,21}, {12,30}, {14,30}, {14,20}, {3,18}, {17,22}, {22,32}, {10,33}, {7,26}, {12,26}, {15,32}, {19,27}, {5,10}, {7,18}, {10,28}, {7,13}, {26,33}, {3,26}, {15,21}, {12,19}, {5,30}, {14,18}, {21,30}, {12,14}, {30,31}, {14,25}, {18,19}, {11,31}, {17,29}, {15,18}, {19,31}, {5,17}, {18,32}, {5,26}, {3,19}, {6,11}, {5,9}, {18,30}, {3,14}, {3,22}, {6,22}, {7,22}, {22,29}, {20,32}, {10,27}, {16,33}, {12,16}, {8,33}, {11,13}, {4,25}, {1,16}, {1,20}, {12,24}, {8,23}, {8,27}, {4,32}, {16,27}, {2,13}, {4,21}, {4,23}, {11,25}, {1,9}, {20,25}, {1,10}, {8,14}, {20,28}, {3,29}, {6,15}, {22,27}, {3,9}, {6,30}, {14,22}, {20,22}, {3,10}, {6,7}, {22,26}, {8,32}, {27,28}, {10,15}, {7,19}, {1,33}, {24,32}, {23,27}, {8,10}, {29,33}, {15,26}, {12,32}, {25,29}, {1,15}, {8,20}, {15,28}, {13,19}, {5,29}, {3,32}, {6,27}, {10,22}, {16,20}, {16,28}, {5,33}, {7,12}, {8,29}, {13,27}, {14,31}, {9,17}, {15,23}, {19,24}, {26,30}, {11,29}, {14,17}, {6,18}, {2,17}, {27,31}, {2,25}, {21,23}, {9,30}, {5,19}, {11,21}, {2,7}, {4,29}, {24,28}, {13,23}, {2,33}, {5,20}, {10,18}, {3,28}, {6,13}, {16,22}, {22,33}, {7,16}, {13,20}, {10,21}, {4,28}, {13,16}, {16,25}, {6,12}, {8,17}, {2,27}, {13,24}, {4,8}, {11,19}, {9,11}, {12,17}, {18,27}, {2,31}, {17,21}, {1,11}, {24,25}, {1,26}, {3,5}, {2,24}, {1,29}, {5,15}, {12,20}, {21,33}, {7,31}, {9,15}, {4,14}, {1,6}, {18,26}, {18,24}, {23,31}, {28,32}, {3,25}, {3,12}, {9,18}, {5,14}, {18,23}, {24,31}, {9,12}, {7,29}, {15,29}, {13,32}, {21,27}, {2,20}, {4,10}, {23,28}, {16,31}, {25,33}, {11,16}, {9,33}, {4,31}, {7,23}, {24,29}, {9,13}, {2,30}, {26,31}, {14,28}, {6,33}, {17,26}, {2,12}, {17,23}, {8,15}, {19,28}, {14,33}, {20,26}, {27,32}, {15,19}, {19,25}, {20,29}, {1,19}, {5,11}, {7,14}, {22,30}, {1,27}, {17,32}, {10,20}, {5,32}, {7,32}, {18,20}, {5,16}, {1,24}, {5,23}, {12,23}, {8,24}, {9,27}, {7,21}, {12,29}, {13,30}, {14,21}, {2,18}, {10,31}, {7,25}, {11,26}, {15,31}, {10,30}, {4,18}, {1,17}, {3,21}, {10,25}, {1,7}, {2,22}, {4,22}, {11,28}, {18,33}, {6,24}, {2,8}, {11,22}, {9,22}, {12,27}, {8,26}, {8,19}, {3,16}, {12,33}, {21,29}, {27,29}, {29,31}, {15,25}, {17,19}, {11,32}, {18,29}, {20,31}, {6,17}, {5,27}, {16,30}, {1,14}, {3,23}, {21,32}, {10,13}, {4,26}, {10,24}, {3,13}, {6,21}, {30,32}, {14,27}, {19,33}, {9,20}, {13,26}, {4,19}, {16,21}, {2,15}, {17,28}, {15,16}, {6,25}, {6,8}, {2,5}, {5,7}, {24,26}, {26,28}, {12,15}, {1,32}, {7,10}, {3,31}, {8,30}, {21,24}, {25,30}, {13,17}, {20,23}, {9,28}, {8,11}, {23,25}, {3,6} } Symmetric graph 6 of order 33 Valency 22 Diameter 2 Girth 3 Automorphism group of order 381608820557217792000000 Number of arcs = 726 Number of 2-arcs = 15246 2-arc-transitive false Edge-set { {1,12}, {1,23}, {11,29}, {12,23}, {20,29}, {19,29}, {16,24}, {11,20}, {3,19}, {2,16}, {11,19}, {10,16}, {2,15}, {3,29}, {2,24}, {11,33}, {10,28}, {2,28}, {10,24}, {1,30}, {9,23}, {19,33}, {16,28}, {15,28}, {17,24}, {13,30}, {13,23}, {15,24}, {12,30}, {22,23}, {20,25}, {10,17}, {1,13}, {9,13}, {5,15}, {4,12}, {4,22}, {3,20}, {10,15}, {9,12}, {1,22}, {8,20}, {3,18}, {5,24}, {4,30}, {4,23}, {3,25}, {10,32}, {9,27}, {1,27}, {8,33}, {3,33}, {9,30}, {11,25}, {8,29}, {2,31}, {7,28}, {15,32}, {12,27}, {22,27}, {20,33}, {18,33}, {14,30}, {21,25}, {21,29}, {17,31}, {17,28}, {22,30}, {19,25}, {18,29}, {16,31}, {14,28}, {13,26}, {9,14}, {11,21}, {8,21}, {2,17}, {7,17}, {7,22}, {6,19}, {6,18}, {5,16}, {5,14}, {4,13}, {9,22}, {8,19}, {11,18}, {7,16}, {2,14}, {6,13}, {4,21}, {7,30}, {6,25}, {6,29}, {5,31}, {5,28}, {4,26}, {9,31}, {8,26}, {11,26}, {7,32}, {2,32}, {6,27}, {4,27}, {8,25}, {10,31}, {7,24}, {1,26}, {6,23}, {3,32}, {5,33}, {22,31}, {19,26}, {18,26}, {16,32}, {14,32}, {13,27}, {21,27}, {22,25}, {18,31}, {18,24}, {14,26}, {14,23}, {21,32}, {21,33}, {18,25}, {15,31}, {14,24}, {12,26}, {21,23}, {20,32}, {17,33}, {17,27}, {8,22}, {10,18}, {7,18}, {1,14}, {6,14}, {3,21}, {5,21}, {9,18}, {8,15}, {8,14}, {7,12}, {7,21}, {6,20}, {6,17}, {5,17}, {8,18}, {7,15}, {10,14}, {6,12}, {1,21}, {5,20}, {3,17}, {4,17}, {5,13}, {9,25}, {8,31}, {8,24}, {7,26}, {7,23}, {6,32}, {6,33}, {5,27}, {8,30}, {7,25}, {10,25}, {6,31}, {1,31}, {5,26}, {3,26}, {4,32}, {5,32}, {7,31}, {9,26}, {6,30}, {11,32}, {5,29}, {2,27}, {4,28}, {4,33}, {3,27}, {18,30}, {15,25}, {14,25}, {12,31}, {21,31}, {20,26}, {17,26}, {17,32}, {13,32}, {19,31}, {15,26}, {15,30}, {22,32}, {22,29}, {18,27}, {18,28}, {14,33}, {14,27}, {14,31}, {22,26}, {21,30}, {19,32}, {17,29}, {16,27}, {13,28}, {13,33}, {20,27}, {21,28}, {7,19}, {9,15}, {6,15}, {11,22}, {5,22}, {2,18}, {4,18}, {4,14}, {3,14}, {11,14}, {10,22}, {10,21}, {9,19}, {9,17}, {8,16}, {8,13}, {7,13}, {7,20}, {6,21}, {7,14}, {6,22}, {9,21}, {5,19}, {11,17}, {4,16}, {2,13}, {3,13}, {4,20}, {2,21}, {6,16}, {11,31}, {10,26}, {10,30}, {9,32}, {9,29}, {8,27}, {8,28}, {7,33}, {7,27}, {6,28}, {7,29}, {6,24}, {9,24}, {5,30}, {11,30}, {4,25}, {2,25}, {3,31}, {4,31}, {2,26}, {6,26}, {8,32}, {5,25}, {10,27}, {4,24}, {1,33}, {3,23}, {3,28}, {2,33}, {5,23}, {1,32}, {14,29}, {22,24}, {21,24}, {19,30}, {17,30}, {16,25}, {13,25}, {13,31}, {20,31}, {21,26}, {16,26}, {12,32}, {12,25}, {19,27}, {19,24}, {15,33}, {15,23}, {22,28}, {22,33}, {18,23}, {18,32}, {17,25}, {15,27}, {13,24}, {12,33}, {20,23}, {20,28}, {16,33}, {17,23}, {8,12}, {5,12}, {10,19}, {4,19}, {1,15}, {3,15}, {3,22}, {2,22}, {5,18}, {1,18}, {1,17}, {11,15}, {11,13}, {10,12}, {10,20}, {9,20}, {9,16}, {8,17}, {4,15}, {10,13}, {3,12}, {1,20}, {2,20}, {3,16}, {1,25}, {11,27}, {11,24}, {10,33}, {10,23}, {9,28}, {9,33}, {8,23}, {4,29}, {10,29}, {3,24}, {1,24}, {2,30}, {3,30}, {11,28}, {2,29}, {2,23}, {1,28}, {15,29}, {13,29}, {12,24}, {20,24}, {20,30}, {16,30}, {12,28}, {12,29}, {19,23}, {19,28}, {16,29}, {16,23}, {11,12}, {2,12}, {2,19}, {1,19}, {1,16}, {11,16}, {1,29}, {11,23} } Symmetric graph 7 of order 33 Valency 30 Diameter 2 Girth 3 Automorphism group of order 14481697524940800 Number of arcs = 990 Number of 2-arcs = 28710 2-arc-transitive false Edge-set { {1,4}, {28,33}, {9,30}, {22,27}, {5,18}, {2,24}, {4,21}, {16,19}, {14,27}, {10,31}, {7,22}, {18,29}, {13,28}, {14,33}, {1,9}, {11,15}, {2,23}, {9,19}, {10,27}, {4,25}, {16,33}, {3,16}, {14,19}, {10,23}, {6,22}, {8,22}, {5,12}, {9,27}, {10,18}, {2,28}, {21,30}, {5,7}, {11,31}, {17,29}, {15,28}, {2,15}, {2,21}, {4,19}, {27,33}, {20,33}, {9,25}, {11,27}, {18,23}, {11,30}, {23,29}, {9,15}, {2,10}, {4,17}, {15,33}, {16,32}, {8,14}, {1,16}, {14,20}, {6,31}, {7,32}, {2,19}, {21,27}, {4,10}, {22,33}, {22,29}, {5,28}, {14,24}, {3,31}, {7,19}, {5,25}, {16,31}, {12,23}, {6,24}, {5,11}, {7,29}, {11,28}, {14,29}, {1,28}, {2,9}, {19,27}, {18,27}, {13,27}, {3,18}, {2,20}, {21,25}, {5,19}, {27,31}, {10,17}, {15,22}, {5,24}, {4,31}, {17,23}, {6,15}, {2,7}, {11,21}, {4,29}, {12,33}, {9,24}, {7,27}, {11,18}, {11,26}, {10,20}, {23,30}, {9,13}, {3,10}, {25,32}, {8,16}, {3,26}, {17,19}, {15,29}, {1,27}, {4,33}, {9,33}, {16,27}, {14,18}, {16,23}, {6,14}, {22,31}, {9,18}, {10,13}, {25,30}, {16,29}, {3,15}, {20,31}, {7,25}, {11,25}, {6,17}, {15,32}, {18,32}, {8,13}, {5,31}, {7,31}, {3,23}, {6,19}, {5,22}, {9,23}, {6,10}, {22,28}, {5,30}, {2,29}, {21,28}, {15,19}, {2,27}, {10,19}, {8,19}, {12,27}, {10,30}, {13,29}, {3,28}, {1,25}, {15,31}, {19,25}, {4,12}, {24,33}, {7,16}, {11,14}, {18,31}, {7,13}, {25,33}, {9,16}, {12,17}, {15,24}, {8,11}, {3,29}, {19,28}, {5,14}, {1,31}, {23,33}, {6,9}, {6,27}, {2,18}, {13,21}, {3,19}, {5,10}, {5,21}, {26,31}, {4,13}, {3,33}, {17,24}, {4,15}, {2,8}, {12,21}, {4,30}, {29,33}, {20,26}, {17,25}, {1,11}, {20,23}, {26,29}, {12,15}, {7,23}, {6,11}, {27,30}, {18,21}, {11,19}, {23,27}, {9,10}, {10,22}, {11,17}, {15,23}, {9,32}, {8,10}, {16,25}, {14,16}, {21,22}, {4,8}, {20,24}, {11,23}, {6,23}, {7,30}, {11,29}, {13,25}, {3,20}, {5,20}, {25,31}, {12,32}, {8,24}, {7,26}, {10,26}, {17,22}, {1,8}, {12,20}, {3,25}, {17,30}, {7,14}, {2,17}, {15,21}, {4,32}, {8,33}, {16,22}, {24,31}, {4,7}, {6,28}, {14,22}, {1,5}, {7,15}, {2,11}, {19,29}, {27,28}, {2,33}, {1,15}, {27,32}, {4,24}, {8,23}, {6,12}, {22,30}, {5,29}, {20,28}, {11,16}, {15,20}, {2,25}, {6,33}, {13,18}, {3,11}, {19,23}, {5,9}, {10,25}, {3,8}, {12,19}, {20,27}, {18,25}, {21,23}, {24,32}, {7,18}, {11,13}, {6,29}, {2,5}, {9,31}, {7,10}, {25,28}, {16,30}, {17,27}, {15,18}, {2,32}, {8,21}, {19,32}, {8,27}, {10,29}, {1,12}, {15,30}, {7,33}, {14,31}, {1,7}, {16,26}, {9,12}, {12,18}, {13,24}, {9,11}, {1,29}, {1,32}, {4,9}, {6,18}, {24,25}, {30,31}, {13,17}, {6,26}, {6,7}, {11,32}, {3,17}, {5,32}, {8,31}, {19,24}, {4,27}, {10,14}, {1,22}, {5,15}, {2,31}, {15,27}, {2,4}, {21,33}, {4,16}, {7,17}, {2,26}, {17,21}, {11,20}, {23,25}, {1,14}, {1,33}, {9,20}, {3,13}, {5,17}, {17,32}, {8,15}, {3,24}, {5,23}, {8,20}, {12,25}, {13,30}, {13,31}, {3,7}, {20,25}, {1,18}, {13,20}, {3,21}, {19,26}, {26,33}, {12,16}, {20,30}, {6,13}, {3,32}, {25,29}, {12,24}, {3,9}, {12,29}, {24,28}, {9,17}, {18,20}, {14,23}, {13,16}, {22,32}, {5,8}, {28,31}, {2,6}, {19,22}, {5,27}, {27,29}, {18,28}, {7,28}, {18,33}, {1,17}, {6,32}, {8,32}, {16,24}, {4,14}, {23,31}, {13,22}, {3,5}, {20,29}, {8,18}, {12,22}, {29,31}, {15,17}, {7,21}, {4,20}, {1,30}, {13,19}, {3,27}, {22,25}, {14,17}, {18,26}, {12,31}, {23,32}, {6,8}, {16,21}, {3,4}, {19,33}, {20,22}, {11,24}, {4,23}, {24,27}, {11,22}, {17,28}, {1,20}, {15,26}, {1,19}, {30,32}, {7,24}, {4,11}, {18,19}, {10,16}, {19,30}, {23,26}, {21,32}, {12,13}, {21,31}, {23,28}, {6,30}, {26,28}, {9,21}, {10,32}, {8,12}, {8,26}, {5,26}, {17,31}, {12,30}, {24,29}, {16,20}, {2,13}, {10,33}, {16,28}, {14,30}, {7,11}, {9,28}, {11,33}, {3,12}, {21,29}, {12,14}, {1,24}, {5,13}, {17,20}, {15,25}, {18,30}, {8,30}, {12,26}, {1,13}, {6,20}, {8,25}, {3,30}, {10,28}, {26,30}, {6,25}, {13,32}, {2,30}, {18,22}, {2,12}, {21,24}, {3,22}, {10,15}, {7,20}, {5,16}, {29,32}, {8,28}, {15,16}, {2,14}, {19,31}, {12,28}, {24,30}, {26,32}, {8,17}, {1,26}, {13,23}, {3,6}, {1,10}, {6,16}, {14,32}, {7,12}, {3,14}, {13,33}, {14,25}, {10,24}, {10,21}, {22,26}, {17,26}, {1,23}, {30,33}, {9,29}, {17,33}, {24,26}, {5,33}, {2,22}, {14,26}, {1,21}, {4,26}, {1,6}, {20,32}, {8,29}, {4,22}, {6,21}, {4,28}, {28,32}, {2,16}, {18,24}, {21,26}, {9,26}, {4,18}, {13,26}, {14,28}, {9,14}, {14,21}, {9,22} } Symmetric graph 8 of order 33 Valency 32 Diameter 1 Girth 3 Automorphism group of order 8683317618811886495518194401280000000 Number of arcs = 1056 Number of 2-arcs = 32736 2-arc-transitive true Edge-set { {1,2}, {2,3}, {19,32}, {1,31}, {3,4}, {6,19}, {30,31}, {20,32}, {14,33}, {18,32}, {4,5}, {6,30}, {29,30}, {7,20}, {14,27}, {4,18}, {21,32}, {1,12}, {13,33}, {15,33}, {5,6}, {11,30}, {28,29}, {7,31}, {3,27}, {4,27}, {8,21}, {12,28}, {13,26}, {15,28}, {15,29}, {5,19}, {22,32}, {1,9}, {12,33}, {2,13}, {1,21}, {24,33}, {16,33}, {6,7}, {3,11}, {27,28}, {12,31}, {3,22}, {7,27}, {1,8}, {18,28}, {2,26}, {4,28}, {6,29}, {5,28}, {9,22}, {9,23}, {12,25}, {13,29}, {5,21}, {22,24}, {16,29}, {7,14}, {5,18}, {16,30}, {6,20}, {2,11}, {14,28}, {23,32}, {1,26}, {11,33}, {2,10}, {1,24}, {20,33}, {3,14}, {19,24}, {20,31}, {2,22}, {9,32}, {25,33}, {17,33}, {17,32}, {7,8}, {3,28}, {26,27}, {4,12}, {22,30}, {7,29}, {1,13}, {18,20}, {2,21}, {4,23}, {6,26}, {8,28}, {2,9}, {1,25}, {19,29}, {5,15}, {19,22}, {5,29}, {7,30}, {7,11}, {10,23}, {21,26}, {11,24}, {10,24}, {16,20}, {14,30}, {24,27}, {4,20}, {6,22}, {9,11}, {23,25}, {17,30}, {25,27}, {4,17}, {8,15}, {19,26}, {11,31}, {17,31}, {4,25}, {3,17}, {7,21}, {3,12}, {13,27}, {22,31}, {7,15}, {24,32}, {10,33}, {2,27}, {1,7}, {5,33}, {17,19}, {23,31}, {2,25}, {13,32}, {21,33}, {4,15}, {6,15}, {19,30}, {20,25}, {9,14}, {12,18}, {3,23}, {10,32}, {26,33}, {8,32}, {18,33}, {16,32}, {1,10}, {8,9}, {23,28}, {25,26}, {4,29}, {5,30}, {22,29}, {5,13}, {20,30}, {21,29}, {4,26}, {8,30}, {2,14}, {1,20}, {19,21}, {13,15}, {9,19}, {5,24}, {10,29}, {9,29}, {7,23}, {5,25}, {3,10}, {24,31}, {4,14}, {6,16}, {11,14}, {20,23}, {11,27}, {8,31}, {3,26}, {8,12}, {22,26}, {8,17}, {22,27}, {7,12}, {11,25}, {13,17}, {17,21}, {15,31}, {3,19}, {25,28}, {6,9}, {12,30}, {10,12}, {24,26}, {8,16}, {8,10}, {18,31}, {4,10}, {3,16}, {26,28}, {6,8}, {10,30}, {9,16}, {14,23}, {18,25}, {20,27}, {1,18}, {10,18}, {2,16}, {5,26}, {8,29}, {6,10}, {8,22}, {9,28}, {12,26}, {4,13}, {21,30}, {24,29}, {1,23}, {18,26}, {25,32}, {9,33}, {6,31}, {2,8}, {28,32}, {6,33}, {14,16}, {8,18}, {16,19}, {14,32}, {22,33}, {12,32}, {5,16}, {18,29}, {7,16}, {18,27}, {2,4}, {12,16}, {8,13}, {10,15}, {15,21}, {13,19}, {4,24}, {11,32}, {1,17}, {23,33}, {27,33}, {7,32}, {19,33}, {31,33}, {15,32}, {9,10}, {21,23}, {24,25}, {5,10}, {16,22}, {27,30}, {4,11}, {23,30}, {6,14}, {20,28}, {21,31}, {3,13}, {9,27}, {5,27}, {9,31}, {3,25}, {3,15}, {15,19}, {19,31}, {20,22}, {12,14}, {14,24}, {10,20}, {6,25}, {11,13}, {17,27}, {21,27}, {8,24}, {10,26}, {11,16}, {6,17}, {13,18}, {15,30}, {7,17}, {12,15}, {21,24}, {10,13}, {18,23}, {9,13}, {21,25}, {23,27}, {9,18}, {16,25}, {26,29}, {6,11}, {14,18}, {18,22}, {1,16}, {2,18}, {2,6}, {5,8}, {7,10}, {3,21}, {13,31}, {17,20}, {13,22}, {7,9}, {9,17}, {17,25}, {17,23}, {1,19}, {2,15}, {5,11}, {23,29}, {27,29}, {7,22}, {5,7}, {10,17}, {17,24}, {15,24}, {10,19}, {16,31}, {21,28}, {12,29}, {6,13}, {2,19}, {31,32}, {1,15}, {11,19}, {15,23}, {19,25}, {6,27}, {11,22}, {7,28}, {9,30}, {23,26}, {5,14}, {24,30}, {20,29}, {4,9}, {25,30}, {2,24}, {19,27}, {26,32}, {8,33}, {3,18}, {3,9}, {19,23}, {25,31}, {29,32}, {7,33}, {3,33}, {27,32}, {15,17}, {15,25}, {14,17}, {17,28}, {27,31}, {17,26}, {19,28}, {29,31}, {3,5}, {23,24}, {14,20}, {13,30}, {1,5}, {28,33}, {29,33}, {6,32}, {1,28}, {2,33}, {1,33}, {2,32}, {1,14}, {10,11}, {13,16}, {11,17}, {28,31}, {3,6}, {5,12}, {4,8}, {1,22}, {2,12}, {6,24}, {10,28}, {6,28}, {11,29}, {18,21}, {4,16}, {18,30}, {15,20}, {11,21}, {12,17}, {13,23}, {7,26}, {8,27}, {22,28}, {6,12}, {9,25}, {17,22}, {7,18}, {16,27}, {14,19}, {16,26}, {22,25}, {9,12}, {10,14}, {20,24}, {24,28}, {4,7}, {26,31}, {11,15}, {2,17}, {3,7}, {11,23}, {8,11}, {4,22}, {18,24}, {2,20}, {11,20}, {10,21}, {16,24}, {10,16}, {28,30}, {4,6}, {8,23}, {11,26}, {11,28}, {11,18}, {16,23}, {13,14}, {4,21}, {3,24}, {3,20}, {14,31}, {1,32}, {12,20}, {2,5}, {14,22}, {8,14}, {20,26}, {3,29}, {12,23}, {10,31}, {12,27}, {3,8}, {2,29}, {4,19}, {6,21}, {16,18}, {30,32}, {1,27}, {4,33}, {1,29}, {15,18}, {10,22}, {2,7}, {1,30}, {5,32}, {30,33}, {4,32}, {1,3}, {32,33}, {3,32}, {11,12}, {5,17}, {22,23}, {5,9}, {25,29}, {2,23}, {1,11}, {19,20}, {7,25}, {5,23}, {17,29}, {4,31}, {16,21}, {12,22}, {7,13}, {8,19}, {15,26}, {20,21}, {12,13}, {26,30}, {12,24}, {9,15}, {12,19}, {12,21}, {13,25}, {3,30}, {9,24}, {10,25}, {5,22}, {5,31}, {15,22}, {8,25}, {14,15}, {13,21}, {4,30}, {13,24}, {8,20}, {17,18}, {13,28}, {6,23}, {5,20}, {2,30}, {14,29}, {1,4}, {2,28}, {1,6}, {2,31}, {21,22}, {6,18}, {16,28}, {8,26}, {10,27}, {9,20}, {14,25}, {13,20}, {9,21}, {14,21}, {14,26}, {16,17}, {9,26}, {15,16}, {18,19}, {7,24}, {3,31}, {15,27}, {7,19} } ................................................................... Symmetric connected graphs of order 34 Symmetric graph 1 of order 34 Valency 2 Diameter 17 Girth 34 Automorphism group of order 68 Number of arcs = 68 Number of 2-arcs = 68 2-arc-transitive true Edge-set { {1,3}, {25,28}, {16,17}, {5,8}, {30,32}, {20,22}, {9,11}, {1,33}, {23,25}, {14,16}, {4,5}, {27,30}, {18,20}, {7,9}, {31,33}, {21,23}, {12,14}, {2,4}, {26,27}, {15,18}, {6,7}, {29,31}, {19,21}, {10,12}, {2,34}, {24,26}, {13,15}, {3,6}, {28,29}, {17,19}, {8,10}, {32,34}, {22,24}, {11,13} } Symmetric graph 2 of order 34 Valency 4 Diameter 5 Girth 4 Automorphism group of order 136 Number of arcs = 136 Number of 2-arcs = 408 2-arc-transitive false Edge-set { {1,3}, {14,15}, {15,24}, {25,28}, {4,29}, {1,28}, {2,4}, {4,6}, {9,18}, {8,16}, {23,25}, {6,14}, {15,18}, {13,16}, {16,23}, {16,17}, {23,32}, {22,30}, {11,14}, {20,27}, {3,5}, {1,9}, {17,25}, {29,32}, {28,30}, {4,11}, {26,27}, {3,30}, {2,27}, {27,29}, {3,12}, {2,10}, {1,33}, {7,33}, {21,29}, {5,31}, {17,19}, {24,31}, {14,22}, {9,12}, {8,10}, {25,33}, {6,7}, {18,26}, {21,23}, {10,17}, {7,15}, {24,26}, {5,13}, {5,8}, {22,24}, {13,21}, {11,19}, {8,34}, {31,34}, {12,20}, {2,34}, {20,21}, {7,9}, {6,32}, {10,11}, {12,13}, {19,28}, {30,31}, {18,20}, {26,34}, {19,22}, {32,33} } Symmetric graph 3 of order 34 Valency 4 Diameter 8 Girth 4 Automorphism group of order 4456448 Number of arcs = 136 Number of 2-arcs = 408 2-arc-transitive false Edge-set { {1,3}, {11,13}, {5,7}, {21,23}, {16,18}, {15,18}, {9,12}, {31,33}, {25,28}, {26,28}, {19,21}, {20,21}, {19,22}, {13,15}, {7,9}, {2,3}, {30,31}, {29,31}, {24,25}, {23,25}, {30,32}, {24,26}, {18,20}, {18,19}, {12,13}, {6,7}, {2,34}, {2,33}, {1,34}, {27,30}, {1,33}, {28,30}, {5,8}, {27,29}, {28,29}, {21,24}, {22,23}, {10,12}, {4,6}, {3,6}, {10,11}, {4,5}, {32,34}, {9,11}, {3,5}, {31,34}, {15,17}, {32,33}, {25,27}, {20,22}, {14,15}, {14,16}, {8,10}, {13,16}, {7,10}, {8,9}, {1,4}, {2,4}, {29,32}, {23,26}, {17,20}, {17,19}, {11,14}, {12,14}, {6,8}, {22,24}, {16,17}, {26,27} } Symmetric graph 4 of order 34 Valency 8 Diameter 3 Girth 4 Automorphism group of order 272 Number of arcs = 272 Number of 2-arcs = 1904 2-arc-transitive false Edge-set { {1,3}, {17,20}, {11,28}, {1,19}, {9,28}, {16,24}, {2,20}, {20,28}, {24,31}, {5,32}, {18,21}, {19,27}, {1,28}, {19,24}, {23,32}, {21,25}, {26,30}, {4,34}, {2,4}, {2,27}, {20,23}, {24,28}, {2,32}, {20,21}, {22,26}, {30,34}, {4,5}, {25,29}, {6,7}, {9,12}, {18,19}, {12,27}, {23,27}, {1,31}, {19,22}, {28,32}, {21,24}, {26,27}, {1,34}, {4,19}, {29,33}, {3,6}, {7,9}, {16,18}, {12,30}, {5,8}, {13,15}, {14,29}, {10,11}, {15,31}, {10,27}, {15,23}, {27,31}, {22,23}, {25,28}, {2,33}, {3,20}, {24,26}, {32,34}, {4,21}, {27,29}, {6,23}, {2,18}, {12,20}, {8,10}, {15,17}, {11,29}, {11,13}, {14,31}, {10,25}, {7,15}, {14,16}, {13,30}, {17,33}, {8,26}, {8,34}, {16,32}, {17,25}, {6,31}, {17,22}, {23,25}, {31,33}, {3,22}, {28,30}, {5,24}, {1,17}, {11,19}, {29,32}, {6,21}, {9,26}, {18,34}, {4,12}, {8,23}, {22,29}, {1,10}, {15,19}, {12,14}, {13,32}, {8,16}, {16,33}, {25,34}, {6,13}, {14,17}, {7,25}, {7,33}, {14,21}, {9,13}, {18,26}, {3,30}, {1,5}, {3,33}, {30,31}, {5,22}, {3,11}, {7,24}, {21,30}, {2,9}, {16,20}, {15,34}, {4,29}, {10,18}, {12,15}, {13,22}, {26,33}, {3,8}, {2,6}, {5,14}, {13,18}, {5,9}, {10,14}, {7,11}, {9,17}, {11,16}, {4,7}, {8,12}, {6,10} } Symmetric graph 5 of order 34 Valency 8 Diameter 3 Girth 4 Automorphism group of order 8912896 Number of arcs = 272 Number of 2-arcs = 1904 2-arc-transitive false Edge-set { {1,3}, {7,16}, {22,24}, {26,28}, {10,17}, {3,30}, {13,21}, {31,33}, {17,20}, {8,15}, {6,7}, {22,29}, {1,4}, {4,11}, {23,31}, {26,27}, {12,20}, {6,8}, {25,27}, {9,18}, {26,34}, {17,19}, {3,5}, {8,16}, {21,24}, {8,10}, {14,21}, {29,31}, {2,27}, {32,33}, {9,12}, {6,13}, {25,34}, {18,19}, {14,22}, {32,34}, {25,33}, {11,20}, {5,8}, {7,33}, {20,22}, {25,28}, {10,18}, {4,30}, {17,25}, {15,18}, {2,4}, {4,12}, {5,31}, {27,30}, {14,15}, {23,32}, {13,16}, {1,34}, {11,19}, {5,7}, {2,3}, {3,12}, {24,32}, {22,23}, {10,12}, {6,14}, {18,20}, {23,26}, {17,26}, {3,6}, {13,22}, {31,34}, {7,15}, {21,29}, {8,34}, {19,27}, {7,9}, {21,23}, {8,9}, {20,27}, {29,32}, {2,28}, {1,28}, {10,11}, {16,24}, {24,25}, {5,14}, {26,33}, {30,32}, {3,29}, {9,17}, {13,15}, {2,34}, {12,19}, {2,33}, {20,21}, {8,33}, {7,34}, {19,22}, {3,11}, {24,31}, {4,5}, {18,25}, {11,14}, {5,32}, {18,26}, {16,17}, {4,29}, {16,18}, {12,14}, {6,32}, {28,30}, {1,10}, {22,30}, {28,29}, {1,27}, {9,11}, {15,24}, {23,25}, {5,13}, {15,23}, {4,6}, {24,26}, {7,10}, {30,31}, {2,10}, {20,28}, {19,21}, {21,30}, {19,28}, {2,9}, {12,13}, {14,16}, {1,9}, {1,33}, {27,29}, {15,17}, {6,31}, {11,13}, {16,23} } Symmetric graph 6 of order 34 Valency 16 Diameter 2 Girth 3 Automorphism group of order 17825792 Number of arcs = 544 Number of 2-arcs = 8160 2-arc-transitive false Edge-set { {1,3}, {3,20}, {1,18}, {12,20}, {1,9}, {3,30}, {18,25}, {12,16}, {6,9}, {3,33}, {18,22}, {20,23}, {1,32}, {25,30}, {13,16}, {6,8}, {2,33}, {20,22}, {20,21}, {1,33}, {27,30}, {25,28}, {10,12}, {9,12}, {3,6}, {15,18}, {23,25}, {30,32}, {13,31}, {8,23}, {2,18}, {4,21}, {17,33}, {12,27}, {9,28}, {12,28}, {9,27}, {3,21}, {18,33}, {7,23}, {14,32}, {8,25}, {13,30}, {16,34}, {6,21}, {16,33}, {6,22}, {2,20}, {1,20}, {14,30}, {7,25}, {10,25}, {12,30}, {6,23}, {15,32}, {5,31}, {16,23}, {10,18}, {3,12}, {4,30}, {17,25}, {19,28}, {2,27}, {21,29}, {26,33}, {7,16}, {6,14}, {8,33}, {13,22}, {8,16}, {6,13}, {7,33}, {14,22}, {20,28}, {1,27}, {21,30}, {25,33}, {10,17}, {4,12}, {6,32}, {15,24}, {23,31}, {23,32}, {8,34}, {2,28}, {20,27}, {13,21}, {9,17}, {9,18}, {24,32}, {25,34}, {2,10}, {7,15}, {1,5}, {16,19}, {10,13}, {8,12}, {30,34}, {21,25}, {16,20}, {1,6}, {19,23}, {2,32}, {25,29}, {26,30}, {8,11}, {4,7}, {14,17}, {24,28}, {27,31}, {21,26}, {29,33}, {13,17}, {4,8}, {20,24}, {18,21}, {23,28}, {13,18}, {3,8}, {2,31}, {17,21}, {4,33}, {27,32}, {9,13}, {3,7}, {14,18}, {30,33}, {29,34}, {2,6}, {15,20}, {9,14}, {7,11}, {5,10}, {6,10}, {12,15}, {3,34}, {7,12}, {28,31}, {23,27}, {22,26}, {22,25}, {11,15}, {4,34}, {18,19}, {11,13}, {8,10}, {31,34}, {21,23}, {16,18}, {22,23}, {32,34}, {12,13}, {8,9}, {2,3}, {18,20}, {10,11}, {4,6}, {15,17}, {24,25}, {30,31}, {23,26}, {29,32}, {3,5}, {17,19}, {2,4}, {24,26}, {5,7}, {14,16}, {26,28}, {27,29}, {21,24}, {31,33}, {29,31}, {9,11}, {28,30}, {25,27}, {4,5}, {16,17}, {28,29}, {26,27}, {19,21}, {6,7}, {14,15}, {17,20}, {1,4}, {32,33}, {22,24}, {12,14}, {7,9}, {1,34}, {2,34}, {5,8}, {7,10}, {19,22}, {11,30}, {15,31}, {5,23}, {18,34}, {5,22}, {10,28}, {10,27}, {15,34}, {16,31}, {3,22}, {4,20}, {1,17}, {9,25}, {5,21}, {2,19}, {14,29}, {7,26}, {16,32}, {10,26}, {12,29}, {6,24}, {1,19}, {11,29}, {4,19}, {2,17}, {9,26}, {13,32}, {8,24}, {8,26}, {13,29}, {7,24}, {14,31}, {11,27}, {5,24}, {15,33}, {11,28}, {3,19}, {4,22}, {17,34}, {15,23}, {5,32}, {5,14}, {1,10}, {12,19}, {22,30}, {7,34}, {14,21}, {5,13}, {1,28}, {2,9}, {3,29}, {18,26}, {19,27}, {4,11}, {24,31}, {17,26}, {4,29}, {8,15}, {26,34}, {16,24}, {6,31}, {11,20}, {3,11}, {11,19}, {22,29}, {10,14}, {15,19}, {19,24}, {11,16}, {28,32}, {17,22}, {24,27}, {1,31}, {2,5}, {5,9}, {26,29}, {11,14}, {13,15} } Symmetric graph 7 of order 34 Valency 16 Diameter 3 Girth 4 Automorphism group of order 711374856192000 Number of arcs = 544 Number of 2-arcs = 8160 2-arc-transitive true Edge-set { {1,4}, {1,16}, {16,31}, {16,20}, {21,31}, {10,20}, {21,30}, {20,25}, {21,24}, {10,11}, {7,30}, {25,27}, {2,24}, {11,23}, {7,11}, {17,25}, {10,24}, {11,32}, {7,26}, {13,27}, {2,20}, {8,23}, {11,18}, {4,17}, {10,27}, {15,32}, {26,32}, {13,31}, {8,13}, {18,20}, {6,17}, {5,10}, {27,32}, {2,26}, {9,13}, {20,29}, {8,18}, {9,18}, {4,34}, {4,27}, {15,25}, {24,32}, {7,31}, {5,13}, {6,20}, {1,6}, {5,16}, {2,27}, {9,19}, {22,29}, {9,29}, {10,34}, {4,30}, {7,34}, {5,25}, {6,24}, {6,22}, {5,33}, {21,27}, {2,34}, {4,9}, {27,29}, {15,18}, {9,32}, {28,34}, {24,25}, {12,24}, {5,7}, {5,28}, {1,29}, {14,16}, {16,27}, {17,19}, {10,22}, {26,29}, {8,10}, {18,30}, {21,34}, {22,25}, {24,33}, {16,22}, {31,33}, {20,21}, {4,15}, {26,28}, {1,23}, {8,12}, {24,28}, {1,12}, {2,14}, {11,16}, {8,29}, {14,18}, {17,21}, {22,32}, {26,33}, {12,22}, {8,33}, {13,34}, {4,11}, {7,27}, {15,29}, {14,32}, {1,28}, {4,24}, {12,27}, {5,19}, {9,28}, {3,29}, {14,28}, {17,32}, {10,26}, {19,26}, {8,21}, {18,34}, {3,21}, {16,24}, {12,31}, {20,33}, {4,20}, {6,26}, {5,23}, {2,8}, {18,24}, {9,12}, {2,17}, {6,11}, {11,29}, {7,14}, {12,17}, {30,32}, {13,26}, {12,20}, {10,30}, {13,30}, {11,25}, {7,24}, {1,19}, {3,18}, {25,31}, {3,32}, {19,31}, {15,33}, {13,20}, {3,6}, {12,14}, {8,19}, {13,17}, {29,34}, {4,14}, {1,13}, {4,8}, {18,27}, {19,24}, {9,33}, {3,16}, {28,31}, {1,32}, {16,26}, {19,27}, {21,26}, {23,34}, {3,28}, {12,15}, {3,33}, {6,9}, {5,29}, {2,9}, {18,26}, {9,23}, {7,17}, {6,14}, {2,11}, {7,15}, {20,32}, {10,14}, {19,30}, {25,30}, {13,24}, {1,25}, {18,22}, {25,34}, {5,32}, {6,15}, {13,22}, {14,25}, {23,27}, {8,32}, {23,31}, {2,5}, {10,17}, {23,30}, {2,22}, {14,33}, {3,19}, {17,23}, {6,34}, {4,5}, {24,29}, {1,33}, {16,34}, {4,31}, {1,7}, {16,17}, {6,27}, {23,26}, {28,30}, {15,21}, {3,10}, {9,16}, {29,31}, {9,21}, {4,26}, {7,9}, {2,3}, {15,28}, {14,19}, {19,22}, {2,30}, {13,15}, {22,28}, {12,34}, {5,18}, {6,8}, {22,33}, {9,25}, {27,33}, {32,34}, {10,31}, {5,12}, {17,29}, {17,33}, {30,33}, {3,13}, {15,23}, {6,31}, {1,21}, {12,26}, {16,30}, {14,21}, {1,10}, {8,16}, {18,31}, {5,21}, {4,22}, {3,23}, {11,28}, {11,19}, {7,22}, {2,15}, {20,28}, {12,30}, {1,18}, {8,28}, {19,34}, {3,12}, {14,29}, {17,28}, {6,30}, {11,13}, {20,23}, {11,21}, {11,33}, {3,7}, {2,31}, {7,20}, {15,19}, {3,25}, {14,23}, {22,23}, {10,15}, {8,25} } Symmetric graph 8 of order 34 Valency 17 Diameter 2 Girth 4 Automorphism group of order 253027093011094340370432000000 Number of arcs = 578 Number of 2-arcs = 9248 2-arc-transitive true Edge-set { {1,18}, {8,28}, {17,25}, {15,21}, {3,20}, {7,18}, {14,33}, {5,31}, {6,32}, {10,30}, {4,26}, {14,28}, {17,28}, {13,23}, {12,24}, {9,27}, {13,25}, {11,19}, {17,23}, {7,21}, {16,18}, {4,21}, {3,23}, {3,33}, {10,31}, {2,34}, {12,22}, {16,20}, {1,29}, {3,18}, {14,31}, {2,30}, {7,33}, {10,33}, {6,28}, {17,24}, {11,31}, {6,18}, {10,26}, {13,26}, {9,21}, {15,34}, {2,32}, {8,22}, {6,30}, {4,24}, {5,25}, {10,28}, {17,26}, {9,23}, {7,34}, {14,26}, {13,28}, {13,21}, {3,19}, {12,33}, {1,24}, {9,30}, {17,19}, {16,21}, {16,31}, {6,29}, {5,27}, {15,32}, {9,25}, {11,34}, {8,20}, {7,19}, {12,18}, {14,27}, {17,21}, {3,21}, {16,33}, {10,29}, {15,28}, {4,19}, {16,23}, {3,31}, {6,31}, {2,26}, {13,22}, {8,34}, {12,25}, {7,29}, {2,33}, {6,24}, {9,24}, {5,19}, {12,20}, {1,27}, {11,32}, {14,29}, {15,30}, {4,20}, {2,28}, {17,22}, {1,23}, {7,31}, {6,33}, {6,26}, {13,24}, {5,21}, {3,32}, {11,29}, {2,18}, {10,24}, {9,26}, {9,19}, {16,34}, {8,31}, {15,27}, {15,20}, {14,22}, {5,28}, {13,34}, {12,19}, {12,29}, {2,27}, {4,22}, {1,25}, {11,30}, {5,23}, {7,32}, {4,18}, {3,34}, {8,33}, {10,25}, {14,24}, {9,28}, {13,19}, {16,19}, {12,31}, {6,27}, {11,26}, {1,22}, {5,30}, {17,34}, {12,21}, {16,29}, {2,29}, {15,24}, {9,20}, {5,20}, {1,32}, {4,32}, {8,23}, {3,27}, {15,31}, {2,22}, {5,22}, {1,34}, {8,18}, {14,25}, {7,30}, {10,27}, {11,28}, {17,18}, {15,26}, {13,20}, {14,21}, {4,34}, {12,23}, {3,29}, {2,31}, {2,24}, {9,22}, {1,19}, {16,30}, {8,32}, {8,25}, {7,27}, {15,33}, {6,22}, {5,24}, {5,34}, {12,32}, {4,29}, {12,30}, {4,27}, {11,25}, {11,18}, {10,20}, {1,26}, {9,32}, {8,27}, {15,25}, {17,20}, {14,23}, {7,28}, {1,21}, {3,30}, {17,33}, {16,32}, {4,31}, {6,23}, {11,27}, {15,18}, {10,22}, {5,26}, {9,34}, {12,34}, {8,29}, {2,25}, {7,24}, {11,20}, {14,20}, {1,28}, {13,32}, {8,19}, {12,27}, {11,22}, {5,18}, {2,23}, {7,22}, {14,30}, {17,30}, {16,25}, {1,20}, {14,32}, {4,33}, {10,23}, {3,28}, {6,25}, {7,26}, {13,33}, {11,24}, {9,18}, {10,19}, {1,30}, {17,32}, {8,21}, {16,27}, {15,29}, {15,22}, {14,34}, {12,28}, {4,30}, {4,23}, {3,25}, {2,20}, {8,30}, {17,27}, {9,33}, {10,34}, {7,23}, {4,25}, {11,23}, {13,18}, {10,21}, {3,26}, {14,19}, {16,28}, {13,31}, {17,29}, {2,21}, {7,25}, {11,33}, {6,20}, {5,32}, {15,23}, {3,22}, {10,18}, {7,20}, {1,33}, {16,26}, {13,29}, {14,18}, {17,31}, {6,21}, {3,24}, {9,31}, {5,33}, {6,34}, {13,30}, {10,32}, {8,26}, {4,28}, {6,19}, {16,24}, {12,26}, {9,29}, {13,27}, {15,19}, {11,21}, {2,19}, {16,22}, {5,29}, {1,31}, {8,24} } Symmetric graph 9 of order 34 Valency 32 Diameter 2 Girth 3 Automorphism group of order 46620662575398912000 Number of arcs = 1088 Number of 2-arcs = 33728 2-arc-transitive false Edge-set { {1,3}, {27,33}, {10,17}, {4,21}, {16,26}, {7,17}, {20,21}, {20,34}, {5,9}, {1,31}, {24,30}, {7,11}, {21,27}, {13,20}, {5,13}, {13,22}, {13,25}, {5,18}, {1,19}, {15,27}, {17,34}, {10,25}, {8,32}, {11,24}, {12,27}, {4,20}, {5,16}, {13,29}, {3,13}, {5,29}, {19,29}, {3,6}, {29,32}, {3,23}, {5,8}, {1,22}, {14,27}, {14,17}, {2,4}, {16,29}, {7,22}, {21,25}, {17,32}, {20,23}, {12,16}, {28,33}, {24,25}, {12,32}, {4,23}, {11,16}, {13,34}, {9,13}, {1,5}, {1,30}, {9,29}, {3,7}, {29,33}, {3,10}, {1,7}, {9,14}, {7,14}, {6,33}, {2,10}, {9,16}, {7,33}, {26,33}, {10,31}, {5,12}, {1,28}, {19,27}, {6,17}, {4,30}, {4,16}, {7,30}, {28,34}, {9,18}, {1,9}, {11,19}, {6,27}, {20,32}, {5,23}, {7,16}, {21,33}, {13,26}, {13,31}, {1,23}, {11,30}, {3,21}, {15,26}, {25,32}, {23,32}, {16,23}, {11,33}, {26,34}, {9,31}, {1,24}, {12,30}, {22,29}, {3,25}, {18,29}, {3,19}, {5,27}, {1,17}, {10,27}, {8,17}, {7,19}, {9,21}, {7,26}, {17,33}, {10,20}, {11,27}, {17,27}, {18,30}, {4,19}, {4,27}, {6,21}, {2,26}, {17,28}, {18,20}, {1,18}, {19,30}, {11,21}, {26,27}, {21,31}, {24,26}, {15,17}, {1,11}, {3,27}, {4,14}, {14,16}, {6,7}, {2,21}, {10,34}, {8,9}, {1,34}, {9,30}, {10,11}, {8,27}, {3,22}, {15,25}, {8,18}, {19,22}, {18,27}, {17,19}, {14,24}, {12,14}, {4,6}, {2,16}, {13,16}, {13,33}, {5,26}, {27,30}, {29,31}, {3,24}, {15,29}, {3,34}, {17,31}, {10,24}, {8,12}, {20,33}, {5,10}, {2,31}, {24,29}, {16,32}, {23,33}, {31,33}, {1,26}, {30,31}, {21,24}, {12,26}, {22,31}, {15,18}, {19,34}, {25,27}, {10,23}, {8,11}, {9,19}, {32,33}, {14,33}, {10,14}, {4,5}, {1,16}, {7,27}, {17,21}, {4,17}, {16,20}, {7,12}, {21,28}, {11,14}, {5,19}, {11,31}, {24,27}, {7,21}, {21,26}, {13,17}, {4,24}, {4,7}, {16,21}, {8,10}, {8,22}, {14,34}, {4,34}, {6,20}, {2,5}, {28,31}, {18,24}, {15,21}, {8,13}, {17,22}, {8,14}, {20,24}, {4,31}, {16,24}, {15,20}, {5,34}, {25,31}, {24,32}, {2,7}, {21,29}, {12,17}, {4,33}, {10,16}, {30,34}, {4,9}, {6,11}, {2,27}, {20,28}, {20,25}, {12,18}, {19,28}, {22,27}, {17,25}, {10,18}, {8,19}, {17,24}, {12,20}, {4,12}, {16,28}, {19,33}, {6,10}, {2,32}, {23,29}, {22,28}, {14,19}, {6,14}, {4,8}, {16,22}, {14,21}, {25,30}, {4,32}, {23,30}, {4,11}, {6,34}, {2,9}, {1,29}, {3,30}, {3,26}, {5,31}, {4,10}, {8,16}, {9,15}, {7,34}, {25,33}, {10,32}, {7,29}, {22,33}, {7,15}, {21,34}, {12,23}, {11,28}, {13,21}, {5,17}, {1,20}, {15,28}, {18,34}, {9,25}, {7,32}, {30,33}, {26,31}, {27,31}, {10,15}, {8,34}, {5,32}, {23,31}, {15,19}, {2,8}, {14,22}, {14,25}, {17,26}, {20,31}, {12,24}, {12,28}, {14,18}, {21,30}, {4,26}, {17,30}, {1,27}, {16,27}, {7,20}, {5,21}, {1,13}, {13,30}, {11,23}, {3,20}, {5,15}, {5,14}, {1,14}, {15,24}, {12,34}, {4,25}, {11,20}, {5,24}, {25,34}, {9,32}, {11,34}, {9,27}, {5,30}, {12,19}, {6,28}, {22,30}, {22,34}, {6,13}, {2,13}, {5,28}, {3,15}, {15,34}, {8,25}, {22,32}, {2,20}, {12,29}, {3,28}, {4,28}, {13,32}, {9,34}, {1,25}, {30,32}, {5,22}, {15,32}, {23,34}, {16,25}, {9,20}, {5,7}, {7,23}, {9,26}, {20,30}, {10,22}, {6,24}, {2,12}, {16,18}, {13,15}, {13,23}, {8,23}, {11,22}, {3,14}, {14,15}, {6,16}, {21,23}, {20,22}, {14,28}, {7,25}, {21,32}, {11,13}, {9,11}, {15,30}, {14,26}, {18,33}, {7,31}, {6,15}, {14,30}, {6,30}, {9,28}, {16,34}, {9,33}, {10,26}, {8,31}, {24,34}, {9,12}, {6,22}, {2,25}, {18,28}, {18,19}, {10,33}, {1,12}, {28,30}, {2,18}, {23,26}, {16,17}, {19,21}, {6,26}, {2,11}, {27,29}, {5,25}, {12,15}, {20,29}, {3,5}, {1,21}, {13,27}, {2,3}, {22,25}, {18,32}, {19,23}, {10,21}, {8,26}, {15,31}, {4,15}, {2,17}, {12,22}, {25,28}, {1,33}, {31,34}, {2,14}, {14,29}, {23,25}, {11,32}, {11,15}, {8,30}, {4,22}, {9,24}, {7,10}, {8,21}, {1,4}, {16,30}, {5,20}, {3,17}, {10,29}, {3,8}, {12,31}, {10,13}, {22,23}, {11,25}, {32,34}, {9,23}, {13,24}, {12,13}, {1,32}, {22,24}, {12,25}, {4,18}, {16,19}, {1,8}, {14,23}, {2,15}, {10,19}, {6,8}, {6,25}, {6,29}, {28,29}, {3,18}, {1,15}, {2,33}, {2,22}, {25,29}, {23,28}, {13,28}, {13,18}, {3,33}, {18,22}, {19,25}, {27,32}, {17,23}, {8,33}, {1,6}, {22,26}, {13,19}, {5,11}, {11,26}, {18,31}, {19,24}, {11,18}, {2,29}, {3,29}, {26,29}, {3,31}, {6,12}, {2,30}, {4,29}, {20,26}, {23,27}, {5,33}, {3,12}, {8,29}, {27,34}, {2,6}, {10,30}, {18,21}, {19,26}, {18,23}, {6,19}, {28,32}, {15,22}, {11,17}, {8,15}, {8,28}, {24,31}, {14,20}, {6,31}, {2,24}, {24,28}, {2,23}, {11,29}, {7,13}, {1,10}, {20,27}, {3,16}, {19,32}, {6,23}, {14,31}, {17,20}, {29,34}, {2,34}, {7,28}, {3,32}, {15,23}, {26,32}, {12,33}, {10,12}, {6,9}, {18,25}, {9,17}, {10,28}, {17,29}, {18,26}, {19,31}, {3,11}, {6,32}, {9,22}, {26,30}, {2,28}, {3,9}, {6,18}, {14,32}, {16,33}, {12,21}, {26,28}, {8,24}, {7,18}, {7,24}, {15,33}, {7,9}, {16,31}, {8,20}, {2,19}, {4,13}, {24,33} } Symmetric graph 10 of order 34 Valency 33 Diameter 1 Girth 3 Automorphism group of order 295232799039604140847618609643520000000 Number of arcs = 1122 Number of 2-arcs = 35904 2-arc-transitive true Edge-set { {1,2}, {2,3}, {1,4}, {1,3}, {2,5}, {2,4}, {1,6}, {3,5}, {1,5}, {3,4}, {2,7}, {2,6}, {4,6}, {4,5}, {1,8}, {3,7}, {1,7}, {3,6}, {5,7}, {5,6}, {2,9}, {2,8}, {4,8}, {4,7}, {6,8}, {6,7}, {1,10}, {3,9}, {1,9}, {3,8}, {5,9}, {5,8}, {7,9}, {7,8}, {2,11}, {2,10}, {4,10}, {4,9}, {6,10}, {6,9}, {8,10}, {8,9}, {1,12}, {3,11}, {1,11}, {3,10}, {5,11}, {5,10}, {7,11}, {7,10}, {9,11}, {9,10}, {2,13}, {2,12}, {4,12}, {4,11}, {6,12}, {6,11}, {8,12}, {8,11}, {10,12}, {10,11}, {1,14}, {3,13}, {1,13}, {3,12}, {5,13}, {5,12}, {7,13}, {7,12}, {9,13}, {9,12}, {11,13}, {11,12}, {2,15}, {2,14}, {4,14}, {4,13}, {6,14}, {6,13}, {8,14}, {8,13}, {10,14}, {10,13}, {12,14}, {12,13}, {1,16}, {3,15}, {1,15}, {3,14}, {5,15}, {5,14}, {7,15}, {7,14}, {9,15}, {9,14}, {11,15}, {11,14}, {13,15}, {13,14}, {2,17}, {2,16}, {4,16}, {4,15}, {6,16}, {6,15}, {8,16}, {8,15}, {10,16}, {10,15}, {12,16}, {12,15}, {14,16}, {14,15}, {1,18}, {3,17}, {1,17}, {3,16}, {5,17}, {5,16}, {7,17}, {7,16}, {9,17}, {9,16}, {11,17}, {11,16}, {13,17}, {13,16}, {15,17}, {15,16}, {2,19}, {2,18}, {4,18}, {4,17}, {6,18}, {6,17}, {8,18}, {8,17}, {10,18}, {10,17}, {12,18}, {12,17}, {14,18}, {14,17}, {16,18}, {16,17}, {1,20}, {3,19}, {1,19}, {3,18}, {5,19}, {5,18}, {7,19}, {7,18}, {9,19}, {9,18}, {11,19}, {11,18}, {13,19}, {13,18}, {15,19}, {15,18}, {17,19}, {17,18}, {2,21}, {2,20}, {4,20}, {4,19}, {6,20}, {6,19}, {8,20}, {8,19}, {10,20}, {10,19}, {12,20}, {12,19}, {14,20}, {14,19}, {16,20}, {16,19}, {18,20}, {18,19}, {1,22}, {3,21}, {1,21}, {3,20}, {5,21}, {5,20}, {7,21}, {7,20}, {9,21}, {9,20}, {11,21}, {11,20}, {13,21}, {13,20}, {15,21}, {15,20}, {17,21}, {17,20}, {19,21}, {19,20}, {2,23}, {2,22}, {4,22}, {4,21}, {6,22}, {6,21}, {8,22}, {8,21}, 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{19,30}, {21,31}, {21,30}, {23,31}, {23,30}, {25,31}, {25,30}, {27,31}, {27,30}, {29,31}, {29,30}, {2,33}, {2,32}, {4,32}, {4,31}, {6,32}, {6,31}, {8,32}, {8,31}, {10,32}, {10,31}, {12,32}, {12,31}, {14,32}, {14,31}, {16,32}, {16,31}, {18,32}, {18,31}, {20,32}, {20,31}, {22,32}, {22,31}, {24,32}, {24,31}, {26,32}, {26,31}, {28,32}, {28,31}, {30,32}, {30,31}, {1,34}, {3,33}, {1,33}, {3,32}, {5,33}, {5,32}, {7,33}, {7,32}, {9,33}, {9,32}, {11,33}, {11,32}, {13,33}, {13,32}, {15,33}, {15,32}, {17,33}, {17,32}, {19,33}, {19,32}, {21,33}, {21,32}, {23,33}, {23,32}, {25,33}, {25,32}, {27,33}, {27,32}, {29,33}, {29,32}, {31,33}, {31,32}, {2,34}, {4,34}, {4,33}, {6,34}, {6,33}, {8,34}, {8,33}, {10,34}, {10,33}, {12,34}, {12,33}, {14,34}, {14,33}, {16,34}, {16,33}, {18,34}, {18,33}, {20,34}, {20,33}, {22,34}, {22,33}, {24,34}, {24,33}, {26,34}, {26,33}, {28,34}, {28,33}, {30,34}, {30,33}, {32,34}, {32,33}, {3,34}, {5,34}, {7,34}, {9,34}, {11,34}, {13,34}, {15,34}, {17,34}, {19,34}, {21,34}, {23,34}, {25,34}, {27,34}, {29,34}, {31,34}, {33,34} } ................................................................... Symmetric connected graphs of order 35 Symmetric graph 1 of order 35 Valency 2 Diameter 17 Girth 35 Automorphism group of order 70 Number of arcs = 70 Number of 2-arcs = 70 2-arc-transitive true Edge-set { {1,7}, {15,16}, {24,30}, {4,33}, {7,13}, {16,22}, {30,31}, {4,10}, {13,19}, {22,28}, {2,31}, {10,11}, {19,25}, {28,34}, {2,8}, {11,17}, {25,26}, {5,34}, {8,14}, {17,23}, {26,32}, {5,6}, {14,20}, {23,29}, {3,32}, {6,12}, {20,21}, {29,35}, {3,9}, {12,18}, {21,27}, {1,35}, {9,15}, {18,24}, {27,33} } Symmetric graph 2 of order 35 Valency 4 Diameter 5 Girth 4 Automorphism group of order 140 Number of arcs = 140 Number of 2-arcs = 420 2-arc-transitive false Edge-set { {1,7}, {11,20}, {10,11}, {21,27}, {20,24}, {17,21}, {14,20}, {5,31}, {30,31}, {27,33}, {24,28}, {21,30}, {23,27}, {18,24}, {6,12}, {5,9}, {2,6}, {5,34}, {2,31}, {4,33}, {28,32}, {30,34}, {27,31}, {29,33}, {22,28}, {16,25}, {15,16}, {12,18}, {9,13}, {6,15}, {8,12}, {3,9}, {5,6}, {2,8}, {4,10}, {1,32}, {3,34}, {2,33}, {4,35}, {26,32}, {25,29}, {22,26}, {19,25}, {16,22}, {13,17}, {15,19}, {12,16}, {14,18}, {7,13}, {9,15}, {8,14}, {1,10}, {3,7}, {4,8}, {1,35}, {3,32}, {26,35}, {23,29}, {25,26}, {24,30}, {19,23}, {18,22}, {11,17}, {13,19}, {10,14}, {7,11}, {29,35}, {28,34}, {20,21}, {17,23} } Symmetric graph 3 of order 35 Valency 4 Diameter 3 Girth 6 Automorphism group of order 5040 Number of arcs = 140 Number of 2-arcs = 420 2-arc-transitive true Edge-set { {1,3}, {2,6}, {1,7}, {4,12}, {5,13}, {2,14}, {1,15}, {1,8}, {9,12}, {10,17}, {11,14}, {4,18}, {5,6}, {2,19}, {2,3}, {10,12}, {11,15}, {16,18}, {8,24}, {9,22}, {11,13}, {4,25}, {5,26}, {4,6}, {5,7}, {16,19}, {20,24}, {21,22}, {3,28}, {16,17}, {8,29}, {9,30}, {10,32}, {11,20}, {8,12}, {9,13}, {10,14}, {20,25}, {21,26}, {27,28}, {19,24}, {17,23}, {6,34}, {7,31}, {18,21}, {3,22}, {15,35}, {16,27}, {7,17}, {15,18}, {27,29}, {19,30}, {26,32}, {20,23}, {23,34}, {31,33}, {25,28}, {24,26}, {13,27}, {14,33}, {22,23}, {21,33}, {29,33}, {25,31}, {32,35}, {34,35}, {29,34}, {30,31}, {28,32}, {30,35} } Symmetric graph 4 of order 35 Valency 6 Diameter 3 Girth 4 Automorphism group of order 210 Number of arcs = 210 Number of 2-arcs = 1050 2-arc-transitive false Edge-set { {1,7}, {5,29}, {11,32}, {7,28}, {9,15}, {14,20}, {16,27}, {5,6}, {8,32}, {2,13}, {20,34}, {12,23}, {5,19}, {10,24}, {4,28}, {15,31}, {1,20}, {27,33}, {11,30}, {12,18}, {17,23}, {22,28}, {4,15}, {3,32}, {24,35}, {6,27}, {8,14}, {13,19}, {20,26}, {23,29}, {5,11}, {10,16}, {15,21}, {3,17}, {25,31}, {2,23}, {6,35}, {8,22}, {13,27}, {18,32}, {24,30}, {4,10}, {7,31}, {1,12}, {19,33}, {11,22}, {4,18}, {9,23}, {14,28}, {15,16}, {3,24}, {1,35}, {13,34}, {20,21}, {25,26}, {30,31}, {22,33}, {10,11}, {7,18}, {3,27}, {14,35}, {26,32}, {15,29}, {11,17}, {16,22}, {21,27}, {3,14}, {2,31}, {23,34}, {6,12}, {8,19}, {13,24}, {18,29}, {5,21}, {9,33}, {6,25}, {10,26}, {16,35}, {7,13}, {19,30}, {9,20}, {14,25}, {2,16}, {1,22}, {10,34}, {7,21}, {12,26}, {17,31}, {4,33}, {18,24}, {3,9}, {28,34}, {1,30}, {5,34}, {12,33}, {19,25}, {29,35}, {21,32}, {6,17}, {2,26}, {8,29}, {17,28}, {4,25}, {9,30}, {2,8} } Symmetric graph 5 of order 35 Valency 8 Diameter 3 Girth 4 Automorphism group of order 1680 Number of arcs = 280 Number of 2-arcs = 1960 2-arc-transitive false Edge-set { {1,7}, {5,7}, {9,13}, {3,7}, {10,13}, {6,14}, {11,17}, {4,7}, {7,13}, {8,14}, {15,17}, {10,11}, {14,16}, {19,23}, {6,13}, {7,14}, {13,17}, {9,11}, {12,16}, {20,23}, {8,15}, {15,19}, {11,20}, {16,24}, {21,27}, {10,14}, {14,17}, {7,11}, {13,16}, {17,23}, {6,15}, {11,19}, {12,20}, {18,24}, {25,27}, {20,21}, {15,18}, {19,25}, {24,26}, {29,33}, {8,11}, {15,16}, {16,23}, {7,15}, {13,19}, {14,20}, {17,24}, {23,27}, {19,21}, {12,18}, {18,25}, {22,26}, {30,33}, {25,29}, {20,22}, {21,30}, {26,34}, {2,31}, {9,15}, {12,19}, {13,20}, {20,24}, {24,27}, {17,21}, {11,18}, {16,25}, {23,26}, {27,33}, {21,29}, {18,22}, {22,30}, {28,34}, {2,35}, {30,31}, {25,28}, {29,35}, {1,34}, {4,8}, {18,21}, {14,18}, {17,25}, {25,26}, {26,33}, {23,29}, {19,22}, {24,30}, {27,34}, {2,33}, {29,31}, {22,28}, {28,35}, {1,32}, {5,8}, {4,35}, {30,32}, {5,31}, {1,9}, {6,12}, {22,29}, {16,22}, {23,30}, {30,34}, {2,34}, {27,31}, {21,28}, {26,35}, {1,33}, {2,8}, {4,31}, {28,32}, {5,32}, {3,9}, {10,12}, {5,6}, {3,35}, {4,10}, {28,31}, {24,28}, {27,35}, {1,35}, {1,8}, {4,33}, {29,32}, {5,34}, {2,9}, {8,12}, {4,6}, {3,32}, {3,10}, {4,32}, {26,32}, {5,33}, {5,9}, {9,12}, {2,6}, {3,31}, {1,10}, {3,6}, {3,34}, {2,10} } Symmetric graph 6 of order 35 Valency 10 Diameter 3 Girth 4 Automorphism group of order 5016453120000000 Number of arcs = 350 Number of 2-arcs = 3150 2-arc-transitive false Edge-set { {1,6}, {17,25}, {9,11}, {2,32}, {21,29}, {23,26}, {14,18}, {11,18}, {1,10}, {3,8}, {30,32}, {5,10}, {27,34}, {29,33}, {16,22}, {26,33}, {18,22}, {17,24}, {9,15}, {19,22}, {6,13}, {1,33}, {16,24}, {8,15}, {3,35}, {8,12}, {4,31}, {25,26}, {10,12}, {2,34}, {4,33}, {22,26}, {1,32}, {21,28}, {23,30}, {14,17}, {4,34}, {25,28}, {11,20}, {12,17}, {2,9}, {1,31}, {22,30}, {13,17}, {14,19}, {4,6}, {22,27}, {13,19}, {15,20}, {5,7}, {2,10}, {29,34}, {24,27}, {15,19}, {13,18}, {3,10}, {12,20}, {2,7}, {4,10}, {26,34}, {11,17}, {1,9}, {3,7}, {30,31}, {5,9}, {27,33}, {29,32}, {16,21}, {13,20}, {29,31}, {26,35}, {18,24}, {27,32}, {19,21}, {18,23}, {10,14}, {15,17}, {4,9}, {28,32}, {20,21}, {16,23}, {20,25}, {7,11}, {28,34}, {20,23}, {30,35}, {10,15}, {8,13}, {3,32}, {28,35}, {30,34}, {17,23}, {28,33}, {20,22}, {19,24}, {6,15}, {27,35}, {18,21}, {20,24}, {7,15}, {10,13}, {3,34}, {26,32}, {9,14}, {6,12}, {5,33}, {8,14}, {2,35}, {8,11}, {3,31}, {25,30}, {5,32}, {22,28}, {6,11}, {1,35}, {24,29}, {15,16}, {17,21}, {7,14}, {24,30}, {5,31}, {25,27}, {21,26}, {12,18}, {7,13}, {5,35}, {11,19}, {9,13}, {3,33}, {21,27}, {7,12}, {2,31}, {4,35}, {24,26}, {1,34}, {23,28}, {6,14}, {24,28}, {21,30}, {3,6}, {10,11}, {23,29}, {14,16}, {12,16}, {2,8}, {22,29}, {13,16}, {5,6}, {11,16}, {1,8}, {4,7}, {26,31}, {5,8}, {2,6}, {29,35}, {4,8}, {14,20}, {12,19}, {15,18}, {3,9}, {27,31}, {25,29}, {1,7}, {28,31}, {30,33}, {19,25}, {16,25}, {18,25}, {17,22}, {5,34}, {4,32}, {19,23}, {9,12}, {2,33}, {23,27} } Symmetric graph 7 of order 35 Valency 12 Diameter 3 Girth 3 Automorphism group of order 5040 Number of arcs = 420 Number of 2-arcs = 4620 2-arc-transitive false Edge-set { {1,2}, {2,4}, {1,5}, {4,8}, {5,9}, {2,10}, {1,11}, {3,8}, {8,9}, {7,10}, {10,11}, {4,15}, {4,5}, {2,16}, {3,6}, {7,8}, {3,7}, {8,10}, {14,15}, {15,16}, {8,19}, {3,9}, {9,11}, {4,20}, {5,21}, {6,12}, {7,13}, {3,14}, {8,15}, {6,14}, {7,15}, {3,15}, {18,19}, {19,20}, {3,21}, {3,25}, {8,26}, {6,7}, {7,16}, {8,27}, {9,19}, {10,26}, {11,23}, {1,12}, {12,13}, {14,17}, {6,18}, {3,19}, {12,18}, {6,13}, {14,19}, {6,19}, {24,25}, {22,26}, {25,27}, {19,26}, {6,26}, {7,23}, {6,29}, {7,30}, {3,32}, {8,20}, {12,14}, {13,15}, {14,20}, {15,21}, {3,23}, {8,33}, {7,25}, {15,32}, {13,16}, {1,17}, {11,18}, {12,24}, {13,22}, {6,25}, {7,26}, {1,24}, {12,22}, {12,17}, {13,14}, {18,25}, {12,25}, {13,26}, {28,29}, {24,30}, {5,32}, {17,20}, {23,29}, {30,33}, {25,32}, {20,26}, {12,32}, {13,20}, {13,29}, {14,31}, {6,35}, {3,27}, {1,18}, {17,19}, {18,27}, {8,34}, {14,29}, {15,30}, {19,35}, {14,21}, {2,11}, {16,24}, {2,22}, {1,28}, {5,17}, {12,29}, {13,30}, {14,32}, {15,20}, {2,28}, {17,18}, {24,29}, {22,30}, {1,29}, {12,30}, {17,32}, {22,34}, {29,31}, {28,31}, {24,32}, {10,35}, {11,25}, {11,27}, {16,29}, {21,31}, {32,34}, {29,35}, {25,30}, {27,32}, {1,35}, {17,27}, {17,22}, {18,33}, {13,28}, {6,23}, {7,33}, {2,24}, {1,22}, {18,26}, {23,24}, {22,33}, {18,22}, {19,31}, {26,28}, {4,16}, {2,5}, {20,28}, {21,24}, {2,34}, {1,31}, {17,31}, {18,35}, {19,27}, {4,34}, {5,31}, {11,24}, {22,28}, {11,35}, {33,34}, {31,35}, {28,35}, {4,28}, {2,30}, {16,23}, {2,33}, {20,22}, {21,29}, {26,33}, {23,35}, {9,35}, {30,32}, {25,33}, {5,11}, {17,34}, {15,34}, {5,24}, {26,35}, {20,31}, {9,21}, {4,10}, {27,34}, {4,9}, {5,27}, {11,33}, {23,25}, {9,27}, {10,33}, {16,28}, {5,34}, {16,30}, {30,34}, {9,31}, {4,31}, {16,21}, {4,21}, {21,32}, {20,34}, {10,28}, {10,16}, {27,33}, {10,23}, {9,23}, {9,10}, {21,23} } Symmetric graph 8 of order 35 Valency 12 Diameter 3 Girth 4 Automorphism group of order 50400 Number of arcs = 420 Number of 2-arcs = 4620 2-arc-transitive false Edge-set { {1,7}, {12,16}, {16,35}, {21,27}, {1,25}, {8,27}, {14,25}, {1,32}, {10,26}, {12,33}, {9,35}, {1,20}, {17,26}, {24,33}, {3,9}, {6,12}, {11,35}, {2,18}, {19,30}, {10,21}, {1,12}, {8,19}, {14,18}, {12,28}, {24,35}, {2,26}, {21,30}, {10,34}, {8,12}, {15,19}, {18,32}, {17,21}, {8,22}, {5,14}, {11,30}, {22,31}, {3,29}, {23,29}, {10,19}, {12,21}, {1,35}, {20,29}, {17,23}, {24,30}, {3,22}, {5,21}, {1,27}, {8,34}, {8,14}, {2,11}, {30,31}, {3,32}, {10,29}, {9,18}, {13,19}, {20,21}, {1,17}, {4,23}, {6,30}, {11,22}, {26,32}, {20,31}, {6,17}, {13,24}, {3,34}, {5,29}, {7,31}, {6,15}, {4,15}, {28,32}, {4,35}, {7,28}, {18,29}, {19,23}, {21,32}, {1,10}, {14,35}, {4,28}, {24,28}, {26,35}, {7,21}, {8,29}, {15,31}, {6,32}, {13,32}, {9,20}, {13,17}, {20,24}, {3,17}, {5,31}, {3,7}, {15,29}, {11,32}, {4,18}, {19,28}, {18,22}, {25,29}, {2,23}, {10,24}, {12,26}, {21,35}, {7,33}, {5,6}, {2,6}, {15,24}, {25,34}, {2,8}, {9,15}, {4,13}, {28,34}, {7,16}, {15,16}, {4,20}, {14,23}, {4,33}, {11,27}, {14,33}, {5,16}, {16,27}, {4,30}, {22,28}, {29,35}, {7,23}, {10,11}, {12,18}, {19,35}, {8,24}, {3,14}, {27,33}, {5,34}, {14,30}, {16,32}, {10,16}, {17,28}, {11,20}, {6,25}, {18,24}, {25,26}, {2,21}, {15,26}, {7,13}, {15,34}, {6,22}, {5,11}, {22,33}, {23,27}, {9,28}, {18,34}, {1,30}, {8,32}, {10,14}, {20,34}, {11,17}, {23,34}, {4,8}, {9,33}, {9,13}, {17,31}, {2,33}, {5,9}, {13,27}, {16,25}, {4,25}, {14,28}, {1,22}, {5,26}, {3,12}, {29,33}, {6,27}, {5,19}, {8,17}, {13,34}, {3,24}, {11,25}, {18,27}, {19,25}, {5,24}, {17,33}, {30,34}, {9,30}, {10,31}, {2,16}, {9,23}, {6,20}, {13,22}, {7,26}, {3,19}, {22,26}, {14,20}, {15,21}, {12,31}, {9,25}, {3,27}, {6,35}, {2,13}, {4,10}, {20,26}, {13,29}, {7,18}, {25,31}, {16,30}, {23,32}, {2,31}, {1,15}, {19,33}, {2,28}, {16,22}, {7,11}, {12,23}, {27,31} } Symmetric graph 9 of order 35 Valency 14 Diameter 2 Girth 4 Automorphism group of order 32520160641024000000 Number of arcs = 490 Number of 2-arcs = 6370 2-arc-transitive false Edge-set { {1,8}, {26,32}, {6,10}, {13,20}, {26,33}, {23,35}, {5,14}, {2,29}, {11,18}, {13,16}, {26,29}, {9,18}, {23,32}, {27,34}, {3,12}, {19,24}, {7,30}, {4,33}, {8,15}, {7,29}, {11,20}, {13,19}, {26,30}, {4,30}, {13,15}, {9,20}, {23,33}, {12,15}, {27,35}, {25,31}, {4,9}, {16,24}, {21,28}, {1,31}, {16,22}, {3,32}, {10,17}, {19,28}, {1,30}, {2,33}, {8,18}, {1,29}, {11,16}, {13,21}, {26,31}, {21,22}, {2,31}, {3,29}, {11,17}, {2,30}, {13,18}, {9,16}, {23,29}, {3,31}, {9,17}, {12,18}, {27,32}, {14,17}, {25,34}, {22,30}, {2,13}, {7,8}, {20,24}, {6,11}, {17,26}, {6,34}, {7,10}, {20,22}, {20,25}, {5,35}, {14,21}, {1,11}, {16,28}, {21,26}, {6,31}, {4,32}, {10,15}, {19,26}, {6,30}, {7,33}, {8,20}, {6,29}, {11,19}, {13,17}, {26,34}, {19,22}, {17,24}, {7,34}, {19,25}, {5,33}, {8,21}, {21,24}, {7,31}, {4,29}, {11,15}, {9,19}, {23,30}, {17,25}, {4,34}, {5,30}, {4,31}, {9,15}, {12,20}, {27,33}, {5,34}, {12,21}, {14,15}, {25,35}, {10,21}, {22,31}, {24,29}, {7,11}, {28,32}, {1,10}, {2,8}, {18,24}, {5,8}, {5,13}, {15,23}, {28,35}, {1,14}, {2,10}, {18,22}, {2,14}, {18,25}, {18,27}, {12,19}, {6,8}, {20,28}, {6,13}, {17,23}, {3,35}, {1,13}, {16,26}, {21,23}, {5,31}, {2,32}, {10,18}, {19,23}, {1,33}, {8,16}, {5,29}, {11,21}, {26,35}, {15,28}, {1,35}, {16,25}, {16,27}, {6,32}, {10,19}, {17,28}, {1,34}, {3,33}, {8,17}, {9,21}, {23,31}, {21,25}, {15,22}, {2,35}, {21,27}, {17,22}, {2,34}, {3,30}, {12,16}, {27,29}, {15,27}, {3,34}, {12,17}, {14,18}, {25,32}, {6,35}, {14,19}, {22,34}, {8,19}, {24,30}, {28,33}, {6,14}, {24,32}, {4,8}, {15,24}, {3,10}, {3,11}, {3,9}, {6,12}, {24,35}, {7,14}, {4,10}, {24,34}, {7,12}, {4,14}, {15,25}, {4,12}, {5,10}, {2,11}, {18,28}, {5,11}, {5,9}, {7,13}, {20,26}, {6,9}, {17,27}, {4,35}, {1,9}, {16,23}, {7,32}, {10,20}, {19,27}, {6,33}, {18,26}, {20,27}, {20,23}, {14,16}, {15,26}, {5,32}, {23,34}, {7,35}, {27,30}, {14,20}, {25,33}, {18,23}, {22,35}, {1,32}, {10,16}, {24,31}, {28,29}, {5,12}, {24,33}, {22,32}, {3,8}, {25,30}, {4,13}, {28,34}, {1,12}, {28,31}, {2,12}, {3,14}, {2,9}, {4,11}, {3,13}, {7,9}, {27,31}, {25,29}, {28,30}, {22,33}, {22,29} } Symmetric graph 10 of order 35 Valency 16 Diameter 2 Girth 3 Automorphism group of order 40320 Number of arcs = 560 Number of 2-arcs = 8400 2-arc-transitive false Edge-set { {1,2}, {2,4}, {3,6}, {4,8}, {4,6}, {6,12}, {5,7}, {3,8}, {8,12}, {4,5}, {1,12}, {5,9}, {10,14}, {7,8}, {1,3}, {8,9}, {8,10}, {3,9}, {7,10}, {2,10}, {15,18}, {12,13}, {3,14}, {1,8}, {2,6}, {3,7}, {3,15}, {6,7}, {14,15}, {4,15}, {19,24}, {15,21}, {1,17}, {9,11}, {6,18}, {7,13}, {2,3}, {4,12}, {5,6}, {6,14}, {1,7}, {6,19}, {7,15}, {12,14}, {1,5}, {18,19}, {13,15}, {8,19}, {25,28}, {19,26}, {15,16}, {2,11}, {3,22}, {7,16}, {12,24}, {5,21}, {14,17}, {1,11}, {4,9}, {10,12}, {2,5}, {12,18}, {5,13}, {2,14}, {12,25}, {5,26}, {14,19}, {1,15}, {1,18}, {9,13}, {24,25}, {21,26}, {17,19}, {11,15}, {3,25}, {8,26}, {29,34}, {25,31}, {25,32}, {24,26}, {19,20}, {4,16}, {7,23}, {14,20}, {1,28}, {9,19}, {10,26}, {2,16}, {11,18}, {13,22}, {4,10}, {9,12}, {1,24}, {9,21}, {10,17}, {4,18}, {6,13}, {1,29}, {9,31}, {10,32}, {2,24}, {18,25}, {13,26}, {2,19}, {3,21}, {7,17}, {10,11}, {28,29}, {19,31}, {26,32}, {16,24}, {11,25}, {22,26}, {16,19}, {6,29}, {7,31}, {3,32}, {8,24}, {9,22}, {27,34}, {29,33}, {28,31}, {29,35}, {30,31}, {28,32}, {25,27}, {20,26}, {8,20}, {13,14}, {18,27}, {13,20}, {2,34}, {7,25}, {15,32}, {4,20}, {14,21}, {5,17}, {11,23}, {8,15}, {9,10}, {2,28}, {3,19}, {7,26}, {10,16}, {12,22}, {4,21}, {12,17}, {5,11}, {2,22}, {3,27}, {7,33}, {10,28}, {15,35}, {12,30}, {4,28}, {24,29}, {21,31}, {17,32}, {11,24}, {4,25}, {6,26}, {11,14}, {1,22}, {22,34}, {25,33}, {26,28}, {32,35}, {24,30}, {20,28}, {16,29}, {14,31}, {5,32}, {23,24}, {20,25}, {18,26}, {5,27}, {14,33}, {6,35}, {7,30}, {3,28}, {10,23}, {9,23}, {33,34}, {21,22}, {27,29}, {22,30}, {27,32}, {31,33}, {28,35}, {34,35}, {25,30}, {23,29}, {20,24}, {17,18}, {11,13}, {21,33}, {17,27}, {11,20}, {6,34}, {14,29}, {1,31}, {19,35}, {15,30}, {8,27}, {13,16}, {4,34}, {6,25}, {14,32}, {15,20}, {6,23}, {15,34}, {19,30}, {9,35}, {8,34}, {22,28}, {19,27}, {26,33}, {16,28}, {11,35}, {8,29}, {4,31}, {12,32}, {5,24}, {16,18}, {3,23}, {23,34}, {21,29}, {29,31}, {32,34}, {30,35}, {30,32}, {20,22}, {18,33}, {13,28}, {10,35}, {2,30}, {20,31}, {24,32}, {21,24}, {2,33}, {18,21}, {13,29}, {1,35}, {16,23}, {22,23}, {27,33}, {5,31}, {23,35}, {30,33}, {30,34}, {9,30}, {31,35}, {27,28}, {16,17}, {22,33}, {16,27}, {5,34}, {18,22}, {13,27}, {8,33}, {17,20}, {12,29}, {18,35}, {13,30}, {26,35}, {23,25}, {21,32}, {20,34}, {16,30}, {17,34}, {20,23}, {16,21}, {17,22}, {11,27}, {17,23}, {21,23}, {10,33}, {11,33}, {9,27}, {17,31} } Symmetric graph 11 of order 35 Valency 18 Diameter 2 Girth 3 Automorphism group of order 40320 Number of arcs = 630 Number of 2-arcs = 10710 2-arc-transitive false Edge-set { {1,4}, {2,8}, {1,9}, {3,4}, {5,8}, {2,7}, {1,10}, {6,8}, {7,9}, {3,10}, {8,11}, {4,14}, {5,15}, {2,15}, {3,12}, {8,13}, {7,14}, {10,15}, {6,15}, {4,7}, {3,16}, {8,18}, {6,9}, {10,19}, {3,11}, {4,19}, {3,5}, {1,6}, {7,12}, {3,17}, {8,14}, {14,18}, {15,19}, {12,19}, {3,13}, {9,15}, {6,20}, {7,21}, {3,24}, {8,22}, {10,13}, {15,25}, {4,26}, {6,16}, {8,25}, {9,26}, {6,10}, {7,11}, {2,12}, {1,13}, {1,14}, {12,15}, {6,11}, {7,18}, {3,18}, {18,24}, {6,22}, {19,25}, {3,26}, {1,25}, {12,26}, {6,17}, {7,19}, {12,27}, {13,19}, {14,26}, {15,23}, {6,28}, {7,24}, {8,17}, {15,17}, {19,29}, {3,30}, {8,32}, {9,20}, {12,20}, {13,21}, {3,29}, {8,30}, {7,32}, {10,20}, {4,13}, {14,16}, {5,12}, {2,17}, {2,18}, {1,19}, {12,16}, {2,13}, {14,24}, {15,22}, {6,24}, {7,22}, {24,28}, {22,24}, {13,17}, {25,29}, {26,30}, {6,32}, {7,20}, {2,29}, {1,30}, {1,32}, {11,12}, {13,18}, {14,25}, {15,26}, {1,23}, {12,33}, {17,25}, {18,32}, {12,34}, {13,31}, {14,28}, {15,24}, {11,19}, {22,25}, {26,29}, {6,31}, {3,35}, {7,27}, {1,27}, {17,26}, {14,23}, {7,29}, {3,31}, {14,35}, {15,27}, {9,14}, {18,20}, {6,21}, {4,11}, {5,18}, {4,24}, {5,22}, {2,25}, {1,26}, {1,20}, {12,21}, {4,17}, {5,14}, {18,28}, {5,19}, {12,28}, {13,24}, {28,34}, {24,31}, {5,28}, {17,24}, {11,17}, {22,29}, {29,30}, {31,32}, {20,32}, {12,35}, {13,25}, {14,27}, {4,22}, {5,29}, {2,31}, {2,35}, {1,16}, {14,22}, {18,29}, {6,30}, {19,32}, {3,20}, {1,21}, {11,29}, {18,30}, {24,35}, {17,33}, {18,34}, {19,28}, {16,25}, {2,26}, {17,30}, {22,32}, {20,29}, {13,35}, {7,28}, {15,33}, {2,23}, {1,33}, {11,32}, {15,29}, {6,33}, {7,35}, {19,23}, {3,33}, {24,27}, {19,22}, {13,23}, {8,16}, {2,9}, {10,24}, {11,22}, {8,28}, {9,24}, {5,10}, {4,29}, {5,30}, {2,32}, {2,27}, {12,23}, {9,18}, {10,18}, {24,34}, {22,31}, {10,25}, {11,26}, {1,34}, {12,31}, {17,28}, {9,34}, {27,31}, {28,33}, {10,34}, {11,31}, {11,28}, {11,16}, {17,29}, {29,32}, {33,35}, {25,35}, {27,35}, {14,30}, {18,23}, {9,17}, {10,22}, {4,33}, {5,35}, {4,30}, {2,20}, {13,32}, {25,26}, {6,27}, {16,22}, {28,30}, {11,21}, {22,27}, {25,34}, {26,31}, {21,30}, {4,32}, {5,20}, {14,34}, {15,31}, {19,21}, {3,34}, {5,16}, {2,21}, {16,35}, {13,34}, {15,28}, {16,26}, {7,34}, {23,28}, {24,33}, {5,25}, {8,21}, {8,31}, {9,29}, {10,31}, {4,35}, {4,23}, {5,33}, {9,28}, {17,35}, {16,32}, {11,34}, {18,31}, {10,27}, {23,33}, {21,34}, {31,34}, {4,27}, {16,33}, {16,34}, {16,20}, {22,35}, {23,30}, {10,30}, {9,32}, {20,30}, {13,33}, {17,21}, {5,23}, {27,30}, {32,33}, {20,35}, {23,32}, {8,35}, {9,25}, {19,33}, {23,26}, {21,28}, {19,34}, {20,21}, {16,31}, {10,29}, {11,30}, {8,23}, {9,16}, {10,21}, {21,25}, {23,27}, {9,33}, {21,27}, {20,27}, {23,31}, {21,35}, {26,34}, {26,27}, {20,33} } Symmetric graph 12 of order 35 Valency 24 Diameter 2 Girth 3 Automorphism group of order 604800 Number of arcs = 840 Number of 2-arcs = 19320 2-arc-transitive false Edge-set { {1,7}, {22,29}, {8,17}, {9,13}, {12,25}, {4,26}, {2,16}, {28,31}, {20,26}, {10,34}, {14,27}, {12,23}, {10,23}, {2,24}, {3,7}, {11,17}, {21,33}, {5,12}, {4,23}, {18,30}, {19,35}, {14,33}, {22,30}, {6,34}, {11,27}, {6,30}, {11,19}, {8,24}, {7,15}, {21,29}, {6,17}, {4,32}, {2,28}, {7,16}, {13,31}, {25,34}, {9,27}, {6,23}, {10,11}, {1,15}, {1,24}, {3,20}, {5,34}, {16,33}, {30,31}, {9,15}, {12,24}, {18,27}, {18,35}, {14,32}, {22,28}, {15,27}, {18,24}, {3,32}, {5,28}, {8,26}, {15,16}, {29,35}, {17,29}, {7,13}, {13,25}, {4,27}, {2,18}, {19,23}, {10,32}, {11,24}, {7,21}, {2,29}, {3,17}, {17,31}, {26,33}, {10,18}, {14,35}, {14,28}, {20,22}, {6,27}, {11,18}, {30,32}, {19,28}, {22,35}, {8,29}, {8,22}, {8,15}, {5,21}, {4,6}, {18,25}, {9,35}, {3,31}, {15,17}, {24,33}, {28,35}, {20,29}, {8,34}, {1,14}, {1,22}, {1,20}, {1,34}, {19,33}, {9,11}, {12,21}, {1,8}, {19,21}, {6,32}, {11,25}, {9,21}, {12,26}, {16,23}, {2,35}, {3,29}, {13,20}, {4,13}, {2,25}, {29,31}, {17,26}, {10,31}, {14,26}, {14,23}, {10,22}, {3,6}, {5,11}, {19,30}, {19,32}, {8,32}, {15,28}, {7,29}, {13,17}, {13,24}, {7,25}, {4,21}, {2,6}, {4,17}, {2,33}, {12,16}, {23,31}, {1,30}, {1,19}, {20,33}, {30,34}, {11,33}, {21,30}, {5,9}, {4,12}, {18,22}, {1,32}, {1,28}, {15,19}, {24,32}, {3,11}, {9,20}, {12,34}, {13,26}, {16,25}, {9,26}, {26,35}, {16,29}, {23,27}, {1,10}, {20,28}, {20,34}, {17,21}, {6,33}, {4,35}, {8,16}, {15,31}, {11,20}, {21,34}, {5,13}, {4,25}, {18,26}, {16,35}, {22,33}, {8,30}, {9,22}, {8,12}, {5,22}, {4,8}, {8,35}, {3,16}, {5,31}, {28,32}, {7,34}, {13,27}, {22,26}, {19,27}, {18,32}, {7,28}, {20,24}, {13,21}, {6,25}, {10,26}, {10,24}, {7,14}, {25,33}, {2,23}, {17,30}, {12,33}, {23,30}, {11,30}, {9,30}, {12,19}, {21,27}, {6,18}, {25,32}, {9,28}, {3,15}, {5,24}, {3,19}, {5,32}, {19,26}, {16,32}, {11,35}, {13,29}, {17,25}, {4,31}, {2,26}, {8,31}, {15,26}, {10,29}, {14,17}, {7,23}, {10,13}, {24,27}, {7,18}, {2,10}, {16,24}, {7,31}, {2,34}, {3,27}, {15,22}, {3,22}, {5,8}, {5,16}, {15,18}, {24,35}, {25,28}, {23,34}, {10,27}, {1,9}, {1,12}, {19,22}, {11,22}, {8,21}, {3,35}, {5,29}, {8,19}, {15,32}, {21,32}, {6,28}, {4,20}, {18,34}, {27,35}, {12,31}, {23,26}, {3,14}, {12,28}, {20,23}, {12,20}, {2,13}, {3,25}, {6,14}, {5,18}, {4,7}, {16,27}, {18,31}, {17,35}, {29,33}, {4,28}, {13,35}, {25,31}, {10,14}, {1,23}, {2,20}, {3,34}, {9,16}, {26,34}, {9,25}, {9,12}, {10,16}, {16,34}, {2,21}, {9,33}, {18,29}, {14,31}, {11,29}, {4,15}, {14,18}, {12,30}, {6,24}, {7,11}, {27,31}, {6,15}, {24,28}, {5,27}, {13,22}, {1,27}, {1,18}, {10,19}, {11,28}, {20,21}, {21,35}, {6,29}, {8,25}, {3,21}, {5,6}, {19,25}, {9,32}, {3,12}, {5,23}, {2,19}, {20,32}, {28,34}, {25,26}, {4,10}, {2,14}, {17,23}, {10,33}, {12,35}, {23,29}, {13,30}, {4,33}, {2,30}, {8,14}, {1,29}, {1,17}, {24,30}, {7,19}, {2,8}, {17,33}, {7,35}, {14,21}, {6,22}, {12,29}, {6,12}, {3,9}, {1,35}, {8,20}, {15,34}, {14,30}, {22,34}, {8,27}, {7,26}, {13,16}, {3,26}, {29,32}, {13,32}, {18,21}, {14,20}, {17,34}, {27,33}, {11,23}, {11,34}, {4,11}, {24,31}, {10,21}, {1,25}, {10,17}, {1,33}, {20,31}, {30,33}, {8,11}, {6,35}, {12,18}, {23,35}, {10,28}, {20,27}, {7,24}, {16,28}, {1,13}, {17,28}, {15,21}, {14,25}, {9,31}, {14,22}, {3,30}, {5,19}, {11,32}, {21,28}, {5,7}, {7,20}, {13,34}, {14,16}, {6,13}, {25,27}, {9,18}, {3,10}, {5,14}, {3,24}, {10,12}, {7,30}, {2,11}, {16,30}, {19,31}, {27,34}, {24,26}, {15,24}, {4,22}, {5,17}, {4,16}, {2,31}, {7,33}, {6,20}, {5,26}, {15,33}, {16,22}, {13,19}, {26,32}, {5,33}, {4,30}, {4,18}, {22,31}, {23,32}, {25,29}, {9,17}, {6,19}, {15,29}, {17,24}, {2,15}, {15,23}, {9,23}, {2,9} } Symmetric graph 13 of order 35 Valency 28 Diameter 2 Girth 3 Automorphism group of order 390241927692288000000 Number of arcs = 980 Number of 2-arcs = 26460 2-arc-transitive false Edge-set { {1,8}, {21,34}, {2,21}, {5,12}, {26,33}, {5,30}, {16,26}, {16,32}, {3,15}, {14,26}, {13,31}, {11,32}, {15,35}, {1,26}, {13,25}, {25,30}, {4,33}, {18,22}, {17,26}, {7,13}, {10,19}, {4,32}, {8,18}, {6,30}, {4,13}, {22,29}, {26,34}, {13,21}, {19,25}, {4,10}, {11,25}, {10,35}, {14,29}, {20,31}, {2,22}, {14,28}, {3,26}, {13,27}, {19,31}, {4,19}, {6,20}, {5,24}, {8,29}, {20,30}, {2,28}, {11,35}, {17,35}, {19,29}, {4,20}, {9,22}, {14,34}, {12,26}, {13,33}, {5,19}, {4,26}, {6,25}, {10,24}, {20,29}, {5,20}, {18,25}, {6,10}, {13,20}, {5,29}, {9,17}, {7,34}, {7,10}, {23,32}, {22,30}, {14,16}, {17,28}, {7,9}, {13,18}, {19,27}, {4,8}, {24,32}, {6,29}, {20,24}, {7,35}, {17,23}, {12,15}, {9,21}, {2,34}, {7,11}, {23,35}, {28,30}, {9,16}, {3,13}, {27,29}, {6,9}, {24,34}, {7,29}, {20,23}, {15,22}, {1,14}, {12,17}, {7,33}, {14,19}, {4,31}, {6,32}, {15,24}, {26,29}, {25,35}, {10,17}, {23,34}, {7,32}, {15,23}, {2,25}, {10,28}, {20,35}, {5,17}, {7,19}, {4,23}, {9,32}, {15,34}, {1,27}, {12,31}, {19,33}, {8,23}, {11,30}, {11,22}, {14,35}, {1,17}, {7,25}, {3,28}, {9,27}, {15,31}, {1,19}, {2,19}, {4,28}, {6,27}, {8,24}, {21,29}, {2,20}, {12,30}, {9,35}, {17,34}, {7,24}, {12,23}, {3,23}, {11,27}, {4,16}, {3,22}, {5,15}, {16,33}, {18,31}, {6,19}, {13,23}, {11,29}, {11,28}, {1,15}, {1,25}, {4,18}, {8,34}, {12,24}, {12,33}, {9,31}, {19,34}, {7,23}, {11,23}, {4,22}, {14,22}, {7,21}, {3,16}, {3,27}, {14,31}, {6,17}, {10,29}, {20,32}, {8,35}, {17,30}, {4,24}, {12,22}, {9,26}, {13,34}, {3,20}, {5,27}, {11,33}, {8,31}, {19,30}, {10,16}, {20,28}, {5,9}, {23,29}, {3,32}, {15,27}, {6,31}, {19,24}, {11,20}, {8,15}, {1,30}, {4,12}, {22,33}, {27,34}, {8,21}, {6,14}, {24,31}, {21,23}, {2,11}, {11,18}, {6,35}, {13,17}, {3,34}, {21,27}, {25,31}, {28,33}, {9,18}, {22,32}, {6,34}, {21,24}, {16,24}, {28,29}, {9,20}, {27,35}, {8,17}, {2,12}, {7,30}, {16,23}, {11,16}, {3,35}, {13,15}, {1,29}, {3,12}, {27,33}, {12,19}, {3,11}, {23,33}, {18,27}, {6,8}, {20,25}, {14,18}, {2,10}, {28,32}, {17,24}, {19,23}, {4,11}, {18,28}, {4,34}, {21,22}, {25,34}, {10,21}, {2,29}, {12,21}, {2,33}, {3,31}, {10,15}, {1,32}, {6,12}, {24,33}, {23,31}, {11,19}, {18,23}, {6,11}, {14,20}, {17,22}, {7,14}, {5,31}, {19,26}, {1,33}, {17,27}, {5,34}, {7,8}, {23,30}, {24,29}, {12,20}, {16,22}, {3,14}, {15,26}, {1,13}, {27,32}, {2,32}, {24,35}, {1,20}, {5,25}, {7,28}, {9,23}, {15,32}, {11,34}, {8,33}, {18,30}, {4,27}, {8,22}, {17,32}, {6,24}, {7,18}, {6,23}, {4,21}, {21,35}, {16,29}, {12,27}, {5,21}, {2,26}, {7,17}, {12,32}, {5,23}, {11,26}, {6,16}, {2,18}, {6,28}, {13,35}, {17,29}, {3,19}, {18,33}, {8,26}, {10,25}, {10,32}, {2,15}, {1,28}, {14,30}, {12,35}, {17,33}, {1,24}, {12,25}, {9,28}, {9,34}, {7,15}, {1,23}, {3,21}, {2,27}, {16,30}, {11,31}, {19,35}, {1,18}, {18,29}, {3,18}, {14,27}, {3,24}, {6,18}, {14,23}, {8,28}, {2,17}, {10,23}, {5,16}, {9,30}, {11,24}, {12,29}, {20,33}, {5,22}, {10,33}, {5,26}, {16,34}, {16,31}, {18,32}, {21,30}, {16,35}, {3,17}, {14,24}, {2,23}, {18,35}, {17,31}, {6,26}, {13,24}, {21,31}, {8,27}, {15,33}, {9,24}, {12,34}, {7,16}, {1,22}, {14,25}, {13,22}, {8,30}, {25,32}, {28,31}, {9,19}, {1,11}, {12,18}, {6,33}, {14,21}, {2,31}, {28,35}, {8,20}, {2,14}, {3,8}, {27,30}, {19,28}, {11,17}, {20,26}, {5,13}, {1,9}, {16,27}, {5,32}, {26,30}, {13,16}, {8,16}, {3,30}, {11,15}, {18,26}, {6,13}, {1,35}, {17,25}, {2,30}, {16,28}, {13,19}, {4,29}, {3,9}, {18,24}, {21,26}, {2,13}, {5,10}, {4,30}, {28,34}, {3,29}, {27,31}, {16,25}, {3,10}, {15,28}, {19,22}, {11,21}, {5,33}, {10,18}, {21,28}, {2,9}, {2,35}, {5,11}, {15,25}, {14,15}, {26,32}, {1,12}, {25,33}, {1,10}, {2,8}, {26,35}, {25,29}, {3,33}, {7,12}, {4,14}, {22,31}, {12,16}, {1,31}, {22,34}, {8,25}, {10,30}, {6,15}, {18,34}, {6,21}, {2,16}, {7,26}, {13,28}, {9,29}, {21,33}, {19,32}, {4,15}, {1,21}, {8,32}, {15,30}, {4,25}, {6,22}, {4,17}, {3,25}, {10,27}, {9,25}, {20,34}, {2,24}, {12,28}, {13,26}, {9,33}, {5,18}, {14,32}, {5,28}, {1,16}, {13,30}, {10,22}, {7,22}, {10,31}, {13,29}, {10,34}, {14,33}, {7,20}, {21,32}, {21,25}, {5,35}, {4,35}, {26,31}, {4,9}, {9,15}, {1,34}, {5,14}, {24,30}, {20,22}, {22,35}, {10,20}, {14,17}, {20,27}, {5,8}, {7,31}, {10,26}, {13,32}, {15,29}, {7,27}, {8,19} } Symmetric graph 14 of order 35 Valency 30 Diameter 2 Girth 3 Automorphism group of order 1805923123200000000 Number of arcs = 1050 Number of 2-arcs = 30450 2-arc-transitive false Edge-set { {1,6}, {3,25}, {6,13}, {5,11}, {8,28}, {7,25}, {13,18}, {2,10}, {10,16}, {22,32}, {15,34}, {11,21}, {14,28}, {7,30}, {18,22}, {4,24}, {7,12}, {24,28}, {12,25}, {13,20}, {2,30}, {9,17}, {4,20}, {10,12}, {16,29}, {8,32}, {19,34}, {21,34}, {14,31}, {13,30}, {22,30}, {1,15}, {9,27}, {6,21}, {14,17}, {15,32}, {27,34}, {6,11}, {17,28}, {7,27}, {18,24}, {4,34}, {7,31}, {23,29}, {1,27}, {9,24}, {6,24}, {12,17}, {28,33}, {25,35}, {20,22}, {2,15}, {17,26}, {4,23}, {4,29}, {8,19}, {1,19}, {7,34}, {18,31}, {13,34}, {30,31}, {3,9}, {6,20}, {23,31}, {11,33}, {13,29}, {8,29}, {19,21}, {9,20}, {2,20}, {17,31}, {4,33}, {10,25}, {13,16}, {29,32}, {21,31}, {14,33}, {15,30}, {22,27}, {1,17}, {4,9}, {1,14}, {26,35}, {3,31}, {6,33}, {15,23}, {11,27}, {15,25}, {13,27}, {6,29}, {17,21}, {16,32}, {3,34}, {11,18}, {5,28}, {24,30}, {7,20}, {29,35}, {21,32}, {9,26}, {1,33}, {9,35}, {22,26}, {3,26}, {6,23}, {4,14}, {19,30}, {1,22}, {7,17}, {4,18}, {1,31}, {5,23}, {8,11}, {25,27}, {13,24}, {14,19}, {1,26}, {3,16}, {7,33}, {18,35}, {22,33}, {15,35}, {12,26}, {23,27}, {11,24}, {4,27}, {7,24}, {19,29}, {1,21}, {1,16}, {12,28}, {7,28}, {18,25}, {20,33}, {2,35}, {12,19}, {1,29}, {8,16}, {3,19}, {9,34}, {20,31}, {13,31}, {30,33}, {3,29}, {1,23}, {9,11}, {3,8}, {6,19}, {5,32}, {5,19}, {1,8}, {16,25}, {3,13}, {9,14}, {20,26}, {10,31}, {16,33}, {20,28}, {18,33}, {25,33}, {13,35}, {12,29}, {21,29}, {2,25}, {5,17}, {4,8}, {10,30}, {16,22}, {2,32}, {10,34}, {27,31}, {21,27}, {14,24}, {5,35}, {12,20}, {2,29}, {23,35}, {11,32}, {3,6}, {18,23}, {30,32}, {14,25}, {13,26}, {9,19}, {26,34}, {6,30}, {14,21}, {1,30}, {9,22}, {2,14}, {10,26}, {10,22}, {15,16}, {11,31}, {7,15}, {18,27}, {8,26}, {19,23}, {3,35}, {6,32}, {8,25}, {16,21}, {3,14}, {18,30}, {5,22}, {3,30}, {9,18}, {5,20}, {6,35}, {17,32}, {26,33}, {10,15}, {16,27}, {9,33}, {15,21}, {14,27}, {3,12}, {3,28}, {6,25}, {17,34}, {14,34}, {11,30}, {22,28}, {3,24}, {5,7}, {6,26}, {17,23}, {3,33}, {5,26}, {8,23}, {4,11}, 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{6,22}, {4,25}, {3,10}, {10,28}, {15,20}, {11,35}, {28,32}, {7,14}, {18,26}, {4,35}, {7,32}, {8,30}, {9,25}, {28,34}, {15,22}, {6,17}, {2,33}, {15,17}, {25,31}, {21,30}, {18,29}, {5,21}, {6,16}, {3,17}, {12,24}, {9,23}, {11,20}, {18,34}, {11,34}, {15,29}, {19,26}, {4,30}, {7,22}, {2,24}, {13,33}, {18,21}, {5,14}, {19,22}, {24,27}, {4,28}, {2,11}, {15,18}, {17,27}, {1,7}, {26,32}, {23,34}, {20,30}, {2,22}, {14,35}, {16,26}, {1,20}, {2,9}, {11,17}, {19,25}, {1,13}, {5,27}, {2,17}, {6,34}, {23,32}, {24,26}, {12,23}, {11,29}, {5,30}, {19,32}, {4,7}, {10,13}, {9,32}, {28,35}, {4,31}, {13,19}, {4,10}, {15,24}, {12,27}, {10,18}, {27,33}, {7,29}, {18,28}, {2,8}, {1,34}, {3,23}, {22,29}, {17,22}, {4,15}, {10,11}, {21,35}, {9,29}, {1,25}, {15,33}, {8,24}, {8,33}, {19,35}, {12,35}, {2,28}, {20,24}, {2,12}, {20,32}, {6,12}, {23,28}, {1,32}, {14,16}, {5,9}, {8,20}, {8,14}, {13,25}, {1,11}, {5,24}, {12,34}, {2,34}, {8,21}, {30,35}, {20,21}, {22,34}, {15,31}, {9,13}, {13,21}, {4,16}, {3,7}, {1,28}, {29,31}, {10,29}, {5,29}, {11,26}, {10,27}, {16,24}, {17,30}, {4,22}, {10,17}, {20,35}, {9,31}, {7,16}, {3,18}, {9,30}, {21,33}, {3,21}, {6,14}, {4,26}, {24,31}, {4,13}, {25,32}, {3,27}, {7,11}, {6,18}, {10,33}, {7,21}, {17,25}, {2,23}, {12,18}, {20,23}, {1,9}, {7,26}, {20,27}, {17,33}, {12,22}, {4,6}, {12,16}, {6,28}, {3,20}, {15,27}, {13,17}, {14,32}, {2,6}, {8,22}, {15,19}, {4,17}, {5,31}, {24,29}, {7,23}, {1,35}, {24,33}, {10,35}, {29,34}, {12,21}, {21,28}, {5,12}, {13,22}, {2,19}, {7,13} } Symmetric graph 15 of order 35 Valency 34 Diameter 1 Girth 3 Automorphism group of order 10333147966386144929666651337523200000000 Number of arcs = 1190 Number of 2-arcs = 39270 2-arc-transitive true Edge-set { {1,2}, {2,3}, {2,4}, {1,3}, {2,5}, {3,4}, {1,4}, {2,6}, {3,5}, {4,5}, {1,5}, {2,7}, {3,6}, {4,6}, {5,6}, {1,6}, {2,8}, {3,7}, {4,7}, {5,7}, {6,7}, {1,7}, {2,9}, {3,8}, {4,8}, {5,8}, {6,8}, {7,8}, {1,8}, {2,10}, {3,9}, {4,9}, {5,9}, {6,9}, {7,9}, {8,9}, {1,9}, {2,11}, {3,10}, {4,10}, {5,10}, {6,10}, {7,10}, {8,10}, {9,10}, {1,10}, {2,12}, {3,11}, {4,11}, {5,11}, {6,11}, {7,11}, {8,11}, {9,11}, {10,11}, {1,11}, {2,13}, {3,12}, {4,12}, {5,12}, {6,12}, {7,12}, {8,12}, {9,12}, {10,12}, {11,12}, {1,12}, {2,14}, {3,13}, {4,13}, {5,13}, {6,13}, {7,13}, {8,13}, {9,13}, {10,13}, {11,13}, {12,13}, {1,13}, {2,15}, {3,14}, {4,14}, {5,14}, {6,14}, {7,14}, {8,14}, {9,14}, {10,14}, {11,14}, {12,14}, {13,14}, {1,14}, {2,16}, {3,15}, {4,15}, {5,15}, {6,15}, {7,15}, {8,15}, {9,15}, {10,15}, {11,15}, {12,15}, {13,15}, {14,15}, {1,15}, {2,17}, {3,16}, {4,16}, {5,16}, {6,16}, {7,16}, {8,16}, {9,16}, {10,16}, {11,16}, {12,16}, {13,16}, {14,16}, {15,16}, {1,16}, {2,18}, {3,17}, {4,17}, {5,17}, {6,17}, {7,17}, {8,17}, {9,17}, {10,17}, {11,17}, {12,17}, {13,17}, {14,17}, {15,17}, {16,17}, {1,17}, {2,19}, {3,18}, {4,18}, {5,18}, {6,18}, {7,18}, {8,18}, {9,18}, {10,18}, {11,18}, {12,18}, {13,18}, {14,18}, {15,18}, {16,18}, {17,18}, {1,18}, {2,20}, {3,19}, {4,19}, {5,19}, {6,19}, {7,19}, {8,19}, {9,19}, {10,19}, {11,19}, {12,19}, {13,19}, {14,19}, {15,19}, {16,19}, {17,19}, {18,19}, {1,19}, {2,21}, {3,20}, {4,20}, {5,20}, {6,20}, {7,20}, {8,20}, {9,20}, {10,20}, {11,20}, {12,20}, {13,20}, {14,20}, {15,20}, {16,20}, {17,20}, {18,20}, {19,20}, {1,20}, {2,22}, {3,21}, {4,21}, {5,21}, {6,21}, {7,21}, {8,21}, {9,21}, {10,21}, {11,21}, {12,21}, {13,21}, {14,21}, {15,21}, {16,21}, {17,21}, {18,21}, {19,21}, {20,21}, {1,21}, {2,23}, {3,22}, {4,22}, {5,22}, {6,22}, {7,22}, {8,22}, {9,22}, {10,22}, {11,22}, {12,22}, {13,22}, {14,22}, {15,22}, {16,22}, {17,22}, {18,22}, {19,22}, {20,22}, {21,22}, {1,22}, {2,24}, {3,23}, {4,23}, {5,23}, {6,23}, {7,23}, {8,23}, {9,23}, {10,23}, {11,23}, {12,23}, {13,23}, {14,23}, {15,23}, {16,23}, {17,23}, {18,23}, {19,23}, {20,23}, {21,23}, {22,23}, {1,23}, {2,25}, {3,24}, {4,24}, {5,24}, {6,24}, {7,24}, {8,24}, {9,24}, {10,24}, {11,24}, {12,24}, {13,24}, {14,24}, {15,24}, {16,24}, {17,24}, {18,24}, {19,24}, {20,24}, {21,24}, {22,24}, {23,24}, {1,24}, {2,26}, {3,25}, {4,25}, {5,25}, {6,25}, {7,25}, {8,25}, {9,25}, {10,25}, {11,25}, {12,25}, {13,25}, {14,25}, {15,25}, {16,25}, {17,25}, {18,25}, {19,25}, {20,25}, {21,25}, {22,25}, {23,25}, {24,25}, {1,25}, {2,27}, {3,26}, {4,26}, {5,26}, {6,26}, {7,26}, {8,26}, {9,26}, {10,26}, {11,26}, {12,26}, {13,26}, {14,26}, {15,26}, {16,26}, {17,26}, {18,26}, {19,26}, {20,26}, {21,26}, {22,26}, {23,26}, {24,26}, {25,26}, {1,26}, {2,28}, {3,27}, {4,27}, {5,27}, {6,27}, {7,27}, {8,27}, {9,27}, {10,27}, {11,27}, {12,27}, {13,27}, {14,27}, {15,27}, {16,27}, {17,27}, {18,27}, {19,27}, {20,27}, {21,27}, {22,27}, {23,27}, {24,27}, {25,27}, {26,27}, {1,27}, {2,29}, {3,28}, {4,28}, {5,28}, {6,28}, {7,28}, {8,28}, {9,28}, {10,28}, {11,28}, {12,28}, {13,28}, {14,28}, {15,28}, {16,28}, {17,28}, {18,28}, {19,28}, {20,28}, {21,28}, {22,28}, {23,28}, {24,28}, {25,28}, {26,28}, {27,28}, {1,28}, {2,30}, {3,29}, {4,29}, {5,29}, {6,29}, {7,29}, {8,29}, {9,29}, {10,29}, {11,29}, {12,29}, {13,29}, {14,29}, {15,29}, {16,29}, {17,29}, {18,29}, {19,29}, {20,29}, {21,29}, {22,29}, {23,29}, {24,29}, {25,29}, {26,29}, {27,29}, {28,29}, {1,29}, {2,31}, {3,30}, {4,30}, {5,30}, {6,30}, {7,30}, {8,30}, {9,30}, {10,30}, {11,30}, {12,30}, {13,30}, {14,30}, {15,30}, {16,30}, {17,30}, {18,30}, {19,30}, {20,30}, {21,30}, {22,30}, {23,30}, {24,30}, {25,30}, {26,30}, {27,30}, {28,30}, {29,30}, {1,30}, {2,32}, {3,31}, {4,31}, {5,31}, {6,31}, {7,31}, {8,31}, {9,31}, {10,31}, {11,31}, {12,31}, {13,31}, {14,31}, {15,31}, {16,31}, {17,31}, {18,31}, {19,31}, {20,31}, {21,31}, {22,31}, {23,31}, {24,31}, {25,31}, {26,31}, {27,31}, {28,31}, {29,31}, {30,31}, {1,31}, {2,33}, {3,32}, {4,32}, {5,32}, {6,32}, {7,32}, {8,32}, {9,32}, {10,32}, {11,32}, {12,32}, {13,32}, {14,32}, {15,32}, {16,32}, {17,32}, {18,32}, {19,32}, {20,32}, {21,32}, {22,32}, {23,32}, {24,32}, {25,32}, {26,32}, {27,32}, {28,32}, {29,32}, {30,32}, {31,32}, {1,32}, {2,34}, {3,33}, {4,33}, {5,33}, {6,33}, {7,33}, {8,33}, {9,33}, {10,33}, {11,33}, {12,33}, {13,33}, {14,33}, {15,33}, {16,33}, {17,33}, {18,33}, {19,33}, {20,33}, {21,33}, {22,33}, {23,33}, {24,33}, {25,33}, {26,33}, {27,33}, {28,33}, {29,33}, {30,33}, {31,33}, {32,33}, {1,33}, {2,35}, {3,34}, {4,34}, {5,34}, {6,34}, {7,34}, {8,34}, {9,34}, {10,34}, {11,34}, {12,34}, {13,34}, {14,34}, {15,34}, {16,34}, {17,34}, {18,34}, {19,34}, {20,34}, {21,34}, {22,34}, {23,34}, {24,34}, {25,34}, {26,34}, {27,34}, {28,34}, {29,34}, {30,34}, {31,34}, {32,34}, {33,34}, {1,34}, {3,35}, {4,35}, {5,35}, {6,35}, {7,35}, {8,35}, {9,35}, {10,35}, {11,35}, {12,35}, {13,35}, {14,35}, {15,35}, {16,35}, {17,35}, {18,35}, {19,35}, {20,35}, {21,35}, {22,35}, {23,35}, {24,35}, {25,35}, {26,35}, {27,35}, {28,35}, {29,35}, {30,35}, {31,35}, {32,35}, {33,35}, {34,35}, {1,35} } ................................................................... Symmetric connected graphs of order 36 Symmetric graph 1 of order 36 Valency 2 Diameter 18 Girth 36 Automorphism group of order 72 Number of arcs = 72 Number of 2-arcs = 72 2-arc-transitive true Edge-set { {1,7}, {8,11}, {12,16}, {15,19}, {20,24}, {23,28}, {27,30}, {29,36}, {3,35}, {4,6}, {5,10}, {9,13}, {14,18}, {17,22}, {21,26}, {25,32}, {31,34}, {1,33}, {2,8}, {7,12}, {11,15}, {16,20}, {19,23}, {24,27}, {28,29}, {30,35}, {4,36}, {3,5}, {6,9}, {10,14}, {13,17}, {18,21}, {22,25}, {26,31}, {32,33}, {2,34} } Symmetric graph 2 of order 36 Valency 4 Diameter 6 Girth 4 Automorphism group of order 144 Number of arcs = 144 Number of 2-arcs = 432 2-arc-transitive false Edge-set { {1,9}, {9,26}, {6,15}, {26,33}, {15,31}, {18,24}, {20,36}, {16,33}, {1,31}, {8,24}, {20,22}, {10,25}, {14,29}, {3,11}, {16,23}, {1,19}, {8,9}, {6,22}, {25,34}, {4,29}, {11,28}, {16,32}, {17,23}, {8,13}, {2,23}, {19,26}, {9,30}, {6,12}, {15,34}, {4,18}, {28,36}, {2,32}, {7,23}, {13,30}, {19,21}, {18,34}, {2,10}, {5,26}, {30,33}, {12,31}, {15,24}, {18,27}, {14,36}, {2,20}, {7,10}, {3,30}, {5,21}, {12,27}, {5,16}, {17,33}, {31,35}, {1,24}, {8,27}, {14,22}, {20,25}, {10,29}, {3,17}, {5,11}, {27,35}, {19,35}, {4,22}, {6,25}, {29,34}, {17,28}, {11,32}, {13,35}, {4,12}, {7,28}, {32,36}, {13,21}, {7,14}, {3,21} } Symmetric graph 3 of order 36 Valency 4 Diameter 4 Girth 6 Automorphism group of order 144 Number of arcs = 144 Number of 2-arcs = 432 2-arc-transitive false Edge-set { {1,7}, {4,22}, {3,16}, {23,27}, {1,10}, {15,24}, {2,20}, {6,26}, {11,23}, {22,36}, {3,5}, {16,25}, {12,19}, {21,30}, {4,31}, {14,21}, {26,34}, {8,11}, {20,27}, {10,28}, {2,24}, {2,13}, {8,15}, {20,22}, {29,33}, {7,32}, {9,33}, {1,36}, {13,28}, {9,17}, {7,18}, {21,25}, {3,34}, {6,30}, {23,31}, {5,36}, {5,24}, {4,12}, {4,18}, {15,19}, {27,30}, {10,31}, {16,35}, {17,35}, {3,28}, {5,14}, {18,24}, {32,35}, {16,29}, {8,28}, {9,22}, {2,25}, {14,33}, {11,26}, {11,36}, {12,13}, {23,33}, {1,29}, {19,32}, {6,10}, {13,17}, {25,31}, {12,29}, {27,35}, {9,15}, {20,34}, {8,21}, {17,26}, {7,34}, {14,32}, {18,30}, {6,19} } Symmetric graph 4 of order 36 Valency 4 Diameter 4 Girth 3 Automorphism group of order 144 Number of arcs = 144 Number of 2-arcs = 432 2-arc-transitive false Edge-set { {1,13}, {24,28}, {10,18}, {12,29}, {21,29}, {15,36}, {7,14}, {3,28}, {7,31}, {1,25}, {20,33}, {18,27}, {7,17}, {12,21}, {6,18}, {7,26}, {9,24}, {10,32}, {4,33}, {11,36}, {13,30}, {18,35}, {14,31}, {3,24}, {19,36}, {6,13}, {16,29}, {2,21}, {5,15}, {4,22}, {8,28}, {2,36}, {13,34}, {6,27}, {17,26}, {1,34}, {16,33}, {19,28}, {23,31}, {20,25}, {5,20}, {22,32}, {11,23}, {12,17}, {8,29}, {1,23}, {9,33}, {11,19}, {6,30}, {10,35}, {4,26}, {12,34}, {22,26}, {15,32}, {5,32}, {23,25}, {14,35}, {3,14}, {24,30}, {10,22}, {4,16}, {8,19}, {2,15}, {11,31}, {3,35}, {5,25}, {9,30}, {2,27}, {17,34}, {21,27}, {8,16}, {9,20} } Symmetric graph 5 of order 36 Valency 4 Diameter 6 Girth 4 Automorphism group of order 288 Number of arcs = 144 Number of 2-arcs = 432 2-arc-transitive false Edge-set { {1,9}, {1,24}, {2,31}, {15,24}, {16,31}, {18,23}, {11,32}, {15,34}, {6,16}, {18,33}, {5,11}, {3,17}, {3,12}, {25,34}, {6,26}, {29,33}, {5,21}, {3,30}, {3,22}, {4,21}, {4,29}, {10,25}, {20,26}, {9,29}, {19,21}, {13,30}, {13,22}, {14,21}, {14,29}, {20,22}, {10,30}, {2,10}, {1,20}, {7,9}, {19,35}, {8,13}, {13,36}, {14,35}, {7,14}, {20,36}, {8,10}, {2,19}, {2,23}, {1,32}, {7,24}, {31,35}, {8,27}, {27,36}, {28,35}, {7,28}, {32,36}, {8,23}, {16,23}, {15,32}, {17,24}, {12,31}, {18,27}, {11,27}, {12,28}, {17,28}, {16,33}, {5,15}, {17,34}, {6,12}, {4,18}, {4,11}, {26,33}, {5,25}, {30,34}, {6,22}, {9,26}, {19,25} } Symmetric graph 6 of order 36 Valency 4 Diameter 4 Girth 4 Automorphism group of order 9216 Number of arcs = 144 Number of 2-arcs = 432 2-arc-transitive false Edge-set { {1,13}, {16,31}, {17,35}, {9,30}, {2,34}, {1,35}, {8,27}, {11,21}, {3,13}, {4,15}, {5,18}, {1,16}, {8,17}, {7,20}, {23,28}, {16,30}, {14,31}, {20,35}, {13,29}, {19,33}, {18,36}, {17,34}, {21,27}, {22,26}, {8,26}, {12,31}, {11,30}, {3,34}, {9,32}, {2,36}, {1,33}, {4,35}, {6,25}, {7,28}, {5,27}, {10,29}, {5,20}, {10,21}, {9,24}, {2,15}, {11,23}, {3,16}, {4,14}, {7,18}, {6,17}, {8,19}, {12,22}, {18,33}, {23,26}, {22,28}, {14,30}, {21,25}, {13,32}, {15,29}, {20,34}, {19,36}, {24,27}, {3,36}, {6,28}, {5,26}, {10,31}, {12,29}, {11,32}, {4,33}, {7,25}, {2,14}, {12,24}, {10,23}, {9,22}, {6,19}, {15,32}, {24,25} } Symmetric graph 7 of order 36 Valency 4 Diameter 9 Girth 4 Automorphism group of order 9437184 Number of arcs = 144 Number of 2-arcs = 432 2-arc-transitive false Edge-set { {1,7}, {30,36}, {15,19}, {22,25}, {6,10}, {5,9}, {27,30}, {16,19}, {2,34}, {1,33}, {18,22}, {17,21}, {4,6}, {6,9}, {28,30}, {27,29}, {12,16}, {11,15}, {31,34}, {32,33}, {13,18}, {2,33}, {18,21}, {17,22}, {3,6}, {4,5}, {24,28}, {23,27}, {7,12}, {8,11}, {26,31}, {28,29}, {11,16}, {12,15}, {31,33}, {32,34}, {14,18}, {13,17}, {3,36}, {4,35}, {19,24}, {20,23}, {3,5}, {23,28}, {24,27}, {7,11}, {8,12}, {25,31}, {26,32}, {10,14}, {9,13}, {29,35}, {14,17}, {3,35}, {4,36}, {19,23}, {20,24}, {2,7}, {1,8}, {21,26}, {25,32}, {9,14}, {10,13}, {30,35}, {29,36}, {15,20}, {2,8}, {21,25}, {22,26}, {5,10}, {16,20}, {1,34} } Symmetric graph 8 of order 36 Valency 5 Diameter 3 Girth 5 Automorphism group of order 1440 Number of arcs = 180 Number of 2-arcs = 720 2-arc-transitive true Edge-set { {1,8}, {13,29}, {4,11}, {23,36}, {25,34}, {15,25}, {2,12}, {18,24}, {3,22}, {22,30}, {22,31}, {30,36}, {16,27}, {12,32}, {15,33}, {11,17}, {5,13}, {11,20}, {13,20}, {1,20}, {24,29}, {24,33}, {26,31}, {5,27}, {8,19}, {2,31}, {18,36}, {6,34}, {9,25}, {12,16}, {9,36}, {16,34}, {9,13}, {4,16}, {12,23}, {15,23}, {4,19}, {20,28}, {6,26}, {7,29}, {1,32}, {3,14}, {10,30}, {27,33}, {8,31}, {1,30}, {10,24}, {3,33}, {10,34}, {8,27}, {8,18}, {7,15}, {2,17}, {9,21}, {14,19}, {3,28}, {23,26}, {17,35}, {5,35}, {2,24}, {4,29}, {12,28}, {5,23}, {7,22}, {11,26}, {29,32}, {11,33}, {10,14}, {7,35}, {17,21}, {18,28}, {21,32}, {6,18}, {6,21}, {1,15}, {2,25}, {21,27}, {19,25}, {28,35}, {14,32}, {5,10}, {13,31}, {4,36}, {16,22}, {14,26}, {17,30}, {19,35}, {6,7}, {20,34}, {3,9} } Symmetric graph 9 of order 36 Valency 6 Diameter 3 Girth 4 Automorphism group of order 216 Number of arcs = 216 Number of 2-arcs = 1080 2-arc-transitive false Edge-set { {1,4}, {3,33}, {16,21}, {2,22}, {3,18}, {7,11}, {26,32}, {12,17}, {2,9}, {18,31}, {29,35}, {14,36}, {23,27}, {2,6}, {8,28}, {33,35}, {1,36}, {15,17}, {9,24}, {1,31}, {14,18}, {22,30}, {5,25}, {5,11}, {17,19}, {19,34}, {7,13}, {16,22}, {3,24}, {8,15}, {28,33}, {6,36}, {10,15}, {1,16}, {9,14}, {30,31}, {4,20}, {8,12}, {29,32}, {20,36}, {27,33}, {13,35}, {14,29}, {4,7}, {12,32}, {10,18}, {15,34}, {13,28}, {19,22}, {3,7}, {15,30}, {28,34}, {16,32}, {20,24}, {1,8}, {10,33}, {21,25}, {21,23}, {22,25}, {3,5}, {13,16}, {24,29}, {14,21}, {9,30}, {23,28}, {2,35}, {31,34}, {13,19}, {7,29}, {4,12}, {12,27}, {15,20}, {7,23}, {2,32}, {6,10}, {10,25}, {3,34}, {11,26}, {4,26}, {18,20}, {6,21}, {9,10}, {11,14}, {26,30}, {5,19}, {17,24}, {1,23}, {12,13}, {27,29}, {21,35}, {25,28}, {5,35}, {2,17}, {4,34}, {18,23}, {25,31}, {11,31}, {19,26}, {30,36}, {20,27}, {6,8}, {11,16}, {5,9}, {24,26}, {17,33}, {6,27}, {8,22}, {32,36} } Symmetric graph 10 of order 36 Valency 6 Diameter 4 Girth 4 Automorphism group of order 432 Number of arcs = 216 Number of 2-arcs = 1080 2-arc-transitive false Edge-set { {1,7}, {8,14}, {10,30}, {13,31}, {21,29}, {16,20}, {25,34}, {2,32}, {3,22}, {19,26}, {13,33}, {29,34}, {18,23}, {4,21}, {6,35}, {4,9}, {9,25}, {12,14}, {22,30}, {17,36}, {3,32}, {5,22}, {4,19}, {6,33}, {28,36}, {15,19}, {10,26}, {11,13}, {5,11}, {10,15}, {11,26}, {15,21}, {26,35}, {17,31}, {21,27}, {20,25}, {14,34}, {2,20}, {1,9}, {4,12}, {12,25}, {11,17}, {3,11}, {5,7}, {6,24}, {30,33}, {17,24}, {16,22}, {25,36}, {18,32}, {22,28}, {12,18}, {8,28}, {16,33}, {24,25}, {18,22}, {26,33}, {13,24}, {1,36}, {2,35}, {3,20}, {23,26}, {18,35}, {4,31}, {6,21}, {7,29}, {9,18}, {8,15}, {10,17}, {11,27}, {17,21}, {27,35}, {20,28}, {12,28}, {8,30}, {7,16}, {5,34}, {14,23}, {14,32}, {19,27}, {29,32}, {3,34}, {5,23}, {16,35}, {14,19}, {5,36}, {27,32}, {6,8}, {2,10}, {9,29}, {15,36}, {1,19}, {7,13}, {24,29}, {28,31}, {13,20}, {1,31}, {23,30}, {4,33}, {6,12}, {1,23}, {30,31}, {2,8}, {2,24}, {3,10}, {15,34}, {7,27}, {9,16} } Symmetric graph 11 of order 36 Valency 6 Diameter 4 Girth 4 Automorphism group of order 432 Number of arcs = 216 Number of 2-arcs = 1080 2-arc-transitive false Edge-set { {1,4}, {9,12}, {17,19}, {14,16}, {15,36}, {22,26}, {25,33}, {21,23}, {30,32}, {6,20}, {22,28}, {4,11}, {1,31}, {3,5}, {25,28}, {10,27}, {3,35}, {2,9}, {20,26}, {30,36}, {8,11}, {12,18}, {19,34}, {1,17}, {16,21}, {31,36}, {5,8}, {17,33}, {6,35}, {16,24}, {7,14}, {15,18}, {27,32}, {4,26}, {9,22}, {13,34}, {23,25}, {2,6}, {1,22}, {11,15}, {13,21}, {3,33}, {5,10}, {20,24}, {23,29}, {12,32}, {14,30}, {28,31}, {4,19}, {7,10}, {18,20}, {9,30}, {11,17}, {28,34}, {19,25}, {27,29}, {1,8}, {3,16}, {21,35}, {12,26}, {2,36}, {13,17}, {14,35}, {24,27}, {26,31}, {9,15}, {18,22}, {33,34}, {4,36}, {8,23}, {5,25}, {6,7}, {16,32}, {19,22}, {29,33}, {5,21}, {24,30}, {6,12}, {2,32}, {14,20}, {15,28}, {11,31}, {3,23}, {10,13}, {26,30}, {11,25}, {1,34}, {3,7}, {21,27}, {29,35}, {10,16}, {20,36}, {2,18}, {8,28}, {32,35}, {4,9}, {18,31}, {5,34}, {17,23}, {8,13}, {6,27}, {7,24}, {2,24}, {12,14}, {15,19}, {10,33}, {13,29}, {7,29} } Symmetric graph 12 of order 36 Valency 6 Diameter 4 Girth 3 Automorphism group of order 432 Number of arcs = 216 Number of 2-arcs = 1080 2-arc-transitive false Edge-set { {1,4}, {8,14}, {3,17}, {10,26}, {22,29}, {15,21}, {15,16}, {5,7}, {16,32}, {21,26}, {24,25}, {30,36}, {20,25}, {13,30}, {7,12}, {2,23}, {20,36}, {11,13}, {1,24}, {5,36}, {6,19}, {29,31}, {25,32}, {3,22}, {6,34}, {27,31}, {25,28}, {5,12}, {9,23}, {13,18}, {18,20}, {32,34}, {6,27}, {8,28}, {14,17}, {17,19}, {7,29}, {2,32}, {1,35}, {3,36}, {6,11}, {16,21}, {9,30}, {1,31}, {2,34}, {4,10}, {3,33}, {2,9}, {11,18}, {20,24}, {19,27}, {14,28}, {19,22}, {14,34}, {11,31}, {10,33}, {22,27}, {15,29}, {21,23}, {15,35}, {12,32}, {23,26}, {13,36}, {17,33}, {6,9}, {1,8}, {10,17}, {18,31}, {4,8}, {3,7}, {12,16}, {18,24}, {17,22}, {19,34}, {4,35}, {26,33}, {27,29}, {16,23}, {21,35}, {26,30}, {8,10}, {2,16}, {4,21}, {30,33}, {9,11}, {1,18}, {5,20}, {28,32}, {12,15}, {10,14}, {7,15}, {9,13}, {14,19}, {23,30}, {31,35}, {4,26}, {13,20}, {24,28}, {33,36}, {5,25}, {7,22}, {8,24}, {12,25}, {11,27}, {29,35}, {28,34}, {3,5}, {2,6} } Symmetric graph 13 of order 36 Valency 6 Diameter 4 Girth 4 Automorphism group of order 4320 Number of arcs = 216 Number of 2-arcs = 1080 2-arc-transitive true Edge-set { {1,7}, {17,23}, {7,18}, {1,21}, {22,26}, {2,23}, {18,24}, {17,35}, {6,7}, {20,29}, {19,27}, {18,21}, {9,26}, {2,19}, {24,25}, {14,22}, {23,27}, {12,18}, {15,34}, {4,36}, {30,36}, {5,21}, {2,35}, {6,24}, {22,29}, {16,19}, {18,36}, {5,9}, {19,28}, {20,25}, {4,20}, {27,32}, {21,30}, {21,26}, {2,31}, {3,24}, {15,31}, {8,25}, {11,13}, {8,13}, {13,35}, {26,35}, {6,10}, {9,14}, {12,25}, {15,20}, {27,36}, {3,36}, {5,23}, {2,8}, {13,24}, {10,16}, {14,36}, {5,34}, {28,34}, {25,34}, {4,11}, {10,30}, {6,35}, {29,35}, {6,19}, {9,28}, {5,12}, {28,31}, {24,28}, {17,20}, {6,33}, {1,33}, {17,33}, {14,33}, {7,29}, {14,19}, {2,12}, {4,22}, {16,32}, {3,20}, {4,31}, {8,30}, {13,21}, {8,16}, {10,26}, {9,17}, {25,33}, {3,32}, {4,8}, {13,32}, {10,15}, {1,11}, {7,27}, {12,14}, {7,15}, {16,34}, {26,31}, {3,10}, {1,34}, {11,27}, {12,29}, {11,17}, {29,32}, {15,23}, {5,32}, {18,31}, {3,9}, {23,30}, {11,28}, {1,22}, {16,22}, {30,33} } Symmetric graph 14 of order 36 Valency 6 Diameter 4 Girth 4 Automorphism group of order 10368 Number of arcs = 216 Number of 2-arcs = 1080 2-arc-transitive false Edge-set { {1,4}, {15,22}, {22,25}, {31,35}, {21,35}, {11,31}, {11,21}, {8,30}, {29,33}, {8,17}, {18,33}, {21,30}, {9,29}, {17,21}, {9,18}, {5,14}, {2,29}, {13,28}, {4,25}, {3,5}, {27,29}, {1,28}, {1,17}, {14,18}, {2,6}, {4,13}, {17,25}, {3,18}, {6,27}, {14,36}, {27,36}, {2,23}, {13,23}, {3,34}, {15,34}, {11,15}, {11,25}, {14,24}, {24,27}, {2,10}, {10,13}, {3,22}, {1,36}, {23,26}, {25,34}, {3,11}, {1,24}, {10,26}, {7,36}, {32,36}, {7,10}, {10,32}, {23,33}, {19,23}, {33,34}, {19,34}, {9,24}, {24,31}, {9,35}, {9,11}, {20,36}, {10,20}, {8,23}, {8,34}, {21,24}, {7,22}, {22,32}, {12,33}, {12,19}, {20,22}, {8,12}, {5,7}, {6,32}, {7,28}, {30,32}, {5,19}, {6,8}, {19,28}, {16,19}, {28,31}, {16,31}, {4,20}, {20,29}, {4,33}, {6,21}, {4,9}, {7,16}, {17,32}, {5,31}, {18,20}, {26,30}, {6,15}, {14,30}, {16,27}, {5,26}, {15,16}, {18,26}, {2,16}, {3,30}, {15,29}, {13,17}, {25,28}, {1,12}, {12,14}, {13,35}, {26,35}, {12,27}, {2,35} } Symmetric graph 15 of order 36 Valency 6 Diameter 4 Girth 4 Automorphism group of order 56623104 Number of arcs = 216 Number of 2-arcs = 1080 2-arc-transitive false Edge-set { {1,7}, {15,34}, {6,22}, {21,29}, {25,32}, {7,13}, {15,23}, {2,8}, {10,16}, {4,20}, {7,27}, {27,34}, {6,33}, {9,29}, {13,32}, {16,33}, {5,21}, {30,35}, {3,31}, {11,17}, {17,20}, {5,34}, {6,12}, {12,25}, {13,22}, {23,26}, {2,36}, {4,10}, {20,27}, {27,33}, {22,30}, {26,31}, {8,14}, {16,24}, {1,23}, {18,19}, {19,28}, {1,35}, {11,26}, {17,35}, {14,21}, {24,25}, {2,23}, {4,32}, {2,7}, {15,33}, {3,9}, {8,13}, {21,30}, {3,20}, {5,11}, {12,17}, {5,22}, {12,26}, {9,15}, {3,19}, {8,28}, {28,33}, {10,30}, {14,31}, {18,36}, {11,18}, {22,29}, {1,8}, {29,35}, {16,34}, {7,14}, {9,16}, {13,21}, {6,21}, {26,32}, {4,19}, {5,33}, {17,19}, {1,24}, {2,35}, {15,24}, {3,32}, {29,36}, {12,18}, {28,34}, {30,36}, {25,31}, {1,36}, {10,15}, {10,29}, {6,34}, {4,31}, {8,27}, {16,23}, {18,20}, {14,22}, {24,26}, {18,35}, {14,32}, {19,27}, {2,24}, {11,25}, {9,30}, {7,28}, {3,10}, {23,25}, {20,28}, {5,12}, {13,31}, {17,36}, {4,9}, {6,11} } Symmetric graph 16 of order 36 Valency 6 Diameter 6 Girth 4 Automorphism group of order 52242776064 Number of arcs = 216 Number of 2-arcs = 1080 2-arc-transitive false Edge-set { {1,7}, {8,28}, {16,34}, {7,15}, {15,24}, {1,11}, {11,20}, {2,8}, {12,16}, {2,34}, {5,12}, {23,28}, {30,34}, {19,23}, {26,30}, {7,27}, {15,33}, {1,24}, {11,29}, {11,27}, {20,33}, {6,24}, {14,29}, {4,20}, {6,25}, {4,22}, {8,16}, {16,23}, {2,12}, {12,19}, {28,34}, {5,34}, {23,30}, {3,30}, {19,26}, {5,13}, {3,9}, {26,36}, {13,21}, {7,36}, {11,15}, {1,33}, {6,11}, {24,27}, {29,33}, {20,24}, {25,29}, {14,20}, {4,6}, {4,35}, {22,25}, {10,14}, {31,35}, {18,22}, {8,10}, {16,18}, {2,23}, {12,30}, {12,28}, {19,34}, {5,23}, {13,30}, {3,19}, {5,26}, {3,21}, {9,26}, {13,36}, {17,36}, {7,21}, {9,32}, {1,17}, {15,32}, {27,33}, {6,33}, {24,29}, {4,29}, {20,25}, {6,14}, {4,10}, {25,35}, {14,22}, {8,35}, {22,31}, {10,18}, {18,28}, {2,31}, {13,19}, {3,5}, {3,36}, {21,26}, {9,13}, {32,36}, {17,21}, {7,9}, {15,17}, {27,32}, {10,25}, {14,35}, {18,35}, {8,22}, {10,31}, {2,18}, {16,31}, {21,32}, {9,17}, {17,27}, {1,32}, {28,31} } Symmetric graph 17 of order 36 Valency 7 Diameter 3 Girth 3 Automorphism group of order 504 Number of arcs = 252 Number of 2-arcs = 1512 2-arc-transitive false Edge-set { {1,3}, {2,10}, {4,11}, {7,14}, {6,23}, {8,24}, {13,26}, {1,26}, {16,18}, {5,21}, {12,17}, {19,33}, {9,27}, {3,34}, {3,11}, {2,34}, {4,13}, {5,31}, {18,29}, {12,22}, {15,32}, {19,28}, {17,27}, {19,34}, {22,33}, {1,33}, {10,35}, {11,25}, {10,26}, {7,33}, {6,35}, {8,25}, {15,30}, {14,30}, {6,25}, {20,28}, {15,20}, {7,9}, {20,32}, {24,31}, {8,35}, {21,34}, {20,24}, {9,23}, {2,24}, {4,23}, {14,36}, {23,27}, {24,28}, {26,29}, {11,14}, {23,34}, {13,24}, {16,24}, {21,23}, {18,36}, {9,29}, {20,31}, {10,30}, {13,17}, {28,32}, {14,25}, {15,35}, {9,14}, {2,8}, {16,22}, {21,22}, {11,30}, {9,36}, {4,27}, {2,28}, {32,35}, {7,25}, {27,32}, {10,15}, {8,16}, {7,27}, {6,11}, {8,10}, {13,16}, {1,12}, {5,36}, {12,33}, {27,28}, {18,26}, {3,5}, {16,33}, {12,35}, {25,33}, {11,31}, {10,29}, {12,32}, {17,32}, {23,29}, {4,31}, {3,19}, {17,26}, {13,18}, {5,34}, {15,36}, {18,22}, {5,22}, {4,6}, {26,30}, {3,31}, {22,36}, {7,28}, {20,36}, {2,29}, {14,15}, {12,21}, {29,34}, {3,30}, {5,20}, {7,19}, {16,25}, {1,30}, {1,19}, {6,21}, {9,18}, {1,17}, {13,31}, {21,35}, {2,19}, {6,8}, {4,17} } Symmetric graph 18 of order 36 Valency 8 Diameter 3 Girth 3 Automorphism group of order 288 Number of arcs = 288 Number of 2-arcs = 2016 2-arc-transitive false Edge-set { {1,13}, {9,16}, {20,30}, {11,21}, {18,27}, {3,34}, {9,24}, {8,24}, {13,25}, {1,30}, {6,21}, {14,28}, {1,31}, {15,27}, {6,17}, {15,35}, {9,31}, {8,20}, {16,34}, {9,30}, {13,33}, {10,29}, {5,19}, {16,36}, {12,30}, {2,20}, {22,33}, {12,26}, {3,17}, {21,36}, {12,27}, {24,35}, {11,28}, {1,18}, {21,34}, {9,27}, {10,28}, {4,19}, {23,34}, {11,25}, {4,18}, {9,26}, {3,15}, {24,29}, {7,27}, {2,14}, {23,32}, {7,26}, {22,31}, {8,25}, {4,13}, {23,30}, {6,26}, {5,25}, {1,16}, {21,30}, {8,28}, {6,27}, {22,29}, {5,28}, {24,31}, {21,32}, {12,14}, {17,31}, {6,33}, {10,15}, {18,30}, {6,36}, {19,29}, {5,35}, {11,16}, {18,32}, {7,36}, {8,35}, {9,13}, {20,32}, {5,34}, {7,33}, {19,31}, {8,34}, {17,29}, {10,14}, {12,15}, {11,13}, {10,23}, {19,26}, {2,36}, {12,22}, {20,27}, {2,33}, {17,28}, {1,34}, {9,21}, {20,25}, {4,33}, {11,24}, {18,25}, {1,35}, {4,36}, {17,26}, {3,35}, {19,28}, {12,23}, {10,22}, {5,22}, {16,28}, {4,32}, {7,23}, {15,25}, {4,29}, {14,26}, {3,30}, {6,24}, {2,29}, {8,21}, {13,27}, {3,31}, {2,32}, {16,26}, {7,22}, {5,23}, {7,19}, {14,34}, {11,29}, {5,18}, {13,35}, {11,32}, {12,31}, {8,17}, {10,32}, {6,20}, {15,33}, {14,36}, {7,18}, {23,36}, {1,19}, {24,33}, {10,25}, {3,20}, {2,17}, {22,35}, {4,16}, {2,15}, {3,14} } Symmetric graph 19 of order 36 Valency 8 Diameter 3 Girth 3 Automorphism group of order 288 Number of arcs = 288 Number of 2-arcs = 2016 2-arc-transitive false Edge-set { {1,13}, {14,35}, {23,27}, {1,36}, {1,28}, {6,32}, {12,29}, {2,14}, {2,23}, {5,14}, {11,23}, {12,17}, {6,20}, {9,24}, {8,13}, {13,36}, {24,28}, {13,32}, {24,29}, {18,36}, {19,28}, {23,32}, {14,29}, {17,26}, {20,34}, {22,31}, {15,30}, {19,35}, {18,27}, {2,35}, {2,27}, {5,31}, {11,30}, {12,35}, {6,27}, {9,31}, {8,30}, {5,25}, {11,33}, {12,32}, {6,29}, {9,36}, {8,28}, {3,26}, {3,34}, {10,34}, {7,26}, {1,25}, {1,33}, {1,24}, {6,13}, {12,24}, {11,18}, {5,19}, {10,23}, {7,14}, {6,17}, {12,20}, {11,22}, {5,15}, {10,19}, {7,18}, {4,23}, {4,14}, {9,17}, {8,20}, {2,22}, {2,15}, {8,16}, {9,21}, {3,16}, {3,21}, {14,31}, {23,30}, {17,35}, {20,27}, {24,31}, {13,30}, {18,25}, {19,33}, {21,32}, {16,29}, {20,36}, {17,28}, {24,26}, {13,34}, {18,34}, {19,26}, {21,25}, {16,33}, {15,32}, {22,29}, {15,36}, {22,28}, {11,36}, {5,28}, {10,32}, {7,29}, {6,26}, {12,34}, {11,31}, {5,30}, {10,35}, {7,27}, {4,25}, {4,33}, {9,33}, {8,25}, {2,26}, {2,34}, {8,31}, {9,30}, {3,35}, {3,27}, {5,18}, {11,19}, {12,21}, {6,16}, {9,20}, {8,17}, {3,24}, {3,13}, {10,18}, {7,19}, {1,21}, {1,16}, {7,15}, {10,22}, {4,15}, {4,22}, {23,25}, {14,33}, {17,33}, {20,25}, {22,26}, {15,34}, {16,31}, {21,30}, {16,35}, {21,27}, {7,32}, {10,29}, {4,36}, {4,28} } Symmetric graph 20 of order 36 Valency 8 Diameter 4 Girth 4 Automorphism group of order 576 Number of arcs = 288 Number of 2-arcs = 2016 2-arc-transitive false Edge-set { {1,7}, {5,9}, {18,36}, {12,20}, {20,32}, {2,25}, {10,28}, {4,17}, {11,30}, {4,32}, {11,14}, {6,13}, {6,35}, {16,19}, {8,31}, {9,33}, {18,30}, {16,29}, {7,32}, {14,33}, {18,24}, {1,29}, {11,23}, {2,19}, {11,26}, {19,27}, {3,22}, {3,12}, {10,31}, {13,17}, {20,28}, {26,32}, {2,30}, {10,16}, {22,29}, {3,15}, {9,32}, {14,18}, {24,28}, {1,26}, {2,35}, {10,21}, {5,29}, {15,36}, {3,6}, {12,35}, {7,12}, {8,33}, {24,34}, {8,17}, {30,34}, {19,31}, {13,31}, {1,23}, {2,9}, {4,16}, {8,11}, {14,32}, {5,14}, {6,30}, {16,35}, {19,22}, {3,31}, {29,33}, {15,24}, {8,21}, {4,34}, {2,24}, {1,10}, {5,36}, {6,26}, {27,35}, {19,34}, {23,31}, {12,29}, {15,20}, {21,25}, {4,28}, {17,26}, {27,30}, {9,17}, {16,25}, {12,13}, {2,13}, {22,36}, {6,20}, {32,35}, {7,22}, {3,33}, {10,18}, {17,29}, {24,32}, {1,14}, {12,24}, {1,20}, {22,26}, {3,27}, {13,34}, {28,29}, {15,26}, {21,35}, {4,21}, {10,34}, {17,23}, {7,27}, {25,33}, {5,19}, {31,36}, {12,25}, {13,22}, {15,30}, {4,11}, {6,23}, {7,16}, {11,19}, {14,27}, {8,28}, {26,34}, {9,15}, {14,21}, {5,24}, {1,36}, {17,35}, {21,30}, {4,5}, {11,36}, {8,15}, {7,34}, {23,27}, {23,33}, {25,31}, {9,22}, {7,18}, {13,28}, {3,18}, {5,25}, {20,21}, {28,36}, {9,27}, {16,23}, {20,33}, {18,25}, {2,8}, {6,10} } Symmetric graph 21 of order 36 Valency 8 Diameter 4 Girth 3 Automorphism group of order 4608 Number of arcs = 288 Number of 2-arcs = 2016 2-arc-transitive false Edge-set { {1,5}, {14,33}, {31,34}, {19,23}, {2,15}, {24,27}, {16,18}, {5,32}, {6,10}, {13,18}, {4,33}, {6,11}, {9,24}, {17,30}, {3,7}, {28,33}, {17,31}, {3,34}, {28,32}, {20,30}, {1,7}, {15,23}, {15,35}, {2,34}, {25,32}, {4,6}, {9,27}, {26,29}, {8,19}, {16,36}, {29,36}, {12,23}, {27,29}, {8,18}, {16,24}, {12,28}, {17,23}, {26,31}, {5,19}, {14,36}, {29,34}, {5,18}, {4,10}, {18,21}, {4,14}, {13,24}, {16,33}, {10,28}, {17,22}, {15,34}, {32,35}, {4,11}, {9,25}, {20,21}, {6,30}, {3,13}, {22,25}, {13,20}, {10,26}, {11,25}, {20,24}, {30,35}, {7,30}, {6,17}, {3,9}, {1,12}, {23,26}, {5,29}, {8,10}, {32,33}, {6,31}, {19,22}, {2,13}, {24,25}, {16,20}, {30,33}, {7,31}, {3,15}, {28,35}, {7,12}, {15,19}, {2,35}, {6,20}, {1,9}, {3,12}, {23,28}, {8,29}, {8,11}, {18,24}, {4,16}, {21,28}, {14,17}, {25,35}, {22,27}, {5,12}, {26,34}, {19,32}, {1,36}, {11,22}, {20,31}, {2,10}, {5,9}, {21,26}, {14,19}, {26,36}, {19,29}, {8,32}, {27,36}, {1,14}, {10,21}, {25,33}, {3,35}, {28,30}, {15,17}, {27,34}, {18,32}, {1,33}, {9,22}, {3,5}, {18,29}, {4,36}, {12,21}, {14,23}, {13,21}, {1,16}, {10,23}, {25,30}, {7,9}, {2,8}, {14,22}, {11,24}, {16,21}, {13,34}, {27,31}, {2,6}, {15,22}, {12,26}, {4,8}, {7,17}, {11,27}, {31,36}, {7,20}, {13,35}, {2,11} } Symmetric graph 22 of order 36 Valency 8 Diameter 3 Girth 4 Automorphism group of order 4608 Number of arcs = 288 Number of 2-arcs = 2016 2-arc-transitive false Edge-set { {1,6}, {14,34}, {32,34}, {19,24}, {2,16}, {24,28}, {16,17}, {6,32}, {6,9}, {13,17}, {3,33}, {6,12}, {9,23}, {17,29}, {3,8}, {28,34}, {17,32}, {4,34}, {27,32}, {20,29}, {1,8}, {16,23}, {15,36}, {1,34}, {26,32}, {4,5}, {10,27}, {25,29}, {8,20}, {16,35}, {30,36}, {12,24}, {28,29}, {8,17}, {15,24}, {11,28}, {17,24}, {25,31}, {5,20}, {14,35}, {30,34}, {5,17}, {3,10}, {18,22}, {4,13}, {14,24}, {16,34}, {9,28}, {17,21}, {15,33}, {31,35}, {3,11}, {10,25}, {20,22}, {5,30}, {3,14}, {22,26}, {13,19}, {9,26}, {12,25}, {20,23}, {29,35}, {8,30}, {6,18}, {4,9}, {2,12}, {23,25}, {6,29}, {8,9}, {31,33}, {5,31}, {19,21}, {2,14}, {24,26}, {16,19}, {29,33}, {8,31}, {3,16}, {28,36}, {7,11}, {15,20}, {1,35}, {6,19}, {2,9}, {4,12}, {23,27}, {7,29}, {8,12}, {18,23}, {4,15}, {21,27}, {14,18}, {25,36}, {22,28}, {5,11}, {26,33}, {19,31}, {2,36}, {11,21}, {20,32}, {1,10}, {5,10}, {21,25}, {14,20}, {26,35}, {19,30}, {7,32}, {27,35}, {1,13}, {10,22}, {25,34}, {4,35}, {27,30}, {15,18}, {27,33}, {18,31}, {2,33}, {9,21}, {3,6}, {18,30}, {3,36}, {12,22}, {13,23}, {14,21}, {1,15}, {10,24}, {26,30}, {7,10}, {2,7}, {13,22}, {11,23}, {15,21}, {13,33}, {28,31}, {2,5}, {16,22}, {11,26}, {4,7}, {7,18}, {12,27}, {32,36}, {7,19}, {13,36}, {1,11} } Symmetric graph 23 of order 36 Valency 8 Diameter 3 Girth 4 Automorphism group of order 37748736 Number of arcs = 288 Number of 2-arcs = 2016 2-arc-transitive false Edge-set { {1,9}, {8,10}, {14,22}, {9,26}, {20,21}, {19,25}, {19,22}, {26,33}, {3,22}, {10,30}, {13,21}, {30,34}, {4,29}, {14,29}, {29,33}, {3,30}, {3,12}, {16,33}, {5,22}, {6,21}, {5,25}, {25,34}, {4,21}, {6,11}, {5,15}, {6,25}, {5,26}, {6,22}, {5,12}, {6,16}, {16,23}, {12,27}, {17,34}, {18,33}, {3,17}, {4,18}, {3,29}, {4,11}, {15,34}, {17,24}, {18,28}, {3,18}, {4,17}, {18,34}, {17,33}, {4,22}, {18,23}, {17,27}, {27,35}, {2,23}, {12,32}, {11,31}, {15,32}, {16,31}, {5,16}, {6,15}, {6,12}, {15,24}, {11,28}, {31,36}, {1,32}, {15,31}, {16,32}, {12,31}, {11,32}, {15,33}, {16,34}, {3,11}, {32,35}, {2,31}, {2,10}, {13,35}, {7,24}, {8,23}, {7,27}, {8,28}, {18,27}, {17,28}, {17,23}, {18,24}, {4,12}, {28,36}, {1,24}, {7,9}, {8,14}, {8,27}, {7,28}, {8,24}, {7,23}, {12,28}, {11,27}, {16,24}, {15,23}, {5,11}, {7,13}, {10,25}, {20,35}, {19,36}, {1,20}, {2,19}, {2,32}, {1,31}, {31,35}, {32,36}, {14,36}, {20,26}, {1,19}, {2,20}, {19,35}, {20,36}, {1,23}, {2,24}, {27,36}, {28,35}, {9,29}, {13,29}, {14,30}, {8,13}, {7,14}, {7,10}, {8,9}, {13,30}, {9,30}, {10,29}, {14,35}, {13,36}, {2,9}, {1,10}, {6,26}, {20,25}, {19,26}, {19,21}, {20,22}, {5,21}, {10,26}, {9,25}, {13,22}, {14,21}, {4,30}, {29,34}, {30,33}, {3,21}, {25,33}, {26,34} } Symmetric graph 24 of order 36 Valency 8 Diameter 4 Girth 4 Automorphism group of order 47552535724032 Number of arcs = 288 Number of 2-arcs = 2016 2-arc-transitive false Edge-set { {1,13}, {20,35}, {12,24}, {6,25}, {16,32}, {14,32}, {6,19}, {11,22}, {2,34}, {4,34}, {21,26}, {4,36}, {23,26}, {22,26}, {2,15}, {13,30}, {5,18}, {8,19}, {11,29}, {8,18}, {10,29}, {12,29}, {17,33}, {10,31}, {12,31}, {20,33}, {12,30}, {18,33}, {19,33}, {1,35}, {24,27}, {21,27}, {1,14}, {24,26}, {3,15}, {2,13}, {5,28}, {3,14}, {8,28}, {2,14}, {6,28}, {7,28}, {8,25}, {7,25}, {16,30}, {6,27}, {7,27}, {14,30}, {7,26}, {15,30}, {6,20}, {12,32}, {9,32}, {19,36}, {9,29}, {17,36}, {20,36}, {12,23}, {9,22}, {19,35}, {11,24}, {10,21}, {9,23}, {10,24}, {3,35}, {11,23}, {10,22}, {2,35}, {10,23}, {4,35}, {3,34}, {1,34}, {2,36}, {1,36}, {23,27}, {4,33}, {1,33}, {22,27}, {22,25}, {2,16}, {4,14}, {6,26}, {4,16}, {5,26}, {15,31}, {13,31}, {5,25}, {16,31}, {14,31}, {7,18}, {15,32}, {13,32}, {5,19}, {15,29}, {8,17}, {7,20}, {6,17}, {5,20}, {11,32}, {8,20}, {6,18}, {10,32}, {11,31}, {9,31}, {10,30}, {9,30}, {18,36}, {11,30}, {18,34}, {19,34}, {11,21}, {12,22}, {2,33}, {12,21}, {3,33}, {24,25}, {21,25}, {3,36}, {23,25}, {1,15}, {22,28}, {24,28}, {3,13}, {1,16}, {4,13}, {3,16}, {4,15}, {8,26}, {8,27}, {5,27}, {14,29}, {13,29}, {5,17}, {7,19}, {7,17}, {17,34}, {20,34}, {18,35}, {17,35}, {9,24}, {9,21}, {23,28}, {21,28}, {16,29} } Symmetric graph 25 of order 36 Valency 9 Diameter 3 Girth 3 Automorphism group of order 648 Number of arcs = 324 Number of 2-arcs = 2592 2-arc-transitive false Edge-set { {1,4}, {20,35}, {18,19}, {24,26}, {5,32}, {22,28}, {23,25}, {8,14}, {16,34}, {7,27}, {4,13}, {7,15}, {12,30}, {12,33}, {2,31}, {27,29}, {9,10}, {10,20}, {18,32}, {11,28}, {10,31}, {3,6}, {14,17}, {3,36}, {9,22}, {5,9}, {13,29}, {2,11}, {2,24}, {28,34}, {13,16}, {2,35}, {21,36}, {17,21}, {30,33}, {21,25}, {11,13}, {19,29}, {11,16}, {15,34}, {1,20}, {25,34}, {14,20}, {2,7}, {4,27}, {29,32}, {1,34}, {20,26}, {6,33}, {23,30}, {8,17}, {6,36}, {6,24}, {7,23}, {10,15}, {1,32}, {5,22}, {15,31}, {1,29}, {27,31}, {4,35}, {19,24}, {4,12}, {24,33}, {20,22}, {9,18}, {5,34}, {19,27}, {4,23}, {8,24}, {17,36}, {8,26}, {6,15}, {3,21}, {17,25}, {26,28}, {18,35}, {19,34}, {31,35}, {9,35}, {5,19}, {16,22}, {18,26}, {5,25}, {14,22}, {3,18}, {14,36}, {13,24}, {2,19}, {16,27}, {15,18}, {25,30}, {12,14}, {3,33}, {8,12}, {11,21}, {17,31}, {21,23}, {7,30}, {4,8}, {2,5}, {22,27}, {1,16}, {26,35}, {11,26}, {23,32}, {8,28}, {7,16}, {12,27}, {13,33}, {32,36}, {21,28}, {3,12}, {25,33}, {10,25}, {14,32}, {22,31}, {9,29}, {11,32}, {28,31}, {6,7}, {14,30}, {1,23}, {16,33}, {30,35}, {6,26}, {15,23}, {6,10}, {20,30}, {12,18}, {16,20}, {9,13}, {1,8}, {10,29}, {3,9}, {10,17}, {17,24}, {7,36}, {33,34}, {13,35}, {5,11}, {15,19}, {29,36}, {13,21}, {2,17}, {3,28}, {4,31}, {24,29}, {12,19}, {2,30}, {27,36}, {1,10}, {26,32}, {4,21}, {9,25}, {5,14}, {3,22}, {8,34}, {6,20}, {18,23}, {7,11}, {15,28} } Symmetric graph 26 of order 36 Valency 9 Diameter 3 Girth 3 Automorphism group of order 1296 Number of arcs = 324 Number of 2-arcs = 2592 2-arc-transitive false Edge-set { {1,4}, {4,12}, {26,28}, {4,8}, {8,26}, {29,34}, {15,17}, {26,34}, {1,34}, {17,34}, {30,31}, {14,32}, {16,24}, {2,5}, {31,34}, {17,32}, {12,31}, {28,32}, {16,31}, {2,32}, {13,23}, {22,27}, {6,22}, {18,20}, {3,19}, {5,11}, {25,30}, {26,31}, {23,32}, {16,27}, {2,22}, {8,23}, {27,29}, {15,22}, {18,26}, {3,23}, {11,27}, {22,30}, {21,23}, {4,20}, {19,36}, {16,21}, {6,19}, {21,27}, {1,10}, {10,14}, {11,29}, {5,9}, {9,25}, {28,35}, {13,18}, {17,23}, {20,22}, {18,36}, {3,16}, {11,19}, {21,30}, {1,21}, {20,34}, {30,36}, {14,16}, {19,24}, {5,21}, {1,17}, {10,21}, {20,29}, {9,36}, {9,16}, {19,28}, {13,21}, {12,20}, {4,15}, {10,26}, {11,33}, {3,12}, {6,14}, {13,36}, {12,16}, {7,12}, {7,28}, {7,22}, {6,7}, {9,30}, {9,14}, {25,36}, {2,35}, {29,33}, {15,31}, {2,20}, {15,19}, {1,33}, {10,18}, {3,29}, {9,11}, {13,28}, {12,13}, {12,28}, {10,32}, {13,33}, {18,22}, {3,6}, {14,20}, {5,13}, {12,25}, {2,28}, {7,13}, {15,30}, {33,36}, {2,18}, {3,36}, {14,29}, {11,15}, {8,15}, {8,10}, {4,24}, {5,26}, {7,34}, {7,17}, {9,24}, {8,29}, {6,27}, {4,33}, {8,18}, {3,8}, {8,35}, {15,35}, {21,35}, {27,35}, {6,36}, {32,35}, {18,33}, {14,24}, {24,26}, {5,23}, {10,30}, {24,28}, {1,7}, {2,9}, {23,29}, {7,27}, {23,25}, {17,19}, {6,10}, {4,25}, {4,35}, {25,32}, {24,33}, {11,17}, {1,30}, {1,24}, {5,34}, {19,26}, {17,25}, {3,31}, {14,34}, {5,31}, {6,32}, {27,33}, {22,31}, {20,25}, {2,11}, {16,35} } Symmetric graph 27 of order 36 Valency 9 Diameter 3 Girth 3 Automorphism group of order 1296 Number of arcs = 324 Number of 2-arcs = 2592 2-arc-transitive false Edge-set { {1,6}, {32,35}, {1,33}, {15,16}, {11,30}, {18,35}, {29,33}, {7,23}, {14,19}, {21,27}, {26,36}, {8,15}, {11,13}, {18,19}, {25,29}, {2,4}, {5,24}, {24,28}, {17,20}, {12,29}, {7,18}, {10,14}, {8,12}, {6,23}, {4,19}, {22,27}, {21,36}, {8,28}, {13,17}, {11,19}, {9,25}, {31,34}, {2,32}, {3,22}, {1,20}, {9,30}, {19,26}, {25,34}, {4,8}, {5,13}, {24,25}, {20,35}, {6,26}, {4,34}, {1,24}, {28,31}, {2,17}, {3,12}, {14,29}, {12,18}, {6,20}, {4,27}, {9,22}, {15,21}, {27,28}, {17,36}, {5,11}, {6,9}, {10,28}, {16,34}, {30,32}, {3,36}, {23,31}, {30,35}, {16,33}, {5,21}, {8,17}, {9,10}, {6,31}, {22,33}, {3,21}, {1,11}, {15,30}, {11,16}, {10,32}, {1,8}, {13,31}, {2,10}, {1,35}, {9,34}, {15,32}, {19,24}, {20,25}, {8,26}, {13,34}, {1,16}, {12,31}, {2,7}, {3,5}, {23,29}, {12,20}, {7,27}, {9,14}, {12,15}, {27,33}, {5,32}, {27,35}, {7,13}, {16,21}, {26,30}, {14,36}, {11,26}, {3,18}, {4,15}, {5,25}, {6,35}, {17,32}, {1,28}, {29,36}, {18,31}, {33,36}, {21,23}, {16,25}, {4,33}, {17,22}, {21,28}, {15,35}, {11,33}, {6,10}, {16,23}, {19,30}, {9,16}, {13,22}, {10,21}, {7,35}, {14,33}, {17,26}, {28,34}, {3,31}, {2,19}, {4,12}, {5,7}, {23,26}, {19,34}, {7,29}, {3,30}, {7,11}, {4,22}, {14,18}, {14,24}, {10,27}, {8,36}, {3,9}, {12,25}, {13,28}, {2,29}, {18,24}, {15,23}, {20,29}, {18,27}, {25,32}, {6,14}, {13,20}, {26,31}, {2,34}, {8,24}, {10,17}, {5,36}, {2,23}, {20,22}, {24,32}, {22,30} } Symmetric graph 28 of order 36 Valency 10 Diameter 3 Girth 3 Automorphism group of order 720 Number of arcs = 360 Number of 2-arcs = 3240 2-arc-transitive false Edge-set { {1,7}, {5,35}, {9,27}, {3,22}, {25,32}, {17,32}, {5,12}, {1,28}, {18,29}, {15,24}, {3,34}, {9,24}, {20,34}, {8,25}, {5,18}, {6,27}, {10,14}, {1,19}, {8,29}, {14,24}, {29,36}, {29,32}, {12,14}, {19,25}, {15,36}, {3,10}, {4,17}, {5,26}, {11,31}, {11,21}, {16,27}, {14,36}, {1,10}, {11,29}, {14,21}, {1,31}, {1,34}, {11,34}, {8,21}, {15,26}, {3,16}, {24,31}, {2,9}, {20,30}, {4,25}, {23,33}, {7,33}, {27,33}, {7,17}, {5,23}, {21,31}, {5,31}, {11,27}, {14,33}, {17,21}, {5,19}, {27,36}, {19,33}, {7,36}, {10,17}, {8,16}, {4,24}, {23,29}, {6,32}, {12,28}, {13,25}, {2,15}, {3,30}, {13,35}, {20,35}, {9,35}, {17,20}, {9,20}, {23,27}, {17,33}, {3,23}, {25,33}, {5,7}, {11,20}, {21,35}, {3,26}, {16,25}, {20,26}, {16,35}, {9,31}, {10,23}, {2,29}, {14,30}, {1,13}, {26,34}, {18,34}, {6,8}, {12,15}, {24,28}, {12,22}, {22,32}, {22,25}, {15,32}, {12,32}, {9,25}, {15,20}, {17,30}, {5,13}, {1,30}, {13,29}, {3,35}, {7,15}, {22,27}, {1,16}, {4,29}, {4,15}, {7,22}, {23,32}, {12,33}, {30,31}, {11,13}, {6,14}, {2,21}, {16,19}, {4,36}, {10,19}, {19,36}, {10,26}, {8,34}, {8,24}, {28,34}, {8,18}, {15,28}, {3,18}, {24,34}, {3,12}, {9,13}, {2,20}, {2,27}, {1,22}, {8,35}, {17,28}, {2,14}, {2,8}, {24,30}, {28,35}, {9,18}, {13,34}, {13,23}, {2,33}, {4,11}, {21,26}, {7,26}, {16,23}, {26,31}, {11,16}, {16,31}, {10,36}, {18,19}, {6,36}, {6,24}, {19,29}, {6,25}, {6,17}, {5,28}, {18,27}, {22,36}, {10,32}, {6,20}, {6,11}, {21,28}, {10,28}, {18,22}, {12,19}, {12,30}, {13,22}, {7,30}, {4,9}, {4,33}, {7,23}, {4,21}, {14,26}, {18,31}, {2,32}, {30,35} } Symmetric graph 29 of order 36 Valency 10 Diameter 2 Girth 3 Automorphism group of order 720 Number of arcs = 360 Number of 2-arcs = 3240 2-arc-transitive false Edge-set { {1,7}, {13,26}, {4,9}, {19,36}, {28,34}, {15,30}, {2,10}, {17,24}, {3,21}, {22,27}, {20,31}, {29,36}, {16,28}, {12,34}, {15,32}, {10,17}, {5,14}, {11,24}, {16,20}, {1,23}, {24,25}, {21,33}, {27,31}, {3,27}, {8,22}, {5,31}, {7,32}, {18,35}, {6,35}, {12,25}, {12,15}, {9,33}, {16,31}, {8,13}, {4,18}, {12,22}, {14,23}, {4,24}, {20,26}, {5,26}, {11,29}, {11,13}, {6,20}, {9,19}, {6,32}, {6,14}, {8,30}, {8,36}, {2,30}, {10,23}, {4,33}, {11,34}, {2,33}, {11,27}, {8,35}, {2,15}, {18,19}, {6,28}, {23,25}, {25,36}, {9,14}, {3,16}, {7,30}, {3,19}, {14,35}, {3,35}, {20,29}, {1,29}, {8,28}, {7,18}, {2,23}, {3,25}, {2,16}, {12,26}, {6,29}, {11,21}, {1,36}, {17,33}, {14,21}, {18,30}, {1,22}, {24,30}, {30,35}, {10,35}, {9,29}, {7,17}, {5,17}, {21,35}, {6,17}, {5,21}, {9,23}, {16,25}, {13,23}, {4,25}, {21,29}, {26,32}, {8,16}, {1,18}, {17,22}, {5,30}, {16,33}, {1,31}, {19,27}, {10,25}, {12,14}, {1,13}, {2,34}, {23,32}, {20,32}, {29,33}, {4,13}, {12,20}, {15,29}, {7,21}, {23,30}, {26,34}, {9,32}, {18,34}, {6,10}, {14,34}, {3,32}, {10,18}, {22,33}, {30,31}, {15,22}, {14,25}, {5,19}, {19,28}, {11,31}, {13,32}, {18,20}, {23,31}, {4,20}, {7,24}, {17,26}, {22,28}, {27,35}, {13,36}, {4,34}, {5,8}, {5,9}, {16,19}, {15,36}, {9,27}, {10,26}, {8,20}, {18,29}, {10,19}, {14,28}, {3,7}, {22,35}, {28,32}, {7,33}, {2,11}, {17,27}, {5,36}, {19,34}, {4,8}, {9,15}, {13,27}, {6,24}, {21,26}, {24,34}, {3,15}, {2,22}, {6,11}, {17,31}, {24,36}, {7,28}, {11,16}, {25,33}, {13,21}, {2,26}, {1,12}, {10,36}, {3,12}, {15,24}, {12,31}, {1,28}, {4,27} } Symmetric graph 30 of order 36 Valency 10 Diameter 3 Girth 4 Automorphism group of order 8640 Number of arcs = 360 Number of 2-arcs = 3240 2-arc-transitive false Edge-set { {1,7}, {5,18}, {12,16}, {4,29}, {13,22}, {16,27}, {9,19}, {2,19}, {17,32}, {25,32}, {23,27}, {19,36}, {13,36}, {8,25}, {6,36}, {15,25}, {11,30}, {2,21}, {11,21}, {2,33}, {23,33}, {30,36}, {10,36}, {6,25}, {10,25}, {6,23}, {17,21}, {11,33}, {3,10}, {6,14}, {21,28}, {20,33}, {15,20}, {10,31}, {6,31}, {15,28}, {15,31}, {10,28}, {6,7}, {3,15}, {7,33}, {3,30}, {10,20}, {10,14}, {3,21}, {14,33}, {14,21}, {3,33}, {14,30}, {30,31}, {7,15}, {1,14}, {7,18}, {3,26}, {14,24}, {24,31}, {28,35}, {7,35}, {20,26}, {12,14}, {3,12}, {24,28}, {20,35}, {12,28}, {1,20}, {3,18}, {1,28}, {18,20}, {18,31}, {14,35}, {7,26}, {14,26}, {7,24}, {1,31}, {18,28}, {3,24}, {26,31}, {12,20}, {5,26}, {16,24}, {18,29}, {12,22}, {1,22}, {18,34}, {26,34}, {24,29}, {12,34}, {1,29}, {9,24}, {5,35}, {9,18}, {5,12}, {22,35}, {16,26}, {1,16}, {24,34}, {29,35}, {9,35}, {18,22}, {5,24}, {16,35}, {22,26}, {12,29}, {9,26}, {1,34}, {4,22}, {13,34}, {27,34}, {19,29}, {22,32}, {16,32}, {9,27}, {5,32}, {8,29}, {8,22}, {4,34}, {19,34}, {29,32}, {8,16}, {4,9}, {5,19}, {5,13}, {13,29}, {4,16}, {9,13}, {9,32}, {5,27}, {22,27}, {16,19}, {8,34}, {5,8}, {2,32}, {17,27}, {4,23}, {8,23}, {4,36}, {11,32}, {2,27}, {11,27}, {13,23}, {8,36}, {4,11}, {2,13}, {17,19}, {2,8}, {4,17}, {4,25}, {11,19}, {8,17}, {13,25}, {19,25}, {23,32}, {11,13}, {27,36}, {6,11}, {2,15}, {23,30}, {21,36}, {17,30}, {17,33}, {2,10}, {6,17}, {11,15}, {15,36}, {15,23}, {25,33}, {10,17}, {21,25}, {2,30}, {10,23}, {6,28}, {20,30}, {21,31}, {7,30}, {6,20}, {28,33}, {7,21}, {12,31}, {3,35}, {1,9} } Symmetric graph 31 of order 36 Valency 10 Diameter 2 Girth 3 Automorphism group of order 1036800 Number of arcs = 360 Number of 2-arcs = 3240 2-arc-transitive false Edge-set { {1,2}, {2,8}, {4,7}, {5,6}, {5,10}, {1,8}, {7,23}, {5,25}, {10,24}, {4,14}, {7,13}, {3,21}, {15,19}, {16,21}, {17,18}, {2,17}, {6,15}, {9,16}, {1,18}, {4,23}, {6,25}, {5,24}, {4,18}, {13,32}, {15,21}, {15,24}, {16,29}, {18,23}, {17,34}, {6,12}, {9,24}, {1,29}, {7,14}, {1,30}, {7,31}, {3,26}, {4,20}, {13,20}, {11,22}, {3,9}, {10,32}, {15,28}, {27,34}, {8,27}, {3,22}, {17,23}, {10,12}, {8,23}, {19,32}, {14,18}, {7,32}, {3,15}, {19,24}, {21,29}, {2,34}, {12,15}, {16,24}, {18,29}, {14,17}, {1,20}, {7,12}, {3,6}, {5,20}, {8,20}, {22,32}, {3,34}, {12,32}, {29,34}, {4,25}, {23,27}, {19,25}, {12,26}, {2,30}, {13,31}, {21,26}, {2,13}, {6,33}, {5,35}, {4,33}, {2,22}, {13,30}, {21,36}, {11,36}, {9,22}, {14,30}, {20,30}, {16,35}, {27,31}, {11,35}, {28,31}, {11,26}, {9,34}, {31,32}, {28,34}, {8,11}, {27,29}, {11,32}, {11,23}, {12,31}, {9,35}, {8,13}, {25,32}, {7,17}, {6,26}, {4,5}, {24,28}, {22,34}, {20,25}, {3,12}, {10,31}, {4,6}, {5,9}, {2,3}, {1,21}, {11,19}, {12,21}, {9,17}, {15,30}, {16,18}, {31,34}, {8,35}, {29,31}, {11,27}, {14,24}, {28,29}, {25,36}, {5,33}, {10,35}, {20,33}, {17,22}, {16,36}, {22,36}, {10,16}, {19,28}, {18,36}, {14,28}, {1,36}, {27,33}, {28,33}, {26,35}, {31,33}, {29,33}, {19,30}, {19,36}, {27,35}, {19,22}, {28,30}, {26,27}, {8,30}, {29,36}, {1,16}, {11,25}, {5,16}, {25,33}, {10,13}, {14,15}, {7,18}, {3,17}, {24,35}, {24,30}, {2,9}, {1,13}, {14,19}, {15,26}, {27,28}, {22,25}, {23,26}, {33,34}, {32,36}, {23,35}, {6,21}, {9,10}, {14,23}, {18,21}, {4,17}, {6,20}, {8,26}, {2,20}, {12,13}, {7,10} } Symmetric graph 32 of order 36 Valency 12 Diameter 2 Girth 3 Automorphism group of order 432 Number of arcs = 432 Number of 2-arcs = 4752 2-arc-transitive false Edge-set { {1,4}, {6,20}, {31,35}, {18,32}, {5,11}, {15,36}, {33,36}, {22,27}, {27,29}, {2,24}, {17,23}, {10,25}, {20,22}, {5,34}, {26,31}, {25,32}, {8,28}, {1,5}, {24,25}, {26,28}, {1,23}, {7,13}, {17,20}, {14,29}, {7,29}, {8,29}, {14,19}, {16,33}, {15,17}, {15,16}, {12,18}, {13,19}, {2,8}, {6,21}, {25,28}, {11,13}, {14,36}, {4,26}, {30,34}, {3,31}, {9,22}, {19,27}, {24,30}, {8,23}, {21,25}, {22,28}, {28,36}, {9,12}, {4,20}, {31,34}, {18,31}, {8,14}, {16,21}, {15,28}, {9,28}, {19,23}, {9,30}, {15,20}, {13,18}, {2,7}, {6,11}, {11,16}, {12,15}, {19,36}, {29,33}, {4,8}, {29,35}, {2,22}, {8,11}, {29,36}, {1,22}, {8,12}, {10,33}, {9,13}, {4,35}, {18,24}, {11,26}, {21,23}, {16,32}, {5,19}, {5,21}, {3,17}, {4,10}, {20,27}, {10,31}, {6,35}, {1,33}, {12,17}, {5,12}, {33,34}, {1,31}, {5,7}, {6,26}, {25,33}, {6,9}, {19,35}, {30,32}, {26,30}, {3,7}, {21,22}, {27,32}, {16,24}, {13,34}, {10,14}, {7,10}, {13,20}, {14,30}, {7,15}, {1,18}, {12,13}, {14,21}, {28,34}, {13,28}, {9,14}, {23,28}, {1,9}, {3,34}, {3,4}, {10,27}, {15,35}, {32,36}, {22,26}, {27,30}, {3,24}, {17,22}, {20,24}, {4,12}, {11,14}, {21,34}, {28,32}, {5,9}, {3,23}, {9,10}, {10,15}, {13,35}, {11,32}, {8,15}, {5,36}, {17,31}, {2,33}, {11,17}, {26,33}, {21,26}, {3,32}, {5,27}, {1,35}, {24,29}, {6,36}, {12,32}, {22,29}, {17,33}, {14,17}, {1,36}, {12,26}, {25,29}, {1,8}, {14,18}, {3,36}, {12,27}, {23,25}, {6,10}, {6,27}, {2,32}, {10,16}, {18,23}, {11,25}, {14,34}, {16,19}, {2,6}, {7,11}, {3,16}, {4,34}, {27,31}, {24,26}, {2,34}, {11,31}, {30,33}, {8,24}, {13,29}, {2,35}, {23,30}, {7,22}, {19,24}, {7,30}, {21,35}, {7,23}, {20,25}, {15,21}, {3,6}, {4,25}, {9,24}, {4,7}, {32,35}, {18,20}, {12,33}, {3,9}, {28,31}, {20,34}, {10,18}, {2,5}, {17,19}, {13,16}, {6,8}, {5,25}, {16,22}, {1,16}, {19,26}, {29,31}, {2,18}, {4,19}, {20,36}, {18,21}, {30,35}, {15,30}, {2,17}, {23,27} } Symmetric graph 33 of order 36 Valency 12 Diameter 2 Girth 3 Automorphism group of order 432 Number of arcs = 432 Number of 2-arcs = 4752 2-arc-transitive false Edge-set { {1,4}, {8,35}, {11,14}, {4,25}, {4,33}, {12,14}, {29,35}, {8,22}, {14,22}, {8,29}, {14,21}, {12,15}, {30,35}, {20,25}, {18,33}, {1,12}, {18,35}, {4,20}, {1,33}, {12,16}, {11,15}, {30,36}, {21,25}, {2,4}, {17,22}, {7,22}, {29,31}, {15,35}, {11,30}, {25,31}, {8,17}, {7,14}, {11,21}, {15,32}, {26,30}, {29,36}, {21,26}, {2,5}, {16,22}, {8,34}, {18,27}, {1,5}, {18,32}, {20,28}, {1,19}, {11,25}, {4,36}, {2,29}, {22,28}, {19,22}, {27,33}, {5,12}, {32,35}, {14,16}, {20,36}, {21,24}, {2,23}, {20,26}, {16,24}, {8,23}, {9,34}, {1,32}, {18,26}, {4,27}, {6,33}, {23,31}, {24,25}, {9,35}, {30,31}, {17,19}, {3,7}, {9,11}, {22,29}, {8,26}, {5,14}, {20,34}, {3,18}, {1,18}, {9,18}, {23,29}, {9,15}, {15,30}, {25,30}, {12,32}, {26,35}, {17,26}, {5,7}, {3,16}, {2,34}, {17,24}, {7,23}, {3,32}, {16,33}, {6,27}, {6,31}, {11,20}, {24,31}, {23,25}, {14,24}, {7,29}, {13,21}, {2,28}, {16,19}, {3,22}, {6,25}, {4,31}, {21,28}, {2,19}, {9,27}, {5,36}, {10,32}, {6,14}, {1,20}, {4,24}, {23,33}, {9,12}, {17,27}, {6,7}, {31,36}, {10,25}, {31,35}, {2,20}, {1,16}, {6,11}, {2,36}, {21,22}, {2,22}, {20,30}, {4,23}, {24,33}, {23,27}, {5,9}, {32,36}, {10,26}, {27,34}, {6,12}, {3,33}, {16,32}, {10,20}, {29,32}, {13,24}, {7,28}, {13,19}, {14,17}, {3,28}, {3,12}, {17,35}, {5,20}, {10,16}, {19,34}, {9,26}, {1,36}, {10,18}, {13,22}, {8,28}, {14,19}, {3,8}, {18,34}, {6,23}, {5,15}, {13,30}, {7,12}, {13,35}, {7,11}, {16,21}, {6,15}, {24,27}, {13,32}, {26,28}, {5,19}, {25,28}, {4,19}, {17,34}, {11,26}, {13,29}, {26,34}, {8,18}, {1,34}, {12,18}, {17,21}, {2,7}, {2,8}, {3,29}, {6,9}, {15,31}, {23,28}, {6,24}, {7,15}, {10,21}, {30,32}, {13,17}, {3,10}, {12,33}, {27,35}, {19,36}, {15,36}, {10,30}, {25,33}, {9,17}, {5,11}, {13,31}, {1,10}, {10,33}, {27,31}, {13,16}, {4,34}, {13,36}, {3,23}, {19,24}, {9,14}, {8,27}, {5,34}, {11,28}, {21,30}, {10,28}, {15,29} } Symmetric graph 34 of order 36 Valency 12 Diameter 2 Girth 3 Automorphism group of order 1728 Number of arcs = 432 Number of 2-arcs = 4752 2-arc-transitive false Edge-set { {1,5}, {9,10}, {11,27}, {13,16}, {6,9}, {18,32}, {8,13}, {21,22}, {2,24}, {11,13}, {6,12}, {23,28}, {15,21}, {2,5}, {26,28}, {18,21}, {8,29}, {20,26}, {2,8}, {11,17}, {7,12}, {30,34}, {19,36}, {1,18}, {8,10}, {11,26}, {33,34}, {15,36}, {24,26}, {18,23}, {5,35}, {27,33}, {15,16}, {8,15}, {5,26}, {8,22}, {14,17}, {4,7}, {6,25}, {17,32}, {9,24}, {23,27}, {5,9}, {18,33}, {29,33}, {6,20}, {1,32}, {15,20}, {24,30}, {19,23}, {4,10}, {11,31}, {13,29}, {20,22}, {1,24}, {10,33}, {11,15}, {15,28}, {5,21}, {3,22}, {12,14}, {2,23}, {22,28}, {30,32}, {13,19}, {10,13}, {6,11}, {23,29}, {1,36}, {29,35}, {12,16}, {2,9}, {27,28}, {20,27}, {1,16}, {20,34}, {25,30}, {17,19}, {3,18}, {8,30}, {21,36}, {2,35}, {16,21}, {9,29}, {18,20}, {1,8}, {10,26}, {11,18}, {7,28}, {21,25}, {3,7}, {19,26}, {28,34}, {2,17}, {8,12}, {30,36}, {19,35}, {27,32}, {4,36}, {31,35}, {17,22}, {7,24}, {6,26}, {32,34}, {13,36}, {9,22}, {24,27}, {5,27}, {16,33}, {14,34}, {23,25}, {15,35}, {5,34}, {4,8}, {26,31}, {22,26}, {18,24}, {6,35}, {16,23}, {9,15}, {8,23}, {14,18}, {7,14}, {4,25}, {25,33}, {15,17}, {33,36}, {5,7}, {17,31}, {2,32}, {13,28}, {10,32}, {3,4}, {30,31}, {14,29}, {4,20}, {11,33}, {12,15}, {28,33}, {6,21}, {29,32}, {13,20}, {1,22}, {24,29}, {5,19}, {3,33}, {14,19}, {1,31}, {5,10}, {15,30}, {20,23}, {4,11}, {12,31}, {22,30}, {19,24}, {1,6}, {3,23}, {10,14}, {21,34}, {2,36}, {2,16}, {9,28}, {10,25}, {3,35}, {12,27}, {10,16}, {17,20}, {1,7}, {1,34}, {29,36}, {12,18}, {28,35}, {21,27}, {20,35}, {25,29}, {19,25}, {3,17}, {3,9}, {27,30}, {9,11}, {16,19}, {7,30}, {6,8}, {26,32}, {13,34}, {6,36}, {16,31}, {9,14}, {25,31}, {7,13}, {16,22}, {4,27}, {32,35}, {17,24}, {7,23}, {4,34}, {31,36}, {13,18}, {14,35}, {22,25}, {5,12}, {2,33}, {12,32}, {3,6}, {3,31}, {14,30}, {14,21}, {2,4}, {21,24}, {28,31}, {4,19}, {10,17}, {7,11}, {26,29}, {12,25}, {3,34} } Symmetric graph 35 of order 36 Valency 12 Diameter 3 Girth 4 Automorphism group of order 4320 Number of arcs = 432 Number of 2-arcs = 4752 2-arc-transitive false Edge-set { {1,7}, {3,36}, {19,29}, {3,20}, {6,24}, {5,10}, {1,23}, {6,20}, {25,36}, {30,33}, {14,35}, {19,26}, {23,29}, {6,36}, {7,25}, {3,7}, {11,16}, {8,15}, {1,31}, {24,27}, {5,9}, {10,26}, {7,29}, {1,36}, {20,29}, {16,32}, {13,23}, {3,12}, {17,19}, {8,25}, {30,34}, {28,35}, {27,33}, {9,14}, {10,29}, {3,19}, {6,23}, {6,10}, {18,23}, {13,20}, {26,32}, {15,20}, {18,24}, {5,24}, {25,35}, {7,30}, {2,11}, {4,8}, {1,12}, {8,16}, {15,34}, {28,31}, {6,33}, {10,14}, {1,24}, {5,20}, {26,36}, {29,33}, {14,36}, {17,20}, {22,26}, {6,32}, {11,27}, {9,18}, {14,23}, {22,25}, {19,30}, {5,36}, {11,29}, {2,32}, {13,21}, {3,31}, {15,19}, {16,35}, {23,30}, {2,33}, {4,12}, {12,17}, {16,36}, {15,33}, {14,31}, {19,25}, {6,35}, {7,27}, {3,9}, {10,16}, {7,15}, {21,27}, {9,27}, {18,36}, {8,13}, {17,34}, {22,28}, {26,31}, {21,25}, {5,11}, {3,35}, {10,13}, {18,21}, {13,22}, {4,32}, {14,24}, {5,33}, {11,26}, {2,10}, {16,21}, {18,31}, {15,24}, {7,16}, {3,23}, {16,33}, {12,15}, {17,31}, {24,25}, {5,7}, {8,29}, {1,34}, {20,28}, {26,34}, {8,28}, {7,17}, {3,22}, {13,35}, {30,32}, {2,24}, {4,21}, {12,27}, {9,17}, {4,7}, {1,8}, {1,20}, {13,33}, {14,32}, {17,22}, {4,22}, {27,32}, {11,28}, {18,34}, {25,31}, {10,30}, {9,13}, {14,21}, {16,22}, {4,23}, {14,19}, {25,33}, {20,26}, {16,23}, {12,18}, {17,24}, {30,36}, {29,35}, {2,19}, {6,12}, {2,9}, {4,35}, {12,30}, {24,29}, {1,21}, {20,27}, {1,32}, {11,18}, {4,34}, {24,28}, {28,36}, {29,34}, {6,19}, {11,15}, {21,28}, {27,34}, {8,18}, {12,13}, {2,22}, {12,25}, {11,14}, {13,34}, {28,32}, {15,22}, {4,31}, {23,27}, {5,31}, {10,25}, {6,9}, {16,20}, {23,26}, {18,19}, {3,11}, {6,8}, {1,10}, {5,21}, {29,31}, {15,36}, {2,34}, {4,19}, {17,32}, {9,28}, {9,26}, {2,8}, {17,35}, {22,30}, {13,31}, {15,32}, {2,21}, {4,11}, {12,28}, {8,26}, {7,14}, {5,22}, {3,33}, {10,17}, {5,34}, {2,35}, {21,30}, {18,33}, {27,35}, {9,30} } Symmetric graph 36 of order 36 Valency 12 Diameter 3 Girth 4 Automorphism group of order 10368 Number of arcs = 432 Number of 2-arcs = 4752 2-arc-transitive false Edge-set { {1,4}, {12,13}, {2,18}, {9,24}, {6,32}, {2,11}, {16,25}, {16,33}, {10,21}, {5,15}, {3,23}, {8,11}, {1,36}, {26,28}, {24,26}, {7,29}, {31,36}, {14,23}, {10,31}, {17,20}, {8,18}, {11,33}, {12,21}, {27,34}, {14,30}, {33,34}, {21,30}, {17,25}, {6,21}, {8,22}, {22,31}, {5,20}, {6,7}, {3,30}, {27,35}, {11,25}, {4,8}, {24,33}, {9,29}, {32,36}, {20,35}, {22,26}, {4,20}, {26,29}, {15,36}, {3,36}, {27,28}, {15,29}, {18,32}, {11,19}, {19,22}, {1,35}, {15,17}, {3,12}, {10,26}, {19,35}, {8,36}, {28,33}, {13,18}, {4,33}, {21,24}, {10,13}, {5,21}, {8,23}, {19,30}, {7,35}, {32,34}, {13,30}, {2,35}, {25,34}, {21,23}, {8,17}, {14,29}, {23,25}, {4,13}, {2,5}, {8,28}, {28,32}, {19,34}, {12,19}, {7,18}, {4,27}, {9,10}, {17,32}, {7,34}, {30,31}, {19,28}, {18,21}, {14,24}, {2,24}, {6,25}, {29,33}, {21,36}, {7,24}, {6,31}, {18,31}, {11,20}, {15,34}, {17,19}, {7,12}, {9,23}, {6,15}, {7,16}, {20,36}, {9,28}, {29,31}, {3,18}, {11,27}, {22,25}, {5,13}, {20,28}, {13,24}, {2,6}, {11,14}, {1,16}, {18,27}, {5,27}, {9,34}, {2,17}, {12,25}, {13,35}, {2,29}, {3,5}, {23,27}, {9,12}, {6,26}, {15,22}, {14,34}, {25,36}, {22,33}, {16,21}, {3,28}, {4,25}, {21,29}, {17,33}, {3,22}, {8,30}, {33,35}, {20,23}, {4,9}, {9,17}, {12,32}, {16,31}, {10,20}, {15,23}, {3,4}, {1,17}, {12,26}, {8,35}, {16,27}, {10,14}, {13,22}, {2,10}, {1,6}, {27,30}, {14,35}, {11,15}, {3,16}, {5,33}, {1,12}, {18,26}, {25,29}, {1,29}, {16,20}, {3,11}, {9,36}, {19,24}, {13,16}, {31,35}, {20,29}, {9,16}, {10,32}, {23,32}, {4,19}, {20,22}, {5,9}, {4,32}, {26,36}, {10,27}, {14,17}, {13,36}, {2,28}, {24,27}, {7,30}, {23,31}, {30,32}, {18,19}, {7,11}, {7,22}, {5,31}, {24,32}, {6,19}, {12,15}, {26,35}, {5,7}, {1,10}, {17,26}, {4,14}, {1,24}, {2,34}, {25,30}, {13,28}, {1,30}, {8,10}, {21,34}, {14,16}, {2,23}, {6,8}, {5,26}, {12,33}, {6,14}, {1,22}, {15,28}, {3,34}, {15,18}, {11,31} } Symmetric graph 37 of order 36 Valency 12 Diameter 3 Girth 4 Automorphism group of order 56623104 Number of arcs = 432 Number of 2-arcs = 4752 2-arc-transitive false Edge-set { {1,7}, {5,21}, {21,28}, {4,9}, {1,19}, {9,16}, {1,35}, {2,24}, {24,29}, {5,8}, {8,29}, {5,34}, {15,21}, {6,11}, {4,22}, {11,18}, {4,32}, {19,27}, {18,22}, {27,32}, {14,19}, {9,30}, {3,20}, {20,25}, {2,10}, {10,25}, {2,35}, {17,24}, {8,15}, {5,36}, {15,35}, {17,36}, {8,27}, {5,11}, {29,31}, {6,23}, {7,13}, {6,34}, {22,30}, {13,23}, {30,34}, {15,22}, {11,26}, {7,27}, {4,33}, {16,19}, {7,15}, {26,33}, {27,36}, {4,20}, {19,25}, {18,36}, {18,32}, {3,12}, {12,28}, {3,32}, {14,20}, {10,17}, {2,31}, {17,32}, {14,31}, {10,30}, {2,7}, {25,33}, {28,36}, {13,24}, {21,30}, {7,28}, {13,33}, {15,33}, {16,36}, {6,24}, {8,13}, {10,16}, {25,35}, {23,26}, {26,35}, {17,23}, {6,36}, {9,17}, {30,31}, {6,21}, {22,28}, {13,31}, {13,34}, {16,33}, {16,35}, {11,28}, {4,12}, {1,31}, {16,21}, {28,35}, {28,31}, {12,13}, {29,33}, {8,16}, {3,11}, {12,27}, {23,29}, {8,30}, {15,34}, {12,14}, {3,33}, {14,34}, {12,26}, {3,9}, {16,20}, {24,26}, {9,29}, {18,31}, {1,20}, {12,18}, {28,32}, {29,34}, {2,19}, {18,21}, {1,8}, {16,34}, {18,35}, {19,28}, {13,32}, {22,29}, {23,25}, {15,19}, {26,36}, {17,22}, {27,31}, {30,32}, {7,14}, {11,14}, {1,24}, {7,29}, {6,8}, {18,24}, {29,32}, {25,36}, {10,18}, {5,7}, {10,26}, {17,35}, {14,32}, {5,22}, {9,25}, {1,10}, {21,27}, {8,14}, {25,34}, {10,15}, {5,35}, {12,17}, {2,32}, {3,34}, {14,33}, {2,9}, {15,36}, {17,31}, {20,27}, {11,25}, {4,21}, {3,22}, {4,10}, {14,23}, {30,33}, {26,34}, {9,15}, {27,35}, {11,17}, {5,23}, {1,36}, {22,27}, {11,27}, {23,30}, {7,30}, {4,34}, {19,26}, {9,26}, {6,35}, {1,32}, {11,13}, {7,16}, {9,18}, {13,20}, {2,23}, {24,30}, {20,26}, {3,19}, {5,33}, {2,36}, {15,20}, {3,31}, {17,21}, {14,24}, {20,28}, {12,25}, {21,29}, {8,28}, {24,25}, {10,29}, {6,12}, {4,31}, {6,33}, {13,19}, {16,22}, {6,7}, {18,23}, {1,9}, {4,11}, {5,12}, {2,8}, {3,21}, {3,10}, {5,24}, {2,20}, {4,19}, {6,22}, {1,23} } Symmetric graph 38 of order 36 Valency 12 Diameter 3 Girth 3 Automorphism group of order 104485552128 Number of arcs = 432 Number of 2-arcs = 4752 2-arc-transitive false Edge-set { {1,13}, {11,18}, {21,28}, {8,23}, {20,30}, {13,28}, {4,36}, {3,16}, {16,33}, {22,30}, {8,32}, {18,28}, {4,28}, {9,36}, {10,23}, {10,19}, {24,25}, {19,33}, {12,25}, {14,30}, {8,35}, {3,32}, {6,16}, {23,28}, {4,30}, {9,28}, {4,23}, {5,36}, {10,17}, {18,33}, {6,21}, {18,31}, {15,25}, {1,34}, {21,33}, {12,31}, {7,25}, {1,19}, {17,30}, {8,27}, {3,35}, {9,16}, {10,32}, {6,24}, {14,25}, {16,28}, {4,33}, {9,30}, {5,28}, {4,17}, {23,33}, {2,36}, {10,13}, {18,29}, {12,30}, {14,36}, {23,31}, {5,30}, {20,25}, {1,26}, {11,34}, {11,21}, {13,33}, {12,36}, {7,31}, {5,19}, {4,25}, {1,15}, {21,31}, {24,30}, {8,29}, {3,27}, {10,35}, {9,24}, {17,25}, {6,32}, {6,18}, {14,34}, {1,27}, {19,28}, {9,33}, {12,23}, {8,17}, {2,28}, {4,13}, {23,29}, {12,33}, {10,22}, {7,30}, {8,19}, {17,36}, {10,27}, {16,31}, {5,33}, {2,30}, {8,13}, {22,25}, {1,32}, {11,26}, {2,21}, {8,34}, {11,20}, {20,36}, {12,28}, {7,36}, {4,31}, {5,15}, {13,31}, {9,25}, {1,23}, {21,26}, {15,30}, {3,29}, {7,16}, {3,24}, {6,35}, {9,18}, {17,34}, {1,29}, {6,14}, {11,27}, {3,21}, {12,17}, {16,29}, {4,22}, {7,33}, {12,19}, {18,35}, {8,15}, {24,36}, {10,29}, {6,27}, {3,18}, {19,31}, {5,25}, {2,33}, {12,13}, {8,22}, {1,35}, {11,32}, {8,26}, {2,20}, {22,36}, {3,34}, {11,16}, {20,32}, {7,28}, {4,19}, {10,15}, {9,31}, {5,23}, {13,26}, {1,17}, {7,24}, {24,34}, {9,14}, {11,29}, {7,21}, {14,27}, {3,20}, {19,29}, {23,35}, {12,15}, {16,26}, {15,36}, {10,34}, {6,29}, {7,18}, {3,14}, {5,31}, {2,25}, {12,22}, {16,35}, {11,35}, {9,21}, {6,20}, {3,26}, {2,16}, {22,32}, {11,24}, {4,15}, {18,26}, {5,17}, {21,29}, {15,34}, {17,27}, {7,20}, {24,32}, {19,26}, {10,26}, {6,34}, {7,14}, {24,27}, {2,31}, {5,13}, {1,22}, {19,35}, {9,20}, {14,32}, {2,24}, {20,34}, {23,26}, {13,29}, {15,32}, {6,26}, {2,18}, {11,14}, {15,27}, {5,22}, {21,35}, {17,32}, {22,34}, {2,14}, {20,27}, {13,35}, {22,27} } Symmetric graph 39 of order 36 Valency 12 Diameter 3 Girth 4 Automorphism group of order 1671768834048000000 Number of arcs = 432 Number of 2-arcs = 4752 2-arc-transitive false Edge-set { {1,7}, {8,35}, {29,33}, {14,36}, {28,34}, {15,24}, {21,25}, {13,20}, {7,27}, {16,32}, {19,26}, {2,18}, {6,13}, {3,29}, {16,17}, {11,19}, {8,9}, {31,35}, {20,33}, {17,22}, {5,23}, {12,30}, {10,18}, {7,10}, {19,34}, {8,36}, {6,24}, {21,31}, {9,17}, {5,11}, {12,28}, {3,10}, {25,36}, {2,34}, {14,21}, {24,28}, {11,15}, {9,25}, {4,9}, {1,33}, {14,35}, {23,27}, {4,22}, {10,26}, {1,12}, {26,35}, {12,16}, {13,36}, {27,34}, {3,21}, {16,24}, {2,11}, {28,33}, {3,35}, {27,32}, {4,19}, {6,26}, {1,31}, {13,29}, {17,27}, {7,16}, {26,30}, {3,20}, {2,32}, {13,19}, {18,28}, {3,6}, {25,29}, {2,17}, {5,25}, {8,15}, {14,20}, {7,28}, {4,5}, {15,32}, {1,18}, {8,27}, {4,29}, {14,30}, {16,31}, {20,26}, {5,13}, {3,30}, {19,25}, {6,14}, {28,31}, {22,31}, {20,23}, {5,12}, {10,32}, {30,34}, {18,36}, {8,21}, {24,29}, {19,24}, {9,31}, {11,20}, {17,35}, {5,33}, {23,30}, {18,22}, {6,11}, {7,22}, {12,19}, {8,10}, {6,34}, {31,36}, {17,21}, {7,9}, {11,30}, {32,35}, {19,33}, {6,23}, {12,29}, {20,34}, {5,24}, {21,32}, {9,18}, {10,17}, {7,36}, {4,21}, {1,11}, {9,14}, {27,33}, {4,35}, {22,26}, {1,23}, {16,23}, {10,13}, {12,27}, {3,36}, {16,34}, {2,24}, {13,21}, {2,12}, {11,28}, {3,9}, {15,33}, {25,35}, {14,22}, {4,10}, {12,15}, {26,36}, {1,34}, {24,27}, {11,16}, {2,33}, {23,28}, {3,22}, {10,25}, {9,26}, {13,35}, {3,5}, {8,28}, {20,25}, {2,7}, {15,31}, {5,14}, {28,32}, {4,30}, {15,18}, {1,8}, {14,29}, {1,17}, {27,31}, {4,20}, {5,26}, {13,30}, {3,19}, {8,16}, {6,25}, {2,31}, {17,28}, {7,15}, {1,32}, {18,27}, {4,6}, {26,29}, {25,30}, {14,19}, {6,33}, {32,36}, {11,29}, {7,35}, {30,33}, {18,21}, {22,32}, {19,23}, {6,12}, {29,34}, {20,24}, {7,21}, {9,32}, {18,35}, {8,22}, {10,31}, {17,36}, {5,34}, {24,30}, {23,29}, {12,20}, {15,34}, {13,22}, {15,23}, {22,25}, {10,14}, {4,36}, {21,26}, {9,13}, {16,33}, {2,23}, {1,24}, {11,27}, {16,18}, {15,17}, {2,8} } Symmetric graph 40 of order 36 Valency 14 Diameter 2 Girth 3 Automorphism group of order 12096 Number of arcs = 504 Number of 2-arcs = 6552 2-arc-transitive false Edge-set { {1,2}, {2,22}, {15,22}, {2,23}, {1,15}, {14,23}, {7,22}, {2,24}, {1,14}, {7,21}, {13,24}, {15,24}, {8,23}, {12,22}, {2,21}, {1,13}, {8,20}, {12,16}, {1,12}, {14,22}, {15,23}, {3,7}, {9,24}, {10,24}, {11,23}, {13,22}, {2,20}, {2,16}, {3,25}, {9,19}, {10,18}, {11,17}, {1,11}, {1,7}, {15,21}, {13,23}, {14,24}, {17,24}, {3,8}, {5,12}, {6,12}, {4,7}, {15,16}, {22,25}, {2,19}, {2,18}, {2,17}, {8,17}, {3,27}, {5,35}, {6,36}, {4,26}, {2,4}, {1,10}, {1,9}, {1,8}, {14,20}, {7,16}, {12,21}, {12,26}, {18,22}, {18,23}, {19,23}, {3,17}, {3,9}, {5,10}, {6,11}, {4,11}, {20,24}, {5,8}, {14,17}, {8,15}, {23,27}, {22,35}, {22,36}, {22,26}, {3,26}, {9,18}, {10,19}, {17,31}, {3,29}, {5,32}, {6,34}, {4,33}, {11,20}, {5,28}, {20,22}, {2,5}, {2,6}, {2,3}, {21,25}, {13,19}, {13,18}, {11,28}, {7,36}, {15,36}, {16,23}, {17,22}, {16,24}, {7,35}, {21,24}, {17,26}, {3,18}, {5,19}, {5,17}, {6,18}, {4,19}, {4,10}, {4,20}, {6,9}, {12,25}, {19,22}, {21,26}, {1,3}, {9,14}, {9,15}, {10,15}, {7,31}, {24,29}, {24,32}, {23,34}, {23,33}, {11,15}, {23,28}, {3,28}, {5,36}, {6,35}, {26,32}, {18,35}, {18,33}, {19,34}, {17,30}, {18,28}, {19,27}, {4,31}, {20,29}, {6,30}, {4,25}, {15,25}, {8,13}, {20,27}, {16,35}, {16,36}, {10,30}, {9,31}, {8,33}, {14,33}, {15,35}, {7,14}, {15,26}, {12,14}, {21,23}, {8,34}, {12,13}, {11,26}, {18,26}, {19,36}, {17,36}, {3,16}, {6,21}, {6,20}, {4,16}, {20,35}, {5,21}, {20,25}, {11,27}, {11,13}, {20,28}, {1,5}, {7,13}, {1,6}, {8,35}, {7,33}, {12,34}, {12,30}, {12,28}, {7,27}, {24,31}, {7,29}, {24,30}, {1,4}, {10,14}, {17,33}, {3,30}, {5,31}, {6,33}, {4,34}, {28,36}, {26,34}, {33,36}, {9,36}, {16,34}, {29,36}, {16,32}, {27,35}, {21,31}, {20,32}, {16,30}, {31,35}, {21,29}, {25,30}, {19,25}, {5,27}, {14,27}, {25,31}, {19,29}, {18,32}, {17,34}, {9,32}, {13,32}, {13,31}, {13,30}, {14,34}, {14,28}, {10,29}, {10,28}, {10,26}, {11,36}, {16,28}, {10,35}, {21,33}, {9,25}, {8,25}, {25,33}, {19,30}, {18,31}, {9,34}, {8,32}, {11,31}, {12,32}, {11,30}, {8,29}, {26,29}, {4,32}, {6,29}, {10,33}, {30,33}, {30,35}, {28,31}, {32,33}, {25,28}, {29,34}, {21,27}, {34,35}, {26,27}, {13,29}, {9,27}, {27,32}, {32,36}, {27,30}, {31,34}, {28,29} } Symmetric graph 41 of order 36 Valency 14 Diameter 2 Girth 3 Automorphism group of order 362880 Number of arcs = 504 Number of 2-arcs = 6552 2-arc-transitive false Edge-set { {1,2}, {3,7}, {2,6}, {4,8}, {10,16}, {11,21}, {7,18}, {6,17}, {8,19}, {9,13}, {1,4}, {14,23}, {23,31}, {24,29}, {22,26}, {26,32}, {5,16}, {18,21}, {18,31}, {17,19}, {9,19}, {3,22}, {3,13}, {12,18}, {5,33}, {16,17}, {12,30}, {30,33}, {25,27}, {20,34}, {11,20}, {7,34}, {13,32}, {12,23}, {15,31}, {14,29}, {6,22}, {5,32}, {5,30}, {18,30}, {19,31}, {8,22}, {1,21}, {10,20}, {9,11}, {3,10}, {11,26}, {5,6}, {5,28}, {18,27}, {12,34}, {15,24}, {17,29}, {28,29}, {27,31}, {30,34}, {13,33}, {32,33}, {14,35}, {15,25}, {14,26}, {3,15}, {2,33}, {16,35}, {21,25}, {4,20}, {12,28}, {27,33}, {15,17}, {9,30}, {20,30}, {10,25}, {17,20}, {12,20}, {7,15}, {14,32}, {15,29}, {14,31}, {6,30}, {5,29}, {8,30}, {9,21}, {2,9}, {2,32}, {4,7}, {8,26}, {1,14}, {10,23}, {11,24}, {26,34}, {14,19}, {6,24}, {28,35}, {15,27}, {25,31}, {19,21}, {25,28}, {17,24}, {29,35}, {4,34}, {3,24}, {23,26}, {7,24}, {23,32}, {10,36}, {10,11}, {18,34}, {5,13}, {1,15}, {9,10}, {8,23}, {23,36}, {22,29}, {27,35}, {24,34}, {24,33}, {22,31}, {30,32}, {13,23}, {31,32}, {14,28}, {2,15}, {9,16}, {20,21}, {16,20}, {10,17}, {12,25}, {15,21}, {14,16}, {4,29}, {2,31}, {22,32}, {7,22}, {7,8}, {7,20}, {6,7}, {8,32}, {2,13}, {1,16}, {2,18}, {4,5}, {26,27}, {11,33}, {34,35}, {13,25}, {10,19}, {8,18}, {11,17}, {28,36}, {9,33}, {13,30}, {19,22}, {11,19}, {25,36}, {21,27}, {16,28}, {1,35}, {1,25}, {1,27}, {11,16}, {2,27}, {10,21}, {7,12}, {24,36}, {6,33}, {5,35}, {18,25}, {4,12}, {8,14}, {22,23}, {22,24}, {12,36}, {33,36}, {11,35}, {27,34}, {17,21}, {7,29}, {4,16}, {3,12}, {26,33}, {7,30}, {10,28}, {6,9}, {8,20}, {19,23}, {13,28}, {15,22}, {9,32}, {7,17}, {2,21}, {9,20}, {3,6}, {3,23}, {12,13}, {33,34}, {24,26}, {26,31}, {19,26}, {3,17}, {35,36}, {8,34}, {4,30}, {3,29}, {13,36}, {34,36}, {23,28}, {3,36}, {4,28}, {8,12}, {14,22}, {2,5}, {11,36}, {6,29}, {1,28}, {4,18}, {16,21}, {27,36}, {26,36}, {3,28}, {33,35}, {19,32}, {2,25}, {1,31}, {1,29}, {1,5}, {11,27}, {11,34}, {2,30}, {16,29}, {21,31}, {23,25}, {24,35}, {17,22}, {4,14}, {16,19}, {3,25}, {26,35}, {6,32}, {1,18}, {10,12}, {10,13}, {6,13}, {4,35}, {5,9}, {18,20}, {6,15}, {24,27}, {19,20}, {8,31}, {9,17}, {5,14}, {15,18} } Symmetric graph 42 of order 36 Valency 15 Diameter 2 Girth 3 Automorphism group of order 51840 Number of arcs = 540 Number of 2-arcs = 7560 2-arc-transitive false Edge-set { {1,4}, {1,8}, {2,8}, {1,15}, {2,16}, {3,15}, {4,16}, {1,26}, {2,27}, {3,28}, {5,26}, {6,27}, {8,28}, {1,30}, {2,26}, {3,31}, {4,34}, {5,34}, {6,29}, {10,30}, {11,26}, {12,31}, {7,34}, {15,34}, {16,29}, {2,22}, {3,30}, {4,26}, {5,9}, {6,12}, {8,11}, {8,36}, {10,11}, {11,36}, {7,12}, {7,9}, {4,18}, {19,22}, {20,30}, {21,26}, {9,17}, {12,13}, {11,13}, {14,36}, {27,36}, {7,28}, {1,9}, {3,6}, {4,33}, {4,5}, {6,22}, {8,30}, {8,26}, {10,14}, {11,17}, {12,17}, {7,13}, {15,20}, {16,21}, {15,21}, {16,23}, {18,20}, {19,21}, {20,21}, {21,23}, {13,17}, {13,14}, {14,17}, {30,33}, {22,24}, {30,32}, {26,32}, {14,25}, {17,18}, {17,23}, {13,20}, {20,23}, {23,25}, {21,31}, {23,34}, {13,34}, {14,29}, {1,14}, {2,17}, {5,12}, {6,7}, {8,10}, {7,33}, {4,15}, {16,22}, {15,30}, {16,26}, {18,19}, {19,25}, {20,25}, {18,21}, {17,25}, {13,18}, {13,23}, {14,20}, {24,27}, {28,32}, {1,32}, {27,32}, {24,28}, {16,32}, {24,32}, {15,32}, {19,23}, {18,25}, {4,36}, {10,22}, {31,33}, {4,35}, {22,35}, {30,35}, {26,35}, {3,25}, {2,25}, {18,28}, {24,25}, {15,18}, {20,24}, {16,24}, {15,24}, {9,32}, {12,32}, {11,24}, {15,36}, {11,23}, {20,36}, {7,19}, {9,25}, {1,19}, {10,17}, {7,14}, {16,19}, {13,36}, {8,27}, {6,28}, {1,33}, {22,27}, {28,30}, {3,24}, {2,32}, {22,25}, {3,18}, {2,23}, {20,28}, {23,24}, {29,31}, {31,34}, {34,35}, {29,35}, {1,35}, {2,35}, {31,35}, {29,34}, {28,35}, {27,35}, {8,21}, {8,23}, {6,18}, {19,33}, {9,36}, {10,12}, {8,33}, {5,8}, {6,33}, {5,33}, {5,22}, {3,22}, {3,4}, {2,34}, {28,29}, {22,29}, {27,28}, {24,31}, {1,31}, {26,29}, {27,31}, {14,35}, {17,35}, {13,35}, {20,29}, {23,27}, {13,27}, {14,30}, {14,22}, {3,17}, {1,27}, {2,30}, {13,19}, {15,31}, {16,34}, {12,34}, {7,29}, {1,36}, {2,10}, {6,31}, {33,34}, {5,29}, {3,35}, {3,33}, {2,5}, {24,29}, {9,12}, {9,11}, {12,36}, {11,33}, {5,36}, {9,33}, {7,11}, {15,16}, {2,12}, {14,21}, {10,16}, {10,15}, {11,16}, {7,10}, {10,36}, {6,10}, {5,6}, {6,8}, {3,11}, {9,29}, {7,30}, {9,26}, {9,31}, {5,25}, {25,33}, {5,18}, {23,33}, {5,20}, {7,16}, {9,24}, {23,31}, {20,34}, {4,19}, {6,19}, {4,22}, {12,27}, {11,28}, {9,14}, {1,21}, {3,10}, {4,11}, {17,21}, {10,21}, {26,28}, {4,13}, {19,32}, {25,32}, {18,26}, {19,27}, {14,19}, {12,18}, {12,15}, {6,21}, {17,26}, {22,36}, {24,36}, {13,28}, {17,31}, {21,29}, {8,20}, {18,32}, {30,34}, {25,30}, {7,32} } Symmetric graph 43 of order 36 Valency 15 Diameter 3 Girth 3 Automorphism group of order 261213880320 Number of arcs = 540 Number of 2-arcs = 7560 2-arc-transitive false Edge-set { {1,7}, {6,35}, {21,30}, {3,22}, {4,25}, {18,30}, {17,31}, {1,29}, {18,27}, {2,15}, {28,36}, {9,18}, {9,31}, {10,24}, {6,10}, {6,17}, {30,32}, {9,14}, {9,33}, {5,8}, {8,29}, {13,21}, {3,34}, {9,23}, {24,31}, {6,23}, {27,32}, {13,24}, {3,32}, {24,25}, {3,10}, {10,25}, {18,23}, {5,31}, {12,31}, {12,23}, {19,31}, {1,23}, {4,36}, {22,26}, {17,36}, {22,32}, {11,30}, {11,17}, {1,20}, {2,27}, {28,31}, {14,23}, {24,27}, {6,13}, {3,28}, {14,25}, {5,33}, {11,27}, {11,13}, {5,27}, {15,27}, {13,36}, {1,32}, {15,32}, {24,36}, {9,28}, {4,24}, {6,26}, {24,33}, {6,20}, {28,33}, {14,20}, {6,16}, {6,28}, {14,30}, {2,21}, {16,29}, {18,35}, {10,21}, {23,29}, {5,18}, {18,34}, {10,34}, {10,19}, {15,30}, {5,14}, {29,33}, {6,34}, {12,28}, {12,14}, {14,27}, {13,33}, {3,11}, {11,25}, {1,13}, {27,34}, {12,15}, {12,36}, {4,19}, {1,26}, {14,34}, {19,33}, {11,34}, {11,19}, {4,14}, {26,33}, {8,14}, {8,33}, {11,21}, {5,30}, {8,23}, {21,27}, {3,13}, {13,31}, {23,34}, {13,28}, {3,16}, {25,35}, {19,27}, {3,26}, {15,25}, {13,19}, {1,34}, {12,26}, {3,7}, {7,25}, {25,34}, {12,18}, {17,29}, {7,17}, {7,32}, {9,22}, {4,9}, {17,24}, {17,28}, {14,32}, {9,26}, {9,20}, {2,9}, {20,32}, {2,24}, {25,32}, {16,24}, {8,18}, {8,31}, {4,12}, {17,19}, {3,20}, {2,25}, {20,34}, {12,33}, {12,20}, {1,11}, {15,34}, {19,36}, {6,11}, {2,33}, {8,20}, {21,33}, {16,28}, {30,35}, {2,12}, {19,25}, {1,16}, {2,19}, {16,19}, {1,35}, {12,22}, {1,22}, {30,34}, {4,18}, {26,31}, {14,22}, {17,33}, {11,24}, {20,28}, {2,14}, {7,27}, {15,22}, {16,33}, {27,35}, {8,15}, {8,36}, {11,16}, {2,30}, {20,35}, {15,35}, {21,36}, {15,20}, {2,36}, {10,17}, {10,32}, {10,35}, {23,35}, {5,21}, {29,31}, {2,31}, {23,28}, {10,27}, {10,13}, {5,12}, {16,31}, {15,23}, {23,26}, {5,15}, {13,29}, {5,36}, {7,13}, {9,36}, {6,22}, {10,16}, {29,36}, {20,26}, {19,30}, {2,8}, {21,25}, {5,19}, {26,36}, {1,17}, {7,34}, {18,22}, {4,31}, {20,29}, {16,36}, {6,7}, {7,30}, {5,25}, {7,16}, {4,30}, {18,20}, {6,29}, {12,29}, {1,10}, {13,26}, {14,35}, {7,19}, {4,33}, {8,22}, {4,15}, {4,8}, {3,17}, {8,26}, {3,29}, {23,32}, {5,24}, {22,28}, {17,26}, {6,32}, {11,32}, {7,24}, {8,28}, {4,21}, {11,35}, {21,31}, {3,23}, {18,25}, {17,21}, {16,26}, {22,29}, {16,21}, {3,35}, {10,30}, {9,29}, {7,21}, {7,35}, {2,18}, {9,15}, {24,30}, {1,28}, {22,35}, {4,27}, {22,34}, {18,32}, {5,9} } Symmetric graph 44 of order 36 Valency 15 Diameter 3 Girth 4 Automorphism group of order 3134566563840 Number of arcs = 540 Number of 2-arcs = 7560 2-arc-transitive false Edge-set { {1,4}, {9,10}, {13,16}, {13,36}, {9,24}, {25,29}, {12,27}, {20,29}, {6,27}, {33,36}, {9,34}, {1,16}, {19,28}, {14,17}, {20,22}, {28,31}, {8,17}, {18,20}, {20,24}, {3,6}, {21,36}, {4,9}, {10,25}, {12,13}, {30,33}, {27,30}, {11,26}, {4,31}, {31,35}, {3,22}, {1,30}, {27,35}, {8,11}, {4,26}, {10,31}, {4,33}, {31,34}, {15,18}, {5,20}, {6,32}, {9,36}, {9,16}, {19,24}, {14,29}, {22,27}, {2,24}, {3,29}, {2,17}, {21,23}, {9,22}, {19,22}, {1,5}, {11,31}, {15,35}, {2,10}, {13,29}, {17,19}, {8,23}, {9,18}, {16,21}, {13,22}, {1,24}, {3,16}, {21,22}, {26,28}, {4,7}, {17,31}, {2,18}, {20,36}, {6,9}, {25,36}, {9,12}, {6,33}, {33,34}, {20,35}, {12,33}, {14,34}, {1,11}, {15,28}, {11,14}, {5,32}, {32,36}, {31,36}, {9,35}, {6,31}, {33,35}, {7,10}, {13,17}, {15,22}, {1,23}, {5,25}, {14,24}, {1,29}, {27,28}, {11,33}, {32,35}, {8,36}, {26,36}, {12,32}, {29,31}, {10,33}, {13,34}, {11,25}, {12,15}, {5,31}, {3,18}, {21,30}, {7,16}, {12,26}, {10,14}, {4,20}, {16,20}, {6,19}, {14,36}, {8,24}, {21,24}, {3,4}, {4,19}, {10,15}, {13,23}, {3,28}, {25,30}, {15,30}, {23,26}, {7,23}, {20,23}, {2,6}, {1,6}, {19,36}, {5,9}, {8,22}, {1,18}, {3,5}, {7,24}, {27,29}, {11,27}, {25,35}, {10,32}, {26,34}, {1,10}, {13,28}, {3,17}, {20,30}, {15,24}, {3,23}, {19,23}, {2,5}, {6,8}, {6,21}, {14,23}, {2,22}, {1,22}, {1,28}, {13,24}, {3,24}, {21,29}, {4,27}, {15,16}, {14,28}, {22,25}, {7,22}, {1,17}, {29,32}, {25,34}, {7,12}, {14,18}, {13,30}, {24,26}, {16,31}, {4,25}, {12,31}, {18,33}, {6,26}, {8,34}, {5,33}, {32,34}, {9,11}, {16,33}, {24,25}, {27,36}, {3,11}, {2,16}, {19,29}, {2,28}, {18,32}, {7,36}, {4,32}, {8,12}, {8,10}, {13,18}, {6,20}, {9,17}, {8,35}, {10,26}, {10,13}, {7,11}, {15,17}, {7,34}, {20,28}, {16,19}, {5,19}, {18,21}, {4,21}, {11,15}, {2,4}, {28,33}, {11,32}, {15,36}, {8,18}, {5,8}, {30,32}, {14,35}, {13,35}, {3,10}, {29,33}, {27,34}, {15,34}, {28,32}, {25,28}, {12,25}, {3,30}, {26,30}, {19,35}, {7,35}, {10,27}, {11,13}, {2,29}, {21,34}, {1,12}, {14,22}, {21,35}, {4,8}, {9,23}, {3,12}, {19,34}, {17,20}, {15,23}, {12,14}, {14,30}, {20,34}, {6,7}, {26,29}, {18,31}, {24,27}, {30,31}, {6,25}, {17,33}, {5,26}, {16,32}, {23,25}, {14,16}, {2,23}, {26,35}, {19,30}, {5,27}, {17,21}, {21,28}, {2,30}, {2,11}, {15,29}, {5,7}, {23,27}, {5,21}, {8,16}, {22,26}, {7,18}, {18,19}, {2,12}, {7,17}, {17,32} } Symmetric graph 45 of order 36 Valency 16 Diameter 3 Girth 4 Automorphism group of order 190253629440 Number of arcs = 576 Number of 2-arcs = 8640 2-arc-transitive false Edge-set { {1,7}, {3,12}, {24,27}, {1,24}, {17,25}, {27,35}, {3,27}, {7,27}, {14,34}, {32,35}, {1,30}, {1,35}, {1,25}, {12,35}, {5,29}, {14,32}, {19,32}, {30,34}, {3,18}, {3,32}, {27,30}, {3,34}, {24,32}, {17,30}, {9,17}, {22,36}, {5,19}, {15,19}, {10,34}, {18,29}, {1,13}, {11,25}, {1,19}, {25,34}, {18,35}, {1,29}, {25,32}, {19,27}, {7,34}, {14,18}, {14,21}, {12,20}, {26,31}, {9,15}, {10,22}, {7,15}, {10,16}, {22,29}, {13,17}, {11,36}, {3,6}, {13,27}, {23,34}, {3,15}, {10,27}, {29,34}, {13,32}, {11,30}, {3,17}, {27,36}, {19,34}, {15,35}, {1,10}, {12,29}, {5,13}, {11,14}, {5,25}, {6,14}, {16,24}, {20,33}, {4,33}, {7,21}, {16,20}, {22,26}, {7,12}, {8,22}, {17,26}, {5,36}, {12,13}, {23,31}, {21,25}, {6,35}, {28,29}, {8,32}, {16,25}, {22,35}, {17,29}, {32,36}, {6,19}, {13,34}, {18,23}, {1,14}, {12,25}, {31,35}, {15,29}, {10,32}, {7,32}, {16,30}, {3,22}, {17,24}, {17,36}, {6,9}, {13,22}, {5,23}, {9,34}, {5,10}, {8,27}, {9,31}, {2,30}, {6,24}, {8,16}, {26,33}, {4,5}, {12,24}, {11,26}, {14,33}, {4,12}, {20,28}, {8,33}, {21,30}, {2,36}, {11,19}, {8,34}, {26,32}, {5,30}, {14,17}, {12,36}, {19,31}, {10,15}, {10,21}, {6,29}, {13,28}, {8,11}, {3,5}, {14,27}, {24,34}, {20,32}, {30,33}, {7,17}, {16,36}, {19,22}, {12,19}, {8,18}, {1,26}, {14,31}, {20,21}, {6,26}, {9,28}, {21,29}, {9,22}, {11,35}, {1,23}, {4,18}, {28,35}, {15,23}, {4,31}, {2,9}, {23,33}, {2,24}, {18,25}, {10,18}, {11,29}, {23,32}, {19,33}, {4,34}, {9,18}, {5,14}, {12,14}, {24,31}, {15,20}, {10,33}, {7,22}, {16,19}, {22,25}, {10,17}, {21,36}, {6,36}, {2,13}, {11,23}, {1,9}, {5,35}, {27,29}, {18,30}, {8,31}, {15,26}, {15,24}, {11,13}, {3,33}, {4,27}, {5,20}, {4,21}, {2,20}, {21,26}, {3,28}, {7,28}, {28,30}, {3,11}, {17,23}, {18,36}, {19,28}, {15,30}, {10,31}, {2,29}, {13,21}, {11,20}, {5,9}, {14,22}, {5,24}, {20,27}, {7,33}, {7,16}, {9,16}, {22,30}, {12,26}, {8,15}, {26,34}, {25,31}, {4,6}, {23,28}, {3,21}, {9,32}, {17,35}, {1,36}, {13,18}, {4,16}, {6,23}, {2,35}, {2,25}, {25,33}, {14,28}, {8,12}, {13,31}, {15,36}, {2,10}, {7,18}, {16,35}, {20,22}, {4,17}, {28,36}, {6,25}, {6,13}, {16,23}, {9,21}, {5,26}, {9,27}, {12,30}, {8,21}, {18,26}, {24,33}, {7,11}, {29,33}, {4,32}, {20,34}, {2,8}, {19,21}, {3,31}, {10,28}, {2,14}, {11,24}, {6,20}, {13,33}, {7,31}, {16,29}, {4,22}, {16,26}, {31,36}, {6,10}, {8,28}, {9,33}, {21,35}, {1,20}, {18,24}, {4,11}, {12,23}, {2,19}, {15,25}, {23,27}, {6,30}, {8,17}, {2,26}, {4,15}, {20,31}, {2,23}, {3,16}, {24,28}, {1,8}, {4,28}, {2,7} } Symmetric graph 46 of order 36 Valency 16 Diameter 2 Girth 3 Automorphism group of order 190210142896128 Number of arcs = 576 Number of 2-arcs = 8640 2-arc-transitive false Edge-set { {1,13}, {23,32}, {6,34}, {5,26}, {18,30}, {12,14}, {9,21}, {10,14}, {7,35}, {19,28}, {19,31}, {4,33}, {17,27}, {2,32}, {18,31}, {1,33}, {10,15}, {12,23}, {3,34}, {16,26}, {17,26}, {11,21}, {7,22}, {4,36}, {15,27}, {5,24}, {5,18}, {6,35}, {17,28}, {11,23}, {6,22}, {1,36}, {19,26}, {4,30}, {12,22}, {8,21}, {1,29}, {14,35}, {14,27}, {20,27}, {3,32}, {15,28}, {12,31}, {7,24}, {15,36}, {13,25}, {10,29}, {13,35}, {10,28}, {9,23}, {3,36}, {16,27}, {20,26}, {3,30}, {14,28}, {9,31}, {6,24}, {1,34}, {14,26}, {7,21}, {7,19}, {4,31}, {11,32}, {8,23}, {6,20}, {10,31}, {23,33}, {15,33}, {15,25}, {5,22}, {8,18}, {16,36}, {6,19}, {4,17}, {12,29}, {9,30}, {24,36}, {13,34}, {1,20}, {10,32}, {23,34}, {3,18}, {1,16}, {2,30}, {9,22}, {8,24}, {4,29}, {15,35}, {14,25}, {8,19}, {3,31}, {16,33}, {6,17}, {2,17}, {9,29}, {6,21}, {1,31}, {14,33}, {12,32}, {15,34}, {12,26}, {7,17}, {5,20}, {11,30}, {9,25}, {6,18}, {1,17}, {11,26}, {22,30}, {22,36}, {13,36}, {13,28}, {16,35}, {11,28}, {24,35}, {14,34}, {9,26}, {21,36}, {7,27}, {4,20}, {2,19}, {24,29}, {21,34}, {6,25}, {1,18}, {21,30}, {22,35}, {8,28}, {23,29}, {5,19}, {2,31}, {16,25}, {11,29}, {7,20}, {10,30}, {23,36}, {13,33}, {16,34}, {8,17}, {14,36}, {9,27}, {5,27}, {2,20}, {9,32}, {6,23}, {11,31}, {22,33}, {4,18}, {12,30}, {1,19}, {4,14}, {12,27}, {10,25}, {3,19}, {2,13}, {9,28}, {6,27}, {3,14}, {7,28}, {24,31}, {24,34}, {23,35}, {3,20}, {3,16}, {21,33}, {2,14}, {24,32}, {4,15}, {12,15}, {7,25}, {8,25}, {20,29}, {21,32}, {9,13}, {6,28}, {19,32}, {23,31}, {11,16}, {8,26}, {20,30}, {10,26}, {5,17}, {2,29}, {8,20}, {12,25}, {7,18}, {24,30}, {22,34}, {21,35}, {11,27}, {24,33}, {2,15}, {4,13}, {5,25}, {2,18}, {3,17}, {22,31}, {4,19}, {6,26}, {21,31}, {7,33}, {5,34}, {2,16}, {9,15}, {8,33}, {3,15}, {12,16}, {17,29}, {21,29}, {23,30}, {22,29}, {8,35}, {22,32}, {5,33}, {18,29}, {7,36}, {19,30}, {12,13}, {11,13}, {20,25}, {18,32}, {17,32}, {2,34}, {9,16}, {18,26}, {17,30}, {3,35}, {11,14}, {19,25}, {1,14}, {10,27}, {11,25}, {12,28}, {19,29}, {5,36}, {7,34}, {10,13}, {5,28}, {8,27}, {17,31}, {7,26}, {9,14}, {11,15}, {10,21}, {5,35}, {2,36}, {11,22}, {8,36}, {4,35}, {20,32}, {20,31}, {10,16}, {10,22}, {20,28}, {12,24}, {4,34}, {2,33}, {18,28}, {18,27}, {5,21}, {2,35}, {1,35}, {19,27}, {3,33}, {13,26}, {6,33}, {1,15}, {3,13}, {4,16}, {8,34}, {10,24}, {12,21}, {6,36}, {1,32}, {10,23}, {9,24}, {11,24}, {7,23}, {18,25}, {17,25}, {16,28}, {13,27}, {5,23}, {15,26}, {8,22}, {4,32}, {1,30}, {3,29} } Symmetric graph 47 of order 36 Valency 17 Diameter 3 Girth 3 Automorphism group of order 4896 Number of arcs = 612 Number of 2-arcs = 9792 2-arc-transitive false Edge-set { {1,3}, {15,19}, {10,22}, {9,18}, {24,30}, {21,32}, {13,35}, {14,31}, {14,34}, {3,26}, {6,12}, {8,22}, {26,36}, {6,36}, {5,7}, {2,25}, {5,11}, {2,28}, {19,29}, {2,24}, {21,27}, {32,35}, {29,35}, {4,8}, {24,35}, {4,19}, {23,28}, {20,31}, {16,30}, {7,9}, {1,23}, {16,20}, {16,34}, {4,18}, {5,30}, {16,26}, {9,12}, {22,33}, {17,36}, {8,36}, {4,36}, {3,5}, {20,27}, {3,12}, {18,20}, {21,30}, {25,34}, {11,18}, {7,17}, {25,29}, {3,10}, {6,23}, {28,31}, {15,25}, {10,11}, {10,17}, {23,29}, {14,20}, {21,34}, {3,23}, {6,20}, {10,29}, {8,23}, {2,31}, {14,15}, {12,21}, {27,35}, {4,33}, {4,32}, {20,35}, {4,21}, {19,23}, {20,22}, {17,33}, {17,29}, {2,19}, {15,22}, {14,17}, {29,34}, {3,22}, {11,30}, {7,28}, {1,14}, {13,28}, {31,33}, {4,30}, {19,32}, {13,22}, {24,25}, {11,19}, {7,34}, {18,25}, {9,30}, {7,24}, {1,32}, {13,16}, {13,32}, {13,33}, {4,25}, {5,17}, {2,29}, {11,22}, {28,36}, {19,25}, {17,24}, {5,13}, {25,27}, {11,32}, {7,16}, {9,25}, {5,9}, {2,22}, {15,36}, {33,36}, {3,17}, {12,20}, {8,20}, {21,26}, {3,29}, {21,36}, {17,21}, {12,13}, {27,33}, {4,13}, {5,33}, {16,18}, {9,21}, {2,33}, {4,11}, {5,28}, {19,21}, {22,35}, {6,16}, {28,34}, {18,31}, {5,15}, {2,10}, {6,34}, {1,18}, {7,12}, {3,20}, {6,21}, {8,18}, {26,30}, {1,35}, {11,28}, {14,30}, {3,31}, {6,14}, {26,28}, {12,31}, {8,15}, {10,26}, {6,10}, {6,8}, {1,26}, {1,27}, {20,30}, {7,21}, {13,23}, {20,33}, {4,16}, {1,21}, {16,35}, {34,35}, {18,30}, {7,30}, {13,26}, {12,33}, {1,20}, {30,33}, {1,8}, {10,28}, {23,31}, {30,31}, {7,14}, {16,21}, {9,35}, {4,24}, {12,35}, {4,27}, {13,19}, {2,17}, {15,29}, {17,27}, {29,32}, {22,29}, {5,22}, {2,6}, {1,15}, {12,23}, {10,14}, {23,34}, {22,31}, {14,36}, {12,16}, {9,27}, {18,22}, {30,36}, {3,35}, {10,24}, {11,34}, {18,28}, {9,23}, {20,24}, {16,32}, {9,13}, {11,24}, {19,28}, {10,34}, {15,31}, {17,19}, {22,24}, {19,36}, {14,27}, {32,34}, {1,34}, {7,19}, {22,25}, {5,24}, {2,7}, {24,32}, {8,13}, {24,27}, {8,10}, {15,33}, {6,29}, {22,28}, {31,36}, {6,25}, {1,11}, {12,17}, {27,29}, {10,20}, {21,23}, {10,36}, {11,36}, {3,28}, {3,14}, {6,31}, {2,12}, {15,27}, {15,17}, {6,27}, {10,32}, {13,18}, {7,25}, {11,25}, {3,7}, {23,36}, {20,26}, {2,36}, {3,15}, {6,18}, {1,30}, {9,33}, {4,9}, {5,26}, {5,35}, {16,24}, {9,19}, {9,15}, {11,15}, {5,32}, {2,13}, {25,35}, {2,4}, {15,23}, {14,21}, {4,6}, {26,32}, {16,28}, {18,34}, {25,31}, {11,14}, {17,26}, {12,29}, {23,26}, {18,35}, {8,11}, {7,35}, {9,31}, {8,26}, {12,26}, {26,33}, {27,32}, {5,19}, {10,16}, {17,32}, {13,29}, {19,34}, {2,16}, {24,33}, {8,32}, {28,30}, {7,31}, {8,29}, {14,24}, {1,9}, {18,23}, {1,5}, {8,33}, {3,34}, {14,25}, {8,27}, {12,27} } Symmetric graph 48 of order 36 Valency 17 Diameter 3 Girth 4 Automorphism group of order 12804747411456000 Number of arcs = 612 Number of 2-arcs = 9792 2-arc-transitive true Edge-set { {1,4}, {12,31}, {13,36}, {17,25}, {19,24}, {7,23}, {6,17}, {16,19}, {11,25}, {4,33}, {10,29}, {21,34}, {27,30}, {6,16}, {16,25}, {10,32}, {19,26}, {11,23}, {10,12}, {13,22}, {14,35}, {7,34}, {9,30}, {4,21}, {13,27}, {1,8}, {1,6}, {16,32}, {1,19}, {11,32}, {18,35}, {20,34}, {4,20}, {26,34}, {23,30}, {25,35}, {24,34}, {7,29}, {3,6}, {8,24}, {5,18}, {9,21}, {21,27}, {8,33}, {12,30}, {4,13}, {7,27}, {22,31}, {28,36}, {6,31}, {16,36}, {1,18}, {20,32}, {4,31}, {10,36}, {18,26}, {20,23}, {15,24}, {3,9}, {3,12}, {9,13}, {9,20}, {12,21}, {13,34}, {8,30}, {11,18}, {9,33}, {21,29}, {14,21}, {6,11}, {14,16}, {22,33}, {28,29}, {5,15}, {15,26}, {30,36}, {10,22}, {22,28}, {13,25}, {7,12}, {6,13}, {1,27}, {17,29}, {3,19}, {23,28}, {2,17}, {1,23}, {17,32}, {15,31}, {26,36}, {3,18}, {12,17}, {13,19}, {23,35}, {17,34}, {15,20}, {12,26}, {3,34}, {2,33}, {29,31}, {11,36}, {14,33}, {14,24}, {7,36}, {6,33}, {3,36}, {25,30}, {4,24}, {7,9}, {6,21}, {8,28}, {23,26}, {14,30}, {4,7}, {4,5}, {6,26}, {16,23}, {5,32}, {3,22}, {14,28}, {2,7}, {2,5}, {2,20}, {13,23}, {8,17}, {29,35}, {2,3}, {7,19}, {21,25}, {24,27}, {6,7}, {27,31}, {1,36}, {7,25}, {4,11}, {10,14}, {28,34}, {2,30}, {31,34}, {16,18}, {20,25}, {19,31}, {11,15}, {14,26}, {24,25}, {6,10}, {18,30}, {9,16}, {9,31}, {12,24}, {9,11}, {22,35}, {14,17}, {17,23}, {8,10}, {5,22}, {5,29}, {21,23}, {17,27}, {16,22}, {8,11}, {12,33}, {13,29}, {21,36}, {27,33}, {6,30}, {4,16}, {2,28}, {8,13}, {5,8}, {5,12}, {13,15}, {6,20}, {12,16}, {1,34}, {30,32}, {11,29}, {3,14}, {21,32}, {27,35}, {15,35}, {3,32}, {9,35}, {25,28}, {7,18}, {10,27}, {19,30}, {1,29}, {16,27}, {23,31}, {17,36}, {19,21}, {11,27}, {8,35}, {5,34}, {9,28}, {2,21}, {13,32}, {9,17}, {1,15}, {26,32}, {4,17}, {10,19}, {2,26}, {8,20}, {19,33}, {6,35}, {16,34}, {8,26}, {32,33}, {25,33}, {24,29}, {23,33}, {8,16}, {5,25}, {3,15}, {5,14}, {7,15}, {30,34}, {4,30}, {1,25}, {22,26}, {10,25}, {22,24}, {7,14}, {1,22}, {1,12}, {28,32}, {2,35}, {7,22}, {6,28}, {15,28}, {24,32}, {13,18}, {2,24}, {18,31}, {14,20}, {24,36}, {18,33}, {19,28}, {2,11}, {15,21}, {26,27}, {14,31}, {1,32}, {4,10}, {18,28}, {5,9}, {4,35}, {2,31}, {31,36}, {18,20}, {12,20}, {10,34}, {12,35}, {6,24}, {1,9}, {20,22}, {12,28}, {10,18}, {11,22}, {22,30}, {5,19}, {8,21}, {12,13}, {20,29}, {19,35}, {11,34}, {29,33}, {3,29}, {5,27}, {25,31}, {3,27}, {2,16}, {15,17}, {3,8}, {10,15}, {4,28}, {2,10}, {20,27}, {20,36}, {5,36}, {15,33}, {17,19}, {9,26}, {3,25}, {9,24}, {18,24}, {16,29}, {33,36}, {26,29}, {3,23}, {11,14}, {11,19}, {1,14}, {32,35}, {2,13}, {34,35}, {5,23}, {7,32}, {10,23}, {17,22}, {4,26}, {8,31}, {18,21}, {15,30} } Symmetric graph 49 of order 36 Valency 18 Diameter 2 Girth 3 Automorphism group of order 1296 Number of arcs = 648 Number of 2-arcs = 11016 2-arc-transitive false Edge-set { {1,4}, {31,35}, {2,33}, {15,17}, {11,28}, {18,34}, {29,32}, {9,23}, {15,19}, {20,27}, {27,36}, {8,13}, {10,13}, {16,19}, {25,30}, {2,5}, {6,24}, {23,28}, {17,19}, {12,30}, {7,16}, {12,14}, {7,12}, {6,22}, {4,21}, {22,25}, {21,35}, {7,28}, {14,17}, {11,21}, {9,26}, {33,34}, {3,32}, {1,32}, {1,22}, {2,20}, {24,27}, {9,28}, {21,26}, {26,34}, {4,7}, {5,14}, {24,26}, {20,34}, {4,26}, {5,34}, {1,23}, {29,31}, {2,18}, {3,11}, {15,29}, {11,18}, {4,20}, {5,27}, {9,24}, {15,20}, {27,29}, {18,36}, {5,10}, {6,8}, {13,18}, {10,29}, {16,36}, {30,31}, {16,35}, {30,33}, {3,35}, {23,33}, {30,34}, {16,32}, {1,12}, {7,22}, {5,20}, {6,27}, {8,18}, {8,10}, {4,31}, {24,33}, {3,20}, {1,10}, {8,22}, {13,30}, {10,16}, {10,31}, {2,8}, {13,33}, {3,10}, {2,35}, {25,28}, {8,34}, {13,32}, {31,36}, {19,23}, {19,25}, {8,27}, {13,36}, {2,16}, {12,33}, {3,7}, {1,5}, {23,30}, {12,19}, {7,25}, {8,14}, {12,13}, {25,33}, {6,32}, {13,21}, {25,35}, {7,14}, {17,21}, {26,28}, {7,15}, {11,14}, {18,21}, {26,29}, {15,36}, {11,31}, {24,29}, {10,26}, {14,30}, {26,35}, {3,4}, {5,23}, {3,16}, {12,32}, {1,7}, {4,13}, {6,25}, {4,35}, {17,31}, {2,28}, {1,18}, {22,29}, {30,36}, {16,31}, {33,35}, {3,6}, {4,23}, {21,22}, {14,35}, {17,25}, {28,35}, {6,34}, {4,32}, {18,22}, {21,29}, {25,36}, {15,34}, {11,32}, {11,20}, {9,27}, {6,13}, {4,10}, {16,22}, {21,30}, {12,28}, {17,24}, {9,17}, {6,12}, {14,22}, {12,21}, {7,34}, {14,32}, {18,26}, {29,34}, {4,36}, {5,31}, {3,33}, {2,21}, {17,34}, {4,11}, {5,9}, {22,26}, {21,34}, {9,29}, {1,30}, {11,15}, {9,11}, {4,24}, {15,18}, {10,20}, {5,19}, {20,36}, {8,29}, {10,19}, {8,25}, {14,23}, {17,27}, {28,36}, {1,19}, {10,25}, {8,35}, {21,24}, {20,26}, {10,15}, {8,11}, {2,31}, {3,24}, {7,36}, {14,31}, {16,26}, {5,33}, {22,31}, {1,9}, {15,31}, {2,11}, {15,28}, {27,32}, {3,19}, {23,25}, {14,21}, {12,26}, {7,17}, {14,28}, {11,29}, {32,36}, {1,31}, {2,24}, {3,29}, {18,23}, {15,24}, {9,15}, {11,27}, {2,30}, {3,8}, {13,23}, {19,29}, {18,25}, {9,12}, {16,27}, {27,30}, {5,12}, {6,7}, {22,32}, {1,21}, {25,31}, {27,34}, {15,22}, {6,15}, {26,32}, {1,34}, {20,23}, {16,24}, {20,30}, {13,19}, {2,12}, {17,33}, {3,28}, {18,32}, {9,13}, {27,31}, {2,36}, {8,23}, {13,29}, {10,18}, {26,33}, {23,27}, {19,36}, {6,36}, {2,22}, {28,33}, {3,17}, {12,16}, {6,19}, {4,25}, {17,35}, {6,11}, {4,9}, {20,24}, {14,20}, {12,27}, {11,25}, {9,35}, {1,29}, {10,30}, {8,16}, {19,35}, {28,32}, {1,36}, {4,14}, {20,28}, {7,10}, {18,33}, {5,35}, {6,33}, {17,23}, {19,28}, {19,27}, {7,30}, {18,20}, {5,15}, {14,16}, {13,24}, {19,22}, {5,26}, {7,26}, {3,34}, {29,35}, {11,17}, {3,23}, {23,32}, {8,30}, {13,35}, {10,33}, {22,28}, {32,34}, {9,18}, {5,22}, {6,21}, {12,17}, {14,34}, {2,6}, {21,25}, {7,24}, {9,36}, {1,17}, {2,9}, {24,30}, {16,20}, {24,31}, {15,33}, {13,16}, {5,8} } Symmetric graph 50 of order 36 Valency 18 Diameter 2 Girth 3 Automorphism group of order 1296 Number of arcs = 648 Number of 2-arcs = 11016 2-arc-transitive false Edge-set { {1,5}, {4,20}, {18,35}, {12,19}, {8,36}, {26,32}, {3,11}, {2,11}, {9,14}, {25,34}, {1,31}, {24,30}, {5,21}, {1,6}, {15,17}, {15,16}, {17,35}, {28,33}, {27,29}, {2,6}, {4,22}, {18,20}, {9,13}, {23,25}, {10,20}, {7,35}, {4,21}, {18,34}, {16,33}, {12,30}, {16,31}, {10,30}, {26,33}, {3,12}, {8,23}, {19,22}, {7,28}, {4,24}, {16,34}, {15,19}, {26,36}, {12,32}, {8,11}, {29,33}, {14,29}, {6,27}, {8,13}, {3,32}, {10,19}, {7,36}, {27,32}, {23,31}, {2,9}, {14,23}, {22,31}, {3,9}, {13,23}, {23,30}, {5,19}, {14,17}, {14,34}, {27,31}, {11,15}, {9,26}, {22,32}, {13,19}, {25,36}, {2,10}, {11,16}, {9,30}, {25,30}, {2,24}, {14,21}, {1,34}, {15,31}, {7,23}, {19,24}, {7,17}, {24,28}, {21,28}, {4,34}, {29,31}, {6,24}, {17,21}, {1,32}, {14,22}, {20,27}, {5,35}, {27,28}, {15,22}, {20,26}, {6,35}, {17,33}, {14,18}, {23,27}, {11,20}, {9,35}, {12,28}, {17,27}, {2,28}, {22,28}, {1,16}, {15,30}, {30,35}, {5,33}, {15,24}, {21,26}, {11,18}, {9,29}, {25,29}, {3,5}, {13,16}, {10,15}, {23,33}, {6,23}, {5,13}, {16,25}, {10,17}, {4,27}, {2,18}, {16,22}, {20,30}, {14,36}, {11,13}, {9,25}, {33,36}, {22,25}, {8,10}, {7,22}, {19,27}, {2,36}, {20,24}, {13,21}, {10,33}, {7,12}, {18,21}, {26,28}, {4,8}, {3,35}, {8,28}, {26,30}, {5,8}, {3,34}, {17,32}, {11,28}, {14,28}, {1,12}, {8,15}, {26,35}, {3,33}, {2,8}, {4,12}, {22,26}, {4,31}, {10,18}, {9,16}, {3,23}, {20,23}, {19,35}, {5,7}, {24,33}, {7,29}, {6,20}, {18,31}, {10,29}, {3,16}, {13,30}, {27,34}, {29,35}, {6,10}, {12,13}, {19,28}, {4,36}, {5,32}, {10,26}, {9,12}, {17,25}, {1,28}, {1,18}, {15,29}, {6,33}, {1,19}, {6,26}, {13,31}, {15,36}, {4,9}, {5,25}, {8,25}, {14,32}, {10,32}, {7,11}, {8,30}, {5,22}, {19,34}, {31,36}, {3,17}, {8,34}, {5,23}, {20,34}, {31,35}, {2,17}, {12,21}, {1,8}, {8,17}, {2,4}, {30,31}, {17,19}, {5,34}, {2,19}, {5,26}, {20,36}, {6,14}, {12,14}, {8,27}, {11,26}, {32,35}, {19,25}, {24,32}, {3,7}, {13,24}, {6,31}, {9,18}, {23,29}, {7,26}, {3,24}, {3,21}, {13,34}, {9,22}, {1,36}, {21,35}, {3,30}, {2,35}, {14,33}, {6,12}, {18,22}, {4,32}, {7,16}, {21,23}, {4,11}, {21,30}, {20,29}, {1,30}, {29,34}, {17,24}, {15,32}, {9,34}, {15,20}, {11,27}, {1,20}, {12,17}, {2,31}, {14,20}, {27,35}, {12,27}, {3,20}, {12,16}, {7,14}, {33,34}, {12,31}, {16,36}, {11,33}, {5,11}, {12,25}, {28,34}, {5,15}, {24,26}, {11,29}, {6,9}, {21,25}, {6,36}, {13,18}, {21,22}, {24,27}, {30,36}, {6,13}, {18,27}, {2,29}, {15,35}, {4,25}, {17,23}, {2,21}, {21,36}, {10,14}, {7,27}, {9,10}, {8,24}, {18,23}, {13,33}, {16,24}, {2,33}, {4,15}, {8,18}, {16,20}, {3,4}, {4,14}, {17,36}, {28,32}, {2,22}, {25,31}, {1,10}, {1,23}, {1,7}, {6,7}, {18,32}, {13,28}, {16,26}, {19,29}, {5,10}, {10,25}, {28,36}, {16,19}, {32,34}, {11,31}, {6,19}, {25,33}, {22,29}, {11,21}, {9,24}, {13,35}, {3,29}, {1,22}, {7,15}, {18,26}, {30,32} } Symmetric graph 51 of order 36 Valency 18 Diameter 2 Girth 3 Automorphism group of order 313456656384 Number of arcs = 648 Number of 2-arcs = 11016 2-arc-transitive false Edge-set { {1,4}, {25,32}, {3,31}, {8,24}, {18,21}, {24,26}, {11,16}, {17,31}, {2,22}, {18,22}, {28,35}, {6,34}, {27,29}, {9,11}, {4,21}, {19,35}, {6,27}, {12,27}, {2,23}, {7,28}, {14,19}, {3,17}, {8,22}, {18,20}, {33,36}, {23,26}, {1,36}, {4,9}, {21,26}, {10,15}, {16,21}, {3,32}, {11,26}, {17,32}, {1,9}, {13,20}, {20,25}, {10,31}, {23,30}, {28,36}, {14,28}, {4,25}, {11,31}, {4,8}, {6,10}, {12,16}, {3,6}, {20,26}, {9,10}, {20,22}, {25,30}, {10,13}, {33,34}, {1,5}, {23,25}, {15,29}, {21,35}, {30,32}, {6,9}, {12,14}, {6,36}, {2,8}, {4,34}, {26,29}, {5,21}, {18,23}, {2,17}, {19,34}, {5,27}, {12,25}, {12,32}, {3,18}, {2,24}, {31,36}, {8,28}, {4,19}, {11,27}, {4,12}, {15,34}, {2,4}, {7,11}, {18,31}, {16,22}, {19,23}, {27,28}, {16,20}, {3,36}, {24,28}, {5,7}, {5,35}, {10,26}, {5,11}, {17,24}, {22,29}, {15,18}, {14,34}, {5,19}, {25,33}, {12,15}, {2,32}, {9,15}, {14,21}, {32,36}, {21,25}, {26,31}, {8,11}, {17,23}, {22,28}, {14,18}, {25,28}, {31,34}, {8,29}, {29,32}, {7,30}, {13,19}, {9,22}, {10,27}, {5,12}, {24,30}, {29,36}, {15,28}, {5,36}, {4,10}, {5,26}, {19,26}, {11,33}, {7,24}, {13,29}, {15,35}, {1,17}, {27,32}, {3,33}, {21,34}, {11,25}, {8,13}, {15,20}, {3,4}, {19,24}, {16,33}, {26,30}, {9,28}, {14,30}, {13,36}, {12,26}, {18,32}, {2,9}, {28,33}, {1,34}, {23,29}, {1,8}, {20,27}, {12,31}, {4,27}, {4,7}, {5,9}, {20,23}, {6,11}, {12,17}, {1,6}, {7,10}, {21,22}, {11,13}, {13,16}, {1,31}, {33,35}, {23,27}, {2,18}, {6,25}, {6,8}, {10,14}, {22,25}, {30,31}, {15,17}, {8,23}, {2,36}, {10,32}, {2,5}, {6,21}, {3,7}, {7,14}, {3,35}, {4,20}, {14,17}, {12,33}, {6,7}, {11,17}, {15,30}, {13,34}, {18,33}, {1,24}, {16,23}, {8,30}, {15,36}, {28,34}, {11,14}, {4,36}, {12,18}, {18,24}, {2,16}, {4,11}, {17,19}, {22,27}, {23,28}, {14,29}, {3,34}, {5,8}, {26,32}, {9,14}, {21,36}, {15,21}, {11,32}, {17,22}, {1,18}, {13,28}, {20,34}, {29,31}, {13,18}, {20,24}, {16,31}, {30,33}, {12,13}, {6,35}, {30,36}, {26,28}, {25,29}, {7,13}, {14,35}, {6,19}, {27,33}, {2,31}, {8,15}, {32,34}, {2,7}, {24,25}, {19,27}, {7,12}, {6,12}, {29,35}, {27,30}, {31,35}, {8,10}, {15,16}, {3,8}, {10,16}, {21,23}, {5,34}, {25,31}, {7,23}, {28,32}, {2,35}, {19,22}, {9,24}, {5,20}, {24,29}, {10,25}, {5,10}, {22,30}, {5,25}, {3,22}, {4,26}, {1,33}, {9,29}, {3,9}, {8,14}, {20,36}, {13,17}, {32,35}, {9,30}, {3,23}, {14,20}, {15,19}, {1,35}, {1,16}, {9,23}, {17,21}, {24,27}, {2,34}, {19,25}, {29,33}, {8,12}, {11,15}, {1,32}, {14,36}, {1,22}, {13,21}, {21,27}, {2,33}, {1,7}, {28,31}, {6,20}, {9,13}, {7,29}, {18,19}, {11,18}, {14,16}, {21,24}, {7,15}, {10,17}, {7,22}, {17,33}, {13,30}, {13,35}, {16,32}, {30,35}, {6,26}, {29,34}, {22,26}, {10,33}, {27,31}, {26,33}, {10,18}, {20,35}, {16,24}, {3,16}, {19,36}, {3,24}, {30,34}, {1,23}, {9,12}, {4,35}, {17,20}, {16,19}, {3,5}, {2,6} } Symmetric graph 52 of order 36 Valency 18 Diameter 2 Girth 4 Automorphism group of order 81980778135594566280019968000000 Number of arcs = 648 Number of 2-arcs = 11016 2-arc-transitive true Edge-set { {1,19}, {4,26}, {13,35}, {6,34}, {2,32}, {16,24}, {9,27}, {2,21}, {7,33}, {3,20}, {11,36}, {17,29}, {17,30}, {4,19}, {3,28}, {16,36}, {9,22}, {8,23}, {5,25}, {14,31}, {10,21}, {14,32}, {5,26}, {6,26}, {13,32}, {5,35}, {3,31}, {17,23}, {10,30}, {11,27}, {15,19}, {18,24}, {1,33}, {1,34}, {12,28}, {16,20}, {15,20}, {11,28}, {2,34}, {2,33}, {1,24}, {9,34}, {5,19}, {12,31}, {14,30}, {18,26}, {6,20}, {8,36}, {4,21}, {13,29}, {17,25}, {4,22}, {8,35}, {7,35}, {3,22}, {18,25}, {14,29}, {3,21}, {7,36}, {4,29}, {17,35}, {11,21}, {7,19}, {1,26}, {13,34}, {12,22}, {15,31}, {6,28}, {2,25}, {14,33}, {10,23}, {10,24}, {16,32}, {5,27}, {6,27}, {15,32}, {9,24}, {9,23}, {13,33}, {1,25}, {5,28}, {16,31}, {6,32}, {5,32}, {14,24}, {9,26}, {8,28}, {16,21}, {13,23}, {4,34}, {2,35}, {7,27}, {15,22}, {18,19}, {12,29}, {3,33}, {1,36}, {12,30}, {18,20}, {17,20}, {11,30}, {2,36}, {4,33}, {11,29}, {17,19}, {16,22}, {8,27}, {1,35}, {3,34}, {2,20}, {11,33}, {1,20}, {11,34}, {15,29}, {17,28}, {2,19}, {10,35}, {3,24}, {16,30}, {18,27}, {6,21}, {7,32}, {9,36}, {4,23}, {13,26}, {13,25}, {5,22}, {8,31}, {7,31}, {6,22}, {14,25}, {14,26}, {3,23}, {10,36}, {8,32}, {5,21}, {17,27}, {15,30}, {4,24}, {9,35}, {3,25}, {14,36}, {8,22}, {8,21}, {4,25}, {14,35}, {7,21}, {18,32}, {5,29}, {3,26}, {13,36}, {12,24}, {9,20}, {17,31}, {6,30}, {2,28}, {16,33}, {11,23}, {10,19}, {16,34}, {2,27}, {1,27}, {15,34}, {9,19}, {12,23}, {15,33}, {1,28}, {5,30}, {18,31}, {10,20}, {11,24}, {6,29}, {17,32}, {5,33}, {1,31}, {15,23}, {10,28}, {10,27}, {15,24}, {6,33}, {1,32}, {9,28}, {16,23}, {13,20}, {11,25}, {5,34}, {2,31}, {7,29}, {17,22}, {14,19}, {12,26}, {3,35}, {3,36}, {8,30}, {18,21}, {17,21}, {7,30}, {4,36}, {4,35}, {11,26}, {13,19}, {18,22}, {8,29}, {12,25}, {14,20}, {1,22}, {8,34}, {12,35}, {18,30}, {18,29}, {12,36}, {4,20}, {2,22}, {8,33}, {11,35}, {3,19}, {16,25}, {14,27}, {1,21}, {7,34}, {9,32}, {5,23}, {15,26}, {13,28}, {5,24}, {9,31}, {10,31}, {6,24}, {14,28}, {16,26}, {6,23}, {10,32}, {13,27}, {15,25}, {4,27}, {15,35}, {7,24}, {13,31}, {6,25}, {7,23}, {10,22}, {3,27}, {15,36}, {8,24}, {9,21}, {17,33}, {1,30}, {4,28}, {16,35}, {11,20}, {11,19}, {18,34}, {2,29}, {1,29}, {17,34}, {12,19}, {12,20}, {2,30}, {18,33}, {6,36}, {4,32}, {9,29}, {16,19}, {12,27}, {9,30}, {18,23}, {5,36}, {4,31}, {10,29}, {17,24}, {14,22}, {8,26}, {6,35}, {3,32}, {8,25}, {14,21}, {13,21}, {7,25}, {7,26}, {13,22}, {2,23}, {10,33}, {11,32}, {17,26}, {13,30}, {11,31}, {6,19}, {1,23}, {10,34}, {12,32}, {5,20}, {15,27}, {15,28}, {2,24}, {9,33}, {16,28}, {16,27}, {3,30}, {18,36}, {8,20}, {14,34}, {2,26}, {8,19}, {12,21}, {4,30}, {18,35}, {7,20}, {11,22}, {3,29}, {17,36}, {5,31}, {6,31}, {10,25}, {15,21}, {7,28}, {10,26}, {13,24}, {9,25}, {14,23}, {12,34}, {12,33}, {18,28}, {16,29}, {7,22} } Symmetric graph 53 of order 36 Valency 20 Diameter 2 Girth 3 Automorphism group of order 1440 Number of arcs = 720 Number of 2-arcs = 13680 2-arc-transitive false Edge-set { {1,7}, {1,8}, {11,23}, {1,11}, {11,20}, {12,29}, {4,19}, {1,12}, {11,19}, {12,30}, {2,19}, {7,17}, {22,26}, {6,27}, {11,22}, {12,27}, {1,19}, {7,18}, {22,27}, {4,27}, {8,32}, {14,23}, {15,28}, {3,25}, {5,14}, {10,28}, {12,28}, {3,19}, {7,14}, {22,28}, {1,27}, {8,36}, {13,23}, {14,28}, {3,28}, {6,14}, {7,28}, {20,35}, {29,33}, {4,15}, {13,31}, {17,30}, {3,16}, {2,33}, {9,15}, {10,13}, {21,30}, {7,13}, {22,30}, {3,27}, {8,33}, {15,23}, {13,28}, {3,30}, {1,14}, {11,28}, {20,34}, {29,35}, {4,16}, {13,33}, {15,30}, {3,13}, {5,33}, {10,15}, {8,13}, {23,30}, {17,19}, {26,32}, {6,31}, {24,35}, {16,36}, {18,32}, {14,27}, {3,34}, {12,18}, {9,31}, {17,24}, {10,35}, {16,21}, {18,25}, {8,35}, {16,23}, {18,28}, {3,14}, {20,32}, {29,31}, {4,17}, {13,35}, {16,30}, {3,18}, {1,33}, {11,15}, {12,13}, {19,30}, {2,31}, {17,22}, {26,33}, {6,34}, {19,35}, {16,32}, {18,31}, {17,27}, {3,35}, {12,16}, {9,32}, {10,31}, {17,21}, {11,35}, {16,20}, {18,29}, {27,32}, {25,35}, {5,24}, {10,36}, {18,34}, {23,36}, {14,33}, {3,21}, {12,31}, {7,36}, {13,22}, {9,24}, {24,36}, {10,22}, {21,33}, {25,34}, {6,18}, {13,29}, {20,33}, {29,34}, {4,18}, {13,36}, {13,30}, {3,33}, {12,15}, {2,35}, {26,36}, {6,32}, {22,35}, {16,33}, {18,27}, {3,36}, {11,32}, {7,35}, {16,22}, {4,24}, {28,32}, {15,19}, {25,32}, {5,21}, {23,34}, {18,35}, {14,32}, {3,22}, {12,33}, {7,34}, {18,22}, {9,23}, {10,24}, {21,36}, {12,22}, {19,33}, {30,34}, {2,18}, {17,36}, {13,26}, {28,35}, {2,26}, {5,9}, {10,20}, {21,34}, {20,29}, {4,34}, {15,32}, {6,12}, {7,24}, {22,36}, {8,20}, {9,26}, {20,26}, {5,34}, {19,25}, {5,36}, {17,35}, {16,26}, {2,32}, {26,31}, {6,36}, {16,34}, {16,27}, {12,32}, {7,31}, {4,22}, {15,20}, {5,23}, {19,34}, {14,36}, {3,20}, {12,34}, {12,23}, {8,22}, {23,33}, {28,34}, {6,26}, {5,7}, {30,35}, {27,31}, {1,17}, {2,25}, {6,9}, {21,29}, {4,31}, {15,35}, {3,12}, {7,19}, {22,32}, {8,21}, {23,31}, {28,36}, {9,29}, {10,26}, {20,25}, {19,27}, {1,32}, {18,21}, {4,36}, {14,34}, {16,25}, {30,33}, {8,25}, {2,9}, {10,30}, {2,21}, {21,25}, {6,21}, {8,26}, {20,28}, {11,30}, {2,20}, {24,25}, {1,29}, {9,34}, {15,34}, {4,23}, {15,24}, {25,36}, {5,20}, {10,34}, {7,23}, {8,24}, {6,28}, {3,7}, {30,31}, {2,17}, {2,29}, {4,9}, {21,27}, {1,31}, {2,12}, {7,21}, {22,31}, {7,29}, {19,29}, {4,32}, {13,21}, {5,15}, {10,25}, {2,8}, {27,33}, {14,24}, {11,14}, {8,29}, {17,25}, {6,24}, {17,33}, {8,27}, {1,23}, {23,28}, {11,25}, {6,20}, {24,29}, {13,20}, {9,17}, {24,26}, {1,28}, {6,13}, {15,31}, {18,19}, {11,16}, {10,18}, {4,25}, {6,8}, {6,29}, {5,25}, {6,10}, {2,30}, {4,30}, {5,29}, {11,26}, {9,21}, {24,31}, {21,31}, {17,31}, {4,7}, {5,17}, {10,21}, {5,13}, {3,8}, {18,24}, {27,36}, {8,14}, {14,25}, {1,24}, {11,36}, {6,23}, {24,28}, {8,17}, {23,26}, {1,26}, {6,16}, {10,16}, {4,11}, {14,19}, {11,17}, {14,29}, {5,26}, {5,10}, {19,32}, {5,30}, {2,10}, {17,26}, {2,16}, {15,26}, {1,13}, {5,35}, {5,11}, {7,27}, {9,25}, {24,32}, {9,14}, {9,16}, {3,11}, {12,20}, {14,20}, {11,33}, {15,29}, {4,10}, {1,15}, {2,15}, {23,27}, {1,35}, {9,27}, {8,18}, {2,22}, {9,33}, {9,19}, {12,19}, {7,30}, {4,28}, {1,22} } Symmetric graph 54 of order 36 Valency 20 Diameter 2 Girth 3 Automorphism group of order 51840 Number of arcs = 720 Number of 2-arcs = 13680 2-arc-transitive false Edge-set { {1,2}, {1,3}, {2,4}, {1,5}, {2,6}, {3,8}, {4,8}, {1,10}, {2,11}, {3,12}, {4,7}, {5,15}, {6,16}, {8,15}, {8,16}, {1,18}, {2,19}, {3,20}, {4,21}, {5,17}, {6,13}, {8,13}, {8,14}, {10,26}, {11,27}, {12,28}, {1,7}, {15,26}, {16,27}, {15,28}, {1,16}, {2,28}, {3,27}, {4,30}, {5,16}, {6,24}, {8,32}, {10,25}, {11,18}, {12,23}, {7,20}, {15,23}, {16,20}, {15,19}, {16,25}, {18,30}, {19,26}, {20,31}, {21,34}, {17,34}, {13,29}, {1,13}, {2,14}, {26,30}, {26,27}, {28,31}, {1,34}, {26,34}, {27,29}, {1,28}, {3,34}, {4,29}, {5,31}, {6,34}, {8,22}, {10,28}, {1,11}, {12,29}, {7,31}, {15,35}, {16,35}, {18,22}, {3,19}, {2,20}, {21,28}, {17,24}, {13,15}, {13,16}, {14,24}, {24,26}, {15,27}, {16,28}, {1,24}, {27,30}, {22,28}, {9,16}, {12,24}, {11,32}, {32,36}, {11,25}, {18,36}, {7,23}, {9,20}, {1,23}, {4,25}, {22,26}, {30,31}, {9,34}, {2,36}, {11,30}, {26,36}, {2,29}, {5,11}, {6,36}, {7,8}, {8,9}, {9,10}, {11,12}, {7,36}, {6,15}, {16,33}, {18,34}, {19,29}, {1,20}, {2,21}, {7,17}, {9,13}, {12,14}, {26,33}, {5,27}, {28,33}, {6,30}, {3,16}, {4,24}, {32,34}, {29,32}, {25,29}, {18,31}, {23,26}, {20,27}, {23,28}, {25,31}, {29,30}, {26,31}, {27,34}, {28,34}, {1,29}, {2,31}, {4,31}, {22,34}, {29,33}, {14,28}, {1,17}, {17,29}, {13,31}, {20,35}, {21,35}, {23,35}, {20,22}, {3,21}, {13,24}, {14,15}, {14,16}, {2,15}, {4,9}, {12,22}, {11,14}, {17,36}, {4,23}, {4,20}, {21,22}, {21,30}, {3,7}, {10,20}, {11,21}, {12,21}, {16,17}, {14,18}, {17,19}, {17,20}, {13,21}, {14,23}, {12,26}, {7,27}, {28,36}, {9,30}, {2,24}, {3,32}, {4,32}, {13,25}, {30,36}, {10,31}, {11,34}, {34,36}, {10,29}, {4,12}, {7,22}, {5,28}, {1,6}, {8,29}, {8,31}, {11,35}, {35,36}, {7,35}, {9,35}, {3,9}, {2,9}, {24,30}, {16,31}, {24,34}, {15,29}, {9,22}, {11,31}, {29,36}, {8,12}, {6,11}, {33,36}, {19,34}, {1,25}, {2,18}, {7,25}, {9,18}, {9,23}, {12,20}, {5,24}, {32,33}, {5,32}, {24,33}, {6,32}, {23,29}, {25,27}, {19,28}, {3,26}, {4,27}, {8,17}, {6,17}, {13,33}, {19,20}, {21,25}, {18,23}, {8,24}, {22,32}, {5,13}, {6,14}, {16,18}, {19,24}, {20,32}, {21,32}, {17,32}, {13,32}, {25,28}, {18,24}, {23,32}, {15,25}, {17,30}, {13,26}, {14,34}, {4,14}, {17,22}, {3,29}, {5,35}, {6,35}, {8,35}, {22,23}, {12,19}, {11,20}, {21,36}, {23,36}, {7,18}, {9,19}, {14,33}, {10,34}, {11,29}, {1,12}, {2,7}, {7,15}, {9,15}, {12,16}, {20,33}, {5,21}, {21,33}, {5,23}, {5,14}, {3,14}, {4,17}, {22,31}, {9,28}, {31,36}, {7,26}, {9,27}, {17,33}, {7,21}, {15,17}, {10,23}, {1,22}, {2,3}, {4,28}, {13,22}, {17,28}, {10,35}, {12,35}, {7,24}, {5,30}, {6,26}, {8,34}, {12,25}, {33,35}, {24,35}, {32,35}, {25,35}, {18,35}, {23,30}, {20,26}, {11,19}, {25,36}, {8,19}, {8,25}, {6,25}, {18,33}, {5,7}, {6,9}, {10,33}, {12,33}, {15,33}, {17,27}, {13,30}, {21,24}, {2,13}, {14,27}, {19,36}, {9,21}, {3,13}, {14,26}, {16,36}, {10,24}, {10,32}, {11,15}, {10,19}, {5,19}, {8,18}, {14,31}, {10,18}, {14,32}, {25,26}, {18,27}, {2,33}, {3,5}, {4,6}, {6,23}, {25,34}, {18,29}, {4,10}, {11,22}, {12,30}, {5,10}, {22,33}, {15,22}, {16,30}, {3,23}, {10,13}, {10,27}, {31,32}, {19,31}, {21,27}, {6,20}, {19,30}, {19,35}, {22,30}, {3,36}, {27,33} } Symmetric graph 55 of order 36 Valency 20 Diameter 2 Girth 3 Automorphism group of order 1132462080 Number of arcs = 720 Number of 2-arcs = 13680 2-arc-transitive false Edge-set { {1,7}, {2,14}, {5,20}, {19,34}, {5,19}, {9,23}, {20,29}, {10,25}, {10,23}, {15,24}, {9,18}, {16,36}, {16,24}, {2,7}, {8,36}, {12,15}, {1,32}, {27,35}, {8,35}, {1,14}, {13,25}, {6,27}, {4,36}, {2,27}, {26,32}, {15,28}, {13,26}, {6,28}, {20,34}, {14,33}, {6,32}, {3,25}, {22,27}, {15,19}, {13,29}, {9,31}, {13,33}, {6,31}, {19,29}, {9,25}, {7,30}, {26,34}, {24,29}, {14,21}, {22,32}, {9,20}, {10,36}, {8,34}, {18,33}, {1,30}, {8,30}, {26,33}, {24,30}, {10,18}, {15,36}, {5,17}, {29,35}, {23,34}, {8,18}, {7,21}, {11,34}, {12,29}, {1,9}, {16,25}, {6,25}, {12,30}, {2,33}, {17,20}, {6,17}, {30,35}, {23,33}, {8,17}, {12,16}, {2,32}, {27,36}, {5,11}, {23,31}, {18,28}, {7,25}, {12,13}, {17,29}, {18,34}, {4,18}, {2,15}, {1,20}, {14,35}, {6,36}, {14,24}, {4,17}, {19,26}, {11,19}, {6,11}, {24,31}, {17,28}, {7,26}, {11,13}, {4,35}, {1,27}, {25,32}, {15,27}, {3,23}, {24,28}, {12,31}, {16,32}, {14,36}, {5,14}, {4,33}, {18,31}, {3,12}, {19,36}, {2,19}, {28,34}, {24,27}, {7,23}, {3,11}, {22,31}, {20,35}, {10,13}, {3,10}, {3,24}, {23,28}, {11,31}, {16,31}, {5,13}, {3,33}, {3,26}, {22,28}, {15,20}, {14,29}, {9,32}, {4,24}, {8,16}, {4,30}, {10,27}, {27,34}, {5,7}, {3,30}, {22,26}, {12,28}, {30,32}, {4,21}, {20,25}, {10,19}, {29,31}, {23,32}, {8,15}, {3,21}, {9,28}, {4,16}, {2,21}, {4,23}, {8,21}, {7,16}, {10,28}, {5,8}, {21,26}, {13,21}, {9,19}, {9,36}, {7,34}, {1,29}, {8,22}, {6,35}, {17,22}, {29,32}, {15,25}, {5,23}, {17,21}, {22,35}, {27,33}, {11,22}, {9,14}, {16,20}, {2,10}, {18,30}, {7,29}, {9,13}, {11,21}, {15,31}, {1,16}, {1,21}, {7,22}, {10,14}, {5,35}, {2,16}, {6,23}, {21,35}, {11,33}, {1,10}, {5,25}, {2,34}, {18,20}, {13,22}, {6,12}, {6,26}, {18,29}, {5,24}, {15,26}, {7,15}, {1,34}, {9,35}, {12,33}, {17,32}, {14,34}, {5,18}, {1,33}, {30,36}, {11,20}, {14,22}, {5,12}, {5,26}, {19,35}, {6,24}, {7,24}, {11,28}, {17,30}, {2,20}, {5,36}, {14,23}, {19,25}, {12,19}, {6,18}, {13,24}, {12,34}, {18,32}, {8,23}, {13,36}, {2,29}, {1,28}, {4,26}, {11,27}, {25,34}, {2,30}, {20,26}, {25,33}, {17,27}, {17,19}, {3,9}, {13,23}, {8,24}, {17,31}, {3,16}, {1,19}, {23,27}, {20,36}, {4,10}, {24,32}, {8,33}, {4,25}, {12,27}, {6,7}, {8,25}, {18,19}, {2,31}, {3,35}, {3,15}, {29,36}, {14,25}, {14,26}, {11,32}, {10,31}, {4,15}, {7,33}, {6,8}, {30,31}, {10,20}, {9,27}, {2,22}, {8,29}, {13,30}, {3,36}, {6,14}, {12,20}, {10,32}, {19,30}, {21,28}, {4,9}, {21,36}, {18,27}, {7,36}, {7,35}, {13,34}, {3,29}, {16,28}, {22,36}, {14,30}, {6,13}, {28,33}, {16,19}, {2,9}, {15,32}, {1,15}, {1,22}, {17,33}, {21,27}, {24,34}, {16,27}, {20,33}, {10,17}, {21,31}, {11,16}, {21,25}, {12,32}, {5,27}, {5,28}, {4,34}, {18,21}, {16,35}, {22,25}, {17,34}, {24,33}, {16,26}, {10,35}, {11,30}, {26,31}, {21,32}, {11,15}, {23,29}, {15,35}, {9,26}, {11,14}, {4,29}, {5,32}, {15,23}, {5,31}, {16,23}, {12,21}, {10,26}, {28,35}, {12,14}, {11,29}, {25,31}, {23,30}, {8,26}, {13,35}, {2,28}, {3,17}, {9,17}, {7,18}, {28,36}, {1,13}, {7,17}, {3,34}, {18,22}, {9,24}, {10,24}, {4,11}, {2,13}, {3,18}, {1,31}, {2,8}, {12,22}, {1,8}, {3,22}, {19,33}, {4,12}, {20,30}, {6,19}, {6,20}, {4,22} } Symmetric graph 56 of order 36 Valency 21 Diameter 2 Girth 3 Automorphism group of order 12096 Number of arcs = 756 Number of 2-arcs = 15120 2-arc-transitive false Edge-set { {1,16}, {2,14}, {1,17}, {1,21}, {21,22}, {2,13}, {2,26}, {1,18}, {1,19}, {1,20}, {13,15}, {20,23}, {16,22}, {2,15}, {11,22}, {2,28}, {2,36}, {2,35}, {2,25}, {14,15}, {7,25}, {19,24}, {18,24}, {17,23}, {1,22}, {4,15}, {10,23}, {10,22}, {9,22}, {22,33}, {2,30}, {2,31}, {2,33}, {2,34}, {8,22}, {2,27}, {13,14}, {8,24}, {8,27}, {12,35}, {12,36}, {7,26}, {1,23}, {5,14}, {6,15}, {6,7}, {12,24}, {11,24}, {12,23}, {5,15}, {7,23}, {15,29}, {23,32}, {22,31}, {22,30}, {22,34}, {22,32}, {22,29}, {2,32}, {22,27}, {2,29}, {3,15}, {9,23}, {16,21}, {3,12}, {3,31}, {9,29}, {10,32}, {11,34}, {11,33}, {8,28}, {2,7}, {1,24}, {18,21}, {6,13}, {4,13}, {4,14}, {4,8}, {5,7}, {4,12}, {7,24}, {6,14}, {1,30}, {14,25}, {15,27}, {15,28}, {7,28}, {24,36}, {24,34}, {24,33}, {15,32}, {23,35}, {15,34}, {23,26}, {22,28}, {23,31}, {23,36}, {15,30}, {23,25}, {15,31}, {23,29}, {3,14}, {17,20}, {3,11}, {17,32}, {3,35}, {3,33}, {5,34}, {5,30}, {6,28}, {4,27}, {10,31}, {4,29}, {9,30}, {22,24}, {2,8}, {2,12}, {13,36}, {16,20}, {17,21}, {16,17}, {16,19}, {20,21}, {5,13}, {3,20}, {5,9}, {4,9}, {6,10}, {6,8}, {5,11}, {19,21}, {3,13}, {1,26}, {1,28}, {1,27}, {8,21}, {13,27}, {13,25}, {13,35}, {1,31}, {14,29}, {1,33}, {14,30}, {8,30}, {7,30}, {12,31}, {10,12}, {12,27}, {12,29}, {23,30}, {14,36}, {15,33}, {7,9}, {24,26}, {14,31}, {7,11}, {24,28}, {7,32}, {24,35}, {7,10}, {24,25}, {1,34}, {14,26}, {7,8}, {24,27}, {1,32}, {14,35}, {25,26}, {18,19}, {4,17}, {3,10}, {26,28}, {18,36}, {18,34}, {19,33}, {9,17}, {3,34}, {3,36}, {5,26}, {17,29}, {3,32}, {18,27}, {6,31}, {6,32}, {6,26}, {4,30}, {20,31}, {5,29}, {20,30}, {5,25}, {12,15}, {22,23}, {3,22}, {2,9}, {2,10}, {2,11}, {10,16}, {17,19}, {13,26}, {18,20}, {17,18}, {16,18}, {19,20}, {17,25}, {3,19}, {5,18}, {5,20}, {6,19}, {4,18}, {1,36}, {1,29}, {9,20}, {9,21}, {16,31}, {14,32}, {8,16}, {9,16}, {1,35}, {21,30}, {13,28}, {21,34}, {9,26}, {9,28}, {10,27}, {8,26}, {11,35}, {12,33}, {7,34}, {6,23}, {11,12}, {11,29}, {11,25}, {10,21}, {13,33}, {5,24}, {8,12}, {21,32}, {13,34}, {4,24}, {8,10}, {9,12}, {8,36}, {6,24}, {11,21}, {3,24}, {8,9}, {8,11}, {27,28}, {35,36}, {20,26}, {6,17}, {28,30}, {26,30}, {31,36}, {10,36}, {16,33}, {17,35}, {27,36}, {29,35}, {7,18}, {8,18}, {8,19}, {17,27}, {10,17}, {11,18}, {4,36}, {18,25}, {19,28}, {17,28}, {5,33}, {16,29}, {19,32}, {4,35}, {11,19}, {4,28}, {20,34}, {6,27}, {25,32}, {19,35}, {18,30}, {6,25}, {25,34}, {19,26}, {11,14}, {7,15}, {23,24}, {15,17}, {3,23}, {5,22}, {6,22}, {4,22}, {12,17}, {11,16}, {26,35}, {25,36}, {26,36}, {25,35}, {3,21}, {6,16}, {4,21}, {20,36}, {5,16}, {1,25}, {7,19}, {7,20}, {21,28}, {7,17}, {16,27}, {8,31}, {11,32}, {10,34}, {4,23}, {10,11}, {10,25}, {9,35}, {12,20}, {12,18}, {9,11}, {3,6}, {5,23}, {9,33}, {12,19}, {10,20}, {3,5}, {3,4}, {9,10}, {31,33}, {29,30}, {31,32}, {33,34}, {27,31}, {33,35}, {29,33}, {26,31}, {18,29}, {26,33}, {19,31}, {28,35}, {21,36}, {20,33}, {25,27}, {34,36}, {16,26}, {10,13}, {9,13}, {8,14}, {7,12}, {14,18}, {15,18}, {15,19}, {15,20}, {28,34}, {27,33}, {28,33}, {27,34}, {13,17}, {14,19}, {13,20}, {4,6}, {4,5}, {5,6}, {29,32}, {32,35}, {30,34}, {28,32}, {27,29}, {32,34}, {30,36}, {16,25}, {21,35}, {25,29}, {13,16}, {14,16}, {14,21}, {30,31}, {30,32}, {29,31}, {13,21} } Symmetric graph 57 of order 36 Valency 21 Diameter 2 Girth 3 Automorphism group of order 362880 Number of arcs = 756 Number of 2-arcs = 15120 2-arc-transitive false Edge-set { {1,3}, {2,10}, {4,11}, {5,12}, {7,14}, {6,23}, {8,24}, {9,25}, {13,26}, {1,26}, {14,27}, {15,28}, {16,23}, {16,18}, {5,21}, {8,29}, {12,17}, {19,33}, {3,20}, {9,27}, {22,34}, {13,22}, {13,21}, {3,34}, {10,24}, {3,11}, {2,34}, {4,13}, {5,24}, {18,33}, {29,33}, {20,35}, {28,30}, {12,31}, {5,31}, {18,29}, {1,32}, {12,22}, {15,32}, {2,16}, {4,21}, {4,22}, {19,28}, {17,27}, {18,23}, {19,34}, {11,15}, {10,14}, {22,33}, {21,33}, {7,26}, {9,26}, {7,10}, {3,32}, {1,33}, {10,35}, {11,25}, {12,26}, {11,23}, {25,34}, {10,26}, {12,27}, {7,33}, {6,35}, {8,25}, {16,34}, {6,34}, {11,32}, {21,24}, {32,36}, {31,35}, {25,29}, {5,17}, {27,30}, {15,30}, {14,30}, {6,16}, {6,25}, {4,32}, {2,7}, {20,28}, {7,23}, {15,20}, {7,9}, {20,32}, {17,30}, {6,31}, {1,9}, {1,7}, {2,14}, {1,20}, {24,31}, {8,35}, {15,26}, {21,34}, {20,24}, {9,23}, {7,11}, {24,32}, {2,11}, {8,11}, {2,24}, {4,23}, {5,11}, {14,36}, {23,27}, {24,28}, {25,35}, {26,29}, {13,27}, {28,34}, {23,24}, {16,26}, {3,33}, {3,27}, {13,35}, {11,14}, {23,34}, {13,24}, {24,25}, {28,33}, {23,33}, {16,24}, {21,23}, {18,36}, {9,29}, {17,35}, {19,25}, {20,26}, {22,27}, {7,36}, {17,36}, {15,19}, {14,17}, {24,30}, {20,31}, {19,30}, {10,30}, {19,29}, {17,31}, {13,17}, {13,20}, {8,21}, {8,9}, {28,32}, {14,25}, {15,35}, {28,31}, {12,16}, {3,8}, {9,14}, {30,31}, {2,8}, {16,22}, {21,22}, {18,19}, {17,18}, {6,20}, {2,22}, {2,3}, {5,8}, {6,18}, {4,15}, {11,30}, {9,36}, {4,27}, {2,28}, {22,35}, {9,34}, {32,35}, {7,25}, {2,26}, {27,32}, {10,15}, {31,34}, {8,16}, {3,21}, {8,27}, {20,27}, {10,32}, {17,34}, {6,26}, {4,26}, {7,27}, {6,11}, {8,10}, {13,16}, {1,12}, {3,14}, {16,27}, {5,36}, {29,36}, {12,33}, {27,28}, {4,24}, {10,33}, {26,28}, {11,12}, {13,29}, {1,24}, {1,34}, {4,36}, {18,26}, {3,5}, {27,29}, {16,33}, {12,35}, {25,33}, {3,26}, {10,34}, {11,13}, {13,34}, {23,35}, {11,28}, {12,24}, {11,31}, {10,29}, {12,32}, {31,36}, {19,27}, {17,28}, {18,35}, {8,13}, {13,15}, {14,34}, {20,33}, {9,12}, {2,35}, {16,36}, {21,36}, {8,36}, {19,36}, {10,31}, {11,29}, {17,32}, {23,29}, {4,31}, {3,19}, {17,26}, {10,18}, {9,22}, {13,18}, {5,34}, {15,36}, {30,35}, {25,30}, {6,28}, {5,23}, {1,23}, {4,10}, {18,22}, {5,22}, {21,29}, {29,30}, {6,19}, {4,6}, {5,19}, {18,32}, {7,21}, {6,10}, {26,30}, {3,31}, {22,36}, {14,33}, {7,28}, {9,28}, {7,35}, {8,33}, {22,25}, {21,26}, {20,36}, {2,29}, {9,24}, {17,33}, {14,15}, {1,22}, {2,12}, {4,33}, {12,15}, {31,33}, {14,20}, {17,25}, {19,35}, {11,18}, {13,19}, {1,13}, {14,24}, {12,21}, {1,10}, {12,29}, {1,11}, {5,26}, {4,25}, {1,36}, {29,34}, {25,26}, {10,27}, {3,35}, {5,27}, {3,30}, {6,27}, {5,20}, {17,23}, {30,36}, {6,36}, {19,24}, {6,12}, {15,33}, {18,28}, {4,9}, {3,4}, {10,22}, {3,9}, {5,25}, {32,34}, {15,23}, {22,28}, {8,28}, {9,35}, {2,36}, {23,30}, {3,16}, {7,19}, {16,25}, {1,30}, {6,14}, {1,19}, {18,24}, {25,32}, {20,22}, {13,14}, {6,21}, {9,18}, {7,32}, {7,16}, {21,32}, {2,4}, {16,31}, {4,19}, {8,17}, {1,17}, {12,19}, {8,15}, {15,16}, {5,7}, {16,32}, {14,18}, {20,25}, {13,31}, {21,35}, {21,28}, {2,23}, {11,22}, {7,13}, {2,20}, {5,15}, {29,31}, {3,18}, {5,10}, {15,34}, {12,14}, {5,18}, {20,23}, {14,21}, {1,8}, {16,30}, {2,19}, {20,29}, {9,15}, {7,31}, {6,8}, {2,17}, {1,6}, {9,31}, {4,17}, {22,30}, {29,32}, {21,30} } Symmetric graph 58 of order 36 Valency 22 Diameter 2 Girth 3 Automorphism group of order 2874009600 Number of arcs = 792 Number of 2-arcs = 16632 2-arc-transitive false Edge-set { {1,4}, {15,22}, {6,24}, {7,29}, {29,34}, {13,28}, {5,35}, {12,31}, {3,13}, {12,26}, {3,25}, {9,10}, {2,28}, {14,25}, {4,27}, {17,35}, {17,19}, {9,24}, {23,28}, {3,17}, {19,31}, {2,24}, {23,32}, {18,32}, {14,21}, {10,23}, {2,22}, {2,8}, {30,32}, {1,15}, {6,33}, {6,25}, {10,27}, {6,19}, {7,10}, {28,32}, {14,35}, {10,30}, {2,36}, {19,35}, {7,17}, {22,35}, {30,36}, {18,36}, {5,36}, {11,18}, {8,21}, {9,30}, {18,30}, {21,36}, {23,29}, {22,34}, {23,33}, {11,36}, {1,18}, {7,22}, {24,29}, {13,34}, {5,16}, {2,13}, {5,32}, {21,33}, {13,19}, {5,7}, {18,31}, {13,21}, {10,36}, {2,18}, {8,25}, {27,30}, {1,21}, {23,27}, {22,26}, {19,25}, {7,27}, {6,31}, {10,13}, {25,29}, {27,34}, {11,27}, {1,26}, {5,27}, {11,26}, {14,27}, {4,26}, {11,20}, {9,15}, {11,32}, {1,14}, {5,11}, {1,11}, {21,27}, {9,26}, {12,30}, {3,36}, {26,29}, {25,34}, {30,34}, {16,36}, {16,27}, {20,26}, {5,22}, {11,24}, {29,31}, {12,28}, {3,35}, {25,28}, {4,14}, {4,12}, {9,23}, {22,28}, {14,36}, {4,18}, {21,34}, {9,16}, {9,19}, {7,28}, {14,31}, {4,13}, {11,17}, {9,21}, {9,28}, {18,27}, {21,26}, {5,23}, {11,22}, {2,33}, {15,32}, {1,33}, {21,22}, {1,30}, {33,36}, {3,29}, {31,34}, {2,19}, {7,32}, {1,31}, {13,33}, {13,35}, {5,17}, {9,18}, {21,28}, {2,12}, {3,32}, {25,33}, {1,16}, {20,33}, {3,22}, {24,31}, {4,33}, {3,16}, {20,31}, {1,8}, {30,33}, {3,15}, {16,20}, {8,20}, {14,29}, {18,20}, {8,22}, {24,30}, {14,16}, {4,20}, {16,22}, {20,24}, {9,33}, {1,19}, {24,27}, {23,26}, {3,12}, {3,31}, {2,26}, {25,32}, {1,25}, {12,33}, {3,20}, {8,31}, {4,34}, {16,28}, {20,35}, {12,35}, {10,17}, {24,25}, {2,10}, {2,32}, {8,15}, {6,30}, {15,17}, {10,29}, {2,34}, {8,27}, {26,30}, {5,15}, {6,11}, {9,25}, {4,32}, {12,14}, {19,32}, {7,14}, {10,31}, {8,35}, {17,30}, {6,28}, {6,16}, {10,20}, {21,32}, {9,14}, {10,32}, {2,14}, {1,5}, {11,33}, {3,21}, {9,31}, {14,30}, {4,36}, {16,29}, {20,34}, {23,34}, {7,36}, {18,29}, {16,24}, {21,29}, {9,34}, {1,24}, {16,26}, {12,24}, {3,23}, {26,35}, {17,25}, {19,23}, {31,36}, {13,18}, {17,24}, {27,28}, {6,14}, {4,10}, {11,14}, {10,21}, {2,9}, {17,23}, {19,22}, {24,36}, {18,23}, {16,32}, {4,22}, {8,16}, {28,35}, {15,34}, {4,24}, {12,23}, {8,17}, {22,33}, {15,24}, {11,34}, {7,24}, {8,12}, {3,30}, {5,20}, {8,11}, {29,33}, {11,28}, {1,35}, {4,8}, {15,20}, {6,8}, {4,29}, {12,34}, {20,28}, {32,34}, {1,28}, {33,35}, {24,35}, {22,31}, {24,32}, {17,34}, {16,19}, {8,23}, {15,26}, {20,25}, {19,27}, {6,18}, {32,35}, {23,36}, {18,22}, {7,33}, {15,29}, {11,13}, {6,7}, {12,18}, {22,25}, {15,33}, {3,11}, {13,16}, {14,32}, {15,36}, {19,30}, {19,36}, {7,18}, {13,30}, {18,35}, {17,21}, {15,27}, {1,10}, {2,5}, {5,12}, {8,32}, {18,21}, {22,30}, {14,22}, {16,34}, {21,24}, {14,17}, {6,26}, {25,36}, {27,31}, {13,26}, {4,28}, {12,21}, {3,9}, {26,32}, {3,4}, {17,28}, {2,6}, {27,35}, {17,26}, {5,9}, {10,35}, {8,13}, {5,30}, {15,18}, {6,21}, {20,30}, {19,29}, {7,34}, {6,34}, {12,15}, {10,25}, {2,27}, {7,26}, {15,28}, {6,35}, {10,15}, {29,35}, {28,31}, {17,33}, {15,19}, {1,23}, {14,20}, {16,33}, {10,16}, {2,20}, {6,15}, {7,20}, {8,29}, {3,6}, {26,36}, {18,25}, {10,22}, {28,36}, {4,19}, {7,12}, {3,7}, {5,13}, {5,29}, {13,31}, {11,19}, {2,29}, {20,23}, {4,9}, {8,36}, {1,7}, {5,31}, {9,11}, {5,25}, {14,23}, {5,21}, {11,29}, {1,34}, {12,25}, {9,35}, {6,23}, {6,10}, {13,23}, {27,33}, {12,19}, {26,31}, {13,25}, {3,27}, {2,17}, {7,19}, {8,30}, {12,16}, {7,13}, {13,24}, {17,31}, {4,17} } Symmetric graph 59 of order 36 Valency 24 Diameter 2 Girth 3 Automorphism group of order 8709120 Number of arcs = 864 Number of 2-arcs = 19872 2-arc-transitive false Edge-set { {1,6}, {16,36}, {17,34}, {22,31}, {15,28}, {20,29}, {22,26}, {10,26}, {2,11}, {8,24}, {13,31}, {18,25}, {4,24}, {6,10}, {11,32}, {8,32}, {2,15}, {7,35}, {11,33}, {12,18}, {23,26}, {2,16}, {7,19}, {23,29}, {11,14}, {12,36}, {1,36}, {8,17}, {2,28}, {1,7}, {28,33}, {1,18}, {15,24}, {13,35}, {30,34}, {19,27}, {2,32}, {7,25}, {3,19}, {5,23}, {6,12}, {9,32}, {15,22}, {15,35}, {19,21}, {12,25}, {4,9}, {2,21}, {7,14}, {3,31}, {5,28}, {16,31}, {28,34}, {20,33}, {18,22}, {8,15}, {31,35}, {16,34}, {19,34}, {25,31}, {16,19}, {23,34}, {11,24}, {12,13}, {23,30}, {16,27}, {27,29}, {3,26}, {5,17}, {21,30}, {1,35}, {7,34}, {19,29}, {13,17}, {21,33}, {12,35}, {9,20}, {3,36}, {4,28}, {10,24}, {11,13}, {24,30}, {13,27}, {9,17}, {10,21}, {3,7}, {5,29}, {4,14}, {6,36}, {9,15}, {10,35}, {21,34}, {14,19}, {13,26}, {2,33}, {8,35}, {20,31}, {8,29}, {26,31}, {18,32}, {24,25}, {10,19}, {11,23}, {24,33}, {13,18}, {26,30}, {2,27}, {22,29}, {15,26}, {17,29}, {21,26}, {7,26}, {2,29}, {17,22}, {15,21}, {12,29}, {9,26}, {7,12}, {3,23}, {5,16}, {12,27}, {3,9}, {5,22}, {15,30}, {5,25}, {4,30}, {6,13}, {32,33}, {20,35}, {20,22}, {9,27}, {3,10}, {16,30}, {27,34}, {29,34}, {19,26}, {17,25}, {4,21}, {20,23}, {16,22}, {10,25}, {3,30}, {5,27}, {4,18}, {6,24}, {8,14}, {31,36}, {1,11}, {8,12}, {2,23}, {7,16}, {11,27}, {3,12}, {4,20}, {6,22}, {1,9}, {8,10}, {13,34}, {19,33}, {25,35}, {14,21}, {14,36}, {17,28}, {1,30}, {8,27}, {9,29}, {17,21}, {6,23}, {16,32}, {15,32}, {30,33}, {18,27}, {18,26}, {2,24}, {25,33}, {6,26}, {19,28}, {1,23}, {7,11}, {1,17}, {8,21}, {2,12}, {7,9}, {19,23}, {16,23}, {6,27}, {3,32}, {5,15}, {30,35}, {4,11}, {13,32}, {20,25}, {4,22}, {6,9}, {10,32}, {6,34}, {19,32}, {15,25}, {4,35}, {10,20}, {11,22}, {9,24}, {10,13}, {3,25}, {4,5}, {4,6}, {6,32}, {3,34}, {5,19}, {9,33}, {22,35}, {15,20}, {3,5}, {5,30}, {4,13}, {6,33}, {11,20}, {24,27}, {3,13}, {14,27}, {23,36}, {16,17}, {28,32}, {1,25}, {18,30}, {10,18}, {6,30}, {1,13}, {8,33}, {22,27}, {3,15}, {25,29}, {4,26}, {6,17}, {21,32}, {7,20}, {9,14}, {10,36}, {10,22}, {11,15}, {3,33}, {5,35}, {20,30}, {11,36}, {12,17}, {14,18}, {5,18}, {12,15}, {9,35}, {22,34}, {15,19}, {2,5}, {7,30}, {5,33}, {24,36}, {11,17}, {4,16}, {1,33}, {8,18}, {16,26}, {17,32}, {21,25}, {9,21}, {10,14}, {21,31}, {14,28}, {8,20}, {4,25}, {22,28}, {1,15}, {24,28}, {27,32}, {6,19}, {23,32}, {7,32}, {12,16}, {9,34}, {2,34}, {16,20}, {4,34}, {12,22}, {5,36}, {17,30}, {13,28}, {24,35}, {13,20}, {27,30}, {3,27}, {2,14}, {7,36}, {23,28}, {1,16}, {7,18}, {24,29}, {4,36}, {1,28}, {1,8}, {29,36}, {17,26}, {1,21}, {7,24}, {13,29}, {14,30}, {27,36}, {2,10}, {8,16}, {7,13}, {29,33}, {14,35}, {20,36}, {17,36}, {28,36}, {26,33}, {17,35}, {20,21}, {4,32}, {6,25}, {10,30}, {18,24}, {13,24}, {27,35}, {3,20}, {14,23}, {32,36}, {2,18}, {5,11}, {12,30}, {13,23}, {16,33}, {5,21}, {12,31}, {9,28}, {8,28}, {1,31}, {1,19}, {8,23}, {3,17}, {5,10}, {11,30}, {13,33}, {4,29}, {6,14}, {1,10}, {18,34}, {19,24}, {8,11}, {20,27}, {3,24}, {2,31}, {7,28}, {19,35}, {5,13}, {10,29}, {11,26}, {17,24}, {13,21}, {32,35}, {11,31}, {12,28}, {2,20}, {7,22}, {14,22}, {15,36}, {25,34}, {18,23}, {20,28}, {1,22}, {14,31}, {18,33}, {16,24}, {3,22}, {15,29}, {26,35}, {14,29}, {26,36}, {31,34}, {9,31}, {15,34}, {11,25}, {4,12}, {6,20}, {22,32}, {9,16}, {10,34}, {11,34}, {12,19}, {23,25}, {21,27}, {3,14}, {5,31}, {28,30}, {22,33}, {15,18}, {25,32}, {18,31}, {8,31}, {28,31}, {9,18}, {1,27}, {3,8}, {11,19}, {12,23}, {12,21}, {23,35}, {2,35}, {4,8}, {6,31}, {12,33}, {16,25}, {14,25}, {21,36}, {14,17}, {8,34}, {19,31}, {2,6}, {9,23}, {10,16}, {2,26}, {2,7}, {24,31}, {7,29}, {26,29}, {18,36}, {10,28}, {6,15}, {1,29}, {8,26}, {5,9}, {14,33}, {4,19}, {2,17}, {7,21} } Symmetric graph 60 of order 36 Valency 24 Diameter 2 Girth 3 Automorphism group of order 659420041922872344576000000 Number of arcs = 864 Number of 2-arcs = 19872 2-arc-transitive false Edge-set { {1,13}, {5,31}, {23,26}, {15,35}, {6,16}, {4,23}, {1,35}, {8,19}, {10,28}, {7,36}, {15,27}, {4,29}, {21,35}, {19,31}, {10,23}, {12,33}, {13,29}, {22,28}, {3,19}, {20,34}, {9,14}, {8,21}, {4,28}, {2,19}, {10,34}, {12,15}, {6,29}, {19,35}, {17,26}, {11,18}, {5,13}, {8,26}, {1,22}, {3,33}, {12,30}, {22,29}, {6,27}, {20,25}, {2,33}, {13,34}, {3,21}, {12,32}, {24,29}, {18,28}, {12,19}, {13,36}, {8,15}, {10,29}, {1,31}, {9,25}, {17,32}, {5,35}, {16,26}, {23,33}, {17,30}, {11,22}, {14,26}, {7,18}, {8,33}, {21,36}, {4,15}, {11,24}, {2,30}, {5,18}, {12,26}, {22,34}, {3,13}, {8,36}, {9,22}, {3,32}, {18,29}, {5,20}, {9,26}, {13,28}, {15,31}, {6,23}, {24,27}, {2,20}, {10,16}, {7,23}, {1,27}, {4,17}, {11,35}, {10,14}, {7,31}, {1,25}, {17,33}, {9,34}, {14,32}, {11,13}, {8,29}, {21,28}, {3,25}, {17,36}, {7,24}, {9,35}, {16,32}, {1,18}, {5,30}, {22,26}, {20,33}, {9,13}, {16,30}, {5,22}, {8,32}, {23,27}, {1,20}, {3,26}, {6,28}, {4,36}, {11,32}, {24,30}, {7,28}, {19,27}, {4,34}, {14,35}, {21,31}, {19,25}, {10,17}, {15,34}, {6,14}, {24,31}, {2,23}, {11,31}, {18,27}, {12,20}, {5,25}, {13,33}, {8,13}, {2,22}, {3,34}, {10,20}, {9,31}, {14,36}, {7,16}, {5,27}, {23,32}, {1,23}, {1,33}, {11,17}, {11,30}, {20,26}, {7,14}, {7,27}, {16,33}, {4,21}, {4,35}, {23,30}, {22,36}, {3,15}, {20,29}, {9,21}, {16,25}, {5,17}, {3,14}, {12,21}, {6,19}, {10,25}, {2,15}, {6,34}, {12,24}, {2,29}, {8,18}, {12,28}, {6,36}, {15,25}, {4,32}, {24,35}, {6,17}, {11,26}, {18,30}, {2,16}, {5,33}, {13,26}, {1,32}, {24,33}, {12,22}, {11,28}, {19,30}, {6,20}, {7,34}, {14,27}, {4,16}, {4,31}, {23,35}, {17,31}, {11,23}, {14,25}, {7,17}, {1,30}, {21,34}, {4,14}, {11,27}, {19,29}, {10,21}, {7,35}, {9,33}, {8,30}, {2,27}, {10,35}, {16,31}, {6,30}, {22,25}, {2,26}, {18,34}, {12,36}, {15,29}, {24,28}, {18,36}, {13,32}, {8,24}, {3,18}, {20,36}, {9,15}, {2,28}, {16,29}, {5,21}, {10,36}, {23,25}, {1,17}, {7,32}, {17,35}, {11,16}, {5,23}, {1,26}, {3,17}, {11,36}, {18,33}, {12,14}, {7,29}, {15,30}, {6,21}, {4,25}, {21,27}, {4,19}, {10,15}, {6,31}, {6,24}, {2,25}, {14,31}, {2,18}, {12,34}, {21,25}, {12,13}, {19,34}, {17,27}, {11,20}, {14,33}, {7,13}, {21,32}, {4,24}, {19,28}, {10,19}, {7,15}, {1,24}, {9,18}, {8,28}, {3,22}, {3,36}, {9,20}, {9,32}, {5,16}, {5,26}, {9,30}, {22,32}, {8,27}, {20,28}, {3,24}, {2,35}, {16,34}, {9,19}, {10,31}, {23,31}, {5,14}, {7,25}, {16,35}, {10,30}, {22,31}, {9,17}, {6,26}, {18,25}, {8,14}, {2,36}, {2,21}, {12,29}, {21,29}, {15,36}, {6,15}, {24,32}, {2,24}, {6,25}, {18,26}, {12,18}, {2,34}, {11,25}, {5,34}, {3,29}, {8,34}, {14,28}, {3,31}, {23,36}, {9,27}, {20,32}, {22,33}, {20,30}, {16,27}, {1,16}, {7,20}, {21,33}, {4,13}, {3,30}, {19,32}, {10,24}, {12,27}, {15,28}, {6,35}, {24,34}, {2,14}, {7,19}, {10,27}, {1,15}, {6,33}, {20,31}, {9,24}, {2,32}, {13,25}, {2,13}, {8,20}, {9,28}, {3,16}, {5,36}, {24,36}, {9,23}, {18,32}, {24,25}, {2,17}, {18,35}, {12,16}, {13,30}, {8,22}, {6,22}, {4,20}, {11,33}, {11,14}, {7,30}, {7,21}, {4,27}, {11,34}, {14,30}, {5,29}, {21,26}, {7,22}, {3,28}, {19,36}, {4,18}, {6,32}, {14,29}, {8,31}, {23,28}, {11,15}, {3,27}, {5,24}, {5,32}, {24,26}, {22,27}, {3,20}, {20,35}, {9,16}, {9,36}, {10,32}, {7,26}, {1,36}, {15,33}, {11,29}, {21,30}, {17,25}, {14,34}, {12,17}, {13,35}, {8,16}, {1,34}, {22,30}, {9,29}, {16,36}, {5,15}, {6,13}, {8,25}, {4,22}, {3,35}, {17,28}, {3,23}, {1,21}, {4,33}, {11,19}, {20,27}, {16,28}, {5,19}, {23,34}, {1,14}, {8,17}, {2,31}, {6,18}, {12,25}, {10,26}, {18,31}, {7,33}, {13,27}, {12,23}, {8,35}, {15,26}, {1,29}, {10,22}, {4,30}, {22,35}, {17,29}, {11,21}, {12,35}, {10,33}, {13,31}, {15,32}, {1,19}, {17,34}, {4,26}, {19,33}, {10,13}, {8,23}, {1,28}, {19,26}, {10,18}, {5,28}, {12,31}, {23,29} } Symmetric graph 61 of order 36 Valency 25 Diameter 2 Girth 3 Automorphism group of order 1036800 Number of arcs = 900 Number of 2-arcs = 21600 2-arc-transitive false Edge-set { {1,7}, {6,30}, {13,24}, {2,33}, {5,15}, {12,24}, {12,30}, {3,17}, {18,35}, {1,19}, {10,17}, {12,26}, {23,30}, {26,33}, {5,23}, {5,20}, {9,16}, {16,23}, {11,33}, {6,8}, {13,28}, {20,28}, {9,21}, {26,34}, {6,23}, {9,33}, {5,29}, {17,34}, {6,35}, {1,9}, {17,29}, {17,27}, {21,29}, {8,20}, {8,29}, {17,25}, {19,35}, {2,27}, {15,22}, {24,31}, {2,12}, {7,31}, {11,29}, {20,26}, {13,34}, {6,34}, {2,9}, {15,29}, {20,35}, {1,36}, {13,20}, {9,34}, {2,16}, {15,33}, {6,29}, {20,36}, {3,9}, {20,32}, {4,9}, {11,36}, {3,26}, {7,27}, {22,27}, {27,36}, {3,22}, {8,16}, {28,33}, {3,32}, {4,18}, {10,19}, {10,25}, {12,14}, {30,32}, {18,23}, {14,30}, {24,32}, {25,36}, {3,19}, {7,34}, {6,27}, {12,34}, {2,13}, {15,34}, {3,29}, {18,20}, {19,36}, {3,10}, {7,16}, {27,33}, {6,18}, {13,36}, {7,24}, {12,27}, {13,29}, {20,34}, {3,21}, {8,18}, {17,19}, {10,35}, {2,36}, {3,15}, {7,18}, {16,20}, {7,15}, {27,31}, {4,29}, {14,20}, {18,25}, {5,34}, {6,16}, {4,24}, {10,32}, {4,25}, {18,32}, {4,36}, {5,10}, {16,25}, {21,27}, {8,22}, {17,31}, {2,35}, {16,31}, {4,23}, {11,14}, {8,28}, {21,28}, {28,35}, {1,21}, {22,26}, {7,23}, {5,31}, {9,23}, {22,33}, {5,7}, {12,15}, {30,31}, {5,8}, {16,28}, {13,30}, {24,34}, {2,32}, {4,15}, {13,26}, {23,34}, {3,24}, {12,18}, {13,19}, {10,34}, {5,36}, {3,16}, {11,27}, {28,36}, {5,28}, {16,21}, {21,30}, {8,24}, {17,32}, {4,35}, {2,23}, {11,15}, {18,24}, {12,36}, {24,30}, {26,32}, {24,36}, {3,12}, {7,13}, {27,34}, {5,11}, {16,26}, {23,27}, {11,22}, {9,28}, {21,33}, {3,18}, {18,36}, {5,19}, {10,16}, {11,24}, {7,21}, {8,27}, {19,30}, {10,24}, {14,32}, {4,32}, {3,14}, {7,22}, {23,35}, {1,11}, {1,13}, {2,21}, {8,15}, {4,12}, {15,28}, {21,31}, {1,14}, {15,23}, {11,31}, {14,36}, {1,28}, {17,21}, {21,35}, {1,8}, {11,32}, {4,26}, {10,27}, {22,25}, {9,32}, {18,33}, {14,21}, {8,32}, {14,29}, {7,19}, {2,22}, {2,26}, {6,11}, {6,25}, {9,30}, {24,29}, {9,29}, {20,29}, {25,35}, {1,30}, {17,24}, {19,26}, {10,23}, {14,33}, {5,32}, {1,27}, {17,22}, {2,8}, {24,33}, {5,12}, {12,13}, {30,34}, {18,31}, {4,19}, {10,14}, {6,12}, {9,13}, {29,34}, {16,30}, {23,26}, {11,23}, {12,28}, {21,34}, {1,18}, {17,36}, {5,21}, {25,32}, {1,31}, {2,17}, {11,21}, {8,26}, {5,26}, {22,30}, {15,20}, {9,31}, {4,16}, {18,29}, {19,25}, {12,23}, {11,30}, {18,26}, {23,36}, {12,33}, {5,30}, {6,31}, {30,36}, {13,32}, {4,34}, {1,25}, {29,31}, {2,20}, {11,17}, {26,35}, {11,16}, {17,28}, {8,21}, {12,25}, {24,26}, {27,32}, {4,22}, {8,33}, {14,31}, {5,22}, {10,30}, {24,25}, {29,33}, {6,24}, {3,11}, {19,27}, {10,22}, {14,23}, {19,31}, {2,10}, {6,22}, {9,19}, {10,29}, {14,25}, {19,32}, {18,22}, {7,36}, {11,20}, {9,26}, {13,22}, {15,25}, {6,14}, {28,32}, {4,21}, {20,31}, {17,23}, {11,35}, {7,26}, {15,27}, {22,31}, {22,36}, {3,7}, {8,30}, {24,28}, {3,34}, {2,25}, {15,19}, {1,15}, {3,30}, {29,36}, {3,20}, {3,27}, {16,35}, {1,33}, {6,33}, {5,13}, {12,20}, {8,34}, {6,28}, {7,35}, {6,32}, {4,13}, {10,20}, {9,25}, {12,17}, {30,35}, {1,26}, {13,33}, {4,8}, {14,28}, {22,28}, {19,29}, {26,31}, {11,13}, {9,36}, {17,26}, {15,35}, {9,18}, {11,25}, {1,34}, {6,17}, {10,33}, {5,25}, {8,14}, {8,35}, {23,29}, {25,33}, {5,17}, {2,14}, {15,32}, {15,24}, {12,31}, {14,34}, {18,27}, {20,25}, {16,34}, {21,25}, {8,19}, {1,23}, {4,31}, {4,10}, {22,35}, {14,22}, {7,32}, {1,10}, {12,35}, {3,35}, {15,30}, {16,19}, {4,28}, {10,28}, {9,22}, {7,29}, {3,28}, {18,21}, {28,31}, {18,30}, {7,25}, {6,20}, {15,31}, {2,31}, {4,11}, {14,26}, {7,14}, {9,20}, {19,33}, {10,18}, {16,24}, {2,30}, {6,19}, {10,13}, {5,33}, {5,16}, {3,36}, {16,27}, {13,35}, {1,24}, {13,27}, {22,34}, {2,15}, {7,28}, {29,35}, {1,20}, {16,33}, {6,13}, {4,27}, {2,7}, {10,31}, {8,36}, {12,19}, {6,9}, {9,15}, {1,35}, {1,17}, {17,35}, {9,17}, {23,32}, {13,21}, {4,14}, {23,33}, {11,26}, {14,19}, {6,7}, {20,27}, {8,17}, {23,28}, {12,21}, {3,33}, {5,18}, {16,36}, {21,32}, {25,34}, {2,24}, {2,29} } Symmetric graph 62 of order 36 Valency 27 Diameter 2 Girth 3 Automorphism group of order 416162911506546032640000 Number of arcs = 972 Number of 2-arcs = 25272 2-arc-transitive false Edge-set { {1,4}, {14,23}, {12,33}, {8,26}, {13,24}, {4,31}, {2,6}, {1,17}, {17,36}, {7,25}, {15,22}, {6,23}, {5,33}, {11,31}, {14,34}, {9,12}, {20,34}, {9,27}, {3,18}, {18,34}, {8,22}, {13,31}, {4,24}, {6,32}, {3,5}, {19,26}, {24,26}, {16,31}, {2,16}, {19,28}, {26,29}, {16,35}, {13,35}, {8,10}, {19,35}, {9,17}, {14,17}, {6,25}, {5,22}, {7,23}, {15,33}, {10,32}, {1,29}, {30,36}, {1,7}, {15,36}, {6,36}, {5,7}, {7,11}, {12,29}, {19,30}, {1,10}, {21,36}, {21,25}, {22,25}, {17,33}, {21,29}, {25,30}, {16,34}, {9,16}, {26,34}, {9,24}, {3,22}, {31,34}, {14,32}, {8,18}, {13,18}, {4,27}, {10,14}, {12,21}, {11,20}, {20,27}, {14,18}, {12,18}, {23,27}, {20,22}, {27,31}, {18,24}, {18,32}, {10,31}, {2,21}, {11,29}, {20,30}, {14,33}, {1,12}, {27,28}, {3,30}, {28,34}, {3,9}, {4,34}, {6,9}, {10,30}, {21,28}, {3,11}, {19,36}, {7,26}, {16,36}, {7,16}, {1,19}, {26,36}, {15,16}, {9,13}, {6,19}, {5,26}, {17,35}, {8,17}, {25,35}, {2,23}, {33,35}, {26,33}, {1,24}, {30,31}, {2,28}, {28,32}, {3,29}, {29,35}, {26,35}, {8,24}, {31,35}, {2,8}, {9,28}, {14,29}, {5,35}, {7,35}, {8,15}, {4,8}, {6,33}, {1,5}, {15,30}, {11,28}, {3,21}, {20,29}, {4,26}, {6,24}, {14,31}, {2,12}, {11,13}, {10,20}, {12,19}, {13,16}, {10,16}, {19,23}, {16,22}, {11,33}, {1,20}, {12,30}, {13,32}, {3,10}, {27,30}, {1,18}, {18,36}, {20,36}, {7,27}, {7,18}, {27,36}, {16,25}, {22,29}, {32,36}, {21,34}, {9,25}, {17,34}, {25,34}, {4,21}, {7,14}, {12,15}, {6,11}, {5,20}, {11,19}, {5,12}, {4,19}, {10,13}, {10,21}, {1,21}, {25,36}, {7,17}, {15,17}, {6,21}, {5,25}, {11,17}, {12,16}, {16,19}, {10,26}, {21,24}, {25,32}, {18,21}, {18,25}, {17,27}, {17,23}, {4,22}, {6,31}, {14,24}, {12,32}, {11,27}, {20,23}, {3,19}, {13,30}, {10,28}, {1,23}, {33,36}, {7,22}, {15,31}, {6,26}, {5,24}, {2,11}, {28,33}, {29,31}, {2,30}, {8,29}, {9,36}, {4,32}, {3,6}, {14,28}, {2,20}, {13,33}, {20,35}, {14,35}, {8,12}, {8,27}, {20,28}, {27,29}, {2,18}, {18,35}, {27,35}, {3,36}, {7,34}, {9,10}, {14,21}, {26,28}, {3,16}, {19,34}, {9,26}, {23,30}, {18,26}, {22,32}, {3,31}, {24,28}, {29,32}, {24,31}, {2,32}, {23,29}, {30,33}, {25,33}, {1,22}, {1,28}, {14,30}, {12,28}, {3,20}, {27,34}, {9,18}, {9,23}, {22,30}, {28,31}, {3,24}, {32,34}, {31,36}, {2,7}, {29,36}, {7,30}, {1,33}, {1,36}, {15,28}, {30,35}, {8,28}, {3,35}, {8,34}, {2,34}, {9,35}, {6,22}, {5,31}, {15,24}, {2,4}, {13,29}, {11,25}, {8,14}, {12,13}, {4,20}, {6,27}, {5,23}, {7,24}, {15,32}, {4,12}, {6,10}, {5,21}, {11,15}, {10,17}, {17,21}, {16,20}, {16,27}, {4,33}, {13,22}, {12,26}, {19,24}, {4,25}, {25,29}, {21,26}, {24,25}, {17,31}, {2,17}, {19,29}, {2,10}, {21,35}, {15,35}, {8,11}, {8,25}, {13,20}, {10,27}, {18,19}, {16,33}, {1,16}, {26,30}, {13,36}, {7,10}, {1,35}, {8,36}, {5,9}, {4,14}, {6,13}, {5,10}, {7,12}, {15,19}, {6,7}, {5,15}, {4,11}, {13,21}, {6,20}, {3,4}, {6,34}, {9,14}, {12,14}, {11,26}, {20,24}, {12,31}, {2,19}, {13,28}, {10,29}, {8,16}, {9,11}, {14,20}, {6,12}, {5,19}, {7,13}, {10,15}, {5,27}, {15,18}, {11,18}, {21,27}, {18,20}, {12,27}, {11,21}, {20,25}, {12,17}, {17,19}, {10,25}, {17,26}, {16,21}, {9,22}, {5,32}, {15,23}, {21,22}, {3,32}, {3,34}, {17,24}, {25,31}, {2,22}, {23,28}, {29,33}, {4,23}, {23,31}, {2,33}, {22,33}, {1,31}, {24,30}, {27,32}, {3,23}, {33,34}, {1,9}, {30,34}, {28,36}, {7,29}, {2,36}, {14,22}, {1,30}, {3,7}, {15,34}, {21,30}, {1,11}, {25,28}, {23,25}, {17,32}, {3,17}, {8,30}, {4,36}, {14,36}, {22,27}, {18,33}, {12,25}, {17,20}, {16,24}, {16,32}, {23,26}, {24,33}, {22,31}, {1,32}, {18,31}, {18,22}, {24,27}, {23,32}, {3,33}, {22,28}, {13,23}, {10,33}, {19,22}, {26,31}, {16,26}, {2,24}, {7,28}, {15,29}, {2,5}, {11,30}, {24,29}, {2,31}, {30,32}, {27,33}, {32,35}, {8,23}, {3,8}, {28,35}, {2,35}, {3,28}, {29,34}, {2,9}, {9,30}, {1,34}, {14,16}, {5,13}, {4,10}, {13,19}, {9,15}, {5,34}, {11,14}, {6,8}, {4,15}, {4,9}, {6,14}, {15,20}, {4,35}, {8,13}, {20,26}, {12,20}, {19,27}, {10,18}, {3,12}, {13,34}, {9,29}, {7,36}, {7,15}, {5,36}, {4,7}, {1,8}, {6,15}, {5,14}, {6,35}, {5,8}, {4,13}, {14,19}, {1,6}, {21,23}, {11,32}, {15,21}, {5,11}, {13,17}, {19,25}, {10,19}, {11,16}, {23,33}, {16,23}, {26,32}, {17,22}, {22,26}, {17,25}, {2,29}, {18,27}, {18,23}, {24,32}, {9,34}, {8,35} } Symmetric graph 63 of order 36 Valency 30 Diameter 2 Girth 3 Automorphism group of order 100306130042880000000 Number of arcs = 1080 Number of 2-arcs = 31320 2-arc-transitive false Edge-set { {1,7}, {5,25}, {17,22}, {19,29}, {12,19}, {15,33}, {3,34}, {23,31}, {1,9}, {4,31}, {1,15}, {8,14}, {26,32}, {7,27}, {24,25}, {11,35}, {5,30}, {2,25}, {14,22}, {11,28}, {23,30}, {14,25}, {22,32}, {6,18}, {18,36}, {12,20}, {11,29}, {5,22}, {7,17}, {19,36}, {6,12}, {3,10}, {16,27}, {24,29}, {10,19}, {19,26}, {12,21}, {18,33}, {3,36}, {3,21}, {8,16}, {24,35}, {5,10}, {18,19}, {12,36}, {12,33}, {3,29}, {16,30}, {20,33}, {9,16}, {28,33}, {4,32}, {2,15}, {3,23}, {29,33}, {3,19}, {5,15}, {17,34}, {9,31}, {1,28}, {4,30}, {15,20}, {1,27}, {13,24}, {13,22}, {7,31}, {23,36}, {6,9}, {1,31}, {1,13}, {20,31}, {1,11}, {4,34}, {4,15}, {26,33}, {9,27}, {24,28}, {27,34}, {4,24}, {6,13}, {18,31}, {10,36}, {6,27}, {1,29}, {13,19}, {16,31}, {1,33}, {4,9}, {15,28}, {4,8}, {15,26}, {23,27}, {9,24}, {10,31}, {8,32}, {2,26}, {2,13}, {14,31}, {8,21}, {8,26}, {12,28}, {23,29}, {14,26}, {21,32}, {27,35}, {5,24}, {8,23}, {9,26}, {27,31}, {1,24}, {14,29}, {19,32}, {7,15}, {25,34}, {2,11}, {14,30}, {21,25}, {8,22}, {10,23}, {14,32}, {2,32}, {22,25}, {7,22}, {17,36}, {6,35}, {17,33}, {3,35}, {5,11}, {17,30}, {9,35}, {5,28}, {2,30}, {14,20}, {11,25}, {22,30}, {17,25}, {22,35}, {11,32}, {3,25}, {16,22}, {7,28}, {23,25}, {14,28}, {23,32}, {8,20}, {11,26}, {2,22}, {7,14}, {21,36}, {6,8}, {7,25}, {28,36}, {6,23}, {20,35}, {11,16}, {30,33}, {13,28}, {7,20}, {9,22}, {17,31}, {1,35}, {11,13}, {30,31}, {8,25}, {22,26}, {2,28}, {14,23}, {14,21}, {6,28}, {18,23}, {5,7}, {2,36}, {6,14}, {13,30}, {18,29}, {20,26}, {11,21}, {17,26}, {21,35}, {11,18}, {30,36}, {6,34}, {4,18}, {6,20}, {4,21}, {8,15}, {23,35}, {5,9}, {18,20}, {11,36}, {12,34}, {4,29}, {10,22}, {29,36}, {6,19}, {5,18}, {2,20}, {11,14}, {11,22}, {7,30}, {25,36}, {6,22}, {9,36}, {12,31}, {5,14}, {17,32}, {7,19}, {12,25}, {3,26}, {16,21}, {18,24}, {19,34}, {4,12}, {6,33}, {3,18}, {5,13}, {12,18}, {12,26}, {21,29}, {19,33}, {3,12}, {5,33}, {3,17}, {9,15}, {28,34}, {10,30}, {20,27}, {26,34}, {10,27}, {24,27}, {16,19}, {15,24}, {10,34}, {2,10}, {14,27}, {8,19}, {24,26}, {10,21}, {18,32}, {12,16}, {24,33}, {15,19}, {10,33}, {3,27}, {16,29}, {19,27}, {12,24}, {13,33}, {3,31}, {5,21}, {8,17}, {19,35}, {5,12}, {18,21}, {8,36}, {12,35}, {5,29}, {6,32}, {2,18}, {3,20}, {9,34}, {4,28}, {6,30}, {5,19}, {12,17}, {9,21}, {8,28}, {30,35}, {5,20}, {10,32}, {2,27}, {3,13}, {8,24}, {10,26}, {17,21}, {8,35}, {5,32}, {2,17}, {2,33}, {3,14}, {11,15}, {30,34}, {10,25}, {22,27}, {16,35}, {11,24}, {3,11}, {21,26}, {18,35}, {5,36}, {18,34}, {4,36}, {21,30}, {17,19}, {21,28}, {18,30}, {20,36}, {17,24}, {10,35}, {16,23}, {9,33}, {20,32}, {4,16}, {11,34}, {4,27}, {3,16}, {16,33}, {10,28}, {20,25}, {16,28}, {23,33}, {30,32}, {4,23}, {5,27}, {2,29}, {14,19}, {16,32}, {3,9}, {4,7}, {15,25}, {23,28}, {9,23}, {9,28}, {1,20}, {2,21}, {16,36}, {3,33}, {10,17}, {9,19}, {2,9}, {4,11}, {15,30}, {12,15}, {29,34}, {5,31}, {1,17}, {4,19}, {13,34}, {1,25}, {15,23}, {8,30}, {17,29}, {4,20}, {23,34}, {8,31}, {1,26}, {8,29}, {15,27}, {24,34}, {2,14}, {7,21}, {10,13}, {2,7}, {1,22}, {7,13}, {22,36}, {6,7}, {13,31}, {14,36}, {13,25}, {13,21}, {18,22}, {7,36}, {6,31}, {1,18}, {6,11}, {1,34}, {4,13}, {15,31}, {6,26}, {1,32}, {1,8}, {13,26}, {7,24}, {13,23}, {22,31}, {6,15}, {26,35}, {11,27}, {24,30}, {16,34}, {4,33}, {18,28}, {4,10}, {12,30}, {20,29}, {16,26}, {21,33}, {27,32}, {2,24}, {10,20}, {29,31}, {1,19}, {15,34}, {2,34}, {4,14}, {6,21}, {8,18}, {10,24}, {29,32}, {2,19}, {1,12}, {13,29}, {17,27}, {6,36}, {6,10}, {18,27}, {12,29}, {21,34}, {24,36}, {12,13}, {22,33}, {3,7}, {6,16}, {16,24}, {20,34}, {10,16}, {27,33}, {9,29}, {19,28}, {7,16}, {25,33}, {9,32}, {15,36}, {1,10}, {13,27}, {13,35}, {2,8}, {12,32}, {16,25}, {22,28}, {7,23}, {24,31}, {8,13}, {26,31}, {1,21}, {2,12}, {5,26}, {10,29}, {28,35}, {5,23}, {22,29}, {23,26}, {1,36}, {14,24}, {17,23}, {5,8}, {2,35}, {25,32}, {9,13}, {28,31}, {8,27}, {2,31}, {1,14}, {3,28}, {15,32}, {9,25}, {19,30}, {22,34}, {1,23}, {25,35}, {19,25}, {12,22}, {14,35}, {6,24}, {10,18}, {28,32}, {2,23}, {7,35}, {9,18}, {7,32}, {6,25}, {18,26}, {5,34}, {4,17}, {3,22}, {5,17}, {17,35}, {17,20}, {11,17}, {4,35}, {17,28}, {11,30}, {20,30}, {3,30}, {16,20}, {11,20}, {6,17}, {5,35}, {11,33}, {25,31}, {8,33}, {10,15}, {13,20}, {11,31}, {8,34}, {4,26}, {7,29}, {26,36}, {11,23}, {9,30}, {7,26}, {12,23}, {4,25}, {15,22}, {7,34}, {20,28}, {1,30}, {7,33}, {15,35}, {13,36}, {9,14}, {21,31}, {15,29}, {3,8}, {4,22}, {15,21}, {11,19}, {29,35}, {6,29}, {21,27}, {7,18}, {18,25}, {12,14}, {12,27}, {19,31}, {3,15}, {27,36}, {1,16}, {2,16}, {14,33}, {3,24}, {24,32}, {13,32}, {3,32}, {9,17}, {9,20}, {5,16}, {10,14}, {14,34} } Symmetric graph 64 of order 36 Valency 32 Diameter 2 Girth 3 Automorphism group of order 958659120196485120 Number of arcs = 1152 Number of 2-arcs = 35712 2-arc-transitive false Edge-set { {1,5}, {7,18}, {4,9}, {5,34}, {10,26}, {20,21}, {3,34}, {7,29}, {9,29}, {13,24}, {24,35}, {27,33}, {16,27}, {17,29}, {1,29}, {8,10}, {1,21}, {8,34}, {14,20}, {26,32}, {14,32}, {15,30}, {23,30}, {12,15}, {17,23}, {1,35}, {8,28}, {1,18}, {4,8}, {6,24}, {11,35}, {18,27}, {4,16}, {6,29}, {11,29}, {11,33}, {19,27}, {3,13}, {5,24}, {3,11}, {5,19}, {4,25}, {7,15}, {9,23}, {18,36}, {25,35}, {15,28}, {18,32}, {4,32}, {6,14}, {11,21}, {18,34}, {4,26}, {6,20}, {8,26}, {12,14}, {22,32}, {32,33}, {15,34}, {23,26}, {12,20}, {3,17}, {1,8}, {8,12}, {1,22}, {8,33}, {22,30}, {30,33}, {15,36}, {23,25}, {10,17}, {1,20}, {7,26}, {9,14}, {17,22}, {1,33}, {7,36}, {9,25}, {16,20}, {3,22}, {5,9}, {10,18}, {21,25}, {31,34}, {26,31}, {16,32}, {18,21}, {5,26}, {3,20}, {3,5}, {8,11}, {12,19}, {22,27}, {16,33}, {29,34}, {26,29}, {13,20}, {3,24}, {12,27}, {6,13}, {11,24}, {11,23}, {19,36}, {3,28}, {5,13}, {3,30}, {5,30}, {18,29}, {13,25}, {15,24}, {23,33}, {27,36}, {17,35}, {1,28}, {6,18}, {4,11}, {6,23}, {11,36}, {18,28}, {4,13}, {6,30}, {11,30}, {4,28}, {7,13}, {4,30}, {7,30}, {9,31}, {18,31}, {16,25}, {15,22}, {28,35}, {18,33}, {4,27}, {10,24}, {19,34}, {13,28}, {18,30}, {5,31}, {10,31}, {16,21}, {22,34}, {12,33}, {17,27}, {17,28}, {1,13}, {7,21}, {9,34}, {24,34}, {26,35}, {16,22}, {2,29}, {2,13}, {3,12}, {5,17}, {27,34}, {16,26}, {9,24}, {17,33}, {1,27}, {7,17}, {1,9}, {6,22}, {23,36}, {25,36}, {13,23}, {12,30}, {17,30}, {8,29}, {8,24}, {10,33}, {20,27}, {17,26}, {1,14}, {15,23}, {22,26}, {14,33}, {22,25}, {15,33}, {31,36}, {25,31}, {14,17}, {7,10}, {9,20}, {4,17}, {1,7}, {4,7}, {7,9}, {1,34}, {10,16}, {20,22}, {9,26}, {14,18}, {25,30}, {15,31}, {23,31}, {32,35}, {28,32}, {4,21}, {12,26}, {3,33}, {8,25}, {22,31}, {31,33}, {14,34}, {21,26}, {10,20}, {7,12}, {4,22}, {7,33}, {3,21}, {5,10}, {4,20}, {3,7}, {4,5}, {2,21}, {6,34}, {2,34}, {6,26}, {12,16}, {9,28}, {13,18}, {21,32}, {30,34}, {26,30}, {15,20}, {3,23}, {24,26}, {14,35}, {29,36}, {25,29}, {10,14}, {4,34}, {2,7}, {6,9}, {2,24}, {6,35}, {16,17}, {28,29}, {13,29}, {30,36}, {15,35}, {23,28}, {21,28}, {5,27}, {21,29}, {14,29}, {13,32}, {24,32}, {12,28}, {13,17}, {1,19}, {2,8}, {10,19}, {2,20}, {1,36}, {7,35}, {15,29}, {23,29}, {12,13}, {17,24}, {30,35}, {28,30}, {15,18}, {4,23}, {5,35}, {10,28}, {16,31}, {10,25}, {4,35}, {7,28}, {1,6}, {11,14}, {24,30}, {23,27}, {13,35}, {24,28}, {11,18}, {4,19}, {19,30}, {16,28}, {13,22}, {9,30}, {2,31}, {6,31}, {2,16}, {19,28}, {10,35}, {21,33}, {20,35}, {5,18}, {4,10}, {5,20}, {3,10}, {5,21}, {10,34}, {4,29}, {12,24}, {28,33}, {13,27}, {13,21}, {11,34}, {19,26}, {7,22}, {2,9}, {2,25}, {6,15}, {3,32}, {5,32}, {3,14}, {3,16}, {24,36}, {1,30}, {6,16}, {11,22}, {2,28}, {2,30}, {19,29}, {16,24}, {24,33}, {27,35}, {5,23}, {10,36}, {20,28}, {10,30}, {1,16}, {7,24}, {9,35}, {20,33}, {3,27}, {1,10}, {7,20}, {3,9}, {12,29}, {8,13}, {12,23}, {17,36}, {14,21}, {21,34}, {20,26}, {5,16}, {9,33}, {17,25}, {1,15}, {13,26}, {14,24}, {11,32}, {19,32}, {1,31}, {8,31}, {8,22}, {19,35}, {20,29}, {3,29}, {2,10}, {8,21}, {12,34}, {2,14}, {8,32}, {12,32}, {12,35}, {8,20}, {4,31}, {7,31}, {9,32}, {14,25}, {15,21}, {14,27}, {8,16}, {1,11}, {8,19}, {3,26}, {5,14}, {14,23}, {21,36}, {6,19}, {2,11}, {19,33}, {2,27}, {10,32}, {8,18}, {1,25}, {8,15}, {10,23}, {20,36}, {14,28}, {7,32}, {4,14}, {18,26}, {20,25}, {3,15}, {21,35}, {2,12}, {6,17}, {22,35}, {20,32}, {10,21}, {4,12}, {7,14}, {15,25}, {14,26}, {26,33}, {3,25}, {4,36}, {7,25}, {17,21}, {7,34}, {2,19}, {2,6}, {6,12}, {2,17}, {14,36}, {27,30}, {16,30}, {27,32}, {20,24}, {3,35}, {9,27}, {7,27}, {9,16}, {24,29}, {29,35}, {3,8}, {14,30}, {21,30}, {10,15}, {20,23}, {10,27}, {22,29}, {29,33}, {13,36}, {24,25}, {5,28}, {10,13}, {19,21}, {16,19}, {2,22}, {8,9}, {12,18}, {11,17}, {12,17}, {1,17}, {14,31}, {4,18}, {22,28}, {13,33}, {14,19}, {15,32}, {23,32}, {9,15}, {24,31}, {31,35}, {21,27}, {4,24}, {32,34}, {15,17}, {1,23}, {18,24}, {5,33}, {8,36}, {6,10}, {11,20}, {28,31}, {11,27}, {27,29}, {16,29}, {24,27}, {9,17}, {16,35}, {9,18}, {11,26}, {3,36}, {5,25}, {2,18}, {4,6}, {6,11}, {6,28}, {11,13}, {32,36}, {25,32}, {8,27}, {19,24}, {2,35}, {6,27}, {11,16}, {11,19}, {3,6}, {5,11}, {5,36}, {6,33}, {2,5}, {19,22}, {16,18}, {11,15}, {19,23}, {18,22}, {4,33}, {6,36}, {11,25}, {1,24}, {7,11}, {9,19}, {15,19}, {27,31}, {12,25}, {2,33}, {2,23}, {3,19}, {13,34}, {2,36}, {8,35}, {13,30}, {20,31}, {3,31}, {10,22}, {5,29}, {10,29}, {8,23}, {12,36}, {11,31}, {19,31}, {4,15}, {7,23}, {17,32}, {1,32}, {23,34}, {5,15}, {12,21}, {17,34}, {1,26}, {8,14}, {7,19}, {7,16}, {18,35}, {25,33}, {15,27}, {23,35}, {8,30}, {14,22}, {9,21}, {6,21}, {26,36}, {28,36}, {20,34}, {20,30}, {19,25}, {2,26}, {2,32}, {6,32}, {16,23}, {18,25}, {26,34}, {22,33}, {1,12}, {8,17}, {15,26}, {28,34}, {17,31}, {9,22}, {5,22}, {12,22}, {22,36}, {12,31}, {25,34}, {9,36}, {2,15}, {6,25}, {3,18}, {16,36}, {5,12}, {18,23}, {11,28}, {13,19}, {16,34}, {13,31}, {21,31}, {9,13} } Symmetric graph 65 of order 36 Valency 33 Diameter 2 Girth 3 Automorphism group of order 1042682221795737600 Number of arcs = 1188 Number of 2-arcs = 38016 2-arc-transitive false Edge-set { {1,4}, {3,25}, {19,35}, {1,9}, {4,20}, {28,33}, {10,23}, {3,23}, {19,30}, {25,30}, {24,35}, {16,36}, {15,26}, {5,10}, {7,31}, {1,10}, {20,31}, {28,34}, {23,27}, {9,34}, {4,27}, {11,33}, {10,32}, {21,31}, {1,12}, {8,15}, {6,16}, {5,26}, {7,34}, {17,22}, {14,29}, {3,5}, {7,19}, {17,30}, {14,24}, {32,36}, {11,26}, {7,10}, {5,31}, {23,32}, {11,30}, {7,25}, {5,35}, {4,16}, {5,18}, {7,13}, {17,29}, {14,22}, {3,6}, {9,19}, {15,24}, {16,28}, {21,27}, {1,36}, {8,26}, {6,34}, {22,32}, {11,29}, {12,20}, {2,33}, {13,35}, {17,25}, {1,26}, {20,34}, {22,28}, {23,29}, {2,27}, {11,13}, {17,32}, {18,31}, {12,13}, {4,8}, {6,8}, {5,22}, {7,29}, {17,26}, {14,34}, {10,18}, {13,31}, {4,34}, {8,27}, {9,22}, {4,29}, {26,33}, {10,34}, {21,25}, {1,35}, {19,26}, {3,34}, {18,29}, {20,35}, {2,25}, {17,33}, {1,27}, {20,36}, {23,28}, {23,30}, {11,15}, {16,32}, {21,36}, {3,31}, {12,19}, {8,24}, {6,28}, {27,32}, {11,36}, {12,18}, {13,33}, {4,35}, {8,25}, {6,30}, {9,24}, {2,16}, {15,21}, {14,33}, {9,20}, {2,4}, {3,8}, {6,19}, {30,32}, {11,24}, {12,36}, {10,35}, {25,31}, {2,7}, {5,21}, {4,14}, {8,18}, {18,20}, {2,13}, {17,19}, {3,14}, {6,14}, {9,18}, {24,25}, {28,35}, {24,27}, {28,36}, {12,26}, {33,34}, {22,35}, {25,29}, {8,20}, {2,6}, {13,32}, {11,17}, {5,19}, {3,7}, {14,17}, {14,18}, {25,32}, {11,35}, {7,24}, {5,28}, {12,23}, {30,33}, {25,35}, {8,16}, {6,15}, {5,32}, {7,11}, {9,29}, {4,22}, {3,33}, {10,19}, {8,28}, {6,23}, {1,32}, {11,20}, {10,24}, {2,9}, {4,21}, {16,20}, {2,15}, {30,31}, {12,24}, {10,36}, {26,31}, {27,31}, {4,15}, {18,21}, {1,13}, {29,31}, {12,22}, {1,17}, {14,20}, {9,23}, {28,32}, {27,36}, {26,36}, {7,18}, {5,13}, {4,31}, {8,12}, {3,9}, {14,16}, {15,18}, {25,33}, {4,28}, {27,34}, {11,23}, {2,21}, {1,21}, {15,29}, {16,22}, {13,16}, {15,17}, {24,30}, {21,35}, {1,24}, {20,28}, {27,28}, {23,36}, {18,34}, {13,27}, {4,11}, {8,32}, {6,31}, {9,12}, {5,33}, {9,17}, {2,22}, {21,29}, {26,29}, {22,34}, {13,25}, {17,35}, {19,24}, {3,28}, {3,24}, {2,14}, {2,23}, {17,20}, {17,36}, {19,23}, {3,30}, {9,11}, {4,32}, {33,36}, {10,26}, {31,36}, {6,9}, {12,33}, {10,33}, {9,35}, {4,25}, {24,28}, {13,18}, {2,8}, {26,28}, {23,34}, {1,22}, {20,29}, {13,20}, {2,17}, {13,19}, {3,17}, {4,13}, {4,33}, {8,10}, {11,22}, {29,32}, {26,34}, {6,10}, {9,31}, {16,34}, {15,27}, {9,33}, {4,10}, {21,24}, {1,28}, {18,26}, {13,34}, {8,29}, {23,35}, {12,25}, {33,35}, {1,16}, {15,20}, {7,23}, {24,36}, {10,27}, {3,18}, {4,30}, {5,11}, {7,32}, {21,30}, {16,21}, {17,34}, {14,27}, {6,11}, {9,32}, {7,12}, {8,17}, {7,17}, {5,14}, {15,25}, {16,35}, {19,29}, {3,22}, {18,19}, {14,25}, {6,12}, {3,20}, {2,19}, {13,30}, {17,24}, {18,36}, {13,26}, {5,12}, {8,31}, {19,22}, {3,29}, {14,26}, {14,35}, {6,24}, {9,28}, {1,23}, {20,30}, {13,21}, {15,19}, {3,16}, {9,16}, {25,36}, {26,35}, {2,29}, {21,22}, {15,35}, {16,25}, {12,21}, {1,33}, {14,21}, {1,18}, {11,34}, {29,33}, {10,22}, {3,11}, {19,32}, {30,36}, {24,26}, {7,36}, {10,31}, {12,31}, {7,14}, {8,35}, {18,24}, {13,28}, {17,27}, {14,36}, {9,30}, {16,26}, {15,34}, {20,23}, {2,30}, {2,12}, {21,33}, {29,35}, {22,25}, {6,25}, {12,32}, {9,14}, {4,18}, {20,33}, {2,10}, {11,28}, {20,26}, {1,11}, {20,32}, {17,21}, {2,24}, {10,28}, {23,31}, {1,34}, {20,27}, {4,23}, {8,30}, {18,25}, {16,31}, {12,15}, {5,8}, {6,7}, {17,31}, {12,14}, {9,15}, {5,16}, {7,15}, {23,33}, {10,30}, {9,25}, {26,32}, {14,19}, {21,28}, {8,36}, {6,26}, {11,31}, {3,12}, {19,33}, {30,35}, {14,30}, {2,20}, {14,28}, {18,23}, {1,20}, {18,35}, {5,24}, {7,28}, {4,12}, {8,33}, {5,27}, {17,23}, {21,32}, {16,23}, {15,30}, {5,25}, {7,35}, {3,36}, {8,19}, {14,32}, {11,18}, {25,28}, {4,9}, {16,33}, {10,15}, {3,21}, {1,19}, {16,24}, {5,7}, {25,34}, {27,35}, {4,26}, {8,34}, {18,22}, {13,29}, {29,34}, {22,27}, {2,11}, {5,17}, {6,22}, {20,24}, {2,28}, {20,22}, {23,25}, {19,28}, {9,13}, {4,17}, {6,27}, {9,36}, {1,30}, {21,23}, {18,27}, {2,32}, {19,31}, {8,14}, {6,18}, {12,28}, {20,25}, {8,13}, {6,17}, {10,17}, {11,27}, {26,30}, {3,10}, {30,34}, {15,28}, {2,35}, {12,29}, {22,33}, {15,33}, {10,16}, {9,21}, {6,29}, {3,19}, {8,11}, {7,33}, {18,28}, {13,23}, {31,34}, {12,27}, {6,32}, {22,31}, {13,22}, {24,33}, {11,19}, {3,32}, {7,20}, {2,5}, {12,17}, {27,30}, {8,21}, {1,6}, {15,32}, {11,16}, {24,31}, {2,34}, {16,29}, {15,22}, {10,25}, {9,27}, {4,36}, {19,25}, {3,35}, {16,30}, {7,21}, {3,4}, {18,30}, {13,24}, {5,36}, {7,26}, {14,31}, {7,30}, {31,35}, {24,34}, {1,14}, {29,36}, {6,13}, {15,23}, {21,26}, {15,31}, {5,34}, {7,27}, {22,26}, {6,36}, {13,36}, {32,34}, {22,36}, {10,20}, {2,31}, {10,21}, {1,31}, {16,27}, {9,26}, {10,29}, {13,17}, {4,19}, {1,15}, {5,15}, {7,16}, {1,29}, {11,21}, {6,35}, {24,32}, {32,35}, {11,25}, {2,36}, {12,30}, {9,10}, {23,26}, {14,23}, {19,27}, {2,18}, {17,28}, {4,24}, {5,20}, {4,7}, {1,5}, {15,36}, {12,16}, {15,16}, {1,7}, {22,30}, {19,36}, {3,26}, {10,14}, {11,14}, {5,9}, {18,33}, {8,23}, {24,29}, {2,26}, {21,34}, {6,20}, {3,27}, {1,8}, {1,25}, {5,30}, {12,35}, {22,29}, {19,34}, {18,32}, {12,34}, {8,22}, {27,29}, {11,32}, {3,13}, {7,22}, {5,29}, {6,33}, {3,15}, {16,19}, {27,33}, {10,13}, {5,23}, {6,21}, {28,31} } Symmetric graph 66 of order 36 Valency 34 Diameter 2 Girth 3 Automorphism group of order 1678343852714360832000 Number of arcs = 1224 Number of 2-arcs = 40392 2-arc-transitive false Edge-set { {1,3}, {17,32}, {20,21}, {8,15}, {3,31}, {2,23}, {2,10}, {3,20}, {8,28}, {7,17}, {20,32}, {22,31}, {22,25}, {31,34}, {22,34}, {17,23}, {2,20}, {3,11}, {8,36}, {4,15}, {3,7}, {8,23}, {2,31}, {1,7}, {9,32}, {1,27}, {6,9}, {7,25}, {13,32}, {1,25}, {9,13}, {15,22}, {3,25}, {23,31}, {2,22}, {14,17}, {20,24}, {3,10}, {8,12}, {18,20}, {19,28}, {4,17}, {7,20}, {3,22}, {8,25}, {7,31}, {22,32}, {4,32}, {7,21}, {8,33}, {31,33}, {12,32}, {21,35}, {30,33}, {29,33}, {4,27}, {6,7}, {5,8}, {16,31}, {27,32}, {6,21}, {5,33}, {16,33}, {1,20}, {9,28}, {17,27}, {6,20}, {7,22}, {25,32}, {1,31}, {9,22}, {6,15}, {3,15}, {21,23}, {2,26}, {17,34}, {20,34}, {3,13}, {16,23}, {2,4}, {11,24}, {1,36}, {15,18}, {3,19}, {4,23}, {2,7}, {1,17}, {9,20}, {3,27}, {6,8}, {4,7}, {7,32}, {1,8}, {9,31}, {8,18}, {19,31}, {7,10}, {3,26}, {8,14}, {7,26}, {14,32}, {8,13}, {2,9}, {10,11}, {26,35}, {14,18}, {26,36}, {12,18}, {19,35}, {4,30}, {7,29}, {3,29}, {8,30}, {7,19}, {31,35}, {2,30}, {10,29}, {26,29}, {14,30}, {19,26}, {14,27}, {23,32}, {2,21}, {11,33}, {33,36}, {12,15}, {3,35}, {23,30}, {2,29}, {1,4}, {7,9}, {8,27}, {6,31}, {21,32}, {1,33}, {9,33}, {20,30}, {28,29}, {17,20}, {20,28}, {10,25}, {28,31}, {5,22}, {15,25}, {23,25}, {2,13}, {5,17}, {16,20}, {19,22}, {25,27}, {18,31}, {14,21}, {24,26}, {10,32}, {12,21}, {4,28}, {17,24}, {18,22}, {19,25}, {4,31}, {15,32}, {3,21}, {23,33}, {2,33}, {12,17}, {20,35}, {3,30}, {8,29}, {4,18}, {4,8}, {3,32}, {8,21}, {7,33}, {32,33}, {3,16}, {7,24}, {1,32}, {4,34}, {7,34}, {17,28}, {5,20}, {3,6}, {5,7}, {15,31}, {3,5}, {8,16}, {22,33}, {14,34}, {24,34}, {5,11}, {6,16}, {10,28}, {5,12}, {13,16}, {9,24}, {1,11}, {18,35}, {18,19}, {4,36}, {17,36}, {4,24}, {11,32}, {34,36}, {28,36}, {6,35}, {24,28}, {1,5}, {6,12}, {15,35}, {8,22}, {25,31}, {10,22}, {14,26}, {14,24}, {10,26}, {12,14}, {13,20}, {23,28}, {9,17}, {11,20}, {22,35}, {18,25}, {31,36}, {17,22}, {18,32}, {19,21}, {4,33}, {3,12}, {8,35}, {7,30}, {29,32}, {2,8}, {10,31}, {26,32}, {26,33}, {14,33}, {23,35}, {2,18}, {11,36}, {15,23}, {2,3}, {11,23}, {2,36}, {27,34}, {6,34}, {7,11}, {32,36}, {1,29}, {9,30}, {20,27}, {6,28}, {22,27}, {6,25}, {5,31}, {16,22}, {15,29}, {19,23}, {2,27}, {1,24}, {1,9}, {12,27}, {7,16}, {2,6}, {10,15}, {21,28}, {5,26}, {8,34}, {10,23}, {11,18}, {19,36}, {15,21}, {1,16}, {4,9}, {24,27}, {1,6}, {7,18}, {19,32}, {8,20}, {2,17}, {10,20}, {22,26}, {14,25}, {26,31}, {14,22}, {13,15}, {3,23}, {9,23}, {2,11}, {17,35}, {3,36}, {8,17}, {16,18}, {4,19}, {3,18}, {8,19}, {20,31}, {8,10}, {4,26}, {7,14}, {8,26}, {14,31}, {17,19}, {4,21}, {8,32}, {21,31}, {13,19}, {4,25}, {7,13}, {11,15}, {23,29}, {17,30}, {20,29}, {4,29}, {28,32}, {17,29}, {1,26}, {9,14}, {21,25}, {13,26}, {14,29}, {24,30}, {19,30}, {27,29}, {11,34}, {13,29}, {5,19}, {16,27}, {21,33}, {21,24}, {9,16}, {4,11}, {16,24}, {10,18}, {12,19}, {18,21}, {24,31}, {12,13}, {12,36}, {11,29}, {11,21}, {21,30}, {13,30}, {11,28}, {8,9}, {7,27}, {6,32}, {1,34}, {9,34}, {5,15}, {15,26}, {28,34}, {5,34}, {6,13}, {5,23}, {2,16}, {11,22}, {25,36}, {15,33}, {3,33}, {14,23}, {2,24}, {9,11}, {4,6}, {1,15}, {3,9}, {1,10}, {18,26}, {14,19}, {13,17}, {20,23}, {8,11}, {4,35}, {17,31}, {32,34}, {26,28}, {5,14}, {6,26}, {14,15}, {11,25}, {4,22}, {10,14}, {12,24}, {20,22}, {25,28}, {24,25}, {12,22}, {12,25}, {13,35}, {25,30}, {4,14}, {12,31}, {17,21}, {33,35}, {18,33}, {12,23}, {2,35}, {11,30}, {29,36}, {1,12}, {9,35}, {27,30}, {6,29}, {30,32}, {1,19}, {9,27}, {20,36}, {22,24}, {21,26}, {30,31}, {22,29}, {10,36}, {5,30}, {25,34}, {14,16}, {10,24}, {21,27}, {19,33}, {21,29}, {4,16}, {8,24}, {23,34}, {2,34}, {1,28}, {5,9}, {6,27}, {7,28}, {5,32}, {9,15}, {16,28}, {20,25}, {25,33}, {10,17}, {12,20}, {3,8}, {16,19}, {18,24}, {16,17}, {4,20}, {3,24}, {7,23}, {2,32}, {3,34}, {18,28}, {7,15}, {3,28}, {15,24}, {10,19}, {8,31}, {5,24}, {18,27}, {6,19}, {4,5}, {14,20}, {22,36}, {17,25}, {23,36}, {18,36}, {15,36}, {3,17}, {5,21}, {6,33}, {6,10}, {5,28}, {5,16}, {6,36}, {15,17}, {24,35}, {1,18}, {13,24}, {5,36}, {24,29}, {1,30}, {27,35}, {27,33}, {19,24}, {26,27}, {16,34}, {1,23}, {4,10}, {5,13}, {10,13}, {14,36}, {2,14}, {5,35}, {11,14}, {24,36}, {4,12}, {7,35}, {29,31}, {13,21}, {13,33}, {28,30}, {13,36}, {25,29}, {16,29}, {1,14}, {10,27}, {20,26}, {14,28}, {17,26}, {6,22}, {24,33}, {18,30}, {19,29}, {17,33}, {20,33}, {21,34}, {6,24}, {22,23}, {2,25}, {3,14}, {9,18}, {11,19}, {13,31}, {15,30}, {5,29}, {15,28}, {9,19}, {15,34}, {23,26}, {11,27}, {1,13}, {13,27}, {6,23}, {11,16}, {6,18}, {15,19}, {2,15}, {9,26}, {16,26}, {13,22}, {14,35}, {12,35}, {30,36}, {24,32}, {1,21}, {12,33}, {2,12}, {2,28}, {5,10}, {10,34}, {12,34}, {29,35}, {15,27}, {26,34}, {10,35}, {19,27}, {13,25}, {21,36}, {12,30}, {7,36}, {28,33}, {27,36}, {23,27}, {6,14}, {13,23}, {16,21}, {18,23}, {2,19}, {11,17}, {26,30}, {12,16}, {18,29}, {9,12}, {10,16}, {12,28}, {10,30}, {30,34}, {29,34}, {12,29}, {15,20}, {9,21}, {11,26}, {16,32}, {32,35}, {11,35}, {12,26}, {18,34}, {19,34}, {16,30}, {9,29}, {10,21}, {13,18}, {2,5}, {6,17}, {34,35}, {6,11}, {16,35}, {1,22}, {9,25}, {27,31}, {13,28}, {22,28}, {5,25}, {22,30}, {5,27}, {11,31}, {13,34}, {9,36}, {28,35}, {1,35}, {10,12}, {7,12}, {25,35}, {6,30}, {16,25}, {5,18}, {16,36}, {11,13}, {10,33}, {4,13}, {30,35} } Symmetric graph 67 of order 36 Valency 35 Diameter 1 Girth 3 Automorphism group of order 371993326789901217467999448150835200000000 Number of arcs = 1260 Number of 2-arcs = 42840 2-arc-transitive true Edge-set { {1,2}, {2,4}, {2,3}, {2,36}, {4,8}, {2,23}, {4,6}, {4,36}, {3,8}, {8,23}, {4,13}, {2,17}, {8,12}, {4,5}, {20,23}, {8,36}, {1,23}, {3,6}, {1,8}, {3,13}, {8,17}, {19,23}, {4,11}, {1,3}, {8,9}, {8,10}, {5,23}, {13,27}, {17,20}, {3,36}, {2,13}, {3,17}, {6,12}, {1,5}, {3,20}, {6,17}, {1,13}, {3,19}, {3,11}, {13,25}, {17,24}, {8,16}, {4,14}, {11,23}, {2,6}, {3,7}, {3,15}, {8,21}, {10,13}, {17,23}, {13,29}, {19,30}, {11,27}, {6,36}, {1,36}, {4,17}, {2,19}, {6,11}, {1,12}, {5,9}, {12,20}, {2,10}, {5,36}, {6,27}, {1,20}, {11,12}, {19,36}, {6,25}, {1,24}, {6,16}, {1,14}, {17,29}, {13,31}, {19,34}, {11,28}, {8,18}, {23,26}, {13,16}, {14,17}, {4,12}, {2,5}, {2,20}, {6,14}, {1,7}, {6,19}, {1,15}, {3,26}, {15,17}, {19,21}, {11,13}, {17,22}, {19,29}, {25,31}, {24,30}, {16,23}, {14,29}, {11,30}, {12,36}, {8,11}, {4,23}, {4,25}, {2,24}, {12,16}, {5,14}, {11,20}, {3,9}, {7,10}, {5,16}, {1,27}, {9,20}, {4,15}, {2,21}, {10,36}, {12,23}, {5,29}, {20,30}, {2,27}, {1,16}, {9,14}, {25,36}, {24,36}, {12,29}, {5,31}, {20,34}, {2,28}, {2,18}, {26,36}, {11,22}, {23,27}, {17,33}, {19,31}, {9,25}, {24,34}, {16,34}, {14,28}, {3,24}, {13,32}, {17,26}, {9,19}, {11,18}, {4,9}, {4,10}, {4,27}, {12,18}, {5,11}, {20,26}, {2,14}, {7,36}, {12,25}, {5,24}, {13,20}, {15,36}, {6,32}, {1,26}, {3,14}, {11,19}, {15,23}, {25,26}, {18,24}, {16,17}, {13,14}, {22,23}, {22,25}, {24,27}, {29,33}, {31,34}, {28,31}, {18,22}, {26,29}, {16,31}, {14,30}, {9,36}, {3,16}, {8,14}, {8,13}, {8,29}, {4,31}, {23,34}, {4,28}, {9,16}, {9,12}, {10,18}, {5,26}, {16,27}, {14,20}, {6,7}, {14,15}, {7,21}, {10,20}, {3,29}, {30,36}, {7,27}, {8,19}, {4,26}, {1,21}, {9,17}, {10,22}, {27,31}, {2,29}, {2,30}, {7,18}, {16,26}, {29,36}, {31,36}, {1,34}, {28,36}, {1,22}, {9,27}, {10,33}, {4,34}, {4,24}, {32,36}, {14,22}, {13,23}, {4,30}, {11,21}, {23,33}, {17,32}, {25,33}, {24,25}, {7,29}, {12,31}, {9,28}, {18,34}, {26,28}, {6,28}, {1,19}, {17,35}, {13,35}, {19,33}, {11,32}, {7,25}, {12,24}, {16,24}, {14,21}, {7,8}, {8,15}, {21,23}, {4,29}, {23,30}, {9,21}, {10,16}, {27,32}, {4,18}, {2,11}, {2,26}, {14,36}, {1,29}, {9,31}, {12,34}, {10,28}, {17,27}, {12,35}, {5,35}, {20,33}, {2,32}, {6,18}, {1,11}, {16,25}, {14,24}, {13,19}, {29,32}, {26,31}, {14,34}, {24,28}, {17,18}, {19,26}, {5,13}, {4,22}, {22,31}, {22,34}, {23,28}, {21,22}, {27,33}, {9,33}, {25,34}, {33,34}, {25,28}, {22,32}, {26,27}, {18,31}, {6,20}, {3,18}, {8,26}, {3,22}, {8,27}, {8,33}, {23,31}, {9,13}, {17,34}, {8,34}, {7,20}, {15,24}, {10,21}, {18,21}, {10,32}, {6,26}, {16,29}, {9,30}, {18,27}, {12,14}, {5,7}, {18,19}, {11,15}, {15,26}, {14,26}, {15,27}, {6,21}, {6,22}, {14,23}, {7,30}, {3,25}, {8,24}, {8,32}, {7,11}, {5,15}, {25,29}, {30,31}, {20,32}, {22,36}, {27,36}, {33,36}, {1,31}, {2,9}, {3,34}, {34,36}, {1,28}, {7,23}, {16,30}, {15,21}, {21,32}, {23,25}, {8,28}, {4,19}, {23,24}, {35,36}, {1,33}, {5,18}, {22,26}, {13,17}, {8,31}, {14,18}, {10,11}, {13,21}, {4,32}, {11,35}, {23,35}, {21,29}, {31,33}, {32,34}, {28,29}, {7,34}, {12,28}, {16,28}, {9,24}, {21,34}, {18,25}, {5,28}, {20,28}, {2,25}, {13,36}, {23,32}, {17,30}, {19,35}, {21,25}, {24,33}, {16,35}, {14,35}, {11,33}, {7,31}, {16,19}, {18,26}, {10,26}, {13,26}, {8,22}, {23,29}, {7,26}, {15,20}, {29,35}, {30,33}, {4,21}, {18,23}, {4,16}, {18,36}, {11,36}, {2,22}, {3,27}, {7,33}, {1,9}, {9,34}, {15,34}, {21,28}, {1,30}, {9,32}, {10,30}, {21,27}, {4,35}, {2,35}, {2,33}, {5,21}, {18,20}, {2,16}, {20,29}, {18,28}, {24,26}, {17,25}, {13,24}, {22,35}, {27,35}, {32,33}, {14,31}, {9,18}, {11,34}, {28,34}, {19,28}, {11,24}, {25,32}, {10,17}, {6,13}, {5,19}, {5,8}, {5,33}, {13,34}, {17,28}, {30,32}, {12,33}, {16,32}, {9,29}, {29,34}, {22,33}, {12,27}, {5,20}, {6,24}, {3,32}, {5,6}, {3,23}, {8,30}, {3,21}, {13,33}, {7,17}, {12,13}, {9,11}, {8,25}, {14,27}, {15,19}, {15,35}, {10,35}, {21,33}, {12,32}, {20,22}, {12,30}, {18,30}, {1,18}, {12,26}, {10,14}, {21,24}, {13,18}, {19,32}, {18,32}, {11,26}, {15,29}, {15,30}, {5,12}, {5,22}, {11,17}, {6,29}, {3,28}, {3,35}, {8,35}, {14,16}, {7,14}, {10,19}, {6,15}, {22,29}, {25,30}, {20,35}, {6,33}, {23,36}, {21,36}, {1,32}, {4,7}, {2,12}, {6,9}, {1,25}, {2,34}, {20,31}, {15,18}, {10,15}, {26,35}, {18,35}, {17,31}, {13,28}, {17,19}, {1,35}, {3,33}, {10,24}, {5,32}, {15,16}, {14,32}, {13,30}, {10,29}, {31,32}, {9,35}, {34,35}, {27,28}, {7,28}, {12,19}, {9,26}, {10,25}, {24,29}, {21,31}, {10,34}, {27,34}, {2,31}, {17,36}, {4,33}, {11,31}, {24,32}, {16,21}, {14,33}, {20,25}, {21,26}, {15,32}, {14,19}, {3,5}, {13,22}, {19,27}, {22,30}, {10,23}, {17,21}, {8,20}, {9,23}, {16,36}, {6,23}, {3,30}, {7,32}, {2,7}, {3,12}, {7,9}, {15,25}, {26,34}, {7,35}, {16,33}, {15,31}, {18,29}, {5,10}, {20,21}, {4,20}, {22,27}, {20,27}, {28,32}, {11,29}, {19,24}, {5,30}, {30,35}, {21,35}, {33,35}, {18,33}, {11,25}, {7,24}, {12,21}, {16,18}, {31,35}, {12,17}, {19,20}, {3,10}, {6,8}, {19,25}, {7,22}, {9,22}, {10,27}, {20,24}, {6,35}, {10,12}, {1,17}, {3,4}, {3,31}, {11,14}, {7,16}, {11,16}, {26,30}, {13,15}, {5,27}, {24,31}, {21,30}, {25,35}, {24,35}, {19,22}, {1,10}, {12,22}, {6,34}, {6,30}, {29,31}, {27,30}, {1,4}, {7,12}, {16,20}, {6,31}, {26,32}, {15,28}, {9,15}, {26,33}, {15,22}, {28,30}, {10,31}, {22,28}, {14,25}, {28,35}, {9,10}, {27,29}, {15,33}, {6,10}, {1,6}, {5,17}, {7,13}, {20,36}, {22,24}, {28,33}, {16,22}, {32,35}, {7,19}, {25,27}, {29,30}, {5,25}, {2,15}, {5,34}, {2,8}, {12,15}, {30,34}, {7,15} } ................................................................... Symmetric connected graphs of order 37 Symmetric graph 1 of order 37 Valency 2 Diameter 18 Girth 37 Automorphism group of order 74 Number of arcs = 74 Number of 2-arcs = 74 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {15,16}, {16,17}, {17,18}, {18,19}, {19,20}, {20,21}, {21,22}, {22,23}, {23,24}, {24,25}, {25,26}, {26,27}, {27,28}, {28,29}, {29,30}, {30,31}, {31,32}, {32,33}, {33,34}, {34,35}, {35,36}, {36,37}, {1,37} } Symmetric graph 2 of order 37 Valency 4 Diameter 5 Girth 4 Automorphism group of order 148 Number of arcs = 148 Number of 2-arcs = 444 2-arc-transitive false Edge-set { {1,2}, {2,3}, {25,31}, {3,4}, {19,25}, {26,32}, {35,36}, {4,5}, {13,19}, {20,26}, {34,35}, {27,33}, {29,30}, {36,37}, {6,12}, {5,6}, {7,13}, {14,20}, {33,34}, {21,27}, {28,29}, {12,18}, {28,34}, {23,24}, {30,31}, {5,11}, {1,37}, {6,37}, {6,7}, {1,7}, {8,14}, {32,33}, {15,21}, {27,28}, {18,24}, {22,28}, {22,23}, {11,17}, {29,35}, {17,18}, {24,25}, {4,10}, {31,32}, {5,36}, {7,8}, {31,37}, {1,32}, {2,8}, {9,15}, {26,27}, {24,30}, {16,22}, {21,22}, {17,23}, {23,29}, {16,17}, {10,16}, {8,9}, {30,36}, {11,12}, {18,19}, {3,9}, {25,26}, {4,35}, {13,14}, {2,33}, {20,21}, {15,16}, {9,10}, {10,11}, {14,15}, {12,13}, {19,20}, {3,34} } Symmetric graph 3 of order 37 Valency 6 Diameter 3 Girth 3 Automorphism group of order 222 Number of arcs = 222 Number of 2-arcs = 1110 2-arc-transitive false Edge-set { {1,2}, {2,3}, {15,26}, {3,4}, {4,15}, {16,27}, {10,20}, {4,5}, {4,30}, {5,16}, {20,30}, {17,28}, {9,36}, {11,21}, {5,6}, {19,30}, {5,31}, {3,30}, {6,17}, {9,19}, {21,31}, {18,29}, {25,35}, {10,37}, {11,12}, {12,22}, {27,28}, {6,7}, {8,19}, {20,31}, {3,13}, {6,32}, {19,29}, {4,31}, {7,18}, {8,35}, {12,13}, {22,32}, {28,29}, {14,24}, {26,36}, {21,22}, {1,11}, {1,37}, {13,23}, {16,17}, {25,36}, {7,8}, {8,34}, {9,20}, {21,32}, {2,29}, {4,14}, {7,33}, {8,18}, {13,14}, {5,32}, {29,30}, {24,34}, {22,23}, {23,33}, {17,18}, {14,25}, {15,25}, {31,32}, {27,37}, {10,11}, {2,12}, {26,27}, {26,37}, {9,35}, {8,9}, {23,34}, {10,21}, {22,33}, {18,28}, {14,15}, {5,15}, {30,31}, {7,34}, {23,24}, {6,33}, {18,19}, {3,14}, {32,33}, {24,35}, {16,26}, {20,21}, {1,28}, {36,37}, {1,27}, {15,16}, {10,36}, {9,10}, {12,23}, {11,22}, {7,17}, {24,25}, {6,16}, {19,20}, {3,29}, {33,34}, {13,24}, {17,27}, {2,28}, {25,26}, {11,37}, {1,12}, {34,35}, {2,13}, {35,36} } Symmetric graph 4 of order 37 Valency 12 Diameter 2 Girth 3 Automorphism group of order 444 Number of arcs = 444 Number of 2-arcs = 4884 2-arc-transitive false Edge-set { {1,2}, {2,3}, {8,16}, {3,4}, {16,24}, {9,17}, {17,27}, {4,5}, {24,32}, {17,25}, {7,17}, {10,18}, {25,35}, {18,28}, {25,31}, {5,6}, {3,32}, {25,33}, {7,34}, {18,26}, {15,25}, {8,18}, {19,25}, {11,19}, {6,33}, {26,36}, {15,21}, {19,29}, {2,33}, {26,32}, {15,26}, {6,7}, {3,11}, {4,33}, {24,34}, {26,34}, {5,15}, {8,35}, {13,19}, {19,27}, {23,33}, {16,26}, {9,15}, {9,19}, {27,33}, {20,26}, {4,15}, {12,20}, {4,14}, {5,11}, {27,37}, {23,29}, {16,22}, {9,20}, {20,30}, {4,10}, {3,34}, {5,16}, {23,34}, {16,27}, {9,23}, {7,8}, {4,12}, {14,24}, {5,34}, {5,32}, {7,13}, {27,35}, {13,23}, {6,16}, {3,9}, {9,36}, {21,27}, {14,20}, {4,30}, {20,28}, {4,31}, {5,36}, {17,23}, {10,16}, {9,35}, {10,20}, {4,35}, {28,34}, {5,31}, {12,23}, {9,32}, {13,21}, {12,22}, {1,32}, {6,12}, {3,14}, {1,28}, {31,37}, {24,30}, {10,36}, {17,28}, {10,21}, {12,35}, {21,31}, {12,18}, {6,32}, {13,24}, {6,17}, {3,17}, {24,35}, {13,36}, {17,31}, {10,24}, {35,36}, {8,9}, {5,13}, {22,32}, {1,7}, {6,35}, {3,13}, {8,14}, {19,30}, {28,36}, {30,36}, {11,17}, {10,37}, {29,35}, {22,28}, {20,31}, {1,12}, {18,32}, {21,29}, {2,12}, {6,37}, {3,29}, {18,24}, {25,36}, {21,35}, {11,21}, {21,32}, {2,13}, {3,26}, {22,36}, {10,33}, {34,35}, {14,22}, {8,34}, {11,22}, {1,24}, {2,29}, {2,8}, {26,37}, {7,18}, {11,37}, {6,29}, {18,29}, {2,25}, {6,20}, {21,22}, {22,33}, {7,33}, {11,34}, {14,25}, {7,30}, {11,25}, {4,18}, {24,25}, {7,21}, {14,37}, {29,30}, {25,26}, {36,37}, {9,10}, {6,14}, {3,30}, {8,19}, {7,36}, {1,27}, {29,37}, {1,11}, {2,28}, {12,26}, {8,22}, {19,33}, {33,34}, {22,30}, {15,29}, {20,21}, {20,34}, {16,30}, {4,27}, {23,24}, {23,37}, {28,29}, {15,23}, {13,27}, {14,28}, {10,11}, {15,16}, {11,12}, {22,23}, {5,28}, {5,19}, {13,14}, {1,15}, {8,31}, {18,19}, {14,15}, {32,33}, {7,15}, {19,20}, {1,37}, {30,31}, {26,27}, {8,37}, {1,30}, {2,16}, {27,28}, {23,31}, {12,13}, {17,18}, {31,32}, {2,10}, {16,17}, {1,9}, {2,31} } Symmetric graph 5 of order 37 Valency 18 Diameter 2 Girth 3 Automorphism group of order 666 Number of arcs = 666 Number of 2-arcs = 11322 2-arc-transitive false Edge-set { {1,2}, {2,3}, {16,32}, {3,4}, {11,32}, {17,33}, {31,34}, {4,5}, {11,27}, {12,33}, {28,31}, {18,34}, {10,13}, {32,35}, {15,26}, {5,6}, {6,27}, {12,28}, {25,28}, {13,34}, {7,10}, {29,32}, {4,15}, {19,35}, {26,29}, {11,14}, {12,23}, {33,36}, {5,31}, {16,27}, {9,18}, {6,7}, {6,22}, {7,28}, {22,25}, {13,29}, {4,7}, {4,30}, {14,35}, {23,26}, {8,11}, {1,12}, {30,33}, {20,31}, {5,16}, {18,27}, {20,36}, {5,8}, {27,30}, {9,20}, {12,15}, {2,28}, {13,24}, {7,35}, {34,37}, {10,21}, {6,32}, {6,15}, {17,28}, {25,34}, {10,19}, {29,33}, {7,8}, {1,22}, {7,23}, {19,22}, {8,29}, {1,4}, {19,30}, {14,30}, {20,23}, {1,27}, {27,36}, {15,36}, {2,5}, {24,27}, {9,35}, {9,12}, {2,13}, {7,16}, {10,36}, {21,32}, {15,24}, {6,17}, {6,34}, {19,28}, {25,29}, {21,37}, {21,24}, {6,9}, {25,36}, {24,33}, {13,16}, {7,18}, {3,29}, {4,32}, {14,25}, {14,23}, {8,36}, {1,5}, {1,35}, {26,37}, {11,22}, {3,12}, {7,33}, {22,31}, {18,22}, {18,29}, {4,13}, {26,35}, {26,30}, {11,20}, {8,12}, {30,34}, {10,20}, {8,9}, {1,17}, {2,23}, {16,19}, {8,24}, {8,19}, {9,30}, {17,20}, {15,31}, {2,36}, {24,35}, {16,25}, {28,37}, {21,25}, {16,37}, {18,21}, {3,6}, {5,33}, {3,14}, {23,32}, {8,17}, {1,34}, {11,37}, {12,21}, {22,33}, {3,31}, {14,18}, {13,22}, {22,26}, {20,29}, {4,8}, {20,30}, {3,37}, {21,30}, {10,14}, {14,17}, {23,34}, {1,29}, {27,31}, {2,30}, {2,35}, {9,37}, {17,21}, {2,6}, {6,16}, {7,11}, {8,34}, {1,10}, {15,19}, {19,23}, {19,29}, {5,14}, {23,27}, {5,9}, {9,36}, {24,28}, {9,13}, {7,17}, {31,35}, {26,36}, {11,21}, {12,24}, {9,10}, {2,18}, {3,24}, {9,25}, {10,31}, {15,18}, {17,26}, {4,37}, {3,30}, {6,10}, {2,11}, {13,17}, {16,26}, {3,7}, {11,15}, {2,29}, {9,19}, {20,24}, {17,27}, {21,31}, {24,36}, {3,36}, {2,12}, {16,20}, {28,32}, {15,25}, {32,36}, {5,32}, {33,37}, {3,13}, {22,32}, {22,34}, {1,28}, {12,16}, {8,18}, {8,35}, {8,20}, {25,35}, {6,33}, {10,37}, {21,33}, {4,14}, {23,33}, {1,13}, {5,15}, {27,37}, {9,21}, {12,22}, {3,28}, {13,25}, {7,14}, {10,11}, {3,19}, {4,25}, {10,26}, {4,31}, {11,36}, {13,23}, {9,34}, {1,11}, {18,28}, {20,32}, {8,33}, {14,24}, {3,15}, {25,37}, {14,21}, {7,32}, {24,34}, {18,30}, {6,31}, {11,23}, {19,31}, {23,35}, {19,26}, {4,16}, {7,34}, {17,29}, {5,17}, {17,24}, {5,30}, {10,22}, {12,37}, {3,10}, {2,27}, {10,35}, {2,14}, {16,23}, {6,18}, {3,33}, {7,19}, {4,29}, {4,11}, {14,26}, {23,30}, {8,15}, {11,12}, {4,20}, {5,26}, {15,27}, {21,28}, {26,33}, {16,28}, {24,31}, {10,17}, {11,18}, {1,26}, {30,37}, {15,22}, {1,31}, {29,36}, {28,35}, {5,35}, {20,27}, {27,34}, {13,20}, {6,13}, {18,25}, {13,14}, {6,36}, {12,19}, {7,37}, {25,32}, {5,12}, {2,32}, {34,35}, {22,29}, {4,34}, {1,8}, {27,28}, {2,9}, {35,36}, {9,16}, {17,18}, {12,13}, {5,21}, {14,15}, {28,29}, {36,37}, {18,19}, {15,16}, {20,21}, {24,25}, {25,26}, {23,24}, {22,23}, {29,30}, {21,22}, {1,37}, {30,31}, {31,32}, {19,20}, {26,27}, {16,17}, {32,33}, {33,34} } Symmetric graph 6 of order 37 Valency 36 Diameter 1 Girth 3 Automorphism group of order 13763753091226345046315979581580902400000000 Number of arcs = 1332 Number of 2-arcs = 46620 2-arc-transitive true Edge-set { {1,2}, {2,3}, {2,4}, {3,4}, {4,6}, {3,5}, {4,8}, {4,5}, {6,8}, {5,7}, {8,12}, {6,10}, {5,9}, {8,16}, {5,6}, {8,10}, {7,9}, {12,16}, {10,14}, {9,13}, {16,24}, {7,11}, {12,20}, {10,18}, {9,17}, {16,32}, {6,7}, {10,12}, {9,11}, {16,20}, {14,18}, {13,17}, {24,32}, {11,15}, {20,28}, {18,26}, {17,25}, {11,32}, {14,22}, {13,21}, {3,24}, {11,19}, {20,36}, {18,34}, {17,33}, {27,32}, {7,8}, {12,14}, {11,13}, {20,24}, {18,22}, {17,21}, {3,32}, {15,19}, {28,36}, {26,34}, {25,33}, {11,27}, {22,30}, {21,29}, {3,19}, {19,27}, {15,36}, {13,34}, {12,33}, {22,27}, {15,23}, {7,28}, {5,26}, {4,25}, {6,11}, {1,22}, {21,37}, {3,35}, {19,35}, {31,36}, {29,34}, {28,33}, {17,27}, {8,9}, {14,16}, {13,15}, {24,28}, {22,26}, {21,25}, {3,11}, {19,23}, {7,36}, {5,34}, {4,33}, {6,27}, {1,30}, {29,37}, {27,35}, {15,31}, {13,29}, {12,28}, {17,22}, {23,31}, {7,23}, {5,21}, {4,20}, {1,6}, {1,17}, {16,37}, {30,35}, {14,35}, {26,31}, {24,29}, {23,28}, {7,17}, {9,30}, {8,29}, {14,19}, {10,15}, {8,13}, {7,12}, {12,22}, {2,23}, {2,7}, {5,37}, {4,36}, {6,33}, {1,33}, {32,37}, {25,35}, {21,31}, {19,29}, {18,28}, {17,34}, {9,10}, {16,18}, {15,17}, {28,32}, {26,30}, {25,29}, {23,27}, {7,15}, {5,13}, {4,12}, {6,22}, {1,9}, {8,37}, {6,35}, {10,31}, {12,17}, {2,31}, {25,30}, {14,30}, {21,26}, {19,24}, {18,23}, {7,34}, {9,25}, {8,24}, {9,14}, {5,10}, {3,8}, {2,12}, {2,18}, {2,34}, {23,33}, {15,25}, {11,21}, {9,19}, {8,18}, {14,34}, {16,21}, {15,20}, {1,28}, {11,16}, {20,30}, {16,26}, {14,24}, {13,23}, {7,24}, {4,9}, {4,14}, {10,37}, {8,35}, {12,29}, {2,29}, {27,37}, {26,36}, {13,33}, {22,32}, {5,25}, {1,21}, {19,36}, {18,35}, {31,34}, {10,11}, {18,20}, {17,19}, {32,36}, {30,34}, {29,33}, {27,31}, {6,14}, {10,26}, {2,10}, {20,25}, {13,18}, {24,34}, {5,15}, {1,11}, {9,36}, {14,31}, {10,20}, {6,16}, {3,13}, {4,24}, {4,31}, {9,29}, {13,30}, {5,22}, {1,18}, {16,36}, {15,35}, {28,31}, {5,32}, {3,30}, {2,19}, {3,23}, {15,32}, {11,28}, {9,26}, {8,25}, {11,14}, {8,28}, {20,37}, {16,33}, {21,24}, {4,21}, {17,37}, {26,29}, {7,27}, {6,26}, {10,13}, {2,22}, {2,5}, {1,35}, {33,36}, {32,35}, {25,31}, {11,12}, {20,22}, {19,21}, {3,36}, {1,34}, {33,37}, {31,35}, {11,31}, {10,30}, {25,28}, {3,20}, {12,32}, {8,11}, {18,21}, {23,26}, {6,23}, {7,10}, {2,36}, {30,33}, {29,32}, {19,25}, {10,27}, {1,4}, {6,9}, {27,30}, {19,22}, {15,18}, {13,16}, {12,15}, {22,28}, {16,19}, {3,37}, {22,25}, {5,11}, {5,8}, {34,37}, {15,21}, {14,17}, {20,26}, {4,7}, {3,6}, {4,10}, {2,33}, {29,35}, {27,33}, {26,32}, {13,25}, {12,13}, {22,24}, {21,23}, {3,7}, {1,5}, {4,37}, {2,35}, {20,23}, {13,19}, {24,27}, {9,12}, {16,22}, {5,36}, {9,15}, {14,20}, {4,35}, {23,29}, {21,27}, {1,13}, {17,20}, {2,8}, {12,18}, {17,23}, {1,7}, {30,36}, {24,30}, {7,19}, {1,32}, {6,37}, {7,13}, {6,12}, {10,22}, {10,16}, {31,37}, {5,30}, {28,34}, {3,15}, {8,14}, {8,20}, {3,34}, {4,29}, {21,33}, {17,29}, {15,27}, {14,26}, {13,26}, {13,14}, {24,26}, {23,25}, {2,6}, {3,9}, {1,26}, {11,17}, {18,24}, {7,32}, {10,35}, {18,30}, {3,28}, {8,33}, {9,21}, {5,17}, {2,14}, {2,26}, {4,16}, {24,36}, {9,34}, {23,35}, {11,23}, {1,14}, {2,27}, {12,37}, {12,24}, {7,20}, {20,32}, {25,37}, {6,31}, {10,23}, {19,31}, {6,30}, {16,28}, {3,16}, {8,21}, {22,34}, {5,29}, {21,34}, {17,30}, {15,28}, {14,27}, {15,26}, {14,15}, {26,28}, {25,27}, {6,18}, {2,15}, {11,36}, {20,33}, {23,36}, {6,19}, {16,29}, {5,18}, {10,34}, {4,28}, {3,27}, {4,15}, {8,32}, {11,35}, {18,31}, {9,33}, {9,22}, {2,28}, {4,17}, {24,37}, {11,24}, {3,14}, {13,37}, {12,25}, {9,20}, {1,25}, {7,31}, {12,23}, {19,32}, {6,32}, {5,16}, {10,21}, {22,35}, {5,31}, {23,34}, {19,30}, {17,28}, {16,27}, {15,30}, {15,16}, {28,30}, {27,29}, {12,36}, {4,30}, {3,29}, {9,35}, {1,12}, {21,32}, {10,36}, {20,31}, {8,19}, {6,17}, {8,30}, {22,33}, {25,36}, {18,29}, {7,18}, {4,19}, {8,34}, {11,37}, {11,22}, {6,28}, {26,37}, {13,24}, {3,18}, {2,13}, {14,25}, {9,24}, {1,27}, {7,33}, {12,27}, {10,32}, {5,20}, {10,25}, {24,35}, {9,31}, {1,23}, {19,34}, {17,32}, {16,31}, {23,30}, {16,17}, {30,32}, {29,31}, {8,23}, {6,21}, {18,33}, {2,24}, {5,27}, {20,35}, {3,25}, {1,16}, {12,34}, {16,23}, {7,29}, {13,35}, {21,36}, {14,36}, {1,8}, {22,37}, {7,22}, {12,19}, {15,37}, {11,26}, {6,36}, {4,26}, {13,28}, {11,18}, {2,17}, {14,29}, {17,24}, {11,33}, {20,27}, {3,10}, {13,20}, {18,25}, {2,9}, {1,31}, {27,34}, {25,32}, {24,31}, {9,23}, {17,18}, {32,34}, {31,33}, {9,16}, {5,12}, {29,36}, {4,11}, {10,17}, {3,33}, {6,13}, {2,32}, {9,32}, {14,21}, {26,33}, {5,35}, {28,35}, {2,16}, {7,37}, {7,14}, {1,24}, {30,37}, {15,22}, {12,35}, {8,15}, {19,26}, {22,36}, {4,34}, {21,28}, {11,34}, {22,29}, {3,17}, {6,20}, {3,26}, {13,36}, {4,18}, {2,25}, {17,31}, {13,27}, {11,25}, {10,24}, {9,18}, {18,19}, {34,36}, {33,35}, {18,32}, {21,35}, {8,22}, {20,34}, {6,29}, {12,26}, {4,27}, {10,33}, {18,27}, {5,28}, {15,29}, {19,33}, {4,32}, {14,37}, {14,28}, {2,11}, {23,37}, {7,30}, {24,33}, {16,30}, {1,15}, {7,35}, {8,31}, {5,19}, {22,31}, {7,21}, {6,34}, {3,12}, {6,15}, {26,35}, {8,36}, {4,13}, {25,34}, {17,26}, {13,22}, {11,20}, {10,19}, {18,36}, {19,20}, {1,36}, {35,37}, {27,36}, {5,33}, {7,16}, {3,31}, {12,21}, {15,24}, {8,17}, {20,29}, {19,28}, {17,36}, {21,30}, {1,29}, {8,27}, {28,37}, {4,22}, {9,37}, {14,23}, {11,29}, {23,32}, {2,30}, {14,33}, {16,25}, {1,10}, {7,25}, {5,14}, {12,31}, {6,24}, {12,30}, {15,33}, {16,35}, {8,26}, {13,31}, {15,34}, {7,26}, {3,22}, {1,20}, {19,37}, {35,36}, {20,21}, {1,3}, {2,37}, {17,35}, {10,29}, {14,32}, {6,25}, {5,24}, {11,30}, {16,34}, {3,21}, {1,19}, {18,37}, {34,35}, {5,23}, {2,21}, {9,28}, {21,22}, {9,27}, {4,23}, {28,29}, {13,32}, {2,20}, {10,28}, {24,25}, {23,24}, {29,30}, {32,33}, {25,26}, {30,31}, {1,37}, {36,37}, {33,34}, {27,28}, {22,23}, {31,32}, {26,27} } ................................................................... Symmetric connected graphs of order 38 Symmetric graph 1 of order 38 Valency 2 Diameter 19 Girth 38 Automorphism group of order 76 Number of arcs = 76 Number of 2-arcs = 76 2-arc-transitive true Edge-set { {1,4}, {12,14}, {21,23}, {32,33}, {3,6}, {13,15}, {24,25}, {34,35}, {5,7}, {16,18}, {26,28}, {36,37}, {8,9}, {17,20}, {27,30}, {1,38}, {10,12}, {19,21}, {29,32}, {2,3}, {11,13}, {22,24}, {31,34}, {4,5}, {14,16}, {23,26}, {33,36}, {6,8}, {15,17}, {25,27}, {35,38}, {7,10}, {18,19}, {28,29}, {2,37}, {9,11}, {20,22}, {30,31} } Symmetric graph 2 of order 38 Valency 3 Diameter 5 Girth 6 Automorphism group of order 114 Number of arcs = 114 Number of 2-arcs = 228 2-arc-transitive false Edge-set { {1,3}, {3,27}, {9,34}, {12,27}, {9,25}, {8,23}, {13,29}, {10,12}, {25,28}, {23,26}, {11,13}, {2,38}, {35,37}, {34,36}, {10,24}, {14,28}, {11,26}, {2,25}, {12,35}, {4,17}, {19,33}, {18,31}, {5,20}, {8,32}, {6,29}, {1,24}, {14,36}, {11,33}, {4,26}, {10,31}, {5,28}, {7,30}, {6,22}, {16,32}, {21,38}, {15,37}, {32,33}, {4,6}, {7,9}, {27,30}, {22,24}, {14,16}, {19,21}, {15,17}, {18,20}, {7,21}, {15,30}, {23,37}, {13,38}, {1,16}, {22,36}, {20,35}, {2,18}, {17,34}, {3,19}, {29,31}, {5,8} } Symmetric graph 3 of order 38 Valency 4 Diameter 9 Girth 4 Automorphism group of order 19922944 Number of arcs = 152 Number of 2-arcs = 456 2-arc-transitive false Edge-set { {1,3}, {15,18}, {1,38}, {29,31}, {13,15}, {36,38}, {6,8}, {27,29}, {28,29}, {12,13}, {33,36}, {20,22}, {4,6}, {3,6}, {25,27}, {26,27}, {25,28}, {9,12}, {10,12}, {31,33}, {34,36}, {18,20}, {17,20}, {2,4}, {1,4}, {2,3}, {24,25}, {23,25}, {24,26}, {7,9}, {8,9}, {8,10}, {32,33}, {31,34}, {32,34}, {16,18}, {16,17}, {2,37}, {15,17}, {2,38}, {1,37}, {22,24}, {21,24}, {22,23}, {21,23}, {5,7}, {6,7}, {7,10}, {30,31}, {29,32}, {30,32}, {14,15}, {14,16}, {35,37}, {13,16}, {36,37}, {35,38}, {19,22}, {20,21}, {19,21}, {3,5}, {4,5}, {5,8}, {27,30}, {28,30}, {11,13}, {11,14}, {34,35}, {12,14}, {33,35}, {18,19}, {17,19}, {26,28}, {10,11}, {9,11}, {23,26} } Symmetric graph 4 of order 38 Valency 6 Diameter 3 Girth 4 Automorphism group of order 228 Number of arcs = 228 Number of 2-arcs = 1140 2-arc-transitive false Edge-set { {1,4}, {24,38}, {6,29}, {9,25}, {15,32}, {13,30}, {20,36}, {2,3}, {7,10}, {5,8}, {11,14}, {29,32}, {35,38}, {34,36}, {23,37}, {5,30}, {4,28}, {9,33}, {14,27}, {19,34}, {18,31}, {11,36}, {1,15}, {2,25}, {10,26}, {16,31}, {14,29}, {19,35}, {15,38}, {6,22}, {3,20}, {21,37}, {4,25}, {12,27}, {18,34}, {2,23}, {8,24}, {7,30}, {8,9}, {6,7}, {12,13}, {30,31}, {36,37}, {33,35}, {14,15}, {18,20}, {3,5}, {10,11}, {16,17}, {2,38}, {21,24}, {19,22}, {25,27}, {23,26}, {32,34}, {28,29}, {3,27}, {10,34}, {13,28}, {20,33}, {17,32}, {12,35}, {2,16}, {1,26}, {8,31}, {14,37}, {22,36}, {5,19}, {4,18}, {9,23}, {7,21}, {15,30}, {11,25}, {16,37}, {5,21}, {4,19}, {22,38}, {3,26}, {11,28}, {17,33}, {1,24}, {7,23}, {8,29}, {6,27}, {12,34}, {10,31}, {2,18}, {14,35}, {13,16}, {17,19}, {4,6}, {9,12}, {15,18}, {1,37}, {22,23}, {20,21}, {26,28}, {24,25}, {31,33}, {27,30}, {7,32}, {13,38}, {21,35}, {6,20}, {3,17}, {10,24}, {8,22}, {16,29}, {12,26}, {5,28}, {11,33}, {9,32}, {1,17}, {13,36} } Symmetric graph 5 of order 38 Valency 9 Diameter 3 Girth 4 Automorphism group of order 342 Number of arcs = 342 Number of 2-arcs = 2736 2-arc-transitive false Edge-set { {1,4}, {3,22}, {30,35}, {4,31}, {14,29}, {20,35}, {9,28}, {3,18}, {21,30}, {27,36}, {27,37}, {11,20}, {9,20}, {15,26}, {11,33}, {4,29}, {26,29}, {32,35}, {13,28}, {16,19}, {10,34}, {1,16}, {4,34}, {7,11}, {6,20}, {11,26}, {2,31}, {7,38}, {6,16}, {3,36}, {27,30}, {34,36}, {2,27}, {17,20}, {9,22}, {15,28}, {33,38}, {9,12}, {19,32}, {25,37}, {12,15}, {3,37}, {15,30}, {6,7}, {6,18}, {11,23}, {20,24}, {7,34}, {2,6}, {18,21}, {21,36}, {9,23}, {24,32}, {4,19}, {10,29}, {16,35}, {28,34}, {19,37}, {10,15}, {16,21}, {11,30}, {20,25}, {26,31}, {11,14}, {31,33}, {2,38}, {3,16}, {8,26}, {5,11}, {12,17}, {19,22}, {1,33}, {8,10}, {5,31}, {10,35}, {28,31}, {6,23}, {18,24}, {23,29}, {24,26}, {7,13}, {8,20}, {6,37}, {15,18}, {21,23}, {24,36}, {29,32}, {13,26}, {10,13}, {14,17}, {8,22}, {3,12}, {19,30}, {25,36}, {12,27}, {9,32}, {15,37}, {15,33}, {1,12}, {10,25}, {12,31}, {13,32}, {7,35}, {6,28}, {1,20}, {18,34}, {2,21}, {7,27}, {18,38}, {4,9}, {5,34}, {2,17}, {7,24}, {8,30}, {5,25}, {14,19}, {22,38}, {21,33}, {13,23}, {13,36}, {14,34}, {2,8}, {1,23}, {4,24}, {17,36}, {22,27}, {25,28}, {12,38}, {4,8}, {5,29}, {12,35}, {19,28}, {19,33}, {1,10}, {8,16}, {17,26}, {11,22}, {10,38}, {16,31}, {5,35}, {25,33}, {8,18}, {5,21}, {17,28}, {9,18}, {15,23}, {24,33}, {29,37}, {21,32}, {2,29}, {3,26}, {24,37}, {6,14}, {3,14}, {32,38}, {13,16}, {13,22}, {3,5}, {17,30}, {23,27}, {5,9}, {22,25}, {17,32}, {30,34}, {2,25}, {7,31}, {14,38}, {1,36}, {4,27}, {1,14}, {35,37} } Symmetric graph 6 of order 38 Valency 12 Diameter 2 Girth 3 Automorphism group of order 59768832 Number of arcs = 456 Number of 2-arcs = 5016 2-arc-transitive false Edge-set { {1,3}, {24,38}, {3,6}, {10,25}, {2,26}, {14,38}, {6,7}, {2,4}, {11,27}, {1,23}, {4,28}, {10,31}, {2,15}, {14,27}, {7,9}, {23,37}, {4,5}, {15,17}, {14,30}, {24,26}, {3,25}, {16,37}, {5,29}, {11,34}, {8,23}, {4,18}, {15,31}, {15,30}, {3,27}, {9,12}, {9,26}, {1,25}, {13,37}, {5,8}, {8,22}, {18,19}, {29,31}, {15,32}, {26,28}, {2,38}, {6,27}, {1,17}, {13,30}, {8,31}, {17,19}, {14,35}, {21,37}, {5,20}, {18,34}, {8,29}, {18,32}, {15,38}, {6,30}, {3,18}, {12,13}, {12,28}, {2,24}, {9,32}, {1,16}, {13,28}, {8,10}, {10,23}, {21,36}, {20,21}, {5,30}, {31,34}, {6,8}, {18,33}, {28,29}, {14,15}, {7,30}, {22,24}, {3,19}, {29,32}, {16,32}, {5,28}, {10,34}, {22,36}, {19,21}, {31,33}, {15,37}, {9,11}, {1,24}, {13,35}, {20,35}, {28,30}, {6,21}, {20,33}, {2,18}, {14,29}, {7,32}, {21,38}, {6,20}, {13,16}, {16,18}, {13,29}, {23,25}, {4,26}, {12,33}, {7,24}, {3,17}, {16,29}, {10,11}, {11,25}, {11,35}, {8,32}, {5,19}, {34,35}, {14,28}, {7,10}, {20,36}, {16,30}, {15,18}, {27,29}, {12,25}, {23,26}, {36,38}, {17,33}, {4,19}, {12,34}, {23,38}, {11,36}, {21,24}, {34,36}, {8,9}, {1,18}, {12,14}, {24,25}, {3,26}, {32,33}, {33,35}, {22,37}, {11,14}, {21,23}, {4,20}, {30,31}, {9,33}, {7,22}, {16,17}, {7,21}, {17,20}, {30,32}, {16,31}, {25,27}, {1,37}, {18,20}, {13,36}, {22,38}, {6,19}, {17,31}, {4,17}, {2,17}, {14,37}, {6,28}, {10,33}, {8,21}, {19,33}, {35,37}, {15,29}, {4,27}, {7,29}, {17,32}, {13,27}, {1,26}, {25,28}, {20,22}, {19,36}, {36,37}, {5,21}, {10,26}, {2,25}, {17,34}, {19,34}, {35,38}, {3,28}, {10,12}, {3,20}, {18,31}, {13,15}, {26,27}, {1,38}, {33,36}, {11,26}, {5,22}, {32,34}, {12,36}, {12,27}, {9,23}, {9,24}, {22,35}, {19,22}, {6,29}, {5,7}, {27,30}, {21,35}, {16,38}, {2,23}, {14,36}, {22,23}, {9,31}, {1,15}, {14,16}, {11,28}, {10,24}, {8,30}, {6,22}, {2,16}, {12,35}, {9,34}, {11,13}, {8,24}, {1,4}, {19,35}, {2,37}, {20,34}, {2,3}, {13,38}, {12,26}, {7,31}, {11,33}, {24,37}, {4,25}, {3,5}, {10,32}, {7,23}, {4,6}, {5,27}, {9,25} } Symmetric graph 7 of order 38 Valency 18 Diameter 3 Girth 4 Automorphism group of order 243290200817664000 Number of arcs = 684 Number of 2-arcs = 11628 2-arc-transitive true Edge-set { {1,3}, {22,37}, {29,38}, {15,29}, {22,33}, {4,16}, {21,27}, {2,4}, {9,27}, {10,29}, {6,33}, {1,21}, {10,37}, {20,30}, {20,34}, {21,38}, {30,37}, {11,20}, {20,24}, {4,12}, {23,27}, {5,10}, {6,8}, {29,34}, {12,15}, {22,23}, {3,7}, {26,28}, {7,9}, {5,26}, {16,30}, {21,34}, {3,15}, {22,28}, {7,33}, {26,32}, {7,13}, {3,26}, {31,37}, {14,20}, {4,20}, {6,12}, {7,23}, {5,27}, {8,15}, {4,9}, {2,34}, {9,31}, {14,29}, {4,33}, {16,38}, {19,36}, {12,19}, {11,28}, {16,24}, {6,36}, {7,12}, {10,28}, {9,30}, {5,34}, {2,22}, {9,38}, {19,29}, {19,33}, {6,16}, {26,36}, {12,35}, {17,28}, {1,16}, {22,36}, {12,38}, {15,25}, {7,18}, {2,26}, {7,21}, {26,37}, {8,31}, {14,28}, {6,20}, {7,20}, {2,27}, {9,15}, {11,21}, {24,37}, {5,30}, {11,25}, {24,36}, {4,18}, {10,21}, {6,37}, {14,25}, {8,34}, {25,31}, {19,32}, {1,13}, {3,10}, {5,31}, {8,14}, {28,34}, {16,31}, {19,23}, {3,11}, {24,28}, {6,9}, {5,7}, {30,33}, {11,16}, {21,24}, {4,8}, {25,27}, {8,10}, {6,25}, {1,5}, {31,36}, {12,14}, {32,34}, {13,31}, {18,19}, {1,37}, {29,31}, {14,33}, {16,34}, {21,31}, {2,35}, {9,11}, {16,17}, {36,38}, {12,30}, {28,30}, {15,36}, {12,22}, {2,19}, {8,26}, {7,28}, {16,26}, {20,38}, {2,11}, {9,24}, {13,15}, {3,22}, {3,6}, {33,35}, {11,32}, {3,14}, {17,37}, {23,34}, {5,15}, {8,22}, {18,35}, {25,35}, {11,36}, {1,29}, {23,38}, {7,36}, {18,27}, {2,15}, {9,19}, {5,19}, {1,25}, {10,36}, {4,25}, {32,38}, {13,19}, {3,19}, {5,11}, {8,24}, {6,28}, {7,16}, {1,33}, {10,32}, {13,30}, {3,34}, {15,37}, {20,35}, {12,27}, {15,23}, {5,35}, {8,11}, {7,29}, {14,36}, {18,34}, {2,31}, {9,26}, {17,25}, {1,36}, {22,29}, {27,36}, {10,18}, {2,6}, {1,9}, {25,30}, {34,36}, {11,33}, {24,32}, {1,23}, {14,21}, {28,31}, {19,28}, {9,14}, {31,33}, {8,38}, {16,19}, {10,12}, {21,26}, {33,38}, {30,32}, {11,13}, {3,24}, {2,17}, {5,22}, {6,13}, {26,33}, {32,35}, {18,22}, {2,38}, {4,5}, {27,29}, {15,33}, {13,17}, {14,32}, {4,37}, {14,16}, {4,21}, {17,20}, {24,25}, {7,25}, {35,37}, {11,29}, {12,31}, {14,23}, {21,35}, {11,37}, {8,17}, {25,38}, {7,32}, {13,27}, {8,19}, {1,28}, {10,16}, {6,29}, {12,26}, {23,35}, {3,17}, {9,22}, {5,38}, {13,26}, {20,31}, {2,14}, {6,32}, {27,33}, {15,32}, {4,28}, {16,27}, {18,31}, {5,17}, {30,36}, {12,24}, {11,18}, {4,29}, {17,23}, {8,30}, {24,29}, {3,35}, {5,14}, {10,33}, {14,37}, {18,30}, {19,25}, {2,24}, {10,25}, {15,21}, {1,8}, {12,34}, {23,31}, {6,21}, {28,35}, {17,33}, {1,32}, {13,22}, {3,38}, {13,35}, {21,30}, {7,37}, {20,27}, {2,10}, {1,18}, {18,26}, {34,37}, {27,32}, {25,34}, {14,18}, {13,34}, {22,32}, {15,18}, {16,35}, {1,20}, {8,27}, {19,37}, {1,12}, {10,23}, {4,13}, {18,38}, {24,33}, {17,36}, {2,30}, {8,35}, {10,20}, {9,35}, {19,21}, {6,23}, {3,31}, {17,32}, {27,37}, {3,27}, {15,28}, {13,38}, {6,18}, {2,7}, {3,30}, {11,23}, {9,34}, {4,36}, {29,35}, {17,29}, {16,22}, {20,26}, {23,30}, {12,17}, {18,24}, {9,17}, {26,29}, {10,13}, {15,20}, {22,25}, {4,23}, {17,21}, {23,26}, {13,24}, {20,22}, {5,24}, {28,38}, {4,32} } Symmetric graph 8 of order 38 Valency 19 Diameter 2 Girth 4 Automorphism group of order 29595060906949638427087208448000000 Number of arcs = 722 Number of 2-arcs = 12996 2-arc-transitive true Edge-set { {1,20}, {18,23}, {5,25}, {16,26}, {9,33}, {3,28}, {18,28}, {14,29}, {13,22}, {7,36}, {16,31}, {1,31}, {3,36}, {3,33}, {12,32}, {17,30}, {11,25}, {14,34}, {5,20}, {7,22}, {18,34}, {7,25}, {1,36}, {16,36}, {10,35}, {2,38}, {15,33}, {12,37}, {9,28}, {11,30}, {3,23}, {5,28}, {14,20}, {16,37}, {11,33}, {18,20}, {1,25}, {1,22}, {8,38}, {6,27}, {19,22}, {10,21}, {13,36}, {15,38}, {7,31}, {3,31}, {12,23}, {1,26}, {9,36}, {5,30}, {14,21}, {15,22}, {16,23}, {5,33}, {18,25}, {14,25}, {6,22}, {4,30}, {8,24}, {17,25}, {19,27}, {11,20}, {1,34}, {10,26}, {5,34}, {7,20}, {9,38}, {18,29}, {13,25}, {12,28}, {12,24}, {19,30}, {14,26}, {9,22}, {16,28}, {18,33}, {18,30}, {4,25}, {14,24}, {2,33}, {4,35}, {15,28}, {18,37}, {8,29}, {9,23}, {5,23}, {13,27}, {3,37}, {11,28}, {10,31}, {16,32}, {17,33}, {3,38}, {10,27}, {4,38}, {12,29}, {13,30}, {14,31}, {3,22}, {16,33}, {12,33}, {2,28}, {18,32}, {12,27}, {19,36}, {16,21}, {6,32}, {13,31}, {3,26}, {17,35}, {7,26}, {9,31}, {8,34}, {1,21}, {15,36}, {7,27}, {14,35}, {2,22}, {10,36}, {8,30}, {8,27}, {10,32}, {17,38}, {12,34}, {7,30}, {14,36}, {16,22}, {16,38}, {19,31}, {3,21}, {16,35}, {10,30}, {17,20}, {1,29}, {2,24}, {11,34}, {7,34}, {6,37}, {5,29}, {13,20}, {11,35}, {18,24}, {19,25}, {8,20}, {12,38}, {6,30}, {1,27}, {6,33}, {12,35}, {8,35}, {2,27}, {10,37}, {11,38}, {12,20}, {1,30}, {14,22}, {10,22}, {17,34}, {7,29}, {1,24}, {14,38}, {8,33}, {15,23}, {5,37}, {4,21}, {9,37}, {11,23}, {15,24}, {3,32}, {17,28}, {6,23}, {16,27}, {4,33}, {5,35}, {10,38}, {8,25}, {4,36}, {16,24}, {6,38}, {6,35}, {8,21}, {15,27}, {10,23}, {5,38}, {12,25}, {14,30}, {14,27}, {15,37}, {11,37}, {5,32}, {18,27}, {12,22}, {6,36}, {13,26}, {9,26}, {19,32}, {7,21}, {15,31}, {4,26}, {1,35}, {2,36}, {9,24}, {8,22}, {6,28}, {18,35}, {2,20}, {1,32}, {4,22}, {10,24}, {6,24}, {19,35}, {8,26}, {9,27}, {10,28}, {18,38}, {12,30}, {13,21}, {15,26}, {9,21}, {3,35}, {16,30}, {10,25}, {4,20}, {11,29}, {13,34}, {2,29}, {5,24}, {19,20}, {13,32}, {6,25}, {4,31}, {3,24}, {19,23}, {5,21}, {2,25}, {14,32}, {4,27}, {4,24}, {6,29}, {13,35}, {8,31}, {3,27}, {10,33}, {11,24}, {19,34}, {13,29}, {7,24}, {1,38}, {14,33}, {8,28}, {2,23}, {9,32}, {17,23}, {17,21}, {4,28}, {2,34}, {7,32}, {17,26}, {9,29}, {19,28}, {18,21}, {2,30}, {8,32}, {4,32}, {17,24}, {6,34}, {7,35}, {8,36}, {4,23}, {17,37}, {11,32}, {5,27}, {18,22}, {12,36}, {6,31}, {19,26}, {2,31}, {19,37}, {11,21}, {15,29}, {13,37}, {17,31}, {3,29}, {19,33}, {12,21}, {2,35}, {2,32}, {4,37}, {6,20}, {2,26}, {15,21}, {9,35}, {3,30}, {16,25}, {10,20}, {4,34}, {17,29}, {15,34}, {7,37}, {17,36}, {16,29}, {19,38}, {6,21}, {2,21}, {15,32}, {19,29}, {13,24}, {7,38}, {1,33}, {14,28}, {8,23}, {2,37}, {11,26}, {15,20}, {1,37}, {17,22}, {10,29}, {19,24}, {19,21}, {17,32}, {11,27}, {5,22}, {18,36}, {12,31}, {6,26}, {13,23}, {5,26}, {15,25}, {14,37}, {17,27}, {4,29}, {15,35}, {9,30}, {3,25}, {16,20}, {10,34}, {9,34}, {13,28}, {18,26}, {15,30}, {8,37}, {13,38}, {7,33}, {1,28}, {14,23}, {11,31}, {3,34}, {13,33}, {12,26}, {11,22}, {5,36}, {18,31}, {7,23}, {11,36}, {16,34}, {9,25}, {3,20}, {9,20}, {1,23}, {7,28}, {5,31} } Symmetric graph 9 of order 38 Valency 36 Diameter 2 Girth 3 Automorphism group of order 63777066403145711616000 Number of arcs = 1368 Number of 2-arcs = 47880 2-arc-transitive false Edge-set { {1,3}, {36,38}, {14,19}, {31,33}, {26,31}, {9,16}, {4,21}, {27,30}, {5,37}, {22,27}, {5,24}, {6,12}, {15,33}, {18,37}, {13,35}, {24,26}, {11,17}, {2,34}, {8,25}, {17,24}, {17,36}, {2,19}, {8,30}, {1,7}, {7,28}, {11,30}, {16,37}, {14,34}, {10,25}, {10,32}, {22,32}, {19,22}, {24,30}, {8,13}, {9,27}, {29,35}, {20,38}, {3,21}, {1,23}, {13,19}, {9,30}, {13,31}, {9,31}, {16,35}, {4,20}, {3,26}, {1,11}, {4,36}, {4,23}, {2,18}, {8,26}, {11,27}, {12,34}, {15,25}, {9,29}, {21,38}, {5,21}, {23,34}, {5,28}, {6,34}, {17,28}, {6,36}, {16,17}, {19,26}, {3,10}, {1,22}, {6,24}, {17,33}, {25,32}, {12,32}, {18,38}, {14,35}, {20,36}, {19,29}, {10,16}, {4,22}, {6,26}, {11,33}, {10,27}, {5,22}, {6,27}, {5,33}, {15,32}, {15,37}, {3,13}, {22,38}, {14,24}, {8,36}, {19,27}, {31,37}, {20,37}, {13,29}, {10,20}, {3,22}, {1,24}, {8,24}, {17,27}, {7,29}, {28,38}, {11,21}, {16,23}, {6,25}, {12,33}, {18,33}, {26,35}, {8,35}, {20,29}, {29,38}, {2,23}, {8,18}, {1,29}, {7,38}, {13,23}, {9,18}, {1,31}, {7,31}, {12,13}, {9,15}, {16,22}, {4,24}, {5,38}, {19,36}, {1,19}, {7,30}, {13,30}, {9,37}, {21,28}, {6,23}, {6,28}, {14,33}, {10,26}, {9,32}, {21,32}, {15,31}, {3,31}, {16,25}, {4,12}, {5,12}, {15,34}, {17,37}, {13,36}, {7,24}, {27,37}, {17,34}, {2,17}, {7,17}, {2,30}, {8,37}, {11,28}, {6,16}, {11,34}, {10,38}, {14,22}, {26,36}, {9,19}, {21,30}, {16,24}, {4,17}, {27,34}, {5,25}, {3,25}, {12,22}, {5,15}, {3,34}, {17,38}, {14,36}, {19,30}, {3,19}, {1,30}, {13,24}, {9,17}, {4,25}, {2,12}, {23,33}, {18,26}, {27,35}, {12,20}, {15,29}, {1,21}, {7,23}, {28,37}, {14,30}, {10,37}, {24,32}, {3,32}, {1,32}, {3,12}, {25,33}, {12,26}, {20,35}, {3,14}, {1,10}, {25,36}, {12,19}, {4,33}, {2,26}, {22,29}, {6,14}, {10,33}, {27,36}, {5,19}, {4,27}, {2,5}, {7,10}, {22,28}, {6,11}, {16,33}, {12,17}, {15,36}, {19,37}, {2,33}, {16,31}, {4,31}, {16,36}, {4,19}, {4,26}, {2,11}, {11,22}, {18,23}, {18,35}, {1,20}, {7,18}, {21,37}, {24,34}, {6,33}, {18,28}, {6,35}, {5,16}, {27,38}, {5,14}, {12,21}, {15,23}, {7,37}, {13,28}, {2,7}, {8,28}, {11,29}, {16,38}, {13,34}, {9,25}, {10,31}, {22,31}, {17,25}, {9,38}, {9,20}, {4,13}, {2,9}, {11,20}, {1,25}, {8,23}, {18,27}, {1,12}, {7,15}, {8,29}, {26,34}, {21,36}, {24,31}, {11,35}, {15,30}, {13,37}, {9,13}, {24,29}, {2,21}, {14,23}, {28,36}, {8,16}, {14,38}, {13,33}, {9,26}, {21,31}, {16,26}, {4,11}, {4,14}, {11,19}, {10,19}, {22,30}, {6,13}, {9,33}, {7,35}, {20,28}, {20,30}, {29,37}, {10,24}, {17,32}, {3,28}, {11,25}, {12,16}, {18,36}, {19,35}, {2,29}, {18,25}, {5,34}, {25,34}, {19,28}, {6,30}, {6,19}, {14,28}, {23,37}, {7,22}, {24,28}, {14,21}, {5,36}, {19,34}, {23,31}, {7,16}, {4,28}, {30,37}, {22,35}, {20,24}, {12,36}, {1,9}, {7,21}, {5,30}, {34,37}, {17,31}, {2,16}, {4,8}, {24,37}, {13,17}, {2,35}, {8,20}, {4,5}, {17,23}, {1,8}, {7,27}, {12,30}, {7,13}, {9,28}, {11,31}, {16,34}, {30,35}, {12,27}, {5,13}, {12,31}, {22,37}, {20,27}, {8,17}, {14,20}, {10,29}, {14,32}, {2,10}, {18,34}, {25,35}, {30,38}, {10,18}, {7,32}, {8,15}, {24,33}, {17,26}, {8,21}, {28,35}, {16,29}, {4,34}, {2,25}, {10,23}, {18,22}, {4,35}, {2,20}, {3,23}, {1,18}, {15,26}, {6,21}, {5,27}, {13,21}, {9,23}, {26,33}, {6,15}, {3,33}, {13,22}, {20,33}, {3,27}, {19,23}, {3,20}, {10,17}, {7,36}, {24,38}, {18,31}, {31,35}, {8,32}, {27,32}, {11,26}, {11,16}, {10,34}, {22,25}, {6,10}, {22,33}, {19,25}, {21,29}, {1,15}, {21,26}, {10,30}, {6,22}, {5,35}, {15,24}, {13,27}, {11,36}, {33,37}, {4,32}, {2,32}, {3,18}, {3,11}, {12,25}, {30,34}, {6,9}, {23,38}, {14,18}, {23,27}, {7,12}, {15,28}, {14,31}, {16,32}, {8,38}, {4,18}, {1,26}, {7,11}, {1,16}, {4,7}, {18,21}, {20,34}, {25,29}, {2,36}, {18,30}, {21,35}, {2,31}, {8,31}, {4,38}, {5,29}, {2,15}, {13,18}, {32,36}, {15,19}, {3,30}, {28,31}, {19,33}, {8,11}, {29,34}, {25,38}, {5,9}, {12,35}, {15,20}, {3,37}, {1,13}, {25,30}, {10,13}, {9,22}, {32,35}, {20,32}, {3,15}, {2,37}, {13,20}, {3,36}, {7,26}, {4,10}, {2,22}, {8,27}, {12,29}, {15,38}, {26,32}, {11,32}, {8,22}, {3,17}, {14,29}, {23,32}, {2,6}, {9,24}, {1,35}, {18,32}, {12,15}, {13,38}, {20,23}, {5,20}, {14,17}, {10,36}, {32,37}, {13,32}, {15,35}, {2,24}, {6,20}, {29,33}, {14,37}, {22,36}, {16,20}, {4,29}, {9,34}, {26,30}, {14,27}, {5,10}, {5,32}, {1,6}, {6,17}, {24,27}, {8,12}, {15,27}, {34,38}, {17,21}, {23,36}, {1,5}, {7,34}, {17,30}, {36,37}, {16,21}, {16,19}, {24,35}, {5,26}, {1,17}, {16,30}, {17,22}, {27,31}, {25,37}, {10,14}, {23,28}, {26,29}, {11,38}, {7,33}, {9,14}, {10,21}, {17,29}, {2,28}, {11,23}, {16,18}, {12,28}, {19,24}, {2,27}, {4,37}, {2,13}, {10,35}, {3,38}, {21,25}, {12,23}, {20,31}, {14,26}, {10,11}, {13,26}, {10,22}, {6,31}, {4,16}, {26,38}, {11,14}, {5,18}, {3,8}, {1,27}, {12,38}, {21,33}, {23,26}, {8,33}, {28,32}, {11,15}, {3,16}, {14,25}, {22,34}, {33,36}, {6,32}, {3,6}, {14,16}, {34,35}, {20,25}, {10,15}, {31,38}, {17,35}, {3,24}, {7,25}, {1,36}, {6,29}, {7,20}, {30,33}, {19,32}, {16,28}, {22,26}, {3,29}, {9,21}, {5,31}, {31,34}, {28,34}, {10,28}, {3,7}, {12,37}, {31,36}, {33,38}, {11,24}, {8,34}, {6,8}, {7,19}, {7,9}, {1,28}, {9,35}, {29,31}, {8,19}, {2,38}, {9,11}, {25,31}, {12,18}, {4,15}, {30,32}, {9,36}, {5,17}, {21,34}, {23,25}, {18,29}, {12,24}, {26,27}, {4,30}, {13,25}, {9,12}, {23,35}, {18,20}, {27,29}, {12,14}, {17,20}, {20,22}, {32,34}, {28,29}, {3,5}, {21,24}, {5,8}, {22,24}, {34,36}, {5,7}, {13,15}, {8,9}, {21,27}, {2,14}, {8,10}, {1,14}, {24,36}, {17,19}, {26,28}, {35,37}, {1,37}, {6,18}, {16,27}, {14,15}, {21,23}, {30,31}, {6,7}, {1,38}, {7,14}, {15,21}, {29,32}, {32,38}, {5,11}, {27,33}, {19,38}, {19,31}, {2,3}, {11,37}, {4,6}, {15,18}, {33,35}, {23,29}, {5,23}, {25,28}, {26,37}, {2,4}, {18,19}, {32,33}, {25,27}, {1,4}, {20,26}, {13,16}, {35,38}, {20,21}, {10,12}, {28,30}, {11,13}, {22,23}, {28,33}, {24,25}, {3,9}, {15,17}, {6,38}, {8,14}, {30,36}, {2,8}, {1,33}, {18,24}, {1,34}, {19,21}, {4,9}, {11,18}, {6,37}, {15,22}, {3,35}, {29,36}, {23,30} } Symmetric graph 10 of order 38 Valency 37 Diameter 1 Girth 3 Automorphism group of order 523022617466601111760007224100074291200000000 Number of arcs = 1406 Number of 2-arcs = 50616 2-arc-transitive true Edge-set { {1,2}, {1,21}, {1,38}, {2,21}, {1,5}, {21,27}, {2,38}, {1,4}, {13,21}, {19,38}, {2,28}, {2,5}, {1,27}, {1,10}, {4,21}, {22,38}, {2,11}, {5,28}, {22,27}, {2,32}, {2,4}, {1,13}, {1,19}, {21,28}, {1,35}, {21,26}, {10,38}, {5,14}, {24,27}, {2,9}, {4,32}, {13,38}, {14,19}, {24,28}, {2,30}, {1,32}, {2,10}, {1,22}, {11,21}, {1,28}, {21,22}, {32,38}, {1,26}, {21,34}, {8,38}, {2,18}, {5,35}, {26,27}, {4,16}, {13,17}, {19,34}, {19,28}, {2,13}, {1,36}, {10,30}, {5,22}, {11,27}, {16,28}, {17,22}, {32,34}, {1,37}, {1,30}, {21,32}, {2,35}, {1,14}, {21,24}, {9,38}, {21,38}, {14,38}, {2,24}, {5,30}, {27,32}, {1,8}, {18,21}, {12,38}, {2,15}, {5,29}, {9,27}, {4,26}, {13,34}, {8,19}, {18,28}, {10,24}, {4,29}, {22,25}, {11,12}, {12,28}, {15,22}, {28,32}, {2,22}, {1,11}, {1,3}, {8,21}, {18,35}, {26,37}, {4,14}, {13,24}, {9,19}, {24,32}, {29,38}, {14,25}, {12,24}, {12,30}, {15,32}, {6,21}, {1,18}, {21,37}, {30,38}, {2,26}, {1,34}, {1,16}, {17,21}, {34,38}, {2,19}, {5,13}, {27,36}, {5,38}, {2,27}, {5,16}, {17,27}, {2,34}, {4,18}, {13,37}, {19,30}, {1,29}, {9,21}, {5,33}, {14,27}, {2,6}, {4,7}, {13,33}, {13,19}, {28,36}, {8,10}, {12,22}, {11,15}, {28,29}, {9,22}, {34,35}, {19,26}, {7,10}, {4,33}, {23,24}, {9,33}, {32,33}, {6,14}, {24,35}, {30,32}, {2,14}, {1,24}, {1,9}, {5,21}, {1,20}, {7,21}, {10,34}, {8,36}, {6,18}, {10,16}, {4,17}, {22,34}, {11,19}, {13,28}, {22,36}, {30,34}, {19,32}, {5,7}, {27,33}, {16,27}, {17,23}, {33,34}, {18,33}, {14,37}, {6,30}, {32,35}, {31,38}, {10,21}, {36,38}, {5,18}, {27,37}, {2,8}, {1,12}, {15,21}, {21,29}, {25,38}, {2,12}, {5,12}, {15,27}, {4,22}, {11,13}, {3,19}, {8,28}, {4,5}, {13,27}, {4,24}, {13,29}, {19,25}, {1,15}, {4,10}, {6,11}, {22,37}, {1,7}, {21,33}, {2,36}, {4,15}, {13,16}, {16,19}, {17,28}, {2,31}, {10,17}, {4,20}, {11,16}, {22,28}, {11,22}, {3,32}, {29,35}, {9,26}, {14,33}, {14,24}, {6,9}, {7,32}, {33,38}, {13,14}, {24,36}, {12,26}, {15,34}, {18,22}, {17,35}, {20,26}, {10,15}, {11,34}, {19,31}, {13,15}, {16,36}, {15,30}, {16,32}, {16,31}, {17,30}, {26,34}, {18,30}, {32,37}, {2,16}, {1,17}, {19,21}, {21,36}, {4,38}, {1,23}, {3,21}, {17,38}, {2,20}, {12,35}, {15,26}, {3,29}, {8,9}, {21,31}, {26,29}, {10,25}, {4,12}, {12,14}, {15,24}, {9,28}, {22,32}, {11,38}, {3,14}, {8,24}, {12,18}, {15,37}, {28,30}, {13,20}, {15,19}, {19,24}, {11,25}, {12,31}, {12,15}, {15,16}, {6,17}, {18,31}, {30,37}, {26,30}, {5,37}, {25,27}, {35,38}, {3,5}, {8,27}, {10,13}, {19,36}, {6,28}, {2,29}, {1,33}, {14,21}, {6,38}, {7,38}, {2,33}, {5,27}, {23,27}, {6,19}, {28,35}, {10,14}, {5,11}, {20,28}, {7,22}, {29,32}, {4,13}, {19,22}, {11,28}, {4,19}, {11,33}, {27,28}, {22,23}, {1,6}, {21,35}, {10,35}, {9,31}, {14,36}, {6,24}, {20,21}, {15,38}, {2,3}, {6,10}, {4,35}, {22,24}, {11,29}, {22,29}, {25,32}, {2,37}, {1,25}, {25,35}, {10,23}, {3,4}, {9,24}, {14,32}, {24,38}, {9,14}, {5,24}, {20,30}, {7,26}, {8,13}, {18,36}, {16,17}, {16,34}, {17,19}, {13,31}, {30,36}, {20,32}, {5,15}, {16,22}, {11,17}, {3,34}, {8,33}, {14,18}, {6,12}, {15,35}, {25,26}, {12,34}, {8,23}, {3,18}, {6,35}, {26,35}, {9,12}, {28,37}, {6,22}, {11,35}, {3,24}, {8,29}, {35,37}, {24,30}, {24,37}, {25,29}, {18,25}, {12,37}, {8,12}, {15,18}, {10,37}, {6,32}, {12,21}, {28,38}, {3,38}, {5,10}, {4,27}, {20,38}, {2,7}, {5,25}, {12,27}, {2,23}, {26,33}, {14,34}, {6,8}, {7,20}, {7,33}, {9,36}, {37,38}, {2,25}, {7,8}, {27,35}, {23,26}, {10,33}, {16,33}, {14,17}, {6,34}, {19,35}, {13,32}, {14,30}, {5,9}, {16,20}, {7,17}, {29,34}, {6,36}, {18,32}, {3,11}, {22,35}, {28,34}, {5,23}, {33,37}, {6,33}, {14,35}, {25,31}, {6,37}, {8,18}, {18,37}, {4,36}, {6,13}, {19,27}, {23,28}, {5,26}, {27,34}, {7,13}, {19,29}, {11,26}, {3,28}, {8,22}, {31,32}, {16,21}, {16,38}, {2,17}, {5,31}, {27,30}, {5,17}, {20,27}, {28,31}, {22,30}, {26,32}, {16,35}, {17,26}, {4,9}, {23,32}, {20,24}, {7,30}, {10,22}, {4,11}, {14,28}, {9,32}, {10,28}, {9,15}, {11,14}, {24,31}, {1,31}, {21,30}, {26,38}, {25,36}, {3,16}, {8,17}, {31,34}, {23,38}, {5,6}, {31,35}, {10,26}, {4,34}, {7,9}, {7,14}, {24,33}, {21,23}, {23,34}, {26,31}, {10,20}, {16,30}, {17,32}, {5,34}, {17,36}, {18,23}, {3,37}, {18,20}, {9,11}, {24,25}, {12,29}, {15,29}, {25,28}, {8,37}, {23,30}, {4,6}, {13,35}, {24,29}, {9,25}, {12,20}, {7,15}, {9,16}, {31,33}, {6,26}, {12,33}, {14,15}, {8,26}, {18,34}, {32,36}, {14,31}, {20,34}, {7,19}, {7,29}, {26,36}, {19,37}, {34,36}, {7,27}, {23,33}, {33,36}, {29,33}, {35,36}, {30,31}, {5,32}, {27,38}, {5,20}, {13,26}, {10,19}, {4,28}, {3,27}, {13,23}, {19,33}, {8,15}, {16,18}, {12,16}, {15,17}, {29,31}, {9,30}, {3,20}, {3,13}, {5,36}, {6,27}, {17,29}, {9,20}, {8,11}, {16,26}, {16,29}, {16,25}, {12,17}, {26,28}, {11,32}, {17,37}, {13,36}, {17,25}, {7,12}, {15,33}, {3,31}, {8,30}, {10,32}, {14,26}, {24,34}, {12,32}, {15,36}, {6,16}, {15,31}, {17,34}, {23,25}, {31,36}, {9,10}, {3,10}, {4,8}, {22,31}, {11,30}, {13,18}, {12,19}, {15,28}, {11,20}, {7,28}, {22,33}, {14,29}, {27,29}, {4,37}, {13,25}, {18,19}, {4,25}, {12,13}, {19,23}, {24,26}, {8,25}, {17,18}, {20,37}, {13,30}, {34,37}, {21,25}, {18,38}, {5,8}, {18,27}, {15,25}, {27,31}, {4,31}, {25,34}, {8,35}, {18,26}, {10,12}, {20,36}, {17,20}, {23,35}, {3,26}, {18,24}, {29,37}, {25,30}, {3,25}, {10,31}, {6,7}, {9,13}, {33,35}, {29,36}, {11,18}, {31,37}, {4,30}, {22,26}, {7,34}, {23,36}, {20,35}, {8,31}, {14,16}, {9,18}, {3,30}, {8,32}, {16,37}, {12,23}, {3,15}, {20,22}, {20,33}, {3,8}, {3,12}, {8,16}, {8,34}, {25,37}, {5,19}, {4,23}, {19,20}, {11,31}, {6,29}, {9,35}, {10,29}, {6,25}, {7,37}, {25,33}, {36,37}, {20,23}, {3,7}, {7,11}, {7,25}, {3,36}, {9,29}, {18,29}, {7,24}, {23,29}, {3,22}, {17,33}, {14,20}, {6,15}, {9,37}, {30,35}, {30,33}, {3,6}, {29,30}, {12,25}, {23,31}, {10,11}, {28,33}, {14,22}, {9,23}, {16,24}, {7,16}, {10,36}, {11,23}, {10,27}, {11,37}, {12,36}, {15,23}, {9,34}, {10,18}, {3,23}, {8,20}, {7,18}, {7,36}, {23,37}, {7,23}, {17,31}, {13,22}, {11,36}, {8,14}, {15,20}, {6,20}, {7,35}, {14,23}, {20,29}, {6,23}, {7,31}, {16,23}, {9,17}, {3,17}, {6,31}, {20,31}, {17,24}, {3,35}, {3,33}, {3,9}, {11,24}, {20,25} } ................................................................... Symmetric connected graphs of order 39 Symmetric graph 1 of order 39 Valency 2 Diameter 19 Girth 39 Automorphism group of order 78 Number of arcs = 78 Number of 2-arcs = 78 2-arc-transitive true Edge-set { {1,4}, {35,37}, {28,31}, {23,27}, {16,19}, {10,13}, {6,7}, {1,39}, {33,35}, {26,28}, {21,23}, {15,16}, {9,10}, {3,6}, {34,39}, {30,33}, {22,26}, {18,21}, {12,15}, {5,9}, {3,38}, {32,34}, {25,30}, {20,22}, {14,18}, {8,12}, {2,5}, {36,38}, {29,32}, {24,25}, {17,20}, {11,14}, {4,8}, {2,37}, {31,36}, {27,29}, {19,24}, {13,17}, {7,11} } Symmetric graph 2 of order 39 Valency 4 Diameter 6 Girth 4 Automorphism group of order 156 Number of arcs = 156 Number of 2-arcs = 468 2-arc-transitive false Edge-set { {1,4}, {15,16}, {13,17}, {25,28}, {26,29}, {27,30}, {2,37}, {3,38}, {1,39}, {10,14}, {11,15}, {12,13}, {22,26}, {23,27}, {24,25}, {36,39}, {34,37}, {35,38}, {8,11}, {9,12}, {7,10}, {21,24}, {19,22}, {20,23}, {32,34}, {33,35}, {31,36}, {6,7}, {4,8}, {5,9}, {17,19}, {18,20}, {16,21}, {30,31}, {28,32}, {29,33}, {3,4}, {1,5}, {2,6}, {13,16}, {14,17}, {15,18}, {27,28}, {25,29}, {26,30}, {2,38}, {3,39}, {1,37}, {12,14}, {10,15}, {11,13}, {23,26}, {24,27}, {22,25}, {35,39}, {36,37}, {34,38}, {9,11}, {7,12}, {8,10}, {20,24}, {21,22}, {19,23}, {33,34}, {31,35}, {32,36}, {5,7}, {6,8}, {4,9}, {18,19}, {16,20}, {17,21}, {29,31}, {30,32}, {28,33}, {2,5}, {3,6}, {14,18} } Symmetric graph 3 of order 39 Valency 6 Diameter 4 Girth 3 Automorphism group of order 234 Number of arcs = 234 Number of 2-arcs = 1170 2-arc-transitive false Edge-set { {1,4}, {2,37}, {8,34}, {36,38}, {9,20}, {4,32}, {24,33}, {31,34}, {21,32}, {5,17}, {14,22}, {2,29}, {6,34}, {20,30}, {28,32}, {5,33}, {18,29}, {6,15}, {3,15}, {25,35}, {11,21}, {26,38}, {9,16}, {1,32}, {33,36}, {17,27}, {14,17}, {25,29}, {6,18}, {3,30}, {4,35}, {13,26}, {16,26}, {1,12}, {12,39}, {7,38}, {30,31}, {8,18}, {11,15}, {22,34}, {21,28}, {5,14}, {22,27}, {29,37}, {6,8}, {15,23}, {25,37}, {24,26}, {16,30}, {1,13}, {26,36}, {27,39}, {7,17}, {2,33}, {10,22}, {28,39}, {27,28}, {9,37}, {8,12}, {9,35}, {12,19}, {21,23}, {4,13}, {11,38}, {18,25}, {15,18}, {3,11}, {35,37}, {16,20}, {24,36}, {3,38}, {20,22}, {1,28}, {14,27}, {10,37}, {8,39}, {22,31}, {23,35}, {19,29}, {23,25}, {30,38}, {4,9}, {7,21}, {2,10}, {18,19}, {5,36}, {12,24}, {12,13}, {34,39}, {13,24}, {26,30}, {7,11}, {20,31}, {17,21}, {2,14}, {11,23}, {7,36}, {10,20}, {19,24}, {2,5}, {19,33}, {3,31}, {13,16}, {27,34}, {9,10}, {32,35}, {1,39}, {17,28}, {15,25}, {8,19}, {6,31}, {23,32}, {10,14}, {5,7}, {29,33}, {4,16}, {3,6} } Symmetric graph 4 of order 39 Valency 6 Diameter 6 Girth 4 Automorphism group of order 339578044416 Number of arcs = 234 Number of 2-arcs = 1170 2-arc-transitive false Edge-set { {1,4}, {6,8}, {29,31}, {7,10}, {33,34}, {32,36}, {18,19}, {12,13}, {36,38}, {35,37}, {21,22}, {34,39}, {20,24}, {6,9}, {15,16}, {3,37}, {1,39}, {24,27}, {3,38}, {23,26}, {23,25}, {8,10}, {2,37}, {22,25}, {22,27}, {7,12}, {7,11}, {33,35}, {18,21}, {2,4}, {3,5}, {26,28}, {2,6}, {25,29}, {27,29}, {12,14}, {1,5}, {27,28}, {11,13}, {26,30}, {11,15}, {10,13}, {34,38}, {3,4}, {25,30}, {10,15}, {10,14}, {12,15}, {36,37}, {36,39}, {35,38}, {21,23}, {20,23}, {4,8}, {30,31}, {5,9}, {28,32}, {28,31}, {13,17}, {4,7}, {30,33}, {30,32}, {15,18}, {29,32}, {14,18}, {15,17}, {1,37}, {14,17}, {14,16}, {3,39}, {28,33}, {13,16}, {2,39}, {5,8}, {13,18}, {2,38}, {1,38}, {24,26}, {24,25}, {23,27}, {8,11}, {22,26}, {31,34}, {33,36}, {16,19}, {9,11}, {32,35}, {17,20}, {31,36}, {17,19}, {8,12}, {16,21}, {16,20}, {18,20}, {32,34}, {1,6}, {2,5}, {3,6}, {26,29}, {17,21}, {25,28}, {31,35}, {9,10}, {27,30}, {11,14}, {19,22}, {35,39}, {21,24}, {4,9}, {5,7}, {19,24}, {34,37}, {20,22}, {6,7}, {29,33}, {19,23}, {9,12} } Symmetric graph 5 of order 39 Valency 8 Diameter 3 Girth 4 Automorphism group of order 312 Number of arcs = 312 Number of 2-arcs = 2184 2-arc-transitive false Edge-set { {1,4}, {14,17}, {20,34}, {26,30}, {3,17}, {7,32}, {28,31}, {3,37}, {24,39}, {13,30}, {17,21}, {4,20}, {12,15}, {1,6}, {13,38}, {12,13}, {5,21}, {11,35}, {6,7}, {3,25}, {1,39}, {30,33}, {17,33}, {17,32}, {31,34}, {22,27}, {2,26}, {14,16}, {20,35}, {10,25}, {22,25}, {1,26}, {18,33}, {33,36}, {8,24}, {27,30}, {16,20}, {12,35}, {13,39}, {21,22}, {11,14}, {6,20}, {3,5}, {14,39}, {5,30}, {4,30}, {15,17}, {13,28}, {36,38}, {9,23}, {15,37}, {19,24}, {26,29}, {3,18}, {8,32}, {30,31}, {23,39}, {36,39}, {9,22}, {14,37}, {20,24}, {5,28}, {5,9}, {14,29}, {21,35}, {7,11}, {3,38}, {29,32}, {18,31}, {8,22}, {11,25}, {9,33}, {24,26}, {3,27}, {16,32}, {31,35}, {13,18}, {21,36}, {11,26}, {3,6}, {34,39}, {2,17}, {1,25}, {1,38}, {9,10}, {4,29}, {19,34}, {8,10}, {12,27}, {2,5}, {2,37}, {24,37}, {16,21}, {4,21}, {11,15}, {11,34}, {6,8}, {9,11}, {6,29}, {19,36}, {12,26}, {32,35}, {7,31}, {1,18}, {18,19}, {10,36}, {8,33}, {10,13}, {2,4}, {6,28}, {13,16}, {5,19}, {10,14}, {35,37}, {7,24}, {21,23}, {15,18}, {25,28}, {1,16}, {29,33}, {24,27}, {15,30}, {17,19}, {20,22}, {19,23}, {34,37}, {28,32}, {22,38}, {23,26}, {5,7}, {33,34}, {2,27}, {27,28}, {10,27}, {2,16}, {9,31}, {22,37}, {4,8}, {14,28}, {25,29}, {23,25}, {35,38}, {32,36}, {8,12}, {7,12}, {18,20}, {7,23}, {2,39}, {15,38}, {4,9}, {12,36}, {23,38}, {15,29}, {6,19}, {16,31}, {10,34} } Symmetric graph 6 of order 39 Valency 12 Diameter 2 Girth 3 Automorphism group of order 468 Number of arcs = 468 Number of 2-arcs = 5148 2-arc-transitive false Edge-set { {1,4}, {26,39}, {2,29}, {12,19}, {14,23}, {8,37}, {1,11}, {5,8}, {30,33}, {31,34}, {10,13}, {13,17}, {3,39}, {2,6}, {13,27}, {17,28}, {9,36}, {10,39}, {24,34}, {26,38}, {4,32}, {18,29}, {20,32}, {12,38}, {3,14}, {25,37}, {1,30}, {20,29}, {22,32}, {7,18}, {12,20}, {16,27}, {2,12}, {4,14}, {24,31}, {26,36}, {11,19}, {15,23}, {26,35}, {29,37}, {8,16}, {5,35}, {7,37}, {5,15}, {30,38}, {3,31}, {10,21}, {13,24}, {9,39}, {2,10}, {7,11}, {32,35}, {35,37}, {15,16}, {18,19}, {1,5}, {5,7}, {17,20}, {21,22}, {1,37}, {26,30}, {29,31}, {36,38}, {19,23}, {23,27}, {3,4}, {6,8}, {28,33}, {33,34}, {19,22}, {23,25}, {8,10}, {11,13}, {17,21}, {22,27}, {25,28}, {10,15}, {13,18}, {27,28}, {9,11}, {34,38}, {3,38}, {4,9}, {32,36}, {12,14}, {14,16}, {2,37}, {3,15}, {6,18}, {22,35}, {10,22}, {13,25}, {21,33}, {4,16}, {8,19}, {27,39}, {2,28}, {15,27}, {18,28}, {5,18}, {7,20}, {6,32}, {9,35}, {2,13}, {9,19}, {10,23}, {8,34}, {11,38}, {11,23}, {4,33}, {20,33}, {22,34}, {3,29}, {17,30}, {7,36}, {12,39}, {24,36}, {8,35}, {4,17}, {9,20}, {7,21}, {12,24}, {16,29}, {19,32}, {12,22}, {6,16}, {11,24}, {15,26}, {14,26}, {23,35}, {27,37}, {5,31}, {21,31}, {10,37}, {1,13}, {28,38}, {3,33}, {16,25}, {19,30}, {25,35}, {2,32}, {4,35}, {21,29}, {24,32}, {6,36}, {17,26}, {4,13}, {8,17}, {14,22}, {1,12}, {20,28}, {22,33}, {7,16}, {19,28}, {30,37}, {1,32}, {2,33}, {4,34}, {3,11}, {6,15}, {6,34}, {29,39}, {5,36}, {7,39}, {8,38}, {9,18}, {10,20}, {18,27}, {5,14}, {23,31}, {27,36}, {13,22}, {17,25}, {18,26}, {1,31}, {11,21}, {21,30}, {23,33}, {25,34}, {27,34}, {9,38}, {12,15}, {21,24}, {24,25}, {22,26}, {25,29}, {31,35}, {36,37}, {27,30}, {20,23}, {26,29}, {29,32}, {30,32}, {1,39}, {2,5}, {7,12}, {35,39}, {15,17}, {18,21}, {4,7}, {8,12}, {9,10}, {24,26}, {3,6}, {11,14}, {14,18}, {16,19}, {16,20}, {28,31}, {20,24}, {34,39}, {2,38}, {6,9}, {33,36}, {1,28}, {5,33}, {6,31}, {8,21}, {25,38}, {7,34}, {11,37}, {2,14}, {1,15}, {14,25}, {5,17}, {19,31}, {23,36}, {3,30}, {16,30}, {28,39}, {6,13}, {9,17}, {15,24}, {3,10} } Symmetric graph 7 of order 39 Valency 12 Diameter 2 Girth 4 Automorphism group of order 679156088832 Number of arcs = 468 Number of 2-arcs = 5148 2-arc-transitive false Edge-set { {1,4}, {1,38}, {14,38}, {35,38}, {14,28}, {10,35}, {28,33}, {33,35}, {5,28}, {10,26}, {8,33}, {5,7}, {26,28}, {19,35}, {5,19}, {2,26}, {35,37}, {8,22}, {7,11}, {4,28}, {19,22}, {2,6}, {23,37}, {22,26}, {11,35}, {16,33}, {2,5}, {2,16}, {2,37}, {22,39}, {11,13}, {33,34}, {5,29}, {4,19}, {22,27}, {6,9}, {9,23}, {1,26}, {16,19}, {2,27}, {3,39}, {13,39}, {20,34}, {26,29}, {11,27}, {9,33}, {5,9}, {17,19}, {2,39}, {13,37}, {14,39}, {13,17}, {34,39}, {13,29}, {19,36}, {27,30}, {9,12}, {9,31}, {28,32}, {6,19}, {34,37}, {1,16}, {2,38}, {19,23}, {10,27}, {3,5}, {24,39}, {5,20}, {24,26}, {22,38}, {11,14}, {14,16}, {2,17}, {23,39}, {10,13}, {36,37}, {15,30}, {12,36}, {30,31}, {17,32}, {1,6}, {11,34}, {9,10}, {19,24}, {24,37}, {15,16}, {36,39}, {13,30}, {12,34}, {29,31}, {10,36}, {30,33}, {12,15}, {16,31}, {32,36}, {6,30}, {12,27}, {31,34}, {2,4}, {23,25}, {8,24}, {21,24}, {26,30}, {20,35}, {3,16}, {32,34}, {6,29}, {14,17}, {35,39}, {13,28}, {16,20}, {8,23}, {7,10}, {15,37}, {21,36}, {25,30}, {1,37}, {21,22}, {11,25}, {27,28}, {10,14}, {17,33}, {15,39}, {13,16}, {20,36}, {8,12}, {7,31}, {4,29}, {4,8}, {25,29}, {3,38}, {9,32}, {5,8}, {7,24}, {16,21}, {2,25}, {21,34}, {31,36}, {4,30}, {12,25}, {7,32}, {6,8}, {27,29}, {8,31}, {4,7}, {25,28}, {8,32}, {14,29}, {17,21}, {4,20}, {3,25}, {7,23}, {8,10}, {29,32}, {6,21}, {1,39}, {13,38}, {20,24}, {12,26}, {4,21}, {22,25}, {18,21}, {11,36}, {1,5}, {14,37}, {15,17}, {30,32}, {6,20}, {3,27}, {10,15}, {33,36}, {5,30}, {31,35}, {1,17}, {18,31}, {3,4}, {24,25}, {34,38}, {18,19}, {9,24}, {23,26}, {7,33}, {15,28}, {12,14}, {17,31}, {21,23}, {1,27}, {24,27}, {22,37}, {14,18}, {3,17}, {12,13}, {18,32}, {3,6}, {1,25}, {36,38}, {20,23}, {23,27}, {10,34}, {23,38}, {12,35}, {20,22}, {15,18}, {7,22}, {3,18}, {14,30}, {28,31}, {8,11}, {1,18}, {13,18}, {4,9}, {29,33}, {11,15}, {16,32}, {5,21}, {15,38}, {32,35}, {6,28}, {2,18}, {11,26}, {15,29}, {18,20}, {3,26}, {10,25}, {19,34}, {18,33}, {7,12}, {3,37}, {24,38}, {17,20}, {6,7}, {21,35}, {9,22}, {9,11} } Symmetric graph 8 of order 39 Valency 18 Diameter 2 Girth 3 Automorphism group of order 1018734133248 Number of arcs = 702 Number of 2-arcs = 11934 2-arc-transitive false Edge-set { {1,4}, {15,16}, {3,10}, {26,28}, {9,37}, {14,23}, {2,28}, {2,38}, {5,36}, {12,20}, {19,33}, {25,34}, {26,39}, {2,13}, {1,5}, {10,13}, {1,31}, {8,17}, {11,23}, {22,31}, {18,30}, {5,33}, {14,17}, {24,35}, {11,38}, {32,36}, {13,27}, {1,38}, {15,17}, {3,11}, {23,27}, {28,38}, {6,15}, {3,15}, {19,29}, {7,21}, {24,34}, {26,29}, {6,36}, {15,25}, {1,30}, {4,8}, {5,17}, {11,14}, {25,29}, {7,39}, {7,35}, {22,27}, {10,24}, {29,31}, {13,23}, {27,39}, {34,38}, {10,15}, {3,31}, {7,37}, {14,24}, {2,29}, {34,39}, {26,34}, {2,10}, {5,31}, {18,26}, {12,37}, {14,26}, {2,37}, {3,33}, {6,17}, {21,32}, {16,20}, {9,35}, {24,27}, {3,38}, {8,18}, {12,23}, {26,37}, {35,37}, {1,15}, {3,4}, {16,19}, {10,21}, {17,29}, {7,11}, {24,25}, {29,39}, {3,37}, {6,35}, {11,21}, {20,32}, {20,22}, {36,39}, {23,35}, {27,28}, {3,6}, {27,34}, {26,38}, {11,39}, {32,34}, {9,10}, {24,31}, {23,26}, {28,37}, {6,14}, {2,15}, {12,21}, {20,33}, {25,35}, {3,13}, {1,6}, {9,11}, {24,32}, {9,38}, {24,36}, {1,28}, {11,15}, {30,38}, {8,36}, {12,22}, {30,33}, {25,38}, {12,13}, {1,33}, {5,14}, {2,14}, {18,29}, {7,12}, {4,32}, {13,16}, {28,31}, {9,18}, {7,20}, {19,22}, {35,39}, {10,14}, {2,31}, {19,30}, {8,21}, {22,34}, {26,30}, {12,38}, {33,36}, {22,33}, {15,26}, {14,16}, {28,33}, {9,17}, {23,32}, {16,28}, {3,29}, {6,7}, {21,24}, {20,29}, {27,35}, {6,32}, {12,14}, {2,33}, {7,18}, {16,29}, {4,31}, {13,18}, {31,36}, {18,25}, {8,11}, {7,34}, {22,26}, {2,39}, {5,34}, {14,18}, {2,12}, {9,39}, {10,38}, {11,24}, {29,32}, {4,9}, {13,24}, {20,23}, {19,28}, {15,27}, {26,36}, {12,39}, {13,26}, {1,37}, {22,32}, {16,30}, {22,35}, {14,27}, {15,18}, {3,12}, {20,24}, {4,35}, {10,20}, {19,31}, {8,35}, {3,5}, {24,26}, {29,37}, {1,10}, {8,19}, {21,23}, {22,36}, {25,30}, {4,14}, {10,37}, {31,35}, {5,15}, {3,14}, {17,25}, {13,25}, {1,39}, {3,30}, {6,8}, {21,22}, {20,30}, {4,16}, {2,6}, {21,31}, {18,20}, {23,25}, {28,39}, {6,13}, {4,17}, {19,32}, {16,21}, {9,36}, {4,36}, {10,22}, {30,31}, {5,8}, {14,25}, {36,37}, {25,28}, {2,5}, {7,19}, {4,34}, {5,9}, {18,21}, {32,35}, {16,27}, {6,18}, {4,18}, {22,25}, {30,39}, {5,13}, {1,14}, {21,30}, {8,20}, {3,28}, {6,9}, {6,16}, {27,30}, {8,38}, {15,23}, {30,37}, {19,24}, {21,29}, {9,21}, {36,38}, {25,36}, {11,13}, {1,32}, {8,39}, {13,22}, {11,20}, {10,23}, {27,29}, {10,19}, {27,38}, {31,34}, {34,37}, {23,36}, {11,22}, {30,32}, {12,15}, {7,36}, {25,39}, {8,37}, {14,22}, {2,30}, {18,27}, {7,16}, {23,31}, {18,28}, {6,33}, {2,11}, {35,38}, {27,36}, {17,21}, {16,26}, {16,25}, {10,39}, {15,22}, {17,26}, {11,37}, {27,37}, {3,32}, {2,4}, {18,19}, {1,12}, {26,35}, {5,32}, {7,10}, {4,33}, {13,17}, {28,32}, {9,16}, {19,23}, {8,16}, {4,15}, {17,19}, {25,37}, {8,12}, {23,33}, {5,35}, {1,11}, {21,33}, {17,20}, {11,19}, {4,7}, {9,34}, {8,10}, {17,27}, {3,39}, {12,19}, {9,12}, {33,35}, {29,38}, {23,34}, {6,34}, {17,28}, {15,24}, {24,33}, {8,34}, {4,13}, {1,13}, {21,28}, {9,20}, {5,18}, {1,29}, {12,24}, {29,33}, {33,34}, {7,38}, {20,28}, {5,16}, {9,19}, {7,17}, {2,32}, {17,30}, {5,7}, {6,31}, {20,31} } Symmetric graph 9 of order 39 Valency 24 Diameter 2 Girth 3 Automorphism group of order 37362124800 Number of arcs = 936 Number of 2-arcs = 21528 2-arc-transitive false Edge-set { {1,4}, {3,16}, {15,33}, {1,39}, {21,31}, {24,36}, {8,39}, {3,25}, {10,33}, {14,35}, {1,7}, {11,29}, {23,28}, {25,31}, {10,36}, {6,31}, {8,36}, {8,18}, {10,23}, {30,37}, {3,32}, {33,34}, {9,20}, {16,27}, {19,30}, {24,26}, {4,35}, {6,7}, {8,11}, {18,28}, {17,35}, {7,13}, {11,31}, {28,36}, {31,37}, {19,36}, {8,30}, {18,24}, {21,27}, {11,25}, {1,34}, {9,31}, {12,36}, {8,29}, {2,35}, {5,39}, {4,21}, {13,21}, {6,29}, {5,23}, {10,16}, {15,30}, {17,32}, {13,34}, {16,36}, {19,37}, {19,26}, {10,38}, {20,30}, {22,32}, {34,38}, {9,35}, {7,16}, {11,19}, {26,28}, {27,35}, {7,11}, {11,13}, {3,28}, {25,36}, {29,37}, {19,23}, {5,14}, {4,9}, {6,16}, {3,12}, {29,33}, {33,35}, {7,35}, {17,28}, {20,31}, {27,36}, {2,10}, {30,32}, {18,25}, {10,14}, {14,16}, {1,15}, {14,22}, {1,38}, {17,20}, {13,27}, {18,30}, {14,24}, {18,21}, {21,24}, {25,39}, {12,22}, {29,38}, {11,39}, {21,28}, {3,11}, {6,13}, {3,5}, {8,26}, {12,18}, {15,21}, {2,25}, {28,34}, {9,22}, {12,26}, {12,29}, {30,35}, {32,39}, {21,34}, {9,13}, {6,19}, {5,26}, {5,10}, {4,30}, {9,32}, {16,34}, {16,38}, {1,19}, {26,31}, {4,11}, {6,28}, {20,27}, {11,27}, {13,30}, {3,24}, {18,23}, {14,37}, {16,33}, {15,35}, {17,39}, {17,31}, {20,36}, {8,27}, {10,32}, {30,34}, {19,38}, {20,26}, {2,7}, {5,11}, {4,28}, {2,8}, {18,32}, {9,25}, {4,37}, {8,23}, {18,37}, {23,39}, {21,37}, {33,39}, {22,37}, {3,26}, {12,33}, {15,38}, {2,20}, {5,22}, {4,38}, {19,25}, {23,29}, {23,37}, {14,29}, {1,23}, {4,25}, {6,10}, {7,28}, {17,22}, {12,27}, {14,19}, {1,26}, {1,9}, {16,31}, {13,38}, {1,18}, {14,31}, {5,36}, {7,37}, {17,19}, {2,4}, {6,32}, {12,19}, {26,29}, {28,33}, {22,35}, {5,17}, {7,20}, {17,27}, {10,21}, {25,30}, {25,34}, {9,10}, {12,14}, {1,29}, {22,33}, {35,38}, {13,17}, {3,13}, {6,18}, {14,18}, {16,21}, {15,25}, {12,39}, {21,29}, {26,39}, {12,21}, {3,33}, {6,35}, {5,7}, {9,16}, {15,16}, {13,26}, {5,15}, {5,9}, {4,16}, {21,22}, {25,38}, {23,31}, {19,24}, {23,27}, {11,37}, {36,39}, {8,21}, {10,24}, {30,39}, {10,20}, {11,15}, {2,28}, {5,31}, {4,36}, {8,34}, {9,18}, {25,29}, {6,15}, {2,5}, {2,32}, {32,34}, {16,19}, {15,26}, {2,31}, {32,36}, {34,37}, {9,19}, {4,33}, {30,31}, {27,37}, {14,27}, {1,11}, {8,10}, {27,28}, {11,22}, {1,6}, {7,36}, {8,17}, {2,15}, {16,26}, {12,15}, {4,13}, {3,6}, {24,27}, {27,30}, {11,24}, {20,23}, {3,30}, {24,33}, {13,18}, {19,32}, {26,34}, {28,38}, {20,22}, {4,17}, {13,23}, {3,37}, {5,33}, {35,39}, {7,21}, {22,26}, {12,38}, {19,33}, {23,35}, {11,18}, {14,28}, {27,32}, {11,34}, {3,20}, {2,16}, {15,32}, {17,34}, {3,17}, {6,20}, {5,27}, {10,28}, {22,30}, {18,38}, {14,20}, {2,34}, {5,38}, {4,20}, {8,14}, {6,25}, {4,12}, {8,33}, {18,35}, {7,23}, {17,37}, {27,33}, {8,22}, {10,26}, {12,30}, {22,38}, {20,38}, {1,22}, {31,38}, {13,19}, {14,39}, {1,21}, {4,24}, {6,39}, {7,25}, {10,17}, {1,27}, {7,14}, {1,17}, {1,36}, {8,31}, {14,34}, {21,35}, {24,39}, {21,39}, {6,22}, {18,33}, {16,39}, {4,26}, {6,12}, {7,24}, {13,29}, {3,23}, {5,30}, {9,27}, {11,16}, {21,25}, {10,25}, {8,15}, {2,18}, {9,24}, {2,19}, {26,32}, {15,28}, {12,31}, {29,36}, {33,37}, {19,35}, {6,27}, {17,24}, {13,39}, {14,32}, {12,34}, {9,29}, {3,21}, {6,24}, {7,32}, {9,28}, {13,33}, {3,35}, {3,9}, {18,36}, {5,19}, {16,22}, {11,32}, {2,24}, {5,21}, {13,31}, {5,29}, {4,23}, {16,23}, {2,22}, {15,20}, {24,38}, {10,30}, {7,26}, {12,17}, {13,36}, {3,8}, {24,30}, {9,37}, {26,37}, {5,34}, {9,12}, {16,29}, {2,39}, {21,32}, {24,34}, {9,39}, {20,29}, {15,17}, {2,13}, {5,18}, {4,14}, {8,19}, {18,26}, {22,25}, {15,23}, {2,37}, {2,12}, {29,32}, {36,37}, {31,36}, {10,37}, {27,38}, {11,20}, {4,8}, {28,31}, {22,36}, {6,8}, {17,25}, {26,35}, {7,12}, {13,22}, {3,38}, {23,25}, {3,14}, {1,33}, {10,13}, {4,32}, {6,34}, {8,38}, {18,20}, {23,32}, {20,33}, {31,35}, {12,23}, {1,30}, {14,25}, {1,10}, {7,17}, {23,34}, {24,31}, {17,29}, {1,14}, {1,31}, {9,34}, {19,28}, {28,39}, {2,29}, {7,38}, {16,30}, {15,24}, {11,35}, {7,33}, {20,39}, {25,33}, {10,35}, {2,27}, {32,38}, {15,37}, {3,36}, {6,37}, {20,34}, {11,28}, {9,15}, {15,36}, {22,28}, {7,30}, {24,29}, {29,35} } Symmetric graph 10 of order 39 Valency 26 Diameter 2 Girth 3 Automorphism group of order 1448745832104550541033472000000 Number of arcs = 1014 Number of 2-arcs = 25350 2-arc-transitive false Edge-set { {1,14}, {23,37}, {22,29}, {12,38}, {7,34}, {3,35}, {6,32}, {11,23}, {10,22}, {12,21}, {7,17}, {4,18}, {6,24}, {21,38}, {19,34}, {18,35}, {24,32}, {14,27}, {21,39}, {26,31}, {14,28}, {1,27}, {11,37}, {10,36}, {4,31}, {1,28}, {9,29}, {2,27}, {13,37}, {8,30}, {10,29}, {9,22}, {7,19}, {5,24}, {8,19}, {3,26}, {13,23}, {6,16}, {11,20}, {9,15}, {12,25}, {2,25}, {3,18}, {26,35}, {16,32}, {22,36}, {20,28}, {15,36}, {25,38}, {17,30}, {17,34}, {24,33}, {19,36}, {16,30}, {23,33}, {15,33}, {18,31}, {7,30}, {4,35}, {6,33}, {5,32}, {13,39}, {5,30}, {11,33}, {2,39}, {12,39}, {8,28}, {4,36}, {5,38}, {9,33}, {8,34}, {5,31}, {3,31}, {2,21}, {4,26}, {8,14}, {1,20}, {13,17}, {9,16}, {2,20}, {5,21}, {13,15}, {2,14}, {10,25}, {4,19}, {5,26}, {1,16}, {8,16}, {10,15}, {3,20}, {8,17}, {20,27}, {15,37}, {19,30}, {25,29}, {23,39}, {17,39}, {26,33}, {16,27}, {20,39}, {20,37}, {25,31}, {15,29}, {18,28}, {26,38}, {20,35}, {22,27}, {25,27}, {24,30}, {18,36}, {25,39}, {11,39}, {9,36}, {12,31}, {2,38}, {3,28}, {13,34}, {2,29}, {8,35}, {9,27}, {13,36}, {7,36}, {3,33}, {6,30}, {10,31}, {1,30}, {11,35}, {7,39}, {9,32}, {11,28}, {2,28}, {4,34}, {13,33}, {13,19}, {5,16}, {3,23}, {11,15}, {10,18}, {12,17}, {6,15}, {7,15}, {4,25}, {11,26}, {5,17}, {4,22}, {8,18}, {9,24}, {3,24}, {9,23}, {2,22}, {7,21}, {13,21}, {6,26}, {10,19}, {13,20}, {12,26}, {5,25}, {25,36}, {17,38}, {16,33}, {18,34}, {21,31}, {24,31}, {14,29}, {14,30}, {22,31}, {21,30}, {19,28}, {19,35}, {16,29}, {26,32}, {15,34}, {16,28}, {17,32}, {16,34}, {15,32}, {21,37}, {17,37}, {14,35}, {24,38}, {17,36}, {23,35}, {20,33}, {4,28}, {5,33}, {1,29}, {8,27}, {10,34}, {3,37}, {8,32}, {6,29}, {9,37}, {3,32}, {2,37}, {10,38}, {4,38}, {6,27}, {1,35}, {12,30}, {10,27}, {1,39}, {10,33}, {12,27}, {6,31}, {7,37}, {12,29}, {4,29}, {1,32}, {5,39}, {7,38}, {8,36}, {10,26}, {8,20}, {6,22}, {9,25}, {12,24}, {7,18}, {1,25}, {6,14}, {7,16}, {6,17}, {1,18}, {12,20}, {11,24}, {1,19}, {9,14}, {7,23}, {2,23}, {11,18}, {13,22}, {5,18}, {8,24}, {11,14}, {3,14}, {12,22}, {6,23}, {3,19}, {1,22}, {2,16}, {11,21}, {4,15}, {18,30}, {24,35}, {15,39}, {14,32}, {26,28}, {23,28}, {22,34}, {22,33}, {24,37}, {21,27}, {24,29}, {14,39}, {23,34}, {23,36}, {21,32}, {22,38}, {26,37}, {21,34}, {20,38}, {19,31}, {25,35}, {20,31}, {25,28}, {19,29}, {18,29}, {23,32}, {14,34}, {18,38}, {22,32}, {15,27}, {19,37}, {26,30}, {9,34}, {2,31}, {7,32}, {13,30}, {6,37}, {10,35}, {13,38}, {12,32}, {5,35}, {7,28}, {11,27}, {6,28}, {13,29}, {12,34}, {5,34}, {1,37}, {11,32}, {7,35}, {12,37}, {11,36}, {3,38}, {4,33}, {8,39}, {3,36}, {13,28}, {6,38}, {3,34}, {1,34}, {10,37}, {11,31}, {6,35}, {9,30}, {12,36}, {2,35}, {12,16}, {3,15}, {1,21}, {2,17}, {7,14}, {4,24}, {11,17}, {1,23}, {4,20}, {10,21}, {9,19}, {13,24}, {10,14}, {3,25}, {12,23}, {10,16}, {7,22}, {6,21}, {4,21}, {12,14}, {5,19}, {1,17}, {8,26}, {2,15}, {13,25}, {4,17}, {10,17}, {1,24}, {12,18}, {10,23}, {7,24}, {8,21}, {4,14}, {9,26}, {5,23}, {7,20}, {14,33}, {23,27}, {17,31}, {22,37}, {20,29}, {21,29}, {19,32}, {19,39}, {23,38}, {26,36}, {18,27}, {16,38}, {25,32}, {17,28}, {18,37}, {18,33}, {14,38}, {24,27}, {22,35}, {14,37}, {19,27}, {23,29}, {16,36}, {22,39}, {15,30}, {17,33}, {26,39}, {24,39}, {22,28}, {23,31}, {24,34}, {21,28}, {25,37}, {26,29}, {16,35}, {20,34}, {21,36}, {5,37}, {8,29}, {11,38}, {3,39}, {12,35}, {6,36}, {3,27}, {1,38}, {2,36}, {11,34}, {4,30}, {9,31}, {1,33}, {10,39}, {7,31}, {8,31}, {11,29}, {9,28}, {4,32}, {7,29}, {9,38}, {6,34}, {5,27}, {13,32}, {2,30}, {5,29}, {13,35}, {2,32}, {10,32}, {8,38}, {12,28}, {13,27}, {7,33}, {3,30}, {4,27}, {6,25}, {11,19}, {13,18}, {4,23}, {5,14}, {9,18}, {11,22}, {5,15}, {12,19}, {2,26}, {3,16}, {8,22}, {2,18}, {3,21}, {8,15}, {6,19}, {13,26}, {1,26}, {3,22}, {11,16}, {10,24}, {9,20}, {6,20}, {7,25}, {1,15}, {6,18}, {11,25}, {13,14}, {9,17}, {5,22}, {24,28}, {19,38}, {25,34}, {26,34}, {16,37}, {16,31}, {21,35}, {20,30}, {14,36}, {15,35}, {15,31}, {17,27}, {25,30}, {24,36}, {17,35}, {23,30}, {18,32}, {21,33}, {22,30}, {14,31}, {19,33}, {17,29}, {16,39}, {20,32}, {10,28}, {1,36}, {12,33}, {10,30}, {7,27}, {8,33}, {4,37}, {9,39}, {2,33}, {5,28}, {4,39}, {2,34}, {1,31}, {8,37}, {9,35}, {3,29}, {5,36}, {6,39}, {8,23}, {2,24}, {9,21}, {8,25}, {7,26}, {13,16}, {5,20}, {10,20}, {2,19}, {12,15}, {4,16}, {3,17}, {15,38}, {15,28}, {26,27}, {25,33}, {20,36}, {18,39}, {11,30}, {13,31} } Symmetric graph 11 of order 39 Valency 36 Diameter 2 Girth 3 Automorphism group of order 81329213300067532800 Number of arcs = 1404 Number of 2-arcs = 49140 2-arc-transitive false Edge-set { {1,4}, {8,19}, {13,37}, {18,39}, {2,33}, {5,36}, {22,25}, {13,34}, {4,26}, {9,27}, {1,20}, {14,28}, {11,31}, {7,35}, {2,5}, {22,29}, {12,19}, {9,13}, {10,16}, {3,8}, {8,37}, {31,37}, {4,30}, {20,23}, {23,25}, {12,16}, {3,17}, {1,30}, {9,20}, {14,39}, {29,31}, {21,35}, {22,39}, {11,33}, {5,16}, {3,22}, {14,24}, {5,10}, {7,18}, {2,38}, {18,36}, {2,25}, {25,36}, {16,25}, {19,28}, {13,19}, {32,37}, {31,36}, {11,32}, {7,36}, {14,22}, {5,11}, {7,15}, {6,38}, {8,28}, {19,37}, {16,37}, {3,31}, {4,34}, {23,26}, {25,29}, {16,21}, {3,38}, {30,32}, {31,34}, {26,35}, {23,27}, {12,18}, {14,20}, {5,14}, {7,31}, {35,38}, {4,33}, {23,34}, {20,24}, {10,14}, {13,17}, {9,35}, {27,39}, {1,13}, {4,28}, {9,11}, {7,39}, {1,11}, {7,28}, {11,14}, {5,7}, {30,39}, {20,33}, {5,39}, {22,33}, {26,36}, {17,25}, {1,25}, {16,28}, {12,17}, {1,17}, {1,28}, {4,31}, {23,35}, {12,14}, {6,17}, {1,24}, {15,27}, {18,30}, {2,20}, {36,39}, {25,33}, {14,36}, {5,25}, {7,25}, {16,38}, {2,19}, {13,29}, {12,32}, {9,36}, {11,29}, {7,21}, {14,38}, {5,32}, {27,38}, {26,28}, {17,19}, {16,29}, {3,12}, {9,30}, {10,32}, {8,36}, {13,22}, {4,11}, {4,37}, {23,31}, {4,20}, {14,23}, {1,16}, {3,35}, {27,30}, {19,27}, {13,18}, {2,32}, {29,36}, {33,37}, {4,24}, {10,23}, {5,15}, {6,22}, {3,16}, {3,30}, {10,34}, {8,26}, {5,8}, {22,37}, {19,30}, {13,20}, {16,23}, {17,34}, {1,26}, {8,23}, {12,37}, {17,30}, {4,23}, {12,23}, {17,20}, {1,14}, {28,34}, {19,26}, {27,37}, {18,31}, {20,34}, {14,26}, {27,31}, {18,35}, {1,12}, {9,28}, {11,15}, {6,7}, {8,11}, {7,37}, {14,30}, {5,20}, {15,22}, {6,11}, {8,15}, {6,37}, {8,30}, {20,37}, {19,25}, {13,16}, {3,32}, {30,36}, {4,22}, {11,23}, {15,21}, {6,15}, {8,33}, {34,37}, {6,10}, {8,24}, {13,28}, {4,19}, {9,37}, {31,39}, {1,34}, {11,27}, {23,28}, {11,20}, {7,14}, {11,17}, {1,7}, {14,35}, {5,27}, {9,39}, {33,39}, {5,29}, {21,22}, {22,26}, {3,28}, {23,29}, {12,21}, {17,38}, {1,32}, {4,35}, {20,26}, {14,17}, {10,35}, {8,27}, {12,30}, {15,39}, {6,33}, {14,29}, {5,21}, {7,22}, {11,38}, {3,19}, {24,26}, {10,17}, {1,18}, {2,28}, {5,31}, {22,35}, {19,23}, {12,13}, {19,36}, {13,25}, {25,32}, {16,36}, {13,31}, {4,32}, {23,36}, {8,14}, {5,37}, {3,7}, {30,38}, {10,28}, {10,39}, {5,13}, {9,26}, {17,39}, {1,29}, {21,28}, {27,36}, {18,25}, {19,33}, {24,32}, {10,36}, {6,20}, {21,31}, {15,35}, {5,38}, {19,38}, {2,24}, {10,29}, {2,9}, {18,20}, {2,14}, {25,35}, {28,39}, {22,31}, {14,32}, {2,15}, {6,29}, {8,12}, {18,32}, {2,36}, {22,36}, {11,25}, {15,28}, {6,19}, {19,32}, {13,36}, {22,32}, {11,36}, {15,37}, {6,31}, {4,8}, {23,37}, {2,30}, {20,29}, {12,39}, {9,33}, {8,25}, {4,16}, {2,37}, {4,12}, {9,23}, {10,25}, {8,16}, {3,13}, {8,22}, {11,37}, {16,30}, {3,20}, {6,23}, {12,24}, {17,21}, {1,15}, {18,23}, {2,12}, {17,36}, {14,31}, {24,35}, {21,23}, {12,15}, {6,18}, {21,36}, {15,25}, {18,28}, {36,37}, {25,31}, {11,39}, {7,33}, {5,22}, {7,26}, {19,31}, {13,35}, {23,32}, {12,36}, {6,21}, {15,24}, {18,27}, {2,18}, {21,24}, {10,15}, {18,33}, {2,34}, {5,30}, {20,22}, {19,39}, {13,33}, {3,25}, {25,34}, {16,26}, {2,8}, {29,37}, {20,36}, {12,31}, {4,17}, {1,23}, {15,23}, {6,12}, {8,17}, {1,37}, {3,4}, {23,30}, {10,20}, {16,34}, {3,26}, {27,34}, {18,26}, {14,21}, {31,38}, {32,35}, {7,30}, {20,38}, {29,32}, {22,38}, {6,27}, {17,37}, {13,30}, {9,31}, {4,15}, {3,24}, {10,30}, {10,18}, {22,28}, {11,19}, {6,34}, {21,27}, {15,18}, {4,29}, {17,31}, {1,35}, {12,27}, {33,38}, {12,33}, {9,34}, {8,13}, {20,39}, {20,25}, {14,16}, {30,35}, {32,39}, {33,36}, {11,22}, {1,39}, {28,33}, {11,26}, {7,17}, {5,28}, {16,22}, {28,36}, {4,18}, {2,23}, {14,25}, {1,38}, {28,35}, {24,30}, {24,34}, {10,26}, {3,9}, {15,34}, {6,26}, {8,29}, {21,37}, {20,32}, {1,10}, {11,13}, {4,7}, {26,33}, {15,31}, {25,38}, {16,32}, {3,6}, {20,35}, {14,27}, {35,39}, {27,33}, {34,39}, {24,29}, {10,21}, {9,16}, {3,39}, {4,9}, {23,39}, {3,11}, {30,34}, {16,35}, {17,23}, {6,9}, {24,39}, {21,29}, {18,22}, {2,11}, {13,26}, {1,9}, {1,31}, {7,12}, {6,30}, {21,39}, {15,33}, {26,39}, {17,33}, {1,5}, {26,31}, {17,35}, {12,28}, {6,36}, {24,25}, {21,25}, {15,16}, {18,19}, {2,13}, {32,36}, {22,34}, {16,27}, {3,18}, {11,18}, {2,7}, {14,19}, {25,39}, {19,22}, {3,36}, {11,24}, {7,10}, {14,18}, {2,35}, {12,25}, {5,19}, {21,32}, {15,36}, {11,34}, {15,38}, {6,32}, {6,8}, {24,37}, {13,32}, {4,36}, {9,22}, {6,28}, {4,25}, {3,33}, {32,38}, {13,21}, {28,32}, {7,24}, {1,36}, {25,28}, {7,16}, {12,26}, {17,27}, {20,31}, {16,33}, {3,5}, {22,30}, {26,32}, {1,22}, {11,28}, {21,38}, {15,32}, {10,13}, {4,39}, {32,34}, {6,24}, {10,24}, {13,27}, {29,39}, {20,28}, {31,35}, {7,11}, {7,38}, {7,29}, {5,9}, {9,18}, {2,39}, {28,31}, {11,16}, {15,19}, {6,13}, {8,32}, {24,36}, {2,6}, {25,37}, {7,19}, {13,38}, {10,31}, {9,38}, {2,10}, {4,38}, {17,28}, {1,19}, {35,37}, {26,29}, {27,35}, {6,25}, {13,24}, {34,38}, {24,28}, {10,19}, {4,10}, {30,31}, {2,21}, {15,29}, {10,38}, {19,29}, {6,16}, {30,37}, {10,22}, {22,27}, {2,16}, {3,29}, {5,18}, {2,22}, {4,14}, {5,23}, {26,34}, {17,26}, {1,27}, {12,35}, {8,34}, {26,37}, {9,12}, {15,17}, {1,6}, {20,30}, {5,35}, {4,13}, {9,32}, {7,23}, {8,35}, {19,34}, {29,34}, {9,10}, {9,15}, {18,29}, {36,38}, {10,37}, {12,22}, {16,24}, {11,35}, {7,27}, {5,17}, {3,37}, {3,34}, {26,30}, {10,27}, {8,18}, {29,33}, {21,34}, {24,38}, {7,34}, {26,38}, {16,19}, {12,38}, {3,14}, {3,15}, {33,34}, {29,38}, {5,12}, {17,22}, {18,24}, {12,34}, {8,20}, {14,37}, {1,21}, {7,32}, {6,14}, {5,24}, {13,39}, {2,31}, {29,35}, {7,13}, {13,23}, {9,17}, {23,33}, {33,35}, {28,38}, {17,24}, {14,33}, {17,32}, {12,29}, {6,35}, {24,27}, {21,26}, {18,21}, {5,26}, {16,31}, {21,30}, {15,20}, {18,38}, {1,8}, {28,37}, {11,30}, {7,20}, {19,35}, {8,31}, {12,20}, {27,32}, {2,26}, {17,29}, {21,33}, {24,33}, {16,20}, {25,30}, {6,39}, {2,17}, {1,33}, {9,21}, {3,27}, {9,24}, {15,30}, {8,39}, {3,10}, {11,21}, {5,33}, {27,29}, {30,33}, {10,33}, {19,24}, {24,31}, {9,14}, {9,29}, {8,10}, {2,29}, {9,25}, {8,21}, {4,21}, {27,28}, {5,34}, {3,23}, {9,19}, {2,4}, {23,38}, {2,27}, {18,37}, {8,38}, {14,34}, {16,39}, {20,27}, {4,27}, {15,26}, {3,21}, {18,34} } Symmetric graph 12 of order 39 Valency 38 Diameter 1 Girth 3 Automorphism group of order 20397882081197443358640281739902897356800000000 Number of arcs = 1482 Number of 2-arcs = 54834 2-arc-transitive true Edge-set { {1,2}, {2,3}, {2,4}, {1,3}, {2,5}, {3,4}, {1,4}, {2,6}, {3,5}, {4,5}, {1,5}, {2,7}, {3,6}, {4,6}, {5,6}, {1,6}, {2,8}, {3,7}, {4,7}, {5,7}, {6,7}, {1,7}, {2,9}, {3,8}, {4,8}, {5,8}, {6,8}, {7,8}, {1,8}, {2,10}, {3,9}, {4,9}, {5,9}, {6,9}, {7,9}, {8,9}, {1,9}, {2,11}, {3,10}, {4,10}, {5,10}, {6,10}, {7,10}, {8,10}, {9,10}, {1,10}, {2,12}, {3,11}, {4,11}, {5,11}, {6,11}, {7,11}, {8,11}, {9,11}, {10,11}, {1,11}, {2,13}, {3,12}, {4,12}, {5,12}, {6,12}, {7,12}, {8,12}, {9,12}, {10,12}, {11,12}, {1,12}, {2,14}, {3,13}, {4,13}, {5,13}, {6,13}, {7,13}, {8,13}, {9,13}, {10,13}, {11,13}, {12,13}, {1,13}, {2,15}, {3,14}, {4,14}, {5,14}, {6,14}, {7,14}, {8,14}, {9,14}, {10,14}, {11,14}, {12,14}, {13,14}, {1,14}, {2,16}, {3,15}, {4,15}, {5,15}, {6,15}, {7,15}, {8,15}, {9,15}, {10,15}, {11,15}, {12,15}, {13,15}, {14,15}, {1,15}, {2,17}, {3,16}, {4,16}, {5,16}, {6,16}, {7,16}, {8,16}, {9,16}, {10,16}, {11,16}, {12,16}, {13,16}, {14,16}, {15,16}, {1,16}, {2,18}, {3,17}, {4,17}, {5,17}, {6,17}, {7,17}, {8,17}, {9,17}, {10,17}, {11,17}, {12,17}, {13,17}, {14,17}, {15,17}, {16,17}, {1,17}, {2,19}, {3,18}, {4,18}, {5,18}, {6,18}, {7,18}, {8,18}, {9,18}, {10,18}, {11,18}, {12,18}, {13,18}, {14,18}, {15,18}, {16,18}, {17,18}, {1,18}, {2,20}, {3,19}, {4,19}, {5,19}, {6,19}, {7,19}, {8,19}, {9,19}, {10,19}, {11,19}, {12,19}, {13,19}, {14,19}, {15,19}, {16,19}, {17,19}, {18,19}, {1,19}, {2,21}, {3,20}, {4,20}, {5,20}, {6,20}, {7,20}, {8,20}, {9,20}, {10,20}, {11,20}, {12,20}, {13,20}, {14,20}, {15,20}, {16,20}, {17,20}, {18,20}, {19,20}, {1,20}, {2,22}, {3,21}, {4,21}, {5,21}, {6,21}, {7,21}, {8,21}, {9,21}, {10,21}, {11,21}, {12,21}, {13,21}, {14,21}, {15,21}, {16,21}, {17,21}, {18,21}, {19,21}, {20,21}, {1,21}, {2,23}, {3,22}, {4,22}, {5,22}, {6,22}, {7,22}, {8,22}, {9,22}, {10,22}, {11,22}, {12,22}, {13,22}, {14,22}, {15,22}, {16,22}, {17,22}, {18,22}, {19,22}, {20,22}, {21,22}, {1,22}, {2,24}, {3,23}, {4,23}, {5,23}, {6,23}, {7,23}, {8,23}, {9,23}, {10,23}, {11,23}, {12,23}, {13,23}, {14,23}, {15,23}, {16,23}, {17,23}, {18,23}, {19,23}, {20,23}, {21,23}, {22,23}, {1,23}, {2,25}, {3,24}, {4,24}, {5,24}, {6,24}, {7,24}, {8,24}, {9,24}, {10,24}, {11,24}, {12,24}, {13,24}, {14,24}, {15,24}, {16,24}, {17,24}, {18,24}, {19,24}, {20,24}, {21,24}, {22,24}, {23,24}, {1,24}, {2,26}, {3,25}, {4,25}, {5,25}, {6,25}, {7,25}, {8,25}, {9,25}, {10,25}, {11,25}, {12,25}, {13,25}, {14,25}, {15,25}, {16,25}, {17,25}, {18,25}, {19,25}, {20,25}, {21,25}, {22,25}, {23,25}, {24,25}, {1,25}, {2,27}, {3,26}, {4,26}, {5,26}, {6,26}, {7,26}, {8,26}, {9,26}, {10,26}, {11,26}, {12,26}, {13,26}, {14,26}, {15,26}, {16,26}, {17,26}, {18,26}, {19,26}, {20,26}, {21,26}, {22,26}, {23,26}, {24,26}, {25,26}, {1,26}, {2,28}, {3,27}, {4,27}, {5,27}, {6,27}, {7,27}, {8,27}, {9,27}, {10,27}, {11,27}, {12,27}, {13,27}, {14,27}, {15,27}, {16,27}, {17,27}, {18,27}, {19,27}, {20,27}, {21,27}, {22,27}, {23,27}, {24,27}, {25,27}, {26,27}, {1,27}, {2,29}, {3,28}, {4,28}, {5,28}, {6,28}, {7,28}, {8,28}, {9,28}, {10,28}, {11,28}, {12,28}, {13,28}, {14,28}, {15,28}, {16,28}, {17,28}, {18,28}, {19,28}, {20,28}, {21,28}, {22,28}, {23,28}, {24,28}, {25,28}, {26,28}, {27,28}, {1,28}, {2,30}, {3,29}, {4,29}, {5,29}, {6,29}, {7,29}, {8,29}, {9,29}, {10,29}, {11,29}, {12,29}, {13,29}, {14,29}, {15,29}, {16,29}, {17,29}, {18,29}, {19,29}, {20,29}, {21,29}, {22,29}, {23,29}, {24,29}, {25,29}, {26,29}, {27,29}, {28,29}, {1,29}, {2,31}, {3,30}, {4,30}, {5,30}, {6,30}, {7,30}, {8,30}, {9,30}, {10,30}, {11,30}, {12,30}, {13,30}, {14,30}, {15,30}, {16,30}, {17,30}, {18,30}, {19,30}, {20,30}, {21,30}, {22,30}, {23,30}, {24,30}, {25,30}, {26,30}, {27,30}, {28,30}, {29,30}, {1,30}, {2,32}, {3,31}, {4,31}, {5,31}, {6,31}, {7,31}, {8,31}, {9,31}, {10,31}, {11,31}, {12,31}, {13,31}, {14,31}, {15,31}, {16,31}, {17,31}, {18,31}, {19,31}, {20,31}, {21,31}, {22,31}, {23,31}, {24,31}, {25,31}, {26,31}, {27,31}, {28,31}, {29,31}, {30,31}, {1,31}, {2,33}, {3,32}, {4,32}, {5,32}, {6,32}, {7,32}, {8,32}, {9,32}, {10,32}, {11,32}, {12,32}, {13,32}, {14,32}, {15,32}, {16,32}, {17,32}, {18,32}, {19,32}, {20,32}, {21,32}, {22,32}, {23,32}, {24,32}, {25,32}, {26,32}, {27,32}, {28,32}, {29,32}, {30,32}, {31,32}, {1,32}, {2,34}, {3,33}, {4,33}, {5,33}, {6,33}, {7,33}, {8,33}, {9,33}, {10,33}, {11,33}, {12,33}, {13,33}, {14,33}, {15,33}, {16,33}, {17,33}, {18,33}, {19,33}, {20,33}, {21,33}, {22,33}, {23,33}, {24,33}, {25,33}, {26,33}, {27,33}, {28,33}, {29,33}, {30,33}, {31,33}, {32,33}, {1,33}, {2,35}, {3,34}, {4,34}, {5,34}, {6,34}, {7,34}, {8,34}, {9,34}, {10,34}, {11,34}, {12,34}, {13,34}, {14,34}, {15,34}, {16,34}, {17,34}, {18,34}, {19,34}, {20,34}, {21,34}, {22,34}, {23,34}, {24,34}, {25,34}, {26,34}, {27,34}, {28,34}, {29,34}, {30,34}, {31,34}, {32,34}, {33,34}, {1,34}, {2,36}, {3,35}, {4,35}, {5,35}, {6,35}, {7,35}, {8,35}, {9,35}, {10,35}, {11,35}, {12,35}, {13,35}, {14,35}, {15,35}, {16,35}, {17,35}, {18,35}, {19,35}, {20,35}, {21,35}, {22,35}, {23,35}, {24,35}, {25,35}, {26,35}, {27,35}, {28,35}, {29,35}, {30,35}, {31,35}, {32,35}, {33,35}, {34,35}, {1,35}, {2,37}, {3,36}, {4,36}, {5,36}, {6,36}, {7,36}, {8,36}, {9,36}, {10,36}, {11,36}, {12,36}, {13,36}, {14,36}, {15,36}, {16,36}, {17,36}, {18,36}, {19,36}, {20,36}, {21,36}, {22,36}, {23,36}, {24,36}, {25,36}, {26,36}, {27,36}, {28,36}, {29,36}, {30,36}, {31,36}, {32,36}, {33,36}, {34,36}, {35,36}, {1,36}, {2,38}, {3,37}, {4,37}, {5,37}, {6,37}, {7,37}, {8,37}, {9,37}, {10,37}, {11,37}, {12,37}, {13,37}, {14,37}, {15,37}, {16,37}, {17,37}, {18,37}, {19,37}, {20,37}, {21,37}, {22,37}, {23,37}, {24,37}, {25,37}, {26,37}, {27,37}, {28,37}, {29,37}, {30,37}, {31,37}, {32,37}, {33,37}, {34,37}, {35,37}, {36,37}, {1,37}, {2,39}, {3,38}, {4,38}, {5,38}, {6,38}, {7,38}, {8,38}, {9,38}, {10,38}, {11,38}, {12,38}, {13,38}, {14,38}, {15,38}, {16,38}, {17,38}, {18,38}, {19,38}, {20,38}, {21,38}, {22,38}, {23,38}, {24,38}, {25,38}, {26,38}, {27,38}, {28,38}, {29,38}, {30,38}, {31,38}, {32,38}, {33,38}, {34,38}, {35,38}, {36,38}, {37,38}, {1,38}, {3,39}, {4,39}, {5,39}, {6,39}, {7,39}, {8,39}, {9,39}, {10,39}, {11,39}, {12,39}, {13,39}, {14,39}, {15,39}, {16,39}, {17,39}, {18,39}, {19,39}, {20,39}, {21,39}, {22,39}, {23,39}, {24,39}, {25,39}, {26,39}, {27,39}, {28,39}, {29,39}, {30,39}, {31,39}, {32,39}, {33,39}, {34,39}, {35,39}, {36,39}, {37,39}, {38,39}, {1,39} } ................................................................... Symmetric connected graphs of order 40 Symmetric graph 1 of order 40 Valency 2 Diameter 20 Girth 40 Automorphism group of order 80 Number of arcs = 80 Number of 2-arcs = 80 2-arc-transitive true Edge-set { {1,5}, {5,12}, {12,14}, {14,17}, {17,21}, {21,25}, {25,29}, {29,35}, {35,37}, {4,37}, {4,7}, {7,10}, {10,15}, {15,20}, {20,23}, {23,28}, {28,32}, {32,33}, {33,40}, {2,40}, {2,6}, {6,11}, {11,13}, {13,18}, {18,22}, {22,26}, {26,30}, {30,36}, {36,38}, {3,38}, {3,8}, {8,9}, {9,16}, {16,19}, {19,24}, {24,27}, {27,31}, {31,34}, {34,39}, {1,39} } Symmetric graph 2 of order 40 Valency 3 Diameter 6 Girth 8 Automorphism group of order 480 Number of arcs = 120 Number of 2-arcs = 240 2-arc-transitive true Edge-set { {1,9}, {1,21}, {5,27}, {21,38}, {27,34}, {16,30}, {15,40}, {20,38}, {3,34}, {6,30}, {18,40}, {25,36}, {10,30}, {18,26}, {10,20}, {3,24}, {6,24}, {15,36}, {11,18}, {8,31}, {19,37}, {2,36}, {11,32}, {2,10}, {24,40}, {26,35}, {16,35}, {8,26}, {9,19}, {4,11}, {7,21}, {14,34}, {13,31}, {4,23}, {8,22}, {19,28}, {4,33}, {7,32}, {2,22}, {6,28}, {1,35}, {7,25}, {14,32}, {13,38}, {5,23}, {12,31}, {23,39}, {14,37}, {13,33}, {9,29}, {17,25}, {22,37}, {28,33}, {15,29}, {16,39}, {20,27}, {3,12}, {17,39}, {12,17}, {5,29} } Symmetric graph 3 of order 40 Valency 4 Diameter 5 Girth 4 Automorphism group of order 160 Number of arcs = 160 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,5}, {25,32}, {32,33}, {3,8}, {6,10}, {3,38}, {2,6}, {27,30}, {30,35}, {22,26}, {26,31}, {35,40}, {31,34}, {7,12}, {2,39}, {4,7}, {9,15}, {5,9}, {33,39}, {4,37}, {24,28}, {28,29}, {34,38}, {29,36}, {17,21}, {21,25}, {2,38}, {36,39}, {11,13}, {8,11}, {35,37}, {1,40}, {16,20}, {10,16}, {31,35}, {34,40}, {19,23}, {23,27}, {4,39}, {33,37}, {15,18}, {18,22}, {4,5}, {1,37}, {14,17}, {12,14}, {29,34}, {36,38}, {19,21}, {15,19}, {25,29}, {32,36}, {13,20}, {20,24}, {1,8}, {3,40}, {11,16}, {16,17}, {8,10}, {3,6}, {18,23}, {13,18}, {27,32}, {30,33}, {22,27}, {20,22}, {26,30}, {10,14}, {14,19}, {6,12}, {2,7}, {12,15}, {7,9}, {24,26}, {17,24}, {28,31}, {21,28}, {9,13}, {5,11}, {23,25} } Symmetric graph 4 of order 40 Valency 4 Diameter 5 Girth 4 Automorphism group of order 160 Number of arcs = 160 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,5}, {16,19}, {36,39}, {27,32}, {24,27}, {7,10}, {3,8}, {3,37}, {10,14}, {33,37}, {14,18}, {17,21}, {30,34}, {12,14}, {2,37}, {21,26}, {26,30}, {5,12}, {2,6}, {29,35}, {20,22}, {23,26}, {26,31}, {12,15}, {2,40}, {35,40}, {15,20}, {19,23}, {31,36}, {1,8}, {7,11}, {34,40}, {15,17}, {4,40}, {9,15}, {23,28}, {28,31}, {8,9}, {4,7}, {32,34}, {17,24}, {16,18}, {33,39}, {6,9}, {4,5}, {28,29}, {22,28}, {9,13}, {4,38}, {34,38}, {13,17}, {18,22}, {29,33}, {3,6}, {5,10}, {27,30}, {21,27}, {13,19}, {36,38}, {1,38}, {11,13}, {22,25}, {25,29}, {6,11}, {30,36}, {19,21}, {14,20}, {35,37}, {25,32}, {24,25}, {11,16}, {1,39}, {20,24}, {32,35}, {2,7}, {8,12}, {3,39}, {10,16}, {31,33}, {18,23} } Symmetric graph 5 of order 40 Valency 4 Diameter 4 Girth 6 Automorphism group of order 160 Number of arcs = 160 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,5}, {24,33}, {18,22}, {3,40}, {12,39}, {1,30}, {35,38}, {11,21}, {15,20}, {5,12}, {16,27}, {24,26}, {6,18}, {10,38}, {9,14}, {2,6}, {28,37}, {17,32}, {30,34}, {5,33}, {22,27}, {13,18}, {2,29}, {3,15}, {4,39}, {21,35}, {7,10}, {14,25}, {8,19}, {26,32}, {23,34}, {17,21}, {1,13}, {28,29}, {7,36}, {26,39}, {6,11}, {33,40}, {12,22}, {2,38}, {20,30}, {31,35}, {23,25}, {5,17}, {16,19}, {9,37}, {3,32}, {15,28}, {4,7}, {11,40}, {36,37}, {20,24}, {18,31}, {10,23}, {12,15}, {4,16}, {6,34}, {21,28}, {27,38}, {14,17}, {8,9}, {29,33}, {22,36}, {13,26}, {7,20}, {19,23}, {10,13}, {34,39}, {27,30}, {8,35}, {25,40}, {19,29}, {2,14}, {1,37}, {32,36}, {4,31}, {25,31}, {11,16}, {9,24}, {3,8} } Symmetric graph 6 of order 40 Valency 4 Diameter 4 Girth 6 Automorphism group of order 160 Number of arcs = 160 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,5}, {25,39}, {21,36}, {7,9}, {10,14}, {17,21}, {3,39}, {16,28}, {5,34}, {3,15}, {6,17}, {17,31}, {3,31}, {9,37}, {10,23}, {2,6}, {15,19}, {24,25}, {36,38}, {1,37}, {20,23}, {26,31}, {31,35}, {35,37}, {23,26}, {11,16}, {5,12}, {26,40}, {22,35}, {1,30}, {20,30}, {7,20}, {1,14}, {12,21}, {11,39}, {19,29}, {2,29}, {8,35}, {13,26}, {11,22}, {12,40}, {8,19}, {2,13}, {14,25}, {7,36}, {8,10}, {9,13}, {18,22}, {4,40}, {34,39}, {21,28}, {29,34}, {28,29}, {14,17}, {3,7}, {30,33}, {27,30}, {33,40}, {22,27}, {4,8}, {13,18}, {15,27}, {6,33}, {4,16}, {5,18}, {18,32}, {4,32}, {10,38}, {9,24}, {24,33}, {27,38}, {28,37}, {23,34}, {16,20}, {2,38}, {19,24}, {25,32}, {32,36}, {12,15}, {6,11} } Symmetric graph 7 of order 40 Valency 4 Diameter 6 Girth 4 Automorphism group of order 160 Number of arcs = 160 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,5}, {12,39}, {11,22}, {21,27}, {34,40}, {17,22}, {4,39}, {18,31}, {3,31}, {15,28}, {5,33}, {6,17}, {4,16}, {27,38}, {24,34}, {15,20}, {1,37}, {20,23}, {32,36}, {25,32}, {12,16}, {6,11}, {35,38}, {24,26}, {26,31}, {31,35}, {7,36}, {13,25}, {25,39}, {22,36}, {7,19}, {2,13}, {2,29}, {19,29}, {21,35}, {26,40}, {14,26}, {8,35}, {20,30}, {1,30}, {1,14}, {8,20}, {9,13}, {7,10}, {29,34}, {27,29}, {13,17}, {4,7}, {8,9}, {10,14}, {3,40}, {18,21}, {3,8}, {14,18}, {28,30}, {30,33}, {33,39}, {22,28}, {9,23}, {10,37}, {3,15}, {5,18}, {6,34}, {16,27}, {9,38}, {10,24}, {23,33}, {28,37}, {4,32}, {17,32}, {19,24}, {2,38}, {23,25}, {36,37}, {5,12}, {11,15}, {16,19}, {2,6}, {12,21}, {11,40} } Symmetric graph 8 of order 40 Valency 4 Diameter 5 Girth 4 Automorphism group of order 320 Number of arcs = 160 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,5}, {7,9}, {8,23}, {11,36}, {6,32}, {12,26}, {33,38}, {30,33}, {10,13}, {29,34}, {27,29}, {3,40}, {36,38}, {16,40}, {19,35}, {16,31}, {15,39}, {12,35}, {15,32}, {22,40}, {3,38}, {1,18}, {13,40}, {21,37}, {19,34}, {14,18}, {2,17}, {14,39}, {34,37}, {13,17}, {9,14}, {1,28}, {3,5}, {22,38}, {7,24}, {18,23}, {1,19}, {4,27}, {4,37}, {21,39}, {20,24}, {15,18}, {17,24}, {2,20}, {4,39}, {35,37}, {19,23}, {16,17}, {20,36}, {7,31}, {23,25}, {5,9}, {8,22}, {3,28}, {11,25}, {2,6}, {24,26}, {7,21}, {21,26}, {4,6}, {2,27}, {22,25}, {20,33}, {11,14}, {6,10}, {26,30}, {9,36}, {8,32}, {12,28}, {5,31}, {28,30}, {8,10}, {25,29}, {11,27}, {15,30}, {10,35}, {16,29}, {32,33}, {12,13}, {31,34} } Symmetric graph 9 of order 40 Valency 4 Diameter 5 Girth 4 Automorphism group of order 20480 Number of arcs = 160 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,5}, {1,19}, {7,21}, {19,36}, {21,39}, {4,39}, {9,36}, {16,39}, {16,17}, {19,24}, {6,9}, {16,31}, {16,30}, {30,34}, {36,38}, {2,6}, {8,31}, {27,30}, {25,30}, {11,36}, {11,25}, {11,13}, {9,13}, {2,20}, {8,22}, {3,27}, {23,25}, {22,25}, {11,27}, {8,9}, {6,31}, {31,34}, {20,35}, {22,40}, {3,40}, {18,23}, {22,37}, {2,27}, {8,23}, {3,6}, {10,35}, {15,40}, {15,18}, {20,23}, {33,37}, {3,37}, {14,40}, {2,18}, {5,10}, {15,32}, {15,29}, {29,33}, {35,37}, {12,14}, {14,18}, {20,33}, {7,32}, {28,29}, {26,29}, {12,35}, {12,26}, {10,14}, {32,33}, {4,28}, {24,26}, {21,26}, {12,28}, {7,10}, {5,32}, {17,24}, {21,38}, {1,28}, {7,24}, {4,5}, {34,38}, {4,38}, {13,39}, {1,17}, {13,17}, {19,34} } Symmetric graph 10 of order 40 Valency 4 Diameter 10 Girth 4 Automorphism group of order 41943040 Number of arcs = 160 Number of 2-arcs = 480 2-arc-transitive false Edge-set { {1,5}, {21,26}, {14,17}, {3,7}, {35,38}, {36,37}, {25,29}, {23,28}, {15,19}, {16,20}, {8,9}, {7,10}, {4,37}, {2,6}, {34,39}, {33,40}, {27,32}, {28,31}, {20,23}, {19,24}, {10,16}, {22,25}, {13,18}, {5,11}, {6,12}, {1,40}, {2,39}, {31,34}, {32,33}, {24,28}, {4,8}, {26,30}, {17,22}, {18,21}, {12,14}, {11,13}, {2,5}, {1,6}, {33,39}, {24,27}, {3,38}, {29,36}, {30,35}, {21,25}, {22,26}, {13,17}, {14,18}, {6,11}, {9,15}, {4,7}, {3,8}, {35,37}, {36,38}, {26,29}, {25,30}, {18,22}, {23,27}, {16,19}, {15,20}, {8,10}, {7,9}, {4,38}, {3,37}, {30,36}, {34,40}, {28,32}, {27,31}, {20,24}, {19,23}, {9,16}, {10,15}, {5,12}, {1,39}, {2,40}, {31,33}, {32,34}, {17,21}, {11,14}, {12,13}, {29,35} } Symmetric graph 11 of order 40 Valency 6 Diameter 4 Girth 4 Automorphism group of order 240 Number of arcs = 240 Number of 2-arcs = 1200 2-arc-transitive false Edge-set { {1,11}, {24,27}, {3,14}, {4,37}, {24,30}, {19,25}, {5,9}, {10,20}, {6,33}, {1,37}, {24,26}, {8,36}, {22,28}, {18,32}, {31,35}, {12,21}, {16,17}, {2,35}, {10,24}, {3,33}, {7,37}, {8,38}, {17,29}, {5,39}, {20,32}, {6,11}, {31,37}, {28,34}, {13,18}, {29,40}, {16,19}, {11,23}, {12,24}, {5,35}, {10,22}, {7,33}, {9,21}, {8,34}, {2,40}, {1,39}, {21,32}, {17,27}, {2,14}, {6,10}, {31,33}, {3,15}, {29,36}, {26,39}, {25,40}, {16,22}, {27,38}, {14,23}, {28,37}, {13,24}, {11,18}, {12,17}, {7,35}, {32,34}, {15,21}, {4,40}, {3,39}, {5,34}, {19,30}, {23,25}, {4,9}, {17,31}, {2,12}, {6,16}, {5,15}, {25,38}, {7,13}, {27,39}, {8,14}, {28,40}, {29,33}, {30,34}, {9,23}, {3,10}, {26,37}, {14,20}, {13,19}, {11,22}, {32,36}, {15,18}, {6,40}, {1,36}, {22,26}, {23,28}, {19,31}, {4,13}, {2,16}, {18,30}, {1,15}, {8,9}, {7,10}, {30,39}, {21,25}, {25,35}, {26,36}, {32,38}, {5,12}, {27,33}, {14,17}, {15,20}, {3,38}, {23,29}, {6,36}, {22,31}, {20,26}, {4,16}, {8,11}, {7,12}, {1,13}, {18,28}, {30,35}, {9,19}, {2,38}, {21,27}, {20,29}, {4,34} } Symmetric graph 12 of order 40 Valency 6 Diameter 5 Girth 4 Automorphism group of order 480 Number of arcs = 240 Number of 2-arcs = 1200 2-arc-transitive false Edge-set { {1,11}, {23,30}, {6,33}, {4,34}, {12,23}, {15,20}, {25,39}, {16,21}, {26,37}, {29,34}, {5,12}, {4,14}, {7,10}, {18,28}, {25,35}, {3,16}, {8,11}, {17,32}, {24,26}, {19,29}, {5,40}, {21,27}, {7,37}, {2,36}, {10,22}, {7,14}, {18,30}, {22,25}, {3,38}, {6,35}, {1,39}, {9,19}, {8,33}, {11,17}, {13,24}, {27,40}, {32,36}, {2,15}, {17,27}, {7,36}, {4,40}, {10,23}, {15,18}, {12,22}, {31,38}, {14,20}, {30,39}, {28,33}, {1,13}, {6,9}, {6,39}, {9,21}, {13,17}, {29,36}, {27,37}, {32,34}, {2,12}, {26,40}, {4,10}, {5,15}, {20,31}, {23,28}, {10,20}, {28,39}, {31,35}, {1,16}, {8,9}, {3,13}, {24,29}, {6,11}, {21,32}, {19,26}, {5,34}, {2,37}, {32,37}, {2,14}, {5,10}, {22,28}, {20,30}, {23,25}, {3,33}, {18,31}, {1,35}, {8,38}, {11,24}, {16,19}, {19,32}, {24,27}, {7,34}, {2,40}, {5,36}, {15,22}, {4,37}, {14,23}, {12,18}, {25,38}, {30,33}, {1,38}, {13,19}, {11,21}, {16,17}, {26,36}, {9,24}, {27,34}, {29,40}, {4,15}, {7,12}, {31,33}, {28,38}, {8,13}, {30,35}, {6,16}, {3,9}, {17,29}, {21,26}, {20,25}, {22,31}, {8,35}, {3,39}, {14,18} } Symmetric graph 13 of order 40 Valency 6 Diameter 4 Girth 3 Automorphism group of order 480 Number of arcs = 240 Number of 2-arcs = 1200 2-arc-transitive false Edge-set { {1,7}, {19,34}, {27,38}, {30,39}, {2,16}, {6,15}, {10,36}, {8,12}, {20,21}, {31,37}, {22,35}, {25,32}, {10,37}, {14,22}, {12,33}, {23,28}, {28,29}, {1,19}, {3,5}, {6,9}, {13,20}, {4,14}, {5,34}, {5,10}, {9,22}, {24,27}, {20,29}, {12,40}, {15,23}, {16,26}, {17,35}, {7,35}, {19,30}, {2,38}, {18,36}, {26,39}, {9,35}, {21,25}, {23,29}, {1,30}, {17,24}, {29,40}, {36,39}, {22,26}, {9,27}, {15,25}, {2,29}, {11,23}, {17,32}, {13,21}, {31,33}, {32,38}, {3,13}, {34,38}, {13,27}, {2,8}, {6,20}, {7,13}, {9,38}, {14,28}, {2,26}, {7,17}, {8,38}, {3,18}, {7,11}, {7,37}, {12,14}, {20,33}, {9,15}, {21,36}, {32,34}, {2,20}, {11,26}, {4,32}, {3,40}, {4,6}, {18,23}, {6,39}, {10,16}, {30,36}, {28,37}, {29,35}, {1,25}, {23,34}, {27,30}, {10,21}, {16,24}, {33,37}, {3,27}, {6,33}, {10,28}, {18,31}, {4,39}, {11,34}, {12,24}, {1,15}, {21,32}, {14,19}, {5,16}, {1,37}, {11,13}, {24,33}, {4,17}, {5,40}, {8,18}, {11,39}, {25,40}, {26,31}, {12,25}, {22,31}, {8,14}, {16,17}, {8,36}, {19,22}, {15,18}, {35,40}, {3,31}, {4,28}, {5,19}, {24,30} } Symmetric graph 14 of order 40 Valency 6 Diameter 3 Girth 5 Automorphism group of order 480 Number of arcs = 240 Number of 2-arcs = 1200 2-arc-transitive false Edge-set { {1,8}, {19,33}, {28,38}, {30,40}, {2,15}, {6,16}, {10,35}, {8,11}, {20,22}, {32,37}, {21,35}, {25,31}, {10,38}, {13,22}, {11,33}, {24,28}, {27,29}, {1,20}, {4,5}, {5,9}, {13,19}, {3,14}, {6,34}, {6,10}, {10,22}, {23,27}, {20,30}, {11,40}, {15,24}, {16,25}, {18,35}, {7,36}, {19,29}, {1,38}, {17,36}, {26,40}, {9,36}, {21,26}, {23,30}, {2,30}, {18,24}, {29,39}, {35,39}, {22,25}, {10,27}, {15,26}, {1,29}, {11,24}, {18,32}, {14,21}, {31,34}, {31,38}, {4,13}, {34,37}, {14,27}, {2,7}, {6,19}, {8,13}, {9,37}, {13,28}, {1,26}, {8,17}, {8,37}, {4,18}, {7,12}, {7,38}, {12,13}, {20,34}, {10,15}, {22,36}, {32,33}, {2,19}, {11,25}, {4,31}, {3,39}, {3,6}, {17,23}, {5,39}, {9,16}, {29,36}, {27,37}, {30,35}, {2,25}, {23,33}, {28,30}, {9,21}, {16,23}, {33,38}, {3,28}, {5,33}, {9,28}, {17,31}, {4,40}, {12,34}, {12,23}, {1,16}, {22,32}, {14,20}, {5,15}, {2,37}, {11,14}, {24,34}, {3,17}, {6,40}, {7,18}, {12,39}, {25,39}, {26,32}, {12,26}, {21,31}, {7,14}, {15,17}, {8,35}, {19,21}, {16,18}, {36,40}, {3,32}, {4,27}, {5,20}, {24,29} } Symmetric graph 15 of order 40 Valency 6 Diameter 4 Girth 4 Automorphism group of order 480 Number of arcs = 240 Number of 2-arcs = 1200 2-arc-transitive false Edge-set { {1,8}, {14,21}, {13,27}, {28,38}, {11,34}, {27,30}, {12,40}, {20,29}, {3,39}, {4,6}, {7,18}, {30,36}, {30,40}, {3,18}, {10,35}, {24,29}, {17,24}, {2,26}, {15,23}, {16,25}, {11,13}, {8,36}, {19,30}, {18,36}, {1,30}, {11,24}, {21,26}, {2,7}, {6,20}, {35,40}, {29,35}, {22,35}, {22,32}, {26,39}, {9,36}, {25,31}, {10,37}, {4,27}, {7,12}, {8,14}, {13,19}, {23,30}, {8,11}, {19,21}, {21,36}, {4,40}, {7,35}, {32,38}, {34,38}, {13,22}, {14,28}, {10,15}, {16,24}, {1,20}, {7,37}, {20,33}, {33,37}, {32,33}, {17,32}, {2,38}, {5,19}, {31,34}, {31,37}, {2,19}, {25,40}, {3,13}, {9,27}, {12,23}, {36,39}, {4,14}, {7,13}, {9,38}, {23,34}, {8,38}, {19,34}, {18,23}, {1,25}, {14,20}, {3,32}, {27,37}, {12,33}, {28,29}, {11,39}, {6,9}, {10,21}, {24,27}, {5,10}, {4,17}, {5,33}, {20,22}, {3,28}, {9,16}, {6,34}, {18,31}, {4,31}, {9,22}, {23,28}, {1,37}, {12,26}, {5,40}, {8,17}, {11,25}, {12,14}, {3,5}, {6,39}, {21,31}, {10,28}, {24,33}, {26,32}, {29,39}, {1,15}, {5,16}, {2,16}, {6,15}, {22,25}, {15,17}, {16,18}, {15,26}, {2,29}, {17,35} } Symmetric graph 16 of order 40 Valency 6 Diameter 3 Girth 4 Automorphism group of order 7680 Number of arcs = 240 Number of 2-arcs = 1200 2-arc-transitive false Edge-set { {1,9}, {12,17}, {2,10}, {20,25}, {11,32}, {10,18}, {3,12}, {26,34}, {6,29}, {19,38}, {9,18}, {18,28}, {12,31}, {11,20}, {4,11}, {4,36}, {7,23}, {16,39}, {19,25}, {8,27}, {14,30}, {17,28}, {10,31}, {28,33}, {5,31}, {20,40}, {11,17}, {19,26}, {9,29}, {9,19}, {1,21}, {14,32}, {26,36}, {6,22}, {15,38}, {27,34}, {6,30}, {15,35}, {24,37}, {25,33}, {5,32}, {18,40}, {2,33}, {5,22}, {13,40}, {7,26}, {16,29}, {9,32}, {27,36}, {7,30}, {17,39}, {10,19}, {17,27}, {10,30}, {12,30}, {2,34}, {24,38}, {1,36}, {7,21}, {25,35}, {8,23}, {14,37}, {4,35}, {16,37}, {3,23}, {13,33}, {13,38}, {7,28}, {16,31}, {3,22}, {13,29}, {28,35}, {14,36}, {22,39}, {17,38}, {1,35}, {8,21}, {20,26}, {6,25}, {15,32}, {18,27}, {8,32}, {18,37}, {12,20}, {20,37}, {4,10}, {8,31}, {14,33}, {1,12}, {2,21}, {3,34}, {6,24}, {5,24}, {3,9}, {1,24}, {14,39}, {5,26}, {22,40}, {11,29}, {21,39}, {19,39}, {3,33}, {21,40}, {8,25}, {2,24}, {15,30}, {7,29}, {16,34}, {23,38}, {5,28}, {13,31}, {15,40}, {2,11}, {4,23}, {13,36}, {16,35}, {15,34}, {6,27}, {4,22}, {23,37} } Symmetric graph 17 of order 40 Valency 6 Diameter 3 Girth 4 Automorphism group of order 7680 Number of arcs = 240 Number of 2-arcs = 1200 2-arc-transitive false Edge-set { {1,10}, {12,18}, {2,12}, {20,28}, {11,31}, {10,20}, {3,11}, {26,33}, {5,29}, {19,40}, {9,17}, {18,26}, {12,29}, {11,19}, {4,9}, {2,36}, {7,22}, {13,39}, {19,28}, {7,27}, {16,30}, {17,25}, {10,32}, {28,36}, {7,31}, {20,39}, {19,27}, {9,30}, {3,21}, {14,29}, {26,35}, {6,21}, {15,39}, {27,33}, {5,30}, {14,35}, {8,26}, {22,37}, {20,38}, {25,34}, {6,32}, {18,38}, {1,33}, {5,21}, {14,40}, {17,26}, {6,26}, {15,29}, {27,35}, {8,30}, {17,37}, {11,30}, {4,34}, {24,39}, {3,36}, {7,24}, {6,23}, {15,37}, {2,35}, {8,22}, {13,37}, {3,24}, {24,40}, {15,36}, {13,35}, {16,38}, {18,25}, {8,28}, {14,31}, {2,22}, {13,30}, {28,34}, {16,40}, {25,36}, {7,32}, {16,36}, {7,25}, {23,39}, {19,37}, {3,35}, {8,24}, {20,27}, {5,25}, {13,32}, {9,20}, {1,23}, {6,31}, {15,33}, {1,11}, {4,21}, {16,32}, {5,23}, {3,10}, {4,33}, {16,33}, {21,37}, {14,38}, {5,27}, {17,40}, {10,29}, {1,34}, {1,22}, {21,38}, {14,34}, {4,24}, {15,31}, {8,29}, {13,34}, {6,28}, {18,39}, {12,32}, {2,23}, {12,19}, {2,9}, {22,38}, {11,18}, {4,12}, {23,40}, {9,31}, {10,17} } Symmetric graph 18 of order 40 Valency 6 Diameter 5 Girth 4 Automorphism group of order 125829120 Number of arcs = 240 Number of 2-arcs = 1200 2-arc-transitive false Edge-set { {1,9}, {9,19}, {21,38}, {9,30}, {2,21}, {6,28}, {10,19}, {8,21}, {20,28}, {19,37}, {16,35}, {25,35}, {10,30}, {2,22}, {28,33}, {19,28}, {16,29}, {1,35}, {5,30}, {2,9}, {13,31}, {14,38}, {13,34}, {1,10}, {8,22}, {20,27}, {20,37}, {16,40}, {15,35}, {16,30}, {2,35}, {7,31}, {19,38}, {13,38}, {1,36}, {8,26}, {9,20}, {21,37}, {3,23}, {6,30}, {6,24}, {10,29}, {23,39}, {22,38}, {27,33}, {15,29}, {5,29}, {11,31}, {13,32}, {1,21}, {8,31}, {20,38}, {13,37}, {3,34}, {6,27}, {2,10}, {6,23}, {13,33}, {9,29}, {5,28}, {18,26}, {17,39}, {8,25}, {18,25}, {7,22}, {7,26}, {12,17}, {10,20}, {15,40}, {15,36}, {7,32}, {2,36}, {3,11}, {4,23}, {3,33}, {6,29}, {5,23}, {18,39}, {16,39}, {25,36}, {22,37}, {26,35}, {17,25}, {23,40}, {15,30}, {7,21}, {16,36}, {4,33}, {3,12}, {14,33}, {28,34}, {14,31}, {4,34}, {27,34}, {12,32}, {1,22}, {11,32}, {14,32}, {5,27}, {14,37}, {11,18}, {24,39}, {17,26}, {17,40}, {18,40}, {15,39}, {7,25}, {26,36}, {4,12}, {12,31}, {14,34}, {11,17}, {8,32}, {19,27}, {12,18}, {24,40}, {3,24}, {4,11}, {5,24}, {4,24} } Symmetric graph 19 of order 40 Valency 6 Diameter 5 Girth 4 Automorphism group of order 251658240 Number of arcs = 240 Number of 2-arcs = 1200 2-arc-transitive false Edge-set { {1,9}, {12,29}, {18,39}, {9,19}, {23,37}, {3,22}, {14,33}, {2,12}, {16,39}, {5,23}, {28,35}, {7,32}, {20,26}, {16,38}, {9,30}, {17,37}, {22,39}, {4,33}, {5,25}, {5,28}, {13,34}, {17,27}, {7,22}, {1,36}, {15,32}, {24,39}, {4,36}, {12,20}, {4,23}, {13,35}, {26,33}, {16,31}, {25,35}, {5,31}, {25,34}, {5,29}, {15,37}, {2,10}, {13,30}, {7,27}, {7,26}, {14,29}, {11,18}, {17,40}, {6,22}, {27,33}, {14,31}, {11,19}, {19,28}, {13,37}, {16,36}, {9,32}, {4,21}, {12,31}, {18,25}, {5,21}, {15,35}, {10,31}, {19,25}, {23,40}, {3,35}, {11,30}, {20,37}, {2,24}, {7,30}, {27,36}, {19,38}, {1,23}, {3,10}, {14,38}, {6,26}, {16,33}, {18,38}, {1,21}, {2,34}, {16,29}, {2,35}, {14,39}, {4,11}, {12,17}, {8,31}, {9,18}, {21,37}, {8,25}, {13,40}, {3,12}, {21,40}, {28,34}, {13,32}, {10,20}, {24,38}, {6,30}, {20,27}, {7,24}, {18,28}, {11,32}, {20,40}, {26,36}, {6,32}, {4,9}, {3,24}, {14,36}, {8,29}, {15,30}, {10,17}, {19,39}, {22,38}, {1,33}, {8,21}, {8,23}, {15,34}, {10,29}, {2,22}, {1,11}, {15,40}, {6,24}, {6,27}, {3,34}, {17,26}, {8,28} } Symmetric graph 20 of order 40 Valency 8 Diameter 4 Girth 4 Automorphism group of order 320 Number of arcs = 320 Number of 2-arcs = 2240 2-arc-transitive false Edge-set { {1,5}, {10,23}, {7,18}, {31,34}, {28,30}, {18,22}, {13,19}, {16,27}, {12,24}, {2,14}, {9,38}, {18,29}, {13,26}, {7,20}, {3,16}, {1,37}, {32,35}, {27,32}, {8,9}, {4,8}, {33,40}, {29,33}, {13,18}, {10,13}, {3,7}, {3,39}, {19,22}, {15,19}, {5,11}, {10,39}, {7,34}, {15,25}, {11,22}, {1,15}, {11,37}, {21,33}, {20,29}, {12,21}, {6,20}, {28,38}, {23,36}, {13,28}, {3,13}, {3,30}, {5,19}, {5,35}, {16,26}, {2,16}, {18,31}, {34,37}, {30,35}, {22,27}, {19,24}, {4,6}, {2,40}, {29,36}, {26,31}, {6,10}, {2,7}, {36,39}, {23,25}, {10,15}, {25,32}, {15,17}, {33,38}, {21,28}, {3,38}, {7,11}, {3,5}, {11,14}, {5,9}, {20,23}, {16,18}, {1,39}, {1,8}, {12,13}, {27,39}, {24,34}, {14,25}, {9,22}, {1,29}, {26,37}, {20,32}, {6,17}, {8,36}, {10,21}, {12,39}, {17,30}, {8,19}, {21,35}, {4,31}, {28,40}, {6,34}, {2,30}, {4,15}, {11,40}, {23,33}, {25,38}, {5,33}, {22,36}, {19,31}, {11,23}, {5,18}, {15,28}, {1,13}, {10,37}, {7,35}, {3,32}, {35,37}, {24,27}, {4,40}, {26,29}, {7,10}, {34,39}, {11,15}, {17,24}, {14,17}, {21,26}, {20,21}, {30,34}, {25,30}, {9,14}, {16,20}, {22,25}, {12,16}, {6,12}, {2,38}, {36,38}, {2,6}, {31,36}, {28,31}, {23,28}, {18,23}, {25,39}, {22,34}, {1,32}, {27,37}, {12,38}, {6,36}, {19,30}, {24,35}, {2,31}, {17,32}, {14,27}, {8,17}, {4,14}, {9,24}, {9,40}, {8,33}, {4,29}, {26,40}, {4,37}, {35,40}, {27,29}, {24,26}, {32,33}, {17,21}, {14,20}, {9,16}, {8,12} } Symmetric graph 21 of order 40 Valency 8 Diameter 4 Girth 4 Automorphism group of order 1920 Number of arcs = 320 Number of 2-arcs = 2240 2-arc-transitive false Edge-set { {1,5}, {26,38}, {19,24}, {5,9}, {25,40}, {20,30}, {4,8}, {15,26}, {15,19}, {6,12}, {28,39}, {29,33}, {7,36}, {27,40}, {17,21}, {12,40}, {1,30}, {8,12}, {13,25}, {14,20}, {7,11}, {27,38}, {23,34}, {30,35}, {21,28}, {18,32}, {28,37}, {17,31}, {2,6}, {12,13}, {14,28}, {33,38}, {24,36}, {13,27}, {14,17}, {4,6}, {9,39}, {3,29}, {7,10}, {13,18}, {8,9}, {25,37}, {22,33}, {31,36}, {7,17}, {2,38}, {32,35}, {5,34}, {6,33}, {20,23}, {4,13}, {9,14}, {3,7}, {10,38}, {9,23}, {25,30}, {20,21}, {4,32}, {9,37}, {3,31}, {6,10}, {11,15}, {15,27}, {34,39}, {22,35}, {16,28}, {16,18}, {15,17}, {26,39}, {18,23}, {21,36}, {32,33}, {28,31}, {6,18}, {23,25}, {31,34}, {24,26}, {19,29}, {4,40}, {9,21}, {3,15}, {10,15}, {18,22}, {9,16}, {16,25}, {36,39}, {17,29}, {2,7}, {35,40}, {21,34}, {16,20}, {1,14}, {1,8}, {12,37}, {11,24}, {27,29}, {1,31}, {11,38}, {2,32}, {5,11}, {19,32}, {3,5}, {23,35}, {30,34}, {25,32}, {5,20}, {6,19}, {3,39}, {8,35}, {2,15}, {1,39}, {12,22}, {1,16}, {12,16}, {11,39}, {11,21}, {27,32}, {6,35}, {17,24}, {2,29}, {3,38}, {10,24}, {10,13}, {14,26}, {8,34}, {35,37}, {36,38}, {24,33}, {13,19}, {19,22}, {29,36}, {26,29}, {7,19}, {8,20}, {22,27}, {1,37}, {12,23}, {24,27}, {2,13}, {11,14}, {34,37}, {22,25}, {20,31}, {4,16}, {10,40}, {10,22}, {26,31}, {4,30}, {18,30}, {28,30}, {8,18}, {3,14}, {4,37}, {7,33}, {2,40}, {5,36}, {33,40}, {5,17}, {21,26}, {23,28} } Symmetric graph 22 of order 40 Valency 8 Diameter 3 Girth 4 Automorphism group of order 1920 Number of arcs = 320 Number of 2-arcs = 2240 2-arc-transitive false Edge-set { {1,5}, {20,28}, {10,28}, {15,40}, {21,29}, {30,40}, {29,33}, {21,36}, {2,38}, {5,12}, {7,13}, {11,36}, {2,14}, {3,12}, {13,17}, {7,19}, {27,34}, {3,27}, {20,32}, {10,35}, {18,23}, {12,39}, {1,31}, {19,36}, {24,27}, {27,40}, {25,32}, {26,35}, {14,23}, {24,39}, {16,18}, {12,22}, {4,39}, {18,30}, {25,39}, {26,30}, {9,15}, {15,21}, {2,30}, {20,33}, {6,23}, {32,35}, {1,35}, {16,28}, {1,16}, {19,22}, {8,39}, {5,30}, {36,39}, {9,37}, {15,31}, {7,24}, {6,40}, {8,35}, {13,22}, {23,37}, {6,32}, {1,25}, {11,13}, {35,37}, {11,38}, {14,32}, {34,38}, {5,21}, {7,38}, {11,27}, {14,27}, {3,15}, {17,21}, {6,9}, {2,9}, {15,20}, {2,28}, {22,40}, {29,37}, {22,28}, {28,37}, {6,16}, {8,22}, {17,35}, {1,11}, {11,20}, {10,14}, {1,19}, {4,34}, {10,21}, {16,38}, {8,18}, {2,17}, {7,33}, {4,6}, {9,19}, {28,31}, {23,31}, {2,33}, {4,20}, {31,34}, {3,36}, {9,24}, {3,18}, {5,20}, {7,10}, {18,34}, {31,39}, {30,36}, {21,25}, {26,38}, {5,14}, {19,29}, {9,34}, {27,29}, {21,38}, {6,36}, {2,8}, {12,33}, {4,13}, {8,29}, {33,40}, {4,29}, {6,17}, {8,11}, {20,24}, {28,36}, {24,30}, {4,26}, {18,25}, {22,34}, {3,37}, {11,23}, {12,17}, {19,26}, {9,25}, {16,29}, {10,40}, {17,27}, {15,26}, {4,10}, {5,34}, {13,25}, {23,26}, {14,19}, {5,37}, {7,31}, {3,32}, {12,16}, {13,30}, {3,7}, {12,26}, {17,31}, {8,15}, {1,40}, {13,37}, {25,33}, {24,35}, {22,32}, {14,39}, {32,38}, {10,18}, {16,24}, {23,33} } Symmetric graph 23 of order 40 Valency 8 Diameter 3 Girth 3 Automorphism group of order 1920 Number of arcs = 320 Number of 2-arcs = 2240 2-arc-transitive false Edge-set { {1,5}, {8,30}, {4,34}, {31,33}, {8,35}, {6,17}, {2,40}, {18,35}, {6,39}, {19,31}, {35,37}, {4,29}, {10,33}, {7,21}, {3,32}, {3,19}, {9,37}, {22,29}, {1,35}, {6,11}, {19,24}, {30,37}, {6,34}, {2,7}, {14,18}, {27,39}, {27,32}, {22,36}, {5,36}, {1,11}, {13,24}, {28,30}, {28,34}, {8,19}, {4,37}, {15,29}, {25,33}, {1,26}, {11,24}, {24,33}, {17,29}, {33,40}, {7,32}, {3,36}, {3,39}, {9,20}, {9,22}, {16,31}, {9,36}, {5,16}, {20,28}, {21,38}, {20,30}, {34,38}, {8,15}, {4,25}, {26,40}, {10,17}, {15,40}, {1,31}, {11,35}, {6,24}, {2,30}, {7,18}, {11,18}, {13,39}, {8,12}, {4,14}, {15,26}, {24,25}, {18,26}, {24,39}, {7,10}, {18,21}, {32,39}, {32,36}, {5,20}, {1,38}, {5,22}, {2,13}, {12,28}, {13,28}, {21,28}, {13,20}, {28,38}, {17,34}, {2,10}, {12,15}, {23,27}, {2,33}, {17,23}, {29,40}, {31,38}, {12,21}, {14,32}, {10,27}, {18,32}, {4,6}, {15,19}, {25,37}, {26,29}, {7,33}, {3,8}, {3,15}, {9,25}, {22,40}, {26,35}, {2,20}, {12,38}, {11,26}, {3,12}, {9,14}, {22,26}, {24,31}, {27,36}, {3,27}, {5,31}, {20,36}, {5,38}, {12,34}, {8,23}, {21,34}, {7,40}, {10,16}, {10,40}, {15,22}, {12,19}, {10,23}, {4,17}, {7,14}, {16,38}, {16,23}, {23,35}, {6,29}, {16,27}, {36,39}, {5,9}, {13,30}, {1,18}, {11,13}, {21,32}, {14,37}, {14,25}, {14,21}, {1,16}, {30,35}, {23,30}, {29,34}, {16,17}, {25,31}, {17,27}, {23,37}, {19,25}, {20,22}, {4,9}, {11,39}, {8,37}, {19,33}, {6,13}, {2,28} } Symmetric graph 24 of order 40 Valency 8 Diameter 4 Girth 4 Automorphism group of order 10240 Number of arcs = 320 Number of 2-arcs = 2240 2-arc-transitive false Edge-set { {1,9}, {15,17}, {17,35}, {23,36}, {29,40}, {27,36}, {1,29}, {28,40}, {2,26}, {2,30}, {6,10}, {5,28}, {2,15}, {10,17}, {6,30}, {6,16}, {8,16}, {13,18}, {1,16}, {9,18}, {22,36}, {16,21}, {16,23}, {18,40}, {18,36}, {29,36}, {9,22}, {9,24}, {22,39}, {12,24}, {23,39}, {21,35}, {30,38}, {15,24}, {17,39}, {30,35}, {28,37}, {2,28}, {24,38}, {27,39}, {24,40}, {26,39}, {28,35}, {2,10}, {17,37}, {25,35}, {29,37}, {19,39}, {25,33}, {5,26}, {27,38}, {1,27}, {1,31}, {7,9}, {25,40}, {5,29}, {6,32}, {16,18}, {31,39}, {7,25}, {5,15}, {30,39}, {6,25}, {8,29}, {5,13}, {6,27}, {32,36}, {7,27}, {1,14}, {2,32}, {8,10}, {29,34}, {5,31}, {4,14}, {13,21}, {7,15}, {3,15}, {11,17}, {24,35}, {7,30}, {6,14}, {10,21}, {4,9}, {12,22}, {3,29}, {5,11}, {7,11}, {14,24}, {10,23}, {21,40}, {5,9}, {14,22}, {2,12}, {21,38}, {15,22}, {4,28}, {4,16}, {12,18}, {3,10}, {11,21}, {19,37}, {11,23}, {13,23}, {20,40}, {20,36}, {1,25}, {1,11}, {22,37}, {18,38}, {14,17}, {19,35}, {28,33}, {2,13}, {10,20}, {21,34}, {11,20}, {24,34}, {25,37}, {26,36}, {16,19}, {18,33}, {31,38}, {23,37}, {30,33}, {20,38}, {27,34}, {32,34}, {8,31}, {26,34}, {26,38}, {15,20}, {17,34}, {32,37}, {8,28}, {31,35}, {3,27}, {20,33}, {3,25}, {7,32}, {8,14}, {4,30}, {3,31}, {32,40}, {8,26}, {31,33}, {4,26}, {3,12}, {3,13}, {7,13}, {23,33}, {4,32}, {8,12}, {6,12}, {14,20}, {4,11}, {9,19}, {13,19}, {12,19}, {22,33}, {19,34} } Symmetric graph 25 of order 40 Valency 8 Diameter 4 Girth 4 Automorphism group of order 83886080 Number of arcs = 320 Number of 2-arcs = 2240 2-arc-transitive false Edge-set { {1,5}, {28,37}, {34,39}, {13,17}, {7,9}, {19,29}, {22,36}, {12,21}, {25,32}, {23,25}, {2,30}, {6,12}, {2,6}, {13,26}, {2,38}, {12,16}, {32,36}, {9,24}, {4,31}, {19,23}, {16,27}, {27,38}, {16,20}, {3,15}, {10,37}, {5,34}, {18,22}, {29,33}, {5,17}, {14,18}, {33,40}, {35,38}, {23,33}, {18,32}, {3,40}, {10,14}, {6,17}, {6,34}, {10,38}, {30,33}, {18,21}, {3,16}, {3,8}, {8,10}, {23,34}, {22,27}, {27,29}, {13,18}, {2,13}, {12,39}, {33,39}, {21,35}, {20,30}, {17,32}, {9,14}, {4,40}, {8,20}, {8,35}, {3,31}, {7,36}, {7,19}, {1,29}, {11,22}, {21,28}, {25,39}, {13,25}, {11,16}, {1,38}, {24,26}, {26,31}, {28,30}, {5,11}, {10,24}, {17,22}, {14,26}, {26,40}, {29,34}, {11,40}, {31,36}, {19,24}, {1,14}, {27,30}, {12,40}, {2,14}, {21,27}, {25,40}, {14,25}, {1,30}, {11,21}, {22,35}, {23,26}, {26,32}, {20,29}, {11,15}, {1,37}, {8,36}, {8,19}, {36,37}, {15,19}, {17,21}, {20,24}, {31,35}, {2,29}, {6,11}, {1,6}, {6,33}, {6,18}, {3,32}, {10,23}, {12,22}, {15,28}, {30,34}, {1,13}, {2,5}, {5,12}, {11,39}, {25,31}, {24,25}, {21,36}, {19,30}, {9,38}, {4,16}, {24,34}, {17,31}, {7,20}, {4,8}, {8,9}, {7,35}, {4,39}, {9,13}, {20,23}, {32,35}, {5,33}, {5,18}, {15,20}, {35,37}, {18,31}, {24,33}, {4,15}, {9,37}, {16,28}, {28,38}, {14,17}, {34,40}, {4,7}, {27,37}, {15,27}, {9,23}, {4,32}, {12,15}, {2,37}, {10,13}, {3,39}, {36,38}, {16,19}, {22,28}, {28,29}, {26,39}, {7,10}, {3,7} } Symmetric graph 26 of order 40 Valency 8 Diameter 4 Girth 4 Automorphism group of order 335544320 Number of arcs = 320 Number of 2-arcs = 2240 2-arc-transitive false Edge-set { {1,9}, {10,17}, {26,38}, {6,18}, {25,35}, {25,33}, {2,15}, {5,13}, {21,36}, {23,34}, {1,30}, {22,34}, {1,31}, {3,9}, {10,37}, {1,14}, {11,22}, {24,30}, {17,29}, {21,32}, {20,32}, {6,38}, {21,29}, {18,32}, {10,40}, {8,38}, {11,17}, {26,40}, {18,26}, {16,25}, {2,10}, {12,38}, {19,29}, {18,28}, {31,37}, {6,19}, {5,35}, {30,39}, {7,17}, {7,39}, {7,34}, {13,25}, {15,21}, {30,38}, {5,17}, {5,39}, {7,36}, {15,24}, {28,35}, {28,33}, {2,13}, {5,33}, {2,36}, {4,34}, {9,18}, {25,37}, {20,25}, {15,27}, {3,36}, {8,16}, {8,13}, {21,33}, {14,23}, {22,30}, {27,37}, {6,14}, {6,15}, {23,35}, {23,32}, {1,34}, {1,11}, {3,30}, {22,35}, {14,27}, {14,22}, {23,29}, {3,31}, {10,19}, {11,37}, {22,31}, {9,24}, {29,37}, {12,21}, {32,39}, {26,36}, {26,34}, {1,16}, {4,10}, {11,24}, {29,40}, {4,16}, {17,31}, {2,32}, {12,20}, {3,13}, {10,21}, {20,30}, {7,20}, {32,38}, {28,38}, {6,40}, {18,30}, {4,12}, {2,29}, {12,18}, {5,20}, {11,40}, {8,40}, {8,18}, {19,26}, {16,28}, {5,16}, {17,27}, {27,39}, {7,14}, {24,33}, {9,38}, {25,39}, {19,31}, {19,28}, {9,39}, {8,35}, {7,37}, {27,34}, {17,25}, {6,34}, {7,15}, {3,15}, {13,28}, {13,21}, {5,37}, {6,36}, {27,36}, {13,24}, {24,36}, {8,33}, {2,33}, {4,35}, {4,14}, {9,22}, {12,23}, {15,26}, {3,33}, {14,26}, {16,23}, {4,32}, {1,35}, {10,23}, {3,11}, {16,22}, {4,29}, {11,19}, {24,31}, {2,12}, {12,39}, {20,27}, {31,40}, {9,20}, {28,40}, {8,19} } Symmetric graph 27 of order 40 Valency 8 Diameter 5 Girth 4 Automorphism group of order 1268067619307520 Number of arcs = 320 Number of 2-arcs = 2240 2-arc-transitive false Edge-set { {1,5}, {30,33}, {14,19}, {33,38}, {18,24}, {28,29}, {7,9}, {3,6}, {22,28}, {24,28}, {3,7}, {8,12}, {3,39}, {19,23}, {15,17}, {10,16}, {35,40}, {32,35}, {32,34}, {13,18}, {34,40}, {9,15}, {16,18}, {12,15}, {33,39}, {16,19}, {36,38}, {11,15}, {30,36}, {26,32}, {1,40}, {6,11}, {20,22}, {1,7}, {4,8}, {24,26}, {2,39}, {25,31}, {22,25}, {23,25}, {2,6}, {20,23}, {27,31}, {8,11}, {23,27}, {2,8}, {8,10}, {1,38}, {26,30}, {21,28}, {22,26}, {3,5}, {1,37}, {26,29}, {18,21}, {5,9}, {13,20}, {31,36}, {11,14}, {25,30}, {2,38}, {34,37}, {12,13}, {29,34}, {30,35}, {35,38}, {36,39}, {20,24}, {9,14}, {5,11}, {2,40}, {20,21}, {36,37}, {29,36}, {11,16}, {15,20}, {28,30}, {19,22}, {3,38}, {10,15}, {33,37}, {16,17}, {9,13}, {14,18}, {32,33}, {33,40}, {27,30}, {19,21}, {4,38}, {13,17}, {10,14}, {3,37}, {17,23}, {4,5}, {21,27}, {5,12}, {29,35}, {18,22}, {25,29}, {6,9}, {21,26}, {3,40}, {5,10}, {28,32}, {12,14}, {29,33}, {2,37}, {17,21}, {7,12}, {15,18}, {9,16}, {1,39}, {8,9}, {26,31}, {24,27}, {4,7}, {2,7}, {24,25}, {4,40}, {6,10}, {27,32}, {3,8}, {23,28}, {28,31}, {7,11}, {17,22}, {4,6}, {31,33}, {14,17}, {18,23}, {10,13}, {25,32}, {17,24}, {7,10}, {27,29}, {4,37}, {1,8}, {23,26}, {19,24}, {36,40}, {32,36}, {13,19}, {12,16}, {34,39}, {15,19}, {31,35}, {35,39}, {16,20}, {35,37}, {31,34}, {4,39}, {14,20}, {11,13}, {30,34}, {6,12}, {21,25}, {2,5}, {1,6}, {22,27}, {34,38} } Symmetric graph 28 of order 40 Valency 9 Diameter 3 Girth 3 Automorphism group of order 1440 Number of arcs = 360 Number of 2-arcs = 2880 2-arc-transitive false Edge-set { {1,5}, {22,26}, {3,14}, {3,34}, {19,24}, {12,23}, {2,10}, {7,23}, {2,27}, {15,35}, {21,38}, {29,36}, {22,32}, {21,31}, {4,29}, {27,36}, {16,22}, {1,21}, {4,17}, {6,9}, {12,25}, {19,33}, {23,36}, {5,40}, {5,26}, {34,38}, {8,24}, {33,37}, {24,40}, {17,26}, {10,34}, {11,24}, {22,33}, {3,23}, {14,24}, {1,40}, {25,32}, {13,30}, {20,32}, {8,15}, {28,38}, {5,36}, {14,34}, {3,26}, {14,19}, {7,19}, {28,35}, {15,21}, {8,20}, {17,35}, {21,34}, {19,40}, {7,31}, {27,29}, {30,35}, {8,34}, {24,28}, {2,22}, {12,35}, {10,21}, {17,22}, {4,38}, {11,39}, {16,38}, {8,37}, {9,28}, {12,15}, {2,19}, {18,36}, {14,26}, {7,12}, {10,27}, {10,38}, {15,27}, {2,6}, {18,25}, {9,33}, {16,28}, {15,37}, {6,14}, {25,40}, {7,33}, {23,27}, {15,17}, {27,37}, {7,16}, {5,17}, {6,39}, {6,25}, {7,28}, {2,35}, {18,21}, {4,24}, {6,29}, {31,33}, {23,29}, {1,36}, {18,30}, {10,19}, {11,36}, {20,28}, {2,32}, {9,29}, {12,32}, {5,13}, {26,39}, {3,12}, {16,32}, {1,31}, {17,29}, {19,31}, {1,9}, {12,17}, {21,25}, {4,13}, {20,39}, {8,32}, {28,30}, {11,18}, {9,20}, {10,13}, {20,34}, {8,27}, {9,14}, {12,40}, {1,20}, {11,16}, {14,40}, {13,33}, {4,25}, {13,20}, {16,18}, {6,21}, {23,39}, {24,35}, {36,40}, {5,22}, {13,39}, {15,31}, {29,38}, {5,30}, {26,31}, {2,16}, {18,37}, {4,8}, {32,40}, {11,26}, {3,18}, {8,11}, {22,37}, {3,7}, {7,38}, {3,30}, {14,29}, {4,33}, {20,23}, {2,39}, {6,18}, {31,39}, {30,37}, {11,31}, {1,28}, {10,30}, {32,34}, {3,37}, {9,37}, {25,33}, {13,23}, {6,35}, {26,34}, {4,11}, {35,39}, {1,15}, {17,38}, {19,27}, {16,36}, {5,10}, {13,25}, {9,22}, {24,30} } Symmetric graph 29 of order 40 Valency 9 Diameter 3 Girth 4 Automorphism group of order 2880 Number of arcs = 360 Number of 2-arcs = 2880 2-arc-transitive false Edge-set { {1,9}, {5,21}, {10,17}, {17,39}, {15,39}, {6,31}, {15,31}, {1,21}, {15,35}, {19,26}, {14,30}, {26,35}, {5,30}, {21,39}, {2,35}, {5,28}, {9,30}, {4,33}, {27,33}, {2,9}, {28,33}, {17,27}, {2,24}, {20,28}, {5,27}, {10,31}, {4,23}, {4,11}, {26,36}, {5,24}, {10,20}, {4,10}, {11,31}, {1,36}, {24,38}, {20,40}, {10,32}, {11,17}, {15,36}, {6,26}, {23,37}, {19,38}, {7,23}, {12,19}, {17,38}, {15,40}, {6,32}, {6,23}, {9,19}, {7,26}, {12,30}, {14,38}, {23,40}, {16,32}, {6,25}, {9,29}, {7,31}, {1,12}, {1,35}, {14,33}, {13,37}, {22,38}, {20,37}, {16,38}, {8,30}, {14,31}, {1,23}, {16,35}, {19,25}, {14,29}, {19,37}, {9,20}, {16,33}, {8,27}, {16,37}, {25,34}, {7,29}, {14,34}, {20,26}, {16,30}, {8,21}, {2,21}, {17,28}, {13,36}, {8,22}, {14,40}, {13,32}, {2,22}, {18,27}, {13,31}, {26,33}, {6,30}, {21,37}, {2,34}, {7,28}, {4,34}, {13,30}, {4,22}, {5,32}, {2,10}, {11,18}, {13,34}, {7,22}, {3,12}, {3,33}, {9,32}, {2,33}, {27,34}, {18,39}, {13,39}, {24,39}, {20,39}, {18,40}, {6,24}, {25,36}, {8,29}, {24,40}, {11,29}, {3,36}, {4,9}, {19,27}, {22,39}, {3,24}, {20,25}, {3,23}, {27,36}, {8,31}, {17,25}, {15,29}, {8,25}, {18,26}, {5,25}, {10,29}, {4,24}, {3,11}, {3,21}, {15,38}, {21,40}, {15,32}, {16,29}, {18,28}, {12,32}, {1,22}, {5,23}, {10,19}, {11,30}, {4,36}, {22,37}, {18,38}, {1,11}, {12,31}, {1,34}, {28,35}, {12,18}, {12,17}, {15,34}, {6,28}, {23,38}, {19,40}, {14,35}, {16,39}, {25,35}, {5,29}, {28,34}, {7,32}, {3,35}, {17,37}, {7,27}, {13,40}, {7,21}, {8,26}, {14,37}, {2,12}, {3,10}, {11,20}, {16,36}, {8,24}, {9,18}, {13,33}, {6,22} } Symmetric graph 30 of order 40 Valency 9 Diameter 4 Girth 4 Automorphism group of order 5760 Number of arcs = 360 Number of 2-arcs = 2880 2-arc-transitive true Edge-set { {1,6}, {1,9}, {8,23}, {5,9}, {23,28}, {4,24}, {6,18}, {2,5}, {7,28}, {24,29}, {18,30}, {11,23}, {17,21}, {1,15}, {8,33}, {2,10}, {7,24}, {3,29}, {5,30}, {23,36}, {17,38}, {15,35}, {33,37}, {18,25}, {16,22}, {19,34}, {9,38}, {14,23}, {4,25}, {6,10}, {24,27}, {3,23}, {5,17}, {12,36}, {22,38}, {2,35}, {7,37}, {3,18}, {16,17}, {10,34}, {28,38}, {4,14}, {15,32}, {31,33}, {21,37}, {13,20}, {14,26}, {10,28}, {24,39}, {15,18}, {11,32}, {21,31}, {8,27}, {23,30}, {17,29}, {12,24}, {18,22}, {2,16}, {7,34}, {3,26}, {10,20}, {12,15}, {22,33}, {16,37}, {13,34}, {6,26}, {2,27}, {10,30}, {11,39}, {15,21}, {34,38}, {14,39}, {25,33}, {1,40}, {9,19}, {13,40}, {16,36}, {31,39}, {6,29}, {27,30}, {20,23}, {12,17}, {15,38}, {14,33}, {25,39}, {19,40}, {4,30}, {24,35}, {18,37}, {17,26}, {20,33}, {10,37}, {13,24}, {12,31}, {22,32}, {6,13}, {27,36}, {8,38}, {21,25}, {1,20}, {9,13}, {26,40}, {1,31}, {8,32}, {6,35}, {27,37}, {7,20}, {12,25}, {14,19}, {20,39}, {25,32}, {5,14}, {28,35}, {11,16}, {3,13}, {12,40}, {1,36}, {30,35}, {29,37}, {18,36}, {8,16}, {26,34}, {10,14}, {20,32}, {11,35}, {4,17}, {9,33}, {16,31}, {32,34}, {13,25}, {9,27}, {23,40}, {21,34}, {19,31}, {5,40}, {16,28}, {4,34}, {6,39}, {1,28}, {4,8}, {9,29}, {5,36}, {26,31}, {2,39}, {7,15}, {28,29}, {8,19}, {11,26}, {4,37}, {15,27}, {3,33}, {2,32}, {36,39}, {5,25}, {32,40}, {19,24}, {11,18}, {22,26}, {2,19}, {35,40}, {7,11}, {13,30}, {2,21}, {8,12}, {4,11}, {6,21}, {3,7}, {3,38}, {29,36}, {30,38}, {7,31}, {9,21}, {14,29}, {1,22}, {20,27}, {3,12}, {17,35}, {19,28}, {10,22}, {5,22} } Symmetric graph 31 of order 40 Valency 10 Diameter 4 Girth 4 Automorphism group of order 687970713600000000 Number of arcs = 400 Number of 2-arcs = 3600 2-arc-transitive false Edge-set { {1,5}, {1,24}, {29,35}, {1,39}, {11,29}, {5,35}, {17,22}, {1,13}, {27,29}, {5,11}, {17,37}, {24,35}, {22,35}, {7,10}, {1,29}, {3,29}, {5,27}, {16,17}, {11,24}, {35,37}, {7,25}, {35,39}, {11,22}, {10,22}, {34,40}, {17,29}, {3,5}, {17,31}, {24,27}, {16,35}, {2,7}, {11,39}, {11,37}, {22,25}, {14,34}, {13,35}, {22,27}, {10,37}, {10,40}, {23,28}, {5,17}, {7,17}, {3,24}, {31,35}, {7,20}, {27,39}, {11,16}, {2,22}, {30,34}, {11,13}, {27,37}, {25,37}, {10,14}, {4,23}, {3,22}, {10,16}, {25,40}, {28,40}, {12,15}, {17,24}, {7,35}, {7,34}, {3,39}, {11,31}, {20,22}, {6,34}, {13,27}, {16,27}, {2,37}, {10,30}, {18,23}, {3,37}, {16,25}, {14,25}, {4,40}, {12,32}, {10,31}, {2,40}, {14,28}, {15,28}, {1,38}, {17,39}, {7,11}, {22,34}, {23,34}, {3,13}, {27,31}, {20,37}, {6,10}, {23,36}, {3,16}, {2,16}, {25,30}, {18,40}, {8,12}, {25,31}, {2,14}, {4,14}, {28,32}, {19,38}, {20,40}, {28,30}, {4,15}, {1,15}, {26,29}, {13,17}, {7,27}, {34,37}, {10,23}, {12,23}, {3,31}, {16,20}, {6,25}, {36,40}, {12,21}, {2,31}, {2,30}, {14,18}, {8,28}, {33,38}, {14,20}, {4,30}, {4,32}, {15,19}, {5,26}, {6,28}, {15,18}, {1,32}, {3,7}, {16,34}, {23,25}, {12,40}, {12,38}, {20,31}, {2,6}, {14,36}, {21,28}, {9,38}, {20,30}, {18,30}, {4,8}, {15,33}, {24,26}, {4,6}, {18,32}, {19,32}, {15,36}, {1,8}, {19,29}, {31,34}, {2,23}, {12,14}, {28,38}, {26,38}, {6,20}, {30,36}, {4,21}, {9,15}, {26,39}, {6,18}, {8,18}, {32,33}, {32,36}, {8,19}, {5,19}, {1,21}, {29,33}, {20,23}, {12,30}, {4,38}, {15,26}, {13,26}, {6,36}, {18,21}, {9,32}, {8,36}, {8,33}, {19,24}, {19,21}, {5,33}, {9,29}, {6,12}, {18,38}, {26,32}, {21,36}, {8,9}, {19,39}, {21,33}, {24,33}, {5,9}, {36,38}, {8,26}, {13,19}, {9,21}, {33,39}, {9,24}, {21,26}, {13,33}, {9,39}, {9,13} } Symmetric graph 32 of order 40 Valency 12 Diameter 2 Girth 3 Automorphism group of order 1920 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,5}, {35,40}, {10,14}, {17,32}, {2,7}, {9,22}, {20,22}, {25,37}, {36,38}, {11,13}, {13,24}, {17,31}, {7,13}, {26,31}, {25,31}, {8,34}, {20,30}, {10,21}, {18,21}, {21,32}, {3,5}, {25,38}, {10,36}, {13,21}, {3,27}, {3,25}, {34,38}, {19,34}, {3,15}, {26,39}, {16,22}, {20,29}, {6,16}, {28,29}, {1,16}, {29,37}, {35,37}, {9,14}, {25,30}, {5,34}, {1,20}, {10,16}, {21,29}, {28,37}, {9,33}, {9,34}, {19,30}, {8,19}, {12,37}, {9,24}, {27,29}, {6,36}, {23,31}, {4,7}, {26,40}, {11,33}, {16,23}, {4,26}, {11,40}, {10,23}, {4,31}, {8,40}, {2,8}, {17,22}, {2,25}, {34,39}, {19,35}, {3,14}, {7,40}, {10,26}, {11,22}, {20,23}, {4,16}, {29,40}, {8,35}, {18,24}, {4,17}, {19,24}, {3,17}, {27,39}, {15,27}, {14,24}, {4,28}, {33,40}, {20,33}, {30,38}, {36,39}, {12,13}, {27,32}, {7,36}, {4,18}, {11,15}, {23,30}, {12,36}, {7,18}, {15,22}, {3,39}, {12,38}, {32,34}, {7,15}, {5,13}, {11,34}, {19,29}, {3,6}, {8,17}, {2,27}, {9,37}, {32,36}, {22,27}, {20,36}, {18,31}, {26,30}, {11,39}, {12,23}, {4,32}, {17,34}, {2,15}, {6,14}, {28,32}, {5,39}, {12,25}, {8,14}, {5,37}, {9,25}, {6,33}, {12,28}, {24,33}, {22,32}, {12,35}, {18,32}, {2,30}, {1,6}, {19,21}, {1,28}, {33,37}, {1,13}, {6,39}, {12,21}, {30,39}, {1,19}, {13,28}, {24,31}, {6,9}, {5,19}, {3,37}, {10,35}, {14,21}, {3,18}, {4,8}, {27,40}, {9,16}, {15,25}, {28,38}, {1,37}, {31,33}, {7,20}, {1,26}, {6,18}, {15,23}, {1,39}, {11,24}, {29,35}, {23,25}, {31,35}, {24,25}, {18,33}, {23,26}, {14,18}, {31,37}, {17,23}, {2,19}, {2,38}, {8,16}, {10,40}, {29,33}, {2,29}, {10,27}, {21,35}, {32,38}, {16,17}, {14,27}, {8,9}, {2,20}, {22,29}, {6,37}, {9,28}, {12,15}, {7,33}, {24,34}, {5,35}, {31,40}, {8,10}, {4,38}, {13,26}, {16,28}, {24,30}, {6,10}, {2,40}, {30,34}, {14,25}, {30,36}, {22,28}, {3,31}, {8,38}, {5,15}, {11,27}, {5,11}, {4,40}, {1,30}, {22,33}, {15,17}, {7,38}, {11,26}, {4,13}, {24,26}, {17,35}, {18,36}, {14,19}, {3,32}, {2,14}, {22,34}, {15,20}, {5,12}, {21,36}, {23,35}, {32,39}, {16,20}, {7,11}, {9,38}, {21,28}, {7,12}, {10,39}, {13,18}, {21,27}, {5,17}, {6,20}, {13,19}, {1,29}, {16,26}, {23,36} } Symmetric graph 33 of order 40 Valency 12 Diameter 3 Girth 3 Automorphism group of order 3840 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,5}, {13,18}, {21,37}, {25,37}, {10,19}, {30,36}, {3,32}, {23,36}, {3,14}, {3,28}, {12,35}, {8,11}, {5,28}, {6,15}, {8,23}, {11,31}, {28,30}, {15,38}, {20,23}, {15,21}, {16,23}, {2,12}, {27,34}, {1,19}, {33,39}, {18,21}, {16,37}, {17,39}, {18,38}, {19,31}, {30,39}, {7,33}, {8,21}, {5,16}, {35,39}, {4,18}, {27,31}, {11,30}, {18,32}, {31,40}, {17,30}, {2,14}, {22,34}, {10,22}, {15,26}, {13,28}, {12,21}, {9,34}, {1,25}, {25,30}, {10,32}, {36,40}, {3,17}, {26,34}, {1,9}, {25,35}, {4,10}, {7,12}, {8,34}, {9,20}, {25,40}, {19,30}, {32,39}, {18,40}, {17,37}, {12,34}, {1,27}, {16,25}, {10,24}, {5,22}, {7,15}, {1,8}, {5,33}, {6,25}, {8,10}, {2,7}, {8,26}, {5,9}, {14,38}, {20,22}, {10,29}, {26,31}, {3,29}, {31,35}, {24,39}, {16,19}, {2,30}, {32,34}, {26,36}, {13,23}, {14,21}, {5,14}, {3,6}, {8,35}, {11,33}, {2,28}, {9,23}, {13,26}, {4,13}, {21,36}, {12,23}, {14,27}, {3,16}, {24,35}, {2,20}, {34,40}, {26,39}, {4,27}, {11,36}, {23,33}, {8,28}, {5,12}, {6,34}, {25,33}, {2,10}, {3,9}, {13,22}, {23,40}, {14,17}, {29,35}, {18,29}, {31,37}, {20,39}, {13,19}, {21,39}, {9,18}, {17,23}, {3,19}, {14,20}, {22,40}, {19,24}, {13,39}, {36,37}, {35,38}, {4,20}, {27,29}, {3,7}, {6,35}, {5,24}, {7,13}, {6,23}, {7,27}, {1,29}, {28,40}, {12,17}, {8,14}, {6,10}, {11,24}, {30,38}, {20,32}, {20,37}, {15,17}, {23,38}, {12,19}, {27,39}, {16,22}, {4,31}, {24,37}, {28,32}, {2,31}, {30,34}, {22,38}, {15,20}, {15,40}, {12,32}, {11,22}, {10,33}, {2,26}, {24,34}, {1,13}, {15,24}, {1,11}, {28,33}, {9,31}, {19,21}, {16,39}, {2,18}, {34,37}, {10,17}, {26,38}, {14,25}, {22,35}, {4,15}, {29,37}, {31,33}, {6,27}, {7,25}, {5,36}, {28,37}, {1,32}, {4,25}, {10,36}, {9,30}, {15,28}, {27,38}, {11,20}, {29,33}, {12,29}, {16,27}, {7,22}, {19,40}, {17,31}, {6,21}, {21,33}, {2,16}, {19,38}, {4,5}, {27,36}, {3,11}, {4,30}, {1,15}, {29,40}, {7,24}, {32,36}, {8,16}, {5,26}, {11,18}, {2,6}, {14,24}, {26,29}, {13,37}, {9,21}, {7,36}, {1,17}, {3,26}, {9,35}, {18,24}, {17,22}, {14,40}, {6,13}, {28,35}, {4,8}, {16,18}, {7,9}, {20,29}, {32,38}, {25,32}, {4,12}, {6,11}, {33,38} } Symmetric graph 34 of order 40 Valency 12 Diameter 3 Girth 3 Automorphism group of order 3840 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,6}, {13,17}, {21,38}, {26,37}, {9,19}, {30,35}, {4,32}, {24,36}, {3,13}, {4,28}, {12,36}, {8,12}, {5,27}, {6,16}, {8,24}, {11,32}, {28,29}, {15,37}, {19,23}, {16,21}, {16,24}, {2,11}, {28,34}, {2,19}, {34,39}, {18,22}, {17,40}, {17,38}, {19,32}, {29,39}, {8,33}, {7,21}, {36,39}, {3,18}, {28,31}, {12,30}, {30,40}, {17,32}, {32,40}, {17,29}, {1,14}, {22,33}, {10,21}, {16,26}, {14,28}, {12,22}, {10,34}, {1,26}, {25,29}, {10,31}, {26,33}, {2,9}, {26,35}, {4,9}, {6,28}, {7,34}, {25,39}, {20,30}, {11,34}, {1,28}, {15,25}, {10,23}, {5,21}, {7,16}, {2,8}, {5,34}, {2,5}, {6,26}, {8,9}, {6,33}, {7,26}, {6,9}, {13,38}, {20,21}, {9,29}, {25,31}, {3,30}, {32,35}, {24,40}, {16,20}, {2,29}, {31,34}, {3,10}, {13,24}, {13,21}, {7,23}, {6,14}, {3,5}, {7,35}, {9,24}, {13,25}, {4,14}, {22,36}, {12,24}, {13,27}, {4,16}, {17,21}, {16,38}, {10,20}, {26,40}, {23,34}, {8,27}, {5,11}, {1,10}, {23,39}, {14,18}, {3,31}, {18,30}, {32,37}, {20,40}, {14,19}, {22,39}, {10,18}, {22,37}, {17,24}, {4,19}, {9,17}, {25,38}, {20,24}, {13,40}, {4,17}, {36,38}, {35,37}, {27,30}, {4,7}, {6,36}, {5,23}, {7,14}, {8,15}, {6,12}, {32,33}, {27,40}, {11,17}, {6,22}, {5,10}, {3,15}, {23,35}, {19,29}, {30,37}, {20,31}, {20,38}, {15,18}, {23,37}, {12,20}, {29,36}, {11,29}, {2,32}, {29,34}, {15,19}, {16,40}, {26,30}, {9,32}, {35,40}, {3,27}, {11,35}, {24,33}, {2,13}, {19,22}, {15,39}, {1,18}, {33,37}, {21,35}, {1,30}, {5,15}, {8,25}, {3,8}, {27,33}, {28,38}, {1,31}, {3,25}, {10,35}, {26,32}, {16,28}, {4,26}, {9,36}, {27,32}, {8,22}, {18,31}, {19,39}, {18,39}, {2,17}, {34,38}, {2,15}, {9,33}, {31,38}, {18,23}, {12,31}, {7,28}, {8,36}, {7,11}, {27,35}, {4,11}, {31,36}, {2,27}, {1,7}, {7,10}, {28,39}, {12,18}, {33,40}, {5,13}, {4,6}, {12,33}, {15,22}, {15,23}, {1,12}, {14,37}, {8,13}, {18,37}, {14,39}, {9,22}, {14,23}, {3,12}, {6,24}, {21,40}, {16,17}, {28,36}, {31,39}, {5,25}, {25,34}, {14,26}, {25,36}, {5,35}, {10,30}, {11,19}, {1,20}, {15,27}, {1,16}, {14,22}, {13,20}, {3,20}, {21,34}, {2,25}, {19,37}, {24,38}, {4,29}, {29,38}, {30,33}, {11,21}, {11,23}, {27,37} } Symmetric graph 35 of order 40 Valency 12 Diameter 3 Girth 4 Automorphism group of order 5760 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,11}, {14,27}, {1,27}, {16,22}, {5,34}, {22,27}, {27,34}, {10,39}, {8,21}, {3,32}, {11,30}, {22,39}, {21,34}, {3,22}, {11,34}, {3,15}, {25,40}, {22,31}, {17,30}, {26,39}, {14,24}, {1,37}, {1,39}, {15,21}, {3,40}, {11,22}, {30,39}, {21,26}, {3,14}, {9,30}, {7,26}, {2,20}, {16,36}, {18,39}, {21,40}, {24,36}, {20,37}, {1,19}, {15,35}, {16,34}, {5,23}, {8,27}, {15,27}, {9,40}, {7,22}, {2,30}, {16,26}, {14,39}, {1,21}, {1,24}, {15,37}, {19,40}, {22,35}, {16,30}, {5,26}, {12,24}, {4,37}, {19,26}, {32,35}, {28,37}, {17,28}, {5,10}, {8,9}, {1,35}, {15,19}, {2,40}, {9,23}, {8,37}, {14,17}, {27,38}, {18,27}, {6,9}, {7,10}, {3,10}, {8,11}, {32,33}, {24,30}, {22,25}, {31,34}, {9,22}, {7,34}, {2,12}, {4,16}, {21,32}, {24,28}, {10,19}, {8,35}, {1,16}, {5,15}, {27,40}, {23,27}, {7,14}, {2,38}, {16,18}, {6,39}, {10,21}, {10,24}, {19,32}, {30,35}, {13,34}, {2,23}, {8,29}, {14,25}, {19,38}, {18,35}, {6,17}, {14,33}, {21,36}, {20,33}, {11,32}, {3,30}, {12,25}, {4,31}, {6,27}, {10,27}, {9,38}, {7,18}, {2,28}, {16,28}, {12,33}, {4,24}, {8,25}, {14,31}, {5,20}, {19,34}, {12,31}, {4,29}, {11,26}, {3,26}, {1,31}, {4,17}, {12,39}, {24,34}, {23,37}, {20,39}, {3,18}, {11,40}, {4,21}, {13,28}, {10,29}, {17,40}, {23,33}, {11,38}, {6,25}, {10,31}, {9,32}, {7,30}, {2,22}, {22,33}, {5,32}, {7,28}, {10,35}, {8,19}, {15,29}, {3,23}, {17,38}, {6,24}, {10,37}, {6,11}, {28,33}, {23,25}, {31,38}, {16,20}, {5,36}, {7,38}, {13,18}, {6,35}, {31,36}, {20,29}, {5,12}, {5,40}, {12,17}, {26,37}, {13,20}, {2,36}, {18,29}, {29,34}, {3,34}, {7,12}, {4,13}, {26,35}, {21,28}, {8,33}, {20,25}, {32,37}, {3,38}, {11,18}, {23,29}, {25,38}, {14,19}, {19,30}, {29,36}, {1,13}, {2,15}, {11,23}, {15,17}, {2,14}, {29,40}, {6,33}, {4,33}, {20,31}, {4,39}, {24,26}, {28,39}, {12,21}, {17,32}, {18,31}, {30,33}, {7,36}, {1,29}, {13,40}, {8,17}, {13,32}, {6,19}, {6,31}, {5,18}, {2,32}, {13,36}, {14,35}, {5,28}, {9,28}, {23,35}, {13,26}, {4,25}, {17,36}, {24,38}, {7,20}, {16,38}, {18,37}, {9,36}, {12,29}, {15,25}, {15,33}, {12,37}, {6,16}, {25,36}, {9,20}, {13,23}, {8,13}, {4,9} } Symmetric graph 36 of order 40 Valency 12 Diameter 2 Girth 3 Automorphism group of order 51840 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,7}, {36,40}, {10,13}, {20,32}, {10,22}, {20,21}, {26,37}, {13,22}, {20,31}, {7,16}, {26,29}, {27,31}, {8,36}, {21,31}, {3,7}, {26,38}, {11,36}, {13,23}, {4,27}, {3,28}, {33,38}, {20,34}, {1,15}, {3,16}, {29,38}, {36,37}, {9,13}, {27,30}, {5,36}, {1,18}, {10,15}, {21,30}, {28,39}, {12,33}, {9,35}, {18,30}, {4,5}, {7,19}, {3,26}, {12,40}, {10,24}, {11,37}, {9,23}, {4,30}, {5,40}, {1,8}, {17,21}, {2,28}, {33,39}, {20,35}, {1,14}, {6,40}, {10,28}, {12,22}, {20,24}, {2,16}, {29,39}, {6,35}, {18,23}, {4,19}, {17,24}, {2,17}, {2,6}, {35,39}, {12,14}, {13,27}, {27,37}, {9,36}, {23,32}, {14,22}, {8,18}, {15,24}, {17,30}, {2,39}, {12,39}, {32,35}, {7,14}, {34,40}, {5,16}, {25,29}, {11,35}, {18,29}, {4,6}, {7,17}, {2,26}, {9,40}, {32,33}, {22,26}, {19,31}, {26,32}, {11,38}, {11,23}, {4,29}, {17,33}, {6,15}, {28,30}, {8,39}, {12,27}, {5,14}, {25,32}, {5,38}, {11,25}, {11,16}, {17,29}, {19,22}, {21,33}, {28,31}, {8,33}, {1,17}, {30,37}, {22,31}, {6,34}, {15,28}, {24,32}, {2,5}, {25,39}, {6,11}, {23,29}, {6,19}, {2,37}, {19,32}, {14,23}, {4,25}, {2,18}, {28,40}, {12,16}, {13,25}, {27,38}, {4,37}, {31,36}, {3,8}, {1,27}, {5,18}, {15,21}, {4,39}, {16,24}, {29,34}, {23,28}, {19,33}, {1,25}, {34,37}, {30,35}, {21,25}, {18,34}, {11,21}, {25,40}, {8,13}, {16,18}, {35,38}, {4,15}, {10,25}, {2,31}, {3,13}, {31,38}, {12,26}, {24,35}, {32,37}, {11,14}, {30,40}, {16,27}, {8,11}, {9,15}, {22,30}, {12,34}, {6,38}, {11,28}, {7,35}, {19,23}, {21,34}, {5,33}, {31,39}, {8,12}, {3,20}, {1,38}, {10,33}, {14,28}, {24,29}, {6,12}, {3,40}, {15,26}, {10,34}, {16,25}, {16,21}, {7,34}, {12,24}, {22,25}, {3,38}, {10,37}, {9,21}, {3,30}, {23,27}, {19,36}, {14,17}, {2,32}, {1,31}, {8,37}, {18,22}, {7,39}, {23,33}, {15,18}, {2,13}, {3,19}, {30,33}, {21,26}, {18,35}, {17,36}, {8,15}, {16,19}, {3,29}, {4,14}, {23,34}, {15,19}, {7,37}, {9,26}, {5,10}, {4,20}, {22,35}, {32,40}, {7,9}, {24,36}, {31,34}, {5,9}, {8,20}, {9,39}, {10,38}, {6,13}, {29,36}, {24,28}, {9,27}, {6,17}, {5,20}, {24,27}, {14,20}, {13,17}, {1,32}, {1,40}, {14,26}, {7,10}, {22,36}, {13,20} } Symmetric graph 37 of order 40 Valency 12 Diameter 2 Girth 3 Automorphism group of order 51840 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,4}, {2,7}, {3,9}, {5,15}, {1,6}, {4,18}, {5,8}, {10,28}, {2,12}, {3,13}, {7,31}, {9,12}, {10,16}, {3,19}, {20,30}, {5,21}, {6,21}, {4,25}, {8,19}, {15,20}, {1,25}, {18,21}, {19,29}, {7,20}, {8,17}, {23,27}, {4,38}, {10,13}, {10,31}, {12,13}, {13,31}, {6,7}, {9,18}, {1,16}, {16,17}, {27,28}, {4,28}, {2,6}, {3,18}, {12,31}, {1,38}, {17,22}, {15,27}, {16,30}, {2,16}, {9,35}, {29,36}, {7,14}, {9,32}, {19,25}, {19,20}, {20,25}, {21,25}, {19,21}, {12,15}, {1,13}, {18,31}, {5,12}, {2,29}, {3,7}, {29,30}, {9,30}, {6,13}, {4,31}, {8,12}, {20,21}, {2,14}, {3,32}, {30,33}, {2,34}, {9,28}, {28,29}, {23,29}, {7,38}, {5,29}, {18,32}, {5,11}, {24,38}, {22,26}, {8,15}, {1,27}, {17,18}, {4,17}, {6,27}, {17,31}, {21,28}, {2,25}, {20,31}, {12,25}, {10,21}, {5,38}, {6,22}, {4,15}, {1,8}, {23,38}, {22,38}, {18,23}, {13,19}, {9,25}, {16,21}, {13,27}, {23,37}, {6,14}, {5,30}, {3,38}, {22,30}, {35,38}, {22,36}, {14,15}, {1,32}, {10,38}, {10,22}, {10,23}, {14,26}, {32,37}, {33,39}, {34,35}, {16,28}, {2,9}, {3,29}, {30,31}, {7,30}, {13,29}, {5,6}, {6,18}, {20,27}, {10,14}, {10,32}, {12,33}, {13,34}, {7,28}, {3,16}, {14,35}, {32,36}, {14,33}, {32,34}, {31,35}, {12,36}, {17,19}, {5,18}, {36,40}, {4,14}, {8,32}, {23,33}, {34,38}, {14,32}, {11,32}, {24,33}, {26,34}, {8,28}, {2,17}, {3,15}, {14,19}, {20,32}, {19,33}, {20,34}, {19,35}, {20,36}, {8,39}, {27,35}, {17,34}, {15,40}, {37,40}, {11,14}, {8,22}, {20,23}, {25,38}, {15,23}, {19,22}, {10,12}, {9,27}, {4,29}, {21,37}, {21,24}, {11,25}, {1,30}, {7,8}, {11,27}, {17,24}, {15,26}, {8,37}, {24,27}, {11,17}, {21,26}, {24,36}, {26,39}, {15,16}, {35,37}, {26,37}, {24,37}, {11,39}, {17,27}, {1,37}, {4,26}, {16,40}, {16,33}, {11,29}, {11,30}, {28,36}, {28,39}, {34,36}, {39,40}, {16,34}, {4,36}, {28,35}, {1,33}, {9,22}, {31,40}, {13,26}, {31,37}, {2,23}, {26,30}, {2,37}, {9,26}, {29,37}, {13,39}, {24,26}, {33,35}, {11,40}, {34,39}, {35,40}, {22,40}, {3,40}, {7,39}, {7,24}, {22,23}, {3,24}, {11,24}, {18,33}, {5,34}, {25,39}, {25,40}, {5,35}, {6,36}, {23,39}, {6,40}, {18,39}, {33,36}, {12,24}, {10,11} } Symmetric graph 38 of order 40 Valency 12 Diameter 3 Girth 4 Automorphism group of order 251658240 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,7}, {5,36}, {26,39}, {2,8}, {36,38}, {17,24}, {12,13}, {6,35}, {25,40}, {2,19}, {10,36}, {19,31}, {12,14}, {35,37}, {18,23}, {11,14}, {25,29}, {2,16}, {29,37}, {21,29}, {2,7}, {1,20}, {9,35}, {20,32}, {11,13}, {23,32}, {14,24}, {3,25}, {9,24}, {27,32}, {5,35}, {25,39}, {26,30}, {1,15}, {30,38}, {22,30}, {1,8}, {20,22}, {11,25}, {23,34}, {14,28}, {15,25}, {6,19}, {15,22}, {35,38}, {17,23}, {24,31}, {13,23}, {4,26}, {10,23}, {28,31}, {6,36}, {26,40}, {28,38}, {18,30}, {8,14}, {20,34}, {11,21}, {4,14}, {7,37}, {10,28}, {4,18}, {1,19}, {10,35}, {20,31}, {19,21}, {12,26}, {24,33}, {13,27}, {16,26}, {5,20}, {16,21}, {36,37}, {18,24}, {10,16}, {31,39}, {6,11}, {2,40}, {4,38}, {30,34}, {8,17}, {11,33}, {2,27}, {9,39}, {5,16}, {33,39}, {26,29}, {1,16}, {29,38}, {21,30}, {27,37}, {17,29}, {7,13}, {19,33}, {12,22}, {3,13}, {8,38}, {9,27}, {3,17}, {2,20}, {9,36}, {19,32}, {9,16}, {3,5}, {12,21}, {8,37}, {18,35}, {10,27}, {4,31}, {6,40}, {31,40}, {8,33}, {22,35}, {15,17}, {6,12}, {8,9}, {3,38}, {12,33}, {24,32}, {13,24}, {3,26}, {10,24}, {27,31}, {9,15}, {32,40}, {5,12}, {1,39}, {3,37}, {29,33}, {7,18}, {12,34}, {1,28}, {10,40}, {6,15}, {34,40}, {25,30}, {2,15}, {30,37}, {22,29}, {3,6}, {8,34}, {14,27}, {7,17}, {6,20}, {9,40}, {32,35}, {16,22}, {5,15}, {21,27}, {11,37}, {18,29}, {33,40}, {7,14}, {19,34}, {3,14}, {7,33}, {19,22}, {12,25}, {24,34}, {13,28}, {16,25}, {5,19}, {15,21}, {10,15}, {4,6}, {11,22}, {7,38}, {17,36}, {9,28}, {3,32}, {5,39}, {32,39}, {7,34}, {21,36}, {16,18}, {5,11}, {7,10}, {4,37}, {11,34}, {23,31}, {14,23}, {4,25}, {9,23}, {28,32}, {28,37}, {5,40}, {15,18}, {1,30}, {3,18}, {8,10}, {22,27}, {13,20}, {2,39}, {29,34}, {2,28}, {4,17}, {4,5}, {8,18}, {10,39}, {31,36}, {6,16}, {22,28}, {12,38}, {17,30}, {34,39}, {8,13}, {20,33}, {4,13}, {20,21}, {11,26}, {23,33}, {15,26}, {11,38}, {4,32}, {23,26}, {17,35}, {21,35}, {27,38}, {6,39}, {16,17}, {2,29}, {7,9}, {21,28}, {14,19}, {1,40}, {30,33}, {1,27}, {13,19}, {24,26}, {31,35}, {12,37}, {3,31}, {24,25}, {18,36}, {22,36}, {1,29}, {14,20}, {23,25}, {32,36}, {2,30} } Symmetric graph 39 of order 40 Valency 12 Diameter 3 Girth 4 Automorphism group of order 251658240 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,11}, {11,21}, {14,19}, {21,31}, {19,31}, {23,30}, {23,28}, {31,33}, {31,34}, {30,33}, {28,34}, {26,40}, {25,40}, {26,38}, {25,36}, {4,33}, {6,34}, {3,33}, {5,34}, {4,40}, {6,40}, {3,38}, {5,36}, {1,35}, {2,37}, {1,36}, {2,38}, {7,35}, {7,37}, {4,14}, {6,11}, {3,15}, {5,15}, {4,13}, {6,12}, {3,16}, {5,16}, {1,14}, {2,11}, {1,15}, {2,15}, {7,13}, {7,12}, {8,12}, {8,13}, {5,11}, {3,14}, {6,10}, {4,9}, {8,10}, {8,9}, {14,23}, {11,23}, {15,21}, {15,19}, {13,17}, {12,18}, {16,17}, {16,18}, {14,24}, {11,24}, {15,22}, {15,20}, {13,18}, {12,17}, {12,21}, {13,19}, {11,17}, {14,18}, {10,24}, {9,24}, {10,22}, {9,20}, {9,22}, {10,20}, {16,21}, {16,19}, {13,23}, {12,23}, {14,20}, {11,22}, {9,19}, {10,21}, {23,26}, {23,25}, {21,26}, {19,25}, {17,31}, {18,31}, {17,30}, {18,28}, {24,27}, {24,29}, {22,28}, {20,30}, {18,27}, {17,29}, {21,25}, {19,26}, {17,32}, {18,32}, {24,28}, {24,30}, {22,27}, {20,29}, {22,31}, {20,31}, {21,27}, {19,29}, {20,25}, {22,26}, {19,32}, {21,32}, {20,32}, {22,32}, {18,30}, {17,28}, {24,26}, {24,25}, {23,29}, {23,27}, {26,35}, {25,37}, {26,36}, {25,38}, {31,35}, {31,37}, {30,36}, {28,38}, {27,33}, {29,34}, {28,33}, {30,34}, {27,40}, {29,40}, {25,39}, {26,39}, {32,38}, {32,36}, {28,37}, {30,35}, {27,39}, {29,39}, {31,36}, {31,38}, {27,34}, {29,33}, {32,37}, {32,35}, {32,33}, {32,34}, {30,39}, {28,39}, {29,36}, {27,38}, {28,40}, {30,40}, {25,35}, {26,37}, {6,35}, {4,37}, {8,36}, {8,38}, {5,35}, {3,37}, {7,36}, {7,38}, {6,33}, {4,34}, {8,33}, {8,34}, {5,40}, {3,40}, {3,39}, {5,39}, {4,38}, {6,36}, {1,37}, {2,35}, {1,39}, {2,39}, {2,36}, {1,38}, {7,34}, {7,33}, {5,33}, {3,34}, {4,39}, {6,39}, {2,40}, {1,40}, {8,35}, {8,37}, {6,15}, {4,15}, {8,14}, {8,11}, {5,9}, {3,10}, {7,9}, {7,10}, {6,16}, {4,16}, {5,10}, {3,9}, {1,16}, {2,16}, {1,13}, {2,12}, {2,13}, {1,12}, {7,14}, {7,11}, {5,12}, {3,13}, {4,10}, {6,9}, {2,14}, {15,17}, {15,18}, {14,17}, {11,18}, {9,23}, {10,23}, {9,21}, {10,19}, {16,20}, {16,22}, {13,20}, {12,22}, {12,24}, {13,24}, {17,27}, {18,29}, {21,28}, {19,30}, {20,26}, {22,25}, {27,37}, {29,35} } Symmetric graph 40 of order 40 Valency 12 Diameter 3 Girth 3 Automorphism group of order 251658240 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,7}, {28,37}, {1,31}, {11,13}, {17,21}, {24,28}, {31,33}, {2,8}, {16,27}, {17,30}, {10,40}, {13,20}, {12,21}, {24,34}, {8,33}, {27,38}, {2,32}, {4,14}, {22,26}, {22,30}, {36,40}, {6,9}, {13,19}, {27,37}, {7,17}, {10,15}, {20,33}, {7,12}, {34,38}, {12,14}, {18,22}, {23,27}, {32,34}, {1,25}, {28,29}, {16,18}, {9,24}, {9,36}, {9,35}, {5,19}, {5,40}, {3,14}, {2,31}, {11,14}, {17,22}, {30,37}, {1,40}, {3,6}, {13,25}, {8,37}, {7,37}, {1,15}, {12,33}, {7,18}, {15,28}, {18,29}, {9,39}, {14,19}, {11,22}, {23,33}, {7,34}, {23,31}, {13,21}, {21,35}, {4,29}, {26,39}, {5,20}, {5,35}, {5,14}, {5,36}, {6,14}, {31,39}, {4,38}, {4,19}, {1,26}, {28,30}, {24,27}, {32,33}, {1,8}, {16,28}, {18,30}, {9,40}, {17,36}, {9,28}, {19,31}, {26,40}, {3,30}, {2,15}, {11,38}, {2,17}, {11,37}, {1,17}, {3,28}, {25,31}, {8,15}, {29,37}, {1,39}, {3,13}, {21,25}, {21,29}, {35,39}, {5,10}, {14,20}, {28,38}, {8,18}, {9,16}, {19,34}, {8,11}, {33,37}, {19,24}, {11,33}, {10,27}, {6,10}, {29,35}, {10,16}, {20,24}, {32,39}, {4,37}, {36,39}, {4,6}, {4,28}, {4,5}, {10,24}, {12,25}, {29,38}, {24,31}, {13,22}, {21,36}, {12,22}, {23,34}, {8,34}, {4,13}, {21,26}, {22,29}, {5,9}, {30,35}, {5,13}, {14,21}, {33,38}, {30,36}, {3,27}, {25,32}, {8,12}, {27,30}, {32,40}, {16,17}, {31,40}, {13,26}, {21,30}, {15,24}, {3,38}, {2,25}, {11,21}, {17,35}, {10,28}, {20,31}, {2,26}, {15,17}, {10,23}, {10,35}, {10,36}, {6,20}, {6,39}, {1,32}, {12,13}, {18,21}, {2,39}, {14,26}, {7,38}, {8,38}, {2,16}, {11,34}, {8,17}, {12,38}, {8,16}, {6,40}, {6,35}, {20,32}, {12,37}, {20,34}, {11,25}, {17,29}, {25,40}, {3,29}, {25,39}, {7,15}, {15,23}, {18,35}, {2,18}, {9,27}, {9,15}, {19,33}, {7,11}, {2,7}, {27,29}, {5,39}, {22,36}, {6,36}, {4,27}, {12,34}, {22,35}, {14,22}, {9,23}, {4,30}, {3,20}, {12,26}, {15,27}, {23,32}, {6,13}, {24,32}, {6,19}, {3,37}, {23,28}, {31,34}, {10,39}, {1,16}, {1,18}, {26,32}, {7,16}, {30,38}, {2,40}, {15,18}, {3,19}, {34,37}, {16,23}, {35,40}, {19,23}, {20,23}, {29,36}, {3,5}, {14,25}, {4,20}, {7,33}, {18,36}, {22,25}, {11,26}, {24,33}, {26,31}, {19,32}, {16,24} } Symmetric graph 41 of order 40 Valency 12 Diameter 3 Girth 3 Automorphism group of order 251658240 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,7}, {13,28}, {20,22}, {11,40}, {4,31}, {23,34}, {33,38}, {15,25}, {25,32}, {8,17}, {17,36}, {3,18}, {12,14}, {10,38}, {2,30}, {31,38}, {2,7}, {14,22}, {21,36}, {19,22}, {10,36}, {21,26}, {18,35}, {8,12}, {26,32}, {3,6}, {14,28}, {27,29}, {6,19}, {3,32}, {8,14}, {13,27}, {12,34}, {32,38}, {19,33}, {10,37}, {24,34}, {34,38}, {10,28}, {33,37}, {1,37}, {20,21}, {9,35}, {31,37}, {15,26}, {18,23}, {12,40}, {4,32}, {30,39}, {3,5}, {15,24}, {26,31}, {7,18}, {21,32}, {11,39}, {3,31}, {11,26}, {7,14}, {18,24}, {4,6}, {17,35}, {3,17}, {11,14}, {6,40}, {4,28}, {4,18}, {12,13}, {13,20}, {23,33}, {5,20}, {9,27}, {8,13}, {1,30}, {35,40}, {1,8}, {25,31}, {7,17}, {2,29}, {6,16}, {16,26}, {10,35}, {32,37}, {13,21}, {22,35}, {31,33}, {7,37}, {16,25}, {8,18}, {1,25}, {22,32}, {21,35}, {35,39}, {17,23}, {9,36}, {22,26}, {18,36}, {7,12}, {1,15}, {15,23}, {25,40}, {4,17}, {21,25}, {8,11}, {11,23}, {16,23}, {24,33}, {5,39}, {3,27}, {21,31}, {28,29}, {6,20}, {1,20}, {9,15}, {2,8}, {13,22}, {22,36}, {27,30}, {5,19}, {23,29}, {9,37}, {1,29}, {9,28}, {7,13}, {11,33}, {20,34}, {9,38}, {18,32}, {4,13}, {14,21}, {28,38}, {2,20}, {31,34}, {7,38}, {20,33}, {9,16}, {36,40}, {10,27}, {34,37}, {1,38}, {19,21}, {20,30}, {30,40}, {2,15}, {22,25}, {2,37}, {7,36}, {29,40}, {12,39}, {2,16}, {16,24}, {26,39}, {32,33}, {8,37}, {4,5}, {23,28}, {5,10}, {14,27}, {11,34}, {19,34}, {29,39}, {30,36}, {5,40}, {28,30}, {4,27}, {11,13}, {22,31}, {12,25}, {7,35}, {11,25}, {17,31}, {12,33}, {3,40}, {4,14}, {23,27}, {17,32}, {3,13}, {5,9}, {1,19}, {10,15}, {6,39}, {3,28}, {14,20}, {6,33}, {6,15}, {19,30}, {2,38}, {13,19}, {10,22}, {5,15}, {19,29}, {1,16}, {18,31}, {17,24}, {4,40}, {24,28}, {5,16}, {6,10}, {25,39}, {7,11}, {32,34}, {8,38}, {2,26}, {9,22}, {2,25}, {8,36}, {12,26}, {1,26}, {15,18}, {36,39}, {24,27}, {26,40}, {12,23}, {23,30}, {24,29}, {6,34}, {14,19}, {11,24}, {10,16}, {24,30}, {5,34}, {20,29}, {8,35}, {15,17}, {4,39}, {3,14}, {27,37}, {27,38}, {2,19}, {10,21}, {28,37}, {30,35}, {3,39}, {29,36}, {12,24}, {6,9}, {29,35}, {16,17}, {5,33}, {9,21}, {16,18} } Symmetric graph 42 of order 40 Valency 12 Diameter 2 Girth 4 Automorphism group of order 7608405715845120 Number of arcs = 480 Number of 2-arcs = 5280 2-arc-transitive false Edge-set { {1,9}, {27,34}, {3,36}, {16,29}, {8,23}, {14,36}, {1,21}, {20,38}, {14,39}, {1,11}, {12,31}, {14,40}, {21,37}, {4,34}, {3,9}, {6,24}, {18,27}, {22,40}, {20,37}, {26,34}, {3,34}, {17,25}, {16,33}, {21,40}, {19,37}, {4,23}, {9,17}, {16,35}, {2,23}, {27,36}, {1,36}, {2,10}, {11,29}, {8,29}, {8,26}, {3,21}, {10,19}, {6,23}, {17,27}, {16,31}, {5,23}, {16,36}, {1,23}, {7,32}, {6,25}, {15,38}, {24,39}, {4,21}, {9,19}, {17,28}, {1,35}, {2,12}, {7,27}, {25,36}, {13,38}, {22,39}, {1,33}, {4,12}, {14,29}, {8,21}, {14,34}, {28,33}, {4,35}, {20,26}, {11,20}, {14,31}, {11,31}, {5,31}, {4,36}, {5,28}, {28,35}, {1,10}, {12,29}, {7,29}, {8,25}, {17,38}, {16,39}, {12,30}, {14,38}, {21,39}, {1,34}, {3,12}, {12,18}, {15,32}, {10,32}, {6,29}, {24,37}, {18,40}, {2,22}, {2,9}, {5,27}, {28,36}, {7,30}, {7,25}, {13,34}, {3,22}, {25,33}, {4,33}, {8,32}, {14,32}, {6,21}, {18,38}, {10,20}, {15,34}, {3,24}, {25,35}, {2,33}, {20,40}, {14,37}, {4,11}, {9,31}, {16,40}, {23,37}, {15,30}, {7,24}, {13,35}, {6,31}, {6,26}, {17,40}, {16,37}, {17,26}, {16,34}, {16,30}, {14,35}, {2,21}, {9,30}, {13,30}, {7,22}, {28,34}, {3,35}, {20,25}, {14,33}, {12,20}, {11,32}, {18,25}, {22,38}, {20,39}, {19,25}, {13,33}, {24,40}, {18,37}, {4,22}, {9,20}, {3,23}, {26,33}, {15,40}, {18,28}, {15,35}, {11,17}, {19,26}, {3,33}, {4,10}, {27,33}, {9,29}, {8,30}, {14,30}, {7,21}, {12,19}, {13,32}, {12,32}, {6,32}, {23,38}, {2,24}, {11,18}, {15,31}, {15,37}, {8,24}, {18,26}, {6,28}, {27,35}, {23,40}, {2,36}, {6,22}, {15,33}, {4,24}, {19,27}, {17,37}, {26,35}, {2,34}, {21,38}, {19,39}, {12,17}, {13,40}, {13,39}, {10,17}, {10,31}, {5,29}, {17,39}, {7,31}, {5,25}, {16,38}, {23,39}, {19,38}, {22,37}, {4,9}, {13,36}, {7,23}, {1,22}, {6,27}, {10,18}, {20,27}, {5,32}, {15,39}, {24,38}, {11,19}, {1,12}, {5,24}, {19,40}, {7,26}, {13,37}, {25,34}, {15,36}, {1,24}, {2,35}, {15,29}, {13,31}, {9,32}, {18,39}, {2,11}, {8,31}, {5,26}, {10,30}, {13,29}, {8,22}, {3,10}, {10,29}, {8,28}, {5,22}, {9,18}, {20,28}, {7,28}, {16,32}, {6,30}, {8,27}, {11,30}, {5,21}, {19,28}, {3,11}, {5,30}, {26,36} } Symmetric graph 43 of order 40 Valency 14 Diameter 3 Girth 4 Automorphism group of order 403200 Number of arcs = 560 Number of 2-arcs = 7280 2-arc-transitive false Edge-set { {1,7}, {9,38}, {17,21}, {6,25}, {3,19}, {14,28}, {12,31}, {8,27}, {16,35}, {11,40}, {14,23}, {20,31}, {28,39}, {3,34}, {6,37}, {10,19}, {18,27}, {2,13}, {10,11}, {22,33}, {5,36}, {30,31}, {33,39}, {3,12}, {6,15}, {20,21}, {4,28}, {1,40}, {9,23}, {8,24}, {2,16}, {7,11}, {14,20}, {15,19}, {13,27}, {35,39}, {22,38}, {7,33}, {20,36}, {5,29}, {8,32}, {23,37}, {1,25}, {3,17}, {6,30}, {5,21}, {4,8}, {34,40}, {16,40}, {12,28}, {15,31}, {24,28}, {19,33}, {10,26}, {18,34}, {13,39}, {11,22}, {9,33}, {17,36}, {15,39}, {11,32}, {14,40}, {19,35}, {27,38}, {2,21}, {4,10}, {25,29}, {3,32}, {5,9}, {8,17}, {12,23}, {1,15}, {16,37}, {7,18}, {24,30}, {2,33}, {21,35}, {16,30}, {28,37}, {25,31}, {10,36}, {18,24}, {1,22}, {13,22}, {5,11}, {20,34}, {6,40}, {20,26}, {28,34}, {8,14}, {9,13}, {4,38}, {29,33}, {32,36}, {5,6}, {8,19}, {1,12}, {21,32}, {4,40}, {4,33}, {7,36}, {22,31}, {5,39}, {2,11}, {10,14}, {19,25}, {3,27}, {20,24}, {16,27}, {29,35}, {7,23}, {12,18}, {30,34}, {33,37}, {32,38}, {21,40}, {13,24}, {9,15}, {13,17}, {17,26}, {8,22}, {2,28}, {10,31}, {11,30}, {6,35}, {1,20}, {15,26}, {13,34}, {29,38}, {25,36}, {5,16}, {9,28}, {18,39}, {19,38}, {3,24}, {8,29}, {4,23}, {8,37}, {16,25}, {14,18}, {34,38}, {21,37}, {7,31}, {22,36}, {5,24}, {1,17}, {3,29}, {6,32}, {4,25}, {20,39}, {11,27}, {14,35}, {19,40}, {23,27}, {12,26}, {15,34}, {13,19}, {10,29}, {9,30}, {17,33}, {13,37}, {2,8}, {3,7}, {22,28}, {5,31}, {26,35}, {12,38}, {18,32}, {6,20}, {30,36}, {10,16}, {15,21}, {26,40}, {1,35}, {11,25}, {19,28}, {4,13}, {3,14}, {23,34}, {18,29}, {24,33}, {10,24}, {2,18}, {11,35}, {3,9}, {2,31}, {6,17}, {23,29}, {1,32}, {26,37}, {25,34}, {14,38}, {12,21}, {7,16}, {27,36}, {24,35}, {4,15}, {10,39}, {5,14}, {19,30}, {27,33}, {9,40}, {20,29}, {8,12}, {2,38}, {18,22}, {17,23}, {28,32}, {3,37}, {7,13}, {15,16}, {1,30}, {11,20}, {31,40}, {5,26}, {10,21}, {35,36}, {24,38}, {23,39}, {13,29}, {8,34}, {7,26}, {19,23}, {3,39}, {6,22}, {12,16}, {7,21}, {2,26}, {1,27}, {9,35}, {31,37}, {11,17}, {10,34}, {24,40}, {4,20}, {25,39}, {14,30}, {5,19}, {15,29}, {18,37}, {3,22}, {13,32}, {12,33}, {7,28}, {2,23}, {17,38}, {21,30}, {15,36}, {25,26}, {1,10}, {9,18}, {14,33}, {16,32}, {11,37}, {17,31}, {22,26}, {21,27}, {2,6}, {12,36}, {9,20}, {5,34}, {15,24}, {4,35}, {30,39}, {14,25}, {29,40}, {23,32}, {7,38}, {17,28}, {8,39}, {2,36}, {6,12}, {26,32}, {27,31}, {16,22}, {1,37}, {9,25}, {4,30}, {4,18}, {6,27} } Symmetric graph 44 of order 40 Valency 15 Diameter 3 Girth 4 Automorphism group of order 2063912140800000000 Number of arcs = 600 Number of 2-arcs = 8400 2-arc-transitive false Edge-set { {1,6}, {31,33}, {12,37}, {19,24}, {1,23}, {27,40}, {17,29}, {5,11}, {14,26}, {9,31}, {12,15}, {32,34}, {6,18}, {24,27}, {36,39}, {19,38}, {1,13}, {8,33}, {18,23}, {2,40}, {5,17}, {20,22}, {2,22}, {25,37}, {11,14}, {14,34}, {21,28}, {4,31}, {5,25}, {26,30}, {7,12}, {24,35}, {1,39}, {8,9}, {15,25}, {10,32}, {6,36}, {27,38}, {13,28}, {12,30}, {10,13}, {16,27}, {29,35}, {8,19}, {1,22}, {2,8}, {10,15}, {16,36}, {19,32}, {11,23}, {35,38}, {13,17}, {21,33}, {34,40}, {17,40}, {3,14}, {28,31}, {12,31}, {18,39}, {2,16}, {5,35}, {20,37}, {4,37}, {14,25}, {30,34}, {4,15}, {7,36}, {17,21}, {7,20}, {6,34}, {3,24}, {26,39}, {12,13}, {30,35}, {10,39}, {2,37}, {5,20}, {3,21}, {4,6}, {22,26}, {9,39}, {15,19}, {23,25}, {3,30}, {7,27}, {10,24}, {1,16}, {2,32}, {6,26}, {27,32}, {1,29}, {23,36}, {19,40}, {17,23}, {8,28}, {25,31}, {6,10}, {3,38}, {28,29}, {11,29}, {8,35}, {17,22}, {2,21}, {21,34}, {4,40}, {7,34}, {28,40}, {22,33}, {9,14}, {7,17}, {28,37}, {20,31}, {27,30}, {10,29}, {28,38}, {9,16}, {32,33}, {11,37}, {13,33}, {18,31}, {2,5}, {5,26}, {15,35}, {9,21}, {14,20}, {3,31}, {6,12}, {20,30}, {10,22}, {33,37}, {22,34}, {12,24}, {26,32}, {6,9}, {15,27}, {16,19}, {23,35}, {25,29}, {9,30}, {15,18}, {24,36}, {3,39}, {13,27}, {10,30}, {10,16}, {11,32}, {15,26}, {32,36}, {1,38}, {8,18}, {29,36}, {7,19}, {23,28}, {14,17}, {18,37}, {20,24}, {30,36}, {27,39}, {19,29}, {4,24}, {1,7}, {10,38}, {13,36}, {33,38}, {2,23}, {3,5}, {16,18}, {9,23}, {33,40}, {17,37}, {13,20}, {12,22}, {2,13}, {11,40}, {2,14}, {5,34}, {3,15}, {17,38}, {18,21}, {11,21}, {4,14}, {20,21}, {3,37}, {6,20}, {20,39}, {19,22}, {5,33}, {4,22}, {25,39}, {26,40}, {9,15}, {15,36}, {8,27}, {7,11}, {14,28}, {4,21}, {31,34}, {5,18}, {24,26}, {12,40}, {4,7}, {24,25}, {1,30}, {9,38}, {3,8}, {6,25}, {1,32}, {6,27}, {27,29}, {7,28}, {4,30}, {7,10}, {8,10}, {22,36}, {2,38}, {2,29}, {5,9}, {16,25}, {8,11}, {16,28}, {9,29}, {7,33}, {5,12}, {13,26}, {12,32}, {11,13}, {31,35}, {4,5}, {14,35}, {34,39}, {1,15}, {8,36}, {11,16}, {25,38}, {14,33}, {17,32}, {17,31}, {12,21}, {18,30}, {16,33}, {35,37}, {34,37}, {14,18}, {24,34}, {15,34}, {36,40}, {20,40}, {4,13}, {25,30}, {36,38}, {18,38}, {3,16}, {6,35}, {35,39}, {19,39}, {18,24}, {1,40}, {4,39}, {19,23}, {3,23}, {11,38}, {22,28}, {2,31}, {21,35}, {6,19}, {1,24}, {1,8}, {22,27}, {23,27}, {10,40}, {16,17}, {8,17}, {21,25}, {3,29}, {8,25}, {11,22}, {21,26}, {4,32}, {7,26}, {28,32}, {23,33}, {5,28}, {26,31}, {11,31}, {19,30}, {10,23}, {26,37}, {12,14}, {12,39}, {13,34}, {20,32}, {3,6}, {16,35}, {18,29}, {9,24}, {13,19}, {15,20}, {9,37}, {29,33}, {2,7} } Symmetric graph 45 of order 40 Valency 16 Diameter 3 Girth 3 Automorphism group of order 7680 Number of arcs = 640 Number of 2-arcs = 9600 2-arc-transitive false Edge-set { {1,6}, {19,28}, {9,28}, {16,40}, {22,29}, {29,40}, {29,34}, {22,36}, {2,37}, {6,12}, {8,13}, {12,36}, {2,13}, {4,12}, {13,18}, {8,19}, {27,33}, {4,27}, {19,32}, {9,35}, {17,23}, {11,39}, {1,32}, {19,35}, {23,27}, {27,39}, {26,32}, {25,35}, {13,23}, {23,39}, {16,17}, {11,22}, {3,39}, {17,30}, {26,39}, {25,30}, {9,16}, {15,22}, {2,29}, {20,34}, {7,14}, {6,24}, {31,35}, {1,36}, {15,28}, {2,16}, {20,22}, {7,39}, {6,30}, {35,39}, {1,30}, {9,38}, {15,32}, {20,31}, {7,23}, {6,39}, {7,35}, {14,22}, {24,37}, {6,31}, {8,36}, {1,26}, {11,14}, {14,24}, {35,38}, {11,37}, {14,31}, {34,37}, {6,21}, {8,38}, {12,27}, {13,27}, {4,15}, {18,21}, {18,24}, {12,40}, {5,9}, {2,10}, {16,20}, {1,28}, {21,40}, {29,38}, {22,27}, {27,37}, {6,15}, {8,21}, {18,35}, {1,12}, {11,19}, {9,14}, {2,35}, {1,20}, {11,28}, {14,28}, {3,34}, {9,21}, {15,38}, {10,15}, {16,21}, {7,18}, {1,9}, {2,18}, {12,20}, {8,40}, {8,33}, {4,5}, {10,19}, {1,17}, {28,38}, {28,32}, {24,31}, {36,40}, {8,24}, {5,40}, {2,34}, {3,20}, {31,33}, {4,36}, {10,24}, {4,33}, {4,18}, {5,19}, {7,9}, {17,34}, {3,11}, {32,39}, {30,35}, {30,39}, {21,26}, {25,38}, {5,13}, {5,23}, {32,36}, {20,29}, {10,34}, {27,30}, {21,37}, {28,40}, {28,29}, {5,36}, {2,7}, {12,34}, {3,13}, {8,30}, {33,39}, {4,30}, {19,21}, {5,17}, {7,11}, {20,23}, {28,35}, {16,31}, {24,29}, {34,40}, {2,27}, {20,27}, {21,28}, {31,40}, {29,36}, {24,40}, {4,25}, {18,26}, {5,29}, {7,34}, {21,34}, {3,38}, {21,30}, {33,38}, {5,22}, {7,37}, {12,23}, {28,34}, {21,35}, {17,36}, {2,11}, {3,17}, {11,17}, {20,26}, {10,25}, {16,30}, {22,33}, {24,28}, {3,29}, {9,40}, {15,29}, {8,10}, {5,16}, {2,19}, {8,17}, {5,11}, {20,36}, {18,27}, {15,25}, {3,10}, {19,25}, {5,33}, {3,26}, {17,25}, {13,26}, {23,25}, {10,22}, {18,29}, {4,14}, {25,31}, {26,36}, {1,15}, {14,20}, {11,35}, {1,14}, {5,38}, {7,32}, {3,31}, {10,39}, {7,20}, {6,10}, {15,19}, {12,15}, {13,21}, {18,33}, {14,30}, {4,7}, {13,29}, {4,32}, {3,35}, {11,26}, {14,25}, {7,22}, {18,31}, {7,15}, {2,40}, {16,37}, {8,12}, {15,39}, {7,29}, {10,36}, {13,19}, {2,5}, {26,37}, {13,38}, {23,32}, {10,13}, {12,18}, {25,34}, {6,20}, {6,35}, {4,40}, {19,24}, {27,31}, {27,36}, {24,26}, {24,36}, {21,32}, {30,37}, {14,37}, {3,6}, {12,25}, {12,21}, {11,33}, {10,37}, {16,27}, {14,17}, {11,24}, {13,39}, {23,30}, {31,38}, {26,33}, {22,31}, {10,17}, {23,38}, {12,13}, {25,40}, {1,38}, {15,24}, {2,31}, {9,18}, {16,26}, {1,33}, {15,18}, {19,30}, {9,33}, {22,38}, {14,40}, {9,26}, {2,25}, {6,18}, {16,23}, {12,38}, {4,37}, {17,32}, {19,33}, {22,39}, {10,27}, {23,34}, {13,32}, {23,35}, {9,20}, {8,16}, {1,39}, {5,32}, {1,8}, {24,33}, {32,37}, {30,33}, {8,31}, {6,14}, {3,16}, {36,37}, {3,28}, {17,28}, {11,16}, {6,34}, {3,8}, {32,34}, {9,23}, {6,37}, {17,22}, {22,25}, {4,19}, {26,29}, {4,9} } Symmetric graph 46 of order 40 Valency 16 Diameter 3 Girth 3 Automorphism group of order 7680 Number of arcs = 640 Number of 2-arcs = 9600 2-arc-transitive false Edge-set { {1,6}, {8,29}, {4,33}, {31,34}, {7,35}, {6,18}, {2,39}, {17,35}, {6,40}, {19,32}, {36,37}, {3,29}, {9,33}, {7,22}, {3,31}, {4,19}, {10,37}, {21,29}, {32,33}, {1,36}, {5,11}, {20,24}, {30,38}, {5,34}, {1,7}, {13,18}, {28,39}, {28,32}, {21,36}, {5,35}, {2,11}, {14,24}, {27,30}, {27,34}, {18,36}, {5,39}, {8,20}, {4,38}, {15,30}, {25,34}, {2,26}, {12,24}, {23,33}, {17,30}, {34,40}, {8,32}, {4,36}, {3,40}, {9,19}, {10,22}, {15,31}, {10,36}, {5,15}, {20,27}, {22,38}, {19,30}, {34,37}, {7,15}, {3,25}, {26,39}, {8,16}, {9,17}, {16,40}, {3,20}, {9,38}, {22,30}, {2,31}, {12,35}, {6,23}, {2,29}, {33,38}, {8,18}, {11,17}, {13,40}, {7,12}, {3,14}, {16,26}, {24,26}, {18,25}, {23,39}, {8,10}, {17,21}, {32,40}, {31,36}, {6,20}, {2,38}, {5,21}, {1,32}, {1,13}, {11,28}, {14,28}, {21,27}, {35,38}, {14,20}, {27,38}, {18,34}, {2,9}, {12,16}, {23,28}, {1,33}, {8,11}, {17,24}, {30,40}, {32,38}, {12,22}, {14,31}, {31,37}, {4,13}, {10,28}, {21,37}, {17,32}, {2,5}, {1,12}, {13,23}, {28,29}, {28,33}, {8,21}, {3,6}, {16,19}, {26,37}, {25,29}, {7,34}, {3,7}, {18,23}, {29,39}, {9,35}, {4,15}, {10,25}, {21,40}, {16,32}, {26,36}, {1,20}, {12,37}, {14,17}, {12,26}, {3,11}, {9,13}, {22,25}, {23,31}, {27,35}, {4,27}, {5,32}, {20,35}, {6,38}, {12,33}, {7,23}, {22,34}, {8,36}, {4,5}, {8,40}, {10,15}, {15,25}, {10,39}, {15,20}, {9,27}, {16,22}, {19,23}, {29,37}, {12,20}, {9,23}, {16,29}, {3,17}, {9,40}, {7,13}, {3,28}, {16,37}, {17,26}, {15,23}, {4,39}, {25,35}, {4,26}, {10,24}, {21,33}, {23,36}, {5,29}, {16,28}, {21,26}, {35,39}, {24,35}, {6,30}, {2,19}, {10,14}, {15,27}, {24,27}, {5,10}, {7,30}, {3,34}, {25,40}, {10,34}, {10,18}, {15,39}, {27,31}, {22,35}, {1,37}, {14,30}, {11,34}, {36,40}, {7,31}, {13,19}, {28,37}, {2,18}, {11,14}, {13,27}, {22,32}, {5,17}, {14,38}, {2,8}, {4,12}, {16,24}, {26,30}, {10,20}, {14,26}, {1,25}, {19,28}, {13,21}, {6,9}, {2,16}, {30,36}, {23,29}, {29,33}, {16,18}, {25,32}, {17,28}, {20,31}, {2,34}, {21,31}, {32,35}, {18,27}, {11,38}, {14,22}, {12,18}, {11,23}, {24,34}, {13,25}, {7,17}, {1,10}, {19,36}, {1,15}, {24,37}, {25,38}, {6,22}, {11,19}, {13,37}, {6,12}, {2,14}, {22,39}, {20,25}, {23,38}, {30,34}, {15,17}, {12,27}, {19,22}, {19,26}, {8,33}, {14,39}, {9,26}, {1,40}, {11,21}, {13,32}, {27,40}, {18,31}, {6,16}, {8,24}, {4,30}, {33,39}, {20,21}, {6,36}, {3,9}, {28,36}, {20,29}, {3,35}, {8,14}, {12,39}, {11,15}, {13,29}, {7,37}, {20,33}, {8,38}, {7,39}, {3,37}, {11,36}, {5,13}, {4,10}, {2,35}, {5,37}, {9,16}, {3,16}, {23,25}, {24,40}, {11,40}, {4,32}, {4,18}, {24,30}, {11,25}, {26,33}, {22,28}, {12,13}, {17,33}, {1,28}, {5,19}, {9,21}, {26,31}, {6,33}, {18,22}, {31,39}, {2,27}, {15,38}, {7,19}, {24,32}, {29,35}, {5,24}, {1,30}, {19,34}, {6,14}, {1,17}, {15,21}, {18,29}, {6,31}, {7,9}, {4,8} } Symmetric graph 47 of order 40 Valency 16 Diameter 3 Girth 4 Automorphism group of order 15216811431690240 Number of arcs = 640 Number of 2-arcs = 9600 2-arc-transitive false Edge-set { {1,5}, {6,11}, {2,16}, {12,16}, {15,25}, {5,20}, {1,40}, {15,20}, {26,40}, {19,29}, {36,39}, {11,22}, {10,16}, {4,6}, {2,29}, {19,22}, {10,39}, {4,30}, {29,35}, {21,33}, {5,9}, {3,37}, {18,30}, {16,25}, {24,25}, {14,20}, {28,40}, {7,12}, {3,15}, {5,33}, {21,25}, {9,24}, {3,14}, {28,30}, {7,34}, {3,6}, {33,38}, {5,17}, {26,39}, {20,23}, {11,13}, {16,27}, {1,8}, {4,32}, {24,34}, {20,29}, {36,40}, {27,29}, {21,36}, {17,22}, {10,37}, {29,33}, {10,15}, {14,26}, {8,19}, {4,39}, {11,39}, {16,20}, {26,29}, {23,36}, {13,27}, {21,27}, {8,17}, {4,37}, {32,34}, {6,33}, {10,40}, {14,19}, {8,12}, {4,15}, {2,39}, {20,31}, {11,23}, {3,30}, {30,35}, {22,28}, {10,22}, {16,18}, {25,38}, {34,40}, {6,9}, {2,13}, {7,35}, {3,7}, {27,40}, {19,21}, {22,33}, {5,10}, {18,29}, {31,33}, {5,34}, {26,37}, {18,23}, {23,25}, {12,24}, {1,14}, {28,32}, {33,39}, {28,39}, {17,30}, {35,37}, {9,21}, {9,13}, {3,16}, {25,30}, {20,22}, {30,33}, {5,35}, {28,37}, {18,22}, {18,31}, {34,38}, {26,31}, {23,34}, {9,23}, {12,13}, {1,7}, {3,32}, {35,40}, {7,19}, {12,39}, {4,14}, {28,29}, {17,21}, {9,37}, {9,15}, {13,26}, {3,39}, {3,5}, {1,30}, {22,36}, {8,10}, {16,28}, {22,25}, {8,34}, {6,17}, {25,32}, {24,33}, {14,25}, {24,28}, {20,24}, {11,40}, {31,36}, {4,40}, {15,27}, {5,18}, {1,38}, {10,38}, {14,17}, {4,31}, {29,34}, {21,26}, {25,39}, {11,14}, {5,11}, {8,20}, {16,19}, {32,35}, {2,37}, {7,33}, {20,30}, {6,12}, {17,32}, {23,27}, {13,18}, {27,38}, {6,36}, {10,24}, {34,39}, {6,20}, {11,38}, {16,17}, {1,32}, {32,33}, {11,24}, {24,36}, {8,11}, {2,40}, {19,31}, {30,36}, {8,35}, {13,28}, {22,27}, {15,18}, {26,38}, {6,10}, {2,14}, {4,7}, {4,38}, {17,29}, {10,21}, {9,14}, {26,30}, {7,17}, {23,26}, {12,23}, {1,13}, {27,32}, {13,19}, {27,39}, {35,38}, {3,8}, {4,16}, {6,34}, {2,6}, {25,37}, {18,24}, {20,32}, {33,40}, {25,29}, {9,40}, {12,15}, {7,36}, {20,21}, {36,37}, {8,18}, {3,29}, {11,16}, {2,31}, {28,31}, {17,23}, {12,37}, {5,19}, {23,35}, {9,22}, {10,13}, {22,34}, {15,26}, {31,34}, {14,27}, {21,28}, {3,40}, {19,30}, {12,22}, {25,31}, {12,40}, {6,35}, {2,7}, {35,39}, {7,20}, {27,37}, {18,21}, {9,16}, {13,25}, {4,5}, {1,29}, {8,9}, {34,37}, {6,18}, {9,38}, {13,17}, {18,32}, {19,24}, {2,30}, {31,35}, {12,14}, {15,28}, {1,37}, {7,10}, {3,31}, {23,33}, {5,12}, {23,28}, {30,34}, {10,23}, {22,35}, {22,26}, {2,38}, {17,31}, {4,13}, {15,19}, {1,15}, {32,36}, {24,27}, {11,21}, {5,36}, {14,18}, {8,33}, {25,40}, {26,32}, {28,38}, {4,8}, {4,29}, {21,34}, {24,26}, {29,36}, {8,36}, {12,38}, {15,17}, {3,38}, {10,14}, {1,31}, {13,20}, {36,38}, {7,11}, {2,5}, {19,32}, {11,15}, {27,31}, {24,35}, {1,6}, {2,32}, {14,28}, {16,26}, {6,19}, {17,24}, {7,18}, {9,39}, {11,37}, {7,9}, {3,13}, {19,23}, {27,30}, {21,35}, {33,37}, {2,15}, {2,8}, {1,16}, {12,21}, {1,39} } Symmetric graph 48 of order 40 Valency 16 Diameter 2 Girth 4 Automorphism group of order 1065620623885074432000000 Number of arcs = 640 Number of 2-arcs = 9600 2-arc-transitive false Edge-set { {1,9}, {30,38}, {20,29}, {18,28}, {26,40}, {5,17}, {7,39}, {8,14}, {6,34}, {16,25}, {27,36}, {7,36}, {5,16}, {26,34}, {14,28}, {2,33}, {2,13}, {22,35}, {15,22}, {4,15}, {4,35}, {13,23}, {23,33}, {23,34}, {14,23}, {4,36}, {4,16}, {16,22}, {22,36}, {2,14}, {2,34}, {21,29}, {21,30}, {1,29}, {1,30}, {9,24}, {10,24}, {3,9}, {3,10}, {3,31}, {3,32}, {24,31}, {24,32}, {1,12}, {1,11}, {12,21}, {11,21}, {12,22}, {11,22}, {2,12}, {2,11}, {23,31}, {23,32}, {4,31}, {4,32}, {4,9}, {4,10}, {9,23}, {10,23}, {2,29}, {2,30}, {22,29}, {22,30}, {10,17}, {9,39}, {10,18}, {9,40}, {17,30}, {29,39}, {18,30}, {29,40}, {11,38}, {12,20}, {11,37}, {12,19}, {32,38}, {20,31}, {32,37}, {19,31}, {20,32}, {31,38}, {19,32}, {31,37}, {11,20}, {12,38}, {11,19}, {12,37}, {30,39}, {17,29}, {30,40}, {18,29}, {10,39}, {9,17}, {10,40}, {9,18}, {7,37}, {5,19}, {26,38}, {20,28}, {8,37}, {6,19}, {25,38}, {20,27}, {7,18}, {5,40}, {17,26}, {28,39}, {8,18}, {6,40}, {17,25}, {27,39}, {28,40}, {18,26}, {5,39}, {7,17}, {27,40}, {18,25}, {6,39}, {8,17}, {19,28}, {26,37}, {5,20}, {7,38}, {19,27}, {25,37}, {6,20}, {8,38}, {27,34}, {14,25}, {6,36}, {8,16}, {16,28}, {26,36}, {5,14}, {7,34}, {27,33}, {13,25}, {6,35}, {8,15}, {15,28}, {26,35}, {5,13}, {7,33}, {8,34}, {6,14}, {25,36}, {16,27}, {7,16}, {5,36}, {14,26}, {28,34}, {8,33}, {6,13}, {25,35}, {15,27}, {7,15}, {5,35}, {13,26}, {28,33}, {13,22}, {22,33}, {2,15}, {2,35}, {23,35}, {15,23}, {4,33}, {4,13}, {4,14}, {4,34}, {16,23}, {23,36}, {2,36}, {2,16}, {22,34}, {14,22}, {13,21}, {21,33}, {1,15}, {1,35}, {24,35}, {15,24}, {3,33}, {3,13}, {3,14}, {3,34}, {16,24}, {24,36}, {1,36}, {1,16}, {21,34}, {14,21}, {1,10}, {9,21}, {10,21}, {3,29}, {3,30}, {24,29}, {24,30}, {12,24}, {11,24}, {3,12}, {3,11}, {21,31}, {21,32}, {1,31}, {1,32}, {2,31}, {2,32}, {22,31}, {22,32}, {4,12}, {4,11}, {12,23}, {11,23}, {23,29}, {23,30}, {4,29}, {4,30}, {9,22}, {10,22}, {2,9}, {2,10}, {30,37}, {19,29}, {10,38}, {9,20}, {10,37}, {9,19}, {17,32}, {31,39}, {18,32}, {31,40}, {11,17}, {12,39}, {11,18}, {12,40}, {11,39}, {12,17}, {11,40}, {12,18}, {32,39}, {17,31}, {32,40}, {18,31}, {10,20}, {9,38}, {10,19}, {9,37}, {20,30}, {29,38}, {19,30}, {29,37}, {18,27}, {25,40}, {6,17}, {8,39}, {28,37}, {19,26}, {5,38}, {7,20}, {27,37}, {19,25}, {6,38}, {8,20}, {7,19}, {5,37}, {20,26}, {28,38}, {8,19}, {6,37}, {20,25}, {27,38}, {7,40}, {5,18}, {26,39}, {17,28}, {8,40}, {6,18}, {25,39}, {17,27}, {8,13}, {6,33}, {15,25}, {27,35}, {7,35}, {5,15}, {26,33}, {13,28}, {14,27}, {25,34}, {6,16}, {8,36}, {28,36}, {16,26}, {5,34}, {7,14}, {13,27}, {25,33}, {6,15}, {8,35}, {28,35}, {15,26}, {5,33}, {7,13}, {1,33}, {1,13}, {21,35}, {15,21}, {3,15}, {3,35}, {13,24}, {24,33}, {24,34}, {14,24}, {3,36}, {3,16}, {16,21}, {21,36}, {1,14}, {1,34} } Symmetric graph 49 of order 40 Valency 18 Diameter 3 Girth 3 Automorphism group of order 1440 Number of arcs = 720 Number of 2-arcs = 12240 2-arc-transitive false Edge-set { {1,5}, {11,29}, {13,22}, {14,34}, {27,32}, {7,18}, {12,17}, {17,38}, {18,34}, {4,36}, {2,29}, {10,23}, {15,37}, {13,24}, {28,38}, {24,26}, {5,38}, {23,38}, {34,37}, {31,39}, {23,35}, {30,34}, {21,32}, {5,15}, {9,25}, {20,25}, {6,20}, {6,18}, {10,17}, {3,26}, {2,6}, {4,10}, {11,26}, {5,13}, {5,26}, {5,9}, {25,38}, {6,34}, {27,35}, {7,30}, {5,40}, {9,36}, {33,38}, {31,34}, {8,36}, {11,20}, {13,20}, {1,16}, {1,21}, {3,39}, {12,21}, {14,39}, {12,23}, {14,37}, {15,24}, {2,32}, {4,24}, {12,30}, {14,21}, {15,31}, {23,25}, {2,14}, {4,27}, {11,18}, {13,17}, {2,11}, {4,13}, {11,16}, {13,26}, {1,26}, {3,5}, {12,38}, {4,40}, {2,36}, {10,33}, {11,28}, {8,13}, {16,39}, {26,35}, {26,37}, {5,33}, {35,38}, {9,39}, {16,35}, {27,39}, {18,21}, {17,39}, {19,29}, {19,22}, {8,29}, {11,22}, {7,24}, {17,27}, {9,28}, {17,25}, {10,20}, {30,36}, {21,29}, {6,31}, {13,33}, {28,31}, {8,17}, {20,35}, {20,30}, {3,9}, {17,30}, {4,31}, {2,23}, {14,23}, {27,37}, {18,24}, {14,30}, {21,27}, {18,31}, {17,23}, {14,19}, {19,27}, {2,18}, {4,17}, {4,22}, {11,32}, {5,28}, {8,23}, {30,39}, {21,35}, {25,33}, {3,14}, {1,27}, {9,18}, {16,17}, {7,19}, {2,40}, {2,25}, {4,6}, {11,37}, {26,40}, {5,36}, {16,27}, {7,26}, {19,40}, {19,36}, {2,7}, {24,27}, {7,38}, {22,34}, {32,40}, {7,22}, {12,40}, {9,34}, {16,32}, {7,14}, {12,27}, {6,10}, {10,15}, {2,38}, {3,16}, {1,24}, {3,38}, {15,21}, {25,39}, {33,39}, {31,35}, {8,34}, {12,35}, {18,37}, {17,33}, {3,35}, {1,30}, {9,24}, {16,38}, {21,40}, {36,39}, {21,33}, {24,33}, {31,38}, {23,30}, {5,30}, {9,21}, {5,17}, {4,25}, {6,23}, {10,37}, {4,8}, {30,37}, {5,24}, {9,38}, {17,22}, {18,40}, {21,37}, {24,31}, {7,31}, {14,36}, {27,29}, {3,11}, {1,13}, {9,16}, {27,33}, {8,40}, {11,36}, {1,37}, {3,33}, {17,32}, {4,29}, {2,22}, {16,23}, {19,24}, {19,38}, {10,22}, {15,40}, {28,30}, {8,21}, {3,21}, {12,31}, {14,25}, {6,27}, {2,28}, {11,39}, {13,35}, {4,19}, {2,19}, {2,10}, {4,15}, {22,28}, {22,39}, {35,40}, {10,30}, {10,26}, {12,34}, {28,36}, {7,10}, {12,15}, {13,28}, {8,28}, {26,34}, {15,18}, {15,20}, {26,30}, {5,21}, {19,32}, {6,29}, {26,32}, {8,20}, {3,7}, {7,33}, {16,34}, {13,40}, {6,37}, {24,37}, {24,36}, {29,33}, {22,31}, {6,16}, {19,26}, {5,19}, {8,11}, {7,35}, {8,37}, {11,33}, {9,31}, {13,31}, {8,16}, {11,24}, {13,38}, {1,31}, {3,23}, {5,12}, {9,14}, {15,25}, {6,25}, {6,11}, {10,13}, {16,26}, {23,28}, {8,25}, {6,35}, {10,35}, {15,30}, {18,35}, {4,34}, {14,32}, {18,29}, {16,19}, {4,37}, {2,33}, {25,29}, {6,22}, {32,37}, {29,38}, {23,32}, {9,19}, {10,40}, {22,26}, {7,15}, {12,25}, {20,28}, {8,9}, {8,32}, {1,17}, {3,18}, {4,12}, {3,30}, {14,27}, {7,27}, {17,36}, {23,40}, {22,30}, {21,25}, {20,31}, {20,23}, {1,12}, {7,12}, {28,40}, {15,33}, {25,31}, {2,15}, {28,34}, {1,35}, {20,37}, {20,21}, {20,39}, {11,13}, {22,36}, {29,40}, {10,32}, {19,34}, {18,28}, {6,14}, {6,39}, {32,33}, {12,19}, {15,36}, {10,27}, {18,26}, {29,35}, {5,32}, {1,20}, {3,20}, {12,14}, {1,9}, {25,36}, {20,33}, {36,37}, {23,34}, {1,34}, {3,32}, {9,29}, {16,22}, {15,28}, {3,28}, {1,39}, {16,29}, {24,29}, {22,38}, {24,39}, {1,8}, {13,29}, {7,39}, {14,18}, {34,40}, {32,36} } Symmetric graph 50 of order 40 Valency 18 Diameter 2 Girth 3 Automorphism group of order 2880 Number of arcs = 720 Number of 2-arcs = 12240 2-arc-transitive false Edge-set { {1,5}, {17,21}, {15,17}, {31,39}, {1,39}, {31,35}, {15,26}, {21,30}, {15,21}, {2,26}, {28,30}, {9,35}, {5,33}, {27,39}, {35,39}, {5,39}, {9,24}, {20,33}, {10,27}, {2,5}, {10,28}, {4,17}, {11,15}, {21,36}, {2,15}, {21,28}, {5,38}, {10,40}, {4,32}, {6,11}, {9,36}, {17,24}, {15,20}, {6,10}, {23,31}, {1,19}, {7,35}, {5,12}, {24,35}, {5,20}, {10,39}, {14,17}, {15,23}, {6,16}, {23,25}, {19,29}, {7,19}, {12,14}, {31,38}, {1,40}, {32,35}, {6,19}, {9,14}, {26,37}, {30,38}, {2,20}, {16,28}, {8,17}, {2,38}, {28,40}, {17,32}, {6,15}, {9,21}, {31,33}, {1,6}, {35,37}, {19,34}, {7,14}, {12,37}, {34,38}, {20,30}, {4,16}, {8,33}, {14,26}, {23,30}, {16,21}, {2,25}, {28,29}, {19,30}, {4,14}, {9,13}, {22,33}, {14,27}, {24,32}, {10,34}, {18,31}, {1,13}, {14,24}, {20,23}, {10,16}, {25,31}, {1,29}, {19,35}, {5,14}, {4,26}, {26,30}, {19,21}, {2,13}, {22,28}, {3,30}, {4,25}, {8,13}, {11,22}, {3,14}, {27,32}, {2,31}, {23,34}, {4,18}, {13,26}, {9,33}, {6,33}, {27,37}, {34,39}, {7,39}, {12,24}, {20,34}, {27,30}, {4,31}, {23,33}, {5,36}, {8,10}, {4,40}, {11,33}, {6,36}, {25,38}, {29,40}, {3,6}, {9,25}, {26,29}, {33,38}, {6,40}, {32,37}, {6,34}, {7,9}, {12,26}, {30,34}, {2,30}, {4,28}, {17,33}, {9,23}, {19,33}, {9,27}, {30,39}, {4,39}, {24,36}, {8,20}, {22,27}, {12,23}, {18,36}, {7,40}, {6,18}, {11,25}, {29,36}, {24,26}, {3,37}, {23,29}, {3,19}, {4,5}, {10,26}, {4,19}, {11,13}, {22,36}, {3,15}, {21,25}, {8,38}, {11,40}, {3,32}, {11,27}, {31,36}, {23,26}, {4,37}, {26,38}, {1,17}, {15,27}, {16,23}, {19,24}, {4,7}, {19,22}, {14,18}, {9,28}, {32,33}, {16,19}, {13,25}, {22,29}, {14,25}, {8,9}, {3,27}, {24,27}, {20,31}, {10,23}, {1,26}, {5,37}, {10,38}, {4,30}, {5,11}, {10,36}, {21,31}, {1,38}, {27,40}, {18,32}, {36,37}, {8,37}, {11,38}, {16,20}, {16,24}, {7,12}, {12,34}, {1,28}, {9,38}, {33,40}, {13,22}, {18,22}, {28,37}, {32,38}, {22,30}, {17,23}, {15,19}, {6,9}, {7,36}, {8,12}, {22,35}, {5,18}, {12,39}, {13,23}, {7,16}, {22,25}, {18,29}, {7,11}, {12,36}, {9,37}, {11,35}, {34,37}, {7,38}, {30,40}, {29,33}, {5,10}, {10,35}, {8,34}, {12,33}, {10,13}, {36,40}, {26,32}, {6,37}, {13,17}, {15,22}, {6,14}, {23,27}, {19,31}, {7,17}, {12,15}, {26,39}, {14,21}, {11,16}, {25,29}, {3,29}, {13,18}, {32,34}, {2,7}, {3,8}, {10,21}, {17,35}, {31,37}, {30,35}, {5,19}, {10,14}, {1,20}, {16,27}, {8,18}, {2,40}, {17,29}, {8,15}, {11,21}, {12,40}, {7,20}, {12,16}, {1,8}, {5,13}, {10,22}, {12,28}, {3,13}, {14,20}, {24,31}, {6,17}, {9,15}, {2,6}, {3,18}, {4,8}, {11,26}, {1,16}, {13,19}, {14,22}, {35,40}, {11,37}, {36,38}, {8,35}, {21,33}, {33,39}, {6,39}, {7,34}, {3,25}, {20,24}, {9,39}, {2,27}, {28,31}, {17,30}, {4,15}, {21,32}, {2,17}, {11,34}, {1,32}, {18,35}, {8,16}, {11,24}, {20,32}, {2,16}, {18,21}, {17,36}, {1,14}, {5,35}, {18,23}, {21,34}, {30,36}, {24,28}, {7,13}, {12,22}, {2,18}, {13,28}, {21,26}, {3,20}, {16,25}, {18,34}, {5,15}, {20,36}, {27,31}, {1,31}, {23,35}, {25,39}, {29,39}, {3,7}, {12,25}, {2,29}, {3,28}, {25,32}, {24,34}, {3,39}, {1,27}, {15,28}, {29,37}, {3,38}, {8,40}, {24,29}, {22,32}, {2,37}, {28,38}, {20,22}, {16,18}, {29,34}, {25,40}, {13,24}, {32,40} } Symmetric graph 51 of order 40 Valency 18 Diameter 3 Girth 3 Automorphism group of order 1509949440 Number of arcs = 720 Number of 2-arcs = 12240 2-arc-transitive false Edge-set { {1,7}, {25,37}, {1,34}, {2,30}, {15,30}, {10,25}, {27,34}, {23,26}, {12,33}, {18,23}, {12,22}, {2,13}, {7,30}, {3,10}, {27,32}, {29,39}, {9,16}, {5,28}, {7,35}, {18,39}, {5,16}, {5,37}, {20,26}, {24,33}, {23,37}, {1,12}, {13,28}, {3,21}, {10,32}, {24,31}, {11,13}, {14,17}, {8,21}, {4,39}, {4,31}, {11,37}, {1,26}, {31,35}, {13,18}, {17,39}, {4,21}, {30,39}, {4,15}, {19,29}, {8,9}, {28,40}, {15,39}, {16,25}, {5,34}, {4,20}, {6,28}, {35,38}, {13,21}, {7,10}, {8,22}, {9,40}, {15,20}, {6,24}, {19,36}, {17,23}, {6,38}, {2,38}, {27,31}, {13,36}, {22,27}, {9,36}, {6,15}, {1,25}, {29,34}, {11,22}, {9,26}, {20,35}, {18,24}, {31,36}, {13,17}, {6,27}, {36,38}, {23,31}, {12,13}, {18,27}, {22,36}, {11,20}, {14,38}, {2,8}, {4,32}, {14,31}, {18,31}, {13,22}, {2,17}, {21,30}, {10,39}, {4,27}, {4,40}, {3,31}, {11,29}, {16,26}, {6,20}, {24,38}, {13,37}, {5,38}, {2,37}, {14,32}, {8,14}, {18,34}, {19,22}, {8,40}, {3,40}, {20,25}, {7,36}, {29,40}, {3,16}, {26,29}, {16,33}, {3,22}, {9,32}, {12,20}, {24,25}, {3,5}, {32,37}, {12,14}, {8,25}, {18,40}, {2,25}, {30,34}, {10,24}, {11,27}, {5,15}, {6,37}, {1,14}, {8,29}, {11,34}, {19,26}, {8,35}, {9,25}, {20,36}, {17,24}, {3,32}, {12,29}, {7,22}, {9,39}, {16,20}, {5,24}, {3,35}, {18,32}, {5,12}, {15,34}, {6,19}, {16,23}, {26,38}, {2,33}, {21,27}, {10,36}, {9,23}, {22,35}, {9,18}, {5,20}, {24,37}, {26,36}, {17,33}, {6,23}, {12,38}, {13,31}, {7,13}, {3,27}, {32,36}, {14,36}, {22,28}, {9,35}, {15,24}, {6,11}, {1,17}, {21,29}, {34,40}, {3,19}, {16,40}, {20,30}, {4,16}, {26,30}, {15,33}, {19,21}, {10,23}, {19,38}, {2,23}, {10,35}, {5,33}, {20,37}, {32,38}, {2,14}, {28,32}, {14,35}, {2,34}, {19,30}, {12,37}, {24,32}, {11,14}, {17,28}, {21,35}, {1,24}, {9,17}, {21,28}, {35,37}, {14,21}, {8,10}, {16,34}, {5,19}, {30,40}, {28,39}, {4,35}, {10,15}, {16,19}, {5,23}, {32,35}, {14,18}, {2,26}, {30,33}, {12,27}, {8,13}, {7,40}, {3,15}, {6,32}, {4,22}, {19,25}, {23,34}, {2,11}, {1,33}, {20,29}, {11,38}, {8,30}, {12,34}, {8,36}, {17,40}, {16,24}, {5,11}, {1,37}, {17,34}, {8,39}, {11,28}, {26,35}, {10,18}, {16,39}, {4,5}, {33,40}, {3,20}, {7,17}, {21,39}, {1,29}, {16,29}, {28,33}, {3,6}, {7,25}, {7,14}, {26,37}, {8,18}, {34,39}, {4,19}, {15,40}, {25,29}, {3,39}, {20,22}, {9,24}, {3,28}, {12,21}, {12,19}, {23,25}, {31,37}, {8,26}, {22,40}, {25,36}, {14,27}, {17,32}, {17,27}, {21,36}, {1,23}, {6,33}, {20,38}, {7,39}, {29,33}, {7,26}, {33,39}, {4,28}, {15,19}, {10,16}, {23,33}, {10,31}, {11,19}, {10,26}, {27,33}, {16,30}, {10,40}, {4,36}, {17,31}, {8,17}, {4,6}, {31,38}, {11,30}, {15,26}, {23,38}, {13,38}, {2,7}, {10,17}, {23,32}, {20,21}, {11,21}, {19,35}, {12,28}, {5,32}, {2,24}, {18,28}, {21,40}, {5,27}, {36,37}, {27,39}, {28,34}, {24,34}, {15,29}, {6,16}, {2,12}, {25,30}, {6,31}, {1,11}, {13,35}, {7,18}, {14,28}, {4,9}, {28,31}, {1,30}, {19,37}, {2,18}, {13,27}, {14,22}, {22,30}, {9,15}, {1,38}, {2,29}, {14,37}, {3,36}, {6,12}, {25,38}, {1,13}, {9,31}, {18,33}, {7,21}, {7,9}, {7,29}, {3,9}, {13,32}, {27,40}, {22,29}, {15,23}, {1,18}, {6,34}, {11,33}, {5,31}, {4,10}, {12,30}, {15,25}, {24,26}, {25,35}, {1,8}, {22,39} } Symmetric graph 52 of order 40 Valency 18 Diameter 3 Girth 4 Automorphism group of order 7610145177600 Number of arcs = 720 Number of 2-arcs = 12240 2-arc-transitive false Edge-set { {1,7}, {13,27}, {18,28}, {35,37}, {3,21}, {6,36}, {4,5}, {17,32}, {34,39}, {11,15}, {20,29}, {25,31}, {26,33}, {16,26}, {19,25}, {6,11}, {20,30}, {22,40}, {16,23}, {8,9}, {3,34}, {1,12}, {29,33}, {2,36}, {33,39}, {2,24}, {8,34}, {22,25}, {2,7}, {8,10}, {12,19}, {30,38}, {10,39}, {24,31}, {23,28}, {15,30}, {20,35}, {13,21}, {15,18}, {1,29}, {9,36}, {14,31}, {17,33}, {36,37}, {9,14}, {28,30}, {27,35}, {12,34}, {1,30}, {14,27}, {17,28}, {24,28}, {8,21}, {7,15}, {2,18}, {10,40}, {20,24}, {14,37}, {3,9}, {12,32}, {10,36}, {4,31}, {2,40}, {10,23}, {7,32}, {11,37}, {21,29}, {6,40}, {5,23}, {1,13}, {9,18}, {23,31}, {13,33}, {3,38}, {12,22}, {5,29}, {17,31}, {23,38}, {13,22}, {4,10}, {32,35}, {21,30}, {15,35}, {2,13}, {10,18}, {35,38}, {3,22}, {5,36}, {4,6}, {4,32}, {11,28}, {27,29}, {27,40}, {6,14}, {5,17}, {19,24}, {14,38}, {7,9}, {8,32}, {17,38}, {22,39}, {15,23}, {13,20}, {4,21}, {14,33}, {3,16}, {14,19}, {10,24}, {4,27}, {17,22}, {16,39}, {1,11}, {9,29}, {26,38}, {10,26}, {13,37}, {18,21}, {6,23}, {5,13}, {3,10}, {12,31}, {29,37}, {21,36}, {20,40}, {12,21}, {1,26}, {9,25}, {3,5}, {6,12}, {31,40}, {12,37}, {16,24}, {11,34}, {2,11}, {10,29}, {32,40}, {23,34}, {17,21}, {6,24}, {5,14}, {18,32}, {34,40}, {12,15}, {26,31}, {25,33}, {16,25}, {19,26}, {4,16}, {11,19}, {22,36}, {1,35}, {19,35}, {25,38}, {22,26}, {5,26}, {6,25}, {18,38}, {23,27}, {13,28}, {4,28}, {11,27}, {5,18}, {12,20}, {30,37}, {7,37}, {11,16}, {19,29}, {29,38}, {15,39}, {8,38}, {7,22}, {9,24}, {14,32}, {16,35}, {3,19}, {5,12}, {6,30}, {20,39}, {24,37}, {16,18}, {1,23}, {9,13}, {18,33}, {24,33}, {2,14}, {17,37}, {21,39}, {10,25}, {26,37}, {21,25}, {15,24}, {14,20}, {1,17}, {9,39}, {11,31}, {7,19}, {11,21}, {15,29}, {15,26}, {20,25}, {12,38}, {24,32}, {22,30}, {14,22}, {16,17}, {1,24}, {4,19}, {11,38}, {10,30}, {31,35}, {5,11}, {6,29}, {26,32}, {19,30}, {21,40}, {3,33}, {2,12}, {29,34}, {1,36}, {8,33}, {8,22}, {7,16}, {30,33}, {13,32}, {18,34}, {7,34}, {1,40}, {12,33}, {2,30}, {2,25}, {25,34}, {6,18}, {5,40}, {10,35}, {3,31}, {16,36}, {22,35}, {6,26}, {5,25}, {7,21}, {8,15}, {2,17}, {17,27}, {28,39}, {1,8}, {1,18}, {9,40}, {23,37}, {12,27}, {9,23}, {4,38}, {11,22}, {32,39}, {24,34}, {7,20}, {21,26}, {15,25}, {8,37}, {9,17}, {6,39}, {5,24}, {10,13}, {18,31}, {32,36}, {11,20}, {1,14}, {2,39}, {23,32}, {7,38}, {20,23}, {12,16}, {8,27}, {7,28}, {16,29}, {33,40}, {2,23}, {15,40}, {4,9}, {11,32}, {5,39}, {8,16}, {18,22}, {16,40}, {10,14}, {3,32}, {1,25}, {9,26}, {4,33}, {2,8}, {7,10}, {20,36}, {14,21}, {15,17}, {9,35}, {13,31}, {28,29}, {27,36}, {12,28}, {27,30}, {27,39}, {2,29}, {4,37}, {5,35}, {28,35}, {13,19}, {15,36}, {10,17}, {14,34}, {30,34}, {3,15}, {31,39}, {2,26}, {26,34}, {28,40}, {6,17}, {3,6}, {18,27}, {6,13}, {19,23}, {13,38}, {21,35}, {19,40}, {16,30}, {4,20}, {9,30}, {7,27}, {8,28}, {11,33}, {25,32}, {8,31}, {3,27}, {1,39}, {36,38}, {4,22}, {20,26}, {25,37}, {24,27}, {5,30}, {19,39}, {24,38}, {4,15}, {13,34}, {23,33}, {19,36}, {14,28}, {7,31}, {22,29}, {3,37}, {2,35}, {4,34}, {3,20}, {6,35}, {18,37}, {8,19}, {3,28}, {28,36}, {7,33}, {17,34}, {8,20}, {31,36} } Symmetric graph 53 of order 40 Valency 19 Diameter 3 Girth 4 Automorphism group of order 4865804016353280000 Number of arcs = 760 Number of 2-arcs = 13680 2-arc-transitive true Edge-set { {1,3}, {14,38}, {23,33}, {7,14}, {18,26}, {19,32}, {3,30}, {7,15}, {27,30}, {28,40}, {22,37}, {12,33}, {10,30}, {15,18}, {7,20}, {1,12}, {2,39}, {2,11}, {10,13}, {18,21}, {32,35}, {12,25}, {10,33}, {18,27}, {15,38}, {21,38}, {23,35}, {31,37}, {24,40}, {24,36}, {4,15}, {8,25}, {9,27}, {5,40}, {3,22}, {21,24}, {29,35}, {25,32}, {20,33}, {1,27}, {1,10}, {14,18}, {9,14}, {5,26}, {3,19}, {13,21}, {20,39}, {6,25}, {4,20}, {18,34}, {24,29}, {16,29}, {16,20}, {1,26}, {6,39}, {11,14}, {9,20}, {5,8}, {3,11}, {22,29}, {32,38}, {20,38}, {1,23}, {23,25}, {3,33}, {7,27}, {3,16}, {7,26}, {6,30}, {14,28}, {33,37}, {4,12}, {8,9}, {27,31}, {38,40}, {5,29}, {13,27}, {34,38}, {17,33}, {11,20}, {11,17}, {17,38}, {23,38}, {23,30}, {31,36}, {7,36}, {16,27}, {26,38}, {6,16}, {14,22}, {33,36}, {8,11}, {10,11}, {1,40}, {19,23}, {24,26}, {19,29}, {32,33}, {20,30}, {1,15}, {15,30}, {5,12}, {2,7}, {2,18}, {13,32}, {34,35}, {16,26}, {1,21}, {1,32}, {14,39}, {8,35}, {6,11}, {1,8}, {1,17}, {14,31}, {28,32}, {22,27}, {36,38}, {22,34}, {28,36}, {1,34}, {14,19}, {12,19}, {4,21}, {14,30}, {9,36}, {5,17}, {7,10}, {6,18}, {4,32}, {16,36}, {15,22}, {25,36}, {23,39}, {26,28}, {19,37}, {8,28}, {11,37}, {18,40}, {22,32}, {12,38}, {10,38}, {18,23}, {12,18}, {21,35}, {6,35}, {30,37}, {15,24}, {24,27}, {4,40}, {8,22}, {3,31}, {9,23}, {17,30}, {22,23}, {7,40}, {22,36}, {5,36}, {29,38}, {16,23}, {23,28}, {3,39}, {7,21}, {19,40}, {2,22}, {1,6}, {4,14}, {10,31}, {6,19}, {2,4}, {23,31}, {3,28}, {7,37}, {21,28}, {35,37}, {12,13}, {9,34}, {3,7}, {7,12}, {4,26}, {6,28}, {15,25}, {5,27}, {13,40}, {6,9}, {4,17}, {10,18}, {6,24}, {4,29}, {26,31}, {2,30}, {2,28}, {13,37}, {2,16}, {13,36}, {27,39}, {11,40}, {10,22}, {14,35}, {14,25}, {26,33}, {19,27}, {21,33}, {27,35}, {3,9}, {3,5}, {10,25}, {18,20}, {20,25}, {1,20}, {34,39}, {11,29}, {10,16}, {19,26}, {7,34}, {12,28}, {11,26}, {10,19}, {30,32}, {15,39}, {4,10}, {4,6}, {9,26}, {17,19}, {2,19}, {33,40}, {12,30}, {9,15}, {37,39}, {10,24}, {5,23}, {3,13}, {21,25}, {5,37}, {24,34}, {26,39}, {19,21}, {2,33}, {13,15}, {2,9}, {2,5}, {16,17}, {15,33}, {21,30}, {15,35}, {13,23}, {30,34}, {19,36}, {18,29}, {20,35}, {8,39}, {13,34}, {28,34}, {25,27}, {5,20}, {8,13}, {11,34}, {12,24}, {2,24}, {9,37}, {17,24}, {4,8}, {20,31}, {36,39}, {11,15}, {3,24}, {7,29}, {20,28}, {1,37}, {9,32}, {14,16}, {6,33}, {25,29}, {27,33}, {27,38}, {17,31}, {31,40}, {11,36}, {17,25}, {15,31}, {2,35}, {30,36}, {15,28}, {25,37}, {12,22}, {25,34}, {5,34}, {26,30}, {28,37}, {24,37}, {18,32}, {32,39}, {12,35}, {2,31}, {26,35}, {8,33}, {9,29}, {6,13}, {30,40}, {18,37}, {24,32}, {8,18}, {16,37}, {17,28}, {9,12}, {5,10}, {3,18}, {8,19}, {7,17}, {12,31}, {4,37}, {11,27}, {3,38}, {29,31}, {16,40}, {8,31}, {20,24}, {1,29}, {6,38}, {8,16}, {17,22}, {13,26}, {13,29}, {16,34}, {6,31}, {18,36}, {8,30}, {2,38}, {22,26}, {5,32}, {8,24}, {1,14}, {21,39}, {6,22}, {4,36}, {28,29}, {10,39}, {6,7}, {11,21}, {10,35}, {17,35}, {7,23}, {2,13}, {2,25}, {13,20}, {22,40}, {5,21}, {3,35}, {16,32}, {7,32}, {12,39}, {25,40}, {20,22}, {29,33}, {13,17}, {19,34}, {16,21}, {14,33}, {1,36}, {17,39}, {29,39}, {8,38}, {11,23}, {5,14}, {10,28}, {4,23}, {9,17}, {4,27}, {12,16}, {14,24}, {35,40}, {9,40}, {4,34}, {5,15}, {3,25}, {15,19}, {11,32}, {21,31}, {31,34}, {9,21} } Symmetric graph 54 of order 40 Valency 20 Diameter 2 Girth 4 Automorphism group of order 11838024362779855370834883379200000000 Number of arcs = 800 Number of 2-arcs = 15200 2-arc-transitive true Edge-set { {1,5}, {18,31}, {13,28}, {14,34}, {9,32}, {2,37}, {36,38}, {11,38}, {6,35}, {10,24}, {17,23}, {14,19}, {8,20}, {24,26}, {20,22}, {7,27}, {4,23}, {8,33}, {3,31}, {29,35}, {25,30}, {4,7}, {4,39}, {1,30}, {26,37}, {3,15}, {12,29}, {5,25}, {9,16}, {7,12}, {11,40}, {20,30}, {15,26}, {15,18}, {11,13}, {19,39}, {16,34}, {16,25}, {12,21}, {28,40}, {24,33}, {21,26}, {17,22}, {15,35}, {11,30}, {34,39}, {32,34}, {22,36}, {18,29}, {6,33}, {3,40}, {33,40}, {2,21}, {17,38}, {4,5}, {2,39}, {1,31}, {9,39}, {7,34}, {11,22}, {6,18}, {6,10}, {1,8}, {12,32}, {5,27}, {19,21}, {16,17}, {5,17}, {2,14}, {20,31}, {15,28}, {14,18}, {9,13}, {22,28}, {18,24}, {6,26}, {1,22}, {27,32}, {23,27}, {13,25}, {10,21}, {28,37}, {5,36}, {2,29}, {31,33}, {28,31}, {14,35}, {9,30}, {34,38}, {32,35}, {24,36}, {2,6}, {1,38}, {4,32}, {27,39}, {1,13}, {10,37}, {3,37}, {36,40}, {2,23}, {19,38}, {10,31}, {8,28}, {12,14}, {5,9}, {9,38}, {7,35}, {11,24}, {6,20}, {7,10}, {4,8}, {17,32}, {14,27}, {13,20}, {10,15}, {18,37}, {13,36}, {19,23}, {16,19}, {8,17}, {3,14}, {20,29}, {9,23}, {25,38}, {21,35}, {24,28}, {20,24}, {7,26}, {4,22}, {27,30}, {23,26}, {15,25}, {13,33}, {35,37}, {30,36}, {23,34}, {19,32}, {8,36}, {3,29}, {29,33}, {25,31}, {16,35}, {12,30}, {3,24}, {20,40}, {2,7}, {4,38}, {4,30}, {26,39}, {1,15}, {11,37}, {3,39}, {34,40}, {12,37}, {7,19}, {8,11}, {3,6}, {10,29}, {8,25}, {12,16}, {5,12}, {9,40}, {7,33}, {11,21}, {4,16}, {17,30}, {14,26}, {15,20}, {11,15}, {18,39}, {13,34}, {19,22}, {16,18}, {6,17}, {23,25}, {26,29}, {22,25}, {16,27}, {12,23}, {25,40}, {21,33}, {21,28}, {17,24}, {5,26}, {2,22}, {15,33}, {11,31}, {35,39}, {30,34}, {22,34}, {18,32}, {6,36}, {1,29}, {32,33}, {27,31}, {3,8}, {12,39}, {1,40}, {33,37}, {3,21}, {17,40}, {2,5}, {2,38}, {4,31}, {28,39}, {1,14}, {5,34}, {9,22}, {7,18}, {6,11}, {1,6}, {10,32}, {8,27}, {12,13}, {5,10}, {9,37}, {19,29}, {18,21}, {13,17}, {5,19}, {2,16}, {17,31}, {14,28}, {14,20}, {9,15}, {18,38}, {13,35}, {6,28}, {1,24}, {26,32}, {22,27}, {13,27}, {10,23}, {25,37}, {21,36}, {23,28}, {19,24}, {16,36}, {2,32}, {31,36}, {28,29}, {14,33}, {9,31}, {35,38}, {30,35}, {24,34}, {20,32}, {7,36}, {27,38}, {4,13}, {10,39}, {1,37}, {36,37}, {3,23}, {19,40}, {2,8}, {3,38}, {4,29}, {10,40}, {10,14}, {8,9}, {12,38}, {5,35}, {9,24}, {7,20}, {7,11}, {4,6}, {10,30}, {8,26}, {20,37}, {15,36}, {18,23}, {13,19}, {8,19}, {3,16}, {17,29}, {14,25}, {16,20}, {12,15}, {21,27}, {23,35}, {24,25}, {20,21}, {7,28}, {4,24}, {26,30}, {22,26}, {15,27}, {11,23}, {25,39}, {19,30}, {8,34}, {3,32}, {29,36}, {25,29}, {16,33}, {12,31}, {35,40}, {30,33}, {21,34}, {3,7}, {4,40}, {2,30}, {26,38}, {4,15}, {11,39}, {1,39}, {34,37}, {3,22}, {18,40}, {11,29}, {6,25}, {10,16}, {8,12}, {12,40}, {5,33}, {9,21}, {7,17}, {5,11}, {16,26}, {15,17}, {11,14}, {20,39}, {15,34}, {18,22}, {13,18}, {6,19}, {1,16}, {12,22}, {27,40}, {23,33}, {21,25}, {17,21}, {5,28}, {2,24}, {26,31}, {33,39}, {31,34}, {22,35}, {18,30}, {6,34}, {1,32}, {32,36}, {27,29}, {1,21}, {17,37}, {3,5}, {2,40}, {2,31}, {28,38}, {4,14}, {5,18}, {6,9}, {1,7}, {11,32}, {6,27}, {10,13}, {8,10}, {2,13}, {19,31}, {16,28}, {14,17}, {9,14}, {20,38}, {28,32}, {24,27}, {13,26}, {10,22}, {27,37}, {23,36}, {14,36}, {9,29}, {33,38}, {31,35}, {24,35}, {10,38}, {4,37}, {36,39}, {1,23}, {19,37}, {8,35}, {12,24}, {5,20}, {7,9}, {20,23}, {15,19}, {8,18}, {3,13}, {7,25}, {4,21}, {28,30}, {3,30}, {29,34}, {25,32}, {26,40}, {2,15}, {11,16}, {6,12}, {17,39}, {22,33} } Symmetric graph 55 of order 40 Valency 24 Diameter 2 Girth 3 Automorphism group of order 1920 Number of arcs = 960 Number of 2-arcs = 22080 2-arc-transitive false Edge-set { {1,5}, {22,25}, {24,29}, {4,5}, {4,10}, {3,13}, {9,28}, {23,25}, {24,30}, {23,34}, {8,30}, {19,24}, {32,34}, {7,33}, {2,7}, {2,5}, {4,12}, {3,15}, {9,27}, {2,37}, {12,14}, {15,27}, {23,27}, {3,31}, {9,37}, {16,37}, {14,25}, {26,40}, {15,21}, {21,26}, {21,31}, {21,25}, {24,31}, {23,35}, {6,30}, {17,24}, {32,36}, {6,33}, {3,7}, {12,21}, {20,31}, {20,35}, {6,17}, {3,36}, {2,6}, {3,12}, {14,24}, {26,32}, {12,33}, {7,20}, {12,18}, {5,20}, {4,33}, {8,11}, {1,19}, {1,17}, {11,36}, {1,8}, {1,11}, {1,14}, {11,26}, {4,11}, {3,14}, {9,26}, {2,38}, {12,16}, {15,28}, {22,27}, {3,32}, {9,38}, {16,39}, {13,25}, {28,40}, {15,22}, {24,26}, {21,32}, {1,35}, {6,11}, {14,29}, {26,39}, {29,38}, {28,32}, {22,38}, {24,39}, {13,32}, {21,28}, {22,31}, {24,35}, {6,32}, {3,20}, {9,33}, {8,16}, {1,25}, {35,40}, {6,15}, {26,29}, {21,39}, {30,35}, {6,40}, {25,29}, {23,40}, {15,30}, {27,36}, {5,23}, {29,37}, {22,32}, {36,39}, {5,13}, {23,29}, {22,36}, {5,29}, {20,22}, {29,33}, {8,36}, {23,36}, {5,30}, {20,24}, {32,33}, {8,33}, {1,7}, {10,21}, {17,31}, {18,35}, {6,35}, {7,17}, {2,36}, {4,6}, {3,10}, {16,24}, {25,32}, {10,33}, {9,18}, {5,19}, {4,34}, {7,11}, {2,19}, {4,17}, {10,36}, {3,8}, {1,9}, {1,16}, {11,25}, {16,29}, {28,36}, {5,22}, {13,20}, {28,33}, {8,9}, {1,18}, {10,13}, {17,28}, {7,16}, {2,25}, {10,17}, {3,9}, {16,19}, {25,34}, {2,11}, {4,14}, {10,26}, {3,38}, {9,16}, {16,28}, {32,39}, {33,40}, {7,15}, {18,27}, {4,29}, {11,38}, {8,13}, {1,28}, {11,18}, {15,38}, {16,27}, {11,28}, {19,22}, {4,28}, {12,19}, {15,17}, {6,39}, {12,24}, {12,13}, {20,28}, {4,16}, {10,25}, {9,39}, {13,18}, {19,25}, {24,34}, {2,13}, {12,28}, {4,39}, {24,28}, {10,39}, {13,40}, {27,39}, {13,23}, {2,39}, {15,25}, {24,27}, {3,29}, {16,40}, {27,40}, {15,23}, {22,26}, {21,29}, {1,34}, {14,32}, {26,38}, {30,38}, {28,38}, {16,22}, {21,38}, {13,31}, {23,28}, {22,30}, {8,32}, {3,18}, {9,35}, {5,16}, {4,25}, {34,40}, {8,15}, {30,33}, {7,40}, {25,31}, {24,37}, {23,37}, {14,30}, {26,36}, {5,21}, {31,37}, {23,32}, {34,39}, {22,33}, {7,29}, {18,22}, {29,35}, {5,36}, {28,35}, {7,39}, {10,24}, {19,29}, {2,15}, {27,33}, {7,23}, {29,40}, {19,34}, {8,34}, {7,32}, {18,26}, {21,35}, {4,31}, {8,38}, {24,33}, {18,31}, {35,37}, {5,37}, {21,36}, {5,31}, {20,23}, {17,32}, {18,33}, {7,35}, {7,18}, {2,35}, {18,25}, {11,40}, {15,19}, {17,26}, {3,40}, {28,30}, {5,17}, {19,27}, {7,22}, {2,29}, {30,36}, {5,40}, {17,36}, {6,18}, {3,35}, {7,36}, {10,37}, {2,30}, {31,35}, {6,37}, {36,38}, {6,9}, {19,35}, {6,34}, {18,23}, {5,34}, {4,8}, {19,30}, {4,37}, {3,37}, {9,14}, {19,21}, {31,34}, {9,23}, {18,30}, {2,9}, {9,34}, {8,18}, {11,19}, {12,34}, {9,21}, {4,36}, {3,6}, {13,24}, {3,19}, {2,17}, {12,36}, {1,10}, {1,13}, {22,37}, {16,20}, {25,33}, {8,10}, {10,15}, {17,27}, {7,10}, {4,18}, {10,35}, {11,17}, {14,19}, {26,34}, {2,12}, {4,15}, {10,27}, {32,40}, {33,38}, {4,30}, {11,37}, {15,40}, {5,14}, {4,26}, {9,20}, {12,20}, {15,20}, {8,39}, {11,24}, {20,26}, {2,16}, {12,25}, {14,18}, {4,40}, {13,26}, {10,40}, {13,38}, {25,39}, {7,38}, {18,21}, {3,34}, {28,37}, {17,21}, {31,36}, {2,26}, {11,13}, {19,28}, {14,37}, {27,37}, {14,23}, {16,26}, {1,40}, {1,38}, {11,16}, {26,30}, {17,23}, {9,15}, {12,38}, {1,39}, {12,39}, {16,32}, {25,38}, {30,40}, {16,21}, {21,40}, {16,31}, {36,37}, {19,32}, {2,27}, {24,38}, {6,31}, {13,21}, {28,31}, {15,39}, {13,27}, {22,40}, {8,20}, {27,31}, {14,38}, {13,17}, {31,38}, {14,22}, {12,40}, {25,37}, {23,30}, {15,31}, {12,23}, {20,30}, {20,32}, {20,33}, {1,31}, {14,26}, {2,33}, {7,12}, {21,33}, {7,31}, {33,37}, {7,14}, {27,30}, {6,14}, {1,33}, {23,39}, {13,30}, {32,37}, {35,39}, {6,13}, {22,34}, {8,29}, {29,34}, {10,20}, {18,29}, {27,34}, {8,23}, {17,34}, {8,21}, {34,38}, {5,38}, {8,37}, {19,36}, {20,25}, {1,30}, {17,29}, {5,9}, {5,35}, {11,23}, {8,19}, {11,34}, {10,19}, {2,20}, {1,32}, {14,39}, {6,12}, {11,22}, {10,22}, {18,36}, {1,27}, {2,32}, {17,33}, {9,22}, {16,18}, {25,35}, {5,10}, {11,15}, {11,35}, {26,35}, {6,21}, {9,17}, {14,28}, {6,19}, {27,29}, {3,26}, {10,14}, {4,20}, {5,12}, {12,27}, {14,17}, {15,29}, {3,27}, {13,37}, {31,39}, {7,24}, {6,22}, {30,39}, {8,24}, {3,28}, {20,34}, {6,24} } Symmetric graph 56 of order 40 Valency 24 Diameter 2 Girth 3 Automorphism group of order 1920 Number of arcs = 960 Number of 2-arcs = 22080 2-arc-transitive false Edge-set { {1,6}, {11,39}, {15,22}, {4,27}, {31,37}, {19,36}, {7,33}, {32,40}, {1,14}, {3,7}, {9,38}, {13,24}, {19,28}, {12,16}, {21,25}, {11,40}, {33,39}, {8,15}, {12,38}, {13,21}, {2,28}, {30,39}, {17,34}, {5,36}, {24,30}, {3,19}, {25,35}, {6,29}, {18,31}, {2,34}, {1,27}, {31,40}, {4,16}, {25,37}, {9,36}, {7,23}, {2,25}, {29,39}, {18,34}, {5,34}, {30,37}, {3,16}, {4,8}, {10,37}, {20,27}, {10,13}, {24,28}, {8,17}, {10,36}, {24,38}, {13,19}, {14,31}, {2,26}, {5,11}, {12,22}, {9,17}, {15,37}, {16,27}, {32,39}, {1,15}, {1,7}, {9,40}, {35,40}, {6,14}, {3,31}, {2,38}, {13,28}, {28,30}, {12,20}, {21,35}, {2,16}, {4,5}, {12,37}, {15,23}, {17,27}, {10,15}, {24,27}, {3,8}, {10,38}, {35,38}, {6,13}, {14,23}, {3,26}, {32,38}, {21,32}, {1,18}, {26,34}, {5,32}, {17,30}, {3,36}, {9,22}, {20,23}, {13,26}, {28,32}, {2,17}, {36,39}, {24,34}, {5,19}, {8,9}, {29,37}, {10,27}, {24,31}, {19,25}, {29,33}, {22,28}, {20,30}, {7,38}, {32,35}, {4,6}, {11,37}, {7,15}, {12,39}, {15,21}, {1,28}, {30,40}, {26,40}, {11,33}, {8,22}, {9,13}, {2,37}, {16,39}, {30,34}, {3,5}, {8,30}, {3,10}, {18,29}, {14,18}, {35,37}, {6,16}, {10,40}, {14,24}, {3,25}, {29,38}, {20,36}, {7,35}, {22,32}, {1,20}, {26,36}, {7,32}, {17,32}, {1,36}, {13,23}, {2,14}, {26,39}, {11,34}, {5,22}, {20,33}, {8,35}, {4,13}, {2,6}, {6,18}, {23,39}, {15,17}, {15,29}, {6,10}, {11,24}, {10,20}, {13,38}, {30,33}, {20,21}, {18,35}, {29,34}, {6,30}, {3,11}, {22,37}, {16,20}, {28,37}, {27,36}, {10,24}, {19,24}, {9,28}, {23,30}, {26,32}, {1,32}, {7,17}, {2,19}, {5,16}, {12,25}, {19,30}, {3,33}, {8,21}, {10,18}, {2,12}, {21,39}, {11,26}, {14,22}, {3,27}, {31,38}, {12,36}, {7,21}, {4,25}, {18,36}, {7,34}, {3,15}, {1,8}, {1,29}, {4,40}, {25,31}, {9,19}, {23,33}, {28,34}, {5,30}, {3,37}, {16,38}, {4,35}, {6,37}, {10,23}, {26,38}, {13,32}, {5,23}, {12,17}, {3,14}, {11,35}, {6,22}, {1,26}, {17,33}, {8,36}, {2,13}, {2,5}, {18,28}, {12,14}, {21,26}, {6,19}, {15,18}, {13,29}, {4,28}, {6,12}, {11,21}, {11,20}, {13,39}, {15,28}, {20,34}, {5,35}, {33,37}, {8,16}, {4,29}, {4,37}, {15,27}, {27,31}, {10,19}, {24,33}, {16,21}, {18,25}, {9,14}, {23,26}, {34,40}, {5,14}, {16,22}, {11,23}, {17,22}, {4,20}, {22,36}, {7,20}, {7,12}, {31,36}, {18,32}, {5,39}, {10,25}, {18,21}, {17,26}, {5,15}, {12,27}, {8,11}, {10,22}, {27,38}, {13,31}, {33,38}, {3,30}, {3,38}, {32,36}, {17,24}, {8,20}, {10,35}, {4,11}, {6,39}, {11,15}, {24,37}, {16,19}, {6,24}, {2,29}, {8,24}, {13,25}, {9,18}, {23,34}, {16,29}, {4,18}, {34,37}, {27,29}, {4,31}, {19,33}, {8,33}, {1,13}, {2,7}, {9,39}, {28,29}, {12,18}, {21,34}, {17,28}, {12,15}, {21,27}, {36,38}, {7,13}, {1,40}, {14,40}, {7,31}, {2,9}, {15,30}, {8,10}, {2,35}, {14,26}, {22,38}, {20,26}, {4,39}, {6,34}, {24,35}, {22,25}, {20,29}, {8,13}, {14,27}, {26,31}, {11,19}, {22,33}, {4,15}, {20,25}, {23,28}, {16,24}, {3,17}, {25,33}, {8,29}, {4,34}, {19,22}, {23,36}, {5,12}, {11,25}, {22,29}, {18,27}, {31,34}, {5,37}, {30,36}, {10,14}, {24,26}, {25,38}, {9,35}, {6,23}, {5,40}, {3,40}, {14,38}, {1,9}, {19,32}, {16,17}, {25,36}, {23,31}, {28,33}, {27,40}, {10,33}, {19,35}, {6,33}, {31,35}, {21,40}, {12,21}, {21,29}, {11,17}, {4,10}, {2,32}, {18,23}, {7,24}, {25,32}, {9,27}, {19,26}, {32,33}, {1,39}, {5,9}, {25,39}, {8,38}, {11,28}, {9,21}, {15,20}, {27,35}, {23,40}, {14,17}, {1,12}, {7,40}, {9,16}, {23,25}, {34,39}, {3,12}, {17,29}, {27,34}, {22,30}, {3,20}, {7,29}, {1,34}, {28,39}, {12,34}, {5,21}, {15,40}, {1,33}, {8,40}, {16,30}, {7,10}, {9,26}, {23,32}, {14,37}, {16,26}, {22,27}, {19,31}, {2,33}, {9,34}, {4,9}, {36,40}, {7,14}, {21,31}, {2,18}, {3,35}, {17,35}, {6,36}, {13,20}, {16,31}, {12,23}, {28,35}, {24,29}, {2,31}, {12,33}, {1,17}, {10,28}, {26,33}, {8,32}, {4,36}, {2,39}, {14,28}, {26,30}, {22,35}, {1,10}, {24,40}, {1,38}, {13,40}, {8,39}, {6,20}, {11,16}, {5,18}, {20,31}, {14,32}, {21,36}, {6,31}, {2,11}, {1,30}, {4,19}, {27,30}, {7,18}, {27,37}, {15,32}, {8,19}, {21,38}, {13,18}, {15,39}, {4,30}, {15,25}, {12,26}, {29,35}, {16,37}, {16,25}, {28,40}, {14,30}, {23,37}, {11,13}, {6,9}, {5,17}, {7,37}, {25,29}, {22,39}, {3,32}, {14,19}, {18,22}, {7,11}, {17,21}, {9,24}, {19,23}, {6,38}, {5,31}, {20,24} } Symmetric graph 57 of order 40 Valency 24 Diameter 2 Girth 3 Automorphism group of order 3019898880 Number of arcs = 960 Number of 2-arcs = 22080 2-arc-transitive false Edge-set { {1,11}, {10,38}, {17,39}, {28,34}, {12,24}, {17,31}, {7,13}, {6,25}, {15,25}, {23,37}, {6,18}, {7,17}, {7,29}, {16,35}, {20,38}, {32,36}, {1,40}, {22,32}, {24,27}, {5,11}, {11,18}, {8,36}, {16,17}, {7,38}, {4,16}, {28,38}, {30,39}, {10,21}, {21,28}, {2,12}, {8,29}, {9,30}, {10,32}, {14,39}, {8,19}, {4,30}, {5,23}, {6,26}, {12,38}, {17,35}, {18,38}, {8,17}, {15,29}, {9,37}, {7,21}, {16,28}, {21,33}, {6,28}, {12,25}, {3,31}, {13,27}, {20,34}, {3,24}, {6,20}, {3,25}, {18,40}, {4,15}, {28,37}, {3,33}, {23,27}, {8,34}, {24,30}, {31,36}, {13,19}, {15,22}, {1,37}, {3,14}, {27,33}, {5,35}, {2,11}, {12,18}, {17,30}, {7,10}, {18,28}, {8,12}, {15,17}, {7,37}, {4,40}, {22,28}, {11,23}, {16,20}, {3,38}, {6,39}, {21,25}, {20,26}, {3,16}, {6,11}, {25,36}, {18,32}, {29,34}, {2,15}, {13,23}, {6,34}, {11,21}, {2,36}, {1,13}, {32,34}, {8,14}, {14,40}, {22,33}, {6,27}, {11,25}, {13,26}, {16,34}, {5,24}, {5,26}, {15,37}, {3,23}, {9,29}, {22,35}, {1,20}, {19,40}, {4,22}, {10,27}, {11,39}, {13,36}, {19,34}, {16,26}, {12,30}, {10,35}, {9,38}, {17,40}, {18,37}, {8,18}, {3,17}, {7,27}, {24,38}, {8,25}, {7,22}, {16,27}, {11,38}, {14,32}, {14,33}, {6,19}, {4,25}, {5,17}, {21,39}, {2,21}, {13,28}, {12,34}, {11,31}, {3,32}, {2,31}, {13,39}, {21,34}, {17,36}, {1,29}, {9,32}, {8,30}, {15,28}, {9,40}, {22,40}, {24,35}, {5,20}, {15,36}, {20,39}, {15,30}, {19,37}, {14,19}, {19,26}, {26,36}, {1,38}, {17,32}, {2,35}, {20,31}, {25,39}, {15,21}, {12,23}, {6,35}, {31,35}, {27,40}, {11,22}, {13,24}, {5,34}, {4,33}, {23,28}, {19,30}, {4,10}, {2,39}, {1,14}, {24,26}, {31,38}, {13,17}, {29,35}, {9,20}, {22,25}, {1,15}, {21,31}, {3,37}, {18,27}, {30,34}, {10,24}, {28,33}, {7,14}, {8,11}, {15,18}, {8,37}, {7,34}, {5,16}, {26,38}, {6,12}, {32,37}, {16,19}, {4,38}, {5,39}, {21,26}, {12,17}, {1,36}, {32,33}, {7,35}, {3,13}, {3,40}, {20,25}, {25,37}, {17,29}, {8,13}, {7,9}, {29,40}, {13,20}, {3,15}, {28,39}, {8,33}, {23,30}, {27,37}, {6,40}, {14,23}, {19,32}, {4,14}, {6,10}, {12,21}, {9,22}, {2,13}, {22,27}, {22,36}, {1,19}, {2,22}, {1,31}, {2,29}, {9,31}, {10,28}, {12,39}, {7,30}, {10,40}, {13,32}, {20,40}, {3,22}, {24,37}, {5,18}, {11,30}, {10,36}, {10,29}, {5,32}, {14,26}, {19,38}, {4,17}, {23,35}, {15,35}, {16,33}, {6,24}, {5,25}, {1,27}, {14,34}, {24,33}, {13,40}, {19,39}, {2,23}, {6,31}, {7,28}, {12,29}, {7,20}, {4,32}, {22,39}, {3,29}, {11,34}, {8,26}, {15,27}, {23,34}, {16,25}, {16,36}, {15,38}, {17,37}, {8,22}, {11,37}, {21,35}, {2,28}, {12,31}, {18,36}, {8,27}, {1,21}, {14,28}, {12,33}, {13,35}, {2,20}, {7,18}, {9,39}, {16,30}, {2,32}, {11,32}, {20,37}, {23,38}, {22,34}, {13,25}, {15,26}, {16,37}, {5,27}, {11,26}, {14,36}, {24,36}, {5,19}, {1,30}, {19,33}, {3,18}, {4,23}, {9,35}, {4,26}, {19,29}, {4,9}, {10,22}, {1,39}, {9,19}, {29,39}, {28,40}, {7,33}, {23,29}, {24,25}, {31,37}, {13,18}, {27,38}, {14,24}, {8,35}, {20,30}, {21,32}, {2,14}, {4,34}, {17,27}, {9,24}, {24,28}, {30,35}, {19,31}, {1,12}, {14,17}, {5,10}, {30,40}, {26,39}, {16,21}, {6,36}, {32,35}, {15,19}, {23,26}, {6,16}, {14,20}, {22,31}, {5,40}, {7,11}, {29,36}, {25,38}, {4,37}, {2,38}, {30,33}, {4,13}, {22,26}, {5,15}, {9,21}, {12,22}, {11,17}, {3,10}, {6,9}, {25,40}, {18,29}, {8,9}, {26,37}, {10,20}, {3,39}, {19,25}, {16,18}, {2,40}, {8,38}, {31,33}, {21,27}, {5,12}, {1,35}, {20,32}, {27,39}, {26,35}, {1,16}, {5,33}, {10,23}, {1,28}, {23,33}, {4,24}, {10,31}, {1,23}, {4,31}, {6,32}, {14,25}, {16,38}, {5,28}, {11,29}, {18,35}, {8,20}, {12,26}, {23,36}, {10,37}, {3,21}, {2,27}, {3,30}, {9,36}, {15,33}, {7,26}, {6,23}, {18,39}, {7,19}, {14,27}, {13,31}, {10,30}, {1,22}, {2,24}, {5,31}, {21,36}, {2,19}, {4,29}, {12,32}, {14,35}, {17,38}, {9,28}, {11,33}, {12,40}, {3,26}, {20,33}, {4,18}, {13,34}, {24,34}, {1,32}, {8,28}, {8,21}, {12,37}, {16,29}, {10,39}, {2,30}, {6,33}, {24,29}, {29,33}, {30,36}, {25,35}, {17,28}, {18,30}, {8,10}, {2,37}, {18,31}, {5,9}, {27,34}, {11,24}, {3,34}, {26,40}, {9,23}, {16,22}, {2,16}, {5,36}, {20,29}, {10,19}, {4,39}, {7,12}, {3,9}, {23,25}, {14,18}, {31,34}, {15,20}, {6,15}, {9,27}, {6,17}, {7,25}, {15,34}, {11,40}, {14,31}, {4,21}, {21,40}, {1,24}, {13,33}, {7,36}, {32,38} } Symmetric graph 58 of order 40 Valency 24 Diameter 2 Girth 3 Automorphism group of order 7608405715845120 Number of arcs = 960 Number of 2-arcs = 22080 2-arc-transitive false Edge-set { {1,5}, {12,13}, {2,28}, {20,21}, {11,39}, {10,33}, {3,5}, {26,30}, {29,34}, {6,19}, {9,15}, {2,18}, {12,22}, {11,13}, {4,28}, {36,37}, {7,20}, {4,39}, {19,23}, {16,27}, {25,30}, {17,23}, {10,37}, {10,28}, {3,31}, {20,29}, {11,35}, {19,21}, {9,39}, {9,33}, {13,21}, {14,26}, {26,29}, {6,9}, {1,15}, {27,32}, {30,36}, {22,35}, {8,38}, {34,37}, {6,20}, {25,32}, {32,36}, {5,18}, {18,33}, {5,12}, {11,40}, {4,17}, {26,39}, {19,29}, {3,19}, {9,24}, {27,30}, {30,34}, {6,17}, {10,15}, {2,17}, {10,22}, {21,30}, {34,39}, {24,36}, {7,40}, {36,39}, {7,19}, {16,17}, {10,25}, {12,23}, {2,37}, {35,38}, {8,18}, {1,37}, {3,29}, {24,35}, {8,15}, {14,27}, {4,5}, {13,23}, {16,26}, {25,29}, {34,38}, {6,18}, {1,38}, {18,21}, {13,28}, {28,31}, {22,31}, {13,20}, {11,28}, {9,16}, {9,25}, {1,32}, {6,36}, {7,15}, {27,39}, {19,30}, {11,27}, {4,30}, {17,31}, {35,37}, {8,20}, {4,37}, {20,23}, {16,25}, {18,23}, {12,37}, {3,32}, {18,29}, {12,35}, {30,37}, {20,34}, {4,6}, {15,23}, {1,31}, {21,33}, {7,14}, {1,6}, {15,21}, {22,25}, {32,38}, {18,34}, {6,12}, {20,32}, {11,36}, {5,10}, {3,13}, {3,8}, {14,24}, {15,28}, {27,31}, {2,13}, {4,19}, {24,33}, {27,37}, {8,40}, {9,13}, {1,28}, {21,32}, {22,36}, {7,38}, {4,8}, {14,23}, {16,28}, {25,31}, {8,12}, {2,14}, {28,30}, {31,34}, {5,39}, {33,40}, {5,17}, {29,40}, {17,35}, {21,26}, {29,39}, {19,33}, {5,9}, {17,22}, {10,38}, {17,34}, {6,10}, {12,38}, {1,16}, {21,25}, {26,37}, {6,35}, {20,30}, {19,35}, {8,9}, {9,37}, {1,20}, {25,40}, {17,32}, {13,24}, {15,26}, {27,29}, {1,13}, {26,32}, {29,36}, {22,34}, {6,38}, {28,32}, {31,36}, {5,20}, {11,38}, {4,18}, {28,39}, {19,31}, {3,20}, {11,24}, {5,37}, {4,26}, {23,29}, {1,25}, {23,32}, {12,40}, {2,30}, {26,40}, {12,16}, {2,25}, {23,30}, {14,18}, {23,31}, {16,20}, {11,25}, {26,38}, {1,19}, {9,21}, {13,18}, {12,28}, {11,21}, {11,15}, {4,27}, {24,31}, {23,33}, {35,40}, {8,17}, {10,21}, {3,39}, {9,27}, {1,30}, {2,31}, {22,33}, {5,35}, {8,13}, {17,21}, {10,39}, {12,33}, {2,5}, {30,38}, {1,29}, {21,35}, {8,14}, {1,27}, {24,32}, {36,40}, {5,38}, {34,40}, {15,20}, {10,24}, {3,40}, {33,37}, {4,40}, {6,13}, {2,7}, {16,22}, {13,25}, {7,39}, {16,19}, {3,25}, {7,34}, {6,39}, {15,19}, {2,27}, {22,30}, {13,17}, {32,35}, {12,14}, {4,25}, {16,18}, {12,25}, {11,14}, {2,38}, {6,34}, {5,36}, {7,13}, {3,16}, {24,25}, {3,27}, {24,30}, {15,17}, {10,27}, {10,13}, {12,26}, {2,29}, {6,16}, {25,38}, {18,32}, {21,31}, {33,39}, {23,36}, {7,37}, {35,39}, {8,19}, {12,21}, {2,39}, {36,38}, {7,18}, {1,39}, {4,29}, {23,35}, {8,16}, {14,25}, {33,38}, {1,40}, {13,26}, {28,29}, {9,14}, {9,28}, {6,33}, {5,15}, {27,40}, {17,30}, {11,26}, {5,13}, {9,36}, {1,7}, {32,39}, {19,36}, {12,34}, {2,6}, {18,36}, {11,16}, {7,36}, {7,16}, {20,22}, {10,34}, {3,6}, {32,37}, {20,36}, {24,28}, {31,40}, {32,40}, {17,36}, {22,26}, {29,38}, {19,34}, {8,36}, {12,27}, {21,28}, {31,39}, {20,33}, {5,11}, {9,34}, {9,35}, {1,8}, {17,33}, {2,32}, {3,7}, {16,24}, {15,25}, {18,30}, {6,11}, {4,15}, {8,10}, {2,20}, {10,40}, {3,17}, {32,34}, {12,15}, {11,22}, {3,28}, {8,37}, {14,20}, {12,39}, {2,19}, {3,30}, {24,34}, {15,24}, {2,8}, {31,38}, {16,21}, {14,28}, {4,7}, {16,23}, {23,26}, {29,37}, {18,31}, {7,11}, {4,16}, {13,22}, {7,9}, {25,39}, {10,14}, {3,26}, {22,29}, {21,34}, {6,14}, {22,27}, {11,34}, {4,14}, {23,27}, {10,35}, {20,35}, {3,38}, {18,24}, {20,24}, {22,28}, {19,24}, {9,40}, {3,14}, {23,25}, {14,21}, {4,38}, {31,37}, {18,35}, {8,34}, {28,38}, {30,40}, {15,22}, {21,36}, {5,14}, {15,27}, {3,15}, {26,31}, {2,15}, {27,38}, {6,40}, {14,22}, {7,12}, {2,16}, {5,19}, {17,24}, {28,37}, {7,35}, {25,37}, {1,17}, {2,26}, {15,18}, {4,20}, {11,23}, {10,16}, {19,22}, {9,38}, {1,14}, {29,35}, {1,26}, {21,29}, {31,33}, {5,33}, {8,39}, {14,19}, {21,27}, {8,11}, {30,33}, {5,34}, {13,19}, {10,23}, {22,32}, {3,18}, {23,34}, {6,37}, {20,31}, {9,23}, {10,26}, {4,32}, {11,37}, {11,33}, {13,27}, {24,26}, {4,31}, {14,17}, {5,40}, {28,40}, {9,26}, {9,22}, {6,15}, {8,35}, {12,24}, {24,29}, {29,33}, {7,17}, {8,33}, {3,37}, {32,33}, {10,36}, {23,28}, {19,32}, {18,22}, {30,35}, {2,40}, {12,36}, {30,39}, {24,27}, {4,13}, {5,16}, {17,29}, {1,18}, {7,33}, {7,10}, {31,35} } Symmetric graph 59 of order 40 Valency 27 Diameter 2 Girth 3 Automorphism group of order 51840 Number of arcs = 1080 Number of 2-arcs = 28080 2-arc-transitive false Edge-set { {1,2}, {2,5}, {3,6}, {5,10}, {6,10}, {4,12}, {8,13}, {10,19}, {10,20}, {12,19}, {13,20}, {7,21}, {9,21}, {16,25}, {16,19}, {1,19}, {17,20}, {19,27}, {4,20}, {1,21}, {17,21}, {25,27}, {4,19}, {13,15}, {1,31}, {13,18}, {5,31}, {6,29}, {7,18}, {1,29}, {7,17}, {3,17}, {27,30}, {2,4}, {1,9}, {17,29}, {7,27}, {4,9}, {2,13}, {3,31}, {13,30}, {2,31}, {6,9}, {18,29}, {1,7}, {9,17}, {25,28}, {19,28}, {2,20}, {3,25}, {25,31}, {10,25}, {12,38}, {13,22}, {15,31}, {1,12}, {2,38}, {3,22}, {15,30}, {4,30}, {2,8}, {9,23}, {29,38}, {5,7}, {2,18}, {3,5}, {30,38}, {2,22}, {9,15}, {5,9}, {5,25}, {6,19}, {8,25}, {23,25}, {19,38}, {5,20}, {6,25}, {12,18}, {5,13}, {31,38}, {12,22}, {2,15}, {1,3}, {18,30}, {17,30}, {5,27}, {4,6}, {8,18}, {6,20}, {18,25}, {18,20}, {14,21}, {21,32}, {25,33}, {19,34}, {20,28}, {2,21}, {3,21}, {5,14}, {6,32}, {4,33}, {8,34}, {23,28}, {28,38}, {7,23}, {9,38}, {5,16}, {6,16}, {18,35}, {5,36}, {14,38}, {22,32}, {10,15}, {1,10}, {6,12}, {4,10}, {8,10}, {14,23}, {32,38}, {5,33}, {6,34}, {18,28}, {5,28}, {10,18}, {13,17}, {16,18}, {6,35}, {18,36}, {1,14}, {17,32}, {10,27}, {21,31}, {12,21}, {14,20}, {25,32}, {21,33}, {21,34}, {6,28}, {3,8}, {23,31}, {23,30}, {9,10}, {10,29}, {7,12}, {9,13}, {16,31}, {12,16}, {12,27}, {4,13}, {6,31}, {27,31}, {6,37}, {18,24}, {1,11}, {14,17}, {3,27}, {8,31}, {12,17}, {7,37}, {9,24}, {11,16}, {14,16}, {3,35}, {30,36}, {3,14}, {30,32}, {15,35}, {1,36}, {14,18}, {5,32}, {7,10}, {12,29}, {7,13}, {31,32}, {11,12}, {10,24}, {10,26}, {8,14}, {27,32}, {17,33}, {15,34}, {2,19}, {3,20}, {13,21}, {7,19}, {9,20}, {16,20}, {8,35}, {27,36}, {15,32}, {10,37}, {13,14}, {12,30}, {3,10}, {10,30}, {19,31}, {12,20}, {25,30}, {29,31}, {12,32}, {11,13}, {24,31}, {12,26}, {9,19}, {20,29}, {8,27}, {4,27}, {6,17}, {15,18}, {13,37}, {14,31}, {3,12}, {4,16}, {8,16}, {20,35}, {25,36}, {23,35}, {36,38}, {18,19}, {20,22}, {15,21}, {5,19}, {7,25}, {21,29}, {13,25}, {25,29}, {12,34}, {13,40}, {26,31}, {12,37}, {3,23}, {8,30}, {2,27}, {8,29}, {21,30}, {1,40}, {18,26}, {5,37}, {22,29}, {4,32}, {8,11}, {23,24}, {26,38}, {4,8}, {17,23}, {15,38}, {28,32}, {11,28}, {2,24}, {3,26}, {10,17}, {15,19}, {1,20}, {21,38}, {21,22}, {15,25}, {21,23}, {19,26}, {20,37}, {19,39}, {16,27}, {15,29}, {30,37}, {14,28}, {1,5}, {1,15}, {1,17}, {18,27}, {4,5}, {27,29}, {4,7}, {16,32}, {26,29}, {17,28}, {15,28}, {20,40}, {8,20}, {19,23}, {20,38}, {17,25}, {21,27}, {4,21}, {6,23}, {18,38}, {22,25}, {20,26}, {25,37}, {21,39}, {21,35}, {1,18}, {5,17}, {27,38}, {4,22}, {9,16}, {16,29}, {7,9}, {9,29}, {28,31}, {12,28}, {25,34}, {19,40}, {8,21}, {7,29}, {7,16}, {4,11}, {6,24}, {32,35}, {11,36}, {14,24}, {26,32}, {27,33}, {4,34}, {13,28}, {6,15}, {13,38}, {22,31}, {6,38}, {18,22}, {11,21}, {20,39}, {25,35}, {21,40}, {4,35}, {8,36}, {16,23}, {16,38}, {16,22}, {13,23}, {2,36}, {3,39}, {31,39}, {12,35}, {10,34}, {10,40}, {33,38}, {22,34}, {26,35}, {36,37}, {14,39}, {30,35}, {5,26}, {4,39}, {19,30}, {1,28}, {3,4}, {13,33}, {31,34}, {13,35}, {31,36}, {1,39}, {17,35}, {27,34}, {4,40}, {22,28}, {23,34}, {38,40}, {2,10}, {2,28}, {3,28}, {2,30}, {2,3}, {9,31}, {7,15}, {38,39}, {22,35}, {3,30}, {28,30}, {1,35}, {17,36}, {14,27}, {6,30}, {13,36}, {6,33}, {18,34}, {27,39}, {18,40}, {31,33}, {13,32}, {11,31}, {9,14}, {29,32}, {7,33}, {9,34}, {7,22}, {5,22}, {6,11}, {17,39}, {13,16}, {1,22}, {11,15}, {22,24}, {23,26}, {8,26}, {27,37}, {9,37}, {24,29}, {7,11}, {14,25}, {19,32}, {20,33}, {12,14}, {27,40}, {11,18}, {7,32}, {9,11}, {16,24}, {16,26}, {29,35}, {7,36}, {14,29}, {29,33}, {7,34}, {19,36}, {5,24}, {6,26}, {8,33}, {11,19}, {14,37}, {24,32}, {11,33}, {14,34}, {32,39}, {11,35}, {24,34}, {26,40}, {8,40}, {23,32}, {11,38}, {10,39}, {10,35}, {7,40}, {9,33}, {1,23}, {17,38}, {8,9}, {19,24}, {11,20}, {20,24}, {25,26}, {2,40}, {3,33}, {2,11}, {9,39}, {30,34}, {14,36}, {5,23}, {6,8}, {14,40}, {32,33}, {11,34}, {4,23}, {8,38}, {2,32}, {3,11}, {24,30}, {2,26}, {12,23}, {24,25}, {13,24}, {9,40}, {12,39}, {15,22}, {15,37}, {1,24}, {15,33}, {1,34}, {10,33}, {30,40}, {2,33}, {3,34}, {26,33}, {34,37}, {35,39}, {35,36}, {16,39}, {16,35}, {29,40}, {5,40}, {22,37}, {15,17}, {4,24}, {9,36}, {29,39}, {7,35}, {11,22}, {15,24}, {1,26}, {22,27}, {37,38}, {17,26}, {16,37}, {17,40}, {11,23}, {11,26}, {36,39}, {16,36}, {15,36}, {14,22}, {18,37}, {2,35}, {3,36}, {14,30}, {17,37}, {26,27}, {4,37}, {6,39}, {8,24}, {10,36}, {8,23}, {5,39}, {21,36}, {19,37}, {28,33}, {28,34}, {28,40}, {3,37}, {28,37}, {24,28}, {23,36}, {37,39}, {24,35}, {32,40}, {22,39}, {33,34}, {34,40}, {7,26}, {22,33}, {26,28}, {2,39}, {29,34}, {30,39}, {24,40}, {12,40}, {26,36}, {33,40}, {11,37}, {15,39}, {33,37}, {23,40}, {24,39} } Symmetric graph 60 of order 40 Valency 27 Diameter 2 Girth 3 Automorphism group of order 51840 Number of arcs = 1080 Number of 2-arcs = 28080 2-arc-transitive false Edge-set { {1,2}, {2,4}, {3,5}, {4,7}, {5,7}, {6,9}, {4,10}, {7,10}, {7,12}, {9,10}, {10,12}, {12,16}, {9,16}, {1,7}, {7,18}, {1,10}, {12,18}, {10,21}, {1,12}, {1,16}, {16,18}, {1,21}, {1,18}, {21,27}, {1,27}, {16,27}, {2,10}, {3,12}, {10,29}, {12,22}, {3,18}, {21,29}, {1,22}, {1,20}, {18,31}, {2,21}, {1,3}, {2,27}, {3,27}, {27,29}, {22,27}, {2,20}, {3,31}, {2,29}, {3,22}, {20,38}, {31,38}, {2,38}, {3,38}, {27,38}, {1,4}, {5,18}, {6,21}, {1,15}, {17,18}, {21,30}, {6,29}, {4,22}, {15,20}, {17,31}, {2,30}, {2,3}, {3,30}, {17,29}, {14,22}, {4,20}, {5,31}, {2,6}, {3,4}, {4,38}, {5,38}, {6,38}, {15,38}, {17,38}, {30,38}, {5,30}, {6,17}, {4,14}, {4,15}, {5,17}, {6,30}, {6,14}, {4,5}, {5,6}, {4,6}, {2,7}, {3,7}, {9,29}, {10,22}, {12,20}, {9,31}, {2,25}, {3,26}, {11,29}, {13,22}, {20,40}, {31,40}, {12,15}, {9,17}, {7,30}, {3,25}, {26,30}, {11,17}, {13,14}, {4,40}, {5,40}, {6,40}, {11,15}, {13,17}, {24,30}, {10,14}, {4,12}, {5,9}, {6,7}, {6,10}, {5,12}, {5,25}, {6,26}, {5,11}, {6,13}, {9,40}, {10,40}, {11,12}, {9,13}, {7,24}, {7,25}, {7,26}, {9,11}, {10,13}, {12,40}, {12,24}, {9,25}, {7,9}, {9,12}, {15,16}, {16,17}, {1,30}, {2,18}, {3,21}, {14,16}, {4,28}, {5,28}, {6,33}, {4,36}, {15,19}, {17,20}, {22,30}, {2,23}, {3,37}, {30,34}, {17,37}, {14,34}, {21,25}, {1,26}, {11,16}, {13,16}, {6,28}, {33,40}, {36,40}, {11,19}, {13,20}, {22,24}, {23,25}, {7,37}, {7,34}, {9,37}, {10,34}, {12,37}, {9,34}, {19,25}, {20,26}, {11,22}, {13,23}, {32,40}, {1,24}, {18,25}, {7,21}, {10,16}, {9,18}, {9,21}, {9,28}, {10,28}, {12,33}, {9,36}, {9,19}, {10,20}, {9,23}, {16,37}, {16,34}, {1,37}, {18,34}, {19,21}, {16,22}, {16,23}, {10,32}, {12,28}, {10,33}, {12,36}, {16,19}, {16,20}, {18,23}, {21,37}, {1,34}, {21,32}, {1,33}, {16,28}, {16,21}, {25,27}, {26,27}, {11,27}, {13,27}, {2,40}, {3,40}, {4,29}, {5,22}, {6,20}, {4,31}, {24,27}, {12,39}, {9,39}, {7,35}, {26,29}, {3,11}, {13,30}, {30,40}, {5,19}, {4,8}, {8,40}, {11,40}, {11,13}, {8,13}, {8,24}, {11,25}, {20,28}, {28,31}, {2,33}, {3,36}, {19,27}, {20,27}, {23,27}, {37,39}, {34,39}, {35,37}, {34,37}, {19,23}, {20,29}, {23,30}, {30,32}, {19,28}, {8,12}, {8,10}, {8,16}, {1,8}, {11,18}, {13,21}, {23,28}, {28,29}, {3,33}, {30,36}, {19,30}, {22,31}, {34,35}, {2,32}, {22,28}, {12,31}, {18,27}, {16,29}, {16,31}, {18,21}, {21,39}, {1,39}, {16,35}, {18,30}, {8,27}, {2,13}, {3,8}, {8,29}, {20,23}, {29,31}, {27,30}, {27,31}, {18,35}, {18,39}, {21,35}, {19,22}, {8,31}, {2,8}, {20,34}, {31,35}, {2,39}, {3,39}, {28,38}, {33,38}, {36,38}, {19,38}, {22,38}, {23,38}, {4,37}, {5,34}, {6,37}, {4,34}, {7,15}, {7,17}, {9,30}, {7,14}, {32,38}, {21,36}, {1,32}, {16,36}, {16,32}, {10,26}, {15,33}, {17,36}, {6,19}, {22,40}, {23,40}, {37,40}, {34,40}, {14,37}, {15,34}, {19,37}, {15,23}, {14,32}, {14,21}, {4,39}, {5,39}, {6,35}, {29,38}, {13,36}, {8,32}, {8,36}, {11,32}, {13,26}, {8,11}, {23,31}, {19,29}, {3,15}, {17,30}, {19,40}, {35,40}, {1,14}, {15,18}, {14,27}, {15,27}, {2,14}, {20,22}, {17,21}, {6,39}, {29,40}, {8,26}, {11,24}, {5,35}, {17,27}, {20,36}, {31,32}, {2,36}, {3,32}, {14,38}, {5,23}, {14,15}, {15,17}, {14,17}, {38,40}, {29,36}, {22,32}, {24,31}, {5,15}, {11,30}, {17,26}, {14,24}, {5,32}, {6,36}, {4,32}, {7,13}, {7,8}, {8,9}, {10,11}, {12,13}, {7,11}, {10,25}, {12,26}, {16,40}, {10,24}, {12,25}, {20,35}, {31,37}, {2,34}, {3,35}, {27,35}, {27,37}, {27,34}, {18,36}, {25,39}, {26,39}, {11,35}, {13,37}, {12,23}, {30,37}, {19,34}, {8,34}, {8,37}, {11,34}, {13,24}, {8,25}, {11,26}, {25,31}, {19,26}, {24,34}, {25,35}, {20,24}, {7,36}, {7,32}, {9,24}, {22,35}, {23,37}, {15,35}, {14,35}, {15,37}, {22,33}, {23,36}, {14,19}, {6,25}, {4,26}, {13,40}, {29,34}, {26,37}, {2,24}, {25,29}, {22,26}, {24,38}, {25,38}, {26,38}, {4,24}, {11,20}, {13,31}, {9,32}, {17,34}, {14,33}, {15,36}, {19,32}, {20,33}, {9,26}, {11,38}, {13,38}, {4,35}, {5,37}, {6,34}, {5,24}, {10,19}, {24,25}, {25,26}, {13,25}, {2,35}, {17,32}, {11,33}, {24,32}, {25,33}, {10,35}, {12,35}, {1,19}, {18,20}, {21,22}, {1,23}, {1,28}, {18,28}, {21,33}, {1,36}, {18,33}, {21,28}, {8,14}, {8,38}, {29,35}, {22,37}, {28,36}, {28,32}, {33,36}, {32,36}, {8,23}, {21,31}, {8,15}, {8,19}, {23,33}, {14,28}, {15,28}, {19,33}, {17,28}, {26,28}, {24,28}, {30,33}, {16,33}, {24,26}, {30,39}, {23,24}, {7,33}, {23,34}, {13,33}, {5,33}, {3,19}, {20,30}, {17,22}, {14,23}, {24,39}, {6,23}, {18,29}, {28,33}, {13,35}, {19,39}, {20,39}, {32,34}, {33,35}, {28,39}, {18,24}, {21,26}, {3,29}, {2,31}, {31,39}, {29,39}, {22,39}, {15,25}, {5,14}, {6,15}, {15,26}, {17,24}, {35,39}, {14,31}, {14,25}, {15,29}, {23,39}, {18,32}, {39,40}, {27,39}, {32,33}, {10,39}, {29,32}, {31,36}, {4,17}, {25,28}, {26,36}, {36,37}, {17,35} } Symmetric graph 61 of order 40 Valency 27 Diameter 2 Girth 3 Automorphism group of order 87091200 Number of arcs = 1080 Number of 2-arcs = 28080 2-arc-transitive false Edge-set { {1,5}, {8,16}, {12,38}, {7,22}, {19,39}, {11,26}, {21,29}, {5,32}, {36,40}, {25,33}, {5,30}, {9,20}, {3,22}, {4,30}, {14,35}, {1,8}, {15,38}, {27,40}, {28,32}, {18,39}, {4,26}, {3,8}, {13,38}, {12,35}, {7,24}, {14,32}, {11,36}, {3,13}, {10,13}, {24,38}, {20,25}, {7,16}, {12,39}, {21,26}, {18,29}, {19,27}, {2,32}, {1,17}, {1,15}, {25,34}, {6,30}, {13,20}, {3,10}, {7,14}, {11,39}, {23,26}, {17,29}, {11,38}, {21,25}, {5,29}, {34,40}, {1,24}, {15,20}, {9,40}, {22,28}, {14,23}, {11,17}, {10,23}, {17,23}, {26,29}, {29,34}, {18,35}, {4,7}, {5,22}, {19,40}, {11,25}, {21,30}, {20,30}, {3,35}, {4,34}, {6,14}, {19,33}, {2,5}, {9,15}, {16,36}, {8,12}, {16,21}, {12,18}, {18,37}, {4,27}, {3,6}, {13,37}, {23,35}, {7,17}, {10,14}, {11,23}, {5,24}, {20,40}, {9,25}, {22,30}, {20,31}, {3,33}, {4,36}, {8,14}, {9,26}, {22,29}, {18,30}, {4,35}, {4,8}, {14,38}, {27,37}, {27,32}, {16,29}, {12,34}, {21,35}, {7,18}, {12,27}, {24,32}, {17,32}, {1,36}, {24,31}, {20,33}, {9,36}, {8,22}, {10,31}, {23,33}, {31,36}, {8,33}, {4,20}, {3,14}, {4,37}, {14,27}, {34,38}, {6,25}, {5,13}, {10,40}, {8,32}, {36,38}, {27,33}, {9,18}, {4,22}, {3,30}, {13,35}, {7,13}, {10,27}, {6,24}, {20,37}, {33,39}, {5,26}, {8,15}, {9,38}, {12,21}, {18,24}, {22,40}, {19,28}, {7,11}, {21,39}, {19,35}, {11,34}, {6,21}, {28,34}, {6,31}, {13,19}, {2,10}, {11,37}, {23,28}, {17,31}, {31,38}, {5,36}, {8,40}, {10,24}, {20,23}, {9,31}, {22,33}, {8,29}, {27,35}, {7,32}, {4,24}, {3,32}, {13,36}, {2,35}, {14,39}, {13,40}, {10,28}, {20,39}, {12,20}, {3,24}, {4,32}, {14,36}, {3,34}, {6,13}, {10,25}, {10,39}, {24,26}, {20,29}, {2,31}, {1,19}, {2,15}, {14,19}, {21,27}, {30,38}, {25,35}, {5,34}, {6,40}, {11,19}, {2,21}, {1,29}, {15,34}, {16,40}, {12,28}, {2,29}, {16,34}, {35,39}, {7,26}, {12,40}, {24,28}, {36,39}, {16,23}, {31,39}, {26,33}, {2,40}, {16,28}, {7,39}, {26,39}, {7,10}, {14,24}, {11,20}, {13,28}, {19,24}, {2,20}, {26,37}, {27,29}, {6,18}, {8,23}, {17,38}, {23,32}, {1,7}, {15,39}, {26,40}, {28,29}, {2,26}, {13,32}, {10,36}, {11,13}, {23,38}, {17,25}, {5,23}, {17,40}, {10,19}, {2,23}, {6,29}, {34,37}, {28,35}, {7,31}, {25,39}, {26,30}, {8,20}, {3,38}, {7,21}, {12,26}, {24,29}, {11,30}, {6,34}, {32,36}, {17,33}, {5,9}, {25,30}, {30,35}, {33,38}, {5,25}, {9,37}, {22,27}, {35,37}, {17,37}, {1,27}, {2,6}, {16,37}, {5,17}, {10,15}, {9,23}, {9,28}, {22,31}, {1,33}, {2,36}, {28,38}, {7,27}, {32,39}, {10,29}, {23,34}, {31,35}, {7,33}, {2,12}, {16,24}, {26,36}, {19,38}, {2,25}, {15,40}, {13,29}, {10,34}, {1,14}, {11,15}, {23,40}, {17,28}, {24,25}, {23,27}, {10,17}, {1,23}, {7,30}, {11,35}, {14,29}, {1,13}, {24,40}, {20,28}, {14,37}, {11,27}, {6,23}, {10,18}, {4,23}, {23,30}, {9,16}, {16,33}, {5,12}, {15,21}, {24,33}, {5,20}, {19,30}, {3,26}, {18,38}, {4,25}, {8,37}, {27,38}, {6,27}, {32,37}, {9,33}, {15,30}, {9,35}, {4,16}, {12,14}, {21,37}, {18,27}, {19,32}, {1,21}, {4,15}, {9,14}, {22,37}, {25,38}, {3,40}, {21,32}, {1,34}, {25,40}, {28,30}, {16,30}, {15,27}, {9,32}, {17,22}, {30,40}, {5,10}, {20,34}, {29,33}, {15,35}, {7,9}, {3,31}, {4,19}, {2,14}, {6,37}, {1,31}, {15,33}, {5,16}, {20,27}, {4,17}, {3,9}, {15,17}, {26,31}, {18,36}, {8,31}, {27,36}, {10,33}, {15,31}, {4,6}, {28,37}, {27,31}, {1,25}, {18,25}, {3,20}, {7,35}, {14,26}, {11,29}, {35,40}, {3,21}, {4,29}, {14,34}, {13,22}, {1,40}, {15,28}, {8,26}, {3,18}, {4,13}, {13,25}, {8,18}, {4,38}, {25,31}, {28,36}, {16,19}, {6,15}, {19,31}, {8,36}, {8,38}, {10,21}, {18,23}, {12,31}, {12,17}, {16,39}, {17,26}, {5,19}, {4,10}, {31,37}, {2,38}, {16,25}, {5,39}, {9,21}, {19,34}, {3,28}, {15,18}, {4,9}, {18,32}, {14,17}, {10,37}, {18,22}, {32,33}, {17,36}, {2,33}, {16,31}, {12,33}, {3,5}, {22,25}, {14,20}, {32,34}, {17,35}, {9,19}, {2,22}, {33,37}, {13,31}, {13,33}, {12,22}, {22,39}, {19,26}, {8,11}, {21,38}, {29,39}, {26,34}, {8,35}, {7,38}, {3,11}, {13,18}, {7,28}, {6,19}, {2,37}, {1,28}, {11,24}, {20,21}, {5,15}, {13,21}, {12,24}, {20,24}, {18,26}, {11,32}, {1,30}, {3,17}, {19,21}, {2,18}, {1,12}, {15,24}, {3,27}, {8,10}, {4,39}, {11,16}, {6,28}, {2,16}, {12,16}, {2,7}, {21,36}, {3,16}, {2,28}, {16,18}, {2,19}, {4,12}, {18,34}, {5,38}, {14,22}, {25,32}, {14,30}, {24,37}, {16,27}, {12,32}, {17,21}, {1,18}, {7,20}, {3,39}, {6,11}, {13,23}, {7,34}, {6,39}, {13,26}, {7,40}, {28,39}, {10,30}, {31,34}, {6,33}, {2,11}, {8,21}, {20,36}, {15,26}, {9,29}, {8,25}, {12,30}, {24,35}, {5,27}, {1,11}, {21,34}, {12,13}, {24,36}, {23,31}, {6,36}, {1,39}, {8,28}, {1,37}, {15,32}, {16,17}, {23,39}, {30,36}, {29,35}, {29,40}, {11,22}, {6,17}, {5,37}, {22,34}, {1,9}, {15,22}, {30,33}, {5,35}, {6,9}, {9,22}, {19,22}, {29,38}, {6,12}, {14,25}, {30,37}, {32,40}, {8,19}, {22,36} } Symmetric graph 62 of order 40 Valency 28 Diameter 2 Girth 3 Automorphism group of order 4838400 Number of arcs = 1120 Number of 2-arcs = 30240 2-arc-transitive false Edge-set { {1,7}, {16,23}, {29,40}, {6,30}, {9,21}, {32,39}, {3,12}, {21,34}, {13,39}, {22,26}, {24,37}, {13,37}, {2,20}, {3,20}, {26,35}, {12,26}, {17,24}, {5,37}, {2,31}, {28,31}, {14,25}, {27,38}, {5,22}, {5,38}, {5,31}, {9,18}, {8,30}, {9,20}, {8,26}, {14,31}, {14,18}, {3,31}, {14,35}, {8,27}, {10,22}, {19,38}, {5,28}, {11,18}, {19,30}, {11,35}, {11,19}, {2,29}, {23,32}, {33,40}, {1,15}, {19,28}, {25,28}, {19,40}, {1,28}, {6,37}, {25,34}, {13,36}, {9,22}, {8,37}, {25,31}, {14,36}, {2,11}, {19,32}, {2,10}, {6,32}, {11,20}, {19,26}, {2,14}, {18,32}, {25,33}, {15,36}, {24,28}, {25,38}, {7,40}, {19,35}, {11,28}, {1,10}, {6,34}, {7,34}, {7,13}, {1,14}, {18,34}, {12,30}, {13,30}, {20,21}, {15,39}, {3,16}, {4,16}, {29,33}, {7,35}, {7,11}, {29,35}, {11,23}, {7,39}, {3,7}, {16,35}, {11,29}, {21,38}, {5,39}, {12,29}, {17,23}, {5,36}, {4,31}, {22,28}, {25,37}, {19,23}, {2,36}, {4,32}, {1,18}, {30,34}, {7,20}, {18,24}, {30,38}, {13,21}, {20,39}, {1,9}, {8,34}, {7,31}, {7,14}, {2,18}, {30,32}, {10,13}, {6,20}, {15,29}, {4,36}, {4,33}, {27,35}, {11,22}, {1,23}, {23,39}, {3,40}, {7,18}, {1,35}, {11,34}, {16,24}, {29,38}, {12,21}, {17,39}, {12,23}, {17,40}, {5,23}, {31,40}, {2,16}, {29,32}, {10,12}, {6,17}, {3,34}, {13,35}, {5,34}, {13,31}, {9,26}, {8,24}, {4,37}, {2,33}, {9,27}, {15,32}, {12,16}, {14,23}, {18,40}, {34,40}, {14,32}, {12,18}, {1,30}, {23,37}, {2,40}, {20,23}, {26,40}, {6,14}, {1,32}, {12,34}, {1,24}, {19,37}, {2,28}, {3,32}, {12,35}, {10,21}, {19,36}, {4,28}, {11,17}, {19,27}, {28,35}, {11,25}, {7,30}, {7,21}, {18,36}, {4,30}, {13,17}, {20,27}, {10,16}, {6,29}, {9,23}, {8,40}, {10,27}, {6,22}, {1,13}, {5,26}, {24,31}, {9,37}, {2,8}, {16,22}, {29,37}, {12,25}, {17,36}, {2,23}, {32,40}, {10,18}, {13,34}, {13,20}, {5,24}, {31,38}, {8,39}, {12,33}, {4,27}, {15,17}, {16,27}, {14,33}, {15,18}, {16,30}, {21,29}, {30,37}, {2,21}, {3,26}, {10,23}, {6,40}, {14,16}, {18,29}, {1,12}, {17,34}, {6,27}, {24,35}, {3,30}, {21,35}, {3,10}, {21,28}, {11,39}, {3,19}, {6,18}, {9,30}, {13,32}, {12,20}, {3,24}, {35,38}, {8,21}, {10,39}, {17,26}, {5,14}, {18,31}, {12,19}, {17,28}, {5,11}, {19,31}, {22,31}, {14,37}, {25,27}, {22,36}, {17,38}, {5,27}, {22,33}, {15,37}, {4,13}, {20,33}, {3,6}, {9,35}, {2,30}, {21,32}, {12,39}, {3,17}, {2,13}, {20,32}, {6,35}, {16,34}, {13,29}, {5,21}, {18,39}, {31,39}, {3,14}, {13,16}, {20,29}, {17,35}, {22,29}, {7,38}, {5,7}, {18,35}, {11,30}, {20,26}, {24,26}, {24,38}, {7,36}, {4,7}, {11,27}, {1,8}, {10,34}, {7,33}, {7,15}, {1,29}, {23,34}, {13,40}, {23,26}, {24,40}, {10,36}, {4,6}, {13,27}, {5,8}, {10,31}, {9,33}, {8,15}, {6,24}, {9,38}, {22,30}, {21,37}, {25,39}, {3,36}, {24,33}, {15,38}, {5,16}, {29,31}, {14,28}, {19,22}, {22,38}, {18,25}, {30,36}, {6,28}, {9,25}, {32,38}, {5,12}, {3,29}, {23,35}, {8,36}, {4,10}, {18,30}, {21,30}, {10,24}, {6,38}, {17,31}, {5,9}, {8,31}, {11,40}, {1,19}, {3,15}, {17,33}, {15,27}, {4,8}, {10,33}, {6,33}, {9,15}, {2,15}, {16,32}, {9,13}, {26,32}, {12,24}, {34,38}, {5,13}, {18,26}, {24,30}, {20,31}, {14,26}, {21,39}, {3,39}, {2,6}, {9,32}, {10,32}, {6,12}, {8,12}, {10,17}, {21,33}, {14,27}, {18,22}, {20,34}, {13,26}, {20,24}, {26,38}, {11,24}, {1,37}, {2,34}, {7,26}, {6,39}, {22,34}, {3,9}, {8,35}, {14,40}, {25,26}, {24,36}, {2,38}, {10,14}, {2,19}, {28,32}, {10,11}, {6,19}, {28,34}, {7,19}, {19,25}, {5,32}, {15,23}, {28,36}, {4,25}, {19,33}, {15,28}, {16,25}, {4,38}, {5,33}, {5,17}, {27,31}, {8,16}, {26,39}, {14,22}, {18,37}, {3,37}, {2,35}, {8,20}, {10,26}, {5,18}, {30,31}, {14,21}, {9,17}, {12,31}, {10,37}, {11,37}, {5,6}, {9,31}, {8,14}, {23,40}, {1,40}, {28,40}, {1,34}, {27,40}, {1,22}, {23,36}, {4,40}, {1,33}, {15,34}, {29,36}, {16,40}, {4,23}, {17,21}, {27,39}, {3,22}, {15,31}, {15,22}, {16,37}, {33,36}, {21,27}, {22,39}, {22,40}, {13,25}, {20,36}, {4,26}, {9,28}, {11,32}, {7,28}, {7,25}, {1,25}, {10,29}, {6,23}, {34,36}, {1,20}, {14,30}, {18,21}, {25,36}, {6,13}, {26,34}, {13,24}, {24,27}, {21,40}, {1,39}, {8,11}, {10,19}, {28,37}, {7,16}, {7,29}, {4,20}, {26,33}, {15,33}, {17,25}, {27,36}, {15,24}, {16,38}, {15,21}, {16,39}, {4,22}, {33,37}, {4,18}, {30,33}, {31,37}, {14,20}, {3,27}, {22,35}, {12,40}, {1,17}, {5,19}, {27,34}, {13,22}, {9,11}, {8,19}, {26,37}, {2,24}, {20,37}, {2,26}, {30,39}, {20,38}, {3,21}, {35,39}, {3,25}, {35,36}, {10,38}, {15,26}, {10,28}, {6,25}, {9,12}, {8,17}, {8,22}, {1,27}, {5,29}, {17,30}, {23,31}, {2,39}, {12,28}, {20,22}, {7,23}, {13,19}, {20,28}, {4,11}, {17,29}, {23,27}, {4,35}, {11,33}, {15,19}, {16,28}, {9,36}, {25,32}, {14,38}, {24,32}, {3,11}, {1,38}, {19,21}, {28,39}, {2,25}, {32,36}, {33,39}, {25,29}, {4,21}, {15,16}, {16,29}, {4,12}, {23,29}, {12,38}, {12,36}, {4,17}, {9,16}, {8,29}, {14,17}, {27,33}, {7,24}, {9,40}, {4,15}, {16,33}, {2,9}, {11,38}, {8,32}, {3,35}, {34,37}, {18,27}, {35,37}, {8,25}, {23,30}, {6,15} } Symmetric graph 63 of order 40 Valency 30 Diameter 2 Girth 3 Automorphism group of order 4161629115065460326400000000 Number of arcs = 1200 Number of 2-arcs = 34800 2-arc-transitive false Edge-set { {1,11}, {28,37}, {10,22}, {2,12}, {13,32}, {6,26}, {8,38}, {27,38}, {9,21}, {17,35}, {19,24}, {4,33}, {11,24}, {6,14}, {14,31}, {5,25}, {7,37}, {16,28}, {7,39}, {30,36}, {15,30}, {1,17}, {22,36}, {21,36}, {4,23}, {18,36}, {20,23}, {3,34}, {12,23}, {5,13}, {2,33}, {25,32}, {5,11}, {3,13}, {15,40}, {26,40}, {28,31}, {10,28}, {6,13}, {15,38}, {15,37}, {8,30}, {1,35}, {15,27}, {8,40}, {29,35}, {16,29}, {2,18}, {21,35}, {22,35}, {3,24}, {9,17}, {10,17}, {19,34}, {22,37}, {3,22}, {2,24}, {12,26}, {9,19}, {12,33}, {20,32}, {2,26}, {8,32}, {4,24}, {11,34}, {14,26}, {12,34}, {13,26}, {6,40}, {14,28}, {10,16}, {1,34}, {26,31}, {6,12}, {4,14}, {16,39}, {25,39}, {27,32}, {9,27}, {5,14}, {16,37}, {16,38}, {7,29}, {2,36}, {25,31}, {7,28}, {8,28}, {18,30}, {13,38}, {6,29}, {2,38}, {7,27}, {9,36}, {9,38}, {21,33}, {7,30}, {17,21}, {17,40}, {19,29}, {9,33}, {17,24}, {6,19}, {1,36}, {18,22}, {23,33}, {18,21}, {9,35}, {24,33}, {19,21}, {4,12}, {23,32}, {26,33}, {8,25}, {10,18}, {9,18}, {20,33}, {21,38}, {4,21}, {1,23}, {11,25}, {10,20}, {19,31}, {1,25}, {7,31}, {3,23}, {13,25}, {11,33}, {14,25}, {5,39}, {13,27}, {9,15}, {20,34}, {2,23}, {5,32}, {6,32}, {3,32}, {27,40}, {11,35}, {14,24}, {4,39}, {11,27}, {9,14}, {5,31}, {7,15}, {7,14}, {5,15}, {17,37}, {5,40}, {12,28}, {30,39}, {15,25}, {7,17}, {28,36}, {21,39}, {4,30}, {13,28}, {10,15}, {8,15}, {27,37}, {7,16}, {17,36}, {30,37}, {30,38}, {1,21}, {8,17}, {19,35}, {17,33}, {10,24}, {6,34}, {26,32}, {8,27}, {17,29}, {14,37}, {5,30}, {1,37}, {10,35}, {10,37}, {22,34}, {8,29}, {18,39}, {20,30}, {10,34}, {18,23}, {5,20}, {2,35}, {24,34}, {17,22}, {10,36}, {23,34}, {20,22}, {3,11}, {24,31}, {25,34}, {7,26}, {16,40}, {18,29}, {3,19}, {4,19}, {2,19}, {1,19}, {12,31}, {16,22}, {7,36}, {23,36}, {22,31}, {25,36}, {7,23}, {3,20}, {5,26}, {5,23}, {3,26}, {19,22}, {3,12}, {21,32}, {11,40}, {26,34}, {23,31}, {5,28}, {2,13}, {15,32}, {11,37}, {3,30}, {1,40}, {24,32}, {8,26}, {1,12}, {13,31}, {15,28}, {13,40}, {14,40}, {6,28}, {14,39}, {16,30}, {15,31}, {17,28}, {8,36}, {16,21}, {4,18}, {19,33}, {1,24}, {6,31}, {4,31}, {28,39}, {12,36}, {13,23}, {3,40}, {10,13}, {8,16}, {8,13}, {6,16}, {18,38}, {6,39}, {29,40}, {16,26}, {8,18}, {27,35}, {22,40}, {3,29}, {14,27}, {9,16}, {28,38}, {18,35}, {29,38}, {29,37}, {2,22}, {7,18}, {20,36}, {18,34}, {9,23}, {5,33}, {12,25}, {4,32}, {27,39}, {29,39}, {2,30}, {1,30}, {9,30}, {10,30}, {20,21}, {6,33}, {25,38}, {15,35}, {6,18}, {20,38}, {15,34}, {8,23}, {5,35}, {2,29}, {9,22}, {3,33}, {8,22}, {3,35}, {9,29}, {2,21}, {5,17}, {19,37}, {12,22}, {18,33}, {20,35}, {9,24}, {17,34}, {19,26}, {12,37}, {13,22}, {2,40}, {19,28}, {10,12}, {19,36}, {10,21}, {20,24}, {2,34}, {12,24}, {11,23}, {25,40}, {20,26}, {2,31}, {28,32}, {13,24}, {6,15}, {25,37}, {30,32}, {1,27}, {15,39}, {17,30}, {4,20}, {1,20}, {2,20}, {11,32}, {15,21}, {8,35}, {24,35}, {26,35}, {8,24}, {6,25}, {6,24}, {4,25}, {4,11}, {12,39}, {25,33}, {6,27}, {1,14}, {16,31}, {12,38}, {4,29}, {2,39}, {7,25}, {2,11}, {14,32}, {16,27}, {13,39}, {5,27}, {15,29}, {16,32}, {18,27}, {7,35}, {15,22}, {3,17}, 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{19,39}, {12,30}, {10,32}, {8,20}, {22,33}, {12,32}, {12,40}, {4,28}, {10,39}, {8,39}, {3,18}, {13,33}, {15,33}, {17,25}, {5,36}, {1,18}, {5,37}, {1,15}, {29,34}, {23,37}, {20,28}, {7,22}, {30,35}, {30,34}, {20,31}, {23,35}, {20,39}, {2,27}, {6,23}, {13,29}, {22,38}, {5,21}, {6,21}, {3,21}, {20,40}, {27,34}, {7,19}, {17,31}, {8,11}, {14,35}, {10,27}, {9,34}, {5,22}, {7,32}, {10,25}, {7,34}, {13,36}, {15,23}, {17,23}, {3,36}, {12,21}, {1,26}, {11,28}, {3,39}, {15,26}, {16,25}, {27,36}, {11,30}, {3,38}, {21,40}, {17,26}, {8,19}, {17,38}, {19,38}, {6,11}, {29,32}, {28,34}, {10,26}, {13,35}, {5,38}, {3,14}, {18,40}, {20,29}, {11,29}, {9,31}, {4,35}, {24,39}, {14,38}, {3,37}, {4,37}, {5,29}, {2,37}, {12,29}, {1,16}, {18,31}, {6,22}, {16,23}, {8,31}, {5,19}, {8,34}, {5,18}, {15,24}, {28,35}, {2,15}, {21,37}, {10,33}, {22,32}, {1,13}, {2,14}, {28,33}, {6,30}, {14,30}, {4,22}, {18,32}, {9,26}, {8,33}, {16,24}, {12,27}, {4,40}, {22,39}, {7,20}, {11,36}, {9,13}, {4,38}, {25,35}, {6,20}, {26,36}, {13,37}, {6,17}, {17,32}, {23,40}, {1,38}, {7,33}, {21,31}, {10,14}, {12,35} } Symmetric graph 64 of order 40 Valency 32 Diameter 2 Girth 3 Automorphism group of order 12787447486620893184000000 Number of arcs = 1280 Number of 2-arcs = 39680 2-arc-transitive false Edge-set { {1,9}, {12,37}, {12,17}, {3,10}, {20,40}, {10,25}, {4,20}, {11,35}, {9,18}, {7,30}, {2,34}, {11,19}, {18,30}, {30,36}, {2,10}, {19,36}, {12,26}, {3,17}, {18,33}, {13,28}, {5,38}, {11,38}, {9,29}, {1,19}, {18,26}, {3,28}, {2,18}, {28,35}, {11,18}, {2,29}, {1,35}, {10,20}, {20,29}, {25,35}, {4,9}, {6,26}, {3,37}, {15,21}, {22,26}, {4,39}, {15,39}, {19,39}, {17,27}, {29,37}, {1,12}, {20,26}, {3,29}, {21,35}, {9,26}, {26,38}, {3,11}, {1,21}, {26,36}, {3,19}, {17,38}, {11,27}, {1,37}, {12,36}, {11,30}, {17,30}, {2,27}, {10,17}, {16,29}, {3,35}, {9,40}, {14,31}, {7,24}, {20,32}, {8,29}, {8,36}, {10,33}, {8,14}, {24,33}, {1,33}, {22,25}, {4,25}, {27,40}, {10,37}, {12,20}, {20,30}, {17,35}, {9,27}, {1,31}, {7,36}, {17,29}, {29,39}, {9,35}, {9,19}, {31,37}, {7,12}, {2,20}, {29,35}, {9,22}, {19,25}, {12,40}, {20,35}, {19,28}, {18,25}, {4,28}, {22,38}, {11,25}, {4,18}, {13,17}, {23,27}, {9,36}, {17,34}, {16,23}, {21,32}, {27,33}, {6,13}, {24,30}, {2,31}, {14,27}, {14,35}, {6,11}, {18,37}, {16,34}, {14,21}, {6,27}, {6,37}, {19,32}, {8,30}, {10,30}, {7,22}, {25,34}, {18,40}, {2,28}, {1,25}, {4,36}, {12,22}, {17,25}, {23,37}, {12,32}, {2,33}, {13,35}, {4,27}, {8,17}, {17,36}, {12,29}, {1,17}, {3,23}, {32,40}, {13,20}, {30,38}, {2,11}, {27,36}, {19,29}, {1,30}, {7,10}, {20,34}, {2,36}, {21,29}, {1,26}, {19,26}, {3,30}, {21,36}, {10,26}, {4,32}, {8,39}, {19,30}, {15,25}, {4,22}, {22,28}, {5,25}, {2,12}, {4,38}, {5,23}, {24,31}, {7,31}, {6,22}, {25,37}, {15,40}, {16,22}, {18,27}, {6,28}, {23,38}, {11,32}, {21,25}, {1,16}, {16,19}, {3,26}, {3,40}, {5,13}, {16,31}, {7,21}, {22,40}, {16,25}, {16,40}, {24,29}, {18,34}, {14,28}, {18,28}, {32,33}, {8,13}, {5,19}, {7,26}, {3,34}, {21,38}, {11,26}, {19,37}, {12,30}, 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{4,24}, {31,39}, {3,21}, {21,27}, {8,25}, {4,33}, {8,40}, {10,19}, {16,17}, {14,20}, {32,35}, {8,9}, {3,33}, {24,26}, {19,33}, {8,37}, {15,19}, {7,38}, {10,22}, {20,25}, {2,35}, {7,20}, {2,15}, {22,35}, {12,18}, {17,28}, {29,38}, {9,25}, {3,31}, {15,38}, {4,16}, {21,39}, {13,40}, {7,40}, {27,38}, {21,33}, {6,34}, {3,39}, {8,32}, {16,28}, {5,21}, {3,13}, {15,31}, {22,39}, {5,33}, {13,38}, {6,14}, {24,37}, {25,40}, {12,31}, {30,39}, {22,32}, {15,20}, {16,24}, {21,31}, {27,34}, {32,39}, {8,15}, {23,39}, {15,32}, {28,40}, {5,16}, {3,24}, {31,40}, {8,22}, {15,23}, {14,17}, {24,27}, {8,12}, {17,33}, {28,33}, {13,27}, {6,39}, {13,24}, {23,31}, {11,40}, {12,33}, {24,35}, {6,15}, {25,38}, {5,10}, {20,38}, {26,35}, {7,28}, {11,29}, {3,12}, {17,40}, {10,29}, {1,20}, {29,40}, {5,29}, {9,31}, {26,39}, {4,21}, {4,13}, {7,19}, {29,34}, {9,23}, {5,11}, {18,38}, {1,10}, {20,36}, {4,17}, {12,38}, {11,22}, {2,16}, {5,36}, {21,34}, {14,26}, {6,10}, {7,9}, {7,25}, {19,34}, {14,30}, {6,36}, {14,34}, {1,18}, {4,23}, {16,30}, {2,21}, {1,24}, {31,36}, {6,29}, {14,40}, {13,39}, {8,18}, {2,30}, {1,38}, {11,36}, {30,33}, {3,20}, {4,26}, {27,39}, {9,32}, {24,39}, {10,23}, {8,31}, {7,33}, {7,15}, {22,34}, {25,39}, {6,31}, {9,33}, {15,35}, {24,32}, {15,37}, {4,15}, {6,40}, {14,24}, {26,34}, {27,35}, {32,34}, {5,24}, {6,25}, {4,37}, {6,21}, {26,37}, {15,27}, {23,28}, {5,32}, {4,19}, {15,18}, {2,39}, {29,36}, {13,26}, {19,27}, {4,34}, {11,17}, {30,37}, {7,17}, {17,32}, {29,33}, {1,13}, {5,17}, {25,36}, {4,10}, {8,19}, {16,20}, {16,18}, {13,30}, {21,28}, {16,35}, {28,36}, {31,38}, {7,11}, {27,37}, {6,12}, {2,23}, {16,27}, {7,16}, {3,14}, {11,28}, {2,9}, {30,35}, {25,33}, {8,27}, {6,33}, {8,38}, {23,40}, {1,14}, {10,40}, {24,25}, {22,29}, {9,21}, {16,37} } Symmetric graph 65 of order 40 Valency 35 Diameter 2 Girth 3 Automorphism group of order 1733686198272000000000 Number of arcs = 1400 Number of 2-arcs = 47600 2-arc-transitive false Edge-set { {1,6}, {6,26}, {2,24}, {6,32}, {24,38}, {14,27}, {3,16}, {6,23}, {6,24}, {14,17}, {14,16}, {33,39}, {5,28}, {4,29}, {6,13}, {20,24}, {6,14}, {16,24}, {1,39}, {30,33}, {5,39}, {29,33}, {18,24}, {7,15}, {30,34}, {1,40}, {29,35}, {5,36}, {6,38}, {24,32}, {4,14}, {16,28}, {6,39}, {24,33}, {5,14}, {16,29}, {18,26}, {2,15}, {24,31}, {7,37}, {18,30}, {1,15}, {24,35}, {7,36}, {2,14}, {16,26}, {7,40}, {25,34}, {25,31}, {8,37}, {19,26}, {2,11}, {21,35}, {9,36}, {20,30}, {1,12}, {6,17}, {14,24}, {14,23}, {6,16}, {29,39}, {5,33}, {5,34}, {29,40}, {6,18}, {15,24}, {7,16}, {30,39}, {1,33}, {5,35}, {29,36}, {2,32}, {26,38}, {27,40}, {3,34}, {14,22}, {10,16}, {13,25}, {2,31}, {26,37}, {26,40}, {2,34}, {14,21}, {9,16}, {7,20}, {12,25}, {27,39}, {3,33}, {5,32}, {29,38}, {7,19}, {11,25}, {15,25}, {8,17}, {15,22}, {10,17}, {8,16}, {13,21}, {3,32}, {27,38}, {27,36}, {3,35}, {11,21}, {9,18}, {9,20}, {12,22}, {4,31}, {28,37}, {24,30}, {14,39}, {16,33}, {13,39}, {20,33}, {5,6}, {24,29}, {18,35}, {15,36}, {1,7}, {25,30}, {1,8}, {19,35}, {11,36}, {2,6}, {24,26}, 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{14,33}, {18,36}, {15,34}, {17,40}, {5,21}, {10,30}, {13,35}, {14,34}, {12,33}, {10,28}, {4,23}, {5,23}, {6,29}, {17,38}, {3,23}, {8,28}, {9,30}, {1,22}, {19,36}, {18,40}, {13,31}, {1,21}, {4,25}, {19,40}, {11,34}, {8,30}, {19,37}, {8,27}, {2,23}, {11,35}, {9,29}, {5,22}, {3,22}, {12,32}, {19,38}, {10,27}, {11,32}, {22,39}, {10,33}, {5,16}, {13,29}, {2,18}, {15,26}, {24,40}, {7,34}, {14,30}, {1,16}, {7,35}, {25,36}, {2,17}, {14,26}, {23,40}, {6,34}, {14,29}, {25,40}, {6,31}, {24,37}, {2,16}, {21,39}, {9,33}, {5,20}, {12,29}, {11,27}, {3,18}, {9,32}, {22,38}, {4,19}, {11,28}, {25,37}, {8,31}, {7,32}, {25,38}, {15,27}, {3,17}, {22,40}, {10,34}, {13,30}, {8,32}, {21,38}, {4,18}, {4,20}, {12,28}, {21,37}, {9,31}, {6,33}, {24,39}, {14,28}, {4,16}, {23,39}, {5,17}, {24,36}, {15,30}, {1,17}, {8,35}, {21,36}, {7,31}, {21,40}, {9,34}, {1,20}, {12,30}, {12,27}, {3,19}, {10,32}, {23,38}, {5,19}, {11,29}, {7,33}, {25,39}, {15,28}, {4,17}, {22,36}, {10,35}, {13,26}, {5,18}, {13,28}, {22,37}, {10,31}, {2,20}, {1,18}, {12,26}, {8,34}, {1,19}, {11,30}, {23,37}, {8,33}, {6,35}, {2,19}, {3,20}, {11,26}, {15,29}, {13,27}, {9,35}, {23,36}, {12,18}, {15,19}, {10,24}, {7,23}, {5,30}, {1,29}, {35,38}, {32,36}, {2,27}, {3,26}, {32,40}, {34,38}, {14,19}, {11,16}, {7,25}, {8,25}, {31,39}, {33,37}, {5,26}, {2,29}, {7,21}, {9,25}, {15,20}, {12,17}, {1,27}, {3,30}, {32,39}, {33,38}, {13,19}, {11,20}, {6,25}, {8,24}, {35,39}, {33,36}, {11,17}, {6,22}, {13,16}, {5,27}, {3,29}, {11,18}, {15,18}, {9,24}, {7,22}, {4,30}, {1,28}, {35,37}, {31,36}, {2,28}, {4,26}, {9,23}, {34,36}, {35,40}, {15,16}, {13,17}, {8,22}, {10,21}, {15,17}, {33,40}, {34,39}, {12,19}, {11,19}, {10,25}, {8,23}, {31,38}, {32,37}, {6,21}, {14,18}, {34,37}, {31,40}, {13,18}, {9,22}, {10,22}, {7,24}, {5,29}, {1,30}, {14,20}, {12,16}, {1,26}, {2,30}, {8,21}, {9,21}, {31,37}, {3,28}, {4,27}, {10,23}, {35,36}, {34,40}, {12,20}, {32,38}, {2,26}, {13,20}, {3,27}, {4,28}, {2,37}, {26,31}, {3,40}, {27,34}, {10,14}, {16,23}, {7,13}, {20,25}, {30,31}, {1,37}, {26,35}, {2,36}, {17,21}, {9,14}, {20,23}, {6,12}, {27,33}, {3,39}, {28,32}, {4,38}, {19,23}, {6,11}, {17,25}, {8,14}, {8,15}, {18,22}, {10,15}, {30,32}, {1,38}, {27,35}, {3,36}, {7,11}, {18,25}, {9,15}, {17,22}, {4,40}, {28,34}, {26,33}, {2,39}, {28,31}, {4,37}, {18,23}, {6,15}, {17,24}, {7,14}, {3,38}, {27,32}, {4,36}, {28,35}, {16,21}, {18,21}, {7,12}, {1,36}, {30,35}, {19,24}, {5,38}, {29,32}, {2,40}, {26,34}, {16,22}, {19,25}, {29,31}, {5,37}, {9,13}, {20,22}, {10,12}, {8,12}, {19,21}, {9,11}, {5,40}, {29,34}, {10,11}, {3,37}, {27,31}, {17,23}, {8,13}, {20,21}, {16,25}, {19,22}, {2,38}, {26,32}, {9,12}, {4,39}, {28,33}, {8,11}, {10,13}, {16,27}, {3,13}, {22,32}, {10,38}, {19,28}, {4,11}, {25,33}, {8,39}, {10,39}, {23,33}, {5,13}, {20,29}, {7,38}, {25,32}, {4,15}, {17,28}, {22,31}, {10,37}, {2,13}, {21,32}, {9,38}, {20,27}, {3,12}, {1,11}, {9,39}, {22,33}, {4,13}, {20,28}, {6,37}, {7,39}, {18,28}, {23,34}, {6,40}, {17,29}, {6,36}, {17,30}, {21,33}, {8,40}, {21,34}, {2,12}, {10,40}, {23,31}, {17,26}, {4,12}, {25,35}, {9,40}, {22,34}, {19,30}, {19,29}, {5,11}, {18,27}, {3,15}, {20,26}, {24,34}, {1,14}, {16,30}, {5,12}, {18,29}, {21,31}, {9,37}, {3,14}, {23,35}, {19,27}, {3,11}, {8,38}, {17,27}, {22,35}, {10,36}, {1,13}, {8,36}, {5,15}, {23,32}, {28,38}, {4,32}, {12,23}, {6,19}, {7,17}, {8,18}, {15,21}, {10,18}, {15,23}, {13,24}, {30,38}, {1,32}, {4,35}, {28,36}, {14,25}, {1,34}, {30,40}, {10,19}, {13,23}, {11,23}, {9,17}, {4,33}, {28,39}, {26,36}, {2,35}, {12,24}, {4,34}, {28,40}, {7,18}, {8,20}, {11,24}, {1,35}, {30,36}, {6,20}, {1,31}, {30,37}, {8,19}, {27,37}, {3,31}, {13,22}, {10,20}, {29,37}, {5,31}, {9,19}, {11,22}, {2,33}, {26,39}, {12,21}, {13,37}, {20,31}, {24,27}, {2,8}, {21,26}, {11,40}, {18,34}, {2,10}, {23,26}, {20,34}, {14,37}, {25,26}, {11,37}, {20,32}, {13,36}, {22,30}, {12,38}, {21,27}, {3,9}, {16,31}, {16,35}, {4,10}, {13,32}, {4,22}, {16,39}, {20,38}, {10,29} } Symmetric graph 66 of order 40 Valency 36 Diameter 2 Girth 3 Automorphism group of order 230078188847156428800 Number of arcs = 1440 Number of 2-arcs = 50400 2-arc-transitive false Edge-set { {1,5}, {6,9}, {20,24}, {5,33}, {19,27}, {1,27}, {8,30}, {6,20}, {20,39}, {2,32}, {29,36}, {9,32}, {24,36}, {8,16}, {2,17}, {19,30}, {1,38}, {16,30}, {10,14}, {3,23}, {15,18}, {14,33}, {3,27}, {18,27}, {8,38}, {8,21}, {10,17}, {4,10}, {23,31}, {2,16}, {2,29}, {9,39}, {14,24}, {16,21}, {2,10}, {24,34}, {12,28}, {7,21}, {3,22}, {12,39}, {12,32}, {21,36}, {3,32}, {32,36}, {8,39}, {14,17}, {8,25}, {6,17}, {4,34}, {28,31}, {11,34}, {22,28}, {13,28}, {4,7}, {10,21}, {10,23}, {10,15}, {1,23}, {33,38}, {16,27}, {24,27}, {8,12}, {21,25}, {6,10}, {10,34}, {23,28}, {8,40}, {31,36}, {25,35}, {7,25}, {6,18}, {12,26}, {5,21}, {36,38}, {16,25}, {14,36}, {3,25}, {18,25}, {6,38}, {12,14}, {3,21}, {14,18}, {3,38}, {16,17}, {4,24}, {12,31}, {17,33}, {4,5}, {19,31}, {11,19}, {22,40}, {13,31}, {4,35}, {19,35}, {26,40}, {26,31}, {5,35}, {11,35}, {7,11}, {18,22}, {25,34}, {6,28}, {28,34}, {7,28}, {22,34}, {9,28}, {7,24}, {14,39}, {21,32}, {10,36}, {27,32}, {8,36}, {17,25}, {25,30}, {6,33}, {5,34}, {19,28}, {19,34}, {28,40}, {7,35}, {8,37}, {15,17}, {13,18}, {4,38}, {17,30}, {33,37}, {7,30}, {18,33}, {3,5}, {19,32}, {6,25}, {18,39}, {14,38}, {21,30}, {10,33}, {18,24}, {12,38}, {12,30}, {21,33}, {3,30}, {32,33}, {5,39}, {14,19}, {12,25}, {6,21}, {3,24}, {14,21}, {4,21}, {10,31}, {11,27}, {8,22}, {13,36}, {4,25}, {4,20}, {31,39}, {6,11}, {20,22}, {2,13}, {4,29}, {2,35}, {26,29}, {26,37}, {5,15}, {13,23}, {4,11}, {11,17}, {22,37}, {29,37}, {15,34}, {13,29}, {20,37}, {17,35}, {18,26}, {3,26}, {5,32}, {33,40}, {5,31}, {35,40}, {7,31}, {18,35}, {19,26}, {5,40}, {31,33}, {27,35}, {7,27}, {8,18}, {24,38}, {12,16}, {14,25}, {3,6}, {18,34}, {28,38}, {14,32}, {3,36}, {17,38}, {4,30}, {2,33}, {5,20}, {19,39}, {6,19}, {20,40}, {2,31}, {29,35}, {2,19}, {29,40}, {31,37}, {15,35}, {7,17}, {18,37}, {13,17}, {4,22}, {9,31}, {11,32}, {11,39}, {14,22}, {4,16}, {13,39}, {7,16}, {2,18}, {3,20}, {32,39}, {6,12}, {20,21}, {2,14}, {3,29}, {5,30}, {19,33}, {16,32}, {24,39}, {2,6}, {20,34}, {28,39}, {8,32}, {36,39}, {16,36}, {2,25}, {20,25}, {6,39}, {2,21}, {14,20}, {3,39}, {16,20}, {2,24}, {12,29}, {30,36}, {25,33}, {5,25}, {12,27}, {24,25}, {11,25}, {6,22}, {13,34}, {4,28}, {32,35}, {26,36}, {8,26}, {5,17}, {18,23}, {11,38}, {11,30}, {22,33}, {1,11}, {22,30}, {13,38}, {1,26}, {11,23}, {11,15}, {1,22}, {23,37}, {15,29}, {1,34}, {9,20}, {22,26}, {5,13}, {15,40}, {1,13}, {19,22}, {9,40}, {15,23}, {1,40}, {13,30}, {4,17}, {32,34}, {21,34}, {6,14}, {15,39}, {6,13}, {17,37}, {15,37}, {7,13}, {4,18}, {3,17}, {32,37}, {29,34}, {6,37}, {15,20}, {13,20}, {4,39}, {17,32}, {36,37}, {7,32}, {18,36}, {3,8}, {27,39}, {8,14}, {10,25}, {24,30}, {12,33}, {5,12}, {19,21}, {3,19}, {32,40}, {14,35}, {3,12}, {12,18}, {21,38}, {14,31}, {11,16}, {2,22}, {10,20}, {23,39}, {1,6}, {20,30}, {2,38}, {16,29}, {2,5}, {19,29}, {1,37}, {15,30}, {10,13}, {4,23}, {23,29}, {1,15}, {13,40}, {4,13}, {17,22}, {9,37}, {18,31}, {3,40}, {13,32}, {11,31}, {11,26}, {5,22}, {13,33}, {4,27}, {35,38}, {16,26}, {24,26}, {11,21}, {10,22}, {23,38}, {10,18}, {3,10}, {23,32}, {1,12}, {3,16}, {5,36}, {19,25}, {1,25}, {6,30}, {10,24}, {12,23}, {12,15}, {1,21}, {6,16}, {2,20}, {29,39}, {27,38}, {5,10}, {19,23}, {1,19}, {30,40}, {31,38}, {16,35}, {18,38}, {16,38}, {18,21}, {10,38}, {10,30}, {23,33}, {1,30}, {30,33}, {5,38}, {16,19}, {6,23}, {1,24}, {10,27}, {8,23}, {15,36}, {16,18}, {33,39}, {20,33}, {25,36}, {27,30}, {8,33}, {30,35}, {26,33}, {5,26}, {5,19}, {11,40}, {22,35}, {3,37}, {18,29}, {34,38}, {8,29}, {17,34}, {4,6}, {20,31}, {3,28}, {35,39}, {14,26}, {2,26}, {20,26}, {9,35}, {11,14}, {9,29}, {28,35}, {7,26}, {9,26}, {5,24}, {15,22}, {1,9}, {9,19}, {24,40}, {1,33}, {11,20}, {9,15}, {9,23}, {11,24}, {5,29}, {15,27}, {7,9}, {15,24}, {16,23}, {2,11}, {22,31}, {6,40}, {12,19}, {22,38}, {9,16}, {5,23}, {4,40}, {9,13}, {7,23}, {11,18}, {3,11}, {22,32}, {4,12}, {21,31}, {14,40}, {3,13}, {15,19}, {13,19}, {9,30}, {16,22}, {4,14}, {3,31}, {18,40}, {7,14}, {3,18}, {32,38}, {17,21}, {8,24}, {12,17}, {30,34}, {28,33}, {2,8}, {20,36}, {25,39}, {6,36}, {6,29}, {2,12}, {21,29}, {14,37}, {3,15}, {17,24}, {12,37}, {12,36}, {25,32}, {13,24}, {21,35}, {10,26}, {28,30}, {5,9}, {19,24}, {1,16}, {2,30}, {10,39}, {14,23}, {15,21}, {1,10}, {20,23}, {2,15}, {1,29}, {2,9}, {23,34}, {11,28}, {7,22}, {15,28}, {1,7}, {9,22}, {9,24}, {11,22}, {4,26}, {13,27}, {4,32}, {13,35}, {26,34}, {6,26}, {22,36}, {17,39}, {27,29}, {8,34}, {5,28}, {3,34}, {28,32}, {12,34}, {21,28}, {14,28}, {3,7}, {9,36}, {12,21}, {20,38}, {29,33}, {24,33}, {5,16}, {27,34}, {8,28}, {28,36}, {9,25}, {6,24}, {10,19}, {23,30}, {15,38}, {6,34}, {20,28}, {2,28}, {7,29}, {24,29}, {16,37}, {10,37}, {21,39}, {6,32}, {34,39}, {16,34}, {7,39}, {2,39}, {10,29}, {7,19}, {9,27}, {9,38}, {10,32}, {16,39}, {1,20}, {30,39}, {18,30}, {2,36}, {8,20}, {2,37}, {20,29}, {35,37}, {15,26}, {17,26}, {5,37}, {12,40}, {13,21}, {1,32}, {8,15}, {1,17}, {4,19}, {31,40}, {5,11}, {27,37}, {24,35}, {15,33}, {17,31}, {6,27}, {9,33}, {1,35}, {26,30}, {6,15}, {7,33}, {22,27}, {8,9}, {7,10}, {10,35}, {23,26}, {13,26}, {25,29}, {26,39}, {5,14}, {7,20}, {11,37}, {7,18}, {3,35}, {26,32}, {12,35}, {21,26}, {11,36}, {22,25}, {13,25}, {24,37}, {2,23}, {11,29}, {16,33}, {2,27}, {12,22}, {12,13}, {15,32}, {3,14}, {6,31}, {8,27}, {8,17}, {4,36}, {25,31}, {2,40}, {8,10}, {17,23}, {1,18}, {30,38}, {5,18}, {19,38}, {23,25}, {15,25}, {9,21}, {8,31}, {36,40}, {25,38}, {14,30}, {3,33}, {23,27}, {8,11}, {16,31}, {20,27}, {10,16}, {16,28}, {24,28}, {7,12}, {9,34}, {1,28}, {7,40}, {31,35}, {26,35}, {5,27}, {27,33}, {34,40}, {1,36}, {8,19}, {17,40}, {20,35}, {21,40}, {19,36}, {25,40}, {6,35}, {24,31}, {1,39}, {2,34}, {28,29}, {2,7}, {22,39}, {9,14}, {19,40}, {1,31}, {23,35}, {7,15}, {1,8}, {16,40}, {10,40}, {7,38}, {27,36}, {14,27}, {14,34}, {13,37}, {22,29}, {31,34}, {9,17}, {4,9}, {4,15}, {17,27}, {4,31}, {7,34}, {18,28}, {28,37}, {29,38}, {12,20}, {18,32}, {21,37}, {14,29}, {17,36}, {25,37}, {26,38}, {11,33}, {27,40}, {8,13}, {10,28}, {23,36}, {3,9}, {12,24}, {4,8}, {4,33}, {17,28}, {24,32}, {20,32}, {16,24}, {7,36}, {8,35}, {27,31}, {7,37}, {4,37}, {17,29}, {34,37}, {19,37}, {9,18}, {15,31}, {30,37}, {23,40}, {11,13}, {1,14}, {21,27}, {13,22} } Symmetric graph 67 of order 40 Valency 38 Diameter 2 Girth 3 Automorphism group of order 2551082656125828464640000 Number of arcs = 1520 Number of 2-arcs = 56240 2-arc-transitive false Edge-set { {1,3}, {26,30}, {30,35}, {7,32}, {14,34}, {7,16}, {14,20}, {10,37}, {3,11}, {23,40}, {8,39}, {10,17}, {3,23}, {14,40}, {8,9}, {21,28}, {17,21}, {6,26}, {26,35}, {11,36}, {16,38}, {9,12}, {4,15}, {28,33}, {5,21}, {26,36}, {35,38}, {11,40}, {8,16}, {9,27}, {4,22}, {1,27}, {3,33}, {5,27}, {20,32}, {32,34}, {16,32}, {20,34}, {6,15}, {19,26}, {17,22}, {18,23}, {22,25}, {18,25}, {24,36}, {1,24}, {1,40}, {3,19}, {27,31}, {15,32}, {19,34}, {16,22}, {18,20}, {6,11}, {16,26}, {9,17}, {4,23}, {2,27}, {2,22}, {4,25}, {28,36}, {2,30}, {24,26}, {35,40}, {2,19}, {2,31}, {14,37}, {9,11}, {23,37}, {11,39}, {17,37}, {11,23}, {14,23}, {9,39}, {24,32}, {13,32}, {10,34}, {4,33}, {5,28}, {34,36}, {6,38}, {4,31}, {31,34}, {6,33}, {15,35}, {19,37}, {30,37}, {11,30}, {16,30}, {13,26}, {10,35}, {2,38}, {2,12}, {18,37}, {11,24}, {13,23}, {10,39}, {4,17}, {23,28}, {6,9}, {6,20}, {26,32}, {17,32}, {23,34}, {27,33}, {5,22}, {25,36}, {36,38}, {2,29}, {4,29}, {28,29}, {25,31}, {33,36}, {1,15}, {1,19}, {7,29}, {14,29}, {32,35}, {34,37}, {11,16}, {16,20}, {13,29}, {10,29}, {29,38}, {12,29}, {21,40}, {8,17}, {6,27}, {22,26}, {21,36}, {17,38}, {6,12}, {15,26}, {21,33}, {5,17}, {6,36}, {26,38}, {36,40}, {8,38}, {12,27}, {15,22}, {35,37}, {11,37}, {37,39}, {7,11}, {21,39}, {24,25}, {1,31}, {15,23}, {19,39}, {20,22}, {18,32}, {25,38}, {12,36}, {23,38}, {12,39}, {20,24}, {32,40}, {16,18}, {13,21}, {7,21}, {14,17}, {6,7}, {14,26}, {7,17}, {32,39}, {7,34}, {16,28}, {20,21}, {22,29}, {18,29}, {5,29}, {25,29}, {21,34}, 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{33,38} } Symmetric graph 68 of order 40 Valency 39 Diameter 1 Girth 3 Automorphism group of order 815915283247897734345611269596115894272000000000 Number of arcs = 1560 Number of 2-arcs = 59280 2-arc-transitive true Edge-set { {1,2}, {17,31}, {4,11}, {6,25}, {23,35}, {30,33}, {9,12}, {19,21}, {3,17}, {3,24}, {15,37}, {20,28}, {8,34}, {6,10}, {36,39}, {27,40}, {10,25}, {7,35}, {10,16}, {7,22}, {14,40}, {21,39}, {28,38}, {29,38}, {22,29}, {13,18}, {19,32}, {3,8}, {12,35}, {26,32}, {5,11}, {24,34}, {21,32}, {8,17}, {18,24}, {2,37}, {20,32}, {8,19}, {7,18}, {2,25}, {2,5}, {14,24}, {35,36}, {26,27}, {26,38}, {31,38}, {30,31}, {7,27}, {25,30}, {9,13}, {5,33}, {4,39}, {16,40}, {10,29}, {7,13}, {10,37}, {4,23}, {16,36}, {1,30}, {1,12}, {16,22}, {18,22}, {4,36}, {16,27}, {25,29}, {13,35}, {13,16}, {22,33}, {31,40}, {11,39}, {4,28}, {16,29}, {29,39}, {13,40}, {2,33}, {21,31}, {11,17}, {1,31}, {1,11}, {2,16}, {14,22}, {12,24}, {32,37}, {11,23}, {34,36}, {23,26}, {31,36}, {6,26}, {23,31}, {6,37}, 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{12,13}, {3,12}, {17,18}, {36,37}, {16,17}, {24,29}, {8,31}, {3,18}, {14,30}, {12,21}, {12,18}, {18,37}, {2,8}, {6,24}, {20,36}, {6,23}, {21,30}, {12,17}, {8,38}, {6,38}, {4,33}, {19,37}, {3,28}, {1,4}, {18,27}, {2,30}, {19,33}, {3,9}, {30,40}, {2,26}, {24,39}, {4,17}, {9,11}, {12,27}, {30,32}, {8,12}, {20,23}, {20,21}, {11,34}, {26,29}, {6,27}, {1,23}, {34,38}, {10,38}, {4,27}, {20,26}, {19,31}, {28,29}, {5,27}, {32,35}, {5,18}, {5,23}, {24,36}, {6,35}, {11,38}, {27,37}, {1,24}, {17,21}, {6,32}, {14,31}, {23,30}, {30,36}, {2,31}, {2,17}, {14,21}, {20,38}, {12,23}, {15,35}, {5,8}, {13,21}, {17,33}, {11,37}, {5,30}, {13,23}, {16,19}, {13,25}, {16,28}, {1,37}, {6,9}, {14,38}, {4,14}, {13,29}, {7,33}, {13,20}, {4,9}, {15,29}, {10,23}, {12,16}, {7,23}, {16,35}, {15,28}, {20,40}, {7,38}, {9,34}, {10,34}, {22,30}, {10,13}, {29,31}, {11,13}, {39,40}, {22,26}, {3,34}, {1,13}, {22,32}, {3,37}, {25,36}, {14,27} } ................................................................... Symmetric connected graphs of order 41 Symmetric graph 1 of order 41 Valency 2 Diameter 20 Girth 41 Automorphism group of order 82 Number of arcs = 82 Number of 2-arcs = 82 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {15,16}, {16,17}, {17,18}, {18,19}, {19,20}, {20,21}, {21,22}, {22,23}, {23,24}, {24,25}, {25,26}, {26,27}, {27,28}, {28,29}, {29,30}, {30,31}, {31,32}, {32,33}, {33,34}, {34,35}, {35,36}, {36,37}, {37,38}, {38,39}, {39,40}, {40,41}, {1,41} } Symmetric graph 2 of order 41 Valency 4 Diameter 4 Girth 4 Automorphism group of order 164 Number of arcs = 164 Number of 2-arcs = 492 2-arc-transitive false Edge-set { {1,2}, {2,3}, {23,32}, {3,4}, {14,23}, {24,33}, {39,40}, {4,5}, {5,14}, {15,24}, {38,39}, {25,34}, {30,31}, {40,41}, {9,18}, {5,6}, {5,37}, {6,15}, {37,38}, {16,25}, {29,30}, {18,27}, {26,35}, {21,22}, {31,32}, {8,17}, {1,41}, {9,41}, {10,19}, {6,7}, {28,37}, {6,38}, {36,37}, {7,16}, {28,29}, {27,36}, {17,26}, {20,21}, {19,28}, {12,13}, {22,23}, {32,33}, {8,40}, {10,11}, {32,41}, {1,10}, {11,20}, {33,34}, {7,8}, {29,38}, {35,36}, {7,39}, {27,28}, {4,36}, {19,20}, {11,12}, {20,29}, {34,35}, {13,14}, {23,24}, {31,40}, {9,10}, {1,33}, {2,11}, {12,21}, {24,25}, {22,31}, {8,9}, {30,39}, {26,27}, {4,13}, {18,19}, {3,35}, {21,30}, {25,26}, {13,22}, {14,15}, {2,34}, {3,12}, {15,16}, {17,18}, {16,17} } Symmetric graph 3 of order 41 Valency 8 Diameter 3 Girth 4 Automorphism group of order 328 Number of arcs = 328 Number of 2-arcs = 2296 2-arc-transitive false Edge-set { {1,2}, {2,3}, {13,27}, {3,4}, {13,40}, {14,28}, {23,32}, {4,5}, {26,40}, {14,41}, {14,23}, {15,29}, {9,18}, {24,33}, {3,6}, {5,6}, {12,26}, {27,41}, {5,14}, {1,15}, {9,41}, {15,24}, {6,9}, {16,30}, {4,36}, {10,19}, {35,38}, {25,34}, {30,33}, {4,7}, {39,40}, {6,7}, {12,39}, {5,37}, {1,28}, {32,41}, {6,15}, {9,12}, {2,16}, {27,36}, {1,10}, {38,41}, {16,25}, {33,36}, {7,10}, {38,39}, {17,31}, {22,31}, {26,29}, {11,20}, {21,24}, {36,39}, {26,35}, {16,19}, {31,34}, {30,31}, {5,8}, {25,26}, {40,41}, {7,8}, {25,39}, {28,37}, {6,38}, {12,15}, {2,29}, {18,27}, {1,33}, {3,41}, {7,16}, {10,13}, {37,38}, {3,17}, {13,22}, {29,32}, {2,11}, {24,27}, {1,39}, {1,41}, {17,26}, {19,22}, {34,37}, {29,30}, {8,11}, {24,25}, {18,32}, {8,17}, {17,20}, {27,30}, {12,21}, {22,25}, {33,34}, {37,40}, {28,29}, {2,5}, {21,22}, {32,35}, {16,17}, {31,32}, {11,12}, {26,27}, {5,19}, {8,9}, {11,25}, {19,28}, {29,38}, {15,18}, {7,39}, {13,16}, {36,37}, {3,30}, {4,13}, {2,34}, {1,4}, {11,14}, {23,24}, {4,18}, {8,40}, {20,23}, {3,12}, {25,28}, {32,33}, {2,40}, {27,28}, {20,21}, {15,16}, {4,31}, {10,11}, {19,33}, {3,35}, {18,21}, {28,31}, {23,26}, {19,20}, {34,35}, {14,15}, {12,13}, {22,23}, {20,34}, {17,18}, {8,22}, {10,37}, {5,32}, {6,20}, {9,10}, {11,38}, {20,29}, {30,39}, {35,36}, {14,17}, {31,40}, {6,33}, {18,19}, {13,14}, {7,34}, {22,36}, {10,24}, {21,30}, {7,21}, {9,36}, {23,37}, {21,35}, {8,35}, {9,23}, {24,38} } Symmetric graph 4 of order 41 Valency 10 Diameter 2 Girth 4 Automorphism group of order 410 Number of arcs = 410 Number of 2-arcs = 3690 2-arc-transitive false Edge-set { {1,2}, {2,3}, {10,20}, {3,4}, {20,30}, {11,21}, {18,36}, {4,5}, {30,40}, {21,31}, {13,36}, {12,22}, {5,28}, {19,37}, {16,32}, {5,6}, {9,40}, {31,41}, {13,31}, {22,32}, {5,23}, {14,37}, {7,32}, {13,23}, {15,38}, {6,29}, {9,34}, {20,38}, {1,26}, {17,33}, {33,37}, {6,7}, {9,19}, {10,41}, {8,31}, {1,32}, {23,41}, {14,32}, {7,23}, {23,33}, {15,33}, {6,24}, {9,25}, {1,17}, {8,33}, {29,33}, {14,24}, {7,25}, {16,39}, {11,27}, {7,30}, {3,19}, {10,35}, {8,12}, {21,39}, {11,36}, {2,27}, {10,14}, {18,34}, {2,6}, {34,38}, {7,8}, {19,29}, {8,26}, {1,11}, {18,41}, {9,32}, {23,39}, {2,33}, {10,33}, {1,24}, {25,41}, {8,24}, {25,29}, {24,34}, {2,25}, {16,34}, {19,35}, {10,26}, {4,8}, {2,18}, {6,10}, {2,39}, {30,34}, {15,25}, {17,35}, {4,29}, {17,40}, {21,37}, {12,28}, {24,28}, {13,29}, {4,20}, {26,30}, {18,22}, {9,13}, {38,39}, {22,40}, {5,21}, {12,37}, {28,32}, {3,28}, {20,24}, {11,15}, {17,18}, {12,16}, {3,7}, {19,20}, {35,39}, {11,12}, {8,9}, {29,39}, {3,26}, {9,27}, {14,39}, {2,12}, {10,28}, {1,19}, {16,41}, {24,40}, {21,25}, {3,34}, {2,20}, {11,34}, {4,41}, {25,35}, {12,35}, {20,36}, {22,26}, {14,18}, {5,9}, {39,40}, {16,20}, {7,11}, {18,19}, {3,40}, {20,21}, {31,35}, {12,13}, {16,26}, {4,27}, {6,22}, {5,30}, {6,31}, {22,38}, {1,5}, {34,35}, {14,30}, {36,40}, {27,31}, {13,14}, {19,23}, {15,16}, {15,31}, {13,38}, {1,38}, {33,34}, {35,36}, {27,28}, {6,16}, {13,17}, {37,38}, {29,30}, {26,36}, {21,22}, {28,38}, {9,10}, {8,39}, {3,21}, {15,40}, {17,21}, {3,13}, {11,29}, {37,41}, {4,35}, {12,30}, {40,41}, {4,22}, {32,36}, {23,27}, {14,15}, {15,19}, {16,17}, {36,37}, {28,29}, {30,31}, {5,36}, {22,23}, {7,38}, {17,27}, {31,32}, {23,24}, {7,17}, {25,26}, {27,37}, {10,11}, {5,15}, {8,18}, {4,14}, {1,41}, {32,33}, {24,25}, {26,27}, {6,37}, {18,28} } Symmetric graph 5 of order 41 Valency 20 Diameter 2 Girth 3 Automorphism group of order 820 Number of arcs = 820 Number of 2-arcs = 15580 2-arc-transitive false Edge-set { {1,2}, {2,3}, {31,36}, {3,4}, {26,31}, {32,37}, {9,25}, {4,5}, {21,26}, {27,32}, {9,34}, {33,38}, {4,20}, {10,26}, {37,39}, {5,6}, {16,21}, {22,27}, {18,34}, {28,33}, {4,29}, {10,35}, {35,37}, {34,39}, {15,40}, {5,21}, {21,23}, {11,27}, {32,34}, {38,40}, {10,20}, {6,7}, {11,16}, {17,22}, {2,18}, {23,28}, {13,29}, {19,35}, {33,35}, {29,34}, {24,40}, {5,30}, {19,21}, {11,36}, {30,32}, {36,38}, {20,30}, {35,40}, {16,41}, {5,7}, {6,22}, {16,18}, {22,24}, {8,18}, {12,28}, {27,29}, {4,35}, {39,41}, {5,15}, {11,21}, {23,32}, {7,8}, {6,11}, {12,17}, {2,27}, {18,23}, {13,38}, {3,19}, {31,33}, {24,29}, {8,24}, {14,30}, {17,19}, {20,36}, {28,30}, {34,36}, {30,40}, {30,35}, {25,41}, {3,5}, {6,31}, {14,16}, {20,22}, {18,28}, {12,37}, {25,27}, {4,14}, {15,25}, {21,31}, {14,23}, {36,41}, {1,17}, {2,41}, {6,8}, {6,16}, {7,23}, {11,13}, {2,33}, {23,25}, {3,13}, {9,19}, {1,33}, {19,29}, {5,36}, {21,30}, {1,40}, {10,41}, {7,16}, {12,22}, {18,27}, {24,33}, {4,8}, {8,9}, {1,6}, {7,12}, {13,18}, {22,38}, {3,28}, {29,31}, {19,24}, {8,33}, {14,39}, {15,17}, {26,28}, {9,40}, {25,30}, {1,3}, {15,31}, {12,14}, {18,20}, {28,38}, {21,37}, {14,24}, {25,35}, {31,41}, {5,14}, {1,26}, {4,6}, {16,26}, {7,32}, {9,11}, {2,12}, {13,23}, {29,39}, {12,21}, {7,39}, {22,32}, {9,18}, {15,24}, {8,12}, {1,37}, {7,9}, {1,11}, {7,17}, {2,11}, {17,27}, {3,34}, {31,40}, {24,26}, {8,39}, {17,26}, {28,37}, {2,34}, {36,40}, {19,28}, {6,37}, {16,25}, {22,31}, {14,18}, {32,41}, {8,17}, {2,6}, {13,22}, {29,33}, {25,34}, {3,40}, {5,9}, {1,21}, {9,10}, {2,7}, {8,13}, {14,19}, {17,33}, {23,39}, {13,15}, {20,25}, {10,12}, {7,38}, {24,34}, {5,37}, {2,4}, {26,36}, {16,32}, {23,33}, {3,12}, {30,39}, {1,32}, {9,41}, {6,15}, {12,16}, {27,37}, {10,19}, {18,22}, {8,40}, {6,10}, {4,13}, {33,37}, {3,7}, {9,13}, {1,22}, {2,38}, {8,10}, {27,36}, {6,38}, {27,31}, {29,38}, {26,35}, {1,10}, {34,38}, {20,24}, {3,35}, {31,35}, {37,41}, {5,25}, {20,29}, {24,28}, {11,20}, {2,39}, {15,19}, {12,33}, {4,41}, {1,38}, {11,31}, {13,17}, {30,34}, {19,40}, {35,39}, {5,26}, {16,37}, {2,22}, {18,36}, {10,11}, {3,8}, {9,14}, {15,20}, {16,20}, {22,26}, {10,14}, {4,36}, {7,11}, {28,32}, {19,23}, {13,33}, {1,5}, {11,32}, {17,21}, {20,40}, {6,26}, {17,37}, {2,23}, {13,36}, {3,39}, {25,29}, {11,15}, {9,29}, {32,36}, {15,35}, {21,25}, {3,23}, {26,30}, {9,30}, {20,41}, {16,39}, {3,24}, {23,27}, {10,31}, {7,28}, {13,34}, {22,40}, {21,41}, {15,36}, {12,32}, {9,27}, {17,38}, {14,35}, {5,28}, {10,30}, {6,27}, {16,34}, {2,20}, {13,31}, {19,37}, {25,33}, {11,12}, {4,9}, {10,15}, {4,24}, {8,28}, {14,34}, {17,40}, {16,36}, {4,27}, {18,38}, {5,23}, {7,27}, {11,34}, {20,38}, {8,31}, {14,37}, {17,25}, {4,40}, {19,39}, {4,25}, {7,30}, {18,39}, {8,26}, {23,41}, {2,10}, {3,26}, {8,29}, {9,32}, {6,24}, {17,35}, {5,13}, {18,41}, {7,25}, {4,22}, {10,28}, {29,37}, {15,38}, {12,30}, {6,29}, {16,24}, {14,32}, {11,29}, {2,35}, {3,21}, {23,31}, {9,17}, {20,28}, {26,34}, {39,40}, {12,13}, {5,10}, {1,24}, {12,35}, {5,38}, {2,25}, {21,29}, {15,33}, {8,16}, {27,35}, {21,39}, {15,23}, {1,9}, {12,20}, {18,26}, {38,39}, {5,41}, {6,14}, {10,33}, {1,34}, {8,41}, {3,11}, {31,32}, {1,19}, {4,37}, {30,38}, {16,17}, {33,41}, {6,39}, {13,21}, {24,32}, {19,20}, {7,15}, {14,22}, {11,19}, {4,12}, {19,27}, {3,36}, {30,31}, {10,18}, {37,38}, {23,24}, {34,35}, {40,41}, {13,14}, {22,30}, {15,16}, {31,39}, {18,19}, {7,40}, {28,36}, {29,30}, {36,37}, {22,23}, {33,34}, {32,40}, {35,36}, {1,41}, {26,27}, {32,33}, {20,21}, {14,15}, {17,18}, {27,28}, {21,22}, {28,29}, {25,26}, {24,25} } Symmetric graph 6 of order 41 Valency 40 Diameter 1 Girth 3 Automorphism group of order 33452526613163807108170062053440751665152000000000 Number of arcs = 1640 Number of 2-arcs = 63960 2-arc-transitive true Edge-set { {1,2}, {2,3}, {6,12}, {3,4}, {12,18}, {7,13}, {31,36}, {4,5}, {18,24}, {13,19}, {26,31}, {8,14}, {1,37}, {32,37}, {11,22}, {5,6}, {24,30}, {19,25}, {21,26}, {14,20}, {27,32}, {22,33}, {9,15}, {2,7}, {2,38}, {6,17}, {33,38}, {17,28}, {12,23}, {9,25}, {6,7}, {30,36}, {25,31}, {16,21}, {20,26}, {22,27}, {3,33}, {15,21}, {28,33}, {28,39}, {23,34}, {9,34}, {10,16}, {8,13}, {3,8}, {1,12}, {3,39}, {7,18}, {20,36}, {34,39}, {18,29}, {4,20}, {13,24}, {15,31}, {10,26}, {13,27}, {7,8}, {1,36}, {31,37}, {11,16}, {26,32}, {17,22}, {3,14}, {21,27}, {23,28}, {9,39}, {4,34}, {18,34}, {16,22}, {29,34}, {29,40}, {4,29}, {24,35}, {15,40}, {10,35}, {13,40}, {11,17}, {14,19}, {9,14}, {7,37}, {4,9}, {2,13}, {6,31}, {4,40}, {8,19}, {1,26}, {21,37}, {11,38}, {35,40}, {19,30}, {5,21}, {24,38}, {14,25}, {16,32}, {8,22}, {11,27}, {19,33}, {14,28}, {37,39}, {8,9}, {1,7}, {2,37}, {6,11}, {32,38}, {12,17}, {27,33}, {18,23}, {9,20}, {4,15}, {2,18}, {22,28}, {24,29}, {10,40}, {13,29}, {5,35}, {24,40}, {19,35}, {26,40}, {17,23}, {30,35}, {30,41}, {5,30}, {10,24}, {25,36}, {16,41}, {8,35}, {11,36}, {5,19}, {14,41}, {35,37}, {20,25}, {15,20}, {2,32}, {10,15}, {8,38}, {1,17}, {5,10}, {12,37}, {7,32}, {22,36}, {5,41}, {2,27}, {6,33}, {22,38}, {3,17}, {12,39}, {23,25}, {36,41}, {20,31}, {6,22}, {3,30}, {25,39}, {21,23}, {15,26}, {17,33}, {9,23}, {7,9}, {12,28}, {20,34}, {32,34}, {15,29}, {2,4}, {38,40}, {17,29}, {9,10}, {2,8}, {1,6}, {3,38}, {7,12}, {33,39}, {13,18}, {28,34}, {19,24}, {10,21}, {13,38}, {5,16}, {8,24}, {3,19}, {12,26}, {23,29}, {25,30}, {11,41}, {14,30}, {10,37}, {6,36}, {25,41}, {21,35}, {5,32}, {27,41}, {33,35}, {1,31}, {16,30}, {11,25}, {19,21}, {26,37}, {9,36}, {5,7}, {6,20}, {30,32}, {1,15}, {2,41}, {36,38}, {5,17}, {27,38}, {7,23}, {17,31}, {8,33}, {1,28}, {23,37}, {9,11}, {3,28}, {7,34}, {34,36}, {23,39}, {4,18}, {18,20}, {29,31}, {24,26}, {15,27}, {21,32}, {4,31}, {16,18}, {27,29}, {22,24}, {3,15}, {16,27}, {13,15}, {8,10}, {1,13}, {28,40}, {3,5}, {12,24}, {39,41}, {23,35}, {18,30}, {10,20}, {10,11}, {3,9}, {4,39}, {34,40}, {29,35}, {14,39}, {7,21}, {18,32}, {31,33}, {2,16}, {17,19}, {28,30}, {5,34}, {14,16}, {25,27}, {20,22}, {3,32}, {11,13}, {6,8}, {1,30}, {16,28}, {1,3}, {12,41}, {11,23}, {6,18}, {20,30}, {2,29}, {4,6}, {15,17}, {10,12}, {13,25}, {1,40}, {11,40}, {26,38}, {10,22}, {21,33}, {8,39}, {14,26}, {10,39}, {9,21}, {4,16}, {8,18}, {8,37}, {7,19}, {2,14}, {6,37}, {29,41}, {4,35}, {21,31}, {24,36}, {5,15}, {19,31}, {16,26}, {11,21}, {19,38}, {11,12}, {4,10}, {5,40}, {35,41}, {26,28}, {22,34}, {12,14}, {20,32}, {6,35}, {30,40}, {27,39}, {9,38}, {4,33}, {18,28}, {25,37}, {7,36}, {2,31}, {6,16}, {4,14}, {31,41}, {15,25}, {26,36}, {16,38}, {8,20}, {27,37}, {25,35}, {23,33}, {9,19}, {3,34}, {9,40}, {7,29}, {2,33}, {19,29}, {3,13}, {14,24}, {7,26}, {7,17}, {1,32}, {2,12}, {7,38}, {17,36}, {10,41}, {5,36}, {5,24}, {22,32}, {3,22}, {8,30}, {17,27}, {14,33}, {12,22}, {3,25}, {20,39}, {23,32}, {12,13}, {5,11}, {6,41}, {28,38}, {16,35}, {29,39}, {13,23}, {24,34}, {4,26}, {1,11}, {14,36}, {2,24}, {22,41}, {8,27}, {11,33}, {17,39}, {14,23}, {5,27}, {15,34}, {13,32}, {18,40}, {13,35}, {1,10}, {12,34}, {10,32}, {18,37}, {2,21}, {1,33}, {1,20}, {6,28}, {12,31}, {1,23}, {11,20}, {19,41}, {11,30}, {6,25}, {21,30}, {9,28}, {4,23}, {9,18}, {9,31}, {7,16}, {2,34}, {18,27}, {21,40}, {29,38}, {24,33}, {15,28}, {13,14}, {5,14}, {10,29}, {15,37}, {2,11}, {12,21}, {9,41}, {7,39}, {25,34}, {20,29}, {15,24}, {2,15}, {30,39}, {8,40}, {28,37}, {26,35}, {5,37}, {6,19}, {31,40}, {19,28}, {17,26}, {3,12}, {6,34}, {6,38}, {4,36}, {22,31}, {6,15}, {25,38}, {32,41}, {16,25}, {27,36}, {3,16}, {4,13}, {10,19}, {13,26}, {13,22}, {8,17}, {1,14}, {3,35}, {12,40}, {26,39}, {10,23}, {21,34}, {16,29}, {4,8}, {14,15}, {2,30}, {12,25}, {3,31}, {13,41}, {1,29}, {27,40}, {10,38}, {8,21}, {8,12}, {7,35}, {4,17}, {5,33}, {17,30}, {7,20}, {32,36}, {22,35}, {4,32}, {20,33}, {18,31}, {36,40}, {23,36}, {11,24}, {9,22}, {8,36}, {23,27}, {28,41}, {14,27}, {11,39}, {14,18}, {24,37}, {19,32}, {33,37}, {9,37}, {2,6}, {5,18}, {31,35}, {29,33}, {15,19}, {3,40}, {10,14}, {5,9}, {7,24}, {15,16}, {12,16}, {27,31}, {18,22}, {37,41}, {6,10}, {35,39}, {19,23}, {3,7}, {9,13}, {7,31}, {1,5}, {20,24}, {30,34}, {16,20}, {1,38}, {11,28}, {24,28}, {34,38}, {22,26}, {11,35}, {11,15}, {21,25}, {7,11}, {15,39}, {4,41}, {2,39}, {25,29}, {2,26}, {17,21}, {28,32}, {17,34}, {13,17}, {12,36}, {26,30}, {5,22}, {10,34}, {8,32}, {18,35}, {2,19}, {13,30}, {8,25}, {1,21}, {16,17}, {14,31}, {22,39}, {9,26}, {17,41}, {19,36}, {5,29}, {15,32}, {1,18}, {13,37}, {1,22}, {6,30}, {21,38}, {16,40}, {14,38}, {6,23}, {12,29}, {4,25}, {4,21}, {23,40}, {9,33}, {5,25}, {3,27}, {1,25}, {8,29}, {24,41}, {10,27}, {12,33}, {3,20}, {4,28}, {20,40}, {20,37}, {11,31}, {16,33}, {9,30}, {19,40}, {7,28}, {5,26}, {12,32}, {16,37}, {7,27}, {2,22}, {3,6}, {17,18}, {9,29}, {13,33}, {20,41}, {11,32}, {10,30}, {8,28}, {6,26}, {17,37}, {2,23}, {6,9}, {16,36}, {3,23}, {14,35}, {15,36}, {10,31}, {24,27}, {3,24}, {15,35}, {13,34}, {27,30}, {18,39}, {6,27}, {7,10}, {21,41}, {19,39}, {31,34}, {18,38}, {4,24}, {35,38}, {17,38}, {22,25}, {14,34}, {13,16}, {32,35}, {1,4}, {30,33}, {28,31}, {14,17}, {1,39}, {9,12}, {4,7}, {18,36}, {18,19}, {10,13}, {34,37}, {38,41}, {25,28}, {16,19}, {33,36}, {17,20}, {12,15}, {13,36}, {11,14}, {15,18}, {2,5}, {8,11}, {19,22}, {21,39}, {18,21}, {5,8}, {37,40}, {16,39}, {26,29}, {36,39}, {1,19}, {3,41}, {29,32}, {22,40}, {23,26}, {21,24}, {5,23}, {20,23}, {9,27}, {2,40}, {14,37}, {5,28}, {6,24}, {16,34}, {4,22}, {2,20}, {6,29}, {13,31}, {1,24}, {19,37}, {11,26}, {19,20}, {17,40}, {23,41}, {4,27}, {14,32}, {11,34}, {20,38}, {8,31}, {11,37}, {2,25}, {8,26}, {12,30}, {7,25}, {9,32}, {3,29}, {3,26}, {7,30}, {17,35}, {14,29}, {10,33}, {11,29}, {6,32}, {18,41}, {10,28}, {9,35}, {15,33}, {3,21}, {15,30}, {15,38}, {13,39}, {12,35}, {2,17}, {4,30}, {21,36}, {14,40}, {9,24}, {12,38}, {10,36}, {22,37}, {6,21}, {17,32}, {12,27}, {25,33}, {20,21}, {20,35}, {15,41}, {24,39}, {2,28}, {25,40}, {23,38}, {7,22}, {17,25}, {7,33}, {16,31}, {1,27}, {13,28}, {10,18}, {18,33}, {1,16}, {5,20}, {2,10}, {19,34}, {10,25}, {28,36}, {26,41}, {4,19}, {5,13}, {8,34}, {3,18}, {8,16}, {8,23}, {29,37}, {5,31}, {12,20}, {16,24}, {3,11}, {2,35}, {13,21}, {23,31}, {11,19}, {9,17}, {3,36}, {20,28}, {31,39}, {26,34}, {27,34}, {21,22}, {5,38}, {8,41}, {21,29}, {4,12}, {27,35}, {15,23}, {1,9}, {18,26}, {20,27}, {1,34}, {14,22}, {6,39}, {4,37}, {19,26}, {6,14}, {30,38}, {12,19}, {32,40}, {19,27}, {4,11}, {33,41}, {24,32}, {30,37}, {7,40}, {7,14}, {7,15}, {10,17}, {22,30}, {31,38}, {14,21}, {18,25}, {5,12}, {3,37}, {15,22}, {25,32}, {13,20}, {11,18}, {4,38}, {22,29}, {33,40}, {28,35}, {39,40}, {22,23}, {23,30}, {7,41}, {3,10}, {24,31}, {5,39}, {8,15}, {6,13}, {26,33}, {21,28}, {38,39}, {6,40}, {2,9}, {29,36}, {17,24}, {32,33}, {2,36}, {16,23}, {31,32}, {32,39}, {24,25}, {34,41}, {1,35}, {1,8}, {9,16}, {26,27}, {30,31}, {27,28}, {37,38}, {25,26}, {23,24}, {34,35}, {40,41}, {1,41}, {29,30}, {36,37}, {33,34}, {35,36}, {28,29} } ................................................................... Symmetric connected graphs of order 42 Symmetric graph 1 of order 42 Valency 2 Diameter 21 Girth 42 Automorphism group of order 84 Number of arcs = 84 Number of 2-arcs = 84 2-arc-transitive true Edge-set { {1,10}, {21,25}, {2,38}, {17,22}, {35,37}, {11,18}, {27,36}, {3,12}, {23,28}, {4,40}, {13,24}, {31,39}, {8,14}, {29,32}, {6,7}, {20,30}, {5,42}, {15,19}, {34,41}, {10,16}, {25,33}, {2,9}, {22,26}, {1,37}, {18,21}, {36,38}, {12,17}, {28,35}, {4,11}, {24,27}, {3,39}, {14,23}, {32,40}, {7,13}, {30,31}, {5,8}, {19,29}, {6,41}, {16,20}, {33,42}, {9,15}, {26,34} } Symmetric graph 2 of order 42 Valency 3 Diameter 6 Girth 6 Automorphism group of order 126 Number of arcs = 126 Number of 2-arcs = 252 2-arc-transitive false Edge-set { {1,4}, {1,35}, {16,33}, {7,35}, {13,16}, {37,42}, {9,42}, {7,12}, {6,13}, {28,37}, {9,34}, {18,25}, {1,29}, {11,25}, {12,19}, {6,21}, {2,28}, {31,34}, {18,31}, {27,29}, {8,11}, {4,15}, {23,39}, {32,35}, {16,26}, {21,23}, {11,20}, {4,19}, {2,5}, {22,31}, {17,27}, {8,40}, {15,40}, {39,40}, {24,32}, {12,26}, {10,21}, {5,20}, {33,36}, {14,17}, {7,41}, {13,41}, {22,37}, {9,10}, {5,14}, {20,24}, {23,33}, {3,34}, {17,32}, {24,38}, {10,27}, {2,36}, {38,41}, {19,22}, {3,6}, {14,42}, {30,38}, {26,28}, {15,18}, {29,39}, {3,30}, {8,36}, {25,30} } Symmetric graph 3 of order 42 Valency 4 Diameter 7 Girth 4 Automorphism group of order 168 Number of arcs = 168 Number of 2-arcs = 504 2-arc-transitive false Edge-set { {1,9}, {13,23}, {21,27}, {33,40}, {5,41}, {6,38}, {25,34}, {11,14}, {15,19}, {22,30}, {18,20}, {3,12}, {10,16}, {30,34}, {36,42}, {1,37}, {4,7}, {31,41}, {23,29}, {28,35}, {33,38}, {1,12}, {7,16}, {17,21}, {24,25}, {27,32}, {9,15}, {2,40}, {5,8}, {11,18}, {15,23}, {21,29}, {25,35}, {32,38}, {3,39}, {6,10}, {12,13}, {27,36}, {14,22}, {19,26}, {30,31}, {36,40}, {5,37}, {2,38}, {3,8}, {10,18}, {20,28}, {29,33}, {35,41}, {6,7}, {34,37}, {4,42}, {7,14}, {17,19}, {24,30}, {18,22}, {23,26}, {28,31}, {2,11}, {8,15}, {20,25}, {12,17}, {16,24}, {32,42}, {1,39}, {31,37}, {4,40}, {5,9}, {26,36}, {3,41}, {29,32}, {35,39}, {13,21}, {9,17}, {14,24}, {19,27}, {2,10}, {8,13}, {34,39}, {6,42}, {22,28}, {26,33}, {16,20}, {4,11} } Symmetric graph 4 of order 42 Valency 4 Diameter 5 Girth 3 Automorphism group of order 336 Number of arcs = 168 Number of 2-arcs = 504 2-arc-transitive false Edge-set { {1,16}, {10,41}, {28,39}, {30,36}, {11,21}, {23,32}, {20,33}, {3,22}, {4,35}, {13,25}, {7,13}, {2,17}, {6,18}, {5,15}, {11,14}, {14,30}, {4,12}, {3,29}, {19,39}, {31,41}, {9,37}, {27,38}, {8,38}, {26,37}, {7,42}, {25,40}, {22,40}, {35,42}, {12,26}, {8,29}, {16,32}, {15,20}, {1,36}, {5,21}, {29,33}, {12,23}, {24,34}, {27,34}, {9,24}, {28,35}, {10,22}, {19,31}, {14,31}, {14,19}, {20,26}, {8,32}, {21,27}, {9,36}, {2,41}, {6,39}, {15,42}, {16,40}, {3,10}, {4,28}, {17,26}, {8,18}, {6,24}, {2,34}, {18,29}, {12,17}, {4,23}, {3,33}, {1,40}, {5,42}, {2,27}, {6,9}, {13,24}, {13,34}, {11,30}, {20,37}, {32,38}, {21,38}, {36,37}, {5,11}, {1,30}, {10,31}, {19,28}, {7,35}, {22,25}, {18,39}, {17,41}, {15,33}, {16,23}, {7,25} } Symmetric graph 5 of order 42 Valency 4 Diameter 5 Girth 4 Automorphism group of order 336 Number of arcs = 168 Number of 2-arcs = 504 2-arc-transitive false Edge-set { {1,24}, {14,42}, {16,28}, {7,30}, {7,13}, {26,35}, {2,30}, {19,39}, {4,34}, {19,29}, {14,34}, {12,37}, {10,26}, {13,39}, {4,15}, {17,24}, {5,21}, {6,28}, {24,40}, {3,21}, {6,30}, {1,31}, {12,32}, {4,37}, {10,18}, {17,29}, {5,14}, {28,36}, {16,42}, {9,22}, {23,38}, {2,37}, {18,42}, {22,27}, {20,23}, {10,39}, {1,33}, {32,41}, {28,31}, {12,19}, {18,35}, {16,40}, {3,36}, {9,30}, {13,38}, {11,26}, {2,25}, {7,35}, {11,27}, {13,31}, {12,15}, {7,15}, {21,25}, {23,41}, {4,17}, {5,18}, {8,33}, {8,41}, {26,34}, {2,42}, {21,32}, {20,25}, {3,39}, {29,32}, {11,14}, {10,31}, {9,15}, {29,34}, {1,36}, {19,36}, {22,38}, {9,23}, {8,27}, {35,38}, {5,20}, {33,40}, {8,20}, {6,37}, {22,33}, {17,27}, {3,41}, {6,40}, {16,25}, {11,24} } Symmetric graph 6 of order 42 Valency 4 Diameter 4 Girth 6 Automorphism group of order 672 Number of arcs = 168 Number of 2-arcs = 504 2-arc-transitive false Edge-set { {1,10}, {18,36}, {5,24}, {9,19}, {11,39}, {13,25}, {4,18}, {27,35}, {13,23}, {32,38}, {22,30}, {3,8}, {31,37}, {9,16}, {1,39}, {2,20}, {12,36}, {8,26}, {17,37}, {23,41}, {7,25}, {5,30}, {15,34}, {24,42}, {11,35}, {18,38}, {17,28}, {6,14}, {19,31}, {11,21}, {4,34}, {20,32}, {10,42}, {26,40}, {3,33}, {5,13}, {12,22}, {25,39}, {18,27}, {9,41}, {35,40}, {7,14}, {3,38}, {24,27}, {8,13}, {29,32}, {16,22}, {23,28}, {36,39}, {4,37}, {15,21}, {2,9}, {30,31}, {20,37}, {12,29}, {7,33}, {19,38}, {15,41}, {2,25}, {8,34}, {6,23}, {11,30}, {1,26}, {17,35}, {16,42}, {28,42}, {14,26}, {6,31}, {21,33}, {27,41}, {12,40}, {3,17}, {22,34}, {10,20}, {5,32}, {4,7}, {14,24}, {21,29}, {2,40}, {28,36}, {10,15}, {16,33}, {1,19}, {6,29} } Symmetric graph 7 of order 42 Valency 4 Diameter 10 Girth 4 Automorphism group of order 88080384 Number of arcs = 168 Number of 2-arcs = 504 2-arc-transitive false Edge-set { {1,9}, {22,26}, {29,31}, {2,38}, {6,8}, {5,7}, {12,18}, {18,21}, {19,30}, {20,30}, {27,35}, {19,29}, {28,36}, {27,36}, {33,42}, {36,37}, {5,42}, {6,42}, {3,11}, {6,41}, {4,11}, {4,12}, {10,16}, {3,12}, {9,15}, {10,15}, {14,23}, {11,17}, {15,20}, {16,19}, {23,28}, {16,20}, {23,27}, {24,28}, {25,34}, {24,27}, {26,34}, {26,33}, {32,39}, {25,33}, {31,40}, {32,40}, {1,37}, {28,35}, {34,41}, {33,41}, {4,40}, {34,42}, {3,39}, {3,40}, {4,39}, {1,10}, {2,9}, {7,13}, {2,10}, {8,13}, {8,14}, {17,21}, {7,14}, {18,22}, {17,22}, {20,29}, {9,16}, {13,24}, {14,24}, {13,23}, {21,25}, {22,25}, {21,26}, {29,32}, {30,31}, {36,38}, {30,32}, {35,38}, {35,37}, {5,41}, {31,39}, {2,37}, {1,38}, {6,7}, {5,8}, {12,17}, {11,18}, {15,19} } Symmetric graph 8 of order 42 Valency 5 Diameter 3 Girth 6 Automorphism group of order 241920 Number of arcs = 210 Number of 2-arcs = 840 2-arc-transitive true Edge-set { {1,24}, {21,42}, {9,27}, {17,26}, {15,32}, {13,25}, {2,30}, {2,31}, {13,31}, {5,30}, {3,37}, {14,24}, {10,23}, {20,34}, {3,23}, {1,34}, {3,32}, {10,40}, {20,25}, {14,41}, {4,23}, {21,28}, {9,39}, {12,35}, {10,38}, {11,29}, {16,22}, {12,41}, {11,42}, {16,27}, {5,41}, {4,35}, {17,38}, {15,29}, {14,22}, {1,28}, {8,39}, {12,27}, {10,29}, {6,26}, {21,32}, {8,25}, {9,24}, {19,36}, {18,35}, {18,38}, {7,33}, {19,37}, {6,40}, {8,36}, {17,34}, {15,33}, {13,37}, {2,40}, {1,40}, {19,29}, {18,31}, {20,30}, {7,37}, {19,28}, {6,39}, {6,42}, {21,27}, {8,33}, {13,24}, {2,36}, {20,35}, {7,38}, {13,26}, {5,26}, {21,25}, {9,30}, {18,39}, {18,28}, {4,42}, {4,36}, {16,33}, {11,41}, {11,31}, {16,31}, {7,30}, {12,37}, {14,32}, {4,24}, {17,27}, {20,22}, {7,42}, {3,39}, {14,38}, {6,22}, {17,36}, {15,26}, {2,32}, {16,23}, {11,34}, {9,29}, {19,22}, {10,25}, {5,28}, {12,40}, {3,34}, {1,33}, {15,35}, {8,41}, {5,23} } Symmetric graph 9 of order 42 Valency 6 Diameter 4 Girth 4 Automorphism group of order 252 Number of arcs = 252 Number of 2-arcs = 1260 2-arc-transitive false Edge-set { {1,9}, {6,22}, {17,30}, {11,20}, {10,15}, {30,33}, {22,39}, {2,10}, {8,25}, {5,28}, {29,37}, {18,33}, {22,34}, {11,41}, {5,21}, {18,29}, {3,36}, {24,27}, {19,31}, {16,20}, {34,40}, {11,17}, {10,33}, {2,37}, {4,25}, {12,19}, {9,16}, {29,34}, {21,40}, {14,24}, {13,35}, {7,32}, {10,27}, {8,38}, {17,42}, {1,33}, {2,30}, {25,39}, {5,18}, {23,36}, {7,26}, {6,27}, {30,38}, {17,34}, {21,33}, {12,42}, {13,25}, {36,41}, {4,15}, {28,31}, {5,32}, {19,29}, {3,39}, {18,22}, {2,24}, {16,40}, {8,14}, {11,35}, {4,35}, {23,28}, {20,32}, {15,19}, {33,39}, {12,18}, {9,34}, {1,38}, {3,26}, {25,36}, {24,41}, {14,37}, {16,31}, {7,21}, {2,13}, {11,29}, {10,40}, {27,42}, {13,23}, {14,36}, {8,31}, {9,28}, {7,37}, {18,41}, {2,34}, {1,29}, {26,40}, {6,17}, {24,35}, {4,12}, {5,42}, {16,27}, {32,38}, {21,25}, {3,19}, {14,26}, {35,42}, {3,16}, {27,32}, {6,31}, {20,30}, {4,40}, {17,21}, {1,23}, {15,39}, {7,13}, {12,36}, {19,38}, {9,24}, {26,35}, {23,42}, {13,38}, {15,32}, {8,22}, {1,14}, {12,30}, {9,39}, {28,41}, {6,7}, {3,11}, {6,41}, {15,28}, {31,37}, {22,26}, {4,20}, {20,37}, {10,23}, {5,8} } Symmetric graph 10 of order 42 Valency 6 Diameter 4 Girth 4 Automorphism group of order 252 Number of arcs = 252 Number of 2-arcs = 1260 2-arc-transitive false Edge-set { {1,4}, {9,35}, {8,18}, {12,20}, {3,42}, {16,21}, {15,41}, {5,32}, {7,23}, {17,25}, {2,17}, {6,14}, {24,33}, {24,26}, {26,36}, {7,11}, {19,30}, {39,40}, {15,18}, {13,30}, {13,16}, {32,34}, {9,22}, {25,28}, {10,37}, {14,28}, {28,37}, {10,14}, {1,28}, {6,19}, {33,40}, {4,21}, {22,39}, {27,35}, {16,33}, {15,24}, {31,42}, {21,23}, {17,31}, {14,23}, {11,26}, {2,11}, {20,29}, {38,42}, {5,37}, {31,36}, {32,41}, {19,22}, {37,41}, {19,36}, {22,31}, {9,41}, {18,19}, {3,34}, {4,9}, {22,25}, {10,27}, {2,35}, {6,8}, {29,39}, {35,38}, {12,13}, {3,29}, {28,33}, {24,37}, {23,27}, {12,25}, {2,30}, {6,39}, {18,27}, {30,32}, {1,40}, {5,20}, {23,38}, {25,34}, {36,37}, {7,36}, {1,12}, {4,38}, {3,10}, {27,29}, {12,38}, {20,24}, {26,42}, {3,16}, {4,15}, {20,35}, {8,42}, {15,29}, {30,38}, {5,13}, {29,31}, {8,12}, {21,34}, {4,31}, {23,32}, {7,40}, {17,20}, {25,41}, {10,19}, {34,39}, {11,21}, {1,36}, {5,7}, {11,15}, {18,32}, {8,34}, {13,40}, {7,17}, {14,17}, {33,35}, {8,24}, {3,5}, {27,40}, {2,6}, {26,30}, {11,39}, {1,18}, {6,33}, {9,10}, {16,26}, {2,41}, {13,22}, {21,28}, {9,16}, {14,42} } Symmetric graph 11 of order 42 Valency 6 Diameter 3 Girth 4 Automorphism group of order 2016 Number of arcs = 252 Number of 2-arcs = 1260 2-arc-transitive false Edge-set { {1,7}, {23,39}, {14,20}, {5,33}, {12,31}, {13,35}, {29,34}, {21,27}, {6,17}, {26,37}, {4,24}, {14,30}, {1,30}, {11,28}, {5,41}, {10,31}, {35,40}, {18,22}, {18,27}, {3,7}, {9,38}, {19,34}, {16,32}, {12,13}, {29,42}, {12,23}, {14,42}, {2,21}, {8,17}, {26,42}, {4,21}, {6,30}, {1,11}, {17,32}, {28,36}, {10,17}, {28,40}, {20,39}, {15,20}, {4,41}, {10,22}, {15,25}, {3,25}, {14,37}, {24,30}, {7,41}, {33,37}, {24,31}, {1,13}, {7,29}, {18,40}, {19,27}, {7,38}, {19,31}, {16,35}, {12,22}, {18,42}, {23,38}, {14,23}, {18,25}, {3,27}, {9,29}, {2,39}, {6,9}, {11,39}, {5,35}, {12,34}, {26,34}, {2,19}, {8,16}, {32,42}, {21,36}, {8,20}, {15,37}, {3,13}, {4,32}, {20,41}, {10,36}, {33,40}, {4,39}, {10,20}, {26,36}, {4,33}, {15,30}, {1,25}, {32,37}, {24,36}, {1,17}, {7,28}, {13,33}, {29,31}, {28,37}, {15,40}, {11,41}, {22,41}, {5,24}, {5,38}, {21,30}, {19,25}, {2,35}, {3,16}, {9,26}, {8,34}, {6,27}, {6,11}, {5,19}, {12,16}, {35,42}, {21,34}, {2,38}, {6,16}, {8,23}, {3,9}, {2,32}, {18,23}, {14,27}, {9,39}, {11,26}, {8,36}, {22,38}, {17,33}, {24,25}, {28,31}, {10,13}, {15,22}, {29,40} } Symmetric graph 12 of order 42 Valency 6 Diameter 3 Girth 5 Automorphism group of order 5040 Number of arcs = 252 Number of 2-arcs = 1260 2-arc-transitive true Edge-set { {1,10}, {27,37}, {17,40}, {9,24}, {2,35}, {8,18}, {4,9}, {35,41}, {20,42}, {1,26}, {18,25}, {7,41}, {25,41}, {13,42}, {3,25}, {12,36}, {1,22}, {22,27}, {17,36}, {17,19}, {7,33}, {10,42}, {3,37}, {10,19}, {3,33}, {12,15}, {19,28}, {16,33}, {5,38}, {28,39}, {27,32}, {24,32}, {19,35}, {5,18}, {9,28}, {18,34}, {6,42}, {12,37}, {1,40}, {2,16}, {34,37}, {24,40}, {6,28}, {16,27}, {16,38}, {11,39}, {21,34}, {6,14}, {8,27}, {7,30}, {11,21}, {5,32}, {2,24}, {26,35}, {20,26}, {1,34}, {24,25}, {17,30}, {7,14}, {21,41}, {32,42}, {4,17}, {12,29}, {1,15}, {9,38}, {2,39}, {14,26}, {2,30}, {8,35}, {4,20}, {21,29}, {15,32}, {14,24}, {6,8}, {4,31}, {23,30}, {13,29}, {31,39}, {23,38}, {18,20}, {25,36}, {22,36}, {4,27}, {20,33}, {9,34}, {10,31}, {3,23}, {2,12}, {9,13}, {11,17}, {11,26}, {13,22}, {23,31}, {13,35}, {12,20}, {29,40}, {15,41}, {15,23}, {3,11}, {5,29}, {6,21}, {7,22}, {5,19}, {28,33}, {6,36}, {4,41}, {30,42}, {16,21}, {26,38}, {18,39}, {22,39}, {36,38}, {10,25}, {8,23}, {10,16}, {14,31}, {29,31}, {19,37}, {30,34}, {15,28}, {3,13}, {5,7}, {11,32}, {33,40}, {14,37}, {8,40} } Symmetric graph 13 of order 42 Valency 6 Diameter 7 Girth 4 Automorphism group of order 2194196594688 Number of arcs = 252 Number of 2-arcs = 1260 2-arc-transitive false Edge-set { {1,4}, {5,9}, {1,5}, {7,10}, {6,9}, {5,7}, {1,6}, {12,15}, {7,12}, {8,10}, {4,9}, {6,7}, {5,8}, {13,16}, {11,15}, {12,13}, {7,11}, {8,12}, {9,10}, {4,7}, {6,8}, {18,20}, {13,18}, {14,16}, {10,15}, {11,13}, {12,14}, {8,11}, {9,12}, {4,8}, {21,23}, {17,20}, {18,21}, {13,17}, {14,18}, {15,16}, {10,13}, {11,14}, {9,11}, {22,25}, {21,22}, {19,23}, {16,20}, {17,21}, {18,19}, {14,17}, {15,18}, {10,14}, {26,30}, {24,25}, {22,26}, {21,24}, {19,22}, {20,23}, {16,21}, {17,19}, {15,17}, {29,32}, {26,29}, {27,30}, {23,25}, {24,26}, {22,27}, {19,24}, {20,22}, {16,19}, {33,36}, {28,32}, {29,33}, {26,28}, {27,29}, {25,30}, {23,26}, {24,27}, {20,24}, {34,39}, {33,34}, {31,36}, {30,32}, {28,33}, {29,31}, {27,28}, {25,29}, {23,27}, {37,42}, {35,39}, {34,37}, {33,35}, {31,34}, {32,36}, {30,33}, {28,31}, {25,28}, {1,40}, {37,40}, {38,42}, {36,39}, {35,37}, {34,38}, {31,35}, {32,34}, {30,31}, {3,5}, {1,41}, {3,40}, {37,41}, {38,40}, {39,42}, {36,37}, {35,38}, {32,35}, {3,6}, {2,5}, {1,42}, {3,41}, {2,40}, {38,41}, {39,40}, {36,38}, {3,4}, {2,6}, {3,42}, {2,41}, {39,41}, {2,4}, {2,42} } Symmetric graph 14 of order 42 Valency 8 Diameter 3 Girth 3 Automorphism group of order 336 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,9}, {28,32}, {24,25}, {9,39}, {17,31}, {1,11}, {35,40}, {24,28}, {10,25}, {14,40}, {4,18}, {29,32}, {23,37}, {9,14}, {31,40}, {11,27}, {26,35}, {18,23}, {13,36}, {3,20}, {7,39}, {17,33}, {2,21}, {18,28}, {1,25}, {23,40}, {9,18}, {10,29}, {12,37}, {14,36}, {2,13}, {3,39}, {17,38}, {6,35}, {19,41}, {14,42}, {4,16}, {3,31}, {23,38}, {9,13}, {11,32}, {24,35}, {2,23}, {13,28}, {3,25}, {7,27}, {26,33}, {21,30}, {18,38}, {1,13}, {10,19}, {14,22}, {4,8}, {34,37}, {5,20}, {12,42}, {18,19}, {15,36}, {6,20}, {2,22}, {8,39}, {17,28}, {2,25}, {29,39}, {1,37}, {2,31}, {23,39}, {9,17}, {11,35}, {19,35}, {16,36}, {3,8}, {34,38}, {13,22}, {17,32}, {2,24}, {5,27}, {26,42}, {26,36}, {20,30}, {21,41}, {7,15}, {6,33}, {19,30}, {5,13}, {3,42}, {16,38}, {6,34}, {22,41}, {4,31}, {24,26}, {10,30}, {11,31}, {23,35}, {7,24}, {10,33}, {21,32}, {10,39}, {14,28}, {4,25}, {29,37}, {5,37}, {15,38}, {6,13}, {8,15}, {4,17}, {2,37}, {14,39}, {1,31}, {12,19}, {11,36}, {12,38}, {6,8}, {34,41}, {16,25}, {5,29}, {34,42}, {16,22}, {5,8}, {11,19}, {15,22}, {4,20}, {36,40}, {18,20}, {1,12}, {8,27}, {26,34}, {29,40}, {27,42}, {16,26}, {24,27}, {10,26}, {20,35}, {7,21}, {7,33}, {21,33}, {17,34}, {5,30}, {21,31}, {7,23}, {18,24}, {1,10}, {32,40}, {29,38}, {22,30}, {20,41}, {12,15}, {11,15}, {4,15}, {6,37}, {28,42}, {6,36}, {3,41}, {30,32}, {12,41}, {9,33}, {12,27}, {14,41}, {25,42}, {16,29}, {8,33}, {21,34}, {3,40}, {27,32}, {7,22}, {16,30}, {5,28}, {9,19} } Symmetric graph 15 of order 42 Valency 8 Diameter 3 Girth 3 Automorphism group of order 336 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,15}, {12,18}, {6,42}, {8,32}, {28,40}, {14,30}, {2,18}, {3,36}, {7,25}, {26,40}, {15,24}, {9,42}, {22,37}, {8,17}, {5,40}, {3,12}, {35,38}, {19,26}, {26,37}, {15,20}, {12,24}, {36,42}, {30,33}, {18,29}, {20,28}, {14,33}, {7,36}, {25,39}, {13,26}, {15,32}, {3,28}, {2,27}, {11,13}, {20,31}, {28,37}, {14,20}, {12,21}, {32,42}, {24,32}, {28,36}, {1,30}, {10,22}, {8,41}, {21,40}, {6,9}, {10,37}, {1,35}, {12,26}, {25,38}, {16,19}, {20,38}, {7,42}, {15,40}, {3,24}, {17,39}, {5,23}, {10,31}, {27,38}, {4,21}, {14,24}, {9,21}, {32,37}, {19,32}, {28,34}, {3,30}, {7,18}, {1,40}, {18,42}, {6,22}, {20,34}, {29,36}, {17,25}, {15,34}, {2,29}, {6,11}, {13,19}, {11,22}, {31,41}, {21,27}, {13,32}, {30,35}, {18,26}, {15,42}, {16,39}, {13,23}, {4,34}, {8,30}, {27,39}, {9,24}, {36,37}, {19,33}, {29,34}, {7,14}, {3,22}, {7,31}, {8,35}, {6,15}, {18,40}, {2,33}, {5,21}, {9,32}, {1,41}, {7,38}, {19,39}, {5,12}, {17,41}, {14,31}, {31,38}, {27,33}, {4,29}, {23,34}, {3,10}, {2,42}, {8,37}, {20,40}, {12,30}, {11,25}, {16,41}, {10,23}, {5,16}, {4,9}, {22,25}, {16,23}, {24,33}, {1,28}, {12,14}, {5,41}, {9,35}, {3,33}, {4,35}, {8,26}, {2,36}, {6,17}, {5,10}, {1,34}, {7,29}, {27,35}, {16,31}, {4,27}, {8,13}, {6,39}, {17,30}, {5,18}, {14,25}, {21,26}, {22,28}, {19,27}, {11,29}, {16,33}, {11,23}, {35,41}, {6,24}, {10,36}, {13,29}, {1,17}, {2,16}, {4,11}, {20,25}, {2,39}, {13,34}, {4,23}, {22,39}, {9,38}, {19,37}, {23,31}, {10,41}, {11,17}, {21,38} } Symmetric graph 16 of order 42 Valency 8 Diameter 3 Girth 4 Automorphism group of order 672 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,9}, {10,29}, {12,28}, {21,30}, {11,36}, {23,26}, {8,33}, {13,22}, {13,35}, {3,25}, {4,7}, {17,20}, {18,32}, {5,27}, {14,39}, {14,41}, {4,39}, {3,41}, {11,19}, {30,31}, {15,37}, {16,38}, {2,38}, {6,37}, {7,24}, {25,34}, {32,40}, {20,42}, {36,40}, {21,42}, {12,32}, {20,29}, {16,25}, {7,15}, {1,22}, {5,35}, {33,42}, {23,40}, {34,41}, {24,39}, {9,34}, {24,27}, {18,28}, {10,17}, {6,19}, {2,31}, {15,35}, {16,22}, {3,31}, {4,19}, {2,26}, {6,8}, {15,21}, {16,36}, {19,41}, {31,39}, {28,42}, {10,40}, {10,14}, {14,28}, {17,31}, {18,19}, {6,36}, {2,21}, {6,29}, {2,12}, {18,24}, {17,34}, {23,38}, {33,37}, {30,37}, {11,38}, {8,16}, {15,26}, {4,42}, {3,40}, {1,11}, {5,30}, {12,16}, {15,29}, {9,20}, {27,32}, {8,27}, {9,26}, {13,42}, {13,40}, {1,32}, {5,20}, {23,35}, {22,33}, {30,40}, {11,42}, {1,37}, {5,38}, {3,8}, {4,26}, {9,13}, {13,27}, {8,21}, {26,36}, {18,38}, {17,37}, {5,33}, {1,23}, {27,41}, {9,39}, {12,35}, {22,29}, {11,31}, {19,30}, {10,25}, {7,28}, {7,22}, {25,35}, {26,41}, {8,39}, {2,24}, {6,34}, {35,39}, {22,41}, {2,10}, {6,28}, {4,17}, {3,18}, {5,14}, {1,14}, {22,31}, {19,35}, {10,33}, {23,28}, {7,34}, {24,25}, {11,27}, {9,30}, {12,20}, {29,32}, {29,39}, {12,41}, {3,20}, {4,32}, {34,38}, {24,37}, {5,7}, {1,25}, {24,36}, {21,34}, {14,21}, {14,36}, {20,36}, {21,32}, {9,18}, {17,27}, {8,23}, {26,33}, {12,37}, {29,38}, {7,40}, {25,42}, {4,16}, {3,15}, {17,23}, {18,33}, {11,15}, {16,30}, {10,19}, {28,31}, {6,13}, {2,13} } Symmetric graph 17 of order 42 Valency 8 Diameter 4 Girth 3 Automorphism group of order 672 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,10}, {10,30}, {11,28}, {22,30}, {11,35}, {23,25}, {7,33}, {14,22}, {14,35}, {4,25}, {3,7}, {17,19}, {18,31}, {5,28}, {14,40}, {14,42}, {4,40}, {3,42}, {12,19}, {29,31}, {16,37}, {15,38}, {1,38}, {5,37}, {7,23}, {25,33}, {31,40}, {19,42}, {35,40}, {22,42}, {12,31}, {19,29}, {16,26}, {8,15}, {1,21}, {5,36}, {33,41}, {23,39}, {34,42}, {24,40}, {10,34}, {24,28}, {17,28}, {10,18}, {5,19}, {1,31}, {16,35}, {15,22}, {4,31}, {3,19}, {1,26}, {5,8}, {16,21}, {15,36}, {20,41}, {32,39}, {27,42}, {9,40}, {10,13}, {13,28}, {17,32}, {18,20}, {6,35}, {2,22}, {6,30}, {2,11}, {18,23}, {17,33}, {23,37}, {33,38}, {30,38}, {11,37}, {7,16}, {15,25}, {4,41}, {3,39}, {1,12}, {5,29}, {11,16}, {15,30}, {10,20}, {28,32}, {7,27}, {9,25}, {13,41}, {13,39}, {2,32}, {6,20}, {24,35}, {22,34}, {30,39}, {11,41}, {2,37}, {6,38}, {4,8}, {3,26}, {9,14}, {14,27}, {8,22}, {26,35}, {17,38}, {18,37}, {5,34}, {1,24}, {28,41}, {10,39}, {12,36}, {21,29}, {11,32}, {20,30}, {10,26}, {8,28}, {7,21}, {25,36}, {25,41}, {7,39}, {2,23}, {6,33}, {36,39}, {21,41}, {2,9}, {6,27}, {4,18}, {3,17}, {6,14}, {2,14}, {22,32}, {20,35}, {9,33}, {23,27}, {8,34}, {24,26}, {12,27}, {9,29}, {11,20}, {30,32}, {29,40}, {12,42}, {4,20}, {3,32}, {34,37}, {24,38}, {6,7}, {2,25}, {23,36}, {21,33}, {13,21}, {13,36}, {19,36}, {21,31}, {9,17}, {18,27}, {8,24}, {26,34}, {12,38}, {29,37}, {8,40}, {26,42}, {4,15}, {3,16}, {17,24}, {18,34}, {12,15}, {16,29}, {9,19}, {27,31}, {5,13}, {1,13} } Symmetric graph 18 of order 42 Valency 8 Diameter 3 Girth 3 Automorphism group of order 672 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,15}, {10,42}, {28,40}, {30,35}, {11,22}, {23,31}, {19,33}, {4,22}, {3,35}, {14,25}, {7,14}, {1,17}, {5,18}, {5,16}, {12,14}, {14,29}, {4,11}, {3,30}, {19,40}, {31,42}, {10,37}, {28,38}, {7,38}, {25,37}, {7,41}, {25,39}, {26,40}, {8,42}, {21,40}, {36,42}, {12,25}, {7,29}, {16,31}, {15,19}, {1,35}, {5,22}, {30,33}, {11,23}, {23,34}, {24,33}, {28,34}, {10,24}, {28,36}, {10,21}, {19,32}, {20,31}, {27,35}, {9,22}, {13,31}, {13,19}, {19,26}, {8,31}, {21,28}, {10,36}, {1,41}, {5,39}, {16,42}, {15,40}, {4,10}, {3,28}, {17,25}, {7,18}, {6,17}, {2,18}, {6,23}, {2,33}, {18,30}, {11,17}, {3,23}, {4,33}, {13,30}, {11,13}, {2,16}, {6,15}, {4,24}, {3,34}, {1,39}, {5,41}, {16,39}, {15,41}, {16,20}, {15,32}, {1,27}, {5,9}, {13,23}, {13,33}, {7,32}, {20,25}, {35,41}, {22,39}, {12,30}, {11,29}, {19,37}, {31,38}, {8,37}, {26,38}, {9,38}, {27,37}, {8,17}, {18,26}, {22,38}, {35,37}, {5,12}, {1,29}, {9,41}, {27,39}, {12,18}, {17,29}, {6,11}, {2,30}, {10,32}, {20,28}, {7,36}, {21,25}, {32,41}, {20,39}, {2,42}, {6,40}, {17,39}, {18,41}, {2,28}, {6,10}, {4,36}, {3,21}, {14,32}, {14,20}, {22,26}, {8,35}, {16,33}, {15,23}, {1,34}, {5,24}, {27,33}, {9,23}, {20,34}, {24,32}, {29,34}, {12,24}, {20,38}, {32,37}, {14,34}, {14,24}, {7,26}, {8,25}, {29,36}, {12,21}, {21,37}, {36,38}, {2,36}, {6,21}, {9,35}, {22,27}, {8,30}, {11,26}, {3,12}, {4,29}, {2,40}, {6,42}, {4,27}, {3,9}, {17,42}, {18,40}, {15,34}, {16,24}, {19,27}, {9,31}, {13,26}, {8,13} } Symmetric graph 19 of order 42 Valency 8 Diameter 3 Girth 4 Automorphism group of order 672 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,9}, {25,33}, {5,29}, {10,17}, {9,20}, {7,28}, {1,22}, {34,38}, {30,39}, {5,33}, {29,31}, {12,32}, {24,26}, {3,25}, {18,24}, {10,13}, {8,22}, {15,21}, {17,28}, {7,16}, {15,35}, {19,35}, {10,30}, {4,20}, {1,37}, {35,40}, {34,42}, {30,38}, {3,31}, {4,39}, {12,38}, {24,39}, {32,40}, {26,41}, {13,39}, {12,42}, {6,13}, {8,34}, {21,30}, {23,25}, {5,14}, {13,21}, {12,16}, {18,19}, {8,24}, {16,30}, {4,8}, {22,29}, {3,15}, {24,35}, {13,28}, {22,42}, {15,38}, {27,42}, {2,38}, {18,31}, {10,25}, {21,34}, {2,10}, {20,36}, {28,41}, {4,42}, {6,37}, {1,31}, {25,35}, {8,40}, {21,41}, {3,7}, {22,33}, {1,13}, {12,35}, {24,38}, {3,19}, {17,33}, {13,42}, {11,19}, {17,23}, {16,37}, {10,34}, {20,30}, {4,18}, {26,34}, {6,30}, {11,31}, {12,20}, {19,29}, {3,17}, {23,27}, {2,14}, {16,25}, {5,8}, {21,31}, {18,34}, {30,32}, {4,26}, {9,33}, {25,42}, {5,38}, {13,35}, {12,28}, {1,24}, {4,32}, {17,38}, {9,39}, {19,42}, {6,36}, {27,32}, {36,39}, {23,40}, {14,41}, {29,37}, {3,40}, {9,18}, {10,19}, {8,27}, {2,21}, {16,36}, {5,35}, {28,31}, {6,7}, {22,32}, {2,11}, {23,36}, {10,40}, {20,41}, {1,25}, {4,16}, {18,37}, {8,15}, {7,21}, {9,29}, {17,20}, {24,28}, {15,29}, {6,19}, {17,32}, {14,27}, {11,15}, {7,23}, {14,22}, {33,37}, {29,40}, {6,34}, {14,40}, {11,41}, {1,12}, {2,26}, {7,33}, {26,36}, {6,27}, {11,36}, {5,20}, {3,41}, {23,37}, {31,39}, {7,39}, {2,32}, {9,14}, {16,22}, {18,27}, {5,28}, {9,26}, {11,27}, {2,23}, {14,36}, {15,26}, {33,41}, {11,37} } Symmetric graph 20 of order 42 Valency 8 Diameter 3 Girth 4 Automorphism group of order 672 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,15}, {25,39}, {5,42}, {10,22}, {15,20}, {19,28}, {1,17}, {3,34}, {30,33}, {5,39}, {31,42}, {6,12}, {24,32}, {25,38}, {18,30}, {4,10}, {8,17}, {9,21}, {22,28}, {16,19}, {27,35}, {2,28}, {7,35}, {10,24}, {13,20}, {8,37}, {21,40}, {29,34}, {3,30}, {31,38}, {4,33}, {3,12}, {24,33}, {6,40}, {32,41}, {11,13}, {12,23}, {12,26}, {6,24}, {13,32}, {1,34}, {30,35}, {23,31}, {14,25}, {4,21}, {16,34}, {7,18}, {8,30}, {16,24}, {8,13}, {17,29}, {3,9}, {4,28}, {9,35}, {21,27}, {2,16}, {36,42}, {27,38}, {2,35}, {28,36}, {1,27}, {15,42}, {7,38}, {18,25}, {5,10}, {12,21}, {8,36}, {10,41}, {20,37}, {4,29}, {18,40}, {32,37}, {26,40}, {8,31}, {21,25}, {1,40}, {35,41}, {22,39}, {12,29}, {3,24}, {13,33}, {4,11}, {23,34}, {6,41}, {14,19}, {11,17}, {11,24}, {13,23}, {13,26}, {12,14}, {11,25}, {5,23}, {19,39}, {17,42}, {10,37}, {20,40}, {28,34}, {1,30}, {4,35}, {14,31}, {20,34}, {7,29}, {3,22}, {21,37}, {16,40}, {15,23}, {7,14}, {16,31}, {8,25}, {5,16}, {12,18}, {15,33}, {9,38}, {29,36}, {3,27}, {2,18}, {10,36}, {20,27}, {36,38}, {27,39}, {1,36}, {2,42}, {9,42}, {19,38}, {28,37}, {6,22}, {15,32}, {17,39}, {14,30}, {5,21}, {13,29}, {16,41}, {5,18}, {10,31}, {7,32}, {22,26}, {4,23}, {14,34}, {2,39}, {26,37}, {8,41}, {20,25}, {28,40}, {1,41}, {35,37}, {11,22}, {11,30}, {5,11}, {14,24}, {19,26}, {6,17}, {19,33}, {2,33}, {15,39}, {7,42}, {22,38}, {18,41}, {7,26}, {2,29}, {3,36}, {6,15}, {9,23}, {20,31}, {27,33}, {6,9}, {19,32}, {9,32}, {17,26} } Symmetric graph 21 of order 42 Valency 8 Diameter 3 Girth 3 Automorphism group of order 672 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,15}, {7,17}, {28,36}, {14,19}, {18,30}, {36,37}, {10,41}, {2,16}, {22,26}, {13,31}, {7,29}, {27,37}, {6,41}, {8,18}, {27,35}, {4,34}, {11,24}, {15,39}, {25,39}, {19,32}, {6,9}, {11,26}, {2,33}, {13,20}, {17,29}, {35,38}, {9,42}, {32,37}, {5,24}, {4,28}, {29,33}, {4,12}, {2,40}, {22,40}, {11,21}, {15,33}, {24,34}, {11,13}, {8,41}, {21,25}, {14,32}, {8,30}, {28,38}, {5,42}, {27,40}, {6,40}, {5,12}, {20,34}, {9,36}, {10,32}, {32,41}, {8,38}, {9,23}, {3,35}, {4,30}, {3,24}, {13,23}, {17,41}, {20,37}, {15,24}, {13,25}, {20,26}, {2,17}, {3,33}, {12,23}, {16,40}, {26,40}, {20,31}, {5,10}, {12,25}, {1,34}, {30,35}, {3,9}, {11,30}, {14,34}, {1,42}, {21,37}, {15,41}, {20,28}, {5,17}, {6,21}, {15,19}, {10,38}, {31,42}, {9,31}, {7,32}, {6,15}, {19,25}, {14,26}, {2,30}, {1,27}, {8,14}, {31,38}, {6,23}, {3,27}, {30,34}, {3,11}, {1,39}, {21,39}, {12,22}, {16,34}, {23,33}, {12,14}, {7,42}, {10,21}, {15,31}, {24,31}, {7,13}, {16,42}, {26,37}, {7,25}, {1,36}, {17,26}, {2,28}, {22,28}, {5,16}, {19,40}, {18,40}, {11,17}, {28,33}, {8,31}, {7,35}, {16,20}, {28,39}, {5,39}, {6,11}, {19,33}, {10,35}, {7,37}, {10,24}, {4,36}, {3,29}, {4,23}, {14,24}, {18,42}, {19,38}, {16,23}, {1,18}, {3,22}, {17,39}, {20,39}, {18,25}, {27,34}, {12,18}, {36,41}, {8,36}, {13,30}, {21,27}, {29,36}, {4,10}, {12,29}, {13,33}, {2,41}, {22,38}, {19,27}, {6,18}, {5,22}, {9,37}, {1,29}, {14,29}, {4,21}, {35,42}, {9,22}, {16,32}, {23,32}, {25,38}, {8,26}, {2,35} } Symmetric graph 22 of order 42 Valency 8 Diameter 3 Girth 4 Automorphism group of order 2016 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,4}, {17,37}, {19,36}, {3,34}, {16,39}, {4,31}, {28,32}, {18,32}, {21,29}, {1,35}, {18,38}, {10,37}, {3,36}, {8,11}, {2,11}, {1,17}, {5,9}, {6,31}, {17,33}, {19,30}, {2,36}, {21,34}, {39,40}, {18,31}, {21,28}, {19,40}, {15,41}, {16,19}, {20,41}, {3,17}, {38,41}, {14,35}, {10,39}, {3,12}, {2,16}, {4,7}, {5,32}, {16,31}, {20,28}, {29,31}, {22,38}, {2,10}, {5,8}, {4,14}, {22,32}, {13,22}, {24,26}, {6,13}, {24,33}, {3,18}, {16,21}, {13,36}, {24,37}, {27,30}, {21,35}, {38,40}, {18,20}, {21,42}, {1,16}, {37,42}, {11,38}, {1,10}, {6,8}, {4,33}, {9,10}, {3,6}, {27,36}, {20,40}, {15,35}, {11,27}, {23,27}, {10,25}, {25,29}, {23,39}, {25,34}, {12,25}, {2,18}, {17,21}, {1,5}, {23,31}, {25,28}, {11,39}, {7,30}, {5,33}, {30,31}, {14,36}, {22,37}, {2,6}, {5,15}, {18,19}, {15,34}, {37,41}, {12,37}, {21,41}, {14,40}, {18,39}, {9,28}, {6,14}, {22,33}, {26,30}, {9,41}, {9,12}, {7,40}, {6,7}, {26,35}, {12,38}, {7,29}, {7,42}, {17,20}, {3,5}, {17,38}, {19,35}, {10,26}, {8,28}, {5,13}, {2,35}, {7,10}, {24,31}, {27,28}, {27,34}, {20,34}, {2,4}, {17,32}, {26,29}, {13,34}, {24,39}, {39,42}, {14,24}, {22,27}, {8,41}, {12,27}, {13,41}, {14,42}, {29,33}, {8,30}, {20,36}, {9,42}, {15,42}, {13,23}, {16,33}, {16,37}, {30,32}, {8,40}, {4,15}, {23,38}, {25,35}, {20,30}, {13,40}, {3,11}, {4,9}, {9,29}, {6,32}, {23,32}, {24,25}, {15,24}, {28,33}, {14,23}, {15,22}, {23,26}, {1,12}, {1,34}, {7,11}, {26,36}, {22,25}, {11,26}, {8,12}, {19,42}, {19,29} } Symmetric graph 23 of order 42 Valency 8 Diameter 3 Girth 4 Automorphism group of order 176160768 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,9}, {21,27}, {4,8}, {6,38}, {28,31}, {23,25}, {18,20}, {11,13}, {5,9}, {4,40}, {25,33}, {31,41}, {35,42}, {29,34}, {19,27}, {4,12}, {13,23}, {9,15}, {4,11}, {9,16}, {17,21}, {8,15}, {1,12}, {24,30}, {6,42}, {28,36}, {23,30}, {34,40}, {33,38}, {27,35}, {23,29}, {6,9}, {27,36}, {4,39}, {32,38}, {25,35}, {1,40}, {21,30}, {5,8}, {2,39}, {15,20}, {11,18}, {5,7}, {2,40}, {29,33}, {12,13}, {15,24}, {6,8}, {20,28}, {30,33}, {20,27}, {6,7}, {19,28}, {14,23}, {10,18}, {13,22}, {20,25}, {13,21}, {2,38}, {29,31}, {19,25}, {14,22}, {7,16}, {35,41}, {35,40}, {19,26}, {2,12}, {7,15}, {1,11}, {30,34}, {5,38}, {35,39}, {5,41}, {2,11}, {6,41}, {28,35}, {20,26}, {5,42}, {33,40}, {33,37}, {3,42}, {34,37}, {4,41}, {34,38}, {31,38}, {18,22}, {7,13}, {4,42}, {25,36}, {32,37}, {26,36}, {8,16}, {17,20}, {8,13}, {22,30}, {26,35}, {21,29}, {24,29}, {18,19}, {8,14}, {16,20}, {16,19}, {12,17}, {22,29}, {11,17}, {3,41}, {15,19}, {12,18}, {15,23}, {14,24}, {16,23}, {9,17}, {13,24}, {9,18}, {31,37}, {32,42}, {26,34}, {4,7}, {10,17}, {3,7}, {1,39}, {32,41}, {25,34}, {1,38}, {2,37}, {29,32}, {3,8}, {30,31}, {31,42}, {36,42}, {1,37}, {36,41}, {36,39}, {30,32}, {16,24}, {36,40}, {33,39}, {27,32}, {34,39}, {27,31}, {14,21}, {10,15}, {3,12}, {24,26}, {23,26}, {2,9}, {28,32}, {2,10}, {10,16}, {17,22}, {24,25}, {18,21}, {7,14}, {1,10}, {17,19}, {11,14}, {6,10}, {22,28}, {12,14}, {21,28}, {3,40}, {5,10}, {3,39}, {26,33}, {22,27}, {6,37}, {3,11}, {5,37} } Symmetric graph 24 of order 42 Valency 8 Diameter 3 Girth 3 Automorphism group of order 704643072 Number of arcs = 336 Number of 2-arcs = 2352 2-arc-transitive false Edge-set { {1,9}, {12,22}, {23,28}, {7,26}, {26,39}, {18,28}, {4,37}, {10,15}, {5,30}, {15,34}, {5,13}, {18,37}, {4,34}, {19,31}, {15,21}, {11,40}, {27,36}, {14,24}, {1,20}, {2,40}, {12,36}, {24,42}, {20,31}, {31,37}, {2,19}, {12,21}, {6,29}, {10,42}, {25,40}, {36,40}, {8,33}, {14,25}, {3,17}, {3,8}, {27,41}, {32,38}, {22,30}, {23,41}, {21,33}, {3,7}, {8,26}, {27,35}, {18,38}, {6,30}, {10,41}, {6,31}, {21,29}, {7,25}, {26,40}, {13,23}, {11,35}, {18,27}, {16,33}, {6,14}, {3,33}, {8,14}, {11,29}, {16,41}, {6,32}, {20,38}, {22,33}, {9,20}, {22,29}, {17,36}, {5,32}, {9,16}, {14,26}, {1,39}, {28,36}, {17,37}, {1,25}, {10,20}, {9,15}, {5,29}, {4,17}, {32,37}, {16,34}, {14,23}, {1,19}, {11,36}, {17,27}, {6,23}, {10,19}, {13,25}, {10,16}, {15,33}, {5,14}, {28,42}, {4,8}, {3,34}, {19,32}, {11,22}, {9,41}, {29,32}, {8,13}, {2,25}, {36,39}, {17,35}, {5,23}, {9,19}, {30,32}, {1,26}, {11,39}, {12,30}, {28,41}, {13,26}, {2,39}, {3,38}, {5,24}, {12,39}, {28,35}, {15,41}, {22,34}, {3,18}, {31,38}, {16,22}, {11,30}, {12,40}, {13,24}, {2,20}, {19,38}, {5,31}, {12,35}, {23,42}, {8,25}, {17,38}, {19,37}, {27,42}, {16,42}, {1,40}, {24,41}, {20,32}, {18,35}, {4,18}, {9,42}, {25,39}, {17,28}, {2,9}, {29,31}, {16,21}, {6,24}, {4,38}, {7,33}, {24,28}, {20,37}, {12,29}, {15,22}, {8,34}, {7,14}, {18,36}, {15,42}, {21,34}, {24,27}, {7,34}, {4,7}, {2,26}, {35,39}, {21,30}, {6,13}, {4,33}, {2,10}, {35,40}, {23,27}, {1,10}, {30,31}, {7,13}, {3,37}, {11,21} } Symmetric graph 25 of order 42 Valency 9 Diameter 3 Girth 4 Automorphism group of order 26330359136256 Number of arcs = 378 Number of 2-arcs = 3024 2-arc-transitive false Edge-set { {1,4}, {16,25}, {8,36}, {24,39}, {25,28}, {7,10}, {24,33}, {5,13}, {28,39}, {3,28}, {9,41}, {23,38}, {4,21}, {13,17}, {18,31}, {7,12}, {1,28}, {3,5}, {26,28}, {3,34}, {19,22}, {6,14}, {14,16}, {8,40}, {22,31}, {12,27}, {19,23}, {18,26}, {9,40}, {23,37}, {3,36}, {7,34}, {28,38}, {3,30}, {12,26}, {32,34}, {6,13}, {15,41}, {17,33}, {9,11}, {11,25}, {21,24}, {6,19}, {15,18}, {37,40}, {29,37}, {14,41}, {26,30}, {8,34}, {21,22}, {2,5}, {4,14}, {10,26}, {33,34}, {9,12}, {23,32}, {3,6}, {2,34}, {38,40}, {30,37}, {12,20}, {16,32}, {17,31}, {32,36}, {10,19}, {17,27}, {8,42}, {22,39}, {39,42}, {13,40}, {2,29}, {33,36}, {11,19}, {30,38}, {2,30}, {24,32}, {15,40}, {18,27}, {7,35}, {16,33}, {8,11}, {38,41}, {12,21}, {17,32}, {22,37}, {5,20}, {17,26}, {9,34}, {32,35}, {6,21}, {2,4}, {37,42}, {20,24}, {10,20}, {13,41}, {27,29}, {1,6}, {5,15}, {1,35}, {31,34}, {10,21}, {13,42}, {39,41}, {2,6}, {27,30}, {2,35}, {4,20}, {13,16}, {26,29}, {23,31}, {17,25}, {7,42}, {14,40}, {20,22}, {16,27}, {4,15}, {22,38}, {8,12}, {22,32}, {11,20}, {16,31}, {14,17}, {8,35}, {38,42}, {31,36}, {12,19}, {1,29}, {9,36}, {18,32}, {31,35}, {1,36}, {5,19}, {9,35}, {11,27}, {15,16}, {24,31}, {12,25}, {29,38}, {1,30}, {14,18}, {27,28}, {20,23}, {11,21}, {6,15}, {15,42}, {24,37}, {25,29}, {8,10}, {7,40}, {6,20}, {19,24}, {18,25}, {22,33}, {7,11}, {3,35}, {18,33}, {37,41}, {16,26}, {10,25}, {13,18}, {7,41}, {29,39}, {4,19}, {39,40}, {28,37}, {3,29}, {25,30}, {2,36}, {23,33}, {11,26}, {14,42}, {9,10}, {4,13}, {24,38}, {21,23}, {15,17}, {9,42}, {23,39}, {1,5}, {8,41}, {1,34}, {5,21}, {2,28}, {3,4}, {30,39}, {10,27}, {33,35}, {5,14}, {7,36} } Symmetric graph 26 of order 42 Valency 10 Diameter 3 Girth 4 Automorphism group of order 10080 Number of arcs = 420 Number of 2-arcs = 3780 2-arc-transitive false Edge-set { {1,7}, {15,24}, {13,23}, {25,35}, {30,36}, {26,31}, {29,34}, {6,40}, {6,38}, {4,39}, {5,39}, {2,38}, {4,41}, {1,41}, {3,37}, {9,18}, {8,14}, {8,18}, {11,14}, {12,17}, {10,17}, {12,16}, {10,18}, {11,15}, {9,17}, {10,15}, {9,13}, {7,13}, {7,16}, {20,30}, {21,28}, {23,29}, {19,25}, {23,30}, {19,28}, {22,29}, {22,25}, {24,26}, {20,26}, {21,27}, {24,27}, {19,30}, {20,28}, {22,30}, {21,26}, {21,29}, {23,27}, {32,39}, {31,39}, {33,37}, {33,42}, {31,41}, {34,37}, {34,40}, {35,38}, {34,39}, {35,42}, {36,41}, {32,37}, {36,40}, {32,38}, {33,40}, {35,39}, {31,42}, {36,39}, {33,38}, {33,41}, {3,12}, {2,10}, {2,12}, {4,10}, {5,7}, {5,11}, {1,12}, {4,9}, {3,7}, {1,9}, {3,8}, {6,8}, {6,11}, {3,10}, {6,12}, {5,9}, {2,7}, {5,8}, {2,11}, {1,8}, {6,10}, {4,12}, {5,10}, {1,11}, {13,21}, {16,24}, {14,19}, {15,20}, {14,21}, {17,19}, {17,20}, {18,23}, {16,22}, {18,22}, {15,21}, {13,24}, {17,21}, {16,23}, {16,19}, {14,22}, {13,19}, {16,20}, {18,21}, {14,24}, {15,23}, {18,19}, {15,22}, {14,20}, {17,24}, {18,20}, {13,22}, {26,33}, {29,33}, {27,35}, {27,36}, {25,32}, {30,31}, {25,33}, {28,34}, {26,35}, {28,32}, {27,32}, {30,33}, {29,36}, {28,33}, {27,31}, {27,34}, {26,34}, {29,35}, {25,36}, {25,31}, {30,34}, {28,35}, {30,32}, {29,32}, {26,36}, {28,31}, {5,38}, {5,41}, {1,37}, {6,42}, {4,42}, {5,40}, {3,40}, {2,39}, {1,38}, {3,42}, {6,41}, {2,42}, {2,40}, {1,39}, {5,37}, {1,42}, {4,40}, {3,41}, {6,37}, {4,38}, {3,39}, {2,37}, {8,16}, {11,18}, {10,16}, {7,15}, {12,14}, {11,17}, {9,16}, {8,15}, {11,13}, {9,14}, {12,15}, {10,13}, {7,18}, {12,13}, {8,17}, {7,14}, {19,27}, {22,28}, {20,27}, {24,25}, {22,26}, {23,25}, {20,29}, {21,25}, {24,30}, {19,26}, {23,28}, {24,29}, {34,42}, {35,40}, {36,37}, {32,42}, {31,40}, {36,38}, {32,41}, {34,38}, {31,37}, {35,41}, {6,9}, {4,7}, {3,11}, {2,9}, {4,8}, {17,23} } Symmetric graph 27 of order 42 Valency 10 Diameter 3 Girth 3 Automorphism group of order 10080 Number of arcs = 420 Number of 2-arcs = 3780 2-arc-transitive false Edge-set { {1,4}, {7,40}, {5,33}, {13,25}, {22,36}, {31,33}, {23,26}, {12,29}, {9,41}, {1,16}, {1,13}, {24,33}, {26,30}, {30,36}, {27,42}, {17,22}, {15,19}, {20,37}, {17,31}, {6,7}, {3,5}, {7,12}, {5,9}, {33,35}, {26,28}, {21,30}, {20,42}, {16,21}, {13,20}, {19,41}, {18,37}, {1,11}, {4,8}, {10,28}, {4,24}, {11,30}, {25,32}, {24,36}, {31,39}, {23,34}, {17,25}, {15,36}, {31,37}, {23,31}, {15,33}, {14,26}, {30,42}, {38,42}, {2,21}, {2,20}, {10,19}, {7,18}, {2,6}, {2,3}, {10,12}, {7,9}, {9,20}, {8,17}, {3,28}, {12,40}, {5,16}, {26,40}, {32,38}, {35,40}, {28,33}, {18,21}, {16,20}, {23,29}, {29,41}, {16,35}, {13,28}, {14,24}, {34,36}, {25,27}, {4,29}, {11,41}, {4,13}, {24,28}, {30,40}, {27,30}, {4,26}, {10,42}, {19,21}, {18,20}, {19,27}, {18,39}, {2,8}, {8,10}, {9,38}, {8,32}, {3,25}, {12,36}, {6,24}, {8,39}, {6,34}, {17,38}, {15,32}, {25,37}, {31,36}, {10,37}, {7,31}, {11,35}, {39,42}, {34,38}, {13,17}, {15,22}, {6,31}, {3,23}, {13,30}, {22,42}, {23,27}, {29,39}, {13,15}, {14,22}, {33,42}, {26,38}, {2,12}, {6,10}, {3,7}, {20,22}, {17,19}, {6,15}, {3,14}, {12,42}, {16,34}, {37,41}, {22,40}, {19,33}, {16,17}, {9,33}, {35,42}, {28,38}, {13,21}, {21,41}, {19,38}, {18,32}, {2,9}, {3,10}, {8,37}, {12,21}, {8,26}, {6,35}, {32,35}, {27,37}, {29,35}, {34,41}, {21,35}, {32,34}, {24,25}, {4,27}, {11,39}, {5,23}, {28,29}, {40,41}, {16,24}, {32,40}, {15,18}, {14,16}, {14,19}, {27,34}, {25,39}, {4,12}, {9,11}, {1,5}, {24,32}, {24,30}, {36,39}, {1,19}, {1,18}, {36,41}, {5,12}, {4,9}, {1,10}, {18,26}, {1,7}, {8,11}, {5,32}, {10,34}, {20,28}, {17,40}, {1,22}, {4,6}, {3,11}, {33,37}, {26,31}, {14,18}, {38,39}, {2,17}, {9,27}, {2,15}, {15,23}, {14,29}, {28,41}, {37,40}, {20,34}, {2,14}, {25,29}, {13,23}, {22,29}, {6,11}, {16,31}, {23,35}, {5,8}, {7,38}, {3,30}, {7,25}, {5,36}, {11,22}, {14,27}, {21,39} } Symmetric graph 28 of order 42 Valency 10 Diameter 3 Girth 4 Automorphism group of order 10080 Number of arcs = 420 Number of 2-arcs = 3780 2-arc-transitive false Edge-set { {1,4}, {11,35}, {6,12}, {28,29}, {4,27}, {30,42}, {3,9}, {24,32}, {15,23}, {31,35}, {6,16}, {23,26}, {14,24}, {36,40}, {2,5}, {19,34}, {33,38}, {10,33}, {34,41}, {20,28}, {27,37}, {9,42}, {16,33}, {31,34}, {6,34}, {33,35}, {13,27}, {25,28}, {12,41}, {10,11}, {7,37}, {20,21}, {17,38}, {18,19}, {38,39}, {1,19}, {25,37}, {13,20}, {8,32}, {15,22}, {18,31}, {16,17}, {26,40}, {2,14}, {9,38}, {19,42}, {20,37}, {37,42}, {9,20}, {28,38}, {19,27}, {5,31}, {16,36}, {15,32}, {25,30}, {3,13}, {29,39}, {18,21}, {7,17}, {3,8}, {22,30}, {1,17}, {18,39}, {2,7}, {21,40}, {14,17}, {18,26}, {7,11}, {12,21}, {15,18}, {17,32}, {5,8}, {22,36}, {19,22}, {8,38}, {4,10}, {29,41}, {2,20}, {37,40}, {1,9}, {39,42}, {13,16}, {25,31}, {17,40}, {2,18}, {7,26}, {14,21}, {8,18}, {17,22}, {8,40}, {2,22}, {7,31}, {16,21}, {20,41}, {10,37}, {9,27}, {28,42}, {10,19}, {38,41}, {5,36}, {2,3}, {30,40}, {1,21}, {7,39}, {4,23}, {24,29}, {1,11}, {12,39}, {1,6}, {35,39}, {2,16}, {31,40}, {21,29}, {4,7}, {3,30}, {2,10}, {40,41}, {22,41}, {8,10}, {24,25}, {13,23}, {8,12}, {11,22}, {13,18}, {17,25}, {11,40}, {2,12}, {14,26}, {5,9}, {36,42}, {15,20}, {32,37}, {1,13}, {25,39}, {3,6}, {30,35}, {13,22}, {8,25}, {4,12}, {11,29}, {26,32}, {14,15}, {27,41}, {10,28}, {12,36}, {5,11}, {3,11}, {12,30}, {24,34}, {23,33}, {14,30}, {3,26}, {11,42}, {9,12}, {14,28}, {26,27}, {3,24}, {23,30}, {21,35}, {6,7}, {23,36}, {5,24}, {13,25}, {4,25}, {13,29}, {22,39}, {1,8}, {15,34}, {32,33}, {5,33}, {34,36}, {4,29}, {1,15}, {32,39}, {23,28}, {24,27}, {4,5}, {29,36}, {16,19}, {31,38}, {6,10}, {35,41}, {27,30}, {3,28}, {34,37}, {20,33}, {6,23}, {24,35}, {26,29}, {4,14}, {6,32}, {15,35}, {16,31}, {21,42}, {7,9}, {27,33}, {28,34}, {5,15}, {32,36}, {19,38}, {14,19}, {26,38}, {17,20}, {18,37}, {23,31}, {16,24}, {33,42}, {9,34}, {6,35}, {10,41} } Symmetric graph 29 of order 42 Valency 10 Diameter 3 Girth 4 Automorphism group of order 10080 Number of arcs = 420 Number of 2-arcs = 3780 2-arc-transitive false Edge-set { {1,24}, {11,34}, {12,33}, {29,37}, {4,20}, {30,38}, {3,19}, {18,24}, {17,23}, {8,35}, {6,22}, {7,36}, {5,21}, {2,34}, {33,40}, {1,33}, {34,39}, {22,28}, {8,27}, {4,42}, {9,29}, {21,27}, {7,28}, {3,41}, {10,30}, {12,37}, {11,20}, {13,38}, {19,25}, {11,38}, {12,19}, {14,37}, {20,26}, {4,32}, {15,29}, {22,31}, {8,16}, {26,35}, {6,14}, {24,40}, {2,23}, {3,31}, {16,30}, {21,32}, {7,15}, {25,36}, {5,13}, {23,39}, {18,30}, {3,17}, {8,29}, {4,22}, {5,17}, {18,36}, {17,29}, {4,18}, {7,30}, {3,21}, {6,18}, {17,35}, {19,35}, {6,38}, {10,24}, {23,41}, {9,22}, {8,42}, {16,28}, {27,31}, {6,42}, {9,35}, {13,34}, {25,33}, {20,36}, {5,37}, {9,23}, {24,42}, {10,21}, {7,41}, {15,27}, {28,32}, {5,41}, {10,36}, {14,33}, {26,34}, {1,36}, {5,39}, {22,24}, {8,23}, {4,35}, {6,29}, {1,41}, {10,39}, {2,27}, {28,40}, {2,35}, {6,40}, {21,23}, {7,24}, {3,36}, {5,30}, {2,42}, {9,40}, {1,28}, {27,39}, {17,42}, {9,18}, {4,40}, {2,29}, {22,26}, {8,14}, {9,32}, {15,42}, {20,31}, {16,37}, {26,42}, {9,14}, {15,38}, {19,32}, {18,41}, {10,17}, {3,39}, {1,30}, {21,25}, {7,13}, {10,31}, {16,41}, {25,41}, {10,13}, {11,27}, {12,28}, {14,41}, {10,26}, {4,34}, {29,33}, {22,33}, {8,34}, {28,35}, {6,27}, {11,25}, {12,13}, {14,39}, {1,26}, {12,31}, {11,16}, {13,32}, {15,25}, {13,42}, {9,25}, {3,33}, {30,34}, {21,34}, {7,33}, {27,36}, {5,28}, {12,26}, {11,14}, {13,40}, {2,25}, {11,32}, {12,15}, {14,31}, {16,26}, {2,40}, {13,35}, {6,25}, {12,24}, {11,23}, {4,16}, {29,31}, {19,40}, {2,38}, {8,20}, {22,37}, {7,19}, {21,38}, {1,39}, {14,36}, {5,26}, {3,15}, {30,32}, {20,39}, {1,37}, {16,39}, {1,31}, {35,37}, {6,20}, {24,38}, {19,23}, {4,38}, {19,29}, {31,42}, {9,16}, {20,30}, {3,37}, {5,19}, {36,38}, {10,15}, {32,41}, {15,40}, {2,32}, {23,37}, {20,24}, {12,17}, {11,18}, {8,22}, {7,21}, {18,28}, {17,27}, {17,34}, {18,33} } Symmetric graph 30 of order 42 Valency 10 Diameter 3 Girth 3 Automorphism group of order 10080 Number of arcs = 420 Number of 2-arcs = 3780 2-arc-transitive false Edge-set { {1,4}, {9,42}, {4,24}, {23,28}, {29,39}, {1,9}, {2,3}, {2,12}, {5,31}, {7,37}, {28,42}, {24,29}, {10,41}, {3,23}, {34,41}, {23,25}, {17,20}, {14,20}, {26,38}, {27,41}, {12,39}, {1,5}, {1,7}, {24,27}, {30,40}, {2,10}, {14,24}, {22,40}, {2,8}, {34,36}, {11,30}, {5,36}, {7,25}, {11,40}, {31,34}, {25,37}, {20,42}, {38,42}, {1,11}, {6,32}, {8,38}, {23,30}, {32,35}, {31,38}, {37,41}, {14,15}, {17,22}, {6,33}, {8,26}, {15,20}, {14,17}, {10,27}, {32,33}, {20,22}, {36,39}, {39,42}, {33,42}, {24,26}, {18,19}, {13,19}, {2,6}, {16,18}, {17,25}, {40,41}, {11,22}, {5,15}, {35,40}, {13,21}, {9,28}, {22,30}, {15,36}, {5,34}, {4,27}, {13,18}, {19,21}, {30,35}, {31,36}, {15,31}, {17,37}, {23,31}, {37,39}, {13,23}, {21,39}, {33,35}, {12,29}, {6,35}, {19,41}, {16,33}, {8,40}, {10,34}, {24,32}, {38,40}, {26,31}, {16,32}, {18,38}, {12,36}, {3,28}, {8,31}, {15,22}, {15,17}, {14,22}, {4,9}, {4,11}, {29,36}, {6,16}, {8,18}, {26,40}, {2,17}, {2,20}, {32,37}, {13,16}, {18,21}, {16,19}, {16,21}, {28,38}, {14,27}, {1,18}, {1,19}, {25,32}, {7,17}, {9,20}, {25,39}, {15,34}, {3,10}, {3,12}, {20,28}, {22,35}, {11,35}, {4,29}, {9,33}, {4,26}, {28,33}, {7,32}, {9,38}, {23,34}, {30,41}, {23,36}, {18,26}, {12,21}, {21,29}, {16,35}, {21,36}, {3,25}, {12,42}, {5,11}, {24,33}, {29,42}, {24,35}, {10,19}, {27,34}, {28,30}, {10,37}, {3,30}, {18,31}, {5,9}, {4,7}, {13,28}, {7,9}, {3,13}, {19,27}, {25,28}, {2,14}, {2,22}, {6,24}, {2,15}, {7,39}, {17,32}, {8,10}, {20,33}, {14,26}, {1,13}, {1,21}, {5,23}, {1,16}, {27,29}, {4,14}, {3,6}, {8,12}, {26,27}, {6,10}, {3,8}, {17,39}, {14,29}, {6,12}, {10,12}, {11,41}, {35,41}, {22,41}, {15,23}, {27,37}, {18,40}, {19,34}, {13,30}, {7,11}, {36,42}, {21,42}, {16,24}, {4,5}, {9,11}, {34,37}, {31,40}, {5,7}, {13,25}, {25,30}, {32,39}, {33,38}, {6,8}, {26,29}, {20,38}, {19,37} } Symmetric graph 31 of order 42 Valency 12 Diameter 3 Girth 3 Automorphism group of order 1008 Number of arcs = 504 Number of 2-arcs = 5544 2-arc-transitive false Edge-set { {1,4}, {17,36}, {20,24}, {31,40}, {13,17}, {14,30}, {1,31}, {8,24}, {8,12}, {21,31}, {13,39}, {5,20}, {27,37}, {24,36}, {14,25}, {1,25}, {4,29}, {24,29}, {8,32}, {11,21}, {36,39}, {18,30}, {12,37}, {34,42}, {14,40}, {1,17}, {20,39}, {37,40}, {24,40}, {6,17}, {20,25}, {6,14}, {22,25}, {4,9}, {2,29}, {28,32}, {11,40}, {5,32}, {15,27}, {1,12}, {29,34}, {7,42}, {10,16}, {8,20}, {31,36}, {13,24}, {11,30}, {12,34}, {8,14}, {16,31}, {13,19}, {30,39}, {16,20}, {19,37}, {2,40}, {17,26}, {6,35}, {4,22}, {9,26}, {2,8}, {12,28}, {18,22}, {9,21}, {38,42}, {1,36}, {6,42}, {16,25}, {7,27}, {6,10}, {3,33}, {25,30}, {4,31}, {8,17}, {14,21}, {1,39}, {2,5}, {27,28}, {1,42}, {16,29}, {4,37}, {24,33}, {21,28}, {33,39}, {5,11}, {27,36}, {30,33}, {14,31}, {33,34}, {8,35}, {12,22}, {31,38}, {13,41}, {16,41}, {18,19}, {2,20}, {26,38}, {5,41}, {25,35}, {26,29}, {13,32}, {2,15}, {7,10}, {10,35}, {36,40}, {17,24}, {7,16}, {10,19}, {3,16}, {19,30}, {23,34}, {7,23}, {5,39}, {27,40}, {25,31}, {4,13}, {20,29}, {32,37}, {11,36}, {18,35}, {21,22}, {26,42}, {7,36}, {10,24}, {6,33}, {12,17}, {20,34}, {14,23}, {1,7}, {26,32}, {11,23}, {2,18}, {17,42}, {5,23}, {8,37}, {23,42}, {25,41}, {4,18}, {1,13}, {11,39}, {9,33}, {11,14}, {15,33}, {30,35}, {22,31}, {10,38}, {35,41}, {9,18}, {39,41}, {18,40}, {6,38}, {9,39}, {19,35}, {22,38}, {3,27}, {6,30}, {3,41}, {8,40}, {27,33}, {3,28}, {5,28}, {15,42}, {3,6}, {11,18}, {21,36}, {12,42}, {24,39}, {17,21}, {9,34}, {17,28}, {32,41}, {15,18}, {13,29}, {2,32}, {7,38}, {10,41}, {3,14}, {1,30}, {16,23}, {7,19}, {30,42}, {15,20}, {3,37}, {6,24}, {9,41}, {32,35}, {15,22}, {7,31}, {10,13}, {3,21}, {12,25}, {4,34}, {7,15}, {3,10}, {17,32}, {2,11}, {28,36}, {23,26}, {5,7}, {28,37}, {19,23}, {18,27}, {5,15}, {9,11}, {12,15}, {11,26}, {5,36}, {28,41}, {18,33}, {2,35}, {34,37}, {5,16}, {19,27}, {8,25}, {4,12}, {23,37}, {21,26}, {16,34}, {15,28}, {29,40}, {10,29}, {29,31}, {13,26}, {9,22}, {19,32}, {15,38}, {6,21}, {25,39}, {22,35}, {10,27}, {3,9}, {24,27}, {14,16}, {1,19}, {22,41}, {2,38}, {6,8}, {23,32}, {3,34}, {23,30}, {9,13}, {22,28}, {4,40}, {26,34}, {21,38}, {2,26}, {29,38}, {33,42}, {4,19}, {35,38}, {14,37}, {20,33}, {12,20} } Symmetric graph 32 of order 42 Valency 12 Diameter 3 Girth 4 Automorphism group of order 60480 Number of arcs = 504 Number of 2-arcs = 5544 2-arc-transitive false Edge-set { {1,7}, {9,36}, {1,22}, {12,39}, {12,23}, {1,36}, {1,14}, {8,16}, {20,26}, {4,8}, {15,20}, {36,39}, {1,12}, {28,36}, {1,40}, {10,30}, {21,42}, {5,24}, {18,31}, {10,31}, {4,21}, {5,29}, {18,41}, {16,39}, {12,26}, {8,36}, {1,20}, {20,39}, {12,34}, {15,36}, {1,25}, {11,22}, {24,35}, {2,17}, {13,27}, {3,33}, {5,16}, {26,42}, {8,38}, {11,42}, {8,24}, {2,31}, {4,13}, {21,33}, {5,36}, {18,26}, {28,38}, {16,30}, {20,31}, {10,39}, {12,21}, {1,18}, {9,20}, {29,39}, {12,41}, {23,36}, {1,32}, {14,19}, {3,40}, {11,16}, {25,35}, {2,37}, {19,27}, {33,39}, {32,37}, {3,10}, {30,33}, {5,42}, {17,24}, {27,31}, {10,13}, {21,29}, {7,17}, {16,21}, {35,42}, {2,8}, {4,39}, {5,12}, {24,26}, {31,38}, {13,20}, {29,34}, {22,30}, {8,18}, {26,36}, {1,38}, {18,23}, {20,28}, {12,15}, {36,41}, {6,28}, {17,40}, {15,32}, {3,25}, {7,30}, {19,42}, {23,40}, {11,32}, {14,35}, {2,30}, {6,19}, {17,33}, {16,37}, {10,26}, {14,41}, {3,24}, {22,37}, {10,35}, {5,27}, {8,33}, {11,27}, {24,39}, {2,21}, {13,36}, {9,25}, {13,42}, {16,31}, {4,26}, {5,20}, {8,29}, {18,39}, {21,38}, {12,31}, {1,29}, {15,38}, {18,34}, {20,41}, {12,28}, {20,34}, {6,34}, {15,25}, {25,37}, {29,41}, {7,41}, {23,32}, {3,32}, {9,22}, {22,35}, {6,17}, {17,27}, {4,15}, {7,19}, {28,40}, {11,40}, {2,35}, {10,37}, {14,30}, {30,42}, {11,24}, {24,31}, {18,28}, {3,16}, {19,33}, {5,33}, {10,21}, {16,26}, {2,13}, {27,39}, {8,42}, {4,31}, {5,18}, {21,36}, {26,38}, {13,29}, {8,20}, {9,38}, {5,38}, {9,18}, {34,38}, {6,9}, {23,29}, {32,41}, {14,23}, {30,32}, {18,21}, {22,28}, {4,41}, {7,15}, {3,7}, {11,14}, {25,34}, {6,37}, {19,25}, {33,37}, {29,31}, {17,22}, {35,40}, {2,11}, {24,30}, {27,35}, {16,19}, {3,42}, {10,17}, {5,10}, {13,24}, {31,42}, {2,39}, {26,33}, {21,27}, {12,13}, {13,33}, {23,38}, {13,38}, {9,29}, {6,23}, {7,28}, {4,28}, {15,40}, {22,41}, {7,35}, {2,26}, {14,34}, {9,32}, {3,22}, {19,40}, {6,30}, {17,32}, {14,37}, {11,25}, {2,19}, {16,35}, {11,33}, {17,42}, {3,27}, {24,37}, {8,27}, {27,37}, {15,29}, {4,34}, {6,15}, {22,34}, {25,41}, {14,28}, {9,40}, {7,23}, {3,14}, {17,25}, {6,35}, {7,37}, {30,40}, {19,32}, {10,19}, {4,9}, {6,41}, {9,14}, {28,32}, {34,40}, {23,25}, {15,22}, {6,11}, {4,23}, {7,34} } Symmetric graph 33 of order 42 Valency 12 Diameter 3 Girth 3 Automorphism group of order 264241152 Number of arcs = 504 Number of 2-arcs = 5544 2-arc-transitive false Edge-set { {1,9}, {14,23}, {21,34}, {25,36}, {6,17}, {2,33}, {15,39}, {3,39}, {27,41}, {17,29}, {4,20}, {1,13}, {22,40}, {9,27}, {9,16}, {9,24}, {12,42}, {11,29}, {29,37}, {4,25}, {15,32}, {14,26}, {5,21}, {10,34}, {10,16}, {23,42}, {29,34}, {23,28}, {2,34}, {23,35}, {18,34}, {11,20}, {12,35}, {19,37}, {8,37}, {7,25}, {23,27}, {5,27}, {1,37}, {25,40}, {6,28}, {18,33}, {15,19}, {2,24}, {33,39}, {24,28}, {11,36}, {12,17}, {2,37}, {25,39}, {36,41}, {17,30}, {2,13}, {22,39}, {4,36}, {17,42}, {2,30}, {19,32}, {14,36}, {35,42}, {8,31}, {7,13}, {8,22}, {7,31}, {21,39}, {27,32}, {36,42}, {18,42}, {19,29}, {8,14}, {7,21}, {10,39}, {10,27}, {17,41}, {20,30}, {1,30}, {3,40}, {27,31}, {13,35}, {18,22}, {9,40}, {35,41}, {18,30}, {3,19}, {20,29}, {4,35}, {8,13}, {7,22}, {9,39}, {3,12}, {11,41}, {29,38}, {4,26}, {13,26}, {5,22}, {9,34}, {3,15}, {23,41}, {4,12}, {13,38}, {22,26}, {5,31}, {13,37}, {3,25}, {6,41}, {4,11}, {6,22}, {31,38}, {21,26}, {5,32}, {22,34}, {16,31}, {6,21}, {32,38}, {9,33}, {9,15}, {5,42}, {3,11}, {12,41}, {11,30}, {31,37}, {13,25}, {22,25}, {6,31}, {21,33}, {24,42}, {29,33}, {12,29}, {14,38}, {10,24}, {6,42}, {30,34}, {3,16}, {10,23}, {11,42}, {30,38}, {3,26}, {13,24}, {32,37}, {14,25}, {4,15}, {16,32}, {9,23}, {16,20}, {24,35}, {12,19}, {7,37}, {8,25}, {15,40}, {26,40}, {5,28}, {16,19}, {2,23}, {34,39}, {16,27}, {1,24}, {12,36}, {11,17}, {15,20}, {7,26}, {5,8}, {34,40}, {16,28}, {6,18}, {19,38}, {8,26}, {5,7}, {16,39}, {24,27}, {23,36}, {17,34}, {6,7}, {8,38}, {33,40}, {15,28}, {5,18}, {2,38}, {17,33}, {1,23}, {1,34}, {11,18}, {24,36}, {12,20}, {11,35}, {26,36}, {6,8}, {7,38}, {26,39}, {20,38}, {1,33}, {12,18}, {20,37}, {25,35}, {11,19}, {16,40}, {26,35}, {6,27}, {15,27}, {28,32}, {2,14}, {20,31}, {8,21}, {7,32}, {1,10}, {10,40}, {10,28}, {18,41}, {19,30}, {28,31}, {13,36}, {17,22}, {2,9}, {28,42}, {2,29}, {14,35}, {18,21}, {3,20}, {1,14}, {21,40}, {19,31}, {2,10}, {28,41}, {9,28}, {18,29}, {3,36}, {4,39}, {17,21}, {20,32}, {1,29}, {4,40}, {3,35}, {4,19}, {8,32}, {7,14}, {27,42}, {5,41}, {30,37}, {6,32}, {22,33}, {15,31}, {14,24}, {10,33}, {24,41}, {30,33}, {12,30}, {4,16}, {13,23}, {10,15}, {14,37}, {21,25}, {5,17}, {1,38} } Symmetric graph 34 of order 42 Valency 12 Diameter 3 Girth 4 Automorphism group of order 26330359136256 Number of arcs = 504 Number of 2-arcs = 5544 2-arc-transitive false Edge-set { {1,4}, {13,23}, {1,10}, {8,42}, {13,35}, {23,26}, {10,39}, {19,35}, {18,20}, {38,42}, {26,35}, {8,11}, {13,24}, {26,30}, {39,40}, {18,38}, {26,28}, {17,32}, {9,29}, {19,28}, {20,41}, {11,38}, {24,26}, {27,35}, {7,42}, {14,35}, {3,11}, {24,31}, {20,30}, {21,40}, {28,32}, {9,41}, {1,11}, {24,32}, {4,33}, {5,7}, {2,36}, {17,33}, {1,18}, {17,21}, {19,29}, {27,28}, {38,41}, {7,11}, {14,24}, {12,38}, {19,34}, {16,20}, {26,34}, {24,27}, {6,14}, {3,17}, {29,31}, {21,30}, {5,32}, {21,36}, {17,19}, {23,27}, {10,38}, {4,7}, {5,14}, {6,13}, {14,34}, {3,16}, {22,37}, {11,27}, {6,33}, {23,32}, {9,10}, {16,33}, {7,30}, {2,18}, {28,33}, {1,12}, {21,28}, {19,41}, {27,34}, {16,38}, {7,41}, {25,28}, {37,41}, {18,39}, {17,31}, {8,29}, {11,39}, {24,25}, {7,12}, {14,23}, {15,41}, {2,34}, {24,33}, {2,5}, {30,31}, {4,14}, {3,5}, {16,37}, {27,30}, {18,33}, {7,28}, {8,12}, {39,41}, {13,34}, {1,16}, {14,41}, {3,34}, {15,42}, {2,35}, {25,34}, {12,27}, {23,38}, {6,15}, {2,4}, {4,8}, {5,13}, {26,36}, {17,39}, {6,31}, {16,31}, {22,32}, {9,11}, {1,6}, {4,32}, {23,25}, {10,37}, {30,32}, {18,21}, {12,39}, {28,31}, {8,41}, {21,34}, {16,19}, {21,29}, {19,42}, {9,40}, {5,33}, {6,7}, {38,40}, {7,10}, {14,22}, {19,36}, {22,39}, {11,25}, {13,41}, {1,34}, {3,12}, {23,31}, {6,32}, {4,9}, {16,32}, {25,35}, {18,37}, {19,40}, {39,42}, {8,10}, {21,41}, {24,39}, {12,25}, {20,36}, {22,38}, {11,26}, {22,25}, {23,37}, {8,28}, {15,40}, {13,22}, {14,42}, {3,35}, {11,37}, {30,33}, {7,40}, {5,15}, {2,6}, {5,31}, {6,8}, {27,36}, {17,38}, {15,23}, {2,10}, {4,13}, {1,5}, {26,29}, {3,4}, {9,30}, {25,30}, {37,40}, {21,35}, {18,19}, {16,39}, {18,31}, {2,16}, {20,28}, {15,34}, {10,27}, {21,42}, {23,39}, {10,25}, {12,37}, {5,8}, {4,15}, {13,36}, {1,17}, {4,31}, {22,26}, {29,32}, {9,42}, {19,30}, {20,40}, {16,21}, {14,40}, {17,37}, {27,29}, {9,28}, {24,38}, {15,22}, {13,42}, {1,35}, {18,32}, {15,35}, {20,34}, {12,26}, {3,6}, {3,36}, {2,11}, {8,40}, {3,10}, {22,31}, {20,29}, {6,9}, {25,36}, {8,30}, {13,40}, {10,26}, {25,29}, {37,42}, {3,18}, {1,36}, {23,33}, {15,24}, {17,20}, {29,33}, {2,12}, {15,36}, {20,35}, {5,9}, {24,37}, {22,27}, {2,17}, {20,42}, {22,33}, {9,12}, {14,36}, {7,29} } Symmetric graph 35 of order 42 Valency 12 Diameter 3 Girth 4 Automorphism group of order 1404285820600320000000 Number of arcs = 504 Number of 2-arcs = 5544 2-arc-transitive false Edge-set { {1,7}, {5,37}, {6,40}, {33,39}, {35,41}, {31,40}, {33,42}, {29,32}, {26,34}, {25,36}, {28,32}, {27,31}, {30,33}, {29,35}, {26,31}, {21,28}, {23,29}, {23,30}, {20,25}, {24,26}, {19,27}, {19,28}, {21,29}, {20,27}, {22,30}, {22,29}, {21,25}, {23,28}, {23,27}, {20,30}, {14,19}, {18,21}, {16,21}, {14,23}, {16,22}, {14,24}, {17,24}, {16,19}, {15,23}, {13,20}, {18,20}, {15,22}, {18,19}, {15,21}, {14,21}, {18,23}, {17,20}, {13,22}, {13,21}, {17,23}, {16,20}, {14,22}, {17,22}, {16,24}, {10,18}, {8,15}, {7,14}, {12,18}, {12,14}, {9,18}, {10,16}, {8,14}, {12,13}, {9,17}, {10,15}, {8,13}, {11,13}, {9,15}, {11,16}, {10,14}, {7,16}, {7,17}, {12,16}, {10,17}, {7,18}, {12,15}, {11,14}, {8,18}, {8,17}, {9,13}, {9,14}, {8,16}, {12,17}, {9,16}, {10,13}, {11,17}, {2,12}, {6,11}, {5,10}, {6,8}, {3,7}, {4,12}, {3,10}, {4,8}, {2,7}, {1,12}, {2,9}, {6,10}, {5,8}, {3,9}, {4,7}, {2,8}, {1,11}, {2,10}, {6,9}, {5,7}, {4,9}, {2,11}, {1,10}, {5,12}, {3,12}, {1,8}, {6,12}, {3,11}, {4,10}, {3,8}, {6,7}, {5,11}, {5,9}, {4,11}, {1,9}, {3,38}, {4,39}, {4,40}, {3,42}, {1,39}, {2,41}, {5,42}, {5,41}, {6,38}, {4,37}, {1,41}, {2,38}, {6,42}, {5,38}, {6,39}, {3,37}, {1,40}, {2,42}, {1,38}, {6,37}, {5,39}, {3,40}, {2,39}, {2,40}, {1,42}, {6,41}, {1,37}, {4,38}, {3,39}, {4,41}, {3,41}, {5,40}, {4,42}, {2,37}, {34,41}, {36,38}, {32,42}, {34,37}, {31,42}, {33,37}, {31,38}, {32,37}, {34,40}, {32,39}, {35,39}, {31,41}, {36,39}, {32,41}, {36,42}, {35,37}, {36,37}, {32,40}, {34,38}, {35,40}, {34,39}, {36,41}, {34,42}, {33,41}, {35,38}, {31,37}, {33,40}, {31,39}, {36,40}, {35,42}, {33,38}, {32,38}, {30,36}, {25,32}, {27,36}, {28,35}, {29,31}, {25,35}, {27,35}, {30,31}, {29,33}, {26,35}, {27,34}, {28,33}, {25,33}, {29,34}, {28,34}, {30,32}, {26,32}, {28,36}, {26,33}, {28,31}, {30,34}, {25,31}, {25,34}, {26,36}, {27,32}, {30,35}, {29,36}, {27,33}, {22,26}, {24,27}, {24,28}, {19,29}, {20,26}, {22,27}, {19,25}, {21,27}, {24,25}, {22,28}, {24,30}, {23,26}, {23,25}, {20,28}, {22,25}, {21,26}, {24,29}, {19,26}, {21,30}, {19,30}, {20,29}, {13,23}, {15,20}, {15,19}, {18,24}, {14,20}, {18,22}, {15,24}, {13,19}, {17,21}, {13,24}, {16,23}, {17,19}, {11,18}, {7,15}, {7,13}, {11,15} } Symmetric graph 36 of order 42 Valency 13 Diameter 3 Girth 3 Automorphism group of order 2184 Number of arcs = 546 Number of 2-arcs = 6552 2-arc-transitive false Edge-set { {1,4}, {16,21}, {7,17}, {22,38}, {39,42}, {24,32}, {12,40}, {8,36}, {3,6}, {11,34}, {2,36}, {9,41}, {5,33}, {6,12}, {14,35}, {13,31}, {10,25}, {17,19}, {9,18}, {4,14}, {15,27}, {13,20}, {8,25}, {10,33}, {18,40}, {16,31}, {6,17}, {14,18}, {15,28}, {19,26}, {29,42}, {21,32}, {2,5}, {13,24}, {24,39}, {37,40}, {23,33}, {11,41}, {16,28}, {1,30}, {20,22}, {29,37}, {21,38}, {2,31}, {10,24}, {5,40}, {12,23}, {35,41}, {22,42}, {32,42}, {17,24}, {23,28}, {19,41}, {26,30}, {20,29}, {3,39}, {23,37}, {11,27}, {30,36}, {38,41}, {33,39}, {18,20}, {8,16}, {9,29}, {5,21}, {9,34}, {12,35}, {1,35}, {7,40}, {4,31}, {4,10}, {15,34}, {22,26}, {21,25}, {7,28}, {8,37}, {6,38}, {27,35}, {36,38}, {20,42}, {8,32}, {5,9}, {5,13}, {12,18}, {16,35}, {6,7}, {10,15}, {26,34}, {8,11}, {6,36}, {33,36}, {9,24}, {7,26}, {4,29}, {10,39}, {34,37}, {3,25}, {27,37}, {30,38}, {19,34}, {2,9}, {7,35}, {15,22}, {13,25}, {25,28}, {10,36}, {3,34}, {34,40}, {22,31}, {10,42}, {27,33}, {11,30}, {18,38}, {16,39}, {14,33}, {6,15}, {14,26}, {15,21}, {12,32}, {16,42}, {17,32}, {5,16}, {13,17}, {14,30}, {20,27}, {3,8}, {6,23}, {2,38}, {26,32}, {12,29}, {31,35}, {1,10}, {17,36}, {3,18}, {1,15}, {13,36}, {11,37}, {31,41}, {18,33}, {11,16}, {18,29}, {14,41}, {26,42}, {5,30}, {3,14}, {23,27}, {18,25}, {13,40}, {25,31}, {9,33}, {5,11}, {3,32}, {16,27}, {17,30}, {5,34}, {2,13}, {1,27}, {2,19}, {1,22}, {25,36}, {3,28}, {14,39}, {20,33}, {15,32}, {12,26}, {8,30}, {6,20}, {2,29}, {21,24}, {2,26}, {24,29}, {14,19}, {9,27}, {12,14}, {8,42}, {6,32}, {1,40}, {4,25}, {23,36}, {3,41}, {22,34}, {2,42}, {28,40}, {19,31}, {19,23}, {20,39}, {6,41}, {11,22}, {36,42}, {24,41}, {33,40}, {18,22}, {21,40}, {19,28}, {1,37}, {9,10}, {4,18}, {20,36}, {6,27}, {15,42}, {7,13}, {25,40}, {21,30}, {7,20}, {13,29}, {4,35}, {32,34}, {23,40}, {4,22}, {30,41}, {10,28}, {3,11}, {9,19}, {1,7}, {2,23}, {21,35}, {11,31}, {15,16}, {24,25}, {8,21}, {1,21}, {7,22}, {28,34}, {31,38}, {14,23}, {17,37}, {9,38}, {5,39}, {3,20}, {8,23}, {28,39}, {19,37}, {1,33}, {6,28}, {17,41}, {12,21}, {2,16}, {10,19}, {8,14}, {11,20}, {29,35}, {32,37}, {7,39}, {4,37}, {10,17}, {18,34}, {4,8}, {11,13}, {12,38}, {35,39}, {26,39}, {16,23}, {13,37}, {25,38}, {1,17}, {29,32}, {2,12}, {24,35}, {27,29}, {17,26}, {7,12}, {5,26}, {4,19}, {9,15}, {15,38}, {4,42}, {22,30}, {5,24}, {7,31}, {28,31}, {27,41}, {3,24}, {30,33} } Symmetric graph 37 of order 42 Valency 14 Diameter 3 Girth 4 Automorphism group of order 196681931556913152000000 Number of arcs = 588 Number of 2-arcs = 7644 2-arc-transitive false Edge-set { {1,16}, {2,27}, {9,39}, {1,26}, {7,40}, {10,38}, {21,31}, {2,23}, {6,39}, {8,37}, {22,33}, {9,35}, {24,32}, {19,29}, {2,15}, {1,22}, {4,40}, {5,38}, {21,35}, {7,36}, {23,34}, {20,31}, {1,28}, {10,33}, {25,31}, {21,30}, {3,16}, {17,42}, {13,18}, {10,40}, {2,20}, {1,39}, {3,37}, {22,38}, {6,35}, {24,36}, {19,33}, {2,25}, {8,34}, {26,33}, {22,32}, {4,27}, {18,29}, {14,15}, {8,39}, {9,31}, {28,32}, {24,29}, {5,15}, {19,41}, {2,17}, {9,37}, {16,40}, {11,20}, {12,42}, {1,18}, {14,40}, {2,38}, {21,39}, {4,36}, {23,37}, {20,35}, {1,24}, {5,33}, {25,35}, {21,34}, {3,26}, {17,31}, {13,28}, {5,40}, {7,32}, {27,34}, {23,31}, {6,28}, {20,30}, {7,38}, {15,42}, {12,18}, {10,41}, {10,29}, {15,31}, {25,30}, {8,16}, {21,42}, {3,18}, {10,36}, {17,39}, {13,19}, {11,40}, {27,37}, {9,22}, {14,29}, {12,39}, {13,37}, {22,41}, {1,35}, {24,40}, {19,38}, {2,21}, {3,34}, {26,38}, {22,36}, {4,23}, {18,33}, {14,25}, {3,39}, {6,31}, {28,36}, {24,33}, {5,25}, {19,32}, {6,37}, {16,29}, {11,15}, {8,42}, {8,30}, {16,33}, {26,32}, {7,27}, {22,29}, {4,15}, {8,35}, {18,41}, {14,17}, {28,40}, {10,20}, {12,30}, {9,42}, {18,32}, {28,29}, {10,15}, {24,41}, {5,17}, {9,34}, {19,40}, {12,37}, {16,38}, {11,21}, {13,42}, {26,36}, {7,23}, {1,31}, {11,38}, {14,36}, {23,42}, {20,39}, {1,19}, {2,33}, {25,39}, {21,37}, {3,22}, {17,35}, {13,24}, {2,40}, {4,32}, {23,35}, {6,24}, {20,34}, {4,38}, {12,28}, {5,41}, {5,29}, {15,35}, {25,34}, {8,26}, {3,28}, {5,36}, {17,30}, {13,16}, {27,42}, {9,18}, {7,41}, {17,34}, {27,31}, {9,28}, {23,30}, {6,16}, {7,33}, {20,42}, {15,39}, {12,19}, {11,41}, {25,37}, {8,22}, {14,32}, {15,30}, {12,16}, {25,42}, {8,18}, {10,32}, {3,19}, {11,36}, {17,37}, {13,22}, {27,35}, {9,24}, {2,29}, {6,26}, {4,33}, {12,35}, {13,34}, {26,41}, {22,40}, {4,20}, {18,38}, {14,21}, {13,39}, {24,38}, {5,21}, {19,36}, {1,37}, {11,25}, {3,42}, {3,30}, {4,25}, {3,35}, {14,27}, {6,42}, {18,36}, {28,33}, {10,25}, {5,27}, {6,34}, {16,41}, {11,17}, {26,40}, {7,20}, {12,31}, {16,32}, {11,27}, {26,29}, {7,15}, {8,31}, {4,17}, {18,40}, {14,20}, {28,38}, {10,21}, {13,30}, {5,23}, {1,34}, {28,41}, {10,17}, {9,30}, {5,20}, {12,34}, {16,36}, {11,23}, {1,42}, {7,25}, {3,31}, {11,33}, {23,39}, {6,19}, {20,37}, {14,38}, {12,24}, {2,41}, {3,24}, {2,36}, {13,26}, {4,41}, {15,34}, {12,26}, {8,28}, {5,32}, {27,39}, {9,19}, {11,29}, {6,22}, {14,33}, {27,30}, {9,16}, {7,29}, {6,18}, {15,37}, {12,22}, {14,41}, {8,24}, {2,32}, {8,19}, {11,32}, {9,26}, {4,29}, {4,21}, {13,35}, {14,23}, {10,27}, {6,30}, {7,21}, {13,31}, {7,17}, {10,23}, {1,30} } Symmetric graph 38 of order 42 Valency 16 Diameter 3 Girth 4 Automorphism group of order 241920 Number of arcs = 672 Number of 2-arcs = 10080 2-arc-transitive true Edge-set { {1,22}, {19,42}, {6,27}, {17,22}, {15,42}, {13,36}, {2,26}, {19,31}, {6,31}, {17,30}, {15,37}, {16,32}, {11,24}, {2,23}, {13,34}, {3,22}, {1,42}, {3,36}, {1,26}, {10,31}, {20,31}, {14,30}, {4,37}, {5,37}, {3,40}, {21,34}, {9,33}, {12,23}, {10,34}, {11,32}, {16,24}, {19,41}, {6,23}, {17,42}, {15,27}, {16,41}, {11,23}, {2,42}, {13,27}, {3,35}, {1,38}, {3,29}, {10,28}, {20,39}, {14,27}, {4,29}, {14,40}, {4,25}, {4,41}, {17,23}, {11,26}, {7,25}, {12,30}, {12,24}, {10,36}, {11,35}, {16,38}, {5,34}, {3,33}, {21,37}, {9,40}, {8,42}, {12,36}, {10,26}, {17,31}, {15,31}, {13,30}, {2,37}, {1,37}, {8,40}, {12,34}, {10,33}, {15,34}, {13,32}, {2,24}, {9,41}, {19,23}, {18,42}, {18,27}, {20,41}, {7,23}, {6,35}, {21,38}, {8,29}, {5,22}, {13,28}, {2,39}, {20,27}, {7,29}, {4,28}, {17,39}, {14,29}, {1,27}, {12,31}, {2,34}, {13,33}, {15,38}, {14,35}, {10,24}, {20,36}, {21,24}, {9,36}, {16,35}, {11,38}, {9,34}, {19,33}, {18,37}, {18,40}, {11,40}, {16,25}, {7,41}, {14,26}, {4,32}, {17,33}, {15,41}, {11,36}, {2,35}, {13,38}, {3,31}, {1,31}, {3,30}, {10,32}, {20,24}, {14,23}, {4,34}, {14,42}, {4,27}, {4,33}, {17,41}, {16,36}, {7,35}, {12,38}, {11,30}, {16,37}, {5,32}, {3,24}, {21,23}, {1,25}, {8,30}, {12,22}, {10,42}, {15,28}, {13,39}, {2,28}, {1,29}, {8,22}, {10,35}, {19,26}, {18,26}, {18,32}, {20,33}, {19,40}, {6,25}, {6,32}, {8,23}, {13,29}, {2,22}, {20,38}, {21,29}, {8,31}, {5,31}, {20,28}, {7,39}, {13,42}, {2,27}, {1,36}, {16,34}, {7,32}, {18,30}, {9,28}, {19,39}, {21,35}, {9,38}, {16,29}, {11,22}, {21,26}, {9,32}, {9,37}, {18,34}, {18,33}, {11,25}, {16,30}, {7,22}, {12,42}, {14,39}, {4,39}, {17,28}, {8,35}, {5,27}, {7,31}, {1,30}, {8,37}, {11,33}, {9,23}, {19,34}, {18,24}, {3,41}, {1,23}, {3,42}, {10,41}, {20,23}, {5,35}, {3,38}, {9,22}, {12,28}, {10,39}, {11,27}, {15,39}, {2,29}, {7,27}, {12,29}, {19,35}, {18,36}, {14,37}, {4,40}, {5,40}, {3,25}, {21,41}, {12,26}, {19,24}, {6,36}, {17,35}, {6,30}, {8,32}, {5,24}, {20,42}, {6,41}, {9,35}, {19,38}, {5,39}, {3,28}, {4,22}, {15,36}, {5,36}, {3,26}, {12,33}, {20,32}, {7,24}, {6,34}, {18,29}, {18,22}, {20,26}, {1,41}, {6,29}, {21,22}, {8,38}, {17,32}, {15,24}, {13,23}, {16,42}, {11,37}, {16,40}, {5,38}, {21,30}, {5,42}, {9,26}, {19,32}, {18,25}, {20,37}, {7,40}, {6,33}, {5,25}, {14,25}, {4,30}, {11,39}, {16,28}, {14,33}, {10,37}, {20,40}, {17,24}, {8,28}, {8,27}, {5,29}, {21,31}, {13,40}, {2,25}, {1,35}, {7,34}, {12,25}, {10,30}, {21,39}, {10,27}, {15,23}, {10,22}, {19,25}, {18,41}, {18,23}, {6,24}, {21,36}, {2,33}, {7,36}, {16,39}, {11,28}, {14,28}, {17,29}, {17,25}, {9,42}, {9,31}, {5,33}, {21,40}, {9,25}, {15,22}, {8,26}, {19,30}, {19,27}, {2,41}, {16,26}, {7,28}, {6,28}, {13,22}, {7,26}, {12,32}, {17,37}, {15,40}, {14,34}, {17,40}, {15,25}, {4,38}, {20,29}, {8,34}, {6,37}, {12,39}, {1,32}, {14,36}, {13,35}, {2,38}, {6,38}, {1,39}, {21,33}, {14,31}, {15,30}, {4,26}, {13,41}, {4,31}, {8,24}, {3,27} } Symmetric graph 39 of order 42 Valency 16 Diameter 2 Girth 3 Automorphism group of order 704643072 Number of arcs = 672 Number of 2-arcs = 10080 2-arc-transitive false Edge-set { {1,9}, {18,33}, {6,29}, {6,8}, {10,40}, {14,41}, {2,21}, {14,36}, {2,25}, {26,34}, {15,30}, {9,29}, {17,37}, {17,19}, {5,34}, {12,37}, {17,38}, {5,19}, {5,37}, {9,20}, {12,42}, {22,42}, {33,41}, {21,29}, {7,28}, {14,39}, {7,22}, {31,39}, {5,13}, {28,32}, {14,28}, {7,27}, {13,39}, {13,22}, {1,31}, {13,28}, {1,14}, {21,33}, {29,32}, {30,32}, {18,28}, {20,30}, {10,17}, {19,41}, {21,34}, {35,40}, {24,26}, {9,25}, {16,37}, {20,35}, {26,33}, {4,25}, {8,16}, {10,13}, {1,38}, {3,40}, {7,24}, {9,40}, {24,37}, {35,39}, {23,26}, {10,25}, {16,38}, {10,20}, {33,38}, {4,18}, {24,38}, {9,18}, {6,37}, {6,19}, {10,34}, {3,41}, {7,21}, {3,42}, {8,40}, {24,40}, {21,42}, {22,32}, {7,34}, {30,39}, {22,29}, {17,31}, {9,34}, {2,26}, {11,15}, {20,36}, {19,29}, {11,28}, {11,32}, {4,19}, {11,36}, {25,41}, {30,38}, {18,27}, {6,13}, {15,26}, {3,15}, {24,35}, {26,36}, {15,29}, {24,28}, {11,16}, {23,37}, {34,38}, {19,30}, {11,27}, {13,41}, {6,27}, {4,40}, {24,27}, {13,36}, {8,33}, {29,40}, {2,14}, {14,22}, {2,31}, {9,30}, {3,17}, {19,35}, {3,18}, {15,25}, {15,36}, {18,34}, {3,20}, {7,33}, {5,35}, {9,26}, {25,42}, {16,22}, {20,41}, {4,7}, {8,39}, {5,33}, {5,20}, {12,31}, {27,42}, {1,21}, {12,32}, {22,41}, {21,31}, {31,40}, {3,31}, {4,31}, {12,27}, {29,38}, {23,40}, {10,14}, {2,38}, {20,42}, {12,15}, {2,24}, {1,37}, {12,20}, {12,41}, {24,36}, {11,31}, {27,41}, {23,28}, {14,35}, {5,27}, {9,13}, {22,31}, {23,27}, {10,29}, {2,23}, {16,26}, {4,15}, {24,39}, {23,36}, {1,10}, {12,38}, {6,36}, {26,41}, {15,21}, {9,17}, {33,37}, {4,17}, {5,8}, {33,42}, {7,15}, {3,39}, {2,22}, {8,15}, {19,42}, {1,12}, {3,32}, {6,35}, {10,26}, {2,13}, {1,11}, {20,29}, {18,19}, {11,20}, {17,32}, {16,35}, {4,26}, {25,36}, {16,25}, {13,21}, {1,32}, {4,32}, {8,28}, {18,23}, {6,34}, {17,33}, {8,34}, {3,8}, {4,16}, {4,8}, {32,39}, {15,35}, {30,37}, {17,27}, {21,30}, {18,32}, {28,42}, {17,24}, {5,36}, {6,14}, {21,32}, {17,28}, {1,24}, {12,36}, {8,27}, {29,39}, {17,23}, {2,9}, {11,37}, {1,23}, {10,33}, {4,20}, {23,39}, {23,35}, {34,41}, {12,16}, {4,42}, {24,25}, {16,36}, {12,35}, {6,30}, {27,32}, {2,12}, {29,37}, {17,20}, {12,19}, {34,42}, {6,28}, {7,16}, {4,39}, {1,25}, {10,18}, {26,42}, {3,16}, {22,30}, {18,31}, {3,7}, {2,11}, {34,37}, {5,38}, {21,41}, {8,22}, {7,39}, {11,41}, {11,38}, {10,19}, {6,7}, {36,40}, {8,23}, {5,14}, {10,39}, {3,25}, {4,41}, {11,42}, {22,34}, {7,40}, {30,40}, {18,24}, {36,39}, {1,13}, {9,14}, {2,37}, {3,19}, {12,28}, {23,25}, {16,21}, {7,23}, {5,29}, {28,31}, {14,27}, {10,30}, {11,35}, {28,41}, {16,30}, {19,36}, {2,32}, {14,42}, {5,28}, {14,21}, {5,30}, {14,40}, {18,38}, {18,20}, {22,33}, {3,26}, {13,27}, {17,34}, {25,33}, {25,35}, {29,31}, {27,31}, {30,31}, {1,26}, {25,34}, {15,38}, {16,29}, {9,33}, {26,35}, {15,22}, {8,24}, {6,38}, {32,40}, {23,38}, {11,19}, {9,39}, {1,22}, {5,7}, {18,37}, {13,40}, {9,19}, {13,42}, {15,37}, {8,21}, {6,20}, {6,33}, {13,35}, {2,10} } Symmetric graph 40 of order 42 Valency 16 Diameter 2 Girth 3 Automorphism group of order 704643072 Number of arcs = 672 Number of 2-arcs = 10080 2-arc-transitive false Edge-set { {1,15}, {9,21}, {6,24}, {15,33}, {30,36}, {24,32}, {3,34}, {9,37}, {16,24}, {26,40}, {17,40}, {32,41}, {14,34}, {19,38}, {2,15}, {7,30}, {10,32}, {23,34}, {3,30}, {3,11}, {5,41}, {12,14}, {7,38}, {15,20}, {1,35}, {8,31}, {9,22}, {5,24}, {18,26}, {16,41}, {14,29}, {31,38}, {19,26}, {1,40}, {13,19}, {1,27}, {5,23}, {4,12}, {7,14}, {20,28}, {1,18}, {8,26}, {9,36}, {21,39}, {6,18}, {17,42}, {13,25}, {15,34}, {30,35}, {23,32}, {4,34}, {12,30}, {22,37}, {5,10}, {12,23}, {7,25}, {20,39}, {1,42}, {8,13}, {31,37}, {3,21}, {6,9}, {8,35}, {19,31}, {21,28}, {6,42}, {23,31}, {4,33}, {14,20}, {2,28}, {7,18}, {20,26}, {27,36}, {12,21}, {6,22}, {17,30}, {25,37}, {15,40}, {10,36}, {12,24}, {3,22}, {6,11}, {11,21}, {8,29}, {9,38}, {15,24}, {26,39}, {18,40}, {31,41}, {14,33}, {20,38}, {14,26}, {28,40}, {2,34}, {7,35}, {16,23}, {4,29}, {14,31}, {28,33}, {18,29}, {26,38}, {4,36}, {6,21}, {8,17}, {19,25}, {2,42}, {7,13}, {19,33}, {1,36}, {17,39}, {18,25}, {35,42}, {13,31}, {27,33}, {36,41}, {31,42}, {13,33}, {20,37}, {2,16}, {7,36}, {20,32}, {22,27}, {12,18}, {22,26}, {32,37}, {28,36}, {24,34}, {3,35}, {11,26}, {21,40}, {2,29}, {3,9}, {9,24}, {16,40}, {17,29}, {14,32}, {28,34}, {19,34}, {13,24}, {3,27}, {17,25}, {25,39}, {8,30}, {9,32}, {4,30}, {10,37}, {3,12}, {5,42}, {12,13}, {7,37}, {16,20}, {8,32}, {9,41}, {22,38}, {5,15}, {18,39}, {10,31}, {23,33}, {20,25}, {2,39}, {7,42}, {13,20}, {27,37}, {12,25}, {22,39}, {1,30}, {8,37}, {20,40}, {2,17}, {24,33}, {3,36}, {11,17}, {21,25}, {29,35}, {5,11}, {8,18}, {35,37}, {16,31}, {6,17}, {4,11}, {10,21}, {12,29}, {6,39}, {11,18}, {8,42}, {28,37}, {16,42}, {5,40}, {12,17}, {11,13}, {16,19}, {2,36}, {7,32}, {10,22}, {17,26}, {22,28}, {30,34}, {2,41}, {27,40}, {17,41}, {32,38}, {19,39}, {13,30}, {3,33}, {22,25}, {5,39}, {15,19}, {15,32}, {3,10}, {9,23}, {11,25}, {7,41}, {27,38}, {15,41}, {35,38}, {15,31}, {19,28}, {11,29}, {21,38}, {10,38}, {25,40}, {14,30}, {2,40}, {7,29}, {14,19}, {1,28}, {6,23}, {8,14}, {2,18}, {7,26}, {14,25}, {1,34}, {4,24}, {13,29}, {16,33}, {29,36}, {4,22}, {8,36}, {19,32}, {28,38}, {10,35}, {21,26}, {6,40}, {11,22}, {5,21}, {16,34}, {19,40}, {1,17}, {21,27}, {29,33}, {36,38}, {13,23}, {4,27}, {10,42}, {11,24}, {2,27}, {28,39}, {6,10}, {11,23}, {3,23}, {4,9}, {11,14}, {19,27}, {22,40}, {5,17}, {18,41}, {11,30}, {21,37}, {27,34}, {35,41}, {5,22}, {5,12}, {3,28}, {9,42}, {1,41}, {4,35}, {19,37}, {1,16}, {29,34}, {4,23}, {4,10}, {9,35}, {24,31}, {14,24}, {1,29}, {30,33}, {5,18}, {12,26}, {5,9}, {1,39}, {27,35}, {27,39}, {1,33}, {3,29}, {20,31}, {6,41}, {7,17}, {12,22}, {18,30}, {26,37}, {6,15}, {8,25}, {20,34}, {2,35}, {8,41}, {16,39}, {36,37}, {3,24}, {13,34}, {15,23}, {9,31}, {36,42}, {6,16}, {13,32}, {10,41}, {2,30}, {20,27}, {28,35}, {4,21}, {13,26}, {2,33}, {15,42}, {14,23}, {4,28}, {6,12}, {7,31}, {25,38}, {15,39}, {32,42}, {18,42}, {10,23}, {8,38}, {10,24}, {5,16}, {20,33}, {16,32} } Symmetric graph 41 of order 42 Valency 18 Diameter 3 Girth 4 Automorphism group of order 789910774087680 Number of arcs = 756 Number of 2-arcs = 12852 2-arc-transitive false Edge-set { {1,4}, {28,33}, {19,35}, {15,16}, {11,25}, {6,21}, {29,37}, {2,42}, {2,18}, {12,39}, {32,40}, {5,31}, {21,28}, {14,23}, {22,26}, {27,29}, {8,36}, {1,29}, {1,36}, {22,37}, {24,31}, {17,26}, {9,12}, {18,32}, {10,20}, {5,15}, {25,28}, {9,41}, {14,16}, {7,10}, {15,42}, {11,14}, {26,41}, {19,34}, {4,38}, {14,28}, {26,35}, {19,28}, {35,38}, {7,23}, {15,22}, {8,18}, {10,13}, {3,10}, {3,42}, {36,37}, {6,31}, {1,17}, {1,12}, {30,33}, {32,42}, {18,20}, {12,15}, {25,40}, {25,36}, {6,7}, {2,41}, {2,16}, {5,33}, {27,42}, {39,41}, {16,32}, {10,25}, {7,42}, {6,20}, {29,39}, {24,33}, {19,23}, {15,41}, {16,25}, {10,21}, {37,42}, {6,15}, {25,29}, {21,24}, {23,37}, {9,35}, {5,14}, {15,18}, {1,34}, {38,40}, {17,33}, {30,38}, {33,34}, {27,30}, {8,34}, {22,38}, {18,31}, {3,28}, {3,35}, {28,37}, {31,35}, {13,16}, {11,27}, {17,27}, {8,12}, {1,30}, {12,26}, {9,40}, {12,19}, {5,21}, {7,36}, {2,29}, {2,36}, {11,20}, {8,41}, {22,25}, {7,24}, {2,17}, {2,12}, {12,38}, {33,40}, {27,35}, {5,8}, {4,31}, {21,30}, {14,22}, {24,26}, {8,16}, {11,13}, {6,9}, {14,29}, {25,42}, {7,18}, {2,40}, {5,38}, {23,27}, {8,22}, {31,42}, {18,21}, {12,14}, {26,40}, {13,28}, {9,23}, {21,36}, {6,37}, {32,41}, {16,20}, {1,42}, {1,18}, {20,28}, {35,39}, {3,16}, {3,11}, {13,24}, {11,39}, {27,41}, {20,34}, {4,39}, {15,23}, {1,10}, {15,30}, {25,34}, {34,37}, {10,37}, {3,41}, {26,36}, {29,31}, {5,32}, {19,29}, {36,38}, {30,32}, {4,7}, {7,12}, {15,40}, {8,35}, {5,13}, {3,29}, {3,36}, {31,36}, {24,37}, {23,31}, {16,26}, {9,11}, {11,21}, {37,41}, {32,34}, {4,20}, {18,33}, {10,19}, {27,28}, {7,41}, {8,10}, {13,42}, {2,34}, {2,4}, {39,40}, {17,32}, {14,41}, {12,27}, {8,40}, {1,35}, {1,5}, {26,29}, {9,36}, {24,32}, {20,23}, {7,34}, {4,15}, {18,27}, {1,28}, {16,31}, {10,26}, {9,42}, {17,25}, {6,14}, {5,19}, {28,38}, {21,22}, {2,30}, {25,30}, {30,39}, {13,17}, {22,39}, {22,33}, {19,24}, {14,18}, {33,35}, {12,20}, {23,38}, {38,42}, {35,37}, {26,42}, {9,18}, {21,34}, {4,37}, {17,20}, {14,30}, {26,34}, {19,30}, {34,38}, {18,19}, {10,38}, {8,23}, {13,22}, {10,14}, {2,10}, {36,39}, {6,32}, {5,39}, {28,32}, {23,25}, {7,22}, {4,33}, {1,16}, {1,11}, {6,38}, {29,33}, {11,15}, {25,41}, {25,35}, {5,7}, {27,40}, {8,17}, {20,29}, {19,36}, {9,24}, {3,17}, {3,12}, {7,16}, {11,37}, {31,41}, {4,9}, {20,35}, {12,13}, {33,42}, {1,41}, {15,28}, {27,36}, {6,8}, {3,40}, {16,21}, {15,24}, {13,29}, {24,27}, {30,31}, {21,23}, {10,27}, {8,42}, {1,6}, {5,20}, {28,39}, {23,33}, {19,22}, {3,4}, {3,30}, {13,41}, {16,27}, {39,42}, {6,13}, {20,24}, {23,39}, {24,38}, {9,34}, {4,14}, {7,40}, {15,17}, {38,41}, {16,33}, {29,38}, {33,36}, {17,31}, {12,21}, {22,32}, {12,25}, {14,40}, {7,35}, {11,19}, {2,28}, {2,35}, {32,35}, {11,26}, {37,40}, {3,34}, {26,30}, {6,19}, {30,37}, {31,34}, {2,5}, {18,25}, {4,21}, {8,11}, {13,18}, {5,9}, {11,38}, {33,41}, {27,34}, {4,8}, {28,31}, {21,35}, {4,32}, {20,30}, {24,25}, {9,16}, {15,29}, {13,30}, {7,17}, {2,11}, {22,27}, {8,24}, {31,40}, {17,21}, {9,22}, {14,24}, {13,23}, {20,36}, {6,39}, {16,19}, {3,18}, {23,26}, {5,37}, {12,37}, {29,32}, {21,29}, {10,39}, {34,39}, {1,40}, {32,36}, {24,39}, {23,32}, {7,11}, {4,19}, {4,13}, {13,40}, {2,6}, {14,42}, {18,26}, {3,5}, {9,10}, {14,17}, {22,31}, {20,22}, {26,28}, {17,19}, {9,17}, {6,33}, {10,15}, {3,6} } Symmetric graph 42 of order 42 Valency 20 Diameter 2 Girth 3 Automorphism group of order 10569646080 Number of arcs = 840 Number of 2-arcs = 15960 2-arc-transitive false Edge-set { {1,23}, {7,36}, {5,27}, {16,25}, {13,36}, {31,41}, {23,37}, {6,29}, {3,41}, {12,16}, {9,13}, {20,24}, {17,30}, {28,36}, {27,40}, {22,32}, {19,24}, {20,39}, {17,34}, {6,17}, {3,15}, {12,37}, {9,31}, {10,35}, {7,28}, {4,21}, {11,20}, {16,42}, {13,38}, {13,41}, {22,37}, {1,29}, {9,35}, {8,28}, {10,14}, {7,21}, {4,34}, {11,25}, {4,32}, {11,24}, {5,39}, {17,28}, {15,40}, {24,37}, {30,31}, {15,38}, {14,32}, {25,42}, {36,38}, {2,40}, {2,33}, {10,18}, {7,16}, {6,19}, {3,18}, {12,27}, {9,39}, {12,20}, {9,17}, {1,28}, {1,40}, {7,22}, {5,19}, {15,37}, {14,31}, {26,42}, {35,38}, {11,38}, {10,32}, {2,25}, {2,36}, {34,40}, {25,33}, {18,29}, {16,41}, {23,40}, {29,33}, {18,35}, {16,28}, {21,23}, {4,42}, {5,13}, {4,22}, {28,35}, {28,40}, {21,24}, {20,30}, {4,39}, {11,23}, {10,29}, {19,29}, {18,41}, {16,27}, {13,39}, {8,13}, {6,22}, {8,33}, {6,26}, {3,38}, {12,32}, {6,25}, {3,36}, {9,32}, {8,24}, {3,39}, {12,34}, {17,41}, {14,37}, {21,31}, {10,17}, {7,15}, {4,37}, {11,31}, {7,42}, {5,38}, {7,13}, {5,22}, {1,25}, {1,36}, {8,23}, {5,28}, {4,40}, {10,30}, {19,30}, {18,42}, {15,27}, {14,39}, {18,27}, {16,39}, {23,38}, {29,32}, {8,29}, {6,41}, {8,16}, {6,13}, {13,34}, {22,25}, {26,41}, {3,22}, {12,19}, {6,20}, {3,17}, {22,27}, {22,33}, {19,26}, {12,14}, {6,42}, {2,27}, {19,40}, {18,33}, {12,31}, {9,23}, {1,33}, {15,42}, {14,38}, {13,42}, {22,38}, {2,35}, {2,28}, {10,21}, {7,20}, {14,40}, {21,33}, {18,36}, {19,32}, {9,22}, {8,19}, {3,20}, {12,17}, {3,37}, {9,21}, {12,26}, {1,32}, {1,24}, {26,33}, {26,35}, {30,32}, {24,42}, {27,39}, {34,39}, {17,23}, {15,29}, {24,41}, {29,31}, {21,34}, {15,25}, {4,20}, {11,17}, {11,28}, {10,40}, {2,24}, {2,30}, {4,38}, {11,32}, {5,25}, {4,36}, {33,40}, {18,24}, {16,30}, {19,25}, {27,31}, {23,39}, {12,25}, {9,36}, {1,31}, {7,29}, {5,41}, {26,36}, {27,35}, {31,42}, {13,40}, {21,38}, {20,32}, {8,20}, {3,19}, {12,18}, {11,14}, {6,14}, {3,21}, {27,36}, {22,23}, {22,26}, {19,35}, {17,24}, {3,35}, {9,24}, {9,25}, {1,41}, {17,42}, {1,39}, {1,34}, {8,15}, {7,24}, {11,34}, {1,37}, {1,26}, {9,30}, {8,42}, {10,15}, {8,41}, {6,37}, {8,22}, {3,33}, {15,30}, {36,37}, {7,33}, {5,26}, {4,18}, {11,27}, {10,39}, {9,18}, {1,27}, {6,38}, {2,38}, {2,32}, {10,25}, {11,13}, {10,22}, {2,26}, {3,16}, {12,13}, {9,26}, {8,35}, {7,34}, {4,17}, {11,15}, {28,39}, {2,37}, {2,31}, {7,23}, {5,29}, {7,35}, {30,33}, {14,42}, {20,29}, {18,28}, {14,41}, {21,37}, {14,34}, {21,25}, {4,19}, {20,35}, {22,24}, {2,34}, {4,41}, {11,16}, {16,38}, {6,28}, {8,21}, {33,39}, {18,23}, {16,29}, {23,41}, {16,40}, {13,33}, {12,28}, {6,21}, {9,29}, {30,37}, {14,36}, {21,27}, {17,29}, {15,41}, {16,37}, {13,31}, {5,30}, {19,36}, {20,31}, {18,30}, {2,39}, {10,23}, {10,26}, {8,34}, {12,15}, {11,18}, {10,16}, {10,24}, {13,37}, {1,30}, {1,42}, {9,15}, {8,14}, {4,35}, {15,39}, {35,37}, {28,31}, {29,37}, {5,17}, {7,14}, {5,21}, {25,35}, {18,34}, {5,40}, {7,30}, {5,42}, {20,26}, {17,35}, {28,32}, {24,40}, {1,35}, {26,34}, {23,42}, {3,40}, {12,33}, {21,32}, {7,41}, {5,37}, {27,32}, {24,39}, {8,27}, {6,39}, {29,38}, {32,41}, {9,16}, {1,38}, {8,30}, {3,34}, {15,26}, {14,35}, {25,34}, {25,36}, {11,33}, {5,18}, {4,16}, {6,40}, {6,30}, {22,31}, {19,23}, {11,19}, {7,19}, {3,42}, {12,38}, {2,29}, {2,41}, {9,40}, {20,40}, {17,33}, {6,18}, {6,27}, {32,42}, {24,38}, {14,33}, {21,26}, {20,36}, {17,27}, {19,31}, {21,28}, {10,13}, {5,20}, {12,24}, {20,23}, {30,38}, {4,15}, {3,32}, {4,31}, {11,26}, {5,14}, {15,28}, {22,28}, {10,36}, {2,23}, {13,35}, {30,34}, {22,34}, {20,25}, {17,36}, {19,39}, {3,31}, {7,27}, {29,34}, {25,41}, {16,26}, {12,23}, {13,32}, {8,36}, {4,33}, {2,42}, {11,37}, {10,31}, {9,14} } Symmetric graph 43 of order 42 Valency 20 Diameter 2 Girth 3 Automorphism group of order 10569646080 Number of arcs = 840 Number of 2-arcs = 15960 2-arc-transitive false Edge-set { {1,3}, {7,9}, {21,29}, {1,5}, {12,40}, {39,42}, {19,27}, {4,9}, {21,36}, {11,21}, {37,42}, {22,35}, {9,38}, {31,33}, {2,3}, {5,8}, {12,30}, {29,42}, {19,33}, {12,42}, {19,41}, {16,35}, {30,41}, {20,34}, {5,15}, {8,12}, {14,24}, {5,31}, {7,10}, {22,29}, {2,4}, {36,39}, {11,40}, {28,42}, {35,39}, {9,27}, {24,33}, {2,5}, {11,35}, {9,42}, {33,36}, {2,10}, {28,30}, {15,34}, {36,40}, {10,28}, {23,34}, {1,6}, {4,27}, {16,36}, {2,11}, {26,38}, {13,24}, {4,14}, {31,36}, {39,41}, {20,27}, {8,10}, {22,30}, {33,38}, {12,21}, {37,41}, {32,35}, {34,38}, {3,12}, {24,26}, {5,24}, {4,10}, {22,36}, {34,41}, {5,35}, {9,12}, {24,29}, {5,33}, {6,10}, {11,22}, {32,40}, {4,28}, {23,27}, {6,16}, {33,37}, {6,32}, {4,11}, {23,25}, {6,23}, {3,9}, {21,35}, {8,31}, {3,30}, {28,29}, {15,33}, {10,12}, {22,41}, {15,18}, {8,26}, {26,37}, {8,38}, {13,30}, {14,29}, {10,38}, {31,34}, {2,6}, {11,39}, {40,41}, {20,28}, {15,24}, {11,42}, {19,42}, {32,34}, {15,23}, {6,8}, {7,11}, {18,26}, {4,26}, {24,36}, {11,30}, {29,41}, {20,33}, {23,36}, {4,30}, {34,36}, {5,11}, {26,39}, {24,27}, {4,24}, {5,36}, {3,6}, {12,41}, {20,41}, {13,21}, {32,37}, {8,32}, {25,31}, {3,23}, {3,28}, {15,35}, {16,24}, {5,7}, {3,13}, {17,25}, {3,25}, {23,35}, {12,29}, {30,42}, {19,34}, {2,14}, {31,39}, {7,40}, {32,39}, {5,16}, {6,11}, {36,41}, {10,20}, {16,17}, {2,18}, {16,18}, {7,26}, {2,15}, {8,39}, {37,40}, {14,28}, {38,39}, {13,27}, {6,15}, {8,11}, {14,23}, {6,31}, {3,10}, {12,22}, {38,41}, {10,37}, {1,4}, {26,27}, {12,35}, {9,41}, {33,35}, {2,9}, {13,23}, {25,27}, {16,23}, {1,12}, {18,19}, {17,26}, {8,18}, {26,30}, {26,29}, {28,41}, {10,27}, {24,34}, {25,29}, {23,33}, {8,40}, {23,29}, {6,33}, {4,12}, {18,22}, {26,31}, {3,24}, {24,30}, {4,29}, {3,7}, {29,35}, {11,36}, {10,42}, {1,10}, {14,19}, {13,16}, {7,32}, {2,13}, {14,17}, {7,25}, {27,30}, {16,34}, {26,28}, {7,37}, {17,20}, {18,25}, {7,17}, {25,30}, {27,42}, {35,40}, {9,28}, {13,22}, {14,22}, {31,38}, {1,21}, {32,38}, {15,36}, {35,41}, {29,36}, {10,33}, {6,34}, {1,11}, {10,19}, {17,22}, {19,28}, {15,17}, {1,18}, {26,40}, {16,22}, {2,22}, {16,21}, {4,13}, {15,22}, {31,37}, {3,14}, {3,27}, {2,12}, {25,38}, {31,35}, {6,7}, {11,29}, {11,41}, {20,42}, {8,9}, {21,30}, {18,31}, {3,26}, {34,42}, {5,34}, {5,10}, {25,37}, {17,31}, {25,28}, {9,11}, {21,42}, {2,17}, {18,20}, {2,19}, {17,39}, {18,40}, {18,39}, {32,36}, {3,11}, {23,26}, {6,24}, {24,25}, {5,23}, {2,21}, {37,39}, {25,39}, {14,18}, {24,28}, {1,7}, {29,40}, {30,39}, {27,34}, {33,41}, {6,35}, {6,9}, {28,37}, {14,15}, {1,13}, {20,38}, {13,18}, {1,17}, {25,40}, {31,40}, {23,28}, {18,32}, {1,16}, {17,19}, {1,20}, {17,40}, {34,37}, {5,32}, {14,20}, {13,20}, {19,21}, {13,15}, {27,29}, {16,33}, {30,36}, {10,34}, {29,39}, {27,33}, {21,41}, {32,33}, {9,19}, {17,21}, {18,21}, {15,20}, {10,41}, {20,22}, {15,19}, {8,37}, {14,30}, {27,41}, {16,20}, {14,16}, {7,31}, {7,38}, {13,29}, {3,29}, {10,11}, {22,42}, {8,25}, {12,39}, {12,36}, {34,35}, {1,9}, {40,42}, {7,18}, {4,23}, {6,36}, {4,6}, {17,32}, {4,25}, {5,12}, {35,42}, {18,38}, {17,37}, {19,22}, {17,38}, {7,12}, {24,35}, {19,38}, {13,17}, {26,32}, {21,40}, {21,39}, {27,37}, {22,40}, {28,38}, {23,31}, {3,5}, {16,32}, {4,7}, {27,38}, {9,37}, {14,21}, {1,8}, {19,37}, {9,20}, {25,32}, {13,19}, {15,21}, {9,34}, {20,21}, {18,37}, {1,14}, {33,42}, {28,33}, {22,39}, {24,31}, {36,42}, {2,16}, {7,39}, {38,40}, {13,28}, {28,34}, {1,15}, {14,27}, {6,12}, {38,42}, {23,30}, {5,9}, {1,19}, {3,8}, {30,35}, {8,17}, {2,20}, {2,8}, {20,37}, {16,31}, {15,32}, {4,8}, {14,25}, {30,40}, {15,31}, {2,7}, {16,19}, {24,32}, {4,5}, {14,26}, {9,33}, {1,22}, {23,32}, {13,25}, {13,26} } Symmetric graph 44 of order 42 Valency 20 Diameter 3 Girth 4 Automorphism group of order 102181884343418880000 Number of arcs = 840 Number of 2-arcs = 15960 2-arc-transitive true Edge-set { {1,3}, {24,42}, {12,15}, {18,19}, {6,22}, {6,33}, {20,36}, {21,31}, {17,33}, {36,40}, {14,31}, {30,40}, {1,14}, {1,32}, {18,28}, {35,37}, {32,40}, {22,30}, {1,34}, {1,8}, {28,29}, {13,37}, {25,40}, {8,26}, {29,41}, {13,24}, {15,25}, {24,38}, {15,39}, {15,21}, {8,33}, {2,4}, {24,27}, {8,38}, {29,39}, {26,36}, {31,41}, {24,29}, {2,15}, {3,15}, {8,42}, {4,14}, {24,26}, {8,9}, {29,37}, {10,27}, {3,38}, {20,25}, {21,42}, {14,18}, {6,26}, {6,9}, {20,37}, {3,18}, {6,23}, {6,7}, {20,30}, {6,35}, {20,32}, {27,30}, {23,41}, {11,16}, {16,18}, {3,27}, {3,23}, {7,25}, {30,42}, {1,10}, {28,38}, {21,40}, {18,25}, {6,42}, {16,20}, {12,20}, {19,27}, {3,22}, {13,41}, {11,25}, {10,18}, {6,38}, {12,27}, {3,9}, {4,25}, {7,10}, {3,42}, {12,23}, {9,32}, {18,37}, {19,35}, {22,32}, {13,21}, {25,33}, {10,40}, {14,38}, {12,40}, {9,14}, {4,32}, {18,24}, {12,33}, {17,40}, {5,14}, {28,40}, {26,32}, {18,41}, {2,40}, {14,27}, {32,38}, {18,39}, {16,26}, {7,41}, {17,20}, {5,21}, {5,34}, {19,33}, {16,42}, {7,12}, {17,42}, {5,12}, {9,28}, {4,37}, {19,26}, {22,41}, {11,24}, {10,15}, {8,23}, {8,35}, {29,32}, {9,21}, {33,37}, {19,40}, {14,22}, {5,32}, {32,33}, {18,36}, {16,31}, {7,17}, {36,42}, {12,31}, {14,20}, {21,26}, {9,34}, {11,21}, {10,33}, {3,40}, {14,23}, {16,33}, {7,36}, {12,42}, {9,12}, {9,41}, {11,37}, {11,28}, {4,10}, {19,42}, {12,22}, {5,36}, {12,38}, {9,39}, {4,21}, {24,33}, {2,31}, {17,27}, {36,38}, {31,39}, {14,35}, {9,30}, {1,37}, {8,11}, {10,29}, {3,13}, {23,25}, {29,36}, {12,13}, {9,25}, {38,41}, {11,39}, {18,21}, {30,33}, {1,36}, {8,22}, {29,34}, {13,39}, {13,25}, {8,15}, {8,29}, {10,38}, {38,39}, {20,21}, {21,33}, {16,29}, {13,16}, {23,39}, {7,21}, {5,10}, {19,38}, {20,28}, {18,34}, {35,39}, {13,32}, {2,13}, {30,31}, {1,17}, {5,19}, {19,22}, {28,33}, {4,36}, {22,34}, {33,39}, {13,36}, {4,41}, {10,31}, {17,38}, {6,11}, {10,20}, {3,5}, {2,27}, {25,38}, {39,42}, {12,35}, {4,30}, {1,24}, {8,31}, {17,29}, {25,31}, {30,38}, {1,39}, {1,21}, {5,37}, {22,28}, {4,34}, {1,19}, {10,35}, {12,29}, {2,9}, {34,35}, {32,35}, {11,30}, {13,17}, {5,25}, {5,30}, {1,28}, {4,28}, {22,36}, {9,36}, {24,35}, {15,34}, {11,41}, {10,11}, {19,31}, {17,22}, {33,36}, {31,36}, {13,28}, {3,33}, {23,36}, {35,41}, {11,32}, {18,30}, {1,6}, {23,37}, {16,40}, {16,22}, {7,34}, {23,28}, {7,37}, {25,27}, {12,26}, {4,24}, {15,24}, {27,34}, {3,35}, {10,42}, {14,42}, {9,17}, {1,25}, {28,42}, {14,33}, {9,37}, {3,20}, {21,23}, {30,35}, {21,35}, {26,30}, {1,41}, {15,28}, {27,36}, {3,31}, {25,29}, {2,42}, {7,14}, {26,37}, {6,27}, {3,11}, {10,23}, {3,7}, {23,30}, {18,32}, {28,35}, {10,13}, {17,23}, {15,32}, {8,18}, {21,29}, {2,33}, {2,7}, {26,39}, {40,41}, {22,24}, {17,31}, {15,30}, {7,30}, {1,30}, {26,28}, {20,41}, {23,34}, {34,40}, {16,23}, {7,16}, {7,19}, {26,41}, {6,15}, {27,37}, {22,25}, {34,42}, {37,40}, {3,26}, {7,24}, {4,39}, {15,36}, {2,11}, {24,31}, {15,17}, {9,16}, {2,29}, {2,38}, {27,39}, {26,34}, {15,41}, {28,31}, {1,12}, {2,18}, {6,29}, {2,20}, {20,34}, {11,34}, {31,37}, {31,34}, {14,15}, {5,28}, {21,27}, {34,38}, {33,41}, {24,40}, {4,17}, {5,24}, {5,8}, {19,29}, {6,18}, {6,20}, {11,19}, {10,22}, {13,19}, {9,24}, {15,37}, {15,19}, {13,30}, {4,12}, {32,42}, {12,18}, {17,35}, {2,26}, {27,41}, {2,35}, {27,32}, {10,26}, {20,24}, {8,20}, {1,16}, {7,28}, {37,42}, {19,23}, {11,17}, {17,26}, {5,41}, {21,38}, {8,27}, {11,14}, {20,39}, {25,35}, {4,16}, {6,31}, {22,37}, {2,5}, {5,17}, {4,19}, {6,40}, {2,22}, {4,8}, {4,6}, {16,35}, {9,19}, {8,40}, {23,32}, {6,13}, {8,13}, {7,32}, {3,29}, {2,23}, {11,36}, {14,26}, {22,39}, {16,38}, {16,27}, {7,39}, {13,34}, {14,40}, {14,29}, {5,39}, {25,42}, {5,16} } Symmetric graph 45 of order 42 Valency 21 Diameter 2 Girth 4 Automorphism group of order 5220568743985916218538183570227200000000 Number of arcs = 882 Number of 2-arcs = 17640 2-arc-transitive true Edge-set { {1,4}, {2,5}, {24,32}, {22,33}, {20,34}, {21,40}, {19,35}, {19,42}, {9,11}, {23,37}, {7,18}, {8,12}, {22,39}, {8,16}, {29,39}, {27,41}, {10,14}, {34,37}, {30,38}, {26,42}, {11,13}, {36,38}, {4,26}, {13,17}, {3,28}, {32,40}, {11,27}, {6,25}, {15,16}, {2,29}, {31,41}, {10,25}, {15,24}, {2,35}, {5,31}, {18,21}, {8,30}, {13,29}, {14,23}, {1,36}, {4,33}, {17,20}, {7,28}, {14,28}, {1,40}, {12,33}, {20,22}, {7,34}, {6,38}, {16,26}, {2,4}, {3,41}, {10,32}, {19,24}, {9,35}, {5,37}, {18,25}, {3,5}, {18,32}, {19,30}, {9,42}, {11,37}, {23,25}, {15,36}, {24,33}, {17,31}, {21,28}, {8,40}, {12,39}, {22,27}, {14,34}, {1,6}, {22,31}, {21,34}, {6,8}, {16,39}, {27,29}, {14,41}, {1,10}, {20,35}, {19,40}, {5,7}, {18,38}, {26,30}, {13,42}, {3,11}, {23,32}, {19,36}, {20,42}, {7,11}, {23,38}, {26,36}, {4,13}, {3,17}, {28,32}, {9,12}, {22,37}, {8,18}, {25,34}, {6,15}, {2,16}, {29,31}, {21,41}, {8,10}, {24,39}, {9,16}, {29,37}, {25,41}, {10,15}, {2,24}, {31,35}, {5,21}, {30,39}, {27,42}, {11,14}, {34,38}, {1,23}, {33,36}, {4,20}, {7,17}, {28,38}, {26,40}, {12,13}, {36,39}, {4,27}, {14,17}, {1,28}, {33,40}, {12,20}, {7,22}, {6,26}, {13,16}, {3,29}, {32,41}, {11,25}, {10,19}, {9,24}, {35,37}, {5,25}, {15,18}, {2,30}, {31,42}, {10,26}, {13,24}, {3,35}, {5,32}, {18,19}, {9,30}, {37,42}, {15,23}, {2,36}, {4,31}, {17,21}, {8,28}, {14,29}, {39,40}, {12,27}, {14,22}, {1,34}, {6,33}, {16,20}, {7,29}, {15,28}, {2,40}, {12,31}, {21,22}, {8,34}, {6,39}, {16,27}, {1,41}, {10,33}, {20,24}, {7,35}, {5,38}, {18,26}, {3,4}, {13,30}, {3,42}, {11,32}, {19,23}, {9,36}, {4,37}, {17,25}, {1,5}, {18,33}, {20,30}, {7,42}, {11,38}, {23,26}, {13,36}, {17,32}, {19,28}, {9,40}, {12,37}, {22,25}, {15,34}, {2,6}, {24,31}, {16,31}, {21,29}, {8,41}, {10,39}, {24,27}, {14,35}, {22,32}, {19,34}, {6,9}, {16,37}, {25,29}, {15,41}, {2,10}, {21,35}, {5,8}, {18,39}, {27,30}, {14,42}, {1,11}, {23,33}, {20,36}, {20,40}, {4,7}, {17,38}, {26,28}, {13,40}, {3,12}, {21,42}, {8,11}, {23,39}, {27,36}, {4,14}, {1,17}, {28,33}, {7,12}, {22,38}, {26,34}, {6,13}, {3,16}, {29,32}, {19,41}, {9,10}, {24,37}, {9,18}, {25,35}, {5,15}, {2,18}, {30,31}, {7,16}, {29,38}, {26,41}, {10,13}, {3,24}, {32,35}, {5,19}, {30,37}, {25,42}, {11,15}, {2,23}, {31,36}, {4,21}, {8,17}, {28,39}, {27,40}, {12,14}, {34,39}, {1,22}, {33,34}, {6,20}, {36,37}, {4,25}, {15,17}, {2,28}, {31,40}, {12,21}, {8,22}, {6,27}, {14,16}, {1,29}, {33,41}, {10,20}, {7,24}, {35,38}, {5,26}, {13,18}, {3,30}, {32,42}, {11,26}, {11,19}, {9,23}, {10,27}, {14,24}, {1,35}, {5,33}, {18,20}, {7,30}, {38,42}, {13,23}, {3,36}, {4,32}, {17,19}, {9,28}, {37,40}, {12,25}, {15,22}, {2,34}, {6,31}, {16,21}, {8,29}, {15,29}, {39,41}, {13,28}, {3,40}, {12,32}, {19,22}, {9,34}, {6,37}, {16,25}, {2,41}, {10,31}, {21,24}, {8,35}, {5,39}, {18,27}, {14,30}, {1,42}, {11,33}, {20,23}, {7,36}, {4,38}, {17,26}, {18,31}, {21,30}, {8,42}, {11,39}, {23,27}, {14,36}, {17,33}, {20,28}, {7,40}, {12,38}, {22,26}, {13,34}, {3,6}, {16,32}, {19,29}, {9,41}, {10,37}, {24,25}, {15,35}, {6,7}, {16,38}, {26,29}, {13,41}, {3,10}, {5,9}, {18,37}, {25,30}, {15,42}, {2,11}, {23,31}, {21,36}, {4,8}, {17,39}, {27,28}, {14,40}, {1,12}, {25,36}, {4,15}, {2,17}, {28,31}, {27,34}, {6,14}, {1,16}, {29,33}, {20,41}, {7,10}, {24,38}, {26,35}, {5,13}, {3,18}, {30,32}, {1,24}, {33,35}, {5,20}, {3,23}, {32,36}, {4,19}, {9,17}, {28,37}, {25,40}, {12,15}, {2,22}, {31,34}, {6,21}, {12,19}, {9,22}, {10,21}, {8,24}, {35,39}, {5,27}, {14,18}, {1,30}, {33,42}, {11,20}, {7,23}, {39,42}, {38,40}, {12,26}, {13,22}, {3,34}, {6,32}, {16,19}, {9,29}, {37,41}, {15,30}, {2,42}, {11,31}, {21,23}, {8,36}, {4,39}, {17,27}, {16,33}, {20,29}, {7,41}, {10,38}, {24,26}, {13,35}, {4,9}, {17,37}, {25,28}, {15,40}, {2,12}, {27,35}, {5,14}, {1,18}, {30,33}, {3,22}, {32,34}, {6,19}, {11,21}, {8,23}, {38,41} } Symmetric graph 46 of order 42 Valency 24 Diameter 2 Girth 3 Automorphism group of order 1008 Number of arcs = 1008 Number of 2-arcs = 23184 2-arc-transitive false Edge-set { {1,5}, {18,36}, {21,24}, {32,40}, {15,17}, {14,29}, {1,32}, {8,22}, {9,12}, {19,31}, {13,38}, {6,20}, {25,37}, {22,36}, {9,24}, {13,25}, {2,4}, {1,26}, {5,29}, {24,28}, {8,33}, {10,21}, {35,39}, {16,30}, {12,39}, {34,40}, {13,40}, {2,17}, {14,26}, {21,39}, {39,40}, {17,35}, {20,22}, {36,38}, {24,41}, {6,18}, {21,25}, {4,14}, {23,25}, {4,7}, {3,29}, {30,32}, {11,41}, {5,33}, {14,27}, {1,11}, {29,36}, {8,42}, {12,16}, {8,21}, {31,35}, {13,22}, {20,38}, {37,41}, {11,29}, {32,36}, {8,11}, {12,36}, {31,41}, {13,18}, {13,30}, {2,31}, {10,40}, {9,14}, {16,32}, {15,19}, {29,39}, {17,20}, {20,37}, {15,39}, {3,40}, {17,27}, {6,34}, {5,22}, {9,27}, {2,9}, {11,28}, {18,23}, {7,21}, {37,42}, {2,36}, {6,40}, {17,25}, {7,25}, {4,10}, {1,33}, {25,29}, {4,32}, {8,18}, {13,21}, {2,39}, {10,30}, {11,34}, {2,6}, {25,28}, {22,40}, {9,17}, {2,25}, {4,28}, {1,40}, {17,29}, {21,32}, {5,21}, {27,39}, {24,35}, {3,8}, {12,30}, {20,26}, {5,37}, {22,33}, {19,28}, {33,38}, {6,11}, {25,36}, {30,31}, {13,31}, {31,34}, {11,19}, {8,34}, {12,23}, {31,37}, {13,42}, {16,42}, {16,19}, {2,21}, {26,37}, {5,42}, {26,35}, {26,28}, {15,32}, {3,15}, {27,29}, {6,32}, {7,12}, {10,34}, {35,40}, {17,22}, {8,16}, {12,19}, {31,39}, {3,17}, {20,30}, {23,36}, {7,24}, {6,39}, {25,40}, {9,20}, {25,32}, {4,15}, {21,29}, {32,39}, {11,35}, {3,5}, {27,30}, {2,42}, {16,28}, {16,35}, {19,22}, {4,39}, {26,40}, {8,13}, {2,12}, {26,31}, {5,13}, {4,17}, {8,36}, {12,24}, {6,31}, {22,29}, {9,32}, {18,29}, {11,37}, {36,42}, {14,41}, {1,18}, {25,34}, {4,23}, {30,38}, {12,18}, {21,34}, {13,23}, {2,7}, {26,33}, {10,23}, {7,35}, {2,16}, {17,40}, {5,24}, {8,27}, {8,39}, {24,42}, {2,28}, {28,33}, {25,42}, {4,16}, {1,15}, {10,39}, {7,33}, {10,14}, {14,33}, {29,35}, {22,32}, {12,38}, {34,41}, {7,18}, {38,41}, {18,41}, {4,38}, {26,41}, {9,38}, {19,34}, {23,38}, {6,37}, {16,22}, {9,19}, {1,27}, {6,29}, {3,42}, {8,41}, {2,13}, {25,33}, {1,28}, {29,33}, {11,24}, {5,30}, {27,31}, {15,40}, {1,6}, {11,16}, {19,36}, {12,40}, {26,30}, {5,31}, {22,39}, {9,40}, {17,19}, {11,22}, {9,36}, {2,41}, {18,28}, {18,34}, {21,23}, {27,42}, {10,22}, {4,33}, {33,41}, {14,18}, {13,28}, {2,33}, {11,17}, {20,36}, {8,38}, {12,41}, {1,35}, {24,38}, {18,21}, {17,31}, {13,20}, {1,14}, {1,29}, {16,24}, {8,19}, {6,13}, {22,26}, {5,9}, {15,25}, {28,34}, {7,40}, {10,17}, {15,24}, {39,42}, {16,40}, {3,20}, {5,10}, {27,35}, {15,29}, {29,42}, {15,21}, {3,39}, {6,22}, {7,41}, {3,30}, {27,41}, {33,35}, {14,22}, {8,31}, {12,13}, {1,21}, {4,42}, {11,25}, {4,36}, {7,14}, {1,10}, {4,35}, {7,26}, {7,39}, {17,33}, {14,20}, {3,11}, {30,36}, {23,27}, {6,7}, {30,37}, {20,23}, {7,37}, {6,41}, {18,25}, {9,42}, {27,32}, {6,15}, {9,10}, {11,15}, {20,35}, {10,26}, {5,35}, {28,42}, {16,33}, {10,15}, {3,35}, {13,33}, {2,14}, {36,37}, {6,16}, {19,25}, {7,34}, {9,25}, {4,11}, {21,35}, {23,39}, {24,26}, {6,23}, {5,18}, {21,27}, {24,37}, {16,36}, {19,24}, {14,28}, {28,40}, {1,8}, {12,29}, {5,38}, {18,24}, {11,13}, {8,26}, {5,12}, {28,31}, {5,17}, {9,35}, {15,26}, {32,42}, {15,16}, {3,32}, {10,42}, {3,13}, {2,30}, {17,23}, {7,20}, {9,23}, {7,11}, {20,32}, {15,37}, {4,21}, {26,39}, {23,35}, {7,22}, {30,40}, {10,25}, {1,9}, {36,41}, {29,32}, {24,31}, {21,30}, {6,36}, {24,25}, {16,21}, {19,39}, {18,26}, {38,40}, {16,26}, {6,12}, {3,31}, {14,19}, {1,38}, {10,36}, {12,14}, {30,34}, {23,31}, {3,18}, {18,42}, {6,19}, {25,38}, {19,29}, {32,38}, {13,16}, {2,19}, {5,34}, {9,37}, {11,42}, {23,41}, {2,37}, {4,8}, {24,32}, {7,17}, {10,20}, {20,27}, {3,36}, {24,30}, {17,41}, {18,20}, {27,38}, {11,27}, {7,13}, {2,34}, {23,28}, {5,40}, {16,27}, {27,34}, {15,30}, {12,27}, {9,16}, {22,37}, {19,38}, {3,26}, {28,38}, {30,41}, {18,31}, {3,38}, {23,33}, {3,19}, {17,34}, {28,39}, {33,40}, {20,28}, {29,41}, {18,32}, {14,38}, {1,41}, {29,37}, {1,34}, {14,17}, {4,20}, {12,26}, {4,24}, {10,18}, {14,32}, {4,41}, {19,33}, {22,34}, {3,7}, {22,27}, {15,31}, {2,27}, {6,28}, {22,30}, {9,31}, {34,38}, {11,38}, {15,41}, {13,27}, {5,8}, {26,36}, {14,24}, {14,39}, {33,36}, {8,10}, {12,35}, {1,16}, {24,34}, {8,23}, {33,37}, {17,30}, {1,20}, {32,34}, {15,23}, {7,32}, {21,33}, {28,35}, {10,28}, {9,15}, {31,42}, {5,14}, {10,37}, {35,42}, {12,21}, {14,42}, {5,19}, {1,37}, {8,15}, {4,30}, {6,9}, {35,37}, {20,31}, {13,37}, {11,20}, {22,42}, {19,26}, {2,10}, {21,37}, {23,40}, {3,25}, {3,4}, {23,29}, {3,12}, {34,39} } Symmetric graph 47 of order 42 Valency 24 Diameter 2 Girth 3 Automorphism group of order 63417876480 Number of arcs = 1008 Number of 2-arcs = 23184 2-arc-transitive false Edge-set { {1,7}, {6,17}, {12,41}, {3,27}, {9,26}, {15,31}, {19,39}, {3,7}, {12,14}, {2,37}, {19,26}, {30,34}, {35,41}, {14,24}, {1,17}, {7,41}, {15,29}, {27,39}, {5,33}, {11,21}, {2,14}, {10,22}, {6,35}, {23,31}, {19,32}, {29,40}, {18,27}, {6,27}, {12,26}, {17,31}, {19,41}, {5,30}, {7,35}, {3,24}, {4,21}, {10,36}, {16,37}, {15,40}, {5,29}, {11,27}, {13,38}, {16,38}, {3,23}, {9,32}, {17,34}, {20,41}, {14,33}, {9,36}, {5,23}, {7,28}, {3,25}, {3,9}, {12,15}, {2,39}, {19,27}, {26,34}, {31,41}, {14,19}, {4,10}, {6,10}, {17,23}, {32,41}, {1,40}, {7,18}, {8,15}, {13,24}, {31,38}, {25,33}, {21,29}, {26,36}, {23,30}, {4,9}, {5,10}, {7,16}, {3,40}, {22,28}, {25,34}, {22,29}, {1,39}, {7,17}, {14,20}, {33,37}, {22,27}, {26,35}, {31,42}, {13,19}, {27,36}, {31,37}, {4,39}, {10,17}, {8,17}, {4,41}, {1,11}, {1,14}, {7,37}, {15,26}, {30,39}, {5,35}, {11,24}, {3,14}, {12,22}, {2,35}, {19,31}, {19,34}, {29,41}, {14,27}, {2,13}, {8,38}, {3,13}, {9,38}, {17,26}, {20,31}, {19,33}, {6,36}, {12,23}, {17,28}, {25,41}, {18,26}, {30,42}, {30,40}, {18,28}, {22,34}, {1,36}, {9,37}, {5,15}, {12,24}, {2,31}, {10,39}, {8,37}, {4,13}, {10,38}, {17,25}, {7,23}, {4,16}, {11,22}, {1,35}, {5,16}, {17,27}, {26,41}, {29,42}, {13,27}, {21,33}, {21,36}, {7,38}, {3,16}, {2,32}, {20,34}, {30,41}, {14,28}, {7,24}, {3,31}, {21,34}, {8,24}, {26,38}, {26,42}, {8,19}, {6,16}, {12,40}, {6,29}, {12,27}, {17,33}, {21,41}, {2,30}, {10,35}, {6,24}, {4,23}, {10,32}, {16,40}, {18,40}, {1,29}, {7,27}, {15,38}, {16,39}, {11,32}, {14,34}, {22,41}, {14,35}, {9,31}, {5,19}, {7,29}, {11,28}, {18,34}, {22,42}, {1,30}, {22,37}, {2,26}, {19,42}, {13,34}, {14,36}, {15,39}, {17,39}, {8,27}, {4,26}, {11,31}, {1,19}, {12,28}, {2,25}, {6,20}, {6,23}, {8,28}, {4,25}, {22,38}, {16,35}, {12,31}, {21,37}, {10,30}, {18,39}, {11,34}, {13,35}, {24,38}, {18,33}, {21,42}, {1,26}, {17,41}, {8,29}, {12,32}, {10,29}, {3,26}, {2,19}, {5,20}, {7,30}, {3,28}, {15,36}, {24,37}, {1,25}, {11,33}, {10,31}, {6,19}, {4,27}, {17,40}, {18,41}, {7,34}, {15,35}, {18,42}, {12,34}, {2,22}, {2,20}, {14,42}, {9,29}, {23,39}, {5,9}, {7,15}, {3,39}, {21,27}, {15,19}, {6,11}, {13,23}, {32,38}, {9,18}, {13,20}, {33,38}, {25,36}, {23,29}, {28,36}, {23,25}, {6,9}, {5,12}, {3,41}, {22,30}, {25,35}, {24,29}, {16,20}, {33,40}, {27,35}, {16,19}, {27,32}, {34,37}, {10,14}, {9,17}, {5,41}, {8,16}, {4,40}, {6,12}, {16,21}, {2,11}, {28,35}, {27,31}, {24,30}, {24,26}, {3,42}, {2,12}, {2,8}, {34,40}, {6,41}, {5,11}, {9,13}, {8,18}, {4,42}, {1,8}, {34,38}, {16,22}, {29,32}, {34,39}, {15,21}, {10,13}, {6,38}, {24,25}, {35,40}, {28,32}, {18,22}, {21,28}, {32,37}, {15,20}, {5,42}, {33,39}, {5,38}, {1,12}, {2,7}, {11,14}, {4,7}, {30,31}, {18,21}, {36,40}, {9,14}, {3,8}, {23,26}, {28,31}, {19,25}, {17,22}, {30,32}, {20,25}, {15,22}, {35,39}, {11,16}, {11,13}, {20,27}, {5,37}, {17,24}, {4,14}, {10,37}, {3,15}, {14,30}, {9,40}, {22,33}, {25,37}, {13,28}, {22,36}, {1,31}, {9,39}, {5,17}, {4,31}, {11,39}, {4,15}, {7,19}, {11,23}, {1,32}, {5,18}, {25,42}, {13,29}, {23,36}, {3,32}, {14,29}, {7,20}, {3,33}, {21,35}, {27,38}, {26,37}, {10,19}, {18,25}, {2,36}, {8,23}, {11,40}, {4,32}, {3,34}, {10,40}, {6,18}, {2,18}, {11,42}, {23,35}, {9,19}, {28,37}, {8,20}, {12,42}, {22,35}, {25,38}, {16,29}, {9,20}, {24,35}, {15,30}, {13,30}, {28,38}, {9,22}, {1,18}, {23,32}, {4,33}, {16,25}, {20,33}, {10,20}, {24,36}, {4,34}, {6,15}, {12,39}, {11,41}, {27,40}, {2,17}, {8,41}, {6,34}, {15,25}, {27,37}, {7,42}, {16,26}, {6,33}, {1,13}, {16,30}, {24,32}, {28,40}, {10,21}, {2,29}, {13,33}, {21,38}, {23,37}, {16,36}, {1,21}, {8,30}, {4,28}, {16,31}, {10,26}, {8,34}, {24,40}, {14,41}, {12,33}, {10,25}, {1,20}, {9,30}, {5,28}, {24,39}, {7,33}, {5,27}, {17,42}, {13,41}, {7,36}, {15,32}, {3,22}, {2,21}, {14,38}, {5,24}, {23,40}, {8,33}, {1,22}, {13,36}, {23,38}, {9,25}, {11,25}, {16,32}, {20,40}, {17,32}, {14,37}, {13,42}, {20,39}, {13,37}, {18,32}, {6,30}, {6,28}, {4,22}, {12,25}, {8,36}, {18,31}, {8,35}, {19,40}, {11,26}, {9,35}, {3,21}, {21,30}, {17,21}, {29,31}, {6,37}, {10,18}, {6,42}, {4,8}, {29,34}, {12,13}, {2,38}, {35,42}, {18,23}, {36,39}, {1,38}, {18,24}, {36,41}, {3,10}, {20,26}, {19,28}, {30,33}, {11,15}, {36,42}, {12,16}, {1,37}, {29,33}, {26,33}, {20,28}, {32,42}, {14,23}, {2,40}, {5,34}, {9,21}, {8,42}, {28,39}, {20,32}, {24,31}, {29,39}, {12,21}, {5,36}, {15,37}, {20,42}, {4,24} } Symmetric graph 48 of order 42 Valency 26 Diameter 2 Girth 3 Automorphism group of order 523069747200 Number of arcs = 1092 Number of 2-arcs = 27300 2-arc-transitive false Edge-set { {1,5}, {33,37}, {4,7}, {19,23}, {30,34}, {9,39}, {8,13}, {3,4}, {16,23}, {12,41}, {2,20}, {8,21}, {14,36}, {7,29}, {15,39}, {31,39}, {5,8}, {4,18}, {23,40}, {13,26}, {10,32}, {2,32}, {6,18}, {1,7}, {15,17}, {10,28}, {3,37}, {9,40}, {13,21}, {21,30}, {36,38}, {21,24}, {29,36}, {7,37}, {7,15}, {17,39}, {8,42}, {4,25}, {12,23}, {26,39}, {15,22}, {28,31}, {22,32}, {6,28}, {17,38}, {9,42}, {9,33}, {4,13}, {16,30}, {38,41}, {15,42}, {19,31}, {5,34}, {8,25}, {12,14}, {1,29}, {1,41}, {17,20}, {10,20}, {3,35}, {17,24}, {10,40}, {3,21}, {9,19}, {13,34}, {9,30}, {13,38}, {16,21}, {36,41}, {7,27}, {11,15}, {34,39}, {23,32}, {21,36}, {26,36}, {6,30}, {22,38}, {24,42}, {19,29}, {6,22}, {22,28}, {38,42}, {16,20}, {35,41}, {8,27}, {11,14}, {8,23}, {14,30}, {29,39}, {8,39}, {18,41}, {20,40}, {20,26}, {10,35}, {27,30}, {11,38}, {3,24}, {16,29}, {12,37}, {2,7}, {7,34}, {15,25}, {13,28}, {32,37}, {33,40}, {4,21}, {26,33}, {4,10}, {2,16}, {2,15}, {18,31}, {11,31}, {5,16}, {24,41}, {12,31}, {1,31}, {5,17}, {3,8}, {14,16}, {12,29}, {2,39}, {8,41}, {14,20}, {20,29}, {35,39}, {1,18}, {17,40}, {10,26}, {3,10}, {9,35}, {13,27}, {33,38}, {12,21}, {2,36}, {4,22}, {23,28}, {1,10}, {3,17}, {10,36}, {3,26}, {9,20}, {6,20}, {22,35}, {5,27}, {11,24}, {3,40}, {6,38}, {9,22}, {6,42}, {19,22}, {20,27}, {11,35}, {2,18}, {18,40}, {11,26}, {7,35}, {15,27}, {14,28}, {15,23}, {28,41}, {20,37}, {21,40}, {7,21}, {15,36}, {17,26}, {10,42}, {2,25}, {12,18}, {18,26}, {33,35}, {5,31}, {5,24}, {13,19}, {32,34}, {9,32}, {6,13}, {9,12}, {2,13}, {25,38}, {29,42}, {19,39}, {28,34}, {23,25}, {12,30}, {1,39}, {8,17}, {23,36}, {26,30}, {8,31}, {18,32}, {6,40}, {30,32}, {14,24}, {29,33}, {18,37}, {7,40}, {5,26}, {10,24}, {13,24}, {29,32}, {24,33}, {4,29}, {16,37}, {7,41}, {7,31}, {5,15}, {18,28}, {37,40}, {13,40}, {21,32}, {6,36}, {7,26}, {10,15}, {2,28}, {2,40}, {18,21}, {11,21}, {1,36}, {17,33}, {4,42}, {16,25}, {26,31}, {15,31}, {8,11}, {1,14}, {29,35}, {27,39}, {20,23}, {30,35}, {1,13}, {17,32}, {3,6}, {6,39}, {8,22}, {15,33}, {4,31}, {16,31}, {5,41}, {3,31}, {31,36}, {2,8}, {14,18}, {2,38}, {9,18}, {6,11}, {1,22}, {35,37}, {5,14}, {25,31}, {5,12}, {20,38}, {6,8}, {14,22}, {27,38}, {9,11}, {16,22}, {2,35}, {18,27}, {1,33}, {17,25}, {12,42}, {28,42}, {19,37}, {4,30}, {23,38}, {26,42}, {10,19}, {2,19}, {18,34}, {1,25}, {12,17}, {1,9}, {13,17}, {10,30}, {3,38}, {16,36}, {26,41}, {6,25}, {32,42}, {17,36}, {11,23}, {1,30}, {24,37}, {5,37}, {7,24}, {3,29}, {16,39}, {12,22}, {29,38}, {14,32}, {20,34}, {25,35}, {27,40}, {4,34}, {13,41}, {20,32}, {21,33}, {4,36}, {7,16}, {15,41}, {3,23}, {15,29}, {17,22}, {22,41}, {20,28}, {5,28}, {17,19}, {34,42}, {9,25}, {12,13}, {36,37}, {24,31}, {5,29}, {24,39}, {22,40}, {21,28}, {5,23}, {24,30}, {39,40}, {18,19}, {34,40}, {9,26}, {10,13}, {9,24}, {13,29}, {30,37}, {7,38}, {17,42}, {19,42}, {19,25}, {12,34}, {25,29}, {12,39}, {17,28}, {10,38}, {3,9}, {9,36}, {15,30}, {31,38}, {6,19}, {25,32}, {6,12}, {1,17}, {10,33}, {30,41}, {25,40}, {24,36}, {26,29}, {7,14}, {28,33}, {4,37}, {11,40}, {1,21}, {21,35}, {27,36}, {2,4}, {18,23}, {11,41}, {1,20}, {4,39}, {5,9}, {21,38}, {6,7}, {23,30}, {30,38}, {8,29}, {18,24}, {29,40}, {26,37}, {7,10}, {7,32}, {6,15}, {37,42}, {6,35}, {14,42}, {14,38}, {6,33}, {11,19}, {1,34}, {28,37}, {24,34}, {13,37}, {18,35}, {9,15}, {22,37}, {20,35}, {27,35}, {8,14}, {14,33}, {11,32}, {1,6}, {17,35}, {27,42}, {23,33}, {16,34}, {25,41}, {3,19}, {39,41}, {8,20}, {4,20}, {23,35}, {3,15}, {3,32}, {6,16}, {2,42}, {33,34}, {13,16}, {32,41}, {8,33}, {4,14}, {20,31}, {5,35}, {10,18}, {34,38}, {22,27}, {11,28}, {10,16}, {3,41}, {33,41}, {5,19}, {31,40}, {5,21}, {36,40}, {2,12}, {11,34}, {12,27}, {10,39}, {2,22}, {1,23}, {17,30}, {30,40}, {6,26}, {10,22}, {7,19}, {3,16}, {16,41}, {2,11}, {8,34}, {14,25}, {32,39}, {3,34}, {24,29}, {1,42}, {7,23}, {20,24}, {21,25}, {12,36}, {16,42}, {12,25}, {8,36}, {14,26}, {21,39}, {19,41}, {13,35}, {16,27}, {3,27}, {11,16}, {32,36}, {15,20}, {31,35}, {8,10}, {3,14}, {9,16}, {22,34}, {25,28}, {16,33}, {4,41}, {30,31}, {25,34}, {5,10}, {21,26}, {9,28}, {23,42}, {19,30}, {12,33}, {4,17}, {1,11}, {2,33}, {8,37}, {9,38}, {9,13}, {20,41}, {15,21}, {19,36}, {26,34}, {13,31}, {19,27}, {27,28}, {11,37}, {19,34}, {2,24}, {11,17}, {8,30}, {1,27}, {7,28}, {15,37}, {4,9}, {11,27}, {4,23}, {10,25}, {15,18}, {8,18}, {4,11}, {5,38}, {22,31}, {18,38}, {27,32}, {2,30}, {18,29}, {22,26}, {28,39}, {31,42}, {12,20}, {19,33}, {23,26}, {24,25}, {1,37}, {7,17}, {3,12}, {13,32}, {6,32}, {4,33}, {5,40}, {7,12}, {25,37}, {21,22}, {28,36}, {2,5}, {27,33}, {13,23}, {11,29}, {3,28}, {14,40}, {14,19}, {4,27}, {15,34}, {14,35}, {14,39}, {2,26}, {35,42}, {5,32}, {6,24}, {22,29}, {21,42}, {24,27}, {23,39} } Symmetric graph 49 of order 42 Valency 28 Diameter 2 Girth 3 Automorphism group of order 3975358563294886684595847168000000 Number of arcs = 1176 Number of 2-arcs = 31752 2-arc-transitive false Edge-set { {1,15}, {19,32}, {7,32}, {12,42}, {11,23}, {12,26}, {23,40}, {27,35}, {16,37}, {1,36}, {15,36}, {3,35}, {4,37}, {8,34}, {5,20}, {6,31}, {8,17}, {7,19}, {8,21}, {20,29}, {6,22}, {17,30}, {9,25}, {21,39}, {24,41}, {25,29}, {9,39}, {26,42}, {11,40}, {25,39}, {13,39}, {14,41}, {13,29}, {3,39}, {13,16}, {2,38}, {2,28}, {14,35}, {4,26}, {3,27}, {4,16}, {3,18}, {16,34}, {2,17}, {28,33}, {14,18}, {26,34}, {3,21}, {16,29}, {18,31}, {20,33}, {22,36}, {3,30}, {21,34}, {5,29}, {22,31}, {8,30}, {21,30}, {10,29}, {9,31}, {10,33}, {9,36}, {14,31}, {8,26}, {11,30}, {10,24}, {10,41}, {12,22}, {7,40}, {14,19}, {13,21}, {14,24}, {13,25}, {14,28}, {26,38}, {11,27}, {24,37}, {10,28}, {22,38}, {7,27}, {19,37}, {11,17}, {24,33}, {25,36}, {28,38}, {15,40}, {17,42}, {11,33}, {18,39}, {13,34}, {17,38}, {2,33}, {18,35}, {4,34}, {17,33}, {6,33}, {5,36}, {6,38}, {5,40}, {6,42}, {10,38}, {2,22}, {7,35}, {4,19}, {5,33}, {6,18}, {4,32}, {7,15}, {1,29}, {9,27}, {10,16}, {9,18}, {10,20}, {9,22}, {10,23}, {22,41}, {7,24}, {19,42}, {5,23}, {18,41}, {4,24}, {15,42}, {1,23}, {27,41}, {5,28}, {18,38}, {20,40}, {22,42}, {23,30}, {26,32}, {27,34}, {5,37}, {28,31}, {8,38}, {27,30}, {10,37}, {28,41}, {12,38}, {27,40}, {14,37}, {28,37}, {1,38}, {2,40}, {1,42}, {2,30}, {1,32}, {2,34}, {5,30}, {10,18}, {4,41}, {12,15}, {1,40}, {14,27}, {13,37}, {1,25}, {12,36}, {3,23}, {9,34}, {5,21}, {6,24}, {5,25}, {6,28}, {5,15}, {6,17}, {5,19}, {18,32}, {4,20}, {15,31}, {1,19}, {27,32}, {13,20}, {25,31}, {12,19}, {23,32}, {9,20}, {21,31}, {13,24}, {25,42}, {28,30}, {15,32}, {17,34}, {19,35}, {21,37}, {24,39}, {13,42}, {23,38}, {2,41}, {24,35}, {4,42}, {23,33}, {6,41}, {24,32}, {7,42}, {23,29}, {9,41}, {24,42}, {11,42}, {12,30}, {11,32}, {12,34}, {11,35}, {12,37}, {11,39}, {1,35}, {4,27}, {13,33}, {6,25}, {12,32}, {7,23}, {9,29}, {9,21}, {8,42}, {11,20}, {6,39}, {13,17}, {3,38}, {2,16}, {1,18}, {2,20}, {1,22}, {2,23}, {1,26}, {2,27}, {1,16}, {27,36}, {13,15}, {25,35}, {12,16}, {23,36}, {9,15}, {21,35}, {8,16}, {20,36}, {6,15}, {17,35}, {3,16}, {16,36}, {8,19}, {20,32}, {22,34}, {23,35}, {26,37}, {27,39}, {16,41}, {18,29}, {20,31}, {8,31}, {19,30}, {10,32}, {20,41}, {12,31}, {19,40}, {14,32}, {20,37}, {1,31}, {19,36}, {3,32}, {20,34}, {5,31}, {19,31}, {8,32}, {7,34}, {8,35}, {7,37}, {8,39}, {7,41}, {8,29}, {7,31}, {12,41}, {12,23}, {9,40}, {14,21}, {8,37}, {1,20}, {6,36}, {3,17}, {3,34}, {5,16}, {2,31}, {8,28}, {14,30}, {10,26}, {11,41}, {12,24}, {11,25}, {12,28}, {11,15}, {12,17}, {11,19}, {12,21}, {11,24}, {12,25}, {23,39}, {9,26}, {21,40}, {8,25}, {20,39}, {6,26}, {17,40}, {3,25}, {16,39}, {2,26}, {28,40}, {14,25}, {26,39}, {11,26}, {24,40}, {2,15}, {28,35}, {15,37}, {17,39}, {19,41}, {21,29}, {24,31}, {25,33}, {28,36}, {15,38}, {2,35}, {16,35}, {4,36}, {15,33}, {6,35}, {16,32}, {7,36}, {15,29}, {9,35}, {16,42}, {11,36}, {15,39}, {13,35}, {16,38}, {2,36}, {15,35}, {4,35}, {3,37}, {4,39}, {3,41}, {4,29}, {3,31}, {4,33}, {3,36}, {4,38}, {8,33}, {6,20}, {6,32}, {7,17}, {3,29}, {9,16}, {2,42}, {11,28}, {14,39}, {13,26}, {11,38}, {2,24}, {10,35}, {4,22}, {7,33}, {6,19}, {5,32}, {7,18}, {8,20}, {7,22}, {8,23}, {7,26}, {8,27}, {7,16}, {8,18}, {7,20}, {8,22}, {20,30}, {6,21}, {17,29}, {3,22}, {16,30}, {2,21}, {28,29}, {14,22}, {26,30}, {11,21}, {24,29}, {10,22}, {22,30}, {7,21}, {19,29}, {5,22}, {18,30}, {10,25}, {22,39}, {23,41}, {26,29}, {27,31}, {16,33}, {18,36}, {20,38}, {22,40}, {23,42}, {10,40}, {25,41}, {12,39}, {26,40}, {14,40}, {25,37}, {1,39}, {26,36}, {3,40}, {25,34}, {5,39}, {26,31}, {8,40}, {25,30}, {10,39}, {26,41}, {12,40}, {25,40}, {13,41}, {14,29}, {13,31}, {14,33}, {13,36}, {14,38}, {13,40}, {14,42}, {13,30}, {14,16}, {2,37}, {1,28}, {14,36}, {3,26}, {11,34}, {5,24}, {10,31}, {7,30}, {10,19}, {5,41}, {12,18}, {4,40}, {14,15}, {1,37}, {1,27}, {4,28}, {3,15}, {4,17}, {3,19}, {4,21}, {3,24}, {4,25}, {3,28}, {4,15}, {2,18}, {28,34}, {14,17}, {26,33}, {11,18}, {24,34}, {10,17}, {22,33}, {19,34}, {5,17}, {18,33}, {4,18}, {15,34}, {1,17}, {27,33}, {13,18}, {17,31}, {19,33}, {21,36}, {24,38}, {28,42}, {15,30}, {17,32}, {6,30}, {21,32}, {7,29}, {22,29}, {9,30}, {21,42}, {11,29}, {21,38}, {2,29}, {22,35}, {4,30}, {21,33}, {6,29}, {22,32}, {9,33}, {10,36}, {9,38}, {9,42}, {10,30}, {9,32}, {10,34}, {9,24}, {10,42}, {11,22}, {7,39}, {13,19}, {5,38}, {1,33}, {6,27}, {13,32}, {7,25}, {12,29}, {9,23}, {13,23}, {14,26}, {13,27}, {14,20}, {13,22}, {14,23}, {10,27}, {22,37}, {7,28}, {19,38}, {5,27}, {18,37}, {27,37}, {13,28}, {25,38}, {12,27}, {23,37}, {9,28}, {27,38}, {16,40}, {18,42}, {23,34}, {26,35}, {1,34}, {17,36}, {3,33}, {18,34}, {5,34}, {17,41}, {12,33}, {18,40}, {14,34}, {17,37}, {6,40}, {5,42}, {6,34}, {5,35}, {6,37}, {5,18}, {4,31}, {8,15}, {1,30}, {9,37}, {1,21}, {8,36}, {3,20}, {9,19}, {10,21}, {10,15}, {9,17}, {4,23}, {15,41}, {1,24}, {27,42}, {21,41}, {8,24}, {20,42}, {6,23}, {24,30}, {25,32}, {19,39}, {11,37}, {28,39}, {13,38}, {28,32}, {7,38}, {27,29}, {2,32}, {2,39}, {1,41}, {2,25}, {12,35}, {3,42}, {11,16}, {6,16}, {5,26}, {12,20}, {23,31}, {16,31}, {2,19}, {20,35}, {8,41}, {24,36}, {11,31} } Symmetric graph 50 of order 42 Valency 30 Diameter 2 Girth 3 Automorphism group of order 5040 Number of arcs = 1260 Number of 2-arcs = 36540 2-arc-transitive false Edge-set { {1,7}, {27,42}, {17,37}, {12,24}, {1,35}, {9,18}, {2,9}, {35,38}, {20,39}, {1,27}, {17,25}, {17,41}, {7,42}, {26,41}, {18,42}, {6,25}, {11,36}, {5,22}, {24,27}, {17,35}, {18,19}, {9,33}, {10,18}, {3,9}, {12,42}, {1,37}, {10,22}, {3,36}, {12,17}, {19,29}, {15,33}, {5,39}, {28,38}, {30,32}, {14,19}, {24,35}, {20,35}, {1,18}, {9,25}, {17,34}, {7,24}, {6,41}, {7,40}, {28,41}, {16,42}, {12,38}, {1,39}, {9,27}, {2,17}, {32,37}, {19,40}, {5,28}, {16,28}, {18,38}, {9,39}, {23,34}, {24,31}, {6,16}, {11,27}, {11,30}, {5,14}, {7,21}, {6,32}, {2,20}, {26,34}, {13,34}, {20,25}, {1,36}, {22,25}, {17,27}, {7,17}, {19,41}, {33,42}, {4,18}, {9,30}, {35,42}, {20,37}, {10,29}, {3,15}, {8,42}, {4,37}, {10,21}, {3,32}, {12,14}, {1,8}, {7,38}, {6,39}, {5,17}, {24,41}, {18,26}, {2,26}, {8,34}, {4,24}, {21,30}, {14,32}, {14,21}, {8,32}, {6,7}, {11,41}, {5,42}, {4,33}, {3,35}, {20,29}, {14,29}, {8,15}, {24,39}, {34,38}, {13,30}, {31,42}, {23,37}, {2,29}, {15,26}, {26,36}, {18,22}, {4,22}, {30,36}, {4,15}, {10,30}, {19,36}, {22,33}, {5,27}, {17,28}, {19,32}, {19,33}, {18,24}, {9,35}, {9,37}, {10,34}, {3,24}, {6,12}, {7,13}, {20,41}, {34,42}, {1,12}, {1,25}, {9,36}, {2,22}, {31,40}, {11,16}, {12,40}, {1,41}, {2,13}, {31,37}, {23,40}, {2,28}, {16,26}, {13,38}, {12,39}, {27,40}, {6,37}, {11,29}, {5,15}, {18,30}, {9,14}, {10,35}, {3,20}, {17,22}, {7,36}, {22,26}, {18,36}, {4,40}, {30,41}, {25,35}, {13,20}, {20,31}, {12,26}, {13,31}, {12,23}, {2,40}, {29,42}, {15,37}, {10,39}, {3,38}, {12,30}, {1,14}, {13,27}, {1,28}, {16,25}, {23,36}, {22,31}, {13,23}, {12,31}, {16,40}, {11,35}, {5,20}, {4,7}, {6,30}, {15,20}, {3,12}, {1,29}, {2,21}, {23,26}, {18,31}, {16,22}, {28,36}, {17,32}, {7,19}, {25,32}, {13,19}, {28,34}, {11,13}, {34,40}, {5,34}, {24,28}, {19,27}, {24,30}, {14,35}, {18,21}, {9,32}, {2,34}, {24,26}, {6,34}, {7,20}, {25,42}, {9,41}, {2,42}, {30,40}, {28,35}, {16,20}, {29,38}, {15,39}, {15,42}, {10,37}, {10,36}, {3,22}, {4,12}, {1,30}, {27,38}, {17,39}, {17,33}, {5,41}, {28,42}, {26,32}, {3,8}, {4,29}, {14,39}, {8,38}, {4,39}, {10,27}, {3,17}, {8,33}, {4,21}, {21,26}, {18,32}, {14,22}, {8,36}, {7,15}, {6,10}, {11,38}, {8,24}, {4,35}, {9,29}, {2,15}, {23,39}, {31,38}, {16,30}, {11,14}, {17,20}, {7,34}, {13,41}, {25,40}, {9,19}, {28,37}, {22,32}, {7,28}, {8,25}, {4,13}, {10,20}, {3,34}, {1,19}, {25,33}, {15,36}, {22,29}, {22,38}, {36,39}, {33,38}, {21,39}, {8,26}, {1,31}, {9,16}, {2,11}, {11,37}, {5,40}, {20,38}, {34,39}, {15,24}, {21,27}, {5,33}, {21,28}, {29,39}, {8,14}, {4,8}, {25,38}, {13,37}, {15,34}, {16,36}, {11,22}, {16,39}, {23,27}, {17,31}, {26,31}, {18,23}, {21,36}, {7,29}, {8,19}, {5,21}, {28,32}, {2,18}, {9,26}, {24,37}, {2,19}, {26,33}, {10,24}, {10,38}, {4,30}, {14,30}, {21,35}, {20,32}, {24,34}, {20,34}, {1,13}, {12,25}, {7,23}, {2,41}, {26,42}, {4,26}, {22,35}, {20,36}, {15,30}, {36,42}, {22,37}, {12,19}, {1,33}, {10,41}, {3,42}, {8,20}, {4,34}, {1,21}, {14,36}, {8,22}, {6,31}, {5,11}, {12,16}, {1,11}, {5,37}, {28,40}, {16,19}, {13,39}, {20,27}, {6,35}, {11,18}, {5,9}, {6,18}, {3,14}, {12,21}, {1,32}, {16,41}, {23,25}, {5,12}, {11,25}, {5,13}, {35,40}, {18,28}, {6,40}, {27,41}, {25,31}, {7,26}, {13,32}, {29,37}, {15,40}, {7,39}, {6,38}, {13,25}, {23,41}, {11,33}, {3,7}, {6,29}, {14,20}, {9,22}, {4,42}, {30,37}, {10,15}, {3,10}, {34,41}, {24,42}, {9,21}, {2,32}, {19,26}, {21,42}, {33,41}, {15,25}, {10,13}, {36,37}, {22,40}, {4,28}, {27,34}, {17,24}, {6,19}, {27,33}, {5,16}, {11,28}, {23,32}, {19,31}, {7,32}, {6,27}, {11,31}, {5,23}, {36,41}, {3,27}, {17,29}, {14,41}, {26,39}, {2,38}, {8,30}, {4,14}, {6,22}, {4,11}, {5,30}, {16,35}, {11,20}, {23,35}, {14,27}, {21,31}, {11,23}, {5,31}, {13,40}, {12,41}, {6,33}, {9,15}, {2,10}, {4,16}, {8,28}, {32,39}, {19,38}, {5,8}, {24,33}, {3,18}, {29,36}, {23,28}, {23,42}, {30,31}, {14,23}, {17,26}, {7,18}, {22,41}, {27,36}, {35,37}, {20,40}, {7,37}, {12,34}, {2,36}, {20,30}, {4,36}, {22,30}, {15,27}, {10,17}, {33,39}, {21,37}, {10,26}, {12,22}, {13,36}, {19,25}, {5,36}, {22,28}, {11,34}, {3,40}, {12,28}, {1,16}, {36,40}, {4,25}, {27,31}, {17,23}, {32,40}, {3,29}, {15,29}, {30,39}, {14,38}, {8,39}, {27,39}, {17,38}, {2,14}, {8,21}, {4,32}, {14,34}, {11,15}, {5,10}, {24,36}, {14,42}, {13,28}, {2,27}, {10,14}, {21,33}, {30,38}, {19,39}, {17,21}, {8,29}, {3,19}, {29,33}, {22,42}, {9,23}, {2,31}, {8,16}, {11,42}, {6,15}, {15,19}, {10,33}, {3,21}, {16,37}, {23,29}, {15,31}, {32,41}, {19,42}, {9,20}, {11,40}, {4,10}, {3,30}, {12,35}, {1,20}, {31,41}, {22,34}, {1,23}, {10,40}, {4,19}, {21,25}, {30,35}, {18,35}, {29,34}, {6,24}, {27,35}, {32,38}, {2,33}, {24,29}, {26,37}, {15,35}, {3,39}, {30,33}, {3,28}, {9,31}, {12,13}, {29,32}, {25,39}, {13,24}, {3,31}, {21,38}, {18,40}, {14,25}, {8,13}, {21,40}, {5,26}, {7,16}, {28,31}, {21,32}, {12,33}, {13,33}, {17,42}, {10,32}, {5,24}, {1,9}, {2,25}, {9,42}, {2,37}, {4,38}, {5,25}, {19,34}, {16,24}, {18,37}, {9,40}, {6,11}, {2,23}, {10,28}, {14,28}, {8,17}, {29,35}, {18,33}, {2,8}, {16,31}, {16,23}, {11,24}, {5,35}, {6,9}, {13,26}, {12,18}, {14,40}, {20,28}, {15,21}, {6,23}, {12,32}, {3,26}, {18,29}, {8,41}, {1,38}, {16,29}, {16,34}, {23,33}, {3,16}, {1,24}, {25,37}, {19,30}, {8,37}, {25,34}, {1,17}, {7,25}, {4,23}, {2,7}, {6,26}, {18,27}, {6,20}, {16,32}, {3,41}, {15,38}, {11,19}, {7,31}, {8,31}, {26,40}, {1,42}, {6,13}, {14,33}, {9,17}, {13,21}, {6,17}, {7,27}, {18,41}, {35,39}, {29,41}, {15,22}, {33,37}, {7,35}, {24,38}, {12,27}, {10,23} } Symmetric graph 51 of order 42 Valency 30 Diameter 2 Girth 3 Automorphism group of order 3628800 Number of arcs = 1260 Number of 2-arcs = 36540 2-arc-transitive false Edge-set { {1,7}, {14,42}, {16,21}, {24,35}, {10,29}, {4,19}, {27,36}, {2,8}, {6,33}, {28,38}, {23,38}, {3,16}, {15,35}, {7,29}, {2,40}, {15,41}, {18,22}, {9,17}, {1,17}, {26,32}, {8,41}, {6,32}, {8,31}, {18,19}, {13,27}, {8,21}, {6,25}, {28,42}, {21,38}, {15,34}, {12,18}, {21,33}, {7,25}, {1,23}, {30,32}, {22,40}, {20,28}, {14,22}, {16,28}, {10,30}, {4,42}, {33,41}, {7,22}, {10,17}, {4,17}, {11,41}, {5,22}, {3,23}, {30,35}, {20,29}, {26,40}, {4,41}, {22,36}, {17,25}, {17,37}, {26,35}, {10,41}, {4,32}, {8,36}, {12,21}, {3,25}, {23,39}, {19,30}, {4,9}, {1,36}, {25,42}, {21,37}, {6,14}, {16,31}, {10,27}, {4,39}, {1,34}, {12,32}, {5,26}, {34,41}, {1,24}, {29,32}, {19,26}, {27,41}, {27,38}, {16,35}, {10,15}, {9,33}, {1,42}, {21,32}, {22,38}, {23,28}, {16,22}, {15,28}, {33,37}, {7,24}, {1,13}, {14,32}, {6,18}, {13,31}, {8,27}, {6,39}, {5,28}, {34,38}, {30,34}, {12,42}, {16,33}, {7,15}, {2,32}, {22,25}, {28,37}, {9,28}, {8,30}, {6,42}, {33,38}, {7,23}, {10,16}, {4,15}, {7,41}, {2,22}, {19,36}, {18,25}, {13,37}, {6,31}, {11,31}, {3,27}, {35,39}, {16,40}, {15,20}, {7,14}, {2,16}, {25,35}, {10,37}, {4,36}, {9,36}, {17,24}, {17,29}, {11,19}, {5,27}, {29,38}, {23,40}, {11,15}, {12,14}, {10,39}, {13,30}, {12,33}, {3,7}, {2,14}, {10,28}, {4,38}, {3,30}, {35,42}, {29,33}, {7,40}, {8,40}, {8,19}, {6,27}, {23,25}, {9,40}, {1,20}, {14,35}, {4,10}, {1,32}, {8,32}, {6,26}, {31,41}, {1,19}, {27,32}, {21,26}, {25,41}, {1,9}, {2,42}, {14,20}, {16,26}, {10,24}, {4,29}, {17,23}, {17,30}, {11,20}, {29,41}, {17,31}, {11,17}, {13,26}, {14,41}, {3,8}, {12,27}, {3,39}, {10,19}, {9,19}, {1,27}, {21,42}, {21,25}, {4,18}, {1,25}, {32,37}, {26,36}, {9,41}, {20,41}, {22,39}, {17,35}, {9,32}, {1,8}, {21,31}, {19,38}, {23,27}, {15,25}, {33,42}, {7,21}, {1,15}, {18,32}, {2,35}, {30,37}, {20,36}, {9,26}, {5,17}, {11,37}, {5,24}, {18,29}, {13,40}, {6,11}, {19,34}, {5,21}, {25,34}, {24,42}, {21,29}, {15,19}, {18,27}, {8,25}, {6,37}, {36,38}, {9,23}, {7,16}, {2,15}, {2,20}, {28,33}, {22,28}, {3,37}, {13,29}, {14,40}, {28,32}, {8,38}, {6,34}, {12,31}, {24,25}, {24,39}, {19,29}, {31,38}, {11,23}, {20,27}, {26,39}, {9,39}, {18,42}, {13,21}, {15,24}, {26,38}, {23,41}, {16,32}, {8,15}, {13,39}, {8,35}, {6,10}, {1,38}, {34,42}, {12,22}, {3,41}, {22,35}, {17,40}, {31,37}, {34,40}, {12,20}, {5,14}, {16,34}, {8,24}, {6,29}, {16,38}, {15,23}, {10,14}, {4,16}, {4,22}, {17,42}, {11,33}, {5,7}, {3,14}, {4,40}, {4,30}, {36,42}, {25,33}, {7,37}, {16,20}, {10,18}, {29,34}, {27,42}, {2,38}, {23,33}, {15,38}, {6,22}, {28,31}, {22,27}, {28,39}, {5,37}, {24,34}, {7,38}, {11,22}, {22,37}, {24,28}, {20,30}, {26,42}, {24,33}, {18,41}, {13,22}, {29,39}, {19,40}, {18,31}, {11,13}, {3,38}, {23,35}, {3,40}, {20,35}, {14,29}, {4,35}, {10,36}, {4,25}, {36,37}, {16,23}, {15,30}, {14,25}, {16,37}, {7,30}, {33,40}, {7,20}, {5,33}, {7,34}, {1,31}, {11,32}, {8,22}, {6,28}, {10,40}, {4,20}, {4,11}, {5,36}, {3,32}, {31,40}, {25,37}, {9,35}, {1,10}, {21,36}, {14,21}, {16,25}, {10,23}, {2,34}, {30,40}, {20,42}, {14,28}, {9,24}, {2,13}, {14,33}, {30,38}, {20,34}, {12,26}, {3,12}, {3,35}, {4,13}, {14,36}, {12,25}, {10,33}, {4,28}, {3,21}, {23,29}, {17,36}, {7,32}, {6,40}, {20,31}, {19,42}, {21,27}, {15,21}, {5,15}, {18,34}, {1,41}, {1,26}, {32,41}, {18,36}, {9,13}, {12,29}, {10,26}, {12,17}, {3,17}, {11,39}, {5,19}, {2,25}, {2,31}, {3,28}, {35,38}, {5,8}, {24,31}, {5,29}, {30,31}, {11,42}, {2,21}, {8,42}, {7,31}, {4,27}, {21,41}, {11,26}, {17,38}, {8,16}, {12,35}, {3,10}, {1,39}, {19,32}, {18,33}, {7,13}, {22,34}, {12,28}, {11,36}, {5,9}, {12,34}, {5,39}, {13,24}, {12,19}, {2,41}, {22,33}, {17,28}, {6,21}, {25,31}, {24,38}, {16,19}, {15,27}, {1,16}, {15,32}, {9,37}, {13,42}, {18,24}, {12,15}, {16,27}, {15,39}, {7,35}, {2,10}, {9,25}, {1,37}, {9,21}, {27,34}, {23,30}, {29,35}, {8,18}, {6,9}, {17,32}, {5,41}, {1,29}, {32,40}, {26,31}, {13,36}, {9,14}, {2,12}, {3,33}, {32,42}, {24,32}, {2,26}, {34,39}, {10,42}, {2,9}, {1,33}, {11,38}, {3,34}, {5,30}, {20,37}, {24,26}, {8,13}, {6,8}, {12,13}, {6,15}, {2,23}, {15,37}, {7,36}, {6,19}, {27,31}, {25,39}, {29,37}, {9,27}, {21,39}, {9,34}, {1,12}, {5,42}, {21,34}, {1,14}, {11,14}, {5,16}, {4,24}, {22,32}, {17,26}, {17,41}, {12,23}, {11,34}, {5,12}, {25,36}, {6,20}, {14,38}, {4,7}, {2,36}, {29,36}, {19,25}, {27,37}, {6,38}, {23,31}, {3,18}, {12,39}, {5,35}, {10,34}, {20,33}, {18,26}, {8,39}, {30,39}, {18,39}, {13,19}, {6,13}, {15,26}, {2,29}, {19,37}, {9,38}, {2,28}, {4,21}, {17,34}, {5,11}, {5,34}, {10,35}, {36,40}, {14,30}, {16,42}, {2,30}, {20,40}, {20,26}, {23,42}, {19,28}, {13,28}, {11,24}, {3,13}, {18,37}, {5,18}, {13,41}, {2,11}, {11,27}, {35,37}, {35,41}, {10,22}, {16,29}, {15,40}, {4,33}, {8,28}, {19,41}, {18,38}, {13,23}, {14,31}, {11,16}, {1,30}, {2,24}, {3,19}, {26,33}, {19,35}, {15,33}, {7,18}, {22,26}, {28,41}, {11,25}, {8,33}, {27,35}, {25,40}, {14,19}, {10,21}, {9,20}, {30,33}, {27,40}, {18,23}, {9,16}, {31,39}, {22,30}, {17,20}, {13,33}, {4,12}, {11,30}, {24,40}, {9,18}, {3,11}, {18,20}, {14,39}, {17,22}, {20,39}, {17,21}, {7,42}, {11,29}, {5,40}, {28,36}, {29,40}, {4,31}, {12,40}, {3,20}, {13,35}, {3,36}, {14,24}, {24,37}, {24,29}, {14,27}, {7,28}, {19,31}, {12,37}, {3,24}, {2,37}, {8,29}, {2,18}, {8,17}, {5,31}, {12,38}, {30,42}, {21,30}, {8,20}, {15,36}, {6,23}, {24,27}, {6,35}, {10,31}, {3,26}, {26,41}, {23,36}, {9,30}, {7,26}, {6,7}, {23,32}, {22,41}, {16,39}, {1,22}, {32,39}, {28,34}, {5,23}, {13,34}, {36,39}, {18,30}, {6,17} } Symmetric graph 52 of order 42 Valency 35 Diameter 2 Girth 3 Automorphism group of order 11800915893414789120000000 Number of arcs = 1470 Number of 2-arcs = 49980 2-arc-transitive false Edge-set { {1,8}, {21,38}, {9,36}, {26,34}, {1,30}, {28,39}, {7,12}, {6,13}, {16,23}, {1,21}, {17,36}, {12,24}, {5,27}, {19,41}, {10,39}, {18,37}, {14,40}, {11,30}, {22,32}, {21,34}, {30,36}, {28,32}, {7,29}, {14,41}, {10,26}, {9,20}, {25,37}, {25,35}, {6,33}, {24,42}, {5,11}, {22,33}, {4,34}, {23,40}, {2,8}, {1,36}, {13,17}, {4,10}, {20,28}, {6,34}, {16,30}, {1,28}, {7,17}, {4,12}, {20,27}, {3,19}, {15,39}, {25,40}, {6,8}, {13,42}, {11,23}, {29,39}, {12,31}, {8,22}, {4,24}, {18,24}, {7,18}, {21,40}, {14,27}, {3,26}, {20,36}, {13,37}, {7,10}, {21,28}, {6,16}, {16,41}, {2,22}, {15,38}, {9,42}, {7,36}, {32,37}, {14,29}, {16,42}, {11,41}, {12,29}, {27,31}, {6,18}, {16,40}, {17,32}, {12,21}, {27,36}, {19,32}, {10,41}, {9,29}, {25,31}, {17,35}, {33,38}, {24,31}, {5,35}, {8,23}, {2,24}, {18,38}, {9,40}, {27,37}, {3,14}, {11,36}, {13,22}, {3,24}, {5,15}, {5,41}, {10,19}, {10,38}, {9,28}, {14,16}, {26,41}, {14,33}, {19,33}, {34,39}, {23,34}, {2,30}, {8,25}, {23,38}, {28,29}, {7,31}, {22,37}, {4,14}, {19,42}, {11,39}, {12,34}, {27,30}, {18,30}, {32,40}, {25,30}, {6,32}, {10,15}, {28,42}, {26,31}, {1,35}, {27,39}, {3,12}, {19,28}, {7,39}, {4,22}, {4,20}, {3,40}, {8,15}, {3,32}, {25,36}, {3,41}, {5,9}, {19,25}, {18,33}, {34,40}, {23,30}, {2,32}, {4,32}, {20,29}, {34,41}, {10,30}, {7,25}, {4,35}, {20,33}, {25,42}, {6,11}, {3,39}, {12,15}, {5,8}, {19,24}, {18,29}, {7,26}, {5,14}, {19,26}, {2,20}, {11,38}, {9,22}, {14,15}, {26,42}, {26,33}, {1,34}, {23,39}, {2,12}, {4,25}, {17,40}, {8,38}, {28,36}, {7,13}, {10,37}, {14,28}, {14,17}, {26,38}, {20,31}, {35,37}, {20,25}, {6,37}, {35,42}, {11,33}, {1,11}, {12,39}, {12,27}, {30,40}, {8,32}, {13,25}, {6,23}, {7,40}, {8,21}, {7,35}, {21,33}, {6,24}, {5,16}, {16,22}, {1,15}, {17,42}, {9,24}, {11,26}, {1,22}, {15,27}, {5,19}, {19,39}, {10,22}, {4,28}, {8,41}, {27,35}, {3,33}, {24,36}, {5,13}, {6,41}, {10,16}, {1,9}, {17,25}, {1,33}, {17,34}, {4,23}, {17,24}, {4,18}, {20,40}, {31,42}, {11,35}, {3,27}, {19,23}, {2,21}, {18,36}, {5,25}, {17,41}, {12,35}, {27,33}, {5,39}, {28,41}, {16,29}, {31,41}, {17,23}, {2,38}, {31,38}, {9,35}, {4,17}, {20,38}, {8,28}, {7,24}, {6,38}, {20,39}, {12,37}, {8,35}, {24,33}, {7,33}, {2,16}, {17,22}, {4,15}, {20,42}, {4,16}, {20,41}, {3,29}, {15,31}, {6,25}, {1,42}, {11,17}, {8,19}, {24,39}, {18,41}, {21,31}, {8,27}, {13,40}, {5,38}, {10,35}, {9,37}, {14,35}, {15,34}, {13,19}, {8,37}, {13,35}, {23,33}, {15,29}, {26,36}, {1,13}, {12,28}, {31,40}, {13,27}, {3,23}, {21,23}, {6,21}, {16,36}, {11,24}, {5,22}, {15,41}, {10,42}, {8,16}, {24,41}, {23,32}, {2,29}, {7,27}, {19,37}, {14,39}, {22,42}, {4,11}, {12,40}, {8,29}, {13,26}, {1,23}, {5,29}, {19,31}, {18,22}, {4,40}, {2,27}, {3,18}, {13,21}, {21,36}, {13,36}, {5,10}, {9,41}, {10,25}, {2,17}, {4,38}, {14,24}, {11,18}, {22,40}, {2,39}, {34,38}, {9,30}, {2,19}, {18,39}, {7,34}, {21,30}, {14,18}, {26,40}, {20,30}, {35,36}, {27,32}, {12,26}, {13,23}, {10,21}, {9,31}, {20,35}, {33,37}, {24,35}, {5,33}, {11,28}, {12,16}, {27,41}, {25,38}, {6,9}, {2,9}, {18,25}, {20,37}, {14,37}, {6,40}, {30,42}, {11,32}, {21,39}, {12,36}, {24,29}, {7,21}, {11,16}, {22,41}, {14,32}, {26,29}, {16,33}, {23,29}, {2,31}, {2,36}, {13,18}, {9,17}, {28,33}, {8,20}, {24,37}, {25,32}, {6,29}, {2,41}, {10,18}, {7,9}, {21,25}, {20,24}, {5,37}, {12,25}, {6,27}, {3,30}, {15,32}, {6,19}, {22,29}, {15,26}, {5,26}, {1,19}, {12,18}, {16,32}, {29,41}, {1,31}, {12,38}, {9,27}, {14,19}, {26,39}, {18,26}, {1,40}, {5,31}, {9,18}, {7,14}, {21,26}, {7,19}, {15,30}, {32,42}, {10,32}, {16,31}, {35,41}, {27,29}, {3,31}, {32,41}, {25,29}, {6,31}, {3,17}, {19,35}, {8,18}, {24,40}, {21,27}, {3,36}, {32,36}, {13,29}, {35,38}, {9,33}, {25,33}, {5,34}, {19,30}, {9,38}, {9,25}, {23,37}, {2,14}, {20,26}, {1,37}, {2,42}, {22,39}, {2,40}, {16,35}, {22,38}, {4,9}, {2,37}, {7,11}, {21,22}, {15,35}, {13,28}, 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{4,30}, {20,32}, {3,25}, {6,15}, {5,21}, {19,36}, {1,10}, {9,39}, {35,40}, {13,24}, {13,33}, {5,20}, {33,39}, {19,40}, {8,39}, {4,27}, {4,42}, {11,20}, {2,25}, {3,9}, {5,17}, {19,38}, {6,20}, {3,8}, {5,18}, {2,35}, {9,34}, {2,26}, {17,28}, {7,38}, {3,37}, {1,18}, {7,8}, {21,24}, {16,37}, {1,12}, {11,22}, {23,31}, {3,42}, {5,28}, {18,32}, {13,39}, {11,19}, {22,34}, {28,40}, {25,41}, {6,10}, {11,25}, {8,40}, {8,24}, {6,36}, {13,16}, {16,34}, {17,27}, {4,19}, {11,31}, {12,22}, {2,18}, {18,40}, {13,38}, {1,26}, {4,39}, {12,20}, {10,29}, {28,31}, {3,35}, {35,39}, {12,33}, {5,24}, {18,28}, {7,16}, {21,41}, {27,38}, {6,14}, {6,22}, {11,42}, {17,26}, {1,38}, {31,39}, {11,40}, {34,36}, {13,30}, {10,28}, {7,28}, {17,29}, {22,31}, {16,27}, {21,29}, {8,17}, {17,39}, {4,13}, {10,40}, {9,23}, {14,31}, {26,35}, {5,36}, {3,21}, {5,32}, {1,32}, {9,16}, {11,15}, {15,36}, {19,29}, {3,16}, {1,25}, {6,17}, {14,21}, {9,21}, {16,38}, {16,28}, {7,41}, {29,37}, {1,20}, {17,37}, {14,20}, {27,40}, {14,38}, {10,31}, {28,35}, {19,27}, {8,31}, {18,27}, {1,14}, {4,41}, {14,42}, {29,36}, {26,32}, {2,33}, {2,11}, {2,34}, {4,29}, {24,38}, {20,34}, {30,37}, {21,42}, {5,12}, {14,26}, {7,37}, {31,37}, {2,15}, {18,42}, {6,39}, {13,15}, {23,42}, {12,32}, {26,30}, {10,36}, {19,22}, {12,23}, {8,36}, {9,26}, {6,30}, {15,33}, {26,37}, {23,36}, {16,24}, {27,34}, {25,34}, {2,13}, {11,27}, {3,34}, {32,38}, {24,32}, {5,40}, {31,36}, {29,40}, {8,30}, {12,30}, {3,22}, {16,25}, {7,15}, {20,23}, {28,38}, {10,17}, {11,29} } Symmetric graph 53 of order 42 Valency 36 Diameter 2 Girth 3 Automorphism group of order 505542895416115200000000 Number of arcs = 1512 Number of 2-arcs = 52920 2-arc-transitive false Edge-set { {1,7}, {9,31}, {1,14}, {3,33}, {16,22}, {9,13}, {1,26}, {6,12}, {3,24}, {15,42}, {27,41}, {14,33}, {16,25}, {9,24}, {8,35}, {6,17}, {12,39}, {3,40}, {16,26}, {28,32}, {20,25}, {6,13}, {24,26}, {15,23}, {8,27}, {33,39}, {16,40}, {2,32}, {13,20}, {8,18}, {6,30}, {27,35}, {17,34}, {12,28}, {15,24}, {7,27}, {4,19}, {10,21}, {23,38}, {8,37}, {8,14}, {6,25}, {24,39}, {7,40}, {28,39}, {20,32}, {6,27}, {24,34}, {15,28}, {27,33}, {4,10}, {2,21}, {14,38}, {25,37}, {17,32}, {13,29}, {8,21}, {2,20}, {9,20}, {5,18}, {23,30}, {19,35}, {10,17}, {16,39}, {28,40}, {20,31}, {9,14}, {11,37}, {4,38}, {34,41}, {30,40}, {36,39}, {29,32}, {13,35}, {13,32}, {13,26}, {8,23}, {6,8}, {27,39}, {34,40}, {28,31}, {19,27}, {10,34}, {21,37}, {8,20}, {6,9}, {5,39}, {23,40}, {16,19}, {10,28}, {6,20}, {11,34}, {4,15}, {10,41}, {2,42}, {13,30}, {26,36}, {23,29}, {4,18}, {21,30}, {14,22}, {11,25}, {32,41}, {13,42}, {10,38}, {2,37}, {33,38}, {16,37}, {7,17}, {5,29}, {21,40}, {20,38}, {18,34}, {15,30}, {15,27}, {27,34}, {19,28}, {10,33}, {3,38}, {22,37}, {13,33}, {29,36}, {18,35}, {11,30}, {4,36}, {5,25}, {23,31}, {21,28}, {12,33}, {1,27}, {19,34}, {4,22}, {11,21}, {2,14}, {4,14}, {21,25}, {14,24}, {7,25}, {32,40}, {13,39}, {8,32}, {20,27}, {9,34}, {5,28}, {23,33}, {3,19}, {10,22}, {20,37}, {9,38}, {5,34}, {29,41}, {35,42}, {32,38}, {13,37}, {8,33}, {6,16}, {15,37}, {27,38}, {10,15}, {8,38}, {6,37}, {5,36}, {18,23}, {11,16}, {4,28}, {25,34}, {15,31}, {10,26}, {14,21}, {12,25}, {1,24}, {7,19}, {22,40}, {11,39}, {11,17}, {4,29}, {21,41}, {12,42}, {26,41}, {23,36}, {4,25}, {21,31}, {14,26}, {25,32}, {30,34}, {15,36}, {10,29}, {2,35}, {24,36}, {15,29}, {18,31}, {14,30}, {7,22}, {5,11}, {28,41}, {33,42}, {30,38}, {36,37}, {5,17}, {16,21}, {16,20}, {9,28}, {5,20}, {9,23}, {19,37}, {6,34}, {12,30}, {3,36}, {29,42}, {35,41}, {6,14}, {24,25}, {1,22}, {11,19}, {2,17}, {20,29}, {21,36}, {12,18}, {1,11}, {7,23}, {5,8}, {22,39}, {19,41}, {10,42}, {6,35}, {17,24}, {1,9}, {5,37}, {11,42}, {4,41}, {36,41}, {18,42}, {10,13}, {2,26}, {11,13}, {4,26}, {23,41}, {8,42}, {26,40}, {21,33}, {14,27}, {4,32}, {13,21}, {9,37}, {5,33}, {16,23}, {5,10}, {6,40}, {12,37}, {34,42}, {15,41}, {29,38}, {35,37}, {30,33}, {16,36}, {5,7}, {5,23}, {22,25}, {11,31}, {4,30}, {14,29}, {25,35}, {6,32}, {13,24}, {8,15}, {16,29}, {28,35}, 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{15,34}, {30,31}, {6,28}, {24,33}, {11,35}, {20,36}, {6,39}, {2,41}, {20,42}, {17,30}, {18,21}, {10,23}, {14,32}, {27,40}, {34,39}, {26,33}, {9,25}, {2,12}, {30,42}, {26,37}, {2,18}, {9,17}, {3,28}, {22,33}, {13,27}, {22,36}, {4,16}, {2,13}, {17,27}, {29,34}, {16,24}, {22,31}, {11,14}, {4,17}, {21,29}, {3,11}, {1,8}, {3,37}, {18,24}, {7,30}, {23,26}, {1,13}, {17,23}, {18,40}, {23,28}, {4,24}, {10,40}, {6,31}, {8,25}, {26,39}, {7,16}, {4,42}, {6,22}, {7,39}, {5,40}, {16,28}, {28,33}, {5,31}, {14,23}, {19,32}, {6,24}, {2,22}, {11,20}, {7,24}, {4,40}, {21,39}, {21,42}, {12,41}, {1,36}, {18,19}, {2,11}, {2,38}, {6,42}, {35,39}, {9,16}, {1,28}, {7,13}, {32,39}, {13,31}, {17,42}, {14,42}, {2,39}, {21,27}, {10,25}, {16,42}, {9,18}, {10,37}, {30,41}, {20,40}, {29,31}, {14,35}, {9,41}, {30,37}, {17,28}, {12,20}, {3,9}, {3,15}, {13,19}, {13,23}, {8,26}, {3,23}, {8,22}, {2,33}, {34,37}, {12,22}, {20,41}, {24,37}, {4,34}, {15,21}, {3,39}, {1,37}, {33,37}, {16,38}, {1,30}, {11,38}, {17,25}, {8,39}, 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{13,38}, {8,34}, {17,38}, {7,42}, {4,35}, {1,32}, {4,9}, {5,41}, {17,36}, {18,29}, {3,20}, {11,29}, {21,32}, {30,35}, {12,13}, {4,20}, {6,18}, {17,22}, {19,30}, {8,36}, {1,21}, {6,36}, {12,38} } Symmetric graph 54 of order 42 Valency 39 Diameter 2 Girth 3 Automorphism group of order 6831653917205672755200 Number of arcs = 1638 Number of 2-arcs = 62244 2-arc-transitive false Edge-set { {1,4}, {32,41}, {35,38}, {9,15}, {11,33}, {12,37}, {18,24}, {27,29}, {8,34}, {14,31}, {10,36}, {13,23}, {17,21}, {1,7}, {22,29}, {5,20}, {3,39}, {16,28}, {6,7}, {25,32}, {15,17}, {8,26}, {16,25}, {3,41}, {2,32}, {30,38}, {19,29}, {9,20}, {26,40}, {36,42}, {22,39}, {18,28}, {2,21}, {2,42}, {30,34}, {9,24}, {4,33}, {4,16}, {3,27}, {3,23}, {6,28}, {2,4}, {15,33}, {11,39}, {9,31}, {33,37}, {12,30}, {19,24}, {20,40}, {1,26}, {29,42}, {6,10}, {14,38}, {12,17}, {11,19}, {9,22}, {17,28}, {1,21}, {25,31}, {37,41}, {30,39}, {16,19}, {7,29}, {8,41}, {31,35}, {18,41}, {2,35}, {22,33}, {5,39}, {20,33}, {8,39}, {28,42}, {21,34}, {31,41}, {35,37}, {4,8}, {27,31}, {11,34}, {14,22}, {29,32}, {8,10}, {23,31}, {30,36}, {13,19}, {21,27}, {7,40}, {13,26}, {10,42}, {23,32}, {6,38}, {14,29}, {12,20}, {35,42}, {15,34}, {6,12}, {24,25}, {16,36}, {3,13}, {27,34}, {14,40}, {1,19}, {9,29}, {3,21}, {38,41}, {7,24}, {4,32}, {10,15}, {11,23}, {11,30}, {19,22}, {18,27}, {2,40}, {2,29}, {20,30}, {3,15}, {11,28}, {7,37}, {18,32}, {1,11}, {31,37}, {18,37}, {8,19}, {11,40}, {22,36}, {31,42}, {3,11}, {22,28}, {14,28}, {12,21}, {25,39}, {16,41}, {7,15}, {11,32}, {10,37}, {18,23}, {28,35}, {7,22}, {5,32}, {34,39}, {14,16}, {6,19}, {9,25}, {3,35}, {15,28}, {7,20}, {8,32}, {17,19}, {5,27}, {22,25}, {5,41}, {2,13}, {10,30}, {5,23}, {6,26}, {14,35}, {12,15}, {8,33}, {12,42}, {24,34}, {6,29}, {20,25}, {26,36}, {13,42}, {14,37}, {12,18}, {4,39}, {16,27}, {13,34}, {21,24}, {4,7}, {18,38}, {2,17}, {5,33}, {26,39}, {5,16}, {6,13}, {10,25}, {27,32}, {38,40}, {1,29}, {20,29}, {25,33}, {39,41}, {11,24}, {7,30}, {9,41}, {33,35}, 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{26,29}, {20,42}, {8,24}, {4,31}, {11,15}, {11,22}, {2,30}, {19,30}, {1,15}, {11,29}, {8,37}, {18,31}, {18,35}, {16,42}, {3,6}, {25,28}, {6,27}, {25,40}, {22,27}, {5,40}, {10,29}, {32,40}, {36,38}, {5,7}, {26,32}, {20,32}, {10,26}, {14,27}, {12,40}, {5,22}, {28,39}, {16,21}, {6,25}, {25,41}, {15,37}, {1,16}, {3,29}, {31,38}, {9,39}, {16,33}, {15,30}, {16,35}, {8,38}, {13,28}, {10,21}, {6,35}, {15,25}, {12,27}, {24,40}, {2,6}, {25,30}, {9,36}, {13,33}, {6,11}, {27,28}, {21,40}, {1,25}, {29,41}, {4,41}, {24,38}, {4,17}, {5,15}, {11,26}, {19,41}, {9,35}, {1,27}, {31,34}, {22,30}, {5,19}, {1,39}, {16,29}, {6,8}, {4,20}, {8,27}, {3,42}, {3,32}, {28,38}, {10,28}, {21,23}, {17,25}, {1,41}, {37,40}, {1,30}, {17,31}, {18,19}, {2,9}, {17,42}, {1,34}, {24,31}, {4,37}, {5,12}, {13,39}, {10,16}, {21,32}, {7,38}, {20,35}, {11,17}, {1,22}, {28,41}, {21,35}, {14,30}, {12,19}, {29,39}, {8,28}, {21,31}, {10,39}, {9,10}, {29,35}, {4,13}, {10,27}, {34,38}, {14,17}, {32,36}, {10,23}, {6,23}, {30,37}, {4,27}, {27,40}, {3,38}, {14,20}, {8,12}, {39,42}, {16,34}, {23,34}, {17,24}, {17,35}, {5,26}, {3,33}, {7,28}, {11,25}, {22,41}, {2,18}, {14,41}, {12,35}, {3,34}, {6,40}, {23,36}, {20,24}, {16,38}, {3,17}, {26,38}, {11,14}, {19,37}, {9,18}, {1,9}, {31,40}, {36,37}, {2,15}, {15,31}, {11,37}, {7,18}, {10,33}, {23,39}, {17,32}, {13,17}, {1,10}, {17,37}, {12,36}, {6,16}, {21,37}, {27,35}, {24,42}, {23,29}, {6,20}, {14,26}, {32,35}, {4,34}, {19,34}, {9,14}, {30,31}, {19,40}, {27,38}, {29,34}, {3,10}, {23,28}, {7,17}, {1,32}, {1,18}, {14,18}, {2,12}, {33,42}, {24,28}, {4,21}, {22,42}, {5,34}, {13,24}, {4,10}, {5,9}, {13,40}, {15,20}, {9,13}, {12,38}, {9,23}, {6,33}, {9,26}, {23,35}, {6,15}, {5,25}, {13,36}, {10,13}, {21,22}, {15,24}, {4,11}, {23,27}, {2,38}, {29,33}, {20,39}, {7,12}, {24,32}, {8,18}, {2,31}, {4,30}, {3,12}, {5,28}, {21,26}, {25,35}, {15,41}, {37,42}, {18,34}, {4,24}, {5,13}, {13,21}, {34,37}, {24,30}, {4,19}, {1,38}, {17,29}, {5,8}, {26,31}, {34,42}, {14,34}, {5,21}, {13,25}, {10,41}, {4,38}, {15,29}, {11,20}, {11,35}, {4,40}, {27,36}, {6,14}, {1,37}, {18,29}, {22,32}, {5,38}, {7,39}, {16,32}, {9,19}, {36,40}, {22,38}, {2,20}, {26,41}, {3,22}, {12,39}, {9,33}, {33,39}, {12,28}, {15,21}, {16,24}, {3,4}, {15,32}, {11,38}, {30,32}, {17,27}, {1,40}, {1,31}, {29,37}, {32,39}, {7,21}, {7,32}, {5,11}, {22,26}, {33,41}, {18,42}, {3,14}, {19,32}, {9,38}, {11,21}, {25,37}, {6,30}, {19,25}, {20,22}, {3,28}, {21,28}, {7,25}, {15,22}, {1,35}, {18,20}, {26,35}, {3,25}, {17,33}, {8,15}, {19,23}, {5,35}, {13,22}, {5,10}, {12,33}, {24,39}, {25,42}, {3,36}, {12,22}, {2,16}, {8,16}, {3,7}, {16,37}, {3,18}, {23,40}, {6,36}, {31,39}, {2,28}, {21,30}, {4,14}, {9,11}, {13,18}, {16,39}, {10,34}, {8,17}, {7,42}, {2,24}, {12,23}, {6,24}, {14,25}, {1,17}, {29,38}, {7,13}, {10,32}, {10,38}, {17,23}, {27,37}, {14,23}, {8,35}, {8,22}, {9,16}, {3,26}, {15,38}, {2,34}, {23,41}, {22,37}, {5,18}, {8,20}, {26,42}, {9,37}, {18,33}, {16,40}, {1,6}, {25,29}, {10,40}, {5,24}, {16,20}, {15,39}, {20,28}, {8,21}, {3,30}, {9,32}, {33,38}, {13,37}, {12,31}, {35,41}, {9,12}, {39,40}, {7,26}, {15,35}, {29,36}, {4,26}, {1,20}, {8,29}, {8,42}, {17,26}, {15,26}, {7,27}, {34,41}, {24,37}, {20,31}, {13,30}, {7,33}, {1,28}, {7,31}, {32,37}, {30,41}, {19,35}, {21,36}, {6,41}, {4,18}, {11,27}, {17,39}, {21,41}, {7,35}, {16,23}, {7,19}, {27,41}, {35,40}, {3,20}, {28,36}, {7,23}, {6,32}, {12,16}, {6,39}, {36,41}, {12,41}, {20,27}, {14,42}, {5,17}, {6,42}, {25,34}, {24,36}, {2,33}, {29,40}, {13,38}, {19,33}, {8,11}, {22,31}, {4,25}, {2,7}, {35,39}, {27,33}, {12,34}, {14,24}, {3,5}, {13,32}, {32,38}, {20,23}, {30,33}, {6,9}, {11,31}, {1,12}, {9,27}, {33,40}, {24,29}, {4,23}, {24,27}, {19,26}, {9,42}, {1,42}, {23,37}, {24,33}, {3,31}, {18,36}, {15,36}, {4,12}, {19,36}, {2,37}, {10,18}, {2,23}, {13,20}, {38,42}, {17,34}, {7,11}, {11,18}, {2,22}, {15,16}, {3,16}, {2,14}, {20,36}, {8,13}, {21,42}, {7,34}, {12,29}, {10,22}, {8,25}, {3,19}, {9,28}, {23,33}, {10,19}, {17,40}, {1,36}, {32,42}, {13,35}, {7,36}, {18,26}, {26,28}, {19,39}, {23,26}, {13,29}, {11,13}, {5,30}, {11,16}, {2,8}, {28,32}, {21,38}, {25,38}, {17,41}, {15,42}, {22,34}, {18,30}, {2,27}, {30,40}, {26,33}, {8,30}, {11,42}, {12,25}, {8,31}, {10,20}, {24,41}, {36,39}, {13,16}, {6,21}, {20,26}, {19,31}, {14,32}, {5,29}, {10,31}, {21,29}, {20,41}, {1,14}, {8,23}, {17,38}, {12,14}, {12,24}, {2,39}, {6,31}, {16,30}, {3,24}, {5,37}, {17,30}, {21,33} } Symmetric graph 55 of order 42 Valency 40 Diameter 2 Girth 3 Automorphism group of order 107145471557284795514880000 Number of arcs = 1680 Number of 2-arcs = 65520 2-arc-transitive false Edge-set { {1,3}, {10,33}, {11,13}, {23,40}, {24,31}, {27,30}, {16,41}, {21,25}, {2,7}, {19,26}, {8,36}, {35,38}, {9,17}, {14,42}, {5,39}, {6,8}, {20,34}, {3,34}, {12,26}, {7,11}, {21,33}, {4,31}, {25,28}, {17,32}, {27,37}, {16,24}, {30,32}, {28,41}, {15,40}, {2,22}, {1,4}, {3,25}, {12,39}, {22,23}, {10,39}, {13,23}, {7,29}, {33,42}, {3,30}, {26,41}, {6,40}, {20,24}, {9,19}, {14,36}, {8,37}, {10,34}, {16,20}, {30,35}, {18,38}, {9,38}, {14,26}, {5,8}, {20,35}, {17,35}, {37,42}, {13,21}, {2,6}, {5,34}, {12,19}, {9,33}, {11,14}, {8,10}, {13,34}, {22,29}, {1,42}, {5,25}, {7,19}, {1,31}, {25,27}, {7,16}, {3,36}, {18,26}, {40,41}, {24,40}, {10,35}, {13,17}, {7,42}, {33,39}, {1,21}, {2,3}, {8,22}, {11,24}, {21,32}, {28,31}, {15,28}, {4,18}, {25,38}, {23,39}, {23,31}, {12,14}, {5,22}, {32,35}, {17,27}, {15,17}, {29,37}, {17,24}, {32,37}, {7,28}, {15,33}, {2,4}, {4,25}, {12,32}, {22,27}, {16,32}, {18,41}, {38,40}, {6,27}, {1,34}, {3,12}, {2,39}, {4,23}, {11,29}, {21,42}, {24,32}, {28,30}, {15,41}, {25,31}, {27,39}, {16,23}, {5,36}, {18,19}, {33,41}, {11,40}, {2,8}, {4,34}, {3,11}, {21,26}, {19,33}, {11,36}, {8,38}, {9,34}, {3,14}, {5,26}, {10,31}, {13,28}, {7,15}, {29,33}, {23,32}, {27,31}, {16,27}, {16,30}, {3,41}, {26,40}, {22,40}, {1,24}, {6,33}, {11,20}, {12,13}, {4,5}, {19,25}, {26,30}, {8,41}, {6,20}, {19,37}, {10,36}, {13,37}, {6,10}, {9,15}, {14,29}, 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{28,42}, {5,15}, {19,29}, {20,42}, {35,39}, {16,34}, {5,13}, {6,19}, {12,35}, {19,28}, {1,14}, {3,5}, {17,22}, {15,39}, {23,29}, {17,29}, {18,30}, {38,41}, {23,26}, {8,31}, {20,27}, {16,35}, {3,42}, {26,39}, {15,19}, {29,36}, {38,42}, {30,41}, {8,25}, {20,39}, {10,37}, {10,13}, {7,13}, {19,32}, {27,36}, {10,22}, {1,13}, {3,29}, {26,42}, {19,24}, {17,38}, {11,19}, {19,22}, {1,36}, {7,10}, {35,41}, {10,25}, {6,23}, {7,9}, {14,33}, {16,17}, {2,12}, {3,27}, {12,16}, {22,30}, {39,41}, {4,36}, {18,25}, {11,35}, {7,27}, {16,19}, {14,22}, {1,5}, {13,33}, {2,42}, {16,31}, {28,35}, {4,15}, {25,29}, {17,39}, {7,38}, {8,15}, {34,41}, {21,36}, {9,31}, {20,36}, {10,12}, {4,29}, {25,42}, {10,20}, {13,35}, {6,18}, {20,38}, {13,18}, {26,34}, {6,9}, {9,35}, {7,39}, {19,21}, {2,36}, {5,11}, {21,39}, {2,23}, {26,29}, {8,42}, {9,12}, {30,39}, {3,21}, {2,26}, {12,41}, {16,25}, {32,36}, {30,40}, {4,40}, {11,22}, {28,37}, {15,24}, {29,32}, {2,21}, {8,23}, {24,37}, {10,32}, {6,15}, {7,22}, {26,35}, {24,42}, {32,39}, {21,28}, {2,15}, {16,21}, {36,42}, {12,18}, {6,37}, {8,40}, {12,33}, {3,18}, {24,28}, {15,32}, {23,30}, {33,36}, {26,38}, {1,41}, {6,25}, {7,20}, {17,26}, {17,37}, {19,36}, {22,39}, {1,37}, {3,10}, {6,22}, {18,42}, {5,41}, {2,20}, {11,38}, {9,21}, {14,37}, {33,35}, {28,34}, {30,38}, {17,23}, {16,18}, {3,40}, {14,18}, {3,7}, {11,21}, {26,31}, {1,17}, {22,32}, {2,29}, {24,26}, {24,41}, {9,23}, {14,31}, {7,24}, {15,25}, {23,27}, {5,18}, {23,33}, {11,31}, {37,41}, {2,13}, {4,6}, {18,21}, {1,27}, {14,39}, {5,23}, {2,27}, {1,11}, {10,21}, {28,33}, {2,10}, {4,13}, {19,30}, {13,22}, {1,6}, {25,36}, {7,18}, {16,36}, {15,35}, {37,39}, {7,25}, {9,22}, {14,32}, {5,27}, {10,41}, {1,33}, {6,21}, {18,28}, {17,41}, {37,40}, {4,8}, {25,34}, {12,22}, {18,23}, {31,38}, {21,35}, {27,33}, {11,16}, {33,40}, {8,21}, {30,37}, {11,30}, {11,28}, {3,23}, {32,42}, {31,34}, {1,25}, {28,40}, {14,16}, {5,30}, {29,34}, {12,42}, {10,38}, {9,13}, {17,19}, {1,39}, {14,28}, {3,38}, {5,28}, {14,19}, {6,14}, {16,22}, {1,30}, {26,37}, {39,42}, {6,31}, {20,28}, {12,31}, {22,28}, {31,42}, {22,31}, {27,32}, {1,15}, {12,17}, {16,29}, {6,11}, {20,21}, {2,30}, {4,41}, {18,33}, {25,40}, {24,29}, {13,20}, {7,34}, {29,42}, {20,31}, {19,41}, {18,37}, {13,26}, {18,35}, {6,34}, {7,32}, {20,22}, {6,12}, {5,20}, {31,41}, {15,29}, {4,21}, {2,25}, {29,40}, {10,15}, {25,35}, {7,17}, {33,37}, {30,33}, {1,19}, {10,23}, {13,31}, {3,19}, {4,39}, {12,34}, {17,30}, {32,40}, {24,27}, {5,29}, {20,41}, {16,33}, {8,33}, {8,39}, {24,25}, {15,36}, {8,26}, {36,41}, {38,39}, {27,34}, {33,38}, {4,7}, {11,41}, {23,34}, {3,15}, {5,24}, {2,38}, {4,9}, {23,42}, {3,20}, {19,42}, {9,24}, {21,40}, {35,40}, {2,35}, {36,39}, {15,21}, {1,28}, {5,19}, {12,37}, {30,42}, {9,42}, {26,36}, {12,27}, {18,40}, {29,38}, {4,22}, {8,34}, {8,32}, {3,16}, {23,25}, {7,31}, {10,11}, {17,40}, {6,13}, {18,29} } Symmetric graph 56 of order 42 Valency 41 Diameter 1 Girth 3 Automorphism group of order 1405006117752879898543142606244511569936384000000000 Number of arcs = 1722 Number of 2-arcs = 68880 2-arc-transitive true Edge-set { {1,2}, {1,41}, {1,15}, {2,41}, {1,13}, {6,41}, {2,15}, {1,5}, {31,41}, {15,24}, {2,30}, {2,13}, {1,6}, {1,38}, {22,41}, {15,25}, {2,12}, {13,17}, {6,29}, {2,4}, {2,5}, {1,31}, {1,24}, {30,41}, {1,35}, {39,41}, {10,15}, {2,27}, {11,13}, {6,33}, {2,31}, {5,27}, {19,31}, {24,41}, {4,30}, {2,16}, {2,38}, {1,22}, {1,25}, {12,41}, {1,17}, {29,41}, {4,15}, {1,23}, {28,41}, {15,19}, {2,20}, {7,13}, {6,8}, {2,9}, {5,42}, {17,31}, {8,24}, {30,42}, {2,25}, {1,12}, {9,38}, {5,22}, {3,25}, {11,12}, {15,17}, {2,29}, {4,16}, {2,37}, {1,37}, {2,35}, {1,39}, {1,10}, {27,41}, {1,11}, {33,41}, {15,31}, {1,27}, {19,41}, {15,41}, {13,16}, {6,24}, {1,36}, {16,41}, {15,21}, {2,14}, {3,13}, {6,11}, {5,40}, {10,31}, {24,29}, {7,30}, {2,22}, {1,18}, {26,38}, {22,25}, {25,27}, {12,19}, {17,29}, {7,29}, {4,26}, {2,11}, {1,33}, {13,41}, {22,35}, {18,39}, {10,38}, {22,27}, {11,34}, {33,36}, {31,42}, {13,27}, {6,19}, {1,4}, {16,37}, {24,37}, {23,41}, {2,23}, {1,28}, {1,19}, {20,41}, {1,7}, {8,41}, {9,15}, {1,42}, {17,41}, {8,15}, {2,42}, {13,25}, {6,12}, {1,9}, {5,41}, {3,15}, {13,15}, {2,6}, {5,37}, {31,37}, {17,24}, {29,30}, {21,41}, {15,37}, {13,39}, {3,6}, {2,33}, {5,34}, {31,36}, {24,42}, {17,30}, {32,38}, {22,32}, {7,25}, {8,12}, {4,29}, {4,40}, {2,10}, {26,41}, {6,35}, {9,39}, {10,11}, {27,33}, {9,11}, {5,33}, {3,31}, {4,19}, {40,41}, {4,10}, {6,16}, {9,24}, {1,8}, {41,42}, {5,15}, {10,23}, {27,28}, {19,28}, {20,26}, {7,35}, {8,39}, {9,10}, {20,42}, {17,40}, {8,18}, {21,42}, {25,26}, {12,25}, {5,9}, {5,31}, {3,24}, {11,30}, {1,16}, {12,37}, {23,37}, {12,17}, {23,29}, {15,36}, {2,36}, {1,21}, {14,41}, {1,3}, {11,41}, {14,15}, {1,40}, {10,41}, {15,29}, {2,7}, {13,22}, {6,18}, {1,26}, {25,41}, {15,27}, {2,19}, {13,29}, {6,7}, {2,26}, {5,11}, {31,33}, {24,31}, {13,30}, {18,41}, {15,38}, {13,34}, {6,36}, {5,13}, {6,31}, {2,24}, {1,30}, {12,38}, {22,23}, {12,23}, 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{18,27}, {19,21}, {16,39}, {7,34}, {8,36}, {21,33}, {6,32}, {9,32}, {7,11}, {8,33}, {3,40}, {28,40}, {4,28}, {10,20}, {14,42}, {8,32}, {25,28}, {12,26}, {5,39}, {12,18}, {21,23}, {20,24}, {30,40}, {23,32}, {7,12}, {8,23}, {13,36}, {7,9}, {3,9}, {13,32}, {30,31}, {18,30}, {23,38}, {22,28}, {7,17}, {8,29}, {4,9}, {28,32}, {26,32}, {3,8}, {12,40}, {10,19}, {28,34}, {26,36}, {8,35}, {39,42}, {18,34}, {21,36}, {8,26}, {23,27}, {29,42}, {21,34}, {39,40}, {32,33}, {32,35}, {7,32}, {18,28}, {23,42}, {8,19}, {4,22}, {4,34}, {16,33}, {24,35}, {30,32}, {10,29}, {7,27}, {26,28}, {11,26}, {25,33}, {29,38}, {7,23}, {8,28}, {9,14}, {3,32}, {11,32}, {11,25}, {12,33}, {21,22}, {25,37}, {18,33}, {31,38}, {34,38}, {22,36}, {13,28}, {6,26}, {2,39}, {21,38}, {9,12}, {17,19}, {20,29}, {1,14}, {13,20}, {5,29}, {7,31}, {25,30}, {38,41}, {9,31}, {30,33}, {15,20}, {5,32}, {31,32}, {7,24}, {8,30}, {17,37}, {4,17}, {35,40}, {10,39}, {3,19}, {4,35}, {10,13}, {5,26}, {24,27}, {19,30}, {29,39}, {11,37}, {33,37}, 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{25,40}, {15,35}, {6,38}, {12,34}, {19,23}, {8,20}, {3,34}, {5,7}, {4,20}, {14,18}, {37,38}, {23,28}, {21,39}, {3,33}, {19,36}, {3,37}, {23,36}, {14,20}, {9,26}, {34,40}, {28,36}, {8,27}, {21,35}, {14,39}, {9,23}, {25,36}, {4,36}, {19,42}, {14,36}, {3,28}, {21,26}, {23,34}, {32,40}, {12,35}, {16,35}, {9,18}, {36,42}, {20,36}, {26,34}, {30,39}, {28,33}, {10,14}, {11,16}, {21,40}, {14,21}, {18,21}, {14,30}, {18,32}, {14,23}, {6,28}, {20,34}, {38,40}, {14,16}, {23,39}, {16,18}, {21,24}, {3,26}, {28,37}, {18,26}, {32,39} } ................................................................... Symmetric connected graphs of order 43 Symmetric graph 1 of order 43 Valency 2 Diameter 21 Girth 43 Automorphism group of order 86 Number of arcs = 86 Number of 2-arcs = 86 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {15,16}, {16,17}, {17,18}, {18,19}, {19,20}, {20,21}, {21,22}, {22,23}, {23,24}, {24,25}, {25,26}, {26,27}, {27,28}, {28,29}, {29,30}, {30,31}, {31,32}, {32,33}, {33,34}, {34,35}, {35,36}, {36,37}, {37,38}, {38,39}, {39,40}, {40,41}, {41,42}, {42,43}, {1,43} } Symmetric graph 2 of order 43 Valency 6 Diameter 4 Girth 3 Automorphism group of order 258 Number of arcs = 258 Number of 2-arcs = 1290 2-arc-transitive false Edge-set { {1,2}, {2,3}, {29,36}, {3,4}, {22,29}, {30,37}, {6,12}, {4,5}, {15,22}, {23,30}, {12,18}, {31,38}, {5,42}, {7,13}, {5,6}, {8,15}, {16,23}, {18,24}, {24,31}, {5,11}, {13,19}, {32,39}, {35,41}, {6,43}, {7,8}, {8,14}, {37,38}, {6,7}, {1,8}, {9,16}, {24,30}, {17,24}, {11,17}, {19,25}, {25,32}, {4,41}, {8,9}, {14,20}, {38,39}, {33,40}, {28,34}, {36,42}, {13,14}, {1,7}, {1,43}, {9,15}, {30,31}, {35,42}, {1,37}, {2,9}, {30,36}, {10,17}, {17,23}, {25,31}, {18,25}, {4,10}, {9,10}, {20,26}, {39,40}, {26,33}, {34,40}, {14,15}, {15,21}, {31,32}, {28,35}, {34,41}, {21,27}, {29,35}, {19,20}, {37,43}, {2,8}, {36,37}, {36,43}, {10,16}, {23,24}, {5,41}, {2,38}, {3,10}, {23,29}, {31,37}, {11,18}, {10,11}, {26,32}, {40,41}, {19,26}, {3,40}, {15,16}, {32,33}, {21,28}, {27,34}, {27,33}, {20,21}, {16,22}, {24,25}, {22,28}, {25,26}, {12,13}, {1,38}, {42,43}, {3,9}, {29,30}, {6,42}, {16,17}, {4,11}, {3,39}, {11,12}, {32,38}, {41,42}, {12,19}, {33,34}, {14,21}, {20,27}, {33,39}, {21,22}, {26,27}, {17,18}, {4,40}, {18,19}, {2,39}, {35,36}, {7,43}, {22,23}, {5,12}, {34,35}, {7,14}, {13,20}, {27,28}, {28,29}, {6,13} } Symmetric graph 3 of order 43 Valency 14 Diameter 2 Girth 3 Automorphism group of order 602 Number of arcs = 602 Number of 2-arcs = 7826 2-arc-transitive false Edge-set { {1,2}, {2,3}, {39,41}, {3,4}, {37,39}, {40,42}, {4,8}, {4,5}, {35,37}, {38,40}, {8,12}, {41,43}, {2,6}, {5,9}, {27,35}, {5,6}, {33,35}, {36,38}, {12,16}, {6,10}, {9,13}, {19,27}, {1,42}, {4,43}, {3,7}, {31,39}, {25,33}, {28,36}, {16,32}, {6,7}, {31,33}, {34,36}, {16,20}, {10,14}, {13,17}, {11,19}, {7,11}, {23,31}, {17,25}, {20,28}, {5,32}, {2,43}, {2,41}, {1,5}, {35,43}, {29,37}, {32,40}, {8,24}, {26,34}, {20,36}, {14,30}, {17,33}, {11,22}, {7,8}, {29,31}, {32,34}, {20,24}, {14,18}, {17,21}, {3,11}, {11,15}, {15,23}, {9,17}, {12,20}, {5,21}, {21,29}, {24,32}, {24,40}, {18,26}, {9,36}, {3,30}, {6,33}, {22,33}, {1,3}, {39,43}, {3,42}, {4,39}, {33,41}, {1,36}, {16,43}, {30,38}, {12,28}, {6,22}, {9,25}, {27,38}, {18,34}, {21,37}, {3,14}, {15,31}, {15,26}, {9,20}, {12,23}, {21,42}, {8,9}, {27,29}, {30,32}, {24,28}, {18,22}, {21,25}, {3,38}, {15,19}, {7,15}, {1,9}, {4,12}, {13,21}, {16,24}, {13,40}, {10,18}, {3,19}, {1,33}, {22,30}, {1,28}, {22,38}, {25,41}, {6,38}, {7,34}, {10,37}, {14,25}, {4,31}, {26,37}, {20,31}, {23,34}, {20,42}, {2,4}, {37,41}, {1,40}, {8,43}, {2,37}, {5,40}, {8,35}, {34,42}, {4,20}, {14,41}, {1,17}, {11,43}, {10,26}, {13,29}, {19,30}, {7,23}, {31,42}, {25,36}, {28,39}, {10,32}, {19,35}, {7,18}, {1,12}, {4,15}, {15,37}, {13,24}, {16,27}, {13,34}, {10,21}, {3,25}, {19,40}, {22,43}, {9,10}, {25,27}, {28,30}, {28,32}, {22,26}, {25,29}, {19,23}, {7,42}, {5,13}, {8,16}, {2,10}, {14,22}, {11,38}, {6,17}, {5,37}, {2,34}, {20,41}, {26,42}, {2,29}, {30,41}, {23,39}, {10,42}, {4,36}, {7,39}, {10,31}, {18,29}, {15,36}, {24,35}, {12,34}, {21,32}, {3,24}, {18,40}, {21,43}, {3,5}, {35,39}, {38,42}, {6,41}, {27,43}, {12,39}, {2,18}, {3,35}, {15,42}, {9,41}, {11,27}, {17,28}, {5,26}, {29,40}, {32,43}, {2,24}, {14,36}, {8,30}, {11,33}, {22,23}, {5,16}, {8,19}, {7,29}, {2,13}, {19,41}, {13,35}, {16,38}, {12,13}, {17,38}, {11,32}, {14,35}, {17,18}, {1,23}, {4,26}, {36,37}, {42,43}, {10,11}, {23,25}, {26,28}, {32,36}, {26,30}, {29,33}, {23,27}, {6,14}, {9,31}, {12,33}, {18,39}, {8,40}, {2,23}, {8,29}, {23,24}, {7,28}, {16,37}, {13,14}, {18,19}, {1,22}, {4,25}, {37,38}, {1,43}, {4,6}, {33,37}, {36,40}, {9,30}, {6,27}, {33,34}, {6,28}, {38,39}, {14,15}, {26,27}, {20,21}, {5,27}, {28,29}, {17,39}, {16,17}, {17,19}, {21,22}, {15,16}, {7,9}, {40,41}, {34,35}, {12,14}, {11,12}, {21,23}, {24,26}, {30,34}, {27,31}, {24,25}, {19,20}, {39,40}, {27,28}, {29,30}, {15,17}, {5,7}, {41,42}, {35,36}, {10,12}, {31,35}, {34,38}, {25,26}, {31,32}, {18,20}, {30,31}, {8,10}, {13,15}, {32,33}, {9,11}, {11,13}, {16,18}, {19,21}, {22,24}, {6,8}, {14,16}, {20,22} } Symmetric graph 4 of order 43 Valency 42 Diameter 1 Girth 3 Automorphism group of order 60415263063373835637355132068513997507264512000000000 Number of arcs = 1806 Number of 2-arcs = 74046 2-arc-transitive true Edge-set { {1,2}, {2,3}, {9,18}, {3,4}, {18,27}, {10,19}, {33,38}, {4,5}, {27,36}, {19,28}, {28,33}, {11,20}, {4,42}, {34,39}, {39,41}, {5,6}, {2,36}, {28,37}, {23,28}, {20,29}, {37,42}, {29,34}, {37,39}, {12,21}, {8,13}, {5,43}, {34,36}, {35,40}, {5,7}, {40,42}, {7,25}, {6,7}, {2,11}, {3,37}, {18,23}, {29,38}, {32,37}, {24,29}, {35,37}, {21,30}, {3,8}, {38,43}, {32,34}, {30,35}, {3,5}, {38,40}, {7,32}, {13,22}, {17,22}, {9,14}, {29,31}, {1,6}, {2,43}, {5,23}, {36,41}, {14,16}, {6,8}, {2,20}, {41,43}, {16,34}, {8,26}, {10,20}, {7,8}, {3,12}, {13,18}, {4,38}, {27,32}, {19,24}, {33,35}, {30,39}, {3,41}, {30,32}, {25,30}, {1,3}, {36,38}, {14,32}, {22,31}, {12,17}, {4,9}, {27,29}, {1,39}, {5,30}, {31,36}, {12,14}, {4,6}, {2,27}, {16,41}, {8,33}, {20,30}, {14,23}, {26,31}, {24,26}, {10,15}, {3,21}, {2,7}, {9,11}, {18,43}, {6,24}, {2,35}, {23,25}, {15,17}, {15,40}, {7,9}, {11,29}, {8,18}, {1,42}, {25,43}, {17,35}, {5,15}, {9,27}, {19,29}, {11,21}, {4,8}, {8,9}, {4,13}, {22,27}, {14,19}, {31,33}, {5,39}, {28,30}, {20,25}, {14,39}, {31,40}, {7,12}, {25,27}, {12,30}, {10,12}, {2,4}, {23,41}, {15,33}, {30,40}, {23,32}, {21,26}, {22,24}, {5,10}, {3,28}, {2,40}, {6,31}, {2,12}, {21,23}, {13,15}, {22,40}, {11,36}, {18,28}, {17,42}, {15,25}, {9,34}, {29,39}, {21,31}, {8,12}, {15,24}, {19,21}, {1,19}, {11,16}, {4,22}, {17,27}, {18,20}, {13,38}, {33,43}, {1,11}, {3,36}, {14,18}, {10,35}, {16,18}, {6,16}, {8,10}, {20,38}, {3,13}, {9,19}, {29,33}, {1,26}, {10,43}, {18,36}, {14,24}, {2,6}, {10,28}, {28,38}, {3,42}, {12,22}, {13,17}, {5,9}, {29,36}, {9,10}, {5,14}, {26,28}, {15,20}, {21,39}, {6,40}, {12,37}, {7,40}, {32,41}, {16,21}, {20,22}, {13,31}, {11,13}, {24,42}, {25,35}, {6,39}, {31,41}, {12,16}, {24,33}, {17,19}, {6,11}, {4,29}, {27,37}, {18,22}, {16,26}, {13,23}, {33,37}, {24,34}, {6,10}, {5,38}, {3,7}, {22,32}, {17,21}, {9,13}, {22,29}, {16,25}, {9,42}, {26,36}, {24,28}, {1,34}, {39,43}, {4,37}, {23,27}, {15,19}, {33,40}, {4,14}, {7,17}, {11,15}, {8,41}, {27,31}, {38,42}, {30,34}, {3,39}, {4,43}, {19,37}, {23,33}, {1,40}, {11,18}, {37,41}, {27,34}, {22,26}, {24,31}, {2,38}, {30,37}, {3,23}, {10,11}, {6,15}, {7,41}, {16,20}, {33,42}, {10,14}, {7,11}, {32,42}, {21,25}, {15,22}, {25,34}, {28,32}, {19,23}, {26,33}, {31,35}, {34,38}, {32,39}, {1,5}, {4,11}, {2,41}, {20,27}, {26,30}, {17,24}, {31,38}, {23,30}, {3,26}, {17,26}, {25,29}, {1,37}, {7,43}, {32,36}, {28,35}, {6,42}, {34,41}, {16,39}, {36,40}, {20,24}, {6,13}, {21,28}, {5,12}, {4,40}, {7,27}, {36,43}, {35,39}, {9,16}, {12,19}, {13,33}, {25,32}, {5,28}, {19,26}, {1,21}, {18,41}, {12,32}, {4,24}, {27,35}, {11,12}, {7,16}, {8,42}, {8,15}, {34,43}, {13,20}, {10,17}, {16,23}, {6,26}, {26,35}, {35,42}, {19,39}, {14,21}, {5,41}, {7,30}, {2,9}, {13,36}, {18,25}, {8,28}, {1,24}, {21,41}, {12,35}, {4,27}, {19,27}, {3,10}, {9,32}, {1,8}, {20,43}, {14,37}, {11,34}, {5,25}, {17,40}, {7,15}, {7,14}, {11,31}, {17,37}, {2,22}, {16,36}, {20,28}, {23,43}, {15,38}, {22,42}, {14,34}, {31,39}, {10,30}, {6,29}, {2,37}, {19,42}, {9,17}, {25,33}, {22,30}, {1,36}, {28,36}, {14,28}, {12,13}, {8,17}, {9,43}, {1,35}, {8,31}, {15,35}, {11,19}, {20,40}, {7,42}, {2,25}, {12,20}, {18,38}, {23,31}, {10,33}, {9,29}, {29,37}, {1,9}, {17,25}, {14,22}, {28,42}, {30,38}, {8,43}, {32,40}, {5,13}, {2,10}, {16,24}, {8,16}, {6,20}, {13,21}, {24,32}, {18,26}, {15,23}, {21,29}, {8,37}, {35,43}, {6,41}, {26,34}, {5,40}, {7,21}, {4,12}, {3,11}, {3,38}, {18,32}, {34,42}, {10,18}, {24,38}, {10,39}, {12,26}, {9,23}, {23,37}, {15,29}, {37,40}, {13,14}, {1,10}, {6,14}, {13,42}, {20,34}, {8,22}, {33,41}, {21,35}, {4,39}, {3,32}, {9,38}, {10,24}, {26,40}, {29,43}, {34,37}, {12,41}, {16,30}, {2,31}, {4,18}, {1,15}, {8,11}, {17,31}, {1,30}, {19,33}, {6,35}, {3,17}, {29,32}, {14,43}, {11,25}, {5,19}, {2,16}, {17,20}, {22,36}, {13,27}, {27,41}, {30,33}, {5,34}, {4,33}, {25,39}, {1,41}, {11,40}, {4,7}, {19,22}, {35,38}, {32,35}, {3,6}, {38,41}, {16,32}, {14,15}, {31,34}, {5,8}, {26,29}, {14,17}, {7,36}, {27,30}, {1,4}, {16,19}, {3,43}, {5,32}, {22,25}, {12,15}, {18,21}, {33,36}, {6,9}, {9,12}, {13,29}, {21,24}, {39,42}, {11,14}, {24,27}, {3,30}, {40,43}, {10,13}, {2,42}, {15,18}, {8,24}, {23,26}, {28,31}, {25,28}, {12,39}, {2,5}, {36,39}, {7,10}, {9,25}, {13,16}, {20,36}, {20,23}, {26,42}, {14,41}, {14,30}, {11,27}, {25,41}, {17,33}, {15,30}, {15,16}, {5,21}, {2,29}, {3,19}, {24,40}, {12,28}, {9,36}, {15,42}, {27,43}, {6,33}, {2,30}, {10,26}, {6,22}, {23,39}, {11,38}, {22,38}, {3,31}, {1,17}, {7,34}, {13,40}, {1,28}, {4,31}, {12,27}, {16,43}, {18,34}, {1,29}, {19,35}, {21,37}, {10,37}, {7,22}, {2,18}, {7,23}, {4,20}, {10,38}, {15,31}, {8,23}, {8,35}, {19,34}, {25,40}, {12,40}, {13,28}, {10,25}, {24,39}, {16,31}, {6,12}, {16,17}, {2,17}, {3,18}, {27,42}, {1,16}, {22,37}, {23,38}, {6,34}, {28,43}, {11,39}, {12,18}, {4,19}, {11,26}, {7,35}, {13,41}, {26,41}, {4,32}, {21,27}, {9,24}, {5,20}, {9,37}, {21,36}, {22,28}, {15,43}, {5,33}, {3,9}, {14,42}, {17,32}, {20,26}, {18,33}, {20,35}, {8,36}, {4,41}, {6,21}, {29,35}, {14,29}, {5,42}, {10,16}, {16,22}, {31,37}, {4,10}, {1,7}, {15,21}, {7,13}, {11,22}, {17,18}, {18,24}, {27,33}, {28,34}, {9,15}, {26,32}, {35,41}, {5,11}, {37,43}, {13,19}, {22,33}, {36,42}, {14,20}, {25,31}, {19,25}, {30,36}, {17,28}, {1,38}, {2,8}, {32,38}, {17,23}, {23,29}, {26,37}, {6,43}, {2,39}, {27,38}, {34,40}, {24,30}, {8,19}, {33,39}, {8,14}, {25,36}, {11,17}, {3,14}, {3,40}, {2,34}, {4,15}, {15,26}, {21,32}, {4,36}, {9,20}, {6,17}, {20,31}, {12,23}, {13,26}, {18,19}, {1,33}, {28,39}, {5,37}, {6,38}, {19,30}, {14,25}, {2,13}, {32,43}, {31,42}, {23,34}, {26,39}, {8,40}, {10,21}, {10,42}, {18,29}, {24,37}, {9,41}, {30,41}, {24,35}, {3,35}, {19,32}, {11,43}, {7,18}, {28,41}, {5,16}, {1,12}, {29,42}, {7,39}, {29,40}, {10,23}, {13,24}, {27,40}, {16,27}, {5,18}, {6,36}, {6,19}, {17,30}, {23,36}, {8,38}, {11,24}, {8,21}, {22,35}, {14,27}, {19,31}, {19,20}, {9,39}, {7,37}, {2,32}, {11,41}, {12,42}, {10,40}, {18,31}, {30,43}, {21,34}, {5,35}, {7,19}, {16,29}, {4,17}, {4,34}, {3,33}, {25,38}, {1,32}, {12,25}, {1,14}, {20,33}, {30,42}, {13,43}, {25,37}, {2,15}, {9,22}, {3,34}, {7,20}, {3,16}, {4,35}, {1,31}, {16,28}, {15,28}, {2,33}, {11,23}, {11,42}, {12,24}, {23,35}, {29,41}, {1,13}, {17,29}, {14,26}, {28,40}, {20,32}, {21,42}, {20,21}, {7,38}, {18,30}, {13,25}, {22,34}, {4,16}, {21,33}, {12,43}, {5,17}, {2,14}, {8,20}, {20,42}, {3,15}, {24,36}, {5,36}, {27,39}, {10,41}, {9,30}, {10,22}, {9,40}, {8,39}, {31,43}, {12,34}, {26,38}, {10,32}, {6,18}, {5,27}, {15,27}, {14,36}, {9,21}, {15,37}, {6,37}, {18,39}, {13,35}, {13,34}, {1,22}, {14,35}, {3,25}, {9,31}, {3,24}, {19,40}, {16,37}, {8,30}, {22,43}, {17,34}, {21,22}, {20,41}, {12,33}, {10,31}, {5,26}, {15,36}, {17,39}, {2,24}, {18,40}, {8,29}, {21,43}, {8,34}, {6,27}, {1,23}, {2,23}, {7,28}, {4,25}, {12,38}, {4,26}, {16,38}, {7,29}, {5,22}, {19,41}, {11,33}, {4,30}, {6,28}, {2,28}, {23,40}, {17,38}, {6,32}, {11,32}, {7,33}, {14,31}, {5,31}, {9,26}, {14,40}, {10,27}, {21,38}, {1,27}, {16,42}, {15,32}, {12,29}, {26,43}, {18,35}, {5,24}, {22,23}, {8,25}, {22,39}, {4,21}, {2,19}, {6,23}, {7,24}, {1,18}, {16,33}, {3,29}, {17,43}, {9,35}, {5,29}, {11,28}, {20,37}, {10,36}, {13,39}, {22,41}, {19,36}, {15,41}, {3,20}, {2,26}, {25,42}, {12,36}, {11,37}, {18,37}, {24,41}, {16,35}, {11,30}, {13,30}, {20,39}, {21,40}, {2,21}, {19,38}, {16,40}, {4,28}, {17,41}, {9,28}, {15,34}, {6,30}, {3,22}, {19,43}, {14,33}, {6,25}, {23,24}, {10,29}, {7,26}, {17,36}, {18,42}, {11,35}, {1,20}, {9,33}, {15,39}, {3,27}, {24,43}, {14,38}, {13,37}, {8,32}, {4,23}, {7,31}, {23,42}, {25,26}, {8,27}, {10,34}, {13,32}, {32,33}, {1,25}, {12,31}, {41,42}, {36,37}, {24,25}, {37,38}, {26,27}, {42,43}, {39,40}, {33,34}, {38,39}, {27,28}, {1,43}, {40,41}, {31,32}, {29,30}, {35,36}, {34,35}, {28,29}, {30,31} } ................................................................... Symmetric connected graphs of order 44 Symmetric graph 1 of order 44 Valency 2 Diameter 22 Girth 44 Automorphism group of order 88 Number of arcs = 88 Number of 2-arcs = 88 2-arc-transitive true Edge-set { {1,3}, {31,34}, {18,20}, {4,6}, {33,36}, {19,21}, {5,8}, {35,37}, {22,23}, {7,9}, {38,39}, {24,25}, {10,11}, {40,42}, {26,27}, {12,14}, {41,44}, {28,29}, {13,16}, {1,43}, {30,31}, {15,18}, {2,4}, {32,33}, {17,19}, {3,5}, {34,35}, {20,22}, {6,7}, {36,38}, {21,24}, {8,10}, {37,40}, {23,26}, {9,12}, {39,41}, {25,28}, {11,13}, {42,43}, {27,30}, {14,15}, {2,44}, {29,32}, {16,17} } Symmetric graph 2 of order 44 Valency 4 Diameter 5 Girth 4 Automorphism group of order 45056 Number of arcs = 176 Number of 2-arcs = 528 2-arc-transitive false Edge-set { {1,21}, {17,42}, {9,35}, {16,39}, {8,32}, {5,32}, {21,41}, {10,36}, {3,26}, {2,27}, {17,37}, {3,27}, {17,40}, {9,31}, {6,31}, {22,42}, {21,43}, {15,33}, {23,41}, {14,36}, {16,34}, {8,27}, {23,43}, {14,33}, {16,35}, {8,25}, {5,28}, {18,41}, {4,28}, {18,39}, {10,32}, {9,30}, {4,23}, {20,40}, {12,31}, {2,22}, {10,29}, {3,24}, {2,23}, {14,37}, {20,37}, {12,30}, {3,21}, {16,37}, {13,40}, {15,40}, {7,31}, {24,44}, {13,34}, {15,36}, {7,26}, {6,27}, {5,26}, {20,41}, {20,44}, {12,34}, {13,35}, {6,25}, {7,28}, {18,44}, {19,42}, {19,43}, {11,33}, {12,36}, {17,43}, {9,33}, {10,34}, {11,35}, {1,25}, {4,25}, {1,28}, {18,38}, {19,38}, {11,29}, {1,24}, {4,22}, {15,38}, {14,39}, {13,38}, {6,29}, {7,29}, {11,32}, {5,30}, {8,30}, {22,44}, {24,42}, {2,26}, {19,39} } Symmetric graph 3 of order 44 Valency 4 Diameter 11 Girth 4 Automorphism group of order 184549376 Number of arcs = 176 Number of 2-arcs = 528 2-arc-transitive false Edge-set { {1,3}, {1,44}, {36,38}, {41,44}, {33,36}, {34,35}, {25,27}, {40,41}, {31,33}, {32,34}, {23,25}, {24,26}, {15,18}, {37,40}, {30,31}, {29,32}, {22,23}, {21,24}, {14,15}, {13,16}, {6,8}, {36,37}, {28,30}, {27,29}, {19,22}, {20,21}, {11,14}, {12,13}, {3,6}, {4,5}, {40,42}, {34,36}, {25,28}, {26,27}, {17,19}, {18,20}, {10,11}, {9,12}, {2,4}, {38,40}, {37,39}, {30,32}, {31,34}, {24,25}, {23,26}, {15,17}, {16,18}, {7,10}, {8,9}, {2,43}, {35,37}, {27,30}, {28,29}, {19,21}, {29,31}, {22,24}, {21,23}, {13,15}, {14,16}, {6,7}, {5,8}, {42,43}, {26,28}, {18,19}, {17,20}, {10,12}, {20,22}, {11,13}, {12,14}, {4,6}, {3,5}, {39,42}, {16,17}, {8,10}, {7,9}, {2,44}, {9,11}, {1,4}, {2,3}, {38,39}, {5,7}, {42,44}, {41,43}, {33,35}, {1,43}, {35,38}, {39,41}, {32,33} } Symmetric graph 4 of order 44 Valency 6 Diameter 5 Girth 4 Automorphism group of order 528 Number of arcs = 264 Number of 2-arcs = 1320 2-arc-transitive false Edge-set { {1,5}, {11,13}, {13,20}, {19,21}, {23,28}, {21,26}, {28,29}, {30,36}, {32,34}, {34,39}, {29,35}, {36,37}, {39,41}, {37,43}, {1,42}, {40,42}, {3,44}, {3,6}, {2,41}, {4,43}, {1,8}, {6,11}, {4,5}, {8,9}, {12,13}, {5,12}, {7,10}, {10,15}, {15,19}, {11,14}, {9,16}, {13,17}, {19,23}, {16,20}, {14,18}, {17,21}, {24,28}, {20,24}, {18,22}, {22,26}, {26,30}, {23,27}, {21,25}, {28,32}, {30,34}, {25,29}, {27,31}, {32,36}, {33,39}, {29,33}, {31,35}, {35,37}, {37,42}, {34,40}, {36,38}, {39,44}, {3,42}, {38,41}, {40,43}, {1,44}, {4,6}, {4,41}, {2,43}, {2,8}, {8,12}, {3,5}, {1,7}, {6,10}, {12,15}, {7,11}, {5,9}, {10,13}, {16,19}, {11,16}, {9,14}, {14,17}, {17,24}, {15,20}, {13,18}, {19,22}, {24,26}, {18,23}, {20,21}, {22,28}, {25,30}, {23,25}, {21,27}, {27,32}, {32,33}, {26,29}, {28,31}, {30,35}, {33,37}, {31,34}, {29,36}, {35,39}, {38,42}, {34,38}, {36,40}, {40,44}, {4,44}, {37,41}, {39,43}, {2,42}, {4,8}, {3,43}, {1,41}, {2,6}, {7,12}, {3,7}, {5,10}, {10,16}, {8,11}, {6,9}, {12,14}, {16,17}, {9,15}, {14,19}, {18,24}, {15,18}, {20,22}, {22,25}, {17,23}, {24,27}, {25,32}, {27,30}, {31,33}, {26,31}, {35,38}, {33,40}, {38,44}, {2,7} } Symmetric graph 5 of order 44 Valency 8 Diameter 5 Girth 4 Automorphism group of order 33476985149718528 Number of arcs = 352 Number of 2-arcs = 2464 2-arc-transitive false Edge-set { {1,5}, {32,35}, {2,41}, {13,20}, {27,30}, {27,31}, {40,42}, {1,42}, {11,16}, {21,26}, {11,14}, {21,28}, {23,28}, {36,39}, {28,32}, {39,41}, {39,43}, {7,10}, {17,23}, {7,12}, {17,22}, {5,12}, {20,22}, {19,24}, {29,35}, {12,13}, {22,27}, {24,27}, {35,40}, {24,25}, {35,37}, {33,37}, {4,5}, {3,5}, {33,40}, {4,8}, {3,8}, {13,18}, {2,8}, {1,8}, {16,18}, {2,6}, {15,19}, {15,20}, {25,30}, {8,11}, {18,21}, {6,11}, {19,21}, {20,23}, {30,36}, {6,9}, {30,33}, {32,33}, {2,43}, {30,35}, {2,44}, {32,36}, {29,34}, {3,43}, {30,34}, {3,44}, {4,42}, {31,34}, {3,42}, {32,34}, {3,41}, {4,43}, {10,14}, {31,36}, {9,15}, {1,44}, {9,16}, {24,26}, {34,39}, {3,7}, {4,7}, {14,17}, {1,7}, {2,7}, {15,17}, {16,20}, {16,19}, {26,29}, {36,38}, {1,6}, {16,17}, {26,32}, {13,17}, {27,32}, {25,31}, {37,42}, {26,30}, {26,31}, {38,42}, {13,19}, {27,29}, {15,18}, {37,44}, {38,44}, {28,29}, {14,18}, {28,31}, {28,30}, {39,44}, {40,44}, {25,29}, {37,43}, {37,41}, {14,19}, {38,41}, {38,43}, {6,10}, {19,23}, {18,24}, {31,35}, {4,44}, {29,33}, {4,41}, {31,33}, {9,13}, {1,43}, {10,16}, {10,15}, {23,25}, {1,41}, {10,13}, {23,27}, {11,13}, {21,27}, {9,14}, {24,28}, {22,28}, {33,39}, {23,26}, {2,42}, {11,15}, {21,25}, {22,26}, {33,38}, {34,38}, {12,15}, {22,25}, {12,14}, {12,16}, {35,38}, {34,40}, {34,37}, {36,37}, {2,5}, {4,6}, {14,20}, {25,32}, {40,43}, {5,10}, {5,9}, {20,24}, {40,41}, {5,11}, {20,21}, {39,42}, {7,11}, {17,21}, {6,12}, {19,22}, {8,12}, {18,22}, {17,24}, {7,9}, {8,10}, {18,23}, {8,9}, {29,36}, {36,40}, {35,39}, {3,6} } Symmetric graph 6 of order 44 Valency 10 Diameter 4 Girth 4 Automorphism group of order 440 Number of arcs = 440 Number of 2-arcs = 3960 2-arc-transitive false Edge-set { {1,7}, {13,23}, {1,31}, {26,44}, {22,35}, {12,23}, {12,31}, {18,29}, {14,40}, {2,27}, {24,26}, {7,26}, {18,22}, {7,12}, {12,18}, {9,34}, {6,9}, {37,43}, {36,42}, {19,24}, {32,37}, {18,25}, {21,40}, {13,18}, {1,40}, {27,34}, {6,24}, {7,13}, {1,18}, {7,34}, {6,18}, {3,6}, {19,28}, {6,16}, {3,19}, {30,39}, {13,44}, {16,25}, {25,35}, {8,21}, {11,39}, {11,44}, {17,34}, {6,39}, {28,37}, {23,42}, {34,44}, {6,35}, {23,37}, {31,42}, {3,21}, {1,35}, {23,34}, {6,31}, {3,13}, {1,28}, {16,34}, {16,22}, {3,29}, {20,35}, {8,38}, {16,41}, {3,33}, {8,29}, {10,38}, {10,41}, {29,44}, {14,35}, {17,41}, {33,39}, {2,17}, {26,39}, {14,28}, {2,23}, {14,17}, {5,28}, {16,38}, {3,41}, {20,39}, {38,44}, {26,31}, {2,16}, {3,26}, {22,44}, {12,16}, {22,28}, {23,29}, {3,12}, {29,35}, {20,23}, {31,38}, {28,33}, {27,41}, {24,33}, {9,22}, {9,29}, {2,36}, {2,43}, {32,41}, {15,33}, {4,22}, {27,29}, {9,14}, {2,9}, {5,40}, {20,43}, {5,32}, {15,20}, {26,36}, {32,33}, {5,15}, {4,38}, {18,38}, {40,41}, {36,38}, {22,32}, {33,43}, {5,36}, {15,29}, {7,41}, {29,40}, {14,43}, {12,40}, {24,41}, {14,24}, {18,33}, {20,27}, {24,38}, {9,26}, {7,22}, {12,43}, {4,20}, {27,38}, {19,32}, {15,37}, {4,25}, {21,27}, {6,27}, {9,19}, {1,24}, {25,32}, {24,30}, {13,32}, {11,32}, {11,15}, {4,42}, {9,37}, {6,43}, {19,36}, {30,36}, {4,11}, {25,40}, {11,27}, {15,42}, {4,34}, {30,43}, {34,40}, {25,43}, {11,24}, {4,30}, {13,27}, {1,15}, {9,42}, {13,36}, {7,37}, {18,42}, {15,21}, {21,36}, {21,43}, {19,40}, {7,30}, {11,35}, {8,11}, {39,42}, {17,21}, {16,19}, {3,37}, {8,19}, {23,25}, {21,31}, {11,17}, {10,25}, {10,21}, {8,42}, {16,30}, {19,44}, {8,25}, {1,10}, {17,30}, {17,37}, {28,30}, {10,30}, {10,13}, {28,42}, {13,39}, {35,37}, {31,34}, {1,44}, {2,8}, {17,26}, {8,14}, {5,23}, {35,41}, {8,33}, {22,39}, {12,28}, {5,17}, {14,31}, {10,33}, {2,39}, {20,31}, {5,10}, {5,44}, {10,20}, {2,32}, {15,26}, {4,14}, {7,20}, {4,5}, {12,36} } Symmetric graph 7 of order 44 Valency 10 Diameter 3 Girth 4 Automorphism group of order 5536481280 Number of arcs = 440 Number of 2-arcs = 3960 2-arc-transitive false Edge-set { {1,5}, {3,33}, {12,39}, {2,38}, {34,38}, {23,27}, {7,28}, {4,26}, {5,40}, {26,37}, {5,33}, {19,32}, {3,29}, {20,36}, {4,9}, {1,17}, {2,37}, {28,33}, {8,12}, {17,25}, {2,6}, {33,38}, {12,34}, {8,43}, {15,18}, {19,38}, {39,44}, {16,35}, {1,22}, {3,42}, {14,39}, {4,25}, {6,40}, {20,38}, {4,34}, {23,35}, {10,28}, {18,42}, {1,14}, {11,40}, {26,38}, {5,34}, {23,37}, {15,35}, {10,22}, {12,41}, {13,41}, {26,43}, {5,15}, {16,27}, {7,21}, {36,42}, {3,30}, {32,39}, {2,14}, {23,38}, {10,27}, {7,43}, {1,18}, {1,37}, {28,34}, {8,11}, {26,44}, {5,16}, {33,37}, {32,40}, {29,36}, {20,21}, {14,41}, {13,23}, {3,10}, {39,43}, {24,28}, {8,27}, {17,26}, {2,5}, {12,33}, {25,32}, {6,29}, {12,40}, {36,41}, {21,30}, {9,13}, {24,44}, {15,17}, {2,22}, {11,19}, {9,31}, {7,18}, {4,10}, {40,43}, {26,32}, {5,29}, {19,21}, {3,25}, {15,36}, {9,22}, {3,41}, {13,39}, {6,39}, {20,37}, {4,33}, {24,35}, {16,17}, {2,21}, {11,33}, {12,42}, {25,38}, {6,34}, {8,28}, {8,18}, {19,35}, {29,44}, {16,31}, {10,13}, {24,43}, {9,32}, {15,27}, {7,22}, {20,31}, {4,30}, {17,42}, {23,28}, {1,21}, {25,37}, {15,28}, {8,22}, {8,17}, {2,18}, {6,33}, {12,19}, {29,43}, {15,31}, {1,38}, {35,41}, {22,30}, {2,13}, {24,38}, {9,27}, {7,44}, {27,34}, {7,11}, {25,44}, {6,16}, {34,37}, {31,40}, {30,36}, {11,42}, {14,42}, {4,29}, {14,23}, {18,26}, {20,35}, {9,21}, {20,32}, {31,39}, {18,25}, {1,6}, {12,20}, {4,41}, {30,35}, {10,32}, {35,42}, {10,14}, {13,40}, {11,34}, {23,43}, {6,15}, {19,22}, {7,12}, {17,41}, {3,26}, {5,39}, {24,36}, {5,30}, {40,44}, {26,31}, {16,36}, {19,37}, {16,18}, {14,24}, {22,29}, {8,44}, {7,27}, {7,17}, {18,41}, {1,13}, {3,34}, {11,39}, {23,44}, {16,28}, {24,37}, {8,21}, {14,40}, {23,36}, {10,21}, {25,43}, {9,28}, {27,33}, {15,32}, {11,41}, {30,43}, {13,42}, {2,17}, {10,31}, {6,30}, {19,36}, {3,9}, {9,14}, {13,24}, {24,27}, {16,32}, {21,29}, {11,20}, {4,42}, {25,31}, {29,35}, {20,22}, {30,44}, {19,31} } Symmetric graph 8 of order 44 Valency 12 Diameter 3 Girth 4 Automorphism group of order 5536481280 Number of arcs = 528 Number of 2-arcs = 5808 2-arc-transitive false Edge-set { {1,23}, {16,41}, {19,38}, {22,23}, {1,24}, {18,33}, {8,39}, {2,41}, {19,43}, {16,42}, {20,38}, {14,40}, {22,42}, {6,43}, {18,29}, {15,23}, {1,37}, {11,39}, {22,24}, {2,24}, {17,33}, {8,40}, {3,44}, {2,43}, {8,29}, {11,28}, {14,28}, {15,42}, {21,41}, {19,23}, {16,34}, {7,38}, {20,43}, {18,36}, {2,42}, {20,37}, {13,40}, {22,41}, {6,44}, {17,29}, {10,30}, {12,31}, {15,29}, {11,37}, {6,28}, {5,36}, {3,37}, {5,33}, {21,24}, {2,23}, {1,44}, {18,41}, {19,39}, {22,39}, {8,30}, {11,40}, {14,31}, {3,42}, {15,24}, {2,37}, {17,34}, {7,40}, {4,44}, {1,43}, {12,28}, {13,28}, {15,41}, {12,27}, {16,25}, {19,25}, {10,35}, {21,28}, {20,34}, {7,36}, {8,37}, {5,28}, {7,31}, {3,27}, {10,34}, {22,27}, {1,42}, {20,44}, {19,37}, {16,30}, {12,38}, {14,23}, {18,43}, {18,39}, {6,27}, {16,29}, {17,36}, {3,25}, {10,33}, {10,24}, {2,31}, {21,42}, {20,23}, {15,34}, {7,37}, {13,39}, {5,44}, {17,30}, {9,30}, {12,32}, {11,38}, {5,35}, {4,37}, {5,34}, {21,23}, {6,35}, {22,35}, {13,24}, {18,35}, {4,25}, {17,39}, {21,40}, {5,31}, {3,30}, {6,34}, {7,29}, {5,27}, {5,25}, {10,38}, {6,31}, {12,39}, {21,25}, {2,38}, {16,24}, {12,40}, {18,34}, {7,39}, {19,33}, {8,35}, {3,41}, {14,29}, {11,42}, {14,43}, {18,42}, {8,38}, {22,28}, {13,31}, {22,25}, {12,42}, {20,25}, {15,25}, {10,37}, {2,44}, {17,41}, {19,40}, {21,39}, {7,30}, {4,43}, {13,27}, {11,27}, {16,26}, {19,26}, {9,35}, {20,33}, {8,36}, {7,32}, {4,27}, {9,34}, {21,27}, {1,41}, {19,44}, {8,32}, {4,28}, {2,32}, {4,42}, {14,32}, {13,32}, {13,43}, {17,44}, {7,25}, {10,27}, {16,31}, {15,30}, {7,35}, {12,33}, {8,25}, {10,28}, {1,35}, {13,44}, {15,33}, {20,24}, {17,35}, {14,39}, {5,43}, {18,30}, {18,40}, {6,32}, {4,29}, {10,23}, {1,31}, {3,28}, {2,36}, {3,29}, {11,33}, {14,24}, {6,33}, {2,35}, {19,24}, {21,35}, {13,23}, {12,34}, {12,37}, {18,44}, {9,29}, {11,32}, {4,38}, {6,36}, {22,36}, {4,26}, {17,40}, {22,40}, {5,26}, {9,38}, {21,26}, {1,38}, {16,23}, {6,26}, {9,37}, {5,32}, {15,26}, {9,24}, {3,26}, {9,33}, {11,34}, {13,30}, {12,41}, {6,25}, {4,30}, {13,29}, {16,32}, {17,42}, {20,40}, {4,41}, {3,43}, {14,27}, {14,44}, {8,26}, {9,28}, {15,32}, {15,31}, {20,39}, {1,32}, {19,34}, {14,30}, {20,26}, {9,36}, {8,31}, {17,43}, {1,36}, {16,33}, {7,26}, {9,27}, {21,36}, {10,36}, {22,26}, {9,23}, {10,29}, {11,31}, {3,38}, {11,41} } Symmetric graph 9 of order 44 Valency 20 Diameter 3 Girth 4 Automorphism group of order 334846387814400 Number of arcs = 880 Number of 2-arcs = 16720 2-arc-transitive false Edge-set { {1,7}, {16,20}, {8,29}, {25,32}, {4,21}, {19,43}, {7,37}, {40,42}, {19,40}, {14,36}, {31,42}, {11,31}, {9,22}, {8,20}, {8,33}, {5,9}, {12,36}, {5,31}, {22,36}, {2,28}, {2,16}, {9,41}, {12,39}, {24,41}, {25,39}, {21,35}, {27,41}, {19,32}, {7,21}, {3,19}, {7,13}, {17,21}, {5,27}, {2,23}, {16,26}, {17,41}, {5,39}, {2,35}, {16,41}, {15,38}, {17,30}, {15,25}, {4,30}, {10,21}, {11,27}, {6,23}, {26,35}, {10,33}, {11,44}, {6,40}, {19,35}, {1,36}, {15,42}, {10,37}, {11,18}, {22,40}, {20,36}, {8,42}, {13,31}, {22,32}, {20,27}, {1,8}, {29,36}, {23,42}, {17,37}, {5,18}, {15,34}, {30,43}, {4,20}, {10,29}, {11,23}, {6,17}, {5,35}, {1,15}, {15,30}, {10,25}, {4,11}, {7,26}, {3,34}, {29,44}, {23,38}, {26,40}, {14,44}, {31,38}, {28,42}, {24,37}, {18,25}, {18,34}, {6,43}, {1,39}, {15,20}, {3,22}, {13,28}, {12,24}, {6,36}, {1,31}, {15,22}, {16,29}, {9,26}, {3,12}, {8,22}, {28,33}, {24,30}, {24,25}, {36,41}, {2,32}, {16,21}, {9,19}, {7,12}, {35,42}, {40,41}, {32,37}, {18,21}, {16,19}, {7,29}, {2,43}, {16,37}, {9,34}, {12,43}, {23,33}, {5,24}, {4,26}, {3,14}, {9,38}, {14,32}, {21,31}, {22,43}, {28,37}, {24,34}, {25,43}, {18,29}, {1,17}, {5,15}, {3,29}, {26,44}, {3,38}, {19,28}, {14,24}, {25,31}, {20,39}, {4,13}, {7,34}, {34,43}, {12,28}, {2,10}, {7,41}, {34,39}, {12,17}, {33,44}, {30,40}, {19,24}, {6,9}, {6,16}, {29,35}, {26,32}, {3,21}, {13,35}, {32,41}, {27,38}, {2,18}, {29,39}, {3,41}, {4,37}, {21,39}, {13,23}, {13,17}, {38,44}, {33,40}, {19,44}, {11,16}, {25,36}, {4,42}, {22,27}, {20,23}, {8,26}, {1,9}, {12,15}, {5,10}, {11,36}, {30,36}, {24,42}, {4,22}, {20,43}, {8,37}, {11,15}, {9,30}, {8,25}, {4,33}, {14,27}, {13,43}, {17,33}, {5,44}, {14,39}, {20,31}, {27,34}, {2,40}, {39,42}, {11,35}, {8,38}, {11,40}, {23,29}, {17,26}, {3,5}, {10,20}, {32,34}, {17,22}, {2,44}, {19,39}, {6,32}, {8,14}, {9,14}, {28,30}, {8,11}, {4,6}, {14,35}, {23,26}, {10,13}, {36,38}, {31,33}, {22,44}, {6,27}, {1,43}, {15,37}, {20,40}, {13,36}, {32,42}, {1,27}, {10,42}, {35,37}, {11,32}, {27,29}, {1,23}, {10,34}, {12,31}, {10,22}, {4,25}, {18,41}, {21,43}, {7,20}, {3,26}, {5,28}, {2,24}, {16,25}, {16,38}, {9,33}, {12,44}, {31,41}, {9,21}, {8,19}, {7,33}, {24,26}, {3,25}, {21,44}, {7,19}, {6,28}, {14,18}, {12,35}, {1,24}, {37,43}, {5,32}, {21,28}, {14,40}, {23,41}, {10,30}, {6,31}, {22,35}, {18,42}, {2,7}, {2,27}, {17,38}, {7,25}, {1,28}, {2,15}, {16,34}, {13,39}, {10,41}, {18,37}, {6,18}, {9,29}, {3,33}, {21,36}, {1,16}, {9,42}, {12,40}, {15,33}, {25,40}, {29,43}, {14,28}, {26,39}, {28,41}, {19,31}, {11,24}, {20,32}, {8,21}, {5,17}, {30,44}, {4,19}, {4,34}, {13,27}, {12,23}, {10,26}, {11,39}, {27,42}, {7,22}, {3,20}, {8,13}, {33,39}, {20,44}, {13,40}, {18,38}, {15,26}, {16,33}, {17,42}, {5,40}, {2,36}, {11,43}, {28,38}, {6,39}, {1,35}, {15,41}, {8,30}, {18,30}, {23,34}, {17,29}, {3,30}, {4,14}, {11,28}, {24,33}, {6,24}, {27,37}, {3,13}, {13,32}, {16,42}, {4,29}, {12,27}, {5,23}, {26,36}, {19,36}, {9,37}, {2,17}, {20,35}, {10,38}, {11,17}, {22,39}, {25,44}, {21,40}, {7,42}, {14,31}, {22,31}, {1,18}, {26,43}, {20,28}, {25,35}, {12,18}, {8,41}, {21,32}, {19,27}, {3,6}, {12,32}, {7,30}, {5,36}, {16,30}, {9,25}, {7,38}, {17,34}, {6,35}, {15,29}, {3,11}, {24,38}, {14,43}, {23,37}, {13,44}, {32,38}, {2,31}, {17,25}, {18,33}, {6,44}, {1,32}, {1,40}, {4,12}, {31,37}, {18,26}, {5,43}, {2,39}, {16,22}, {27,33}, {23,30}, {15,21}, {28,34}, {24,29}, {23,25}, {35,41}, {10,19}, {36,42}, {9,20}, {8,12}, {39,41}, {15,19}, {7,11}, {18,22}, {13,18}, {5,16}, {4,38}, {8,34}, {14,23}, {6,15}, {3,37}, {13,24}, {34,44}, {2,9}, {33,43}, {1,10}, {34,40}, {30,39}, {29,40}, {19,23}, {6,10}, {26,31}, {20,24}, {30,35}, {4,41}, {38,43}, {3,42}, {14,17}, {37,44}, {22,28}, {12,16}, {21,27}, {27,30}, {4,5}, {7,14}, {31,34}, {32,33}, {1,44}, {10,14}, {9,13}, {28,29}, {35,38}, {36,37}, {2,8} } Symmetric graph 10 of order 44 Valency 21 Diameter 3 Girth 4 Automorphism group of order 2248001455555215360000 Number of arcs = 924 Number of 2-arcs = 18480 2-arc-transitive true Edge-set { {1,3}, {1,8}, {14,34}, {1,26}, {14,30}, {28,42}, {22,26}, {1,38}, {6,14}, {28,32}, {22,41}, {11,29}, {36,40}, {15,38}, {6,28}, {1,23}, {10,14}, {18,28}, {3,22}, {29,34}, {8,40}, {12,15}, {28,35}, {13,31}, {2,42}, {22,43}, {16,24}, {10,23}, {10,43}, {18,29}, {3,40}, {1,36}, {14,37}, {20,28}, {22,31}, {29,40}, {19,40}, {8,15}, {28,34}, {31,42}, {26,42}, {16,30}, {1,43}, {29,44}, {23,40}, {27,33}, {7,21}, {2,11}, {13,36}, {3,15}, {11,28}, {9,35}, {38,44}, {20,36}, {31,37}, {3,20}, {11,31}, {31,40}, {19,42}, {8,22}, {16,34}, {14,24}, {24,28}, {9,22}, {6,29}, {17,40}, {15,33}, {7,28}, {16,42}, {5,22}, {16,18}, {10,26}, {30,43}, {29,42}, {26,40}, {11,33}, {7,36}, {11,38}, {6,36}, {9,32}, {41,44}, {11,14}, {4,31}, {12,42}, {22,36}, {16,37}, {30,41}, {25,39}, {16,25}, {27,29}, {2,13}, {27,43}, {21,24}, {8,10}, {34,43}, {13,29}, {2,40}, {19,44}, {23,32}, {4,23}, {10,12}, {6,43}, {17,24}, {24,33}, {7,9}, {6,8}, {17,34}, {13,33}, {2,7}, {22,33}, {7,16}, {5,11}, {18,36}, {15,26}, {28,30}, {9,42}, {26,44}, {22,38}, {29,35}, {38,40}, {15,19}, {18,31}, {3,42}, {22,39}, {16,20}, {10,41}, {25,43}, {25,29}, {9,11}, {36,44}, {15,17}, {4,28}, {9,40}, {20,38}, {6,31}, {3,32}, {11,41}, {36,42}, {6,16}, {13,41}, {2,25}, {24,29}, {13,23}, {2,10}, {18,43}, {3,24}, {19,34}, {8,32}, {4,12}, {12,35}, {13,28}, {2,22}, {7,33}, {15,43}, {9,24}, {9,44}, {12,32}, {35,41}, {21,37}, {5,15}, {9,37}, {5,44}, {30,31}, {39,42}, {2,27}, {13,21}, {3,30}, {11,39}, {16,35}, {27,38}, {20,26}, {11,26}, {27,31}, {21,42}, {13,16}, {4,5}, {12,18}, {34,36}, {8,37}, {33,37}, {14,20}, {1,31}, {3,18}, {3,11}, {35,39}, {25,38}, {19,25}, {29,32}, {18,26}, {27,41}, {21,25}, {15,41}, {25,28}, {9,25}, {13,17}, {2,4}, {40,43}, {19,24}, {10,38}, {40,41}, {11,19}, {32,36}, {4,38}, {6,12}, {15,23}, {10,28}, {31,44}, {23,42}, {22,23}, {10,16}, {5,10}, {33,40}, {7,19}, {8,11}, {15,21}, {15,28}, {6,9}, {17,44}, {12,20}, {31,35}, {3,37}, {5,42}, {13,19}, {2,32}, {4,43}, {12,24}, {10,39}, {20,43}, {7,29}, {19,22}, {16,32}, {6,23}, {10,17}, {18,33}, {3,7}, {8,34}, {12,13}, {2,35}, {11,43}, {24,36}, {9,18}, {3,44}, {12,27}, {21,35}, {2,37}, {5,13}, {38,42}, {27,36}, {2,20}, {8,35}, {34,38}, {26,34}, {8,30}, {7,14}, {1,33}, {14,44}, {21,40}, {2,15}, {25,41}, {3,10}, {19,35}, {32,38}, {4,19}, {12,44}, {23,35}, {9,27}, {4,17}, {32,33}, {7,41}, {11,21}, {15,36}, {2,30}, {13,39}, {16,27}, {21,27}, {34,41}, {23,44}, {23,30}, {6,38}, {6,17}, {13,38}, {2,6}, {30,33}, {7,39}, {11,16}, {21,44}, {7,17}, {4,33}, {14,40}, {1,19}, {42,43}, {24,26}, {9,30}, {24,41}, {17,22}, {8,13}, {2,34}, {23,37}, {5,37}, {5,18}, {31,34}, {8,42}, {6,19}, {12,30}, {5,27}, {35,43}, {29,37}, {5,40}, {19,37}, {5,32}, {27,39}, {20,21}, {5,35}, {18,38}, {20,23}, {10,31}, {12,22}, {2,18}, {8,24}, {7,23}, {10,33}, {14,18}, {10,36}, {37,43}, {20,29}, {7,12}, {11,36}, {36,37}, {28,37}, {9,20}, {17,20}, {5,25}, {13,26}, {10,29}, {18,19}, {4,39}, {1,17}, {33,44}, {9,34}, {11,17}, {4,36}, {18,21}, {14,35}, {15,31}, {3,6}, {25,31}, {8,44}, {20,39}, {20,31}, {8,25}, {26,30}, {14,27}, {1,21}, {2,44}, {3,13}, {24,38}, {19,32}, {4,8}, {12,34}, {1,39}, {16,44}, {23,27}, {2,24}, {9,13}, {17,27}, {4,21}, {11,23}, {24,39}, {6,26}, {26,32}, {22,29}, {1,41}, {14,25}, {16,22}, {13,43}, {12,37}, {8,20}, {18,23}, {23,34}, {5,7}, {4,14}, {1,12}, {19,30}, {32,39}, {20,33}, {12,25}, {24,43}, {39,44}, {26,35}, {37,41}, {18,39}, {10,21}, {32,41}, {15,29}, {4,16}, {25,33}, {22,28}, {1,5}, {35,38}, {15,39}, {26,27}, {21,30}, {4,9}, {33,42}, {7,26}, {30,36}, {14,32}, {17,30}, {24,31}, {5,24}, {10,19}, {17,37}, {7,31}, {14,15}, {1,28}, {30,38}, {25,36}, {20,41}, {28,40}, {17,42}, {1,29}, {17,32}, {6,39}, {6,21}, {4,41}, {7,43}, {16,40}, {19,27}, {28,44}, {8,18}, {3,34}, {4,26}, {6,33}, {26,37}, {5,30}, {6,41}, {1,16}, {8,27}, {21,34}, {5,34}, {14,42}, {37,39}, {21,32}, {30,39}, {9,15}, {3,27}, {1,9}, {17,25}, {4,29}, {1,14}, {18,41}, {3,35}, {32,43}, {33,35}, {7,38}, {17,35}, {5,20}, {34,39}, {3,25}, {12,40}, {14,22}, {23,25} } Symmetric graph 11 of order 44 Valency 22 Diameter 2 Girth 4 Automorphism group of order 2526755272089183449772480847989964800000000 Number of arcs = 968 Number of 2-arcs = 20328 2-arc-transitive true Edge-set { {1,23}, {3,38}, {3,33}, {6,30}, {5,25}, {18,30}, {5,44}, {8,43}, {8,39}, {20,44}, {7,35}, {19,39}, {10,44}, {7,31}, {9,35}, {10,32}, {22,35}, {10,28}, {22,31}, {12,36}, {9,24}, {21,28}, {11,31}, {1,36}, {9,42}, {12,27}, {12,24}, {2,28}, {11,41}, {1,24}, {14,28}, {11,38}, {1,42}, {14,23}, {4,27}, {12,34}, {2,38}, {13,42}, {3,23}, {15,27}, {12,30}, {13,41}, {14,37}, {4,41}, {14,34}, {4,38}, {16,42}, {13,29}, {3,34}, {15,38}, {6,42}, {13,25}, {3,30}, {15,33}, {6,37}, {17,41}, {14,43}, {4,25}, {16,30}, {5,33}, {18,37}, {8,41}, {14,39}, {16,33}, {16,29}, {5,34}, {15,26}, {6,29}, {17,34}, {15,43}, {6,25}, {17,30}, {7,33}, {16,40}, {5,43}, {18,25}, {8,30}, {20,33}, {16,35}, {5,39}, {18,44}, {8,26}, {20,29}, {9,34}, {15,32}, {6,35}, {17,39}, {7,44}, {19,26}, {10,29}, {22,34}, {15,28}, {18,26}, {17,44}, {7,26}, {17,40}, {7,43}, {19,25}, {18,36}, {8,40}, {20,43}, {9,25}, {18,32}, {8,35}, {20,39}, {9,44}, {21,26}, {17,27}, {7,32}, {19,35}, {10,39}, {22,44}, {12,26}, {17,24}, {7,28}, {19,31}, {10,36}, {22,40}, {12,43}, {2,25}, {18,41}, {8,24}, {20,28}, {9,31}, {21,36}, {11,40}, {1,43}, {14,25}, {18,38}, {19,36}, {10,40}, {20,31}, {9,36}, {21,40}, {20,27}, {9,32}, {21,35}, {11,39}, {19,23}, {10,27}, {22,32}, {12,35}, {2,39}, {19,41}, {10,24}, {22,28}, {12,31}, {2,36}, {13,40}, {20,37}, {9,41}, {21,24}, {11,28}, {1,31}, {14,36}, {4,40}, {20,34}, {9,38}, {21,42}, {11,23}, {1,27}, {14,32}, {4,35}, {16,39}, {19,29}, {10,34}, {22,38}, {12,42}, {2,23}, {13,27}, {3,32}, {15,35}, {6,39}, {21,23}, {11,27}, {1,32}, {22,42}, {12,23}, {2,27}, {13,32}, {22,37}, {12,41}, {2,24}, {13,28}, {3,31}, {21,33}, {11,37}, {1,41}, {14,24}, {4,28}, {16,31}, {21,29}, {11,34}, {1,38}, {14,42}, {4,23}, {16,27}, {5,32}, {22,26}, {12,29}, {2,34}, {13,38}, {3,42}, {15,23}, {6,27}, {17,32}, {22,43}, {12,25}, {2,30}, {13,33}, {3,37}, {15,41}, {6,24}, {17,28}, {11,43}, {1,25}, {14,30}, {4,33}, {16,37}, {5,41}, {18,24}, {8,28}, {2,33}, {13,37}, {3,41}, {15,24}, {1,30}, {14,33}, {4,37}, {16,41}, {5,24}, {1,26}, {14,29}, {4,34}, {16,38}, {5,42}, {18,23}, {2,44}, {13,26}, {3,29}, {15,34}, {6,38}, {17,42}, {7,23}, {2,40}, {13,43}, {3,25}, {15,30}, {6,33}, {17,37}, {7,41}, {19,24}, {14,40}, {4,43}, {16,25}, {5,30}, {18,33}, {8,37}, {20,41}, {14,35}, {4,39}, {16,44}, {5,26}, {18,29}, {8,34}, {20,38}, {3,35}, {15,39}, {6,44}, {17,26}, {7,29}, {19,34}, {10,38}, {4,44}, {16,26}, {5,29}, {18,34}, {8,38}, {3,39}, {15,44}, {6,26}, {17,29}, {7,34}, {19,38}, {3,36}, {15,40}, {6,43}, {17,25}, {7,30}, {19,33}, {10,37}, {4,31}, {16,36}, {5,40}, {18,43}, {8,25}, {20,30}, {9,33}, {21,37}, {16,32}, {5,35}, {18,39}, {8,44}, {20,26}, {9,29}, {21,34}, {6,32}, {17,35}, {7,39}, {19,44}, {10,26}, {22,29}, {6,28}, {17,31}, {7,36}, {19,40}, {10,43}, {22,25}, {18,28}, {8,31}, {20,36}, {9,40}, {21,43}, {11,25}, {6,31}, {17,36}, {7,40}, {19,43}, {10,25}, {22,30}, {5,28}, {18,31}, {8,36}, {20,40}, {9,43}, {21,25}, {11,30}, {5,23}, {18,27}, {8,32}, {20,35}, {9,39}, {21,44}, {11,26}, {1,29}, {17,23}, {7,27}, {19,32}, {10,35}, {22,39}, {12,44}, {2,26}, {7,24}, {19,28}, {10,31}, {22,36}, {12,40}, {2,43}, {20,24}, {9,28}, {21,31}, {11,36}, {1,40}, {20,42}, {9,23}, {21,27}, {11,32}, {1,35}, {10,42}, {22,23}, {2,32}, {13,35}, {8,42}, {20,23}, {9,27}, {21,32}, {11,35}, {1,39}, {14,44}, {7,38}, {19,42}, {10,23}, {22,27}, {12,32}, {2,35}, {13,39}, {3,44}, {19,37}, {10,41}, {22,24}, {12,28}, {2,31}, {13,36}, {3,40}, {9,37}, {21,41}, {11,24}, {1,28}, {14,31}, {4,36}, {21,38}, {11,42}, {14,27}, {4,32}, {12,38}, {2,42}, {13,23}, {3,27}, {12,33}, {2,37}, {3,24}, {1,33}, {16,24}, {10,30}, {22,33}, {12,37}, {2,41}, {13,24}, {3,28}, {15,31}, {6,36}, {21,30}, {11,33}, {1,37}, {14,41}, {4,24}, {16,28}, {5,31}, {11,29}, {1,34}, {14,38}, {4,42}, {16,23}, {5,27}, {2,29}, {13,34}, {15,42}, {6,23}, {13,30}, {15,37}, {6,41}, {4,30}, {5,37}, {4,26}, {1,44}, {14,26}, {4,29}, {16,34}, {5,38}, {18,42}, {8,23}, {13,44}, {3,26}, {15,29}, {6,34}, {17,38}, {7,42}, {3,43}, {15,25}, {17,33}, {7,37}, {16,43}, {8,33}, {8,29}, {15,36}, {6,40}, {17,43}, {7,25}, {19,30}, {10,33}, {5,36}, {18,40}, {20,25}, {9,30}, {18,35}, {9,26}, {8,27}, {20,32}, {21,39}, {11,44}, {19,27}, {12,39}, {22,41}, {13,31} } Symmetric graph 12 of order 44 Valency 30 Diameter 2 Girth 3 Automorphism group of order 958003200 Number of arcs = 1320 Number of 2-arcs = 38280 2-arc-transitive false Edge-set { {1,5}, {12,26}, {33,41}, {19,42}, {27,37}, {8,38}, {7,22}, {30,37}, {5,10}, {18,22}, {14,38}, {21,27}, {16,34}, {2,28}, {2,36}, {22,35}, {14,29}, {26,44}, {26,33}, {2,31}, {2,9}, {13,21}, {16,20}, {1,18}, {4,38}, {7,15}, {17,24}, {11,17}, {40,43}, {5,11}, {21,43}, {2,6}, {2,23}, {13,36}, {20,31}, {19,39}, {8,37}, {8,19}, {22,37}, {11,34}, {30,43}, {11,43}, {28,43}, {1,14}, {4,18}, {15,29}, {12,17}, {12,31}, {9,41}, {9,21}, {16,42}, {16,28}, {19,36}, {4,32}, {3,11}, {32,41}, {11,25}, {23,40}, {6,13}, {26,41}, {25,33}, {1,40}, {4,6}, {35,43}, {1,43}, {5,14}, {18,21}, {29,34}, {12,30}, {24,30}, {10,15}, {22,27}, {14,34}, {27,30}, {10,34}, {2,22}, {2,14}, {7,41}, {24,25}, {35,40}, {6,29}, {40,41}, {6,25}, {17,40}, {6,40}, {12,13}, {20,41}, {9,31}, {9,42}, {16,36}, {19,31}, {32,42}, {11,27}, {34,42}, {38,43}, {7,28}, {4,28}, {15,37}, {5,17}, {15,17}, {5,30}, {10,21}, {9,33}, {10,41}, {25,44}, {33,38}, {7,32}, {25,39}, {3,23}, {1,13}, {14,25}, {18,35}, {19,38}, {7,37}, {8,20}, {22,39}, {12,23}, {13,41}, {9,25}, {35,42}, {6,23}, {12,40}, {6,41}, {13,26}, {20,33}, {1,31}, {4,9}, {7,36}, {24,31}, {27,29}, {4,35}, {3,29}, {16,44}, {19,26}, {2,18}, {2,38}, {7,13}, {20,24}, {29,38}, {7,44}, {24,26}, {2,11}, {2,43}, {11,13}, {20,43}, {28,38}, {4,20}, {3,39}, {13,23}, {25,36}, {31,35}, {23,38}, {20,25}, {35,39}, {23,32}, {23,25}, {13,35}, {14,42}, {18,27}, {7,12}, {34,43}, {28,30}, {37,43}, {5,28}, {5,15}, {17,21}, {30,34}, {10,30}, {33,37}, {5,32}, {18,41}, {25,38}, {5,24}, {21,40}, {6,16}, {17,28}, {36,40}, {9,17}, {40,42}, {16,22}, {14,19}, {26,32}, {11,33}, {16,32}, {11,19}, {26,35}, {29,33}, {1,44}, {4,26}, {8,43}, {22,28}, {38,44}, {7,26}, {20,39}, {8,39}, {8,21}, {28,33}, {32,36}, {15,39}, {3,10}, {12,14}, {13,20}, {6,31}, {9,23}, {21,30}, {10,16}, {14,36}, {12,34}, {2,24}, {2,15}, {3,42}, {1,27}, {7,18}, {28,39}, {6,37}, {5,23}, {3,25}, {1,35}, {23,42}, {13,27}, {7,35}, {18,37}, {8,29}, {12,22}, {30,41}, {9,43}, {28,42}, {21,36}, {4,34}, {3,30}, {18,36}, {31,38}, {6,9}, {10,36}, {31,44}, {8,17}, {19,30}, {10,37}, {11,31}, {11,21}, {16,43}, {14,28}, {4,29}, {3,12}, {16,31}, {8,36}, {4,19}, {3,37}, {11,41}, {25,43}, {11,40}, {6,43}, {14,41}, {18,25}, {29,40}, {6,12}, {16,40}, {9,29}, {12,42}, {10,24}, {15,44}, {3,14}, {5,20}, {21,39}, {6,34}, {23,30}, {3,21}, {1,16}, {20,29}, {12,39}, {6,24}, {15,23}, {3,33}, {1,32}, {3,20}, {1,39}, {6,14}, {18,23}, {13,37}, {18,31}, {9,38}, {27,36}, {7,40}, {17,35}, {22,40}, {17,26}, {33,40}, {16,26}, {19,33}, {4,11}, {24,29}, {35,44}, {26,29}, {8,22}, {14,22}, {32,33}, {7,9}, {20,21}, {16,39}, {1,23}, {4,13}, {15,25}, {17,32}, {32,43}, {11,28}, {23,37}, {5,13}, {2,17}, {13,30}, {10,20}, {32,37}, {8,41}, {22,25}, {15,33}, {10,25}, {6,19}, {22,31}, {9,19}, {37,42}, {27,40}, {2,40}, {8,16}, {19,28}, {36,37}, {12,15}, {24,27}, {15,34}, {5,33}, {21,32}, {16,24}, {15,19}, {10,44}, {13,42}, {20,27}, {12,18}, {25,34}, {30,35}, {3,43}, {1,28}, {7,42}, {11,16}, {19,43}, {5,44}, {38,41}, {28,31}, {9,36}, {15,40}, {14,35}, {3,26}, {1,33}, {39,44}, {23,41}, {14,18}, {18,38}, {6,28}, {23,36}, {9,14}, {31,34}, {2,42}, {2,27}, {35,38}, {7,29}, {17,37}, {5,40}, {4,21}, {24,42}, {10,35}, {29,44}, {5,31}, {21,34}, {16,30}, {28,35}, {21,26}, {34,39}, {8,30}, {27,32}, {10,29}, {22,44}, {14,26}, {34,41}, {25,30}, {1,41}, {4,25}, {6,17}, {13,17}, {20,40}, {31,42}, {10,42}, {27,44}, {17,30}, {5,27}, {9,30}, {10,22}, {14,44}, {7,25}, {6,39}, {13,25}, {25,40}, {6,35}, {13,38}, {7,20}, {9,39}, {13,31}, {25,42}, {27,35}, {36,43}, {4,44}, {10,13}, {20,44}, {12,33}, {1,24}, {4,15}, {24,35}, {3,35}, {1,29}, {1,10}, {17,41}, {29,36}, {15,27}, {3,16}, {1,19}, {8,10}, {12,44}, {12,24}, {15,41}, {20,35}, {3,31}, {1,9}, {5,18}, {21,38}, {23,28}, {6,32}, {11,23}, {2,13}, {19,32}, {11,37}, {8,23}, {13,22}, {4,36}, {31,37}, {2,34}, {2,20}, {8,33}, {22,32}, {28,36}, {4,12}, {15,24}, {18,42}, {11,32}, {3,22}, {18,33}, {18,29}, {22,33}, {14,32}, {27,38}, {7,34}, {2,39}, {19,22}, {26,39}, {2,30}, {10,28}, {13,43}, {17,34}, {10,40}, {5,22}, {14,21}, {19,27}, {3,38}, {7,16}, {19,24}, {8,26}, {3,17}, {10,19}, {14,37}, {12,38}, {9,27}, {24,39}, {23,29}, {6,44}, {28,37}, {5,36}, {17,25}, {30,40}, {6,10}, {5,43}, {21,28}, {16,23}, {13,19}, {20,23}, {37,44}, {8,12}, {22,41}, {8,15}, {1,7}, {9,20}, {21,31}, {9,16}, {3,5}, {1,21}, {20,28}, {11,18}, {6,21}, {31,36}, {11,14}, {23,26}, {13,33}, {4,42}, {4,37}, {36,39}, {8,31}, {26,34}, {30,33}, {4,24}, {15,35}, {17,29}, {7,24}, {32,38}, {36,44}, {26,31}, {2,8}, {20,37}, {7,38}, {29,39}, {39,42}, {25,32}, {11,35}, {34,37}, {5,26}, {18,39}, {32,35}, {11,29}, {18,26}, {28,29}, {2,44}, {2,26}, {13,39}, {14,20}, {23,35}, {16,18}, {12,36}, {24,43}, {15,28}, {18,30}, {5,39}, {6,18}, {8,42}, {3,41}, {23,44}, {31,41}, {7,11}, {17,44}, {8,27}, {3,27}, {16,38}, {7,19}, {30,44}, {12,43}, {28,41}, {4,16}, {1,25}, {18,43}, {10,32}, {1,34}, {5,9}, {21,42}, {22,34}, {14,30}, {2,33}, {2,32}, {27,42}, {3,19}, {2,10}, {9,22}, {20,32}, {24,36}, {11,24}, {15,43}, {29,43}, {26,40}, {14,40}, {10,38}, {17,36}, {4,30}, {11,44}, {10,26}, {16,27}, {3,15}, {3,36}, {8,35}, {17,22}, {21,33}, {11,39}, {13,29}, {6,33}, {1,17}, {4,40}, {10,18}, {1,12}, {8,14}, {27,34}, {2,7}, {19,34}, {12,28}, {36,41}, {33,44}, {4,41}, {5,34}, {1,37}, {9,37}, {5,42}, {15,21}, {24,37}, {22,29}, {19,23}, {15,31}, {32,39}, {14,24}, {9,15}, {25,31}, {31,40}, {15,18}, {12,20}, {3,6}, {16,17}, {19,40}, {9,35}, {1,8}, {34,38}, {7,30}, {8,11}, {6,27}, {17,38}, {17,42}, {39,41}, {24,41}, {26,43}, {4,5}, {22,43}, {5,38}, {12,32}, {21,44}, {29,42}, {8,25}, {19,44}, {26,37}, {23,34}, {4,22}, {9,26}, {27,41}, {20,34}, {24,38}, {7,21}, {24,33}, {15,32}, {30,39}, {12,27}, {3,7}, {33,42}, {16,33}, {4,8} } Symmetric graph 13 of order 44 Valency 33 Diameter 2 Girth 3 Automorphism group of order 60930411873673404638822400000000 Number of arcs = 1452 Number of 2-arcs = 46464 2-arc-transitive false Edge-set { {1,12}, {11,26}, {22,38}, {10,44}, {16,23}, {20,32}, {2,41}, {9,18}, {9,21}, {24,37}, {31,37}, {33,36}, {29,36}, {1,19}, {11,17}, {8,23}, {15,42}, {8,27}, {15,44}, {13,43}, {10,32}, {13,41}, {10,28}, {17,42}, {7,30}, {17,40}, {7,26}, {11,28}, {22,39}, {10,29}, {16,34}, {7,37}, {20,31}, {15,30}, {3,40}, {7,39}, {20,24}, {18,30}, {9,40}, {22,31}, {6,35}, {9,36}, {21,29}, {19,31}, {11,35}, {9,34}, {21,25}, {15,29}, {3,34}, {14,27}, {12,29}, {8,34}, {6,44}, {14,23}, {10,34}, {16,25}, {16,32}, {5,41}, {21,26}, {14,24}, {1,37}, {6,13}, {10,14}, {33,41}, {28,36}, {30,35}, {27,40}, {2,12}, {8,12}, {6,16}, {5,14}, {33,43}, {32,36}, {23,35}, {27,42}, {8,15}, {32,41}, {28,41}, {5,21}, {4,19}, {8,17}, {7,15}, {26,44}, {28,39}, {10,21}, {4,16}, {8,14}, {1,15}, {27,38}, {33,44}, {30,40}, {26,40}, {2,14}, {25,39}, {24,43}, {26,38}, {7,14}, {1,20}, {5,18}, {9,19}, {25,37}, {31,43}, {9,14}, {1,21}, {24,38}, {33,37}, {24,36}, {29,37}, {11,13}, {27,44}, {23,44}, {25,43}, {32,43}, {10,22}, {5,31}, {19,35}, {9,25}, {21,43}, {19,42}, {11,30}, {17,34}, {7,25}, {21,35}, {4,27}, {12,39}, {8,24}, {1,26}, {17,38}, {20,38}, {5,24}, {19,37}, {4,25}, {22,42}, {6,30}, {17,36}, {7,29}, {21,37}, {4,31}, {15,39}, {3,24}, {20,40}, {19,36}, {11,29}, {19,34}, {11,25}, {13,44}, {3,28}, {18,39}, {20,34}, {14,40}, {18,44}, {9,23}, {5,25}, {9,27}, {21,44}, {18,37}, {20,43}, {22,40}, {20,39}, {2,24}, {18,42}, {9,30}, {12,35}, {12,44}, {1,25}, {17,43}, {16,38}, {5,33}, {22,43}, {6,32}, {20,44}, {2,23}, {6,25}, {14,43}, {11,33}, {22,36}, {4,23}, {13,42}, {8,28}, {13,38}, {10,33}, {22,41}, {6,28}, {8,25}, {15,43}, {11,27}, {22,44}, {2,32}, {10,30}, {7,32}, {13,40}, {10,26}, {10,31}, {16,35}, {9,24}, {9,31}, {6,33}, {6,29}, {9,32}, {21,41}, {4,41}, {13,28}, {21,28}, {4,39}, {8,38}, {15,33}, {22,27}, {15,28}, {3,39}, {10,35}, {16,27}, {14,29}, {1,34}, {6,38}, {14,33}, {21,27}, {4,44}, {18,24}, {16,26}, {5,38}, {7,43}, {11,44}, {22,23}, {20,29}, {2,34}, {20,33}, {2,36}, {4,43}, {13,32}, {10,39}, {3,38}, {18,33}, {15,32}, {3,41}, {5,35}, {19,27}, {17,29}, {7,34}, {6,40}, {14,26}, {13,27}, {18,28}, {16,30}, {5,40}, {2,43}, {12,32}, {12,33}, {8,36}, {17,28}, {10,40}, {14,28}, {1,39}, {10,38}, {16,33}, {18,31}, {9,35}, {12,25}, {5,42}, {1,36}, {8,43}, {18,23}, {9,42}, {8,37}, {15,31}, {4,38}, {13,33}, {8,39}, {15,24}, {18,27}, {9,44}, {13,23}, {10,42}, {22,33}, {6,36}, {8,41}, {5,36}, {1,43}, {17,32}, {15,23}, {3,42}, {8,35}, {15,27}, {18,26}, {9,38}, {11,38}, {22,29}, {6,34}, {2,37}, {4,42}, {13,30}, {22,32}, {6,41}, {19,29}, {17,31}, {19,33}, {22,25}, {6,43}, {7,41}, {3,37}, {3,35}, {20,25}, {2,35}, {21,30}, {19,32}, {11,41}, {5,34}, {19,25}, {7,38}, {22,30}, {16,24}, {18,32}, {9,41}, {12,31}, {21,23}, {21,24}, {4,37}, {19,30}, {19,26}, {3,19}, {11,18}, {31,34}, {25,35}, {27,34}, {25,44}, {3,16}, {7,20}, {2,20}, {30,42}, {32,39}, {24,41}, {30,34}, {25,40}, {2,16}, {5,12}, {4,21}, {24,39}, {26,43}, {11,14}, {1,22}, {5,20}, {2,19}, {25,42}, {30,43}, {27,39}, {24,44}, {3,18}, {23,43}, {32,42}, {23,37}, {4,20}, {2,13}, {6,22}, {6,14}, {10,18}, {9,16}, {32,37}, {31,41}, {33,40}, {26,36}, {1,14}, {1,17}, {33,42}, {30,36}, {7,17}, {3,22}, {6,18}, {31,36}, {29,35}, {23,42}, {29,40}, {11,12}, {4,13}, {26,34}, {8,19}, {31,39}, {24,35}, {23,34}, {27,37}, {4,12}, {8,13}, {6,17}, {29,38}, {26,42}, {30,38}, {29,34}, {25,34}, {9,12}, {8,21}, {11,16}, {5,22}, {9,20}, {2,21}, {24,42}, {30,37}, {23,41}, {28,42}, {4,15}, {33,38}, {3,13}, {7,22}, {6,20}, {31,42}, {3,15}, {7,13}, {10,20}, {30,41}, {28,40}, {3,20}, {2,18}, {7,16}, {32,40}, {23,39}, {8,18}, {9,15}, {31,35}, {3,21}, {5,17}, {7,19}, {11,20}, {4,17}, {11,22}, {31,40}, {2,15}, {3,12}, {7,21}, {30,39}, {24,40}, {8,20}, {26,41}, {1,13}, {10,17}, {27,35}, {29,41}, {5,19}, {11,19}, {26,39}, {28,34}, {32,38}, {6,19}, {10,12}, {29,39}, {10,19}, {4,14}, {28,38}, {33,39}, {32,35}, {27,41}, {23,36}, {29,42}, {11,15}, {31,44}, {27,43}, {32,44}, {28,35}, {28,44}, {2,28}, {10,23}, {16,42}, {14,41}, {1,28}, {21,38}, {4,33}, {14,39}, {1,24}, {18,38}, {9,33}, {12,37}, {14,36}, {1,33}, {15,35}, {3,27}, {16,36}, {5,29}, {19,43}, {11,32}, {14,35}, {1,27}, {12,38}, {8,33}, {17,37}, {4,26}, {16,43}, {5,32}, {6,23}, {10,25}, {13,36}, {17,39}, {15,38}, {3,33}, {22,35}, {6,27}, {16,39}, {18,43}, {12,42}, {22,37}, {6,31}, {15,36}, {3,29}, {13,37}, {18,36}, {1,31}, {17,35}, {19,41}, {21,42}, {15,37}, {8,30}, {17,44}, {7,23}, {22,34}, {3,30}, {7,27}, {14,34}, {12,41}, {5,23}, {17,41}, {7,28}, {21,40}, {3,31}, {12,40}, {8,26}, {18,35}, {14,44}, {1,23}, {16,41}, {5,28}, {4,32}, {14,37}, {13,39}, {10,24}, {3,26}, {7,31}, {20,35}, {2,26}, {3,23}, {2,27}, {14,38}, {16,37}, {3,32}, {13,35}, {10,27}, {11,31}, {15,34}, {3,25}, {18,40}, {20,42}, {2,30}, {2,31}, {15,41}, {21,36}, {12,34}, {2,33}, {12,36}, {6,24}, {8,29}, {15,40}, {4,28}, {4,29}, {13,34}, {18,34}, {1,30}, {5,27}, {12,43}, {8,32}, {7,33}, {20,36}, {19,44}, {11,23}, {9,29}, {21,34}, {21,39}, {4,24}, {19,40}, {16,44}, {2,29}, {19,39}, {9,26}, {16,40}, {5,26}, {9,28}, {2,25}, {5,30}, {11,24}, {18,41}, {17,25}, {9,37}, {21,31}, {11,43}, {11,34}, {20,27}, {2,44}, {5,43}, {20,23}, {2,42}, {8,42}, {13,26}, {11,42}, {4,40}, {2,39}, {12,24}, {17,24}, {22,28}, {6,39}, {10,36}, {16,29}, {11,39}, {22,24}, {20,26}, {2,38}, {7,42}, {20,30}, {13,29}, {3,44}, {6,37}, {4,36}, {5,37}, {21,33}, {7,35}, {2,40}, {12,30}, {21,32}, {5,39}, {19,24}, {6,42}, {15,26}, {10,41}, {19,28}, {17,30}, {7,40}, {12,26}, {13,31}, {17,23}, {4,34}, {18,29}, {14,31}, {14,32}, {1,41}, {12,27}, {14,25}, {8,44}, {12,28}, {7,44}, {18,25}, {9,43}, {11,37}, {13,25}, {3,36}, {10,43}, {16,31}, {12,23}, {1,44}, {13,24}, {10,37}, {4,35}, {9,39}, {16,28}, {14,30}, {1,40}, {1,35}, {17,27}, {11,40}, {1,38}, {1,42}, {17,26}, {8,40}, {22,26}, {7,36}, {17,33}, {5,44}, {3,43}, {15,25}, {19,23}, {33,34}, {10,15}, {1,16}, {1,18}, {9,17}, {4,22}, {3,17}, {29,43}, {32,34}, {25,41}, {5,16}, {26,37}, {10,16}, {2,17}, {6,15}, {3,14}, {33,35}, {27,36}, {26,35}, {5,13}, {7,18}, {10,13}, {30,44}, {6,21}, {29,44}, {28,43}, {5,15}, {23,40}, {11,21}, {6,12}, {23,38}, {25,36}, {25,38}, {8,22}, {31,38}, {7,12}, {9,22}, {28,37}, {9,13}, {4,18}, {8,16}, {24,34}, {2,22}, {14,42}, {6,26}, {1,29}, {19,38}, {4,30}, {7,24}, {8,31}, {20,37}, {20,41}, {1,32}, {20,28}, {11,36} } Symmetric graph 14 of order 44 Valency 40 Diameter 2 Girth 3 Automorphism group of order 60740641855649297203200 Number of arcs = 1760 Number of 2-arcs = 68640 2-arc-transitive false Edge-set { {1,5}, {2,21}, {12,18}, {1,15}, {17,24}, {39,42}, {3,30}, {2,18}, {18,38}, {14,40}, {21,29}, {8,27}, {25,33}, {4,9}, {6,20}, {1,39}, {17,30}, {6,39}, {30,35}, {7,20}, {34,39}, {10,15}, {5,24}, {23,36}, {9,16}, {31,33}, {14,41}, {3,43}, {2,19}, {22,38}, {11,31}, {2,8}, {18,33}, {9,40}, {6,29}, {8,22}, {11,33}, {9,30}, {6,43}, {24,38}, {10,31}, {8,32}, {33,42}, {18,44}, {1,38}, {14,21}, {12,21}, {13,29}, {22,44}, {17,43}, {2,37}, {8,41}, {20,28}, {26,39}, {4,25}, {20,27}, {1,37}, {17,32}, {6,16}, {23,35}, {11,41}, {4,8}, {1,23}, {9,17}, {31,39}, {30,41}, {7,43}, {2,34}, {10,22}, {5,11}, {16,23}, {9,23}, {31,41}, {4,41}, {9,43}, {2,6}, {22,25}, {11,27}, {6,14}, {21,35}, {11,44}, {1,8}, {12,23}, {7,9}, {27,31}, {25,41}, {28,30}, {18,35}, {15,20}, {24,39}, {15,42}, {3,24}, {10,19}, {5,40}, {16,26}, {23,28}, {25,40}, {27,29}, {17,36}, {9,26}, {35,38}, {15,31}, {8,34}, {13,33}, {3,33}, 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{21,30}, {7,27}, {25,34}, {4,10}, {5,20}, {23,44}, {21,31}, {12,41}, {11,15}, {14,36}, {16,21}, {1,14}, {3,12}, {7,19}, {27,38}, {25,31}, {20,26}, {28,39}, {24,28}, {2,42}, {24,40}, {10,29}, {1,40}, {34,42}, {3,13}, {26,37}, {28,32}, {32,41}, {4,42}, {19,29}, {40,44}, {18,25}, {30,42}, {35,40}, {12,14}, {29,36}, {12,39}, {7,30}, {7,24}, {10,34}, {10,32}, {23,40}, {9,29}, {5,31}, {11,23}, {14,31}, {20,44}, {7,44}, {25,37}, {17,28}, {2,39}, {18,30}, {7,15}, {24,34}, {10,42}, {3,5}, {19,35}, {13,23}, {1,34}, {13,27}, {26,32}, {3,7}, {8,31}, {5,13}, {26,35}, {17,29}, {5,39}, {30,36}, {9,44}, {1,6}, {10,44}, {37,42}, {31,44}, {1,41}, {7,32}, {12,43}, {38,44}, {16,19}, {33,38}, {19,36}, {12,20}, {7,39}, {10,16}, {4,39}, {23,25}, {27,32}, {1,7}, {25,44}, {3,32}, {29,38}, {5,36}, {1,20}, {7,41}, {4,34}, {5,9}, {13,44}, {7,11}, {13,31}, {1,43}, {18,21}, {10,38}, {5,21}, {12,36}, {22,40}, {5,30}, {36,43}, {8,20}, {4,43}, {33,39}, {12,30}, {32,37}, {6,12}, {7,35}, {30,34}, {9,14}, {16,41}, {5,29}, {8,23}, {35,39}, {10,39}, {15,32}, {21,25}, {1,29}, {17,44}, {4,6}, {9,27}, {6,34}, {34,41}, {16,29}, {22,28}, {11,26}, {13,25}, {22,27}, {27,41}, {17,41}, {16,28}, {23,26}, {3,41}, {4,19}, {1,31}, {20,35}, {15,39}, {15,34}, {13,24}, {9,38}, {6,31}, {3,6}, {12,31}, {15,23}, {9,24}, {24,42}, {18,26}, {20,39}, {3,16}, {24,32}, {24,36}, {28,42}, {8,40}, {29,33}, {6,36}, {19,22}, {13,18}, {6,42}, {11,24}, {34,38}, {12,25}, {3,25}, {18,42}, {3,38}, {20,24}, {17,25}, {27,37}, {31,43}, {2,41}, {16,37}, {9,15}, {31,34}, {13,41}, {2,20}, {11,32}, {4,23}, {4,7}, {2,31}, {18,41}, {20,40}, {14,30}, {21,43}, {2,7}, {11,43}, {38,43}, {19,23}, {4,5}, {32,43}, {30,33}, {14,43}, {5,27}, {6,24}, {14,42}, {3,44}, {8,24}, {39,44}, {15,17}, {24,37}, {18,39}, {16,35}, {15,33}, {15,21}, {1,27}, {25,42}, {12,28}, {7,26}, {3,27}, {10,37}, {6,25}, {3,39}, {5,44}, {8,42}, {6,10}, {14,24}, {10,21}, {32,44}, {12,44}, {7,13}, {10,43}, {11,21}, {4,22}, {11,20}, {8,39}, {28,31}, {15,29}, {21,42}, {27,44}, {4,21}, {4,24}, {10,20}, {19,21}, {10,40}, {6,44}, {2,28}, {1,28}, {12,24}, {38,42}, {3,8}, {19,33}, {14,22}, {7,16}, {2,24}, {10,18}, {2,38}, {18,31}, {28,40}, {11,19}, {24,30}, {1,35}, {9,21}, {9,31}, {33,41}, {5,12}, {8,30}, {7,38}, {5,18}, {26,40}, {22,32}, {11,42}, {26,42}, {10,17}, {16,36}, {17,35}, {15,37}, {13,34}, {3,37}, {19,32}, {2,11}, {8,18}, {30,38}, {2,35}, {4,17}, {14,29}, {27,35}, {15,25}, {7,23}, {30,40}, {11,25}, {35,42}, {3,14}, {14,20}, {27,39}, {14,38}, {18,43}, {1,11}, {9,20}, {1,24}, {3,21}, {21,36}, {12,16}, {25,39}, {38,41}, {15,18}, {3,15}, {16,20}, {22,33}, {21,39}, {19,24}, {8,15}, {31,37}, {23,39}, {1,30}, {6,9}, {27,30}, {20,38}, {8,36}, {4,18} } Symmetric graph 15 of order 44 Valency 42 Diameter 2 Girth 3 Automorphism group of order 4714400748520531002654720000 Number of arcs = 1848 Number of 2-arcs = 75768 2-arc-transitive false Edge-set { {1,3}, {28,30}, {15,42}, {12,34}, {10,35}, {20,23}, {20,25}, {10,22}, {6,37}, {35,43}, {1,34}, {14,37}, {11,24}, {14,18}, {24,31}, {25,35}, {34,43}, {5,39}, {3,8}, {7,43}, {1,29}, {22,30}, {6,42}, {39,42}, {8,18}, {9,38}, {12,38}, {32,42}, {18,40}, {2,38}, {12,13}, {18,43}, {1,31}, {7,22}, {6,29}, {6,16}, {4,28}, {15,21}, {3,7}, {22,29}, {30,33}, {36,42}, {25,34}, {5,23}, {3,20}, {16,23}, {20,28}, {4,32}, {21,40}, {36,40}, {7,33}, {10,40}, {7,37}, {1,23}, {14,20}, {15,32}, {27,40}, {29,40}, {7,41}, {10,41}, {17,37}, {7,32}, {2,30}, {13,42}, {3,25}, {22,43}, {5,33}, {3,36}, {5,19}, {3,26}, {12,27}, {10,16}, {20,26}, {25,44}, {3,28}, {15,22}, {25,33}, {36,43}, {21,34}, {5,35}, {23,44}, {2,20}, {18,22}, {6,31}, {4,11}, {14,28}, {15,24}, {19,37}, {11,26}, {12,14}, {10,24}, {1,27}, {14,16}, {15,26}, {27,44}, {15,44}, {2,27}, {3,21}, {5,22}, {15,35}, {27,34}, {3,39}, {8,22}, {30,37}, {11,42}, {14,42}, {18,24}, {1,20}, {14,25}, {11,15}, {9,27}, {15,33}, {27,36}, {3,24}, {19,22}, {24,35}, {19,34}, {31,39}, {8,39}, {14,22}, {29,34}, {35,41}, {23,41}, {17,20}, {18,28}, {15,31}, {7,25}, {29,43}, {6,21}, {4,5}, {28,44}, {2,15}, {6,13}, {4,23}, {17,28}, {10,11}, {9,37}, {19,35}, {26,34}, {14,17}, {24,32}, {30,31}, {12,28}, {10,15}, {25,43}, {18,21}, {5,31}, {7,44}, {2,29}, {22,26}, {6,44}, {6,43}, {1,4}, {8,37}, {11,30}, {14,29}, {24,41}, {25,32}, {40,43}, {2,5}, {3,13}, {16,38}, {12,42}, {10,18}, {20,38}, {12,25}, {13,39}, {8,23}, {9,17}, {32,38}, {10,42}, {18,37}, {35,38}, {9,42}, {19,42}, {18,26}, {8,11}, {9,30}, {8,20}, {25,30}, {11,29}, {9,41}, {26,28}, {6,25}, {4,43}, {20,43}, {1,25}, {11,22}, {6,9}, {16,28}, {15,28}, {4,25}, {21,43}, {34,39}, {8,35}, {9,23}, {23,42}, {18,20}, {12,40}, {14,30}, {24,42}, {18,42}, {18,31}, {9,20}, {25,38}, {11,36}, {9,33}, {20,21}, {5,25}, {11,44}, {2,9}, {28,38}, {12,15}, {13,25}, {23,43}, {38,43}, {1,12}, {13,22}, {6,23}, {2,16}, {13,28}, {4,16}, {21,28}, {25,42}, {22,33}, {6,36}, {24,43}, {1,19}, {24,37}, {11,19}, {14,31}, {24,39}, {12,32}, {3,18}, {22,31}, {29,36}, {5,26}, {3,44}, {6,27}, {8,12}, {10,30}, {20,29}, {25,41}, {5,41}, {3,17}, 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{26,44}, {17,42}, {18,32}, {8,38}, {12,30}, {5,32}, {3,40}, {13,16}, {4,36}, {7,35}, {3,35}, {22,34}, {14,35}, {24,34}, {8,31}, {2,31}, {3,15}, {22,27}, {23,39}, {29,39}, {6,39}, {4,8}, {9,28}, {13,33}, {17,24}, {19,32}, {11,13}, {17,19}, {32,37}, {30,34}, {11,40}, {2,14}, {13,24}, {31,44}, {4,29}, {6,8}, {4,30}, {28,29}, {10,33}, {34,41}, {16,40}, {7,28}, {17,33}, {23,29}, {20,41}, {32,41}, {17,40}, {30,35}, {15,20}, {25,27}, {18,29}, {31,41}, {5,30}, {2,41}, {4,12}, {10,21}, {4,38}, {28,36}, {27,35}, {16,34}, {26,39}, {8,44}, {1,6}, {21,42}, {3,12}, {13,27}, {16,20}, {25,28}, {9,16}, {23,33}, {29,35}, {39,41}, {8,17}, {19,43}, {1,26}, {6,10}, {21,30}, {5,42}, {15,25}, {27,43}, {3,5}, {3,22}, {8,19}, {26,27}, {6,26}, {4,44}, {13,31}, {7,16}, {6,30}, {4,42}, {28,42}, {15,18}, {29,37}, {11,41}, {10,27}, {15,34}, {3,23}, {20,22}, {3,19}, {22,39}, {16,43}, {1,28}, {21,29}, {41,44}, {2,17}, {4,20}, {24,28}, {15,19}, {21,26}, {13,29}, {5,27}, {3,16}, {12,21}, {5,10}, {20,44}, {6,38}, {11,23}, {8,26}, {30,44}, {26,37}, {6,14}, {4,24}, {1,8}, {15,29}, {22,37}, {17,34}, {15,23}, {20,27}, {18,25}, {31,43}, {36,44}, {11,38}, {9,12}, {13,19}, {23,26}, {10,38}, {12,37}, {23,34}, {11,37}, {9,11}, {7,30}, {29,42}, {30,42}, {17,21}, {13,38}, {12,23}, {13,17}, {17,36}, {32,33}, {8,29}, {30,41}, {29,41}, {17,41}, {6,12}, {23,28}, {7,39}, {38,42}, {19,30}, {26,42}, {16,25}, {23,25}, {8,30}, {9,29}, {38,41}, {18,44}, {9,31}, {20,30}, {9,18}, {19,21}, {27,32}, {8,25}, {30,43}, {8,10}, {3,27}, {22,41}, {10,29}, {17,44}, {2,35}, {13,34}, {16,39}, {15,27}, {25,36}, {33,43}, {2,37}, {1,22}, {15,43}, {2,21}, {5,13}, {1,39}, {35,42}, {2,22}, {1,9}, {14,38}, {27,33}, {34,44}, {23,31}, {7,17}, {29,32}, {28,35}, {21,41}, {4,7}, {18,33}, {23,30}, {20,42}, {11,43}, {5,14}, {8,27}, {22,38}, {30,39}, {8,42}, {18,38}, {18,19}, {20,24}, {11,31}, {9,39}, {40,41}, {20,39}, {1,32}, {7,21}, {10,34}, {19,41}, {17,26}, {3,43}, {28,43}, {42,43}, {13,41}, {11,25}, {9,43}, {16,37}, {11,28}, {5,16}, {4,27}, {5,17}, {31,38}, {12,39}, {14,23}, {17,38}, {8,14}, {6,35}, {9,15}, {27,38}, {16,36}, {12,33}, {10,36}, {21,35}, {5,34}, {22,24}, {6,19}, {21,31}, {33,37}, {14,24}, {14,19}, {24,25}, {11,18}, {2,24}, {6,34}, {4,35}, {26,35}, {10,28}, {15,37}, {24,26}, {12,18}, {19,36}, {26,33}, {1,36}, {16,24}, {19,28}, {21,39}, {7,13}, {17,30}, {3,34}, {35,44}, {9,32}, {16,30}, {20,32}, {25,40}, {9,24}, {19,38}, {11,35}, {28,37}, {7,19}, {26,29}, {6,11}, {4,34}, {24,30}, {5,40}, {4,17}, {21,32}, {17,39}, {8,32}, {12,16}, {8,43}, {31,40}, {17,23}, {7,34}, {22,35}, {20,36}, {26,31}, {4,33}, {19,39}, {3,37}, {22,28}, {23,40}, {7,20}, {33,36}, {32,36}, {33,40}, {4,18}, {1,41}, {8,41}, {25,29}, {5,9}, {12,43}, {19,44}, {7,9}, {29,38}, {13,32}, {1,30}, {7,23}, {7,36}, {11,27}, {2,26}, {1,44}, {6,22}, {13,44}, {12,35}, {6,15}, {27,31}, {14,44}, {28,39}, {10,43} } Symmetric graph 16 of order 44 Valency 43 Diameter 1 Girth 3 Automorphism group of order 2658271574788448768043625811014615890319638528000000000 Number of arcs = 1892 Number of 2-arcs = 79464 2-arc-transitive true Edge-set { {1,2}, {1,44}, {1,28}, {2,44}, {1,22}, {4,44}, {2,28}, {1,43}, {5,44}, {25,28}, {2,40}, {2,22}, {1,4}, {1,39}, {37,44}, {6,28}, {2,21}, {19,22}, {4,41}, {2,27}, {2,43}, {1,5}, {1,25}, {40,44}, {1,30}, {32,44}, {18,28}, {2,19}, {22,38}, {4,42}, {2,37}, {3,43}, {5,43}, {25,42}, {24,40}, {2,24}, {1,9}, {2,39}, {1,37}, {1,6}, {21,44}, {1,19}, {41,44}, {27,28}, {1,35}, {14,44}, {14,28}, {2,16}, {22,31}, {4,6}, {2,3}, {33,43}, {5,38}, {25,44}, {18,40}, {2,18}, {5,39}, {27,37}, {6,39}, {21,37}, {19,44}, {18,41}, {27,34}, {2,34}, {1,41}, {3,44}, {2,30}, {1,32}, {1,18}, {1,38}, {42,44}, {28,37}, {1,3}, {43,44}, {28,42}, {22,24}, {4,9}, {1,21}, {12,44}, {9,28}, {2,7}, {9,22}, {4,7}, {2,29}, {11,43}, {5,35}, {25,38}, {40,42}, {2,5}, {1,27}, {15,39}, {29,37}, {6,33}, {21,38}, {19,28}, {2,41}, {27,31}, {2,31}, {6,30}, {21,32}, {18,24}, {9,19}, {30,38}, {32,42}, 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{8,23}, {6,13}, {19,35}, {20,31}, {20,23}, {20,36}, {18,20}, {23,26}, {17,32}, {10,37}, {31,33}, {18,39}, {3,21}, {25,27}, {6,17}, {23,33}, {3,20}, {32,36}, {12,30}, {25,30}, {12,20}, {9,31}, {6,7}, {10,21}, {19,36}, {30,41}, {17,27}, {9,20}, {10,14}, {16,26}, {30,34}, {4,36}, {3,8}, {19,39}, {6,27}, {20,32}, {26,38}, {23,42}, {10,42}, {15,24}, {9,29}, {17,39}, {20,30}, {20,42}, {17,24}, {6,42}, {7,20}, {10,33}, {18,30}, {14,19}, {8,31}, {3,11}, {26,34}, {12,41}, {7,42}, {8,32}, {13,32}, {16,41}, {14,26}, {9,17}, {14,21}, {12,16}, {11,27}, {3,34}, {8,39}, {3,14}, {9,15}, {7,29}, {29,33}, {36,43}, {5,30}, {8,25}, {13,40}, {17,25}, {7,15}, {21,35}, {12,14}, {14,36}, {16,30}, {23,34}, {4,8}, {32,40}, {20,39}, {17,21}, {3,26}, {8,13}, {13,34}, {10,34}, {15,20}, {26,33}, {23,38}, {30,36}, {8,11}, {12,13}, {16,43}, {16,31}, {8,37}, {26,29}, {12,26}, {20,41}, {8,9}, {13,16}, {7,43}, {7,8}, {8,17}, {8,35}, {10,32}, {11,15}, {19,23}, {23,36}, {7,12}, {10,13}, {14,17}, {14,35}, {14,16}, {17,35}, {17,36}, {7,31}, {8,14}, {29,35}, {30,31}, {8,38}, {36,38}, {8,24}, {8,30}, {7,36}, {23,29}, {8,16}, {14,23}, {16,20}, {8,41}, {17,29}, {13,41}, {10,36}, {10,15}, {8,19}, {13,36}, {11,36}, {8,20}, {26,32}, {7,13}, {20,33}, {17,23}, {29,39}, {36,39}, {16,23}, {16,33}, {10,30}, {10,20}, {13,26} } ................................................................... Symmetric connected graphs of order 45 Symmetric graph 1 of order 45 Valency 2 Diameter 22 Girth 45 Automorphism group of order 90 Number of arcs = 90 Number of 2-arcs = 90 2-arc-transitive true Edge-set { {1,4}, {5,8}, {7,11}, {12,13}, {14,16}, {18,19}, {20,22}, {23,26}, {27,30}, {28,31}, {32,34}, {35,39}, {38,42}, {40,45}, {1,43}, {3,5}, {6,7}, {9,12}, {10,14}, {15,18}, {17,20}, {21,23}, {24,27}, {25,28}, {29,32}, {33,35}, {36,38}, {37,40}, {41,43}, {3,44}, {2,6}, {4,9}, {8,10}, {11,15}, {13,17}, {16,21}, {19,24}, {22,25}, {26,29}, {30,33}, {31,36}, {34,37}, {39,41}, {42,44}, {2,45} } Symmetric graph 2 of order 45 Valency 4 Diameter 7 Girth 4 Automorphism group of order 180 Number of arcs = 180 Number of 2-arcs = 540 2-arc-transitive false Edge-set { {1,5}, {26,30}, {30,31}, {4,7}, {9,11}, {7,10}, {11,13}, {28,32}, {32,35}, {31,34}, {34,39}, {35,38}, {39,41}, {8,12}, {10,15}, {12,14}, {15,17}, {13,16}, {16,19}, {14,18}, {17,21}, {19,23}, {33,36}, {36,37}, {38,42}, {37,40}, {42,45}, {41,44}, {1,44}, {40,43}, {3,45}, {1,6}, {18,20}, {21,22}, {20,24}, {22,26}, {23,27}, {27,30}, {24,25}, {26,29}, {30,33}, {2,43}, {3,4}, {2,5}, {4,9}, {6,7}, {7,11}, {5,8}, {9,12}, {11,14}, {25,28}, {29,32}, {28,31}, {32,34}, {33,35}, {35,39}, {31,36}, {34,37}, {39,40}, {8,10}, {12,15}, {10,13}, {15,16}, {14,17}, {17,19}, {13,18}, {16,20}, {19,24}, {36,38}, {37,42}, {38,41}, {42,44}, {40,45}, {1,45}, {41,43}, {2,44}, {18,21}, {20,22}, {21,23}, {22,27}, {24,26}, {23,25}, {27,28}, {3,43}, {2,4}, {3,6}, {5,9}, {6,8}, {25,29}, {29,33} } Symmetric graph 3 of order 45 Valency 4 Diameter 5 Girth 4 Automorphism group of order 180 Number of arcs = 180 Number of 2-arcs = 540 2-arc-transitive false Edge-set { {1,4}, {13,17}, {13,25}, {27,29}, {16,29}, {27,37}, {16,21}, {39,42}, {20,32}, {28,42}, {28,32}, {5,39}, {20,23}, {6,8}, {22,34}, {31,43}, {40,43}, {8,40}, {31,34}, {6,16}, {22,27}, {18,20}, {26,39}, {2,36}, {9,10}, {10,45}, {2,45}, {9,20}, {36,39}, {18,28}, {26,28}, {30,31}, {30,40}, {6,38}, {19,22}, {3,14}, {12,14}, {12,22}, {3,6}, {19,31}, {38,40}, {41,45}, {33,45}, {9,41}, {33,36}, {4,18}, {24,26}, {15,26}, {15,18}, {24,36}, {4,9}, {7,12}, {3,35}, {12,44}, {3,44}, {7,19}, {35,38}, {17,30}, {25,30}, {25,38}, {17,19}, {21,24}, {4,37}, {1,15}, {11,15}, {11,24}, {21,33}, {37,41}, {29,41}, {29,33}, {32,35}, {7,42}, {5,17}, {23,25}, {23,35}, {5,7}, {32,44}, {42,44}, {1,43}, {11,43}, {8,21}, {34,37}, {1,34}, {8,11}, {10,13}, {2,13}, {10,23}, {2,5}, {14,27}, {14,16} } Symmetric graph 4 of order 45 Valency 4 Diameter 5 Girth 4 Automorphism group of order 180 Number of arcs = 180 Number of 2-arcs = 540 2-arc-transitive false Edge-set { {1,7}, {24,27}, {20,38}, {33,39}, {29,35}, {10,41}, {16,43}, {9,12}, {11,34}, {2,25}, {3,42}, {14,23}, {19,25}, {12,18}, {26,40}, {4,26}, {37,45}, {13,31}, {8,35}, {6,14}, {6,33}, {28,37}, {5,44}, {11,17}, {13,22}, {20,21}, {18,24}, {16,22}, {36,44}, {10,32}, {3,30}, {5,23}, {22,30}, {1,28}, {2,29}, {7,34}, {8,44}, {15,16}, {31,37}, {30,31}, {27,36}, {34,40}, {32,38}, {29,38}, {14,20}, {3,21}, {17,44}, {7,15}, {10,13}, {17,40}, {39,42}, {18,45}, {19,41}, {38,41}, {1,24}, {26,32}, {3,9}, {15,24}, {11,25}, {9,45}, {5,6}, {4,43}, {2,41}, {2,8}, {7,43}, {27,33}, {19,37}, {15,33}, {23,26}, {21,29}, {12,35}, {18,36}, {40,43}, {20,42}, {16,39}, {4,10}, {12,21}, {28,34}, {6,42}, {1,45}, {25,28}, {14,32}, {4,22}, {5,27}, {35,36}, {13,19}, {30,39}, {8,11}, {9,31}, {17,23} } Symmetric graph 5 of order 45 Valency 4 Diameter 4 Girth 3 Automorphism group of order 1440 Number of arcs = 180 Number of 2-arcs = 540 2-arc-transitive false Edge-set { {1,14}, {2,31}, {4,7}, {6,12}, {5,19}, {10,31}, {9,31}, {17,23}, {13,16}, {15,20}, {3,21}, {15,22}, {18,21}, {4,26}, {8,31}, {4,25}, {19,33}, {12,30}, {16,36}, {11,23}, {19,38}, {11,17}, {16,35}, {17,32}, {6,33}, {12,34}, {14,42}, {1,43}, {17,41}, {4,24}, {14,28}, {1,28}, {16,37}, {21,29}, {5,18}, {21,45}, {15,40}, {3,35}, {15,43}, {13,40}, {14,39}, {27,33}, {3,29}, {5,38}, {19,27}, {20,22}, {12,44}, {13,30}, {22,27}, {20,29}, {7,45}, {22,24}, {3,39}, {2,37}, {5,32}, {1,41}, {7,25}, {2,9}, {6,44}, {13,37}, {18,32}, {7,34}, {6,42}, {23,36}, {11,44}, {23,26}, {18,45}, {24,26}, {35,36}, {30,40}, {37,38}, {35,39}, {8,11}, {10,20}, {9,28}, {2,38}, {8,10}, {30,34}, {34,45}, {25,28}, {33,42}, {32,41}, {39,42}, {41,43}, {40,43}, {24,27}, {8,44}, {10,29}, {26,36}, {9,25} } Symmetric graph 6 of order 45 Valency 6 Diameter 4 Girth 3 Automorphism group of order 2160 Number of arcs = 270 Number of 2-arcs = 1350 2-arc-transitive false Edge-set { {1,7}, {28,41}, {3,8}, {6,39}, {22,45}, {30,42}, {2,9}, {21,33}, {34,37}, {9,27}, {29,40}, {4,37}, {24,43}, {14,43}, {19,31}, {17,31}, {5,38}, {12,29}, {7,15}, {23,44}, {35,38}, {7,26}, {27,41}, {13,44}, {20,32}, {11,20}, {36,39}, {17,23}, {2,28}, {8,25}, {16,32}, {10,28}, {8,14}, {6,12}, {15,45}, {26,42}, {15,34}, {18,33}, {23,25}, {11,30}, {39,40}, {1,22}, {9,13}, {12,21}, {16,22}, {1,30}, {21,35}, {17,34}, {25,40}, {4,10}, {2,17}, {5,25}, {10,19}, {11,25}, {13,30}, {18,24}, {5,33}, {37,44}, {3,29}, {14,35}, {22,27}, {37,41}, {3,24}, {14,16}, {6,31}, {5,11}, {19,36}, {16,35}, {23,40}, {1,11}, {13,36}, {11,34}, {13,18}, {3,37}, {24,26}, {20,43}, {8,31}, {38,42}, {2,23}, {1,16}, {6,27}, {12,27}, {15,29}, {38,45}, {21,44}, {20,34}, {18,36}, {4,32}, {30,44}, {34,41}, {3,18}, {4,26}, {5,18}, {10,26}, {31,42}, {2,38}, {14,28}, {33,41}, {9,20}, {39,43}, {22,41}, {3,12}, {12,35}, {15,17}, {9,32}, {19,45}, {8,37}, {24,42}, {6,17}, {5,45}, {2,10}, {20,24}, {10,36}, {4,44}, {32,40}, {1,39}, {6,43}, {7,33}, {29,45}, {35,42}, {7,21}, {30,31}, {9,38}, {28,43}, {21,23}, {36,40}, {15,26}, {28,33}, {4,16}, {8,19}, {29,32}, {7,39}, {14,25}, {19,22}, {13,27} } Symmetric graph 7 of order 45 Valency 6 Diameter 4 Girth 4 Automorphism group of order 77760 Number of arcs = 270 Number of 2-arcs = 1350 2-arc-transitive false Edge-set { {1,7}, {17,40}, {2,40}, {10,21}, {6,10}, {21,42}, {6,42}, {28,35}, {21,45}, {15,35}, {21,30}, {20,28}, {4,45}, {15,20}, {4,30}, {37,43}, {8,13}, {8,28}, {23,45}, {22,43}, {13,38}, {28,38}, {9,45}, {30,37}, {8,44}, {23,29}, {22,30}, {38,44}, {9,29}, {24,32}, {18,24}, {3,39}, {18,37}, {3,8}, {8,31}, {17,23}, {7,33}, {2,24}, {31,39}, {2,37}, {8,16}, {1,23}, {1,38}, {9,32}, {9,18}, {3,22}, {7,17}, {33,38}, {2,9}, {22,31}, {16,39}, {25,32}, {16,25}, {11,32}, {11,16}, {3,41}, {33,41}, {1,11}, {18,41}, {18,26}, {3,26}, {10,31}, {10,17}, {17,27}, {2,27}, {32,42}, {16,42}, {26,33}, {1,42}, {12,18}, {3,12}, {31,40}, {1,25}, {2,10}, {27,31}, {12,33}, {4,25}, {25,34}, {4,12}, {12,34}, {20,25}, {12,20}, {19,41}, {5,41}, {19,27}, {5,27}, {34,40}, {20,40}, {11,19}, {5,11}, {11,36}, {36,41}, {26,35}, {21,26}, {10,35}, {35,42}, {27,36}, {4,40}, {6,26}, {4,13}, {29,34}, {14,34}, {13,36}, {19,29}, {36,45}, {14,19}, {34,44}, {30,36}, {19,44}, {5,43}, {5,28}, {6,29}, {35,43}, {6,14}, {6,44}, {20,43}, {5,15}, {13,21}, {13,24}, {29,39}, {39,45}, {7,14}, {14,37}, {24,44}, {15,39}, {7,43}, {15,23}, {14,22}, {9,15}, {24,28}, {7,30}, {23,33}, {32,37}, {16,22}, {17,38} } Symmetric graph 8 of order 45 Valency 6 Diameter 7 Girth 4 Automorphism group of order 14105549537280 Number of arcs = 270 Number of 2-arcs = 1350 2-arc-transitive false Edge-set { {1,4}, {34,37}, {1,45}, {23,27}, {32,36}, {33,34}, {40,45}, {10,13}, {19,24}, {20,22}, {30,31}, {21,23}, {28,32}, {29,33}, {39,40}, {2,45}, {9,10}, {8,11}, {16,20}, {7,12}, {18,21}, {17,19}, {25,29}, {26,30}, {27,28}, {34,39}, {33,36}, {40,44}, {41,45}, {4,9}, {42,43}, {5,8}, {6,7}, {14,18}, {15,17}, {13,16}, {22,27}, {23,25}, {24,26}, {32,34}, {21,22}, {28,31}, {29,32}, {39,42}, {30,33}, {38,40}, {37,41}, {3,5}, {2,6}, {11,15}, {12,13}, {10,14}, {21,24}, {19,22}, {20,23}, {30,32}, {9,12}, {17,21}, {16,19}, {26,29}, {18,20}, {27,30}, {25,28}, {35,39}, {36,38}, {3,43}, {2,44}, {8,12}, {7,10}, {9,11}, {17,20}, {16,21}, {18,19}, {25,30}, {41,44}, {4,7}, {5,9}, {13,17}, {6,8}, {14,16}, {15,18}, {24,25}, {22,26}, {31,35}, {41,43}, {42,44}, {5,7}, {6,9}, {4,8}, {13,18}, {14,17}, {15,16}, {22,25}, {38,42}, {37,40}, {1,6}, {39,41}, {3,4}, {2,5}, {11,14}, {12,15}, {38,41}, {37,42}, {3,6}, {2,4}, {1,5}, {10,15}, {11,13}, {12,14}, {26,28}, {35,37}, {27,29}, {36,39}, {34,38}, {1,43}, {3,44}, {35,38}, {36,37}, {2,43}, {1,44}, {3,45}, {8,10}, {7,11}, {23,26}, {24,27}, {31,34}, {32,35}, {33,35}, {31,36}, {42,45}, {40,43}, {19,23}, {20,24}, {28,33}, {29,31} } Symmetric graph 9 of order 45 Valency 8 Diameter 3 Girth 4 Automorphism group of order 720 Number of arcs = 360 Number of 2-arcs = 2520 2-arc-transitive false Edge-set { {1,5}, {26,39}, {2,45}, {32,34}, {24,34}, {13,25}, {40,43}, {11,23}, {28,33}, {20,23}, {20,33}, {29,31}, {10,22}, {3,15}, {37,41}, {17,19}, {8,21}, {12,44}, {27,30}, {7,19}, {16,21}, {7,12}, {16,30}, {10,45}, {26,29}, {1,35}, {36,38}, {8,41}, {15,17}, {5,9}, {4,18}, {14,18}, {9,42}, {33,43}, {23,25}, {4,8}, {5,17}, {42,43}, {14,25}, {13,16}, {7,40}, {32,45}, {24,26}, {22,36}, {31,35}, {4,38}, {30,41}, {12,15}, {6,39}, {2,6}, {37,40}, {3,13}, {28,40}, {11,13}, {19,31}, {21,22}, {5,37}, {3,4}, {39,41}, {2,15}, {28,31}, {11,22}, {29,42}, {10,14}, {20,32}, {20,24}, {10,24}, {29,32}, {36,37}, {3,35}, {1,43}, {25,38}, {18,30}, {9,12}, {34,38}, {1,34}, {27,29}, {10,44}, {3,44}, {27,37}, {17,29}, {8,10}, {9,21}, {18,19}, {35,39}, {2,36}, {25,30}, {12,43}, {17,21}, {8,19}, {16,28}, {7,11}, {7,20}, {16,20}, {11,45}, {26,28}, {22,35}, {31,36}, {24,27}, {32,44}, {15,26}, {41,45}, {6,18}, {6,9}, {23,36}, {33,35}, {23,26}, {33,45}, {14,16}, {7,42}, {14,27}, {42,44}, {5,16}, {4,7}, {8,40}, {13,17}, {22,25}, {31,43}, {15,18}, {9,41}, {5,8}, {4,17}, {21,24}, {19,32}, {11,14}, {28,42}, {30,32}, {12,24}, {1,13}, {38,40}, {6,38}, {1,6}, {19,22}, {21,31}, {12,13}, {30,40}, {2,4}, {5,39}, {2,14}, {39,42}, {4,37}, {3,5}, {29,41}, {10,15}, {9,20}, {18,20}, {8,11}, {17,28}, {2,44}, {27,39}, {11,43}, {25,28}, {3,36}, {35,37}, {26,38}, {1,45}, {9,10}, {18,29}, {3,43}, {25,37}, {34,39}, {2,34}, {6,7}, {6,16}, {41,44}, {15,27}, {33,34}, {23,34}, {31,44}, {22,27}, {24,35}, {32,36}, {13,26}, {40,45}, {38,42}, {1,14}, {30,33}, {12,23}, {19,23}, {21,33} } Symmetric graph 10 of order 45 Valency 8 Diameter 3 Girth 3 Automorphism group of order 720 Number of arcs = 360 Number of 2-arcs = 2520 2-arc-transitive false Edge-set { {1,5}, {22,39}, {18,44}, {18,43}, {4,30}, {1,6}, {14,32}, {14,33}, {25,38}, {16,19}, {22,37}, {17,44}, {8,12}, {8,34}, {7,12}, {8,35}, {35,45}, {2,6}, {3,32}, {13,42}, {5,30}, {15,32}, {19,41}, {23,38}, {19,28}, {20,41}, {23,37}, {19,30}, {26,38}, {26,31}, {17,45}, {8,24}, {34,43}, {11,15}, {25,39}, {18,19}, {8,10}, {9,34}, {11,42}, {6,28}, {27,32}, {21,42}, {11,41}, {5,28}, {25,32}, {19,42}, {36,45}, {9,36}, {1,36}, {2,4}, {15,31}, {29,38}, {25,33}, {10,40}, {9,22}, {35,43}, {1,32}, {14,42}, {24,38}, {21,28}, {15,40}, {12,22}, {27,37}, {17,21}, {3,34}, {12,40}, {14,40}, {11,22}, {27,39}, {18,21}, {2,34}, {12,42}, {4,29}, {27,31}, {21,29}, {22,29}, {27,44}, {16,45}, {9,10}, {26,45}, {6,20}, {7,35}, {2,35}, {10,24}, {30,39}, {26,33}, {8,22}, {34,44}, {12,15}, {6,29}, {21,40}, {10,13}, {18,41}, {23,30}, {3,5}, {2,31}, {24,28}, {25,43}, {13,41}, {10,23}, {12,13}, {18,40}, {22,30}, {3,4}, {1,31}, {23,28}, {25,45}, {15,41}, {12,23}, {16,20}, {3,36}, {20,40}, {18,26}, {20,30}, {6,34}, {13,31}, {24,39}, {4,36}, {33,37}, {17,41}, {26,37}, {16,42}, {24,29}, {4,19}, {7,36}, {1,35}, {30,38}, {10,41}, {9,23}, {17,20}, {7,24}, {1,14}, {11,14}, {17,25}, {16,27}, {5,35}, {2,33}, {7,11}, {17,42}, {7,23}, {1,13}, {10,14}, {18,25}, {16,43}, {36,44}, {17,27}, {4,35}, {9,11}, {3,33}, {27,43}, {13,33}, {28,37}, {7,44}, {2,14}, {3,15}, {16,26}, {20,29}, {32,38}, {26,44}, {6,19}, {11,24}, {28,39}, {29,37}, {8,44}, {2,15}, {3,13}, {5,34}, {5,21}, {32,37}, {8,45}, {9,43}, {6,36}, {16,40}, {4,21}, {5,20}, {9,45}, {7,43}, {31,39}, {31,38}, {33,39} } Symmetric graph 11 of order 45 Valency 8 Diameter 3 Girth 4 Automorphism group of order 720 Number of arcs = 360 Number of 2-arcs = 2520 2-arc-transitive false Edge-set { {1,4}, {4,43}, {9,10}, {4,38}, {5,10}, {11,16}, {15,18}, {4,25}, {10,45}, {5,16}, {12,18}, {18,30}, {17,24}, {23,29}, {19,23}, {10,32}, {16,37}, {4,18}, {5,30}, {12,24}, {17,29}, {16,23}, {8,29}, {23,35}, {28,42}, {22,28}, {9,40}, {30,34}, {36,40}, {27,30}, {13,16}, {18,39}, {24,44}, {4,29}, {10,23}, {5,8}, {12,35}, {17,42}, {16,28}, {9,28}, {22,34}, {30,40}, {24,30}, {13,34}, {21,40}, {7,32}, {3,36}, {7,41}, {29,36}, {11,31}, {1,15}, {8,20}, {35,41}, {19,31}, {1,42}, {2,8}, {31,35}, {20,24}, {26,29}, {23,43}, {39,42}, {6,28}, {4,9}, {10,34}, {16,40}, {12,13}, {17,21}, {28,32}, {3,22}, {7,30}, {24,36}, {7,11}, {15,36}, {20,41}, {29,41}, {8,31}, {1,35}, {8,42}, {28,35}, {1,26}, {14,39}, {19,44}, {12,33}, {2,14}, {9,19}, {34,42}, {17,38}, {13,25}, {21,33}, {2,40}, {27,38}, {32,43}, {3,9}, {7,13}, {15,21}, {38,40}, {25,28}, {33,34}, {26,32}, {3,43}, {6,7}, {11,36}, {4,11}, {10,15}, {16,20}, {18,41}, {30,31}, {1,24}, {22,26}, {36,39}, {41,44}, {8,12}, {14,35}, {19,42}, {14,17}, {2,25}, {9,33}, {2,34}, {13,38}, {21,43}, {3,13}, {7,21}, {6,27}, {22,45}, {15,27}, {20,32}, {3,41}, {26,37}, {31,45}, {1,7}, {5,39}, {11,44}, {8,15}, {14,20}, {19,26}, {25,31}, {1,45}, {32,36}, {37,41}, {33,39}, {38,44}, {6,12}, {11,14}, {18,19}, {10,17}, {24,25}, {29,33}, {2,23}, {35,38}, {42,43}, {2,6}, {21,22}, {3,27}, {15,37}, {20,45}, {5,26}, {14,26}, {25,39}, {33,44}, {12,43}, {9,14}, {6,17}, {13,19}, {21,25}, {27,33}, {32,38}, {37,43}, {2,44}, {6,45}, {18,22}, {23,27}, {34,37}, {40,45}, {3,5}, {6,37}, {11,22}, {20,27}, {31,37}, {39,45}, {5,44} } Symmetric graph 12 of order 45 Valency 8 Diameter 3 Girth 3 Automorphism group of order 720 Number of arcs = 360 Number of 2-arcs = 2520 2-arc-transitive false Edge-set { {1,4}, {2,44}, {16,25}, {1,15}, {26,33}, {5,24}, {23,34}, {2,27}, {20,25}, {6,21}, {2,36}, {16,43}, {18,41}, {17,42}, {42,45}, {26,35}, {5,36}, {30,34}, {34,45}, {17,28}, {1,41}, {26,44}, {13,24}, {23,31}, {22,39}, {22,33}, {24,38}, {14,33}, {32,38}, {6,40}, {36,43}, {41,43}, {18,44}, {8,42}, {9,45}, {14,42}, {32,45}, {9,22}, {7,24}, {2,31}, {25,39}, {6,15}, {33,36}, {21,41}, {17,20}, {3,42}, {18,30}, {18,21}, {2,40}, {16,29}, {4,41}, {21,26}, {2,19}, {19,29}, {17,37}, {13,41}, {31,44}, {13,31}, {31,39}, {15,23}, {10,33}, {12,38}, {12,14}, {11,32}, {19,38}, {14,19}, {1,32}, {12,18}, {11,40}, {11,16}, {10,41}, {1,20}, {3,26}, {5,30}, {6,34}, {27,45}, {31,34}, {28,39}, {22,36}, {24,30}, {3,33}, {27,38}, {8,23}, {22,28}, {26,37}, {16,39}, {28,36}, {1,35}, {26,29}, {7,35}, {8,29}, {25,31}, {21,39}, {15,20}, {3,21}, {20,30}, {3,6}, {17,27}, {20,42}, {2,13}, {29,37}, {4,14}, {29,35}, {4,29}, {1,25}, {23,37}, {14,22}, {15,37}, {13,39}, {25,30}, {27,36}, {8,43}, {9,18}, {17,45}, {32,35}, {3,45}, {9,30}, {6,7}, {40,44}, {8,16}, {9,41}, {4,35}, {10,17}, {12,42}, {7,40}, {6,28}, {6,23}, {7,44}, {25,43}, {8,36}, {10,43}, {7,10}, {8,12}, {5,20}, {3,34}, {27,28}, {4,22}, {24,35}, {30,38}, {7,28}, {5,8}, {16,19}, {2,5}, {25,34}, {5,42}, {18,26}, {19,40}, {9,34}, {35,44}, {10,13}, {12,31}, {12,23}, {11,22}, {24,32}, {1,43}, {3,14}, {27,32}, {9,11}, {11,45}, {15,32}, {33,37}, {10,24}, {11,39}, {14,38}, {10,37}, {7,17}, {11,15}, {5,13}, {12,44}, {4,9}, {16,40}, {23,29}, {33,43}, {18,38}, {15,40}, {13,21}, {20,37}, {19,27}, {4,19}, {21,28} } Symmetric graph 13 of order 45 Valency 8 Diameter 3 Girth 3 Automorphism group of order 720 Number of arcs = 360 Number of 2-arcs = 2520 2-arc-transitive false Edge-set { {1,5}, {2,43}, {18,25}, {1,13}, {26,31}, {5,23}, {22,34}, {2,25}, {21,25}, {6,20}, {3,36}, {17,43}, {18,42}, {40,45}, {26,34}, {5,34}, {28,34}, {36,45}, {17,30}, {3,41}, {27,44}, {13,22}, {24,31}, {23,33}, {22,38}, {14,32}, {32,37}, {6,42}, {42,43}, {18,45}, {9,42}, {7,45}, {14,41}, {32,44}, {8,22}, {9,24}, {3,31}, {27,39}, {4,15}, {33,35}, {21,40}, {16,20}, {17,21}, {2,42}, {18,29}, {4,40}, {19,26}, {1,19}, {19,28}, {33,45}, {17,38}, {13,33}, {31,38}, {14,23}, {22,32}, {12,33}, {11,38}, {11,14}, {10,32}, {19,39}, {15,19}, {1,33}, {10,18}, {12,40}, {12,16}, {11,41}, {3,20}, {3,27}, {4,30}, {6,35}, {32,34}, {28,37}, {24,36}, {23,30}, {24,28}, {26,38}, {7,23}, {16,37}, {29,36}, {2,35}, {25,29}, {9,35}, {7,29}, {14,21}, {2,32}, {22,29}, {4,24}, {2,21}, {20,29}, {3,4}, {17,26}, {19,42}, {18,19}, {1,40}, {21,37}, {2,14}, {29,38}, {30,35}, {6,29}, {27,35}, {23,39}, {14,37}, {24,37}, {15,39}, {27,30}, {8,44}, {9,16}, {1,45}, {9,28}, {5,7}, {16,41}, {41,44}, {8,17}, {7,41}, {4,36}, {11,17}, {10,42}, {26,43}, {8,34}, {11,43}, {7,11}, {8,10}, {1,26}, {7,18}, {8,40}, {16,44}, {1,34}, {26,28}, {7,36}, {8,30}, {3,44}, {16,27}, {6,22}, {23,35}, {25,37}, {5,28}, {4,8}, {9,43}, {35,43}, {5,19}, {16,28}, {5,41}, {10,15}, {12,24}, {11,23}, {25,32}, {9,12}, {15,31}, {33,39}, {10,22}, {11,31}, {10,39}, {15,24}, {13,38}, {6,13}, {31,36}, {12,45}, {12,13}, {2,6}, {25,36}, {12,37}, {25,45}, {6,9}, {10,44}, {3,15}, {27,33}, {17,40}, {13,40}, {31,43}, {18,39}, {13,20}, {15,42}, {20,27}, {21,30}, {20,38}, {30,39}, {20,41}, {4,21}, {34,44}, {5,14} } Symmetric graph 14 of order 45 Valency 8 Diameter 2 Girth 4 Automorphism group of order 1440 Number of arcs = 360 Number of 2-arcs = 2520 2-arc-transitive false Edge-set { {1,9}, {2,12}, {11,25}, {1,37}, {14,26}, {5,38}, {15,34}, {2,28}, {5,25}, {6,26}, {19,36}, {29,43}, {4,18}, {27,42}, {20,45}, {7,26}, {5,43}, {18,34}, {6,45}, {17,36}, {35,41}, {29,44}, {7,13}, {8,31}, {23,44}, {16,22}, {4,33}, {35,38}, {14,36}, {30,32}, {6,11}, {10,36}, {13,43}, {18,31}, {23,42}, {22,45}, {14,45}, {17,32}, {22,41}, {24,44}, {31,40}, {39,43}, {7,15}, {8,33}, {10,21}, {10,20}, {3,12}, {15,17}, {33,42}, {18,24}, {23,40}, {21,44}, {2,16}, {29,40}, {4,43}, {26,41}, {19,44}, {8,19}, {38,45}, {39,41}, {13,44}, {13,25}, {21,31}, {20,23}, {3,22}, {17,33}, {38,42}, {14,18}, {32,40}, {19,32}, {19,22}, {1,24}, {39,40}, {15,16}, {33,41}, {20,32}, {3,37}, {13,30}, {6,31}, {11,27}, {34,39}, {13,28}, {36,39}, {14,27}, {22,27}, {20,24}, {21,33}, {2,38}, {16,23}, {37,42}, {28,33}, {23,26}, {7,32}, {8,37}, {16,31}, {15,35}, {29,33}, {10,35}, {12,29}, {14,29}, {4,32}, {30,31}, {6,39}, {15,25}, {21,34}, {20,34}, {3,28}, {30,42}, {3,18}, {27,40}, {21,22}, {2,24}, {4,38}, {19,35}, {1,29}, {18,35}, {25,41}, {6,37}, {24,27}, {2,39}, {1,30}, {5,27}, {8,25}, {9,21}, {3,17}, {9,25}, {7,21}, {30,41}, {6,44}, {4,26}, {35,40}, {16,36}, {17,24}, {2,7}, {6,17}, {36,42}, {11,19}, {1,10}, {10,28}, {5,12}, {3,23}, {20,43}, {2,8}, {7,37}, {8,14}, {1,16}, {8,20}, {3,9}, {30,45}, {34,42}, {28,45}, {7,27}, {9,38}, {35,37}, {28,40}, {4,16}, {22,43}, {5,31}, {5,17}, {5,10}, {12,34}, {11,28}, {11,34}, {9,39}, {15,45}, {37,43}, {24,41}, {1,11}, {10,26}, {38,44}, {15,29}, {13,36}, {12,26}, {12,19}, {23,25}, {12,30}, {9,32}, {9,14}, {4,11}, {13,18} } Symmetric graph 15 of order 45 Valency 8 Diameter 4 Girth 4 Automorphism group of order 2160 Number of arcs = 360 Number of 2-arcs = 2520 2-arc-transitive false Edge-set { {1,4}, {26,37}, {11,31}, {32,36}, {5,43}, {10,18}, {1,13}, {12,24}, {2,27}, {15,38}, {9,12}, {16,42}, {15,16}, {26,28}, {31,38}, {17,21}, {14,20}, {25,33}, {32,45}, {30,34}, {4,39}, {4,17}, {14,34}, {1,41}, {18,30}, {30,41}, {18,39}, {24,43}, {10,34}, {7,40}, {17,41}, {8,29}, {37,40}, {3,44}, {12,14}, {2,8}, {22,44}, {22,26}, {35,37}, {6,11}, {11,17}, {22,29}, {3,26}, {29,31}, {42,44}, {16,22}, {35,42}, {6,16}, {15,21}, {9,20}, {15,26}, {2,6}, {28,35}, {3,40}, {17,29}, {23,36}, {2,36}, {5,28}, {13,27}, {7,33}, {14,37}, {5,25}, {13,19}, {7,19}, {19,32}, {19,43}, {10,13}, {18,40}, {13,17}, {19,23}, {27,32}, {33,43}, {10,43}, {1,23}, {7,30}, {19,41}, {18,19}, {25,30}, {39,41}, {4,8}, {34,40}, {30,32}, {39,43}, {25,39}, {10,32}, {23,45}, {24,25}, {28,33}, {40,43}, {17,23}, {20,24}, {21,27}, {38,45}, {3,35}, {29,36}, {5,37}, {12,44}, {9,28}, {38,42}, {6,9}, {2,42}, {9,15}, {9,42}, {16,28}, {28,40}, {17,38}, {21,42}, {12,33}, {2,45}, {11,15}, {3,9}, {20,26}, {21,31}, {6,44}, {22,35}, {29,42}, {31,44}, {6,29}, {11,36}, {2,22}, {15,35}, {31,35}, {12,16}, {2,15}, {8,21}, {20,44}, {11,45}, {3,24}, {20,40}, {41,45}, {23,27}, {36,38}, {5,12}, {7,14}, {4,45}, {24,34}, {1,34}, {4,30}, {1,25}, {34,39}, {18,24}, {24,28}, {1,7}, {3,14}, {14,25}, {8,32}, {13,39}, {4,27}, {33,34}, {7,10}, {19,25}, {1,43}, {23,30}, {10,23}, {14,18}, {32,39}, {5,7}, {36,41}, {8,13}, {20,33}, {21,45}, {8,11}, {21,22}, {26,31}, {37,44}, {11,22}, {6,26}, {16,20}, {27,29}, {33,37}, {6,38}, {9,31}, {16,37}, {12,35}, {8,41}, {5,18}, {13,36}, {3,5}, {4,10}, {27,38} } Symmetric graph 16 of order 45 Valency 10 Diameter 4 Girth 4 Automorphism group of order 92876046336000000000 Number of arcs = 450 Number of 2-arcs = 4050 2-arc-transitive false Edge-set { {1,4}, {5,36}, {25,42}, {2,35}, {21,27}, {27,39}, {12,16}, {3,6}, {19,40}, {23,37}, {10,13}, {37,40}, {10,32}, {13,28}, {4,34}, {26,41}, {24,26}, {14,18}, {9,41}, {33,45}, {14,45}, {18,33}, {4,8}, {22,34}, {1,36}, {20,25}, {25,38}, {11,17}, {8,38}, {11,44}, {29,44}, {17,37}, {7,28}, {28,36}, {17,29}, {1,7}, {21,36}, {20,43}, {2,5}, {21,42}, {22,39}, {12,15}, {39,42}, {12,31}, {15,30}, {31,38}, {5,29}, {23,29}, {30,41}, {2,33}, {19,33}, {21,22}, {30,31}, {2,23}, {5,19}, {13,21}, {10,22}, {6,35}, {27,40}, {23,27}, {13,16}, {7,40}, {32,43}, {13,43}, {16,32}, {6,9}, {24,35}, {16,42}, {9,31}, {31,35}, {23,45}, {25,32}, {17,24}, {6,17}, {7,14}, {7,23}, {9,24}, {40,45}, {14,27}, {13,34}, {4,43}, {3,34}, {19,26}, {26,37}, {10,18}, {9,37}, {10,45}, {28,45}, {18,39}, {8,30}, {30,34}, {18,28}, {3,8}, {20,34}, {19,44}, {27,28}, {3,16}, {16,20}, {9,19}, {9,11}, {8,12}, {2,44}, {2,26}, {36,39}, {39,45}, {8,20}, {37,44}, {11,26}, {10,36}, {1,45}, {25,30}, {20,41}, {24,38}, {11,14}, {38,41}, {11,33}, {14,29}, {33,37}, {4,28}, {22,28}, {29,40}, {1,32}, {21,32}, {20,24}, {29,33}, {1,22}, {4,21}, {15,20}, {12,24}, {3,41}, {3,15}, {14,37}, {5,37}, {6,38}, {6,12}, {11,40}, {2,40}, {28,32}, {15,38}, {12,41}, {5,11}, {2,14}, {28,42}, {32,39}, {22,25}, {15,17}, {8,42}, {31,44}, {15,44}, {17,31}, {5,7}, {23,36}, {17,41}, {7,33}, {33,36}, {22,43}, {26,31}, {18,23}, {5,18}, {8,13}, {8,22}, {42,43}, {13,25}, {15,35}, {6,44}, {4,25}, {35,41}, {41,44}, {27,33}, {34,42}, {6,26}, {15,26}, {18,40}, {5,27}, {36,40}, {16,22}, {8,32}, {7,39}, {12,43}, {30,43}, {16,38}, {9,29}, {29,35}, {16,30}, {2,9}, {19,35}, {21,45}, {2,17}, {17,19}, {7,21}, {7,10}, {1,27}, {34,38}, {38,43}, {10,27}, {12,34}, {3,43}, {26,29}, {12,25}, {3,25}, {11,35}, {1,18}, {35,37}, {18,21}, {6,30}, {24,30}, {3,31}, {20,31}, {19,23}, {3,24}, {6,20}, {14,19}, {11,23}, {13,39}, {4,39}, {10,42}, {1,42}, {4,10}, {1,13}, {32,34}, {24,44}, {4,16}, {9,15}, {14,36}, {5,45} } Symmetric graph 17 of order 45 Valency 12 Diameter 2 Girth 3 Automorphism group of order 2160 Number of arcs = 540 Number of 2-arcs = 5940 2-arc-transitive false Edge-set { {1,8}, {30,41}, {3,9}, {6,37}, {24,45}, {29,42}, {2,7}, {21,31}, {34,38}, {9,26}, {28,40}, {4,38}, {23,43}, {14,44}, {20,31}, {17,32}, {5,39}, {10,29}, {7,14}, {22,44}, {19,32}, {35,39}, {7,25}, {27,42}, {15,44}, {20,33}, {23,45}, {11,21}, {36,37}, {36,38}, {16,23}, {1,28}, {8,27}, {13,45}, {21,32}, {16,33}, {11,28}, {8,13}, {4,12}, {15,43}, {2,8}, {25,42}, {19,33}, {9,25}, {30,40}, {14,34}, {18,31}, {18,32}, {4,39}, {22,25}, {12,30}, {39,41}, {3,22}, {9,15}, {26,40}, {14,45}, {22,43}, {12,19}, {34,39}, {18,22}, {3,30}, {19,35}, {17,35}, {25,41}, {1,9}, {4,11}, {13,43}, {11,29}, {7,13}, {5,37}, {24,44}, {1,17}, {5,27}, {10,20}, {10,21}, {35,37}, {11,27}, {13,29}, {17,24}, {6,33}, {37,45}, {2,29}, {5,10}, {27,40}, {7,27}, {29,41}, {13,35}, {17,33}, {24,27}, {37,42}, {2,24}, {13,16}, {6,32}, {6,11}, {3,7}, {19,34}, {18,35}, {26,41}, {18,23}, {3,28}, {8,26}, {28,42}, {23,41}, {3,11}, {12,20}, {15,36}, {14,36}, {16,31}, {6,38}, {12,34}, {15,18}, {3,38}, {23,26}, {21,43}, {9,31}, {38,40}, {1,23}, {20,36}, {16,36}, {5,12}, {12,28}, {8,15}, {3,16}, {6,26}, {11,19}, {12,26}, {15,28}, {4,31}, {38,43}, {21,45}, {21,34}, {18,34}, {13,17}, {5,32}, {16,24}, {6,10}, {24,25}, {10,30}, {39,42}, {2,22}, {9,14}, {6,25}, {30,45}, {34,42}, {2,18}, {15,35}, {4,25}, {1,18}, {4,27}, {5,17}, {10,25}, {32,42}, {2,39}, {14,30}, {31,41}, {29,44}, {7,20}, {39,44}, {4,33}, {20,35}, {17,36}, {17,22}, {2,30}, {22,42}, {2,12}, {13,34}, {10,35}, {14,17}, {19,44}, {7,32}, {31,40}, {5,31}, {3,23}, {11,26}, {20,45}, {21,36}, {22,26}, {16,34}, {13,28}, {37,43}, {1,29}, {9,37}, {24,40}, {4,17}, {5,43}, {1,10}, {2,16}, {24,41}, {3,10}, {20,23}, {11,36}, {4,45}, {33,40}, {1,37}, {6,44}, {8,38}, {23,42}, {8,33}, {19,43}, {15,16}, {23,27}, {37,40}, {1,24}, {29,43}, {35,40}, {3,17}, {5,26}, {6,16}, {28,45}, {8,21}, {5,44}, {20,44}, {10,34}, {14,18}, {10,27}, {14,29}, {3,39}, {7,31}, {38,41}, {29,31}, {7,38}, {28,44}, {19,23}, {11,35}, {36,41}, {22,40}, {1,12}, {36,42}, {15,25}, {30,33}, {4,18}, {9,19}, {30,32}, {9,39}, {30,43}, {32,41}, {12,25}, {15,30}, {38,44}, {5,16}, {2,11}, {21,22}, {8,20}, {33,42}, {12,36}, {1,38}, {2,37}, {39,45}, {28,32}, {8,39}, {13,25}, {6,18}, {35,41}, {4,43}, {19,24}, {21,24}, {29,33}, {7,37}, {6,45}, {8,32}, {20,22}, {34,40}, {14,27}, {9,33}, {13,26}, {7,19}, {14,26}, {28,31}, {9,21}, {15,27} } Symmetric graph 18 of order 45 Valency 12 Diameter 2 Girth 3 Automorphism group of order 4320 Number of arcs = 540 Number of 2-arcs = 5940 2-arc-transitive false Edge-set { {1,7}, {11,26}, {4,37}, {7,19}, {9,32}, {6,32}, {20,43}, {22,26}, {37,40}, {27,40}, {34,39}, {31,40}, {19,34}, {18,24}, {23,41}, {9,26}, {6,38}, {13,43}, {9,38}, {8,13}, {5,44}, {28,45}, {38,42}, {13,36}, {22,44}, {28,40}, {3,28}, {10,25}, {2,39}, {15,27}, {7,27}, {9,39}, {4,31}, {19,44}, {13,18}, {1,23}, {4,27}, {39,44}, {13,25}, {1,38}, {17,33}, {21,22}, {16,36}, {16,24}, {14,44}, {1,29}, {1,17}, {36,38}, {13,16}, {12,36}, {5,16}, {8,21}, {7,31}, {5,10}, {6,45}, {9,15}, {3,8}, {8,37}, {5,27}, {39,45}, {32,42}, {20,36}, {17,22}, {22,40}, {13,28}, {1,10}, {2,11}, {8,20}, {5,17}, {22,45}, {4,11}, {4,44}, {30,41}, {11,35}, {26,42}, {29,43}, {12,29}, {3,29}, {12,25}, {14,17}, {2,22}, {4,17}, {11,30}, {4,43}, {29,44}, {13,29}, {1,12}, {29,33}, {12,21}, {23,25}, {36,37}, {21,33}, {21,31}, {16,31}, {19,24}, {3,39}, {5,38}, {6,25}, {38,43}, {9,33}, {24,45}, {14,34}, {24,43}, {29,41}, {1,30}, {13,26}, {1,16}, {11,21}, {10,19}, {24,25}, {38,41}, {30,33}, {24,26}, {19,32}, {20,32}, {17,32}, {20,22}, {15,18}, {19,45}, {30,32}, {7,37}, {9,14}, {18,35}, {17,23}, {20,35}, {12,35}, {7,33}, {14,30}, {6,26}, {11,20}, {18,32}, {20,23}, {17,35}, {13,35}, {4,33}, {35,41}, {33,42}, {2,8}, {6,43}, {35,42}, {23,42}, {36,42}, {29,42}, {3,22}, {25,40}, {5,12}, {5,45}, {21,44}, {8,31}, {4,18}, {23,44}, {27,41}, {35,39}, {3,16}, {2,28}, {3,18}, {15,17}, {11,34}, {7,13}, {1,9}, {11,29}, {4,12}, {19,23}, {7,25}, {4,39}, {15,44}, {34,41}, {3,7}, {9,25}, {34,40}, {24,40}, {30,40}, {1,24}, {26,41}, {15,28}, {3,10}, {16,22}, {18,34}, {37,43}, {14,27}, {10,30}, {2,30}, {11,27}, {20,45}, {35,37}, {2,18}, {9,19}, {32,41}, {10,34}, {2,24}, {30,45}, {13,45}, {15,30}, {37,41}, {14,35}, {18,31}, {37,45}, {2,37}, {14,29}, {5,26}, {8,38}, {20,33}, {16,33}, {21,24}, {22,42}, {25,42}, {28,32}, {10,20}, {2,17}, {22,27}, {8,15}, {10,36}, {6,16}, {12,28}, {3,11}, {1,37}, {19,35}, {8,26}, {5,32}, {12,26}, {5,37}, {8,27}, {7,39}, {38,44}, {3,38}, {34,38}, {4,25}, {15,36}, {5,31}, {28,44}, {10,28}, {6,18}, {23,43}, {21,34}, {8,32}, {24,41}, {30,43}, {6,10}, {39,40}, {15,34}, {28,31}, {16,34}, {6,39}, {15,43}, {14,45}, {28,42}, {9,21}, {3,23}, {14,26}, {7,14}, {36,40}, {31,41}, {6,11}, {15,25}, {21,43}, {29,31}, {12,19}, {33,40}, {7,20}, {6,33}, {21,36}, {17,36}, {23,27}, {18,23}, {19,31}, {14,16}, {39,42}, {2,12}, {2,9}, {10,27} } Symmetric graph 19 of order 45 Valency 12 Diameter 2 Girth 3 Automorphism group of order 51840 Number of arcs = 540 Number of 2-arcs = 5940 2-arc-transitive false Edge-set { {1,2}, {3,5}, {2,4}, {6,10}, {5,9}, {5,8}, {4,7}, {12,18}, {11,17}, {10,16}, {9,14}, {10,15}, {3,9}, {8,14}, {7,13}, {11,19}, {18,26}, {2,25}, {15,24}, {18,24}, {17,23}, {16,20}, {18,22}, {17,21}, {6,16}, {5,14}, {15,20}, {3,8}, {1,13}, {11,27}, {26,37}, {5,34}, {4,36}, {22,33}, {21,31}, {11,33}, {26,31}, {25,35}, {24,34}, {24,28}, {23,27}, {11,29}, {26,32}, {25,30}, {24,29}, {12,24}, {11,23}, {10,20}, {8,9}, {22,28}, {21,27}, {6,15}, {2,38}, {15,38}, {27,39}, {37,43}, {10,36}, {9,35}, {8,31}, {7,42}, {13,29}, {16,32}, {17,30}, {19,29}, {2,13}, {15,16}, {17,27}, {19,37}, {34,42}, {33,36}, {31,35}, {33,40}, {31,39}, {35,38}, {34,38}, {37,41}, {34,41}, {22,36}, {4,33}, {6,31}, {19,33}, {18,31}, {2,35}, {15,34}, {18,28}, {3,14}, {29,40}, {32,39}, {30,38}, {29,38}, {12,22}, {11,21}, {5,44}, {4,44}, {22,44}, {21,44}, {23,38}, {25,38}, {26,39}, {12,43}, {17,42}, {16,42}, {14,33}, {15,17}, {3,19}, {14,37}, {13,28}, {4,9}, {1,6}, {21,24}, {23,41}, {25,41}, {22,24}, {1,4}, {21,23}, {24,38}, {1,39}, {10,43}, {36,37}, {28,35}, {13,31}, {19,25}, {42,44}, {33,44}, {36,44}, {35,44}, {39,45}, {43,45}, {36,45}, {35,45}, {29,31}, {32,42}, {8,13}, {7,16}, {12,17}, {19,26}, {5,42}, {21,35}, {11,40}, {6,20}, {41,44}, {6,44}, {18,32}, {2,30}, {15,29}, {9,40}, {8,43}, {7,40}, {29,43}, {32,40}, {30,43}, {34,44}, {25,37}, {24,37}, {23,28}, {13,20}, {8,16}, {22,25}, {5,10}, {20,39}, {7,14}, {3,12}, {2,11}, {30,33}, {34,45}, {29,33}, {31,32}, {2,7}, {30,35}, {29,34}, {31,44}, {3,23}, {42,43}, {40,42}, {33,39}, {9,17}, {1,19}, {1,34}, {28,40}, {13,43}, {16,40}, {31,43}, {23,32}, {12,30}, {30,42}, {4,17}, {6,19}, {21,37}, {28,41}, {9,15}, {1,3}, {14,24}, {13,23}, {1,27}, {10,37}, {9,28}, {12,28}, {40,45}, {26,41}, {5,41}, {4,22}, {6,21}, {14,20}, {15,26}, {4,26}, {6,12}, {7,21}, {20,41}, {36,43}, {35,40}, {34,39}, {32,36}, {10,18}, {25,27}, {5,18}, {2,5}, {4,15}, {13,41}, {16,22}, {4,13}, {19,41}, {41,42}, {6,35}, {17,43}, {19,40}, {7,37}, {20,28}, {16,25}, {2,10}, {3,36}, {9,26}, {1,12}, {7,24}, {20,23}, {17,26}, {12,19}, {8,25}, {10,11}, {30,39}, {14,21}, {3,6}, {20,33}, {3,38}, {18,39}, {14,39}, {7,32}, {20,30}, {27,45}, {37,45}, {10,45}, {9,45}, {8,29}, {8,27}, {22,27}, {11,18}, {14,30}, {28,45}, {12,42}, {23,36}, {36,38}, {8,22}, {1,45}, {1,7}, {25,26}, {16,27}, {2,18}, {27,34}, {5,11}, {32,38}, {3,32} } Symmetric graph 20 of order 45 Valency 12 Diameter 3 Girth 4 Automorphism group of order 77760 Number of arcs = 540 Number of 2-arcs = 5940 2-arc-transitive false Edge-set { {1,7}, {8,13}, {11,17}, {15,20}, {18,23}, {32,37}, {25,35}, {21,40}, {14,22}, {38,43}, {27,31}, {22,28}, {2,42}, {17,26}, {4,30}, {2,41}, {15,19}, {19,44}, {24,33}, {29,36}, {16,23}, {5,40}, {5,44}, {33,37}, {12,20}, {18,37}, {6,25}, {6,10}, {3,7}, {12,21}, {21,42}, {13,22}, {34,42}, {24,45}, {32,41}, {4,25}, {29,39}, {39,43}, {26,31}, {2,12}, {12,34}, {8,44}, {24,28}, {31,40}, {14,34}, {28,38}, {2,27}, {4,45}, {11,33}, {36,45}, {9,13}, {10,17}, {31,41}, {15,34}, {1,41}, {20,44}, {23,33}, {1,27}, {20,28}, {35,45}, {9,32}, {3,22}, {4,43}, {3,39}, {30,36}, {6,40}, {7,31}, {28,34}, {8,18}, {5,45}, {2,23}, {19,40}, {19,27}, {5,29}, {1,37}, {7,16}, {5,12}, {10,35}, {9,43}, {24,32}, {35,41}, {9,29}, {14,20}, {25,36}, {3,23}, {21,27}, {3,8}, {11,21}, {34,40}, {8,14}, {24,43}, {8,16}, {5,11}, {14,37}, {26,35}, {9,30}, {16,42}, {9,44}, {10,33}, {10,36}, {7,43}, {3,10}, {29,38}, {2,11}, {19,45}, {13,23}, {17,40}, {5,27}, {28,37}, {15,38}, {18,27}, {12,35}, {12,31}, {13,19}, {5,13}, {4,12}, {39,44}, {8,28}, {13,39}, {34,44}, {26,33}, {14,36}, {22,45}, {32,42}, {3,26}, {21,30}, {4,14}, {16,39}, {14,24}, {17,25}, {4,29}, {10,31}, {16,41}, {5,15}, {9,15}, {10,18}, {15,35}, {19,28}, {18,24}, {7,32}, {15,39}, {18,26}, {12,32}, {35,44}, {2,24}, {6,30}, {6,14}, {16,38}, {1,39}, {20,26}, {36,41}, {25,33}, {13,36}, {7,17}, {9,33}, {35,42}, {20,43}, {23,31}, {2,37}, {19,25}, {12,16}, {5,28}, {21,29}, {1,22}, {30,34}, {20,42}, {23,44}, {34,43}, {20,30}, {27,34}, {6,41}, {24,29}, {9,18}, {10,19}, {30,39}, {17,37}, {4,10}, {36,40}, {21,26}, {22,44}, {14,21}, {16,22}, {33,38}, {27,36}, {22,30}, {5,42}, {13,37}, {38,45}, {27,32}, {17,42}, {18,38}, {6,27}, {22,31}, {26,34}, {8,30}, {7,45}, {6,11}, {11,19}, {1,26}, {3,11}, {18,40}, {3,25}, {17,24}, {4,41}, {20,25}, {23,29}, {7,14}, {23,43}, {7,28}, {4,13}, {31,39}, {37,44}, {1,40}, {8,31}, {14,38}, {16,27}, {21,45}, {32,39}, {33,42}, {3,38}, {2,25}, {36,43}, {19,29}, {18,41}, {6,15}, {8,33}, {19,41}, {15,24}, {16,25}, {6,44}, {1,12}, {29,35}, {1,9}, {11,16}, {33,40}, {6,28}, {13,35}, {9,17}, {11,32}, {2,38}, {37,45}, {25,32}, {21,43}, {10,20}, {23,30}, {3,40}, {2,8}, {15,23}, {1,24}, {5,26}, {3,42}, {20,41}, {1,10}, {7,29}, {4,42}, {13,21}, {22,32}, {17,39}, {4,26}, {11,34}, {8,45}, {28,35}, {2,9}, {17,22}, {7,15}, {6,43}, {31,38}, {12,18}, {11,36}, {30,37} } Symmetric graph 21 of order 45 Valency 12 Diameter 3 Girth 4 Automorphism group of order 28211099074560 Number of arcs = 540 Number of 2-arcs = 5940 2-arc-transitive false Edge-set { {1,4}, {1,43}, {12,24}, {42,43}, {12,45}, {8,20}, {39,42}, {32,45}, {8,40}, {4,18}, {35,37}, {36,39}, {21,32}, {30,40}, {4,38}, {33,35}, {1,13}, {24,27}, {32,34}, {33,36}, {9,21}, {16,30}, {26,38}, {29,33}, {1,35}, {19,24}, {28,32}, {11,43}, {12,15}, {20,22}, {30,31}, {7,42}, {28,33}, {9,40}, {5,16}, {15,26}, {26,29}, {24,35}, {16,19}, {25,28}, {32,43}, {8,12}, {17,20}, {27,30}, {28,42}, {9,42}, {3,45}, {18,21}, {5,37}, {29,41}, {6,39}, {27,28}, {28,40}, {5,38}, {2,15}, {22,26}, {13,16}, {24,25}, {20,32}, {4,8}, {15,17}, {23,27}, {17,28}, {30,42}, {42,45}, {14,18}, {25,37}, {18,29}, {27,39}, {5,39}, {32,36}, {40,44}, {2,34}, {3,36}, {21,23}, {22,27}, {18,28}, {27,38}, {2,35}, {19,22}, {10,13}, {21,24}, {11,15}, {20,23}, {4,17}, {18,30}, {37,42}, {12,14}, {13,25}, {6,18}, {14,27}, {26,39}, {29,32}, {39,40}, {23,34}, {22,36}, {2,36}, {21,22}, {30,33}, {38,41}, {33,44}, {31,45}, {7,10}, {9,11}, {5,18}, {13,27}, {22,35}, {18,19}, {8,10}, {17,21}, {7,11}, {16,20}, {4,39}, {9,12}, {3,13}, {6,37}, {1,14}, {13,26}, {27,29}, {34,39}, {11,23}, {10,22}, {24,36}, {16,21}, {25,30}, {36,38}, {21,33}, {19,31}, {6,7}, {5,9}, {33,45}, {9,10}, {26,28}, {29,40}, {28,41}, {41,43}, {2,13}, {11,22}, {15,18}, {5,8}, {13,17}, {4,7}, {14,16}, {25,39}, {6,9}, {3,34}, {26,37}, {1,36}, {11,44}, {10,43}, {11,24}, {15,16}, {22,25}, {31,36}, {7,21}, {9,19}, {3,6}, {2,5}, {20,33}, {4,9}, {23,26}, {17,29}, {16,28}, {40,43}, {5,7}, {25,38}, {27,37}, {28,31}, {11,45}, {10,15}, {3,5}, {12,13}, {2,4}, {11,14}, {15,25}, {1,6}, {24,34}, {14,26}, {23,36}, {31,44}, {33,43}, {9,41}, {3,44}, {2,45}, {9,20}, {3,4}, {5,17}, {6,16}, {37,40}, {1,5}, {14,25}, {15,27}, {38,42}, {2,6}, {22,34}, {23,35}, {17,19}, {18,20}, {3,43}, {7,12}, {2,44}, {8,11}, {1,15}, {1,45}, {10,24}, {3,14}, {12,23}, {20,31}, {19,33}, {41,44}, {40,45}, {36,37}, {1,44}, {2,14}, {3,15}, {34,38}, {2,43}, {12,22}, {10,23}, {14,17}, {13,18}, {35,39}, {19,32}, {21,31}, {6,8}, {42,44}, {1,34}, {41,45}, {10,44}, {3,35}, {12,43}, {7,20}, {8,19}, {37,41}, {38,40}, {33,34}, {12,44}, {10,45}, {10,14}, {11,13}, {31,35}, {7,19}, {8,21}, {17,30}, {16,29}, {39,41}, {32,44}, {31,43}, {7,41}, {8,42}, {34,37}, {35,38}, {7,40}, {8,41}, {6,17}, {4,16}, {25,29}, {26,30}, {30,41}, {29,42}, {31,34}, {32,35}, {6,38}, {4,37}, {23,25}, {24,26}, {29,31}, {30,32}, {19,23}, {20,24} } Symmetric graph 22 of order 45 Valency 12 Diameter 3 Girth 3 Automorphism group of order 56422198149120 Number of arcs = 540 Number of 2-arcs = 5940 2-arc-transitive false Edge-set { {1,4}, {11,14}, {33,37}, {26,31}, {9,23}, {1,36}, {6,28}, {3,6}, {19,30}, {18,44}, {35,43}, {14,42}, {25,37}, {7,10}, {2,31}, {10,13}, {31,39}, {1,15}, {20,29}, {16,42}, {21,40}, {17,27}, {31,38}, {10,23}, {4,36}, {6,21}, {8,44}, {3,15}, {30,38}, {27,32}, {8,22}, {3,34}, {5,30}, {14,33}, {24,37}, {3,14}, {28,38}, {10,41}, {24,39}, {11,13}, {20,40}, {3,35}, {4,30}, {27,44}, {8,35}, {11,42}, {25,33}, {10,24}, {13,31}, {16,20}, {16,45}, {13,33}, {9,35}, {2,5}, {16,43}, {36,45}, {13,41}, {26,39}, {9,12}, {1,32}, {1,31}, {23,28}, {6,34}, {23,39}, {7,35}, {2,4}, {27,37}, {8,12}, {34,45}, {5,34}, {26,32}, {9,22}, {22,39}, {13,40}, {27,39}, {9,11}, {1,33}, {5,20}, {16,40}, {27,45}, {26,38}, {9,10}, {21,28}, {8,34}, {3,32}, {22,30}, {22,28}, {14,41}, {19,28}, {18,41}, {18,40}, {27,43}, {12,15}, {32,38}, {17,41}, {19,42}, {18,25}, {32,37}, {12,22}, {5,19}, {7,43}, {2,14}, {29,37}, {30,37}, {7,44}, {2,35}, {34,44}, {5,35}, {17,40}, {11,15}, {33,38}, {5,36}, {6,20}, {16,25}, {7,45}, {19,41}, {18,26}, {12,41}, {2,6}, {19,29}, {18,43}, {36,43}, {34,43}, {32,39}, {11,22}, {9,43}, {1,14}, {28,37}, {14,32}, {28,39}, {11,41}, {18,20}, {6,35}, {4,19}, {18,27}, {8,43}, {7,24}, {2,13}, {16,41}, {26,45}, {29,39}, {2,36}, {31,37}, {12,23}, {7,23}, {2,15}, {12,42}, {5,21}, {17,20}, {4,29}, {12,40}, {23,38}, {10,15}, {21,42}, {6,29}, {25,43}, {7,36}, {15,32}, {17,21}, {17,44}, {15,31}, {8,36}, {9,36}, {1,6}, {16,44}, {15,40}, {27,38}, {20,41}, {16,26}, {30,39}, {11,40}, {26,33}, {9,24}, {1,35}, {4,28}, {25,32}, {10,22}, {14,31}, {21,41}, {17,19}, {23,37}, {7,12}, {8,23}, {21,29}, {17,42}, {17,25}, {17,26}, {2,34}, {5,29}, {26,43}, {18,21}, {17,43}, {23,29}, {7,34}, {26,37}, {22,29}, {10,40}, {27,31}, {11,23}, {15,33}, {20,42}, {16,21}, {17,45}, {22,38}, {6,19}, {18,19}, {3,5}, {15,42}, {25,38}, {3,36}, {6,30}, {25,44}, {35,44}, {24,38}, {12,24}, {13,32}, {14,40}, {8,11}, {3,33}, {25,39}, {7,11}, {4,35}, {27,33}, {8,24}, {8,10}, {3,31}, {4,21}, {2,33}, {24,29}, {24,30}, {20,30}, {25,45}, {18,42}, {10,14}, {20,28}, {33,39}, {11,24}, {4,20}, {22,37}, {12,14}, {9,34}, {1,5}, {18,45}, {23,30}, {12,13}, {36,44}, {35,45}, {3,13}, {19,40}, {15,41}, {13,42}, {21,30}, {26,44}, {6,36}, {24,28}, {16,27}, {4,34}, {2,32}, {9,45}, {1,13}, {9,44}, {8,45}, {1,34}, {29,38}, {10,42}, {7,22}, {5,28}, {25,31}, {16,19}, {3,4} } Symmetric graph 23 of order 45 Valency 16 Diameter 2 Girth 3 Automorphism group of order 1440 Number of arcs = 720 Number of 2-arcs = 10800 2-arc-transitive false Edge-set { {1,7}, {13,30}, {3,36}, {17,36}, {20,24}, {26,35}, {40,41}, {23,35}, {28,41}, {9,22}, {7,29}, {2,20}, {21,34}, {32,45}, {11,44}, {2,6}, {10,34}, {16,45}, {11,25}, {8,14}, {2,8}, {13,19}, {3,22}, {22,28}, {29,38}, {4,10}, {6,32}, {3,42}, {14,33}, {40,44}, {12,16}, {15,28}, {1,38}, {4,12}, {4,32}, {25,42}, {14,26}, {7,40}, {9,16}, {11,39}, {5,17}, {11,28}, {5,38}, {24,36}, {20,27}, {8,26}, {8,40}, {8,16}, {8,25}, {19,31}, {22,45}, {12,29}, {4,37}, {3,15}, {1,33}, {26,43}, {13,40}, {1,39}, {17,35}, {32,44}, {12,44}, {25,38}, {18,26}, {16,37}, {19,25}, {30,31}, {36,45}, {18,37}, {3,29}, {33,37}, {7,43}, {9,13}, {20,39}, {17,21}, {13,32}, {3,44}, {14,25}, {2,26}, {34,40}, {16,42}, {23,27}, {28,39}, {16,40}, {16,25}, {27,31}, {39,45}, {9,35}, {7,41}, {18,22}, {23,29}, {11,20}, {5,21}, {11,32}, {5,44}, {5,26}, {7,11}, {5,9}, {5,24}, {8,42}, {19,38}, {29,33}, {37,43}, {26,37}, {19,40}, {1,30}, {35,36}, {20,41}, {15,21}, {32,36}, {20,44}, {30,34}, {36,42}, {2,23}, {28,34}, {12,33}, {38,44}, {12,18}, {7,31}, {9,45}, {20,21}, {21,30}, {25,33}, {7,24}, {9,27}, {24,31}, {35,42}, {14,41}, {21,33}, {30,43}, {19,26}, {22,40}, {35,43}, {13,41}, {14,36}, {22,34}, {29,42}, {10,23}, {6,28}, {20,33}, {26,44}, {12,40}, {7,39}, {9,17}, {20,28}, {21,38}, {25,43}, {13,26}, {6,18}, {16,34}, {25,32}, {7,25}, {9,26}, {5,18}, {23,31}, {34,42}, {14,42}, {2,14}, {2,34}, {13,45}, {3,11}, {8,21}, {8,30}, {6,19}, {10,22}, {16,29}, {10,27}, {6,39}, {3,40}, {16,33}, {27,44}, {12,39}, {21,39}, {3,16}, {14,27}, {2,39}, {11,43}, {5,13}, {27,45}, {1,19}, {22,35}, {33,41}, {15,43}, {21,43}, {24,32}, {17,30}, {2,35}, {34,41}, {11,29}, {10,37}, {3,35}, {22,44}, {4,17}, {10,38}, {4,16}, {18,35}, {31,44}, {12,45}, {18,30}, {3,31}, {6,29}, {10,17}, {6,24}, {3,7}, {14,18}, {2,43}, {13,34}, {11,17}, {1,10}, {6,35}, {17,41}, {15,24}, {21,27}, {8,32}, {8,44}, {2,41}, {15,34}, {35,39}, {4,8}, {19,43}, {13,22}, {6,12}, {15,16}, {1,25}, {1,22}, {29,35}, {12,21}, {32,38}, {18,44}, {14,23}, {2,28}, {16,22}, {25,29}, {10,31}, {6,45}, {9,15}, {20,36}, {4,25}, {26,32}, {9,33}, {7,13}, {3,9}, {14,20}, {2,21}, {30,39}, {5,6}, {4,43}, {39,43}, {13,17}, {17,38}, {4,28}, {26,40}, {10,11}, {1,27}, {8,12}, {22,26}, {4,23}, {1,42}, {12,23}, {34,38}, {18,42}, {6,42}, {25,26}, {18,39}, {17,23}, {38,42}, {27,36}, {24,30}, {8,34}, {1,45}, {11,35}, {37,41}, {15,19}, {10,41}, {6,15}, {7,33}, {24,28}, {4,45}, {28,37}, {12,31}, {31,40}, {15,38}, {4,36}, {20,32}, {23,40}, {16,28}, {12,30}, {2,15}, {1,34}, {23,45}, {9,37}, {7,19}, {10,18}, {6,23}, {5,33}, {5,12}, {28,45}, {11,38}, {19,32}, {5,37}, {24,41}, {15,27}, {8,36}, {8,20}, {1,18}, {25,37}, {7,30}, {9,36}, {2,19}, {33,45}, {21,44}, {4,31}, {15,42}, {1,14}, {14,37}, {29,41}, {3,20}, {13,36}, {2,40}, {22,39}, {17,29}, {10,28}, {6,38}, {17,34}, {24,42}, {15,37}, {23,36}, {1,13}, {7,20}, {9,21}, {30,42}, {31,43}, {23,41}, {4,11}, {5,32}, {24,37}, {19,27}, {18,31}, {31,37}, {19,45}, {10,44}, {18,24}, {4,30}, {10,14}, {13,24}, {3,27}, {27,38}, {3,24}, {27,33}, {19,23}, {5,41}, {11,22}, {5,29}, {30,36}, {9,43}, {14,35}, {33,39}, {17,43}, {29,40}, {28,32}, {15,31} } Symmetric graph 24 of order 45 Valency 16 Diameter 2 Girth 3 Automorphism group of order 1440 Number of arcs = 720 Number of 2-arcs = 10800 2-arc-transitive false Edge-set { {1,4}, {16,19}, {9,22}, {26,34}, {6,20}, {5,14}, {31,39}, {41,45}, {11,42}, {21,25}, {5,23}, {20,38}, {24,36}, {11,32}, {1,44}, {7,28}, {17,30}, {23,30}, {25,29}, {27,44}, {4,40}, {13,20}, {24,32}, {25,33}, {2,5}, {15,42}, {10,33}, {10,23}, {25,45}, {9,16}, {9,18}, {13,37}, {2,36}, {14,19}, {2,13}, {14,32}, {3,44}, {15,40}, {9,43}, {18,41}, {19,29}, {22,28}, {25,37}, {5,34}, {10,15}, {33,45}, {12,44}, {40,43}, {17,20}, {8,24}, {30,39}, {29,35}, {12,24}, {27,43}, {13,24}, {27,32}, {7,44}, {17,40}, {20,39}, {5,35}, {21,39}, {31,37}, {3,34}, {17,42}, {8,10}, {26,38}, {6,36}, {17,37}, {8,34}, {10,38}, {36,45}, {7,18}, {29,39}, {28,35}, {5,8}, {16,39}, {21,30}, {3,26}, {6,15}, {1,14}, {13,31}, {31,44}, {3,40}, {20,41}, {11,24}, {24,39}, {27,35}, {7,12}, {17,43}, {18,26}, {8,29}, {16,28}, {25,36}, {5,19}, {33,38}, {2,32}, {12,15}, {15,22}, {26,33}, {8,43}, {16,41}, {15,37}, {33,34}, {10,43}, {4,9}, {18,37}, {29,36}, {19,28}, {25,32}, {1,5}, {20,40}, {11,31}, {7,11}, {30,36}, {6,24}, {27,38}, {2,42}, {21,42}, {31,36}, {3,19}, {6,41}, {11,38}, {24,33}, {2,27}, {7,42}, {10,17}, {4,35}, {21,37}, {3,32}, {1,15}, {1,40}, {12,13}, {24,38}, {32,34}, {1,20}, {4,14}, {18,45}, {23,35}, {16,38}, {9,36}, {11,37}, {34,44}, {9,11}, {18,44}, {18,29}, {25,28}, {5,30}, {15,23}, {15,32}, {1,33}, {12,41}, {4,22}, {26,37}, {8,36}, {35,45}, {3,6}, {15,38}, {1,34}, {42,44}, {10,40}, {20,26}, {12,33}, {2,43}, {8,45}, {22,39}, {26,35}, {14,39}, {31,35}, {12,45}, {42,43}, {6,8}, {28,34}, {20,30}, {3,35}, {11,43}, {16,27}, {3,21}, {3,42}, {1,26}, {6,13}, {10,44}, {40,45}, {16,20}, {9,24}, {5,28}, {11,23}, {25,44}, {4,23}, {10,14}, {15,21}, {23,33}, {33,43}, {2,41}, {27,30}, {4,29}, {6,7}, {21,28}, {2,25}, {8,41}, {4,30}, {29,37}, {19,27}, {19,40}, {12,22}, {27,31}, {3,4}, {10,18}, {7,45}, {9,35}, {16,29}, {9,28}, {22,37}, {15,33}, {2,33}, {10,41}, {11,45}, {16,25}, {5,9}, {19,38}, {22,36}, {7,35}, {17,21}, {13,40}, {12,32}, {2,20}, {5,42}, {10,39}, {23,31}, {3,25}, {9,41}, {11,18}, {25,39}, {18,21}, {14,24}, {13,39}, {32,35}, {12,16}, {26,30}, {22,31}, {31,45}, {6,42}, {7,40}, {12,17}, {7,23}, {33,39}, {2,35}, {9,30}, {24,29}, {27,28}, {26,43}, {8,17}, {8,16}, {17,38}, {1,31}, {12,42}, {32,38}, {1,36}, {11,40}, {7,22}, {17,26}, {8,30}, {6,21}, {23,38}, {1,41}, {11,13}, {18,40}, {8,23}, {34,43}, {18,27}, {4,7}, {18,30}, {7,29}, {16,45}, {9,42}, {23,34}, {17,28}, {25,34}, {5,20}, {5,15}, {13,23}, {9,44}, {13,19}, {22,32}, {27,36}, {27,39}, {32,43}, {8,12}, {16,43}, {14,41}, {4,21}, {23,37}, {1,27}, {4,13}, {17,44}, {8,40}, {6,28}, {30,38}, {2,19}, {14,22}, {3,31}, {3,15}, {26,29}, {26,31}, {41,44}, {18,19}, {24,35}, {21,27}, {5,40}, {12,39}, {15,20}, {14,31}, {35,43}, {24,28}, {17,25}, {2,6}, {14,42}, {10,31}, {12,37}, {4,19}, {10,22}, {26,45}, {32,44}, {33,36}, {32,37}, {22,34}, {2,45}, {11,14}, {23,29}, {28,37}, {19,26}, {1,43}, {13,41}, {16,42}, {6,34}, {11,16}, {22,30}, {9,10}, {19,42}, {14,38}, {13,33}, {21,41}, {14,21}, {7,34}, {20,25}, {5,24}, {18,39}, {6,22}, {28,38}, {19,37}, {6,29}, {1,21}, {2,14}, {3,45}, {4,41}, {20,29}, {36,44}, {7,17}, {3,13}, {30,34}, {4,36} } Symmetric graph 25 of order 45 Valency 16 Diameter 2 Girth 3 Automorphism group of order 4320 Number of arcs = 720 Number of 2-arcs = 10800 2-arc-transitive false Edge-set { {1,4}, {9,40}, {23,29}, {11,23}, {25,35}, {29,35}, {17,19}, {33,35}, {17,43}, {4,21}, {15,37}, {4,29}, {19,37}, {18,37}, {12,37}, {14,37}, {1,32}, {9,17}, {6,29}, {25,44}, {9,29}, {19,29}, {18,25}, {4,40}, {25,38}, {3,40}, {25,31}, {40,45}, {25,43}, {8,40}, {2,40}, {23,37}, {1,25}, {7,29}, {19,28}, {15,21}, {15,31}, {19,25}, {18,29}, {4,19}, {21,38}, {3,15}, {9,11}, {21,27}, {15,42}, {11,42}, {24,35}, {3,21}, {10,15}, {11,13}, {14,21}, {15,32}, {11,24}, {27,35}, {11,41}, {22,35}, {17,40}, {21,40}, {15,23}, {22,29}, {19,26}, {18,28}, {17,44}, {6,9}, {3,44}, {9,10}, {18,21}, {4,15}, {29,38}, {3,19}, {9,18}, {17,27}, {6,42}, {42,44}, {9,24}, {23,33}, {6,14}, {12,44}, {9,36}, {12,33}, {36,43}, {4,36}, {17,42}, {6,24}, {32,44}, {9,44}, {33,45}, {7,43}, {6,8}, {2,44}, {33,36}, {18,43}, {10,33}, {34,43}, {4,34}, {16,37}, {11,37}, {1,35}, {11,17}, {6,35}, {35,44}, {29,34}, {16,19}, {18,20}, {4,13}, {28,38}, {1,31}, {7,23}, {25,28}, {24,31}, {23,32}, {17,38}, {3,6}, {27,29}, {19,42}, {18,42}, {4,24}, {23,38}, {3,25}, {1,14}, {7,12}, {28,36}, {12,15}, {31,36}, {23,36}, {12,17}, {8,28}, {31,45}, {5,23}, {12,45}, {5,14}, {32,38}, {5,9}, {1,36}, {7,36}, {2,15}, {11,31}, {1,13}, {14,22}, {26,32}, {7,24}, {27,28}, {15,41}, {22,31}, {1,5}, {12,38}, {14,38}, {3,32}, {32,39}, {29,39}, {25,39}, {25,33}, {40,43}, {33,37}, {1,43}, {4,7}, {28,37}, {31,37}, {19,39}, {18,39}, {2,4}, {16,38}, {3,5}, {9,45}, {21,42}, {10,23}, {17,26}, {21,28}, {3,36}, {10,18}, {2,35}, {27,37}, {1,42}, {7,42}, {24,28}, {14,19}, {12,18}, {15,24}, {8,23}, {26,45}, {5,28}, {31,44}, {10,38}, {5,35}, {1,45}, {3,13}, {8,35}, {17,30}, {13,31}, {8,43}, {8,30}, {2,27}, {25,30}, {5,40}, {5,22}, {26,38}, {41,44}, {9,22}, {3,33}, {10,43}, {8,16}, {2,20}, {22,36}, {18,26}, {10,44}, {9,34}, {3,34}, {10,16}, {23,30}, {27,31}, {42,45}, {27,43}, {8,42}, {2,42}, {2,26}, {26,29}, {19,41}, {21,26}, {1,21}, {11,14}, {32,35}, {12,40}, {14,40}, {10,40}, {4,41}, {3,41}, {9,41}, {27,39}, {24,30}, {13,23}, {6,36}, {20,37}, {17,28}, {6,21}, {5,42}, {24,38}, {22,37}, {12,22}, {26,36}, {4,8}, {31,38}, {3,45}, {36,44}, {13,20}, {13,33}, {21,30}, {10,31}, {27,32}, {30,37}, {13,40}, {1,20}, {7,10}, {14,24}, {20,27}, {15,20}, {8,11}, {30,35}, {8,34}, {16,30}, {13,42}, {31,34}, {23,34}, {16,25}, {12,24}, {14,32}, {24,39}, {16,41}, {5,34}, {20,38}, {6,23}, {17,20}, {10,14}, {12,13}, {27,36}, {12,41}, {20,41}, {13,22}, {20,29}, {13,19}, {6,13}, {33,43}, {35,45}, {11,43}, {11,32}, {10,42}, {24,34}, {25,34}, {14,41}, {30,36}, {7,17}, {5,7}, {6,28}, {8,12}, {16,40}, {16,45}, {5,20}, {13,38}, {3,27}, {24,33}, {5,15}, {6,20}, {2,19}, {20,40}, {11,45}, {7,35}, {22,32}, {26,44}, {8,18}, {16,44}, {4,30}, {30,39}, {10,39}, {17,39}, {21,39}, {18,45}, {2,43}, {18,41}, {2,34}, {16,27}, {32,43}, {8,44}, {7,45}, {5,19}, {34,45}, {7,16}, {16,29}, {7,28}, {12,32}, {14,33}, {2,33}, {15,39}, {5,30}, {1,26}, {8,22}, {26,30}, {27,45}, {11,39}, {13,39}, {9,30}, {4,22}, {11,16}, {26,37}, {2,31}, {1,41}, {6,41}, {22,39}, {2,14}, {26,33}, {33,39}, {22,28}, {20,30}, {41,43}, {7,41}, {20,25}, {10,22}, {28,34}, {26,34}, {16,21}, {32,34}, {2,6} } Symmetric graph 26 of order 45 Valency 16 Diameter 2 Girth 3 Automorphism group of order 8640 Number of arcs = 720 Number of 2-arcs = 10800 2-arc-transitive false Edge-set { {1,4}, {11,35}, {36,39}, {6,39}, {24,43}, {4,30}, {23,27}, {30,34}, {27,37}, {33,45}, {12,33}, {3,35}, {16,39}, {23,44}, {11,15}, {3,5}, {16,22}, {23,28}, {15,26}, {27,32}, {21,31}, {27,38}, {21,44}, {6,10}, {24,35}, {30,40}, {5,27}, {31,44}, {11,32}, {18,39}, {2,43}, {10,36}, {35,38}, {40,43}, {5,10}, {2,44}, {11,18}, {18,22}, {2,13}, {23,26}, {15,19}, {19,25}, {8,20}, {23,29}, {15,25}, {19,31}, {8,32}, {34,37}, {37,45}, {6,45}, {12,24}, {3,9}, {16,29}, {23,36}, {15,38}, {25,31}, {20,32}, {26,39}, {19,43}, {30,41}, {6,27}, {33,34}, {4,37}, {23,45}, {6,29}, {24,25}, {9,33}, {29,33}, {36,37}, {38,45}, {12,31}, {32,34}, {39,41}, {6,43}, {41,43}, {12,16}, {3,34}, {22,44}, {11,13}, {18,20}, {2,9}, {20,24}, {9,14}, {15,21}, {7,42}, {1,44}, {11,17}, {18,24}, {2,14}, {20,25}, {9,20}, {19,42}, {5,28}, {22,26}, {28,32}, {26,31}, {31,37}, {12,44}, {10,14}, {35,41}, {1,40}, {5,17}, {4,44}, {11,23}, {18,29}, {2,25}, {14,20}, {21,26}, {7,19}, {22,30}, {13,27}, {20,33}, {3,7}, {16,30}, {23,34}, {15,37}, {21,22}, {28,35}, {32,44}, {11,31}, {1,34}, {17,37}, {24,45}, {12,14}, {14,27}, {21,41}, {1,27}, {17,21}, {4,28}, {29,32}, {25,38}, {20,44}, {5,26}, {19,22}, {7,30}, {27,30}, {33,37}, {7,33}, {30,33}, {38,40}, {5,44}, {22,35}, {31,43}, {10,32}, {3,43}, {6,7}, {34,41}, {21,45}, {7,12}, {14,17}, {1,41}, {18,19}, {2,8}, {8,13}, {28,40}, {32,36}, {39,42}, {4,43}, {41,45}, {6,12}, {12,17}, {21,24}, {7,14}, {14,21}, {7,41}, {9,28}, {2,36}, {18,38}, {22,43}, {10,13}, {2,26}, {22,25}, {13,20}, {25,28}, {20,26}, {31,38}, {1,45}, {24,30}, {9,11}, {29,36}, {36,42}, {4,38}, {31,35}, {32,39}, {39,44}, {11,43}, {6,17}, {14,34}, {1,7}, {9,40}, {10,16}, {16,23}, {3,15}, {21,27}, {7,21}, {35,40}, {3,40}, {5,16}, {11,22}, {18,28}, {8,10}, {2,6}, {19,32}, {25,39}, {20,43}, {5,11}, {22,36}, {28,42}, {4,26}, {32,45}, {17,38}, {17,23}, {1,15}, {8,30}, {15,36}, {4,8}, {2,35}, {1,26}, {17,19}, {24,29}, {14,25}, {7,32}, {13,38}, {9,10}, {3,13}, {16,40}, {3,23}, {15,16}, {27,28}, {21,40}, {3,27}, {16,21}, {9,29}, {25,29}, {31,36}, {32,38}, {10,24}, {25,33}, {26,37}, {19,45}, {10,33}, {33,35}, {13,34}, {37,40}, {5,7}, {8,31}, {40,44}, {17,42}, {7,11}, {30,36}, {20,41}, {6,9}, {12,15}, {34,42}, {3,42}, {19,23}, {33,39}, {30,31}, {34,38}, {37,44}, {38,42}, {8,12}, {13,17}, {1,8}, {7,13}, {18,41}, {4,12}, {29,41}, {6,25}, {33,43}, {16,37}, {3,45}, {12,22}, {2,24}, {14,18}, {14,39}, {29,35}, {26,30}, {19,27}, {1,22}, {36,40}, {5,45}, {10,18}, {8,15}, {13,19}, {8,40}, {5,38}, {39,43}, {10,43}, {2,41}, {6,18}, {42,45}, {12,34}, {9,19}, {21,33}, {38,43}, {10,23}, {13,39}, {26,32}, {29,42}, {4,25}, {42,44}, {4,11}, {16,42}, {4,18}, {2,23}, {15,35}, {24,34}, {13,36}, {20,42}, {4,9}, {17,24}, {1,14}, {13,26}, {19,40}, {3,25}, {14,37}, {5,29}, {10,44}, {18,40}, {2,5}, {15,18}, {8,29}, {5,8}, {17,41}, {1,24}, {20,23}, {26,29}, {12,45}, {24,27}, {22,28}, {9,31}, {3,22}, {8,42}, {3,4}, {37,41}, {16,20}, {28,31}, {13,16}, {6,30}, {17,30}, {27,33}, {1,6}, {9,15}, {2,42}, {6,37}, {9,41}, {8,21}, {11,45}, {17,28}, {35,39}, {11,34}, {4,16}, {7,28}, {14,35}, {1,36}, {12,36}, {10,35}, {28,34}, {5,39} } Symmetric graph 27 of order 45 Valency 16 Diameter 3 Girth 4 Automorphism group of order 3628800 Number of arcs = 720 Number of 2-arcs = 10800 2-arc-transitive false Edge-set { {1,7}, {17,31}, {2,23}, {26,37}, {12,38}, {23,32}, {3,44}, {12,41}, {7,33}, {7,13}, {18,34}, {23,27}, {13,44}, {4,33}, {4,30}, {18,27}, {17,28}, {14,23}, {8,17}, {19,23}, {29,38}, {15,39}, {23,42}, {8,44}, {4,8}, {19,30}, {28,34}, {5,14}, {34,45}, {5,6}, {38,42}, {8,39}, {37,43}, {9,38}, {9,23}, {20,44}, {18,37}, {24,38}, {23,39}, {40,44}, {10,34}, {10,14}, {16,35}, {28,44}, {4,18}, {24,30}, {5,24}, {39,45}, {6,40}, {29,43}, {9,15}, {9,35}, {1,20}, {5,29}, {15,26}, {1,22}, {2,13}, {14,18}, {24,35}, {3,12}, {29,33}, {13,19}, {25,34}, {25,44}, {4,40}, {30,36}, {33,39}, {13,24}, {35,44}, {4,15}, {30,31}, {20,29}, {15,21}, {9,20}, {20,21}, {11,37}, {4,43}, {9,30}, {34,38}, {5,39}, {24,45}, {6,45}, {1,45}, {26,35}, {15,16}, {22,31}, {10,29}, {10,19}, {16,25}, {11,25}, {31,40}, {2,36}, {1,10}, {10,41}, {7,16}, {2,43}, {8,32}, {3,19}, {20,39}, {11,45}, {19,40}, {25,29}, {15,41}, {4,25}, {30,41}, {15,34}, {5,31}, {6,32}, {14,28}, {14,35}, {8,24}, {19,45}, {11,30}, {5,16}, {26,45}, {6,12}, {10,36}, {10,21}, {16,42}, {25,36}, {21,40}, {36,42}, {17,33}, {3,34}, {6,25}, {13,29}, {1,35}, {22,26}, {2,26}, {7,11}, {16,37}, {12,43}, {37,41}, {17,41}, {12,31}, {11,32}, {3,32}, {20,31}, {2,21}, {21,27}, {17,36}, {23,37}, {3,29}, {14,40}, {35,36}, {17,26}, {16,27}, {5,41}, {6,27}, {1,12}, {13,22}, {9,43}, {11,20}, {18,24}, {26,40}, {6,17}, {1,37}, {7,26}, {18,22}, {21,32}, {21,42}, {28,37}, {32,41}, {31,42}, {2,11}, {28,32}, {14,38}, {22,41}, {7,43}, {3,7}, {17,23}, {12,36}, {33,37}, {18,29}, {27,33}, {27,38}, {12,18}, {13,17}, {4,13}, {3,42}, {8,42}, {32,38}, {12,23}, {33,44}, {4,10}, {7,38}, {8,37}, {1,27}, {8,22}, {7,31}, {2,18}, {19,43}, {22,38}, {2,33}, {7,23}, {39,43}, {13,42}, {28,42}, {9,33}, {13,27}, {12,28}, {3,17}, {27,43}, {9,13}, {20,34}, {23,29}, {4,23}, {38,44}, {18,32}, {14,33}, {10,39}, {8,14}, {8,34}, {18,39}, {19,38}, {5,19}, {4,28}, {24,28}, {13,34}, {18,44}, {14,30}, {5,21}, {23,34}, {24,33}, {2,8}, {24,43}, {3,39}, {29,40}, {34,43}, {3,14}, {23,44}, {29,35}, {19,28}, {9,28}, {14,25}, {8,19}, {9,18}, {4,38}, {8,29}, {19,25}, {15,36}, {10,44}, {5,44}, {30,34}, {13,39}, {14,20}, {21,35}, {20,24}, {15,24}, {35,39}, {34,40}, {1,40}, {5,9}, {9,45}, {15,19}, {30,39}, {6,20}, {1,42}, {15,44}, {14,45}, {3,24}, {29,45}, {4,35}, {10,31}, {15,29}, {4,20}, {30,44}, {10,11}, {9,40}, {9,25}, {20,41}, {24,40}, {25,39}, {5,34}, {10,24}, {40,41}, {16,32}, {21,30}, {1,30}, {6,15}, {19,35}, {20,36}, {11,42}, {36,45}, {16,45}, {11,35}, {15,31}, {2,31}, {1,25}, {25,26}, {16,40}, {6,35}, {22,36}, {2,28}, {16,30}, {20,26}, {4,45}, {10,26}, {5,11}, {12,21}, {10,16}, {5,36}, {6,30}, {17,21}, {25,31}, {25,41}, {27,36}, {31,45}, {35,41}, {1,15}, {21,45}, {27,31}, {13,37}, {6,42}, {2,6}, {16,22}, {11,40}, {32,36}, {26,32}, {11,17}, {12,16}, {2,41}, {7,41}, {31,37}, {11,22}, {32,43}, {3,9}, {6,37}, {7,36}, {5,26}, {7,21}, {1,17}, {18,42}, {21,37}, {1,32}, {6,22}, {27,41}, {12,26}, {11,27}, {2,16}, {26,42}, {8,12}, {19,33}, {22,28}, {3,22}, {13,32}, {17,38}, {3,27}, {12,33}, {17,43}, {22,33}, {2,38}, {28,39}, {33,42}, {22,43}, {8,27}, {7,18}, {3,37}, {7,28}, {14,43} } Symmetric graph 28 of order 45 Valency 16 Diameter 2 Girth 3 Automorphism group of order 3628800 Number of arcs = 720 Number of 2-arcs = 10800 2-arc-transitive false Edge-set { {1,2}, {2,7}, {2,4}, {6,10}, {5,9}, {1,7}, {2,14}, {10,23}, {9,13}, {7,14}, {10,17}, {9,16}, {20,26}, {8,21}, {8,22}, {18,25}, {9,19}, {3,8}, {4,14}, {6,23}, {5,13}, {7,31}, {10,12}, {26,33}, {8,15}, {25,30}, {1,31}, {12,23}, {13,19}, {19,26}, {12,25}, {36,42}, {11,43}, {38,41}, {11,35}, {17,24}, {24,35}, {28,32}, {28,33}, {34,37}, {21,25}, {11,24}, {14,31}, {12,17}, {16,19}, {20,33}, {15,21}, {3,22}, {18,30}, {1,4}, {23,31}, {13,31}, {15,26}, {29,42}, {18,43}, {41,45}, {16,24}, {28,40}, {28,35}, {37,43}, {4,31}, {6,31}, {5,31}, {15,33}, {3,15}, {21,30}, {5,16}, {21,22}, {21,42}, {5,43}, {21,41}, {4,35}, {15,28}, {3,28}, {4,11}, {15,37}, {40,45}, {34,43}, {27,39}, {27,37}, {29,32}, {38,45}, {24,38}, {27,44}, {20,30}, {19,39}, {22,41}, {14,32}, {21,36}, {39,44}, {30,41}, {32,40}, {25,27}, {9,29}, {44,45}, {37,39}, {17,28}, {6,28}, {11,16}, {12,37}, {20,41}, {29,36}, {12,31}, {19,31}, {15,19}, {12,21}, {11,18}, {16,17}, {33,35}, {6,17}, {4,33}, {15,31}, {3,31}, {4,30}, {16,31}, {22,31}, {16,42}, {23,43}, {19,41}, {17,35}, {32,37}, {32,34}, {24,42}, {12,39}, {13,41}, {15,32}, {14,36}, {25,36}, {9,44}, {40,44}, {38,42}, {26,37}, {17,31}, {4,20}, {21,31}, {4,18}, {16,29}, {18,23}, {19,45}, {17,40}, {6,35}, {12,43}, {12,18}, {6,45}, {16,34}, {12,27}, {18,37}, {3,33}, {7,32}, {17,38}, {6,24}, {14,44}, {1,30}, {23,25}, {19,44}, {9,11}, {13,44}, {6,38}, {14,27}, {1,20}, {23,37}, {19,20}, {27,36}, {26,39}, {3,34}, {18,20}, {26,28}, {5,23}, {39,45}, {36,40}, {5,34}, {35,38}, {5,42}, {7,27}, {6,40}, {16,43}, {29,34}, {38,40}, {8,37}, {2,44}, {8,34}, {22,25}, {21,38}, {9,20}, {7,44}, {22,38}, {13,20}, {14,29}, {15,34}, {3,37}, {36,38}, {4,15}, {4,21}, {16,21}, {19,21}, {4,17}, {15,17}, {3,6}, {4,16}, {12,15}, {27,32}, {12,19}, {13,22}, {14,15}, {14,21}, {29,44}, {1,18}, {17,45}, {14,40}, {1,35}, {4,12}, {13,45}, {33,37}, {1,33}, {3,32}, {5,24}, {22,30}, {20,39}, {28,45}, {10,39}, {30,38}, {22,42}, {23,27}, {7,40}, {8,25}, {2,20}, {10,45}, {34,42}, {4,19}, {1,11}, {32,33}, {22,36}, {20,44}, {3,26}, {7,36}, {13,39}, {20,35}, {28,34}, {11,29}, {1,5}, {23,39}, {7,29}, {2,40}, {5,29}, {8,28}, {2,29}, {20,45}, {2,36}, {5,11}, {33,34}, {8,42}, {13,26}, {32,36}, {11,33}, {11,34}, {9,42}, {25,43}, {41,44}, {18,33}, {1,3}, {3,7}, {8,41}, {30,36}, {30,33}, {6,13}, {27,43}, {39,41}, {29,40}, {25,42}, {10,18}, {27,29}, {25,41}, {24,34}, {10,37}, {10,28}, {7,22}, {10,25}, {24,43}, {9,26}, {10,40}, {8,38}, {2,11}, {1,22}, {35,45}, {29,43}, {25,39}, {14,16}, {1,23}, {17,19}, {14,17}, {1,6}, {12,16}, {15,16}, {12,14}, {17,21}, {5,6}, {14,19}, {22,23}, {11,20}, {7,13}, {6,22}, {1,13}, {3,23}, {3,5}, {18,39}, {26,45}, {30,35}, {5,22}, {7,23}, {6,7}, {25,37}, {2,32}, {24,28}, {35,40}, {8,36}, {9,41}, {36,44}, {8,26}, {2,30}, {8,33}, {24,29}, {10,35}, {10,38}, {26,41}, {8,30}, {10,43}, {26,34}, {27,40}, {2,27}, {18,27}, {24,45}, {25,38}, {11,42}, {11,30}, {9,43}, {26,44}, {28,37}, {2,18}, {5,7}, {10,27}, {9,24}, {36,41}, {9,39}, {24,40}, {10,24}, {9,34}, {30,42}, {39,43}, {9,45}, {13,23}, {18,35}, {26,32}, {2,35}, {32,44}, {28,38}, {2,33}, {3,13}, {8,32}, {41,42}, {42,43} } Symmetric graph 29 of order 45 Valency 18 Diameter 2 Girth 3 Automorphism group of order 338533188894720 Number of arcs = 810 Number of 2-arcs = 13770 2-arc-transitive false Edge-set { {1,7}, {5,44}, {2,12}, {3,7}, {32,40}, {4,18}, {4,10}, {6,44}, {2,11}, {28,41}, {7,14}, {1,11}, {21,33}, {1,16}, {5,33}, {2,7}, {31,40}, {4,17}, {6,10}, {31,42}, {15,26}, {21,44}, {2,22}, {5,17}, {6,12}, {14,29}, {8,37}, {5,12}, {12,20}, {3,29}, {8,32}, {4,44}, {2,10}, {30,41}, {9,14}, {1,10}, {19,33}, {2,16}, {5,31}, {30,40}, {9,13}, {20,23}, {16,23}, {37,40}, {4,26}, {10,36}, {3,10}, {19,32}, {2,18}, {4,31}, {21,32}, {22,27}, {37,45}, {1,30}, {3,18}, {4,32}, {15,18}, {4,39}, {6,32}, {11,27}, {28,45}, {33,40}, {4,16}, {5,10}, {33,42}, {15,25}, {21,43}, {3,22}, {5,16}, {13,29}, {8,38}, {4,12}, {10,20}, {3,30}, {9,32}, {33,41}, {14,25}, {19,43}, {3,24}, {34,39}, {12,25}, {20,34}, {37,41}, {14,30}, {1,23}, {16,33}, {16,36}, {6,16}, {5,11}, {13,28}, {7,38}, {4,11}, {10,21}, {9,33}, {14,28}, {7,37}, {22,26}, {17,36}, {30,42}, {6,11}, {11,21}, {1,28}, {7,33}, {11,20}, {21,23}, {1,38}, {28,33}, {2,28}, {7,31}, {17,22}, {6,17}, {8,31}, {26,42}, {29,41}, {8,14}, {1,12}, {20,33}, {3,16}, {5,32}, {29,40}, {8,13}, {20,24}, {18,23}, {6,26}, {11,36}, {3,12}, {20,32}, {24,27}, {39,45}, {1,29}, {1,18}, {4,33}, {15,16}, {5,39}, {6,33}, {11,25}, {28,43}, {29,42}, {8,15}, {21,24}, {18,22}, {38,41}, {6,27}, {11,35}, {35,38}, {18,24}, {15,35}, {39,43}, {37,42}, {15,30}, {22,25}, {5,25}, {12,34}, {12,29}, {8,20}, {12,36}, {20,44}, {20,31}, {3,17}, {19,31}, {24,26}, {39,44}, {2,29}, {1,17}, {14,16}, {5,37}, {29,43}, {3,8}, {21,31}, {37,44}, {2,30}, {23,26}, {19,44}, {13,25}, {2,17}, {6,31}, {14,17}, {6,37}, {12,26}, {29,44}, {2,8}, {15,17}, {6,39}, {34,37}, {29,31}, {8,26}, {10,26}, {30,44}, {2,9}, {19,36}, {30,45}, {1,9}, {23,40}, {13,16}, {32,42}, {15,27}, {21,45}, {1,22}, {5,18}, {15,29}, {8,39}, {3,28}, {7,32}, {32,41}, {14,27}, {19,45}, {1,24}, {35,39}, {21,34}, {2,23}, {16,31}, {6,18}, {15,28}, {7,39}, {17,35}, {28,42}, {12,27}, {12,21}, {8,33}, {3,38}, {28,32}, {17,24}, {9,31}, {26,41}, {13,27}, {20,45}, {35,37}, {11,26}, {21,36}, {39,42}, {17,31}, {17,34}, {6,45}, {29,45}, {21,35}, {23,45}, {9,38}, {13,30}, {23,25}, {18,36}, {18,32}, {18,35}, {4,43}, {4,27}, {15,45}, {1,39}, {7,15}, {39,40}, {9,39}, {11,19}, {23,27}, {16,35}, {28,40}, {10,27}, {12,19}, {20,22}, {3,37}, {30,32}, {27,41}, {9,37}, {10,25}, {16,34}, {7,13}, {38,40}, {19,24}, {10,19}, {19,22}, {2,37}, {30,31}, {27,40}, {4,45}, {19,23}, {2,38}, {28,31}, {30,43}, {9,27}, {25,40}, {13,36}, {38,44}, {25,42}, {5,43}, {25,41}, {14,34}, {17,23}, {5,26}, {3,11}, {38,45}, {28,44}, {21,22}, {38,42}, {5,27}, {12,35}, {34,38}, {14,35}, {37,43}, {4,25}, {10,34}, {12,30}, {9,20}, {13,26}, {14,18}, {4,37}, {1,8}, {11,29}, {7,26}, {19,35}, {3,9}, {23,42}, {14,36}, {10,30}, {9,19}, {10,35}, {27,42}, {8,25}, {34,42}, {24,25}, {18,34}, {11,28}, {7,21}, {11,34}, {17,33}, {5,38}, {12,28}, {38,43}, {13,17}, {6,38}, {31,41}, {14,26}, {16,22}, {13,18}, {4,38}, {36,39}, {11,30}, {7,25}, {22,42}, {16,24}, {20,43}, {2,24}, {39,41}, {36,38}, {30,33}, {9,25}, {22,41}, {10,29}, {9,26}, {22,43}, {24,41}, {24,44}, {24,40}, {24,42}, {19,34}, {3,23}, {16,32}, {26,40}, {36,37}, {17,32}, {22,45}, {18,33}, {15,43}, {3,39}, {1,37}, {5,45}, {23,44}, {13,34}, {6,43}, {22,44}, {13,43}, {22,40}, {24,45}, {35,40}, {14,44}, {8,19}, {29,32}, {18,31}, {2,39}, {9,15}, {20,36}, {29,33}, {6,25}, {20,35}, {24,43}, {15,36}, {23,43}, {36,41}, {7,27}, {13,35}, {7,20}, {23,41}, {10,28}, {7,19}, {36,42}, {8,21}, {34,40}, {36,40}, {8,27}, {35,42}, {34,41}, {14,45}, {13,45}, {9,21}, {15,34}, {35,41}, {15,44}, {13,44}, {14,43} } Symmetric graph 30 of order 45 Valency 18 Diameter 2 Girth 4 Automorphism group of order 62923832219789760135168000000 Number of arcs = 810 Number of 2-arcs = 13770 2-arc-transitive false Edge-set { {1,4}, {8,27}, {32,35}, {17,45}, {8,42}, {12,39}, {16,19}, {24,34}, {2,15}, {32,45}, {8,12}, {3,29}, {27,39}, {22,42}, {10,13}, {21,24}, {6,9}, {29,31}, {34,39}, {15,16}, {3,45}, {7,19}, {33,45}, {17,29}, {39,42}, {15,32}, {12,22}, {25,28}, {13,41}, {5,24}, {26,44}, {9,36}, {19,37}, {10,29}, {21,39}, {6,22}, {1,29}, {7,34}, {15,33}, {42,43}, {4,7}, {34,38}, {15,18}, {19,24}, {2,45}, {29,32}, {6,39}, {16,29}, {3,15}, {22,27}, {18,21}, {41,44}, {4,31}, {10,28}, {13,25}, {16,36}, {13,40}, {11,44}, {9,20}, {28,42}, {4,37}, {1,19}, {25,45}, {29,41}, {5,39}, {15,26}, {22,36}, {8,19}, {10,43}, {7,21}, {6,38}, {18,29}, {12,14}, {27,43}, {7,35}, {10,30}, {21,38}, {6,23}, {13,42}, {4,24}, {9,34}, {15,31}, {19,39}, {16,45}, {26,29}, {36,39}, {19,22}, {1,45}, {6,7}, {29,33}, {15,17}, {23,41}, {3,5}, {31,36}, {27,37}, {17,35}, {1,21}, {25,44}, {4,18}, {28,41}, {11,22}, {1,20}, {4,33}, {11,28}, {2,36}, {13,26}, {40,44}, {21,32}, {12,44}, {27,28}, {35,37}, {4,32}, {18,34}, {15,41}, {19,31}, {10,45}, {25,29}, {6,16}, {29,40}, {11,15}, {20,22}, {42,45}, {4,8}, {1,35}, {14,25}, {41,43}, {5,7}, {26,30}, {36,38}, {19,23}, {27,30}, {14,42}, {12,43}, {25,43}, {30,41}, {5,38}, {14,26}, {23,36}, {12,28}, {13,27}, {24,35}, {10,44}, {9,21}, {6,37}, {29,42}, {4,39}, {22,34}, {1,15}, {40,45}, {11,29}, {20,39}, {15,42}, {4,22}, {8,34}, {26,43}, {7,36}, {19,38}, {18,45}, {6,24}, {2,29}, {14,31}, {10,23}, {7,25}, {33,34}, {11,37}, {17,20}, {17,28}, {37,42}, {12,24}, {2,19}, {8,41}, {5,32}, {18,36}, {23,27}, {3,35}, {21,31}, {22,26}, {8,40}, {6,32}, {27,38}, {18,35}, {2,21}, {9,11}, {20,31}, {4,16}, {28,40}, {33,36}, {11,13}, {39,41}, {5,16}, {3,36}, {17,21}, {42,44}, {16,35}, {3,21}, {6,31}, {4,17}, {1,34}, {15,25}, {18,19}, {41,45}, {1,36}, {19,33}, {11,45}, {2,6}, {15,40}, {32,34}, {12,15}, {27,45}, {8,35}, {19,32}, {5,18}, {31,35}, {10,14}, {16,20}, {40,43}, {11,30}, {20,38}, {4,23}, {12,30}, {14,27}, {14,41}, {25,30}, {30,40}, {11,14}, {20,23}, {27,44}, {12,13}, {5,9}, {26,28}, {36,37}, {12,45}, {27,29}, {35,39}, {10,15}, {21,22}, {6,8}, {26,45}, {12,29}, {15,27}, {22,35}, {8,21}, {14,40}, {11,43}, {7,20}, {30,42}, {4,38}, {23,34}, {24,36}, {9,19}, {31,45}, {5,37}, {17,30}, {1,14}, {23,25}, {18,43}, {7,41}, {10,38}, {2,28}, {26,37}, {24,40}, {2,44}, {28,32}, {12,37}, {3,13}, {24,27}, {9,42}, {8,10}, {25,39}, {16,34}, {11,23}, {3,20}, {14,17}, {23,42}, {7,12}, {37,41}, {5,17}, {22,40}, {8,11}, {26,39}, {38,42}, {12,23}, {3,19}, {9,41}, {5,31}, {9,26}, {37,40}, {6,17}, {21,33}, {11,38}, {18,20}, {2,4}, {10,39}, {22,25}, {7,11}, {20,33}, {24,41}, {2,5}, {32,36}, {5,33}, {17,36}, {2,35}, {6,18}, {3,4}, {31,34}, {20,32}, {2,34}, {6,33}, {16,21}, {3,6}, {17,34}, {3,34}, {17,19}, {1,5}, {1,6}, {33,35}, {2,20}, {23,35}, {20,37}, {5,22}, {8,36}, {5,8}, {35,38}, {21,23}, {20,24}, {4,9}, {34,37}, {2,43}, {30,32}, {14,18}, {3,14}, {31,43}, {7,10}, {1,30}, {25,38}, {31,44}, {16,28}, {13,33}, {11,24}, {13,31}, {16,44}, {3,28}, {28,33}, {13,17}, {24,42}, {32,44}, {9,12}, {8,25}, {10,22}, {2,14}, {23,26}, {7,40}, {2,30}, {14,32}, {3,43}, {7,27}, {28,31}, {10,37}, {24,25}, {8,26}, {39,40}, {12,38}, {7,42}, {9,10}, {25,37}, {9,40}, {24,26}, {38,41}, {26,38}, {23,40}, {9,27}, {22,41}, {7,26}, {38,40}, {10,24}, {9,25}, {11,39}, {8,20}, {5,23}, {9,35}, {21,37}, {16,43}, {3,30}, {30,33}, {1,43}, {32,43}, {18,30}, {1,44}, {18,28}, {2,13}, {1,13}, {33,44}, {18,44}, {13,32}, {13,16}, {3,44}, {30,31}, {14,16}, {33,43}, {16,30}, {14,33}, {17,43}, {17,44}, {1,28}, {13,18} } Symmetric graph 31 of order 45 Valency 20 Diameter 2 Girth 3 Automorphism group of order 371504185344000000000 Number of arcs = 900 Number of 2-arcs = 17100 2-arc-transitive false Edge-set { {1,4}, {1,18}, {5,25}, {6,18}, {5,38}, {3,15}, {3,27}, {2,6}, {26,38}, {3,7}, {27,40}, {10,17}, {4,36}, {14,17}, {2,16}, {6,26}, {7,13}, {2,40}, {17,41}, {4,29}, {14,37}, {5,27}, {13,39}, {1,24}, {12,25}, {5,11}, {34,39}, {4,16}, {6,37}, {2,13}, {2,26}, {12,41}, {29,35}, {16,37}, {5,39}, {17,39}, {1,44}, {25,32}, {9,11}, {34,42}, {3,14}, {1,27}, {8,12}, {35,41}, {18,20}, {5,45}, {15,26}, {3,25}, {14,27}, {8,22}, {11,41}, {25,37}, {2,9}, {26,42}, {12,16}, {6,35}, {13,16}, {26,39}, {15,17}, {23,44}, {10,32}, {4,9}, {37,42}, {3,8}, {27,41}, {5,8}, {39,41}, {18,33}, {5,20}, {15,28}, {25,40}, {14,30}, {22,38}, {11,16}, {11,17}, {4,34}, {14,18}, {1,5}, {23,39}, {3,31}, {19,27}, {10,13}, {2,36}, {3,4}, {11,14}, {1,34}, {19,42}, {28,44}, {25,39}, {9,15}, {3,42}, {16,40}, {6,30}, {13,38}, {4,26}, {15,37}, {2,23}, {10,26}, {4,12}, {35,37}, {8,13}, {2,41}, {5,10}, {36,39}, {21,33}, {20,43}, {27,28}, {1,40}, {25,30}, {9,38}, {16,42}, {17,42}, {4,28}, {14,39}, {1,17}, {8,39}, {3,35}, {22,27}, {10,43}, {31,36}, {3,18}, {11,45}, {33,34}, {7,19}, {40,44}, {4,25}, {1,22}, {11,25}, {6,11}, {34,38}, {8,21}, {41,43}, {17,29}, {4,8}, {14,34}, {12,27}, {13,35}, {16,24}, {6,12}, {18,22}, {33,43}, {20,31}, {8,15}, {3,41}, {10,40}, {30,36}, {17,38}, {4,37}, {18,37}, {2,45}, {26,33}, {7,12}, {35,40}, {1,13}, {2,25}, {9,10}, {36,42}, {16,21}, {6,43}, {13,27}, {1,26}, {15,25}, {9,23}, {10,42}, {12,42}, {28,35}, {16,39}, {6,17}, {8,24}, {32,35}, {21,22}, {14,43}, {1,31}, {5,18}, {15,45}, {3,33}, {7,40}, {30,40}, {4,38}, {1,43}, {25,31}, {8,11}, {34,41}, {8,42}, {28,41}, {17,23}, {4,10}, {14,19}, {27,32}, {13,21}, {24,29}, {22,30}, {33,37}, {1,15}, {18,19}, {5,44}, {14,26}, {7,22}, {11,40}, {23,28}, {32,39}, {17,21}, {1,42}, {25,28}, {11,22}, {11,34}, {12,23}, {10,35}, {4,20}, {37,45}, {6,19}, {38,44}, {30,32}, {9,21}, {28,36}, {4,17}, {27,37}, {13,18}, {24,45}, {12,33}, {5,7}, {39,40}, {1,9}, {25,42}, {6,9}, {38,42}, {16,31}, {13,30}, {26,41}, {15,29}, {23,37}, {10,18}, {12,18}, {5,35}, {15,16}, {3,6}, {24,38}, {2,32}, {21,26}, {12,14}, {1,35}, {2,5}, {10,15}, {3,36}, {21,40}, {30,43}, {27,38}, {23,43}, {10,31}, {37,41}, {20,42}, {28,45}, {7,10}, {19,36}, {11,32}, {21,34}, {18,29}, {17,30}, {1,7}, {18,32}, {5,21}, {14,28}, {22,39}, {16,28}, {39,43}, {17,31}, {13,25}, {24,34}, {12,36}, {23,35}, {20,44}, {32,45}, {19,45}, {33,44}, {9,30}, {9,42}, {5,36}, {6,34}, {20,27}, {11,13}, {2,34}, {19,41}, {29,44}, {21,43}, {31,43}, {8,28}, {7,41}, {18,38}, {5,16}, {15,43}, {19,25}, {14,44}, {22,25}, {23,27}, {9,31}, {24,26}, {7,33}, {20,40}, {36,40}, {23,30}, {24,43}, {12,31}, {9,14}, {35,38}, {26,30}, {27,29}, {8,37}, {18,41}, {18,40}, {5,30}, {15,38}, {3,16}, {7,38}, {12,45}, {33,35}, {2,17}, {10,44}, {32,36}, {42,43}, {6,27}, {3,23}, {10,27}, {36,37}, {7,20}, {40,45}, {6,7}, {13,36}, {11,26}, {15,34}, {18,23}, {17,24}, {7,14}, {21,32}, {9,39}, {16,22}, {19,31}, {13,29}, {12,24}, {22,36}, {11,23}, {6,44}, {32,38}, {33,39}, {5,29}, {6,28}, {11,43}, {31,34}, {8,19}, {41,44}, {4,43}, {31,37}, {8,32}, {21,41}, {12,15}, {20,22}, {21,23}, {28,31}, {19,24}, {30,33}, {9,20}, {38,40}, {16,30}, {3,24}, {2,22}, {14,35}, {20,32}, {29,32}, {21,36}, {11,33}, {20,34}, {15,19}, {3,44}, {14,21}, {29,40}, {8,30}, {13,20}, {30,41}, {9,29}, {24,37}, {21,45}, {26,29}, {30,34}, {7,23}, {13,45}, {2,33}, {1,32}, {28,42}, {6,39}, {3,45}, {27,33}, {26,31}, {24,28}, {2,14}, {9,24}, {22,29}, {12,35}, {10,22}, {11,36}, {6,21}, {38,43}, {39,45}, {29,34}, {8,40}, {4,19}, {37,44}, {12,44}, {20,26}, {21,25}, {7,28}, {9,41}, {2,43}, {17,20}, {15,36}, {19,35}, {22,44}, {29,43}, {8,31}, {30,45}, {9,33}, {7,37}, {4,45}, {16,19}, {10,34}, {7,32}, {24,36}, {22,35}, {17,33}, {23,34}, {42,45}, {28,33}, {19,23}, {13,44}, {22,45}, {18,28}, {2,8}, {31,45}, {19,44}, {32,44}, {23,26}, {24,25}, {15,20}, {29,31}, {16,32}, {10,24}, {19,33}, {29,42}, {7,29}, {20,24}, {31,38}, {20,35} } Symmetric graph 32 of order 45 Valency 24 Diameter 2 Girth 3 Automorphism group of order 338533188894720 Number of arcs = 1080 Number of 2-arcs = 24840 2-arc-transitive false Edge-set { {1,4}, {12,45}, {5,30}, {12,13}, {32,34}, {26,32}, {9,20}, {11,16}, {28,42}, {14,38}, {1,34}, {11,32}, {20,24}, {30,40}, {20,45}, {42,43}, {17,20}, {35,42}, {22,26}, {7,14}, {16,30}, {13,35}, {33,35}, {21,27}, {3,41}, {4,39}, {3,8}, {10,22}, {2,22}, {40,45}, {5,45}, {12,43}, {30,35}, {20,33}, {21,42}, {26,39}, {30,33}, {16,19}, {1,42}, {6,38}, {14,26}, {9,30}, {3,27}, {4,8}, {14,36}, {25,30}, {20,42}, {3,43}, {4,44}, {5,37}, {17,39}, {31,35}, {3,24}, {8,10}, {18,22}, {13,16}, {27,38}, {11,43}, {24,44}, {21,43}, {41,44}, {6,27}, {15,18}, {28,36}, {2,6}, {5,11}, {7,12}, {23,30}, {1,13}, {23,43}, {6,9}, {11,17}, {36,37}, {31,39}, {19,31}, {37,44}, {10,31}, {19,32}, {1,26}, {26,28}, {9,14}, {33,34}, {27,32}, {8,20}, {16,42}, {38,44}, {14,21}, {30,41}, {20,27}, {3,15}, {4,28}, {5,7}, {17,23}, {1,35}, {16,28}, {38,41}, {13,25}, {27,29}, {3,5}, {4,12}, {22,29}, {2,15}, {10,17}, {22,35}, {16,22}, {7,42}, {16,38}, {6,43}, {6,18}, {11,36}, {12,23}, {13,17}, {10,44}, {22,45}, {4,16}, {34,38}, {20,26}, {3,14}, {4,30}, {33,43}, {8,11}, {12,31}, {7,13}, {9,11}, {24,28}, {23,36}, {1,25}, {29,42}, {19,43}, {40,44}, {39,43}, {11,33}, {9,31}, {17,19}, {15,37}, {34,39}, {26,31}, {11,35}, {24,27}, {6,8}, {2,36}, {27,33}, {8,21}, {25,38}, {7,33}, {15,27}, {8,28}, {21,31}, {2,25}, {6,10}, {18,29}, {15,36}, {12,34}, {23,26}, {17,41}, {39,45}, {4,29}, {10,15}, {28,33}, {24,34}, {8,32}, {18,20}, {37,42}, {32,38}, {1,45}, {12,24}, {33,38}, {27,37}, {7,29}, {15,16}, {14,35}, {33,36}, {21,25}, {9,41}, {3,45}, {19,23}, {1,40}, {25,29}, {13,19}, {29,40}, {24,25}, {3,7}, {29,36}, {19,40}, {13,20}, {5,17}, {12,35}, {35,39}, {3,22}, {7,10}, {28,40}, {21,45}, {41,43}, {6,30}, {36,42}, {17,30}, {3,35}, {4,27}, {8,31}, {22,25}, {2,7}, {22,28}, {16,21}, {2,42}, {5,38}, {6,26}, {14,18}, {30,36}, {2,43}, {6,12}, {11,23}, {12,17}, {13,39}, {11,24}, {25,32}, {42,45}, {5,43}, {12,44}, {35,41}, {27,39}, {2,5}, {18,40}, {6,28}, {11,14}, {30,32}, {18,37}, {39,40}, {31,37}, {2,44}, {10,23}, {31,36}, {19,25}, {31,44}, {13,37}, {27,31}, {4,18}, {8,13}, {2,27}, {10,33}, {8,15}, {29,34}, {15,26}, {33,44}, {32,37}, {20,32}, {1,14}, {25,31}, {7,19}, {13,27}, {8,40}, {5,26}, {14,17}, {11,22}, {12,16}, {30,42}, {13,38}, {8,41}, {23,35}, {9,33}, {17,21}, {20,40}, {1,24}, {18,24}, {33,39}, {32,45}, {4,45}, {5,16}, {3,40}, {4,37}, {25,33}, {8,29}, {6,7}, {23,27}, {1,8}, {28,35}, {21,33}, {21,41}, {16,40}, {14,25}, {13,36}, {2,9}, {3,23}, {7,40}, {23,45}, {1,43}, {5,29}, {35,40}, {21,44}, {6,39}, {18,38}, {9,29}, {15,17}, {10,45}, {18,21}, {36,41}, {9,15}, {17,28}, {2,34}, {18,41}, {12,18}, {15,19}, {10,34}, {10,36}, {29,31}, {34,40}, {26,37}, {2,41}, {20,43}, {17,37}, {32,35}, {5,25}, {7,32}, {1,9}, {39,41}, {38,45}, {17,42}, {14,34}, {26,30}, {3,4}, {8,30}, {20,22}, {9,12}, {21,22}, {3,36}, {2,13}, {3,42}, {10,43}, {22,44}, {28,41}, {41,45}, {28,34}, {32,43}, {29,32}, {19,45}, {1,5}, {34,37}, {11,13}, {24,29}, {18,19}, {6,37}, {24,43}, {11,18}, {37,45}, {6,29}, {24,30}, {34,42}, {20,44}, {1,44}, {37,43}, {11,31}, {24,36}, {1,41}, {9,28}, {5,8}, {10,16}, {15,38}, {20,41}, {3,44}, {14,16}, {11,44}, {18,30}, {23,29}, {9,19}, {17,40}, {16,39}, {31,34}, {10,18}, {15,35}, {27,28}, {4,10}, {2,14}, {5,10}, {17,29}, {16,41}, {42,44}, {15,20}, {35,38}, {33,37}, {21,32}, {32,36}, {20,25}, {1,7}, {16,20}, {3,26}, {4,9}, {8,14}, {7,20}, {5,44}, {18,23}, {1,36}, {10,14}, {29,41}, {15,39}, {38,42}, {1,23}, {1,6}, {19,24}, {4,25}, {36,38}, {19,44}, {36,40}, {12,15}, {30,34}, {13,26}, {17,24}, {6,44}, {19,41}, {2,23}, {28,31}, {7,41}, {14,20}, {12,22}, {6,17}, {35,37}, {13,34}, {4,38}, {2,24}, {21,23}, {32,44}, {7,21}, {14,27}, {25,28}, {19,26}, {12,33}, {26,33}, {7,28}, {9,42}, {12,32}, {9,13}, {6,11}, {3,13}, {34,41}, {9,40}, {10,24}, {5,9}, {39,44}, {15,21}, {5,28}, {22,34}, {24,45}, {4,7}, {38,43}, {9,32}, {33,45}, {5,27}, {8,12}, {14,37}, {19,42}, {15,25}, {1,15}, {2,26}, {16,37}, {12,36}, {23,25}, {15,34}, {16,23}, {25,39}, {31,45}, {37,40}, {2,4}, {3,25}, {4,11}, {18,42}, {22,43}, {17,38}, {14,39}, {30,31}, {11,45}, {3,6}, {8,19}, {7,31}, {5,39}, {8,42}, {12,14}, {21,24}, {18,39}, {38,40}, {26,29}, {9,10}, {8,33}, {21,26}, {24,26}, {3,9}, {4,43}, {7,30}, {29,35}, {19,33}, {21,40}, {5,12}, {17,22}, {19,27}, {2,8}, {31,43}, {6,25}, {7,11}, {10,35}, {22,27}, {26,38}, {16,29}, {14,19}, {1,27}, {40,43}, {23,44}, {36,39}, {25,37}, {13,21}, {2,35}, {20,31}, {27,30}, {4,26}, {19,22}, {2,40}, {29,33}, {2,45}, {6,45}, {20,23}, {24,35}, {7,15}, {10,32}, {5,18}, {22,30}, {32,39}, {28,32}, {18,28}, {22,36}, {4,17}, {1,22}, {16,24}, {6,16}, {31,38}, {23,28}, {13,18}, {23,34}, {10,13}, {11,34}, {3,34}, {9,21}, {11,15}, {37,41}, {39,42} } Symmetric graph 33 of order 45 Valency 24 Diameter 2 Girth 3 Automorphism group of order 338533188894720 Number of arcs = 1080 Number of 2-arcs = 24840 2-arc-transitive false Edge-set { {1,4}, {19,41}, {3,35}, {6,13}, {32,45}, {16,42}, {2,6}, {3,21}, {26,34}, {9,45}, {21,40}, {4,22}, {12,43}, {1,34}, {14,42}, {2,31}, {10,17}, {5,14}, {9,29}, {7,40}, {31,44}, {19,27}, {29,35}, {7,35}, {17,41}, {3,5}, {27,43}, {40,44}, {1,20}, {23,36}, {11,16}, {27,36}, {29,38}, {7,23}, {5,28}, {8,44}, {20,42}, {12,13}, {15,32}, {16,38}, {6,23}, {16,28}, {6,8}, {11,45}, {2,36}, {7,12}, {15,41}, {5,8}, {42,44}, {3,33}, {18,25}, {4,30}, {22,34}, {12,18}, {4,15}, {32,38}, {23,39}, {25,28}, {8,30}, {20,39}, {22,36}, {9,42}, {33,43}, {17,26}, {2,45}, {21,25}, {22,32}, {12,39}, {30,34}, {22,39}, {12,22}, {21,30}, {9,34}, {18,40}, {28,35}, {8,17}, {25,45}, {20,30}, {9,36}, {4,8}, {42,43}, {2,19}, {11,24}, {10,13}, {19,37}, {24,35}, {17,27}, {5,29}, {25,35}, {21,39}, {25,33}, {30,37}, {11,39}, {13,22}, {9,24}, {15,33}, {33,37}, {18,27}, {4,29}, {7,43}, {10,23}, {11,14}, {9,40}, {1,40}, {13,31}, {27,45}, {21,29}, {33,35}, {17,37}, {5,24}, {27,33}, {29,37}, {27,35}, {17,29}, {14,37}, {24,31}, {5,7}, {10,44}, {16,39}, {6,22}, {23,30}, {9,11}, {13,40}, {15,37}, {24,33}, {18,29}, {4,7}, {19,30}, {9,35}, {41,43}, {1,32}, {18,28}, {3,36}, {16,26}, {6,28}, {12,23}, {11,15}, {20,38}, {14,33}, {31,37}, {11,43}, {13,19}, {24,38}, {33,34}, {18,37}, {3,27}, {26,29}, {7,28}, {2,43}, {19,25}, {31,43}, {19,38}, {12,24}, {10,15}, {23,35}, {8,41}, {25,36}, {16,30}, {7,44}, {5,41}, {3,44}, {20,26}, {9,12}, {15,40}, {14,38}, {23,31}, {16,43}, {6,19}, {11,38}, {28,36}, {15,19}, {31,38}, {23,38}, {12,16}, {6,15}, {11,23}, {1,31}, {27,38}, {26,44}, {20,28}, {8,36}, {22,33}, {12,37}, {21,27}, {29,34}, {25,37}, {24,30}, {7,18}, {25,38}, {26,43}, {19,28}, {8,35}, {13,37}, {24,32}, {16,29}, {6,7}, {41,45}, {24,39}, {10,22}, {18,42}, {2,4}, {12,14}, {17,30}, {2,34}, {33,39}, {1,43}, {7,34}, {18,41}, {3,13}, {26,32}, {28,39}, {17,43}, {5,19}, {10,38}, {12,42}, {2,15}, {14,23}, {8,22}, {1,41}, {11,13}, {13,32}, {20,41}, {32,39}, {26,35}, {17,28}, {16,25}, {6,30}, {11,18}, {4,13}, {22,37}, {8,28}, {8,42}, {6,20}, {36,45}, {2,42}, {7,17}, {2,5}, {25,44}, {27,39}, {7,22}, {12,41}, {13,21}, {32,34}, {18,39}, {2,13}, {25,32}, {32,44}, {30,39}, {22,35}, {12,17}, {2,21}, {25,34}, {18,30}, {41,44}, {3,20}, {12,32}, {15,39}, {8,10}, {4,9}, {19,29}, {31,35}, {17,38}, {15,31}, {5,23}, {11,31}, {13,38}, {26,37}, {24,28}, {11,32}, {13,39}, {7,10}, {14,41}, {6,9}, {3,31}, {26,38}, {26,45}, {21,28}, {22,38}, {8,34}, {40,45}, {26,33}, {28,37}, {4,24}, {10,43}, {19,40}, {1,35}, {23,37}, {17,40}, {1,5}, {7,41}, {3,41}, {6,24}, {10,45}, {3,42}, {2,26}, {14,21}, {11,41}, {13,20}, {32,36}, {4,35}, {2,40}, {1,25}, {27,30}, {6,41}, {3,45}, {3,34}, {18,26}, {21,26}, {33,45}, {21,37}, {10,16}, {6,14}, {11,22}, {24,34}, {10,18}, {3,19}, {27,31}, {9,22}, {9,43}, {15,21}, {9,18}, {4,40}, {23,28}, {8,11}, {20,40}, {1,36}, {13,42}, {12,33}, {27,28}, {8,29}, {6,35}, {17,45}, {3,14}, {26,31}, {5,21}, {10,37}, {3,40}, {1,26}, {8,45}, {21,42}, {24,37}, {16,27}, {6,29}, {11,17}, {14,40}, {5,13}, {10,24}, {42,45}, {15,42}, {2,33}, {35,45}, {17,21}, {30,36}, {9,16}, {23,32}, {16,44}, {2,44}, {20,25}, {34,44}, {18,20}, {3,32}, {26,39}, {10,31}, {22,28}, {34,45}, {18,21}, {8,16}, {1,6}, {2,20}, {10,32}, {14,39}, {9,10}, {22,31}, {27,32}, {29,39}, {5,9}, {14,19}, {31,39}, {19,26}, {7,36}, {16,41}, {3,6}, {25,31}, {30,38}, {11,44}, {6,42}, {28,34}, {16,40}, {4,42}, {10,40}, {1,14}, {6,34}, {18,45}, {3,15}, {4,21}, {16,19}, {5,40}, {1,44}, {15,24}, {6,21}, {17,42}, {10,14}, {14,31}, {1,21}, {27,34}, {24,36}, {2,32}, {12,44}, {15,20}, {27,29}, {7,29}, {2,14}, {24,29}, {35,44}, {25,39}, {22,30}, {5,15}, {33,44}, {3,4}, {35,43}, {17,19}, {15,22}, {9,23}, {16,21}, {11,40}, {1,42}, {2,27}, {14,20}, {31,36}, {5,42}, {10,41}, {9,30}, {4,14}, {28,38}, {12,15}, {21,38}, {23,34}, {27,44}, {26,36}, {40,43}, {25,43}, {1,19}, {6,40}, {22,29}, {8,40}, {13,33}, {10,33}, {36,44}, {16,20}, {9,17}, {14,24}, {21,41}, {1,33}, {27,37}, {29,36}, {7,16}, {20,29}, {12,45}, {33,38}, {1,13}, {20,37}, {14,32}, {32,37}, {34,43}, {17,39}, {5,22}, {4,19}, {5,36}, {5,34}, {2,25}, {5,20}, {31,34}, {4,23}, {20,27}, {4,28}, {12,38}, {15,23}, {8,23}, {1,27}, {11,33}, {8,43}, {19,42}, {2,35}, {13,23}, {25,29}, {7,30}, {14,22}, {12,31}, {18,44}, {4,41}, {3,43}, {12,40}, {1,15}, {4,20}, {36,43}, {6,36}, {16,45}, {7,24}, {17,25}, {5,30}, {8,12}, {7,11}, {13,41}, {23,29}, {9,44}, {8,18}, {31,45}, {15,38}, {18,38}, {23,33}, {32,43}, {19,39}, {3,26}, {1,45}, {11,37}, {32,35}, {4,36}, {17,20}, {33,36}, {17,44}, {30,35}, {25,30}, {18,19}, {9,41}, {3,25}, {26,30}, {8,24}, {10,42}, {7,42}, {2,41}, {5,35}, {4,34}, {26,28}, {10,39}, {7,45}, {18,43}, {11,42}, {16,37}, {13,24}, {9,28} } Symmetric graph 34 of order 45 Valency 28 Diameter 2 Girth 3 Automorphism group of order 3628800 Number of arcs = 1260 Number of 2-arcs = 34020 2-arc-transitive false Edge-set { {1,3}, {2,6}, {3,9}, {4,10}, {6,14}, {3,14}, {7,15}, {2,15}, {9,19}, {10,20}, {6,19}, {3,20}, {10,12}, {11,21}, {3,12}, {4,21}, {1,14}, {14,25}, {15,26}, {15,27}, {1,9}, {10,25}, {6,26}, {3,27}, {15,17}, {16,28}, {6,17}, {3,17}, {7,28}, {2,28}, {2,19}, {1,20}, {19,32}, {20,26}, {12,33}, {7,21}, {12,34}, {21,35}, {2,14}, {15,32}, {9,33}, {7,10}, {6,34}, {3,35}, {12,23}, {19,21}, {5,36}, {13,22}, {9,23}, {10,19}, {6,23}, {3,19}, {10,36}, {11,13}, {3,36}, {4,13}, {4,25}, {2,26}, {1,27}, {1,39}, {6,25}, {26,33}, {7,27}, {17,21}, {17,40}, {10,28}, {11,28}, {17,41}, {17,36}, {28,42}, {9,28}, {4,20}, {12,39}, {6,21}, {14,21}, {14,40}, {10,15}, {11,15}, {9,41}, {6,42}, {4,17}, {17,30}, {1,28}, {25,28}, {8,31}, {8,42}, {18,29}, {4,14}, {14,30}, {1,15}, {15,25}, {4,9}, {10,30}, {1,6}, {3,25}, {15,31}, {15,42}, {16,18}, {6,31}, {3,42}, {7,18}, {2,18}, {7,32}, {3,33}, {4,7}, {2,34}, {1,35}, {2,43}, {1,37}, {9,32}, {10,26}, {21,33}, {7,40}, {10,34}, {11,35}, {23,28}, {19,28}, {23,25}, {19,33}, {15,36}, {13,15}, {16,36}, {13,16}, {23,27}, {19,34}, {23,31}, {19,42}, {20,36}, {13,44}, {14,36}, {13,14}, {7,26}, {2,27}, {17,43}, {17,37}, {20,28}, {19,25}, {20,33}, {12,15}, {15,21}, {12,16}, {16,21}, {14,27}, {14,34}, {9,20}, {10,44}, {7,23}, {23,35}, {2,36}, {1,13}, {32,36}, {13,26}, {13,38}, {5,38}, {13,20}, {5,44}, {24,37}, {7,19}, {2,20}, {19,35}, {20,32}, {2,12}, {1,21}, {12,32}, {21,26}, {7,14}, {15,35}, {2,9}, {1,10}, {6,32}, {3,26}, {12,38}, {21,38}, {12,20}, {21,44}, {5,24}, {22,23}, {9,38}, {10,38}, {6,20}, {3,44}, {10,24}, {11,23}, {3,24}, {4,23}, {10,39}, {6,11}, {3,40}, {2,11}, {3,41}, {4,36}, {2,42}, {3,45}, {4,45}, {2,30}, {14,39}, {15,33}, {21,28}, {28,40}, {11,33}, {15,41}, {16,42}, {9,16}, {13,30}, {1,36}, {13,25}, {4,32}, {26,30}, {25,40}, {12,31}, {21,42}, {12,18}, {18,21}, {5,31}, {22,42}, {5,18}, {18,22}, {4,34}, {30,35}, {1,41}, {25,36}, {4,38}, {30,38}, {25,44}, {26,31}, {27,42}, {18,41}, {19,31}, {20,42}, {18,19}, {18,20}, {10,33}, {7,11}, {3,34}, {4,35}, {23,45}, {19,45}, {23,30}, {19,39}, {26,36}, {13,27}, {1,32}, {25,26}, {27,40}, {12,17}, {12,28}, {5,17}, {17,22}, {5,28}, {22,28}, {20,35}, {19,41}, {14,26}, {15,22}, {11,30}, {4,42}, {9,30}, {3,31}, {1,18}, {31,39}, {18,33}, {18,40}, {18,43}, {8,40}, {8,43}, {18,26}, {18,27}, {8,22}, {8,41}, {11,25}, {4,27}, {1,42}, {9,25}, {26,39}, {6,27}, {17,39}, {28,33}, {11,20}, {12,42}, {9,21}, {9,39}, {6,10}, {6,33}, {3,7}, {28,43}, {17,26}, {17,27}, {28,41}, {8,11}, {4,29}, {29,30}, {14,43}, {15,40}, {15,43}, {9,26}, {10,27}, {6,22}, {4,16}, {16,30}, {15,37}, {10,16}, {3,16}, {7,31}, {4,44}, {6,44}, {7,44}, {2,24}, {19,43}, {20,37}, {12,21}, {21,40}, {28,36}, {13,28}, {13,33}, {16,40}, {12,27}, {21,34}, {5,20}, {22,44}, {5,14}, {14,22}, {18,35}, {18,32}, {2,31}, {7,39}, {33,35}, {25,32}, {17,38}, {28,44}, {17,24}, {17,23}, {24,28}, {8,38}, {20,29}, {29,44}, {8,24}, {8,23}, {24,29}, {23,29}, {7,41}, {35,42}, {1,34}, {31,32}, {26,42}, {35,40}, {32,43}, {22,32}, {26,41}, {33,38}, {7,38}, {20,34}, {35,44}, {24,27}, {23,34}, {1,38}, {25,38}, {27,44}, {1,24}, {24,26}, {11,16}, {6,41}, {7,42}, {24,30}, {1,44}, {24,25}, {30,32}, {1,43}, {25,37}, {31,33}, {18,34}, {2,39}, {32,33}, {25,34}, {17,19}, {13,17}, {8,19}, {19,29}, {8,36}, {8,13}, {29,36}, {13,29}, {9,27}, {7,20}, {12,29}, {21,29}, {16,35}, {16,32}, {2,44}, {14,35}, {14,32}, {6,38}, {3,38}, {1,23}, {38,43}, {37,38}, {21,24}, {23,40}, {23,33}, {24,45}, {5,33}, {13,45}, {5,45}, {24,33}, {24,34}, {5,29}, {5,34}, {16,26}, {7,34}, {2,35}, {33,43}, {7,37}, {9,34}, {10,35}, {23,43}, {19,37}, {21,36}, {13,40}, {16,27}, {17,20}, {17,44}, {14,28}, {14,37}, {9,15}, {10,40}, {3,11}, {36,45}, {27,36}, {13,34}, {5,16}, {35,37}, {20,45}, {12,25}, {12,45}, {21,45}, {14,33}, {15,34}, {9,29}, {10,29}, {5,7}, {2,22}, {5,35}, {12,30}, {21,39}, {5,15}, {5,6}, {3,22}, {11,38}, {7,22}, {2,41}, {9,22}, {10,41}, {10,22}, {11,41}, {4,31}, {1,45}, {25,45}, {27,39}, {17,28}, {31,36}, {13,42}, {18,36}, {13,18}, {5,25}, {22,33}, {17,34}, {17,35}, {8,26}, {8,27}, {22,29}, {29,41}, {8,20}, {24,42}, {24,39}, {10,43}, {11,37}, {9,40}, {32,39}, {22,36}, {13,41}, {19,30}, {11,36}, {13,31}, {5,43}, {26,37}, {22,37}, {12,41}, {5,30}, {4,37}, {11,34}, {9,44}, {38,39}, {25,42}, {39,45}, {6,45}, {29,39}, {6,29}, {27,33}, {40,43}, {11,43}, {31,35}, {4,41}, {30,36}, {2,40}, {32,40}, {26,43}, {22,34}, {35,41}, {1,31}, {16,22}, {11,44}, {11,32}, {35,39}, {2,45}, {38,40}, {24,41}, {23,36}, {3,43}, {6,40}, {32,41}, {18,23}, {5,42}, {31,37}, {18,37}, {11,27}, {28,37}, {5,39}, {2,4}, {1,30}, {40,45}, {43,45}, {30,40}, {39,43}, {28,31}, {30,33}, {24,31}, {8,21}, {18,44}, {18,24}, {8,44}, {31,40}, {8,37}, {8,12}, {11,39}, {14,41}, {30,45}, {25,39}, {18,25}, {22,35}, {23,26}, {19,27}, {19,36}, {20,39}, {12,14}, {6,16}, {31,44}, {31,34}, {5,8}, {30,42}, {26,44}, {17,32}, {20,40}, {8,10}, {3,29}, {8,9}, {16,43}, {11,29}, {14,29}, {15,29}, {16,34}, {2,38}, {32,44}, {34,43}, {13,19}, {31,38}, {38,42}, {23,42}, {8,32}, {29,40}, {23,41}, {29,37}, {27,37}, {5,27}, {15,45}, {16,39}, {6,37}, {29,31}, {29,42}, {16,31}, {18,38}, {8,45}, {8,35}, {7,30}, {16,41}, {37,43}, {43,44}, {12,37}, {9,37}, {33,45}, {16,45}, {32,42}, {4,33}, {7,45}, {42,43}, {4,24}, {23,39}, {13,39}, {44,45}, {25,35}, {37,45}, {36,38}, {22,24}, {11,24}, {5,41}, {16,37}, {24,32}, {5,9}, {22,38}, {38,41}, {22,45}, {4,43}, {22,39}, {41,45}, {30,44}, {30,34}, {30,37}, {8,34}, {12,44}, {24,40}, {8,14}, {29,43} } Symmetric graph 35 of order 45 Valency 28 Diameter 2 Girth 3 Automorphism group of order 7846046208000 Number of arcs = 1260 Number of 2-arcs = 34020 2-arc-transitive false Edge-set { {1,5}, {20,23}, {8,28}, {27,32}, {4,25}, {5,8}, {15,39}, {18,36}, {33,34}, {21,35}, {9,36}, {5,20}, {8,39}, {3,13}, {23,42}, {40,43}, {16,19}, {17,45}, {17,31}, {33,44}, {18,26}, {4,43}, {16,37}, {20,32}, {8,25}, {5,13}, {23,39}, {2,22}, {30,40}, {27,30}, {3,4}, {29,39}, {2,12}, {31,42}, {21,27}, {38,41}, {11,20}, {16,41}, {17,37}, {10,31}, {34,40}, {19,35}, {21,39}, {9,12}, {14,42}, {21,22}, {18,32}, {25,33}, {5,35}, {36,39}, {2,20}, {8,40}, {13,27}, {4,23}, {24,25}, {6,29}, {9,29}, {2,13}, {13,34}, {9,30}, {7,13}, {14,23}, {11,24}, {29,45}, {16,30}, {3,32}, {33,36}, {26,34}, {15,28}, {1,24}, {10,32}, {25,44}, {28,42}, {1,21}, {14,41}, {20,22}, {12,16}, {32,43}, {2,17}, {31,44}, {18,27}, {13,33}, {23,26}, {4,11}, {37,45}, {1,30}, {3,41}, {6,26}, {18,40}, {19,33}, {17,35}, {31,36}, {20,44}, {8,18}, {13,43}, {16,23}, {24,32}, {25,29}, {5,29}, {2,39}, {2,36}, {4,9}, {26,35}, {5,36}, {7,19}, {7,14}, {4,7}, {14,37}, {2,24}, {29,40}, {2,45}, {17,40}, {13,37}, {2,6}, {38,40}, {1,27}, {4,41}, {10,26}, {5,44}, {7,38}, {11,14}, {9,42}, {13,21}, {18,22}, {30,33}, {17,43}, {16,31}, {34,45}, {3,8}, {15,42}, {5,28}, {12,18}, {33,43}, {35,37}, {10,36}, {8,30}, {3,15}, {23,33}, {26,28}, {1,28}, {1,41}, {25,32}, {6,25}, {11,42}, {21,45}, {18,39}, {12,33}, {24,41}, {20,29}, {36,40}, {19,34}, {31,40}, {27,34}, {4,35}, {10,21}, {9,44}, {14,38}, {11,22}, {9,23}, {13,28}, {22,28}, {7,35}, {2,19}, {27,31}, {41,44}, {18,20}, {16,43}, {16,32}, {32,37}, {10,25}, {5,40}, {19,39}, {12,40}, {27,42}, {4,21}, {5,33}, {14,36}, {7,20}, {8,14}, {13,24}, {23,29}, {24,43}, {16,29}, {9,37}, {34,44}, {18,35}, {20,43}, {8,16}, {6,31}, {27,38}, {1,6}, {6,21}, {9,38}, {1,14}, {22,41}, {24,26}, {7,29}, {2,14}, {24,38}, {11,29}, {29,41}, {22,40}, {19,24}, {15,29}, {23,36}, {28,34}, {21,28}, {1,9}, {12,34}, {35,43}, {20,37}, {8,10}, {6,15}, {1,10}, {4,30}, {3,37}, {2,33}, {26,40}, {25,40}, {6,19}, {9,17}, {13,31}, {39,41}, {12,20}, {16,42}, {21,32}, {38,45}, {11,17}, {5,22}, {30,39}, {3,30}, {3,42}, {8,20}, {8,15}, {11,40}, {19,45}, {17,39}, {12,31}, {14,44}, {12,43}, {5,9}, {13,39}, {3,22}, {30,42}, {17,27}, {4,31}, {8,34}, {15,35}, {8,23}, {23,28}, {7,36}, {10,30}, {3,44}, {33,38}, {11,26}, {13,40}, {19,23}, {31,45}, {7,32}, {14,25}, {29,43}, {2,16}, {2,32}, {36,45}, {17,34}, {21,44}, {9,18}, {26,43}, {4,37}, {10,37}, {1,15}, {6,44}, {4,27}, {2,8}, {15,40}, {18,38}, {24,31}, {27,29}, {16,36}, {32,34}, {28,37}, {32,40}, {19,25}, {39,42}, {12,21}, {18,42}, {21,33}, {14,18}, {22,33}, {12,35}, {36,43}, {23,27}, {30,36}, {3,34}, {9,26}, {17,20}, {8,31}, {1,43}, {6,32}, {25,38}, {2,26}, {7,27}, {4,14}, {26,39}, {5,12}, {7,42}, {14,21}, {22,37}, {10,17}, {40,44}, {18,19}, {32,39}, {12,25}, {5,42}, {15,36}, {24,34}, {7,28}, {7,26}, {4,15}, {24,37}, {1,23}, {28,41}, {25,28}, {6,7}, {15,26}, {5,24}, {7,10}, {26,31}, {5,27}, {3,7}, {27,43}, {4,16}, {8,45}, {15,17}, {8,33}, {11,45}, {39,44}, {14,32}, {22,25}, {39,43}, {3,19}, {12,23}, {28,43}, {9,21}, {9,13}, {14,22}, {22,30}, {17,24}, {29,31}, {29,34}, {2,35}, {29,35}, {19,31}, {11,32}, {25,45}, {3,21}, {18,33}, {26,33}, {15,38}, {10,41}, {20,25}, {6,8}, {13,23}, {9,22}, {13,30}, {5,32}, {25,39}, {3,5}, {10,29}, {2,44}, {31,38}, {11,27}, {13,41}, {11,16}, {32,45}, {1,37}, {11,39}, {12,45}, {4,20}, {8,37}, {23,40}, {6,30}, {36,41}, {20,34}, {16,21}, {9,32}, {5,45}, {4,39}, {8,27}, {6,43}, {16,38}, {10,34}, {35,44}, {2,29}, {2,40}, {6,18}, {1,35}, {7,39}, {12,14}, {24,42}, {21,29}, {18,24}, {29,33}, {38,43}, {41,45}, {33,37}, {4,40}, {19,37}, {34,39}, {22,43}, {3,23}, {21,36}, {9,34}, {3,29}, {2,42}, {16,26}, {14,34}, {42,43}, {18,45}, {17,33}, {15,22}, {18,29}, {31,35}, {27,36}, {11,33}, {26,45}, {1,40}, {19,41}, {17,25}, {11,44}, {4,34}, {9,43}, {13,16}, {22,45}, {17,30}, {32,41}, {5,16}, {12,28}, {7,33}, {24,36}, {6,36}, {34,38}, {9,41}, {23,35}, {3,38}, {1,33}, {26,41}, {6,22}, {12,41}, {29,37}, {2,10}, {19,27}, {13,18}, {11,35}, {20,30}, {3,43}, {5,17}, {6,34}, {35,38}, {14,26}, {4,28}, {8,35}, {35,42}, {20,26}, {6,12}, {16,34}, {32,35}, {20,36}, {30,38}, {21,42}, {5,38}, {20,42}, {31,39}, {10,38}, {10,23}, {1,18}, {33,41}, {25,35}, {22,31}, {4,45}, {12,15}, {4,33}, {26,37}, {2,4}, {37,40}, {1,25}, {6,41}, {9,25}, {6,13}, {7,16}, {7,45}, {14,17}, {24,44}, {7,44}, {10,18}, {11,36}, {26,30}, {25,36}, {5,19}, {2,27}, {6,37}, {2,9}, {13,35}, {7,12}, {14,43}, {15,16}, {2,28}, {10,42}, {10,13}, {23,44}, {11,38}, {5,14}, {22,39}, {9,19}, {1,16}, {33,42}, {21,26}, {4,18}, {20,38}, {8,11}, {21,24}, {37,44}, {7,24}, {14,29}, {24,29}, {19,40}, {18,28}, {23,38}, {1,11}, {7,17}, {14,31}, {12,24}, {28,38}, {22,27}, {13,45}, {17,23}, {7,22}, {14,30}, {24,30}, {34,42}, {1,45}, {17,41}, {3,12}, {11,19}, {20,31}, {3,25}, {6,42}, {7,40}, {14,19}, {16,44}, {28,31}, {35,41}, {10,44}, {12,37}, {21,40}, {6,11}, {13,20}, {8,21}, {15,45}, {6,17}, {19,43}, {27,44}, {11,28}, {18,44}, {13,25}, {12,30}, {20,41}, {15,44}, {1,34}, {9,15}, {30,44}, {3,18}, {42,45}, {17,21}, {16,25}, {3,26}, {15,20}, {8,24}, {30,32}, {23,32}, {12,27}, {19,28}, {17,28}, {1,31}, {21,38}, {9,11}, {3,11}, {9,31}, {22,35}, {28,36}, {1,7}, {36,37}, {6,38}, {5,10}, {10,43}, {4,24}, {1,39}, {27,37}, {4,10}, {10,15}, {1,20}, {8,41}, {6,23}, {3,31}, {15,32}, {5,26}, {10,22}, {15,19}, {15,27}, {28,44}, {15,24}, {2,38}, {27,41}, {30,45}, {3,17}, {19,30}, {37,42}, {10,19}, {28,32}, {23,45}, {22,34}, {30,35}, {25,42}, {5,39}, {15,33}, {8,43}, {16,22}, {12,39}, {3,36}, {11,13} } Symmetric graph 36 of order 45 Valency 30 Diameter 2 Girth 3 Automorphism group of order 13416835151120242560510984192000000000 Number of arcs = 1350 Number of 2-arcs = 39150 2-arc-transitive false Edge-set { {1,4}, {37,42}, {31,45}, {30,32}, {23,35}, {17,24}, {21,25}, {21,22}, {13,27}, {8,14}, {12,16}, {15,34}, {18,39}, {11,45}, {11,13}, {4,17}, {5,44}, {2,8}, {6,26}, {7,30}, {1,36}, {4,7}, {9,10}, {29,35}, {22,38}, {3,17}, {21,41}, {3,5}, {8,41}, {34,42}, {39,45}, {16,40}, {19,44}, {26,38}, {41,43}, {3,43}, {13,28}, {9,37}, {11,31}, {25,42}, {28,45}, {2,27}, {29,40}, {8,20}, {12,15}, {34,39}, {33,39}, {4,36}, {39,40}, {33,44}, {26,31}, {30,36}, {7,32}, {10,35}, {17,29}, {33,36}, {34,37}, {5,19}, {28,43}, {3,24}, {18,31}, {20,36}, {20,33}, {27,30}, {23,29}, {25,41}, {32,45}, {1,35}, {17,19}, {14,21}, {38,44}, {2,32}, {10,26}, {6,30}, {9,42}, {7,29}, {10,22}, {22,26}, {29,33}, {22,34}, {16,23}, {19,26}, {24,43}, {3,25}, {9,21}, {22,25}, {27,28}, {12,40}, {20,34}, {15,39}, {9,23}, {11,26}, {10,23}, {18,19}, {14,20}, {18,33}, {24,35}, {25,38}, {6,11}, {21,44}, {2,13}, {15,16}, {17,22}, {21,27}, {8,37}, {12,31}, {12,34}, {5,39}, {16,28}, {19,24}, {27,32}, {2,43}, {3,40}, {13,43}, {20,25}, {15,28}, {17,40}, {20,23}, {15,26}, {7,13}, {10,17}, {14,36}, {16,37}, {12,43}, {15,18}, {18,20}, {1,33}, {11,27}, {4,29}, {13,45}, {1,17}, {2,14}, {7,10}, {6,10}, {9,22}, {14,27}, {16,29}, {3,41}, {12,35}, {5,38}, {6,7}, {8,15}, {12,18}, {1,24}, {11,16}, {4,19}, {8,32}, {13,34}, {17,39}, {11,44}, {2,4}, {26,30}, {23,30}, {1,7}, {10,42}, {22,44}, {19,36}, {14,37}, {5,18}, {18,38}, {20,32}, {33,34}, {10,45}, {1,6}, {9,14}, {10,14}, {6,16}, {4,43}, {3,9}, {5,25}, {8,28}, {2,34}, {6,9}, {7,11}, {23,37}, {1,18}, {20,42}, {4,35}, {9,38}, {6,38}, {3,44}, {2,41}, {15,45}, {5,17}, {8,21}, {31,39}, {2,25}, {28,40}, {40,43}, {6,44}, {2,7}, {15,37}, {1,8}, {12,42}, {24,44}, {4,26}, {9,30}, {38,42}, {3,36}, {37,41}, {5,45}, {5,7}, {8,10}, {29,34}, {22,39}, {3,16}, {19,41}, {21,43}, {3,13}, {13,16}, {25,37}, {28,31}, {35,40}, {9,12}, {5,11}, {7,23}, {28,35}, {24,38}, {6,27}, {2,17}, {21,40}, {31,43}, {2,6}, {7,40}, {36,41}, {37,43}, {18,42}, {20,45}, {27,39}, {40,45}, {1,44}, {14,30}, {7,38}, {10,32}, {27,41}, {29,43}, {28,41}, {35,37}, {31,38}, {6,35}, {8,42}, {12,45}, {24,29}, {16,39}, {19,33}, {32,36}, {34,40}, {39,44}, {4,30}, {38,45}, {1,32}, {14,34}, {16,41}, {19,43}, {28,32}, {26,37}, {30,31}, {35,42}, {42,43}, {3,45}, {13,29}, {9,39}, {11,33}, {23,36}, {25,40}, {28,44}, {2,26}, {30,40}, {7,20}, {10,15}, {36,39}, {33,37}, {5,36}, {11,18}, {4,20}, {8,33}, {30,45}, {1,23}, {14,25}, {1,27}, {29,42}, {41,44}, {8,19}, {12,14}, {18,24}, {34,38}, {32,39}, {4,34}, {38,41}, {32,43}, {25,33}, {28,34}, {9,31}, {11,36}, {18,30}, {32,35}, {35,38}, {6,21}, {29,44}, {2,22}, {17,33}, {21,34}, {19,31}, {25,28}, {24,28}, {27,40}, {31,44}, {2,36}, {15,20}, {8,30}, {12,23}, {24,25}, {26,32}, {30,35}, {21,42}, {29,36}, {22,37}, {5,26}, {7,33}, {10,34}, {19,22}, {17,28}, {21,24}, {27,31}, {31,36}, {36,37}, {5,20}, {30,43}, {3,23}, {13,25}, {18,32}, {20,35}, {21,33}, {27,29}, {22,29}, {26,41}, {33,45}, {1,34}, {16,19}, {14,19}, {38,43}, {3,32}, {10,25}, {6,28}, {9,40}, {9,29}, {11,22}, {23,26}, {3,35}, {6,45}, {17,21}, {13,21}, {16,31}, {37,44}, {2,31}, {15,35}, {12,26}, {5,30}, {7,42}, {7,28}, {10,24}, {22,27}, {24,36}, {18,22}, {20,27}, {23,45}, {1,26}, {7,19}, {24,27}, {25,29}, {11,41}, {21,35}, {13,38}, {8,22}, {12,27}, {12,24}, {16,20}, {15,19}, {17,32}, {23,34}, {26,39}, {4,10}, {19,45}, {1,14}, {14,18}, {16,24}, {19,25}, {11,32}, {21,26}, {13,30}, {16,42}, {22,43}, {3,27}, {12,13}, {9,20}, {11,15}, {17,23}, {23,25}, {26,28}, {10,40}, {19,34}, {14,39}, {4,18}, {9,24}, {11,25}, {11,23}, {18,21}, {13,20}, {16,33}, {22,35}, {27,38}, {6,12}, {20,44}, {2,15}, {15,17}, {7,37}, {10,31}, {12,36}, {5,37}, {18,28}, {20,24}, {27,33}, {2,45}, {1,40}, {14,43}, {15,29}, {17,41}, {8,39}, {12,33}, {11,34}, {4,39}, {4,8}, {16,30}, {19,23}, {25,32}, {1,43}, {3,42}, {13,44}, {14,28}, {18,40}, {9,15}, {13,35}, {17,38}, {10,44}, {14,17}, {16,21}, {3,31}, {12,25}, {5,28}, {15,44}, {2,18}, {1,15}, {8,11}, {4,12}, {8,24}, {13,26}, {17,30}, {2,42}, {10,36}, {6,37}, {5,9}, {7,14}, {10,16}, {3,22}, {12,17}, {5,21}, {7,31}, {15,36}, {18,37}, {1,5}, {11,43}, {3,4}, {8,13}, {13,18}, {17,20}, {2,33}, {10,27}, {6,29}, {9,41}, {14,45}, {1,16}, {3,14}, {7,12}, {5,10}, {7,22}, {15,27}, {18,29}, {1,41}, {11,35}, {4,38}, {6,8}, {2,24}, {6,19}, {9,32}, {25,30}, {23,28}, {1,9}, {11,42}, {23,44}, {19,35}, {14,38}, {6,18}, {21,32}, {31,34}, {26,29}, {22,30}, {26,42}, {3,7}, {10,41}, {22,45}, {21,36}, {13,37}, {5,16}, {20,31}, {33,35}, {4,27}, {5,8}, {8,12}, {24,39}, {2,16}, {19,40}, {6,34}, {7,39}, {4,37}, {1,45}, {1,42}, {14,44}, {4,16}, {9,19}, {32,38}, {3,26}, {30,41}, {42,45}, {5,43}, {3,8}, {13,39}, {2,9}, {11,40}, {23,43}, {6,25}, {37,40}, {39,42}, {4,44}, {4,9}, {9,11}, {23,38}, {3,18}, {20,41}, {5,35}, {8,38}, {6,39}, {2,44}, {2,40}, {15,43}, {6,17}, {7,21}, {31,37}, {1,25}, {28,42}, {40,44}, {15,38}, {12,41}, {24,45}, {21,45}, {1,13}, {14,16}, {27,37}, {29,31}, {35,41}, {5,12}, {7,24}, {20,43}, {3,15}, {13,17}, {25,39}, {28,33}, {36,40}, {4,11}, {8,23}, {42,44}, {26,40}, {30,44}, {30,42}, {36,38}, {32,37}, {5,34}, {7,41}, {10,43}, {22,28}, {17,37}, {21,31}, {31,35}, {36,42}, {37,45}, {5,29}, {39,43}, {3,33}, {13,36}, {30,33}, {29,32}, {34,41}, {41,45}, {27,42}, {29,45}, {29,41}, {35,39}, {33,38}, {6,36}, {8,40}, {12,44}, {24,30}, {16,38}, {19,32}, {32,34}, {4,28}, {1,31}, {14,35}, {11,17}, {4,21}, {8,31}, {2,23}, {15,25}, {10,18}, {6,20}, {9,33}, {1,22}, {14,26}, {16,32}, {33,43}, {3,34}, {13,19}, {9,28}, {11,24}, {23,27}, {25,31}, {28,36}, {20,40}, {30,34}, {23,39}, {4,25}, {21,23}, {20,22}, {26,33}, {17,31}, {32,44}, {2,35}, {15,21}, {8,29}, {12,22}, {24,26}, {19,42}, {24,37}, {5,27}, {39,41}, {4,45}, {38,40}, {6,43}, {22,36}, {18,23}, {20,26}, {10,33}, {19,27}, {14,29}, {18,41}, {11,14}, {10,13}, {16,22}, {24,34}, {12,32}, {15,30}, {17,42}, {9,13}, {3,6}, {2,5}, {7,15} } Symmetric graph 37 of order 45 Valency 32 Diameter 2 Girth 3 Automorphism group of order 51840 Number of arcs = 1440 Number of 2-arcs = 44640 2-arc-transitive false Edge-set { {1,5}, {3,10}, {2,9}, {6,18}, {5,17}, {5,16}, {4,14}, {11,12}, {11,26}, {10,25}, {9,24}, {10,24}, {9,23}, {8,20}, {7,8}, {2,19}, {15,18}, {2,27}, {15,37}, {18,34}, {17,36}, {16,33}, {14,31}, {18,33}, {17,31}, {16,35}, {14,34}, {15,28}, {3,27}, {14,15}, {3,13}, {4,10}, {11,22}, {21,26}, {5,38}, {4,38}, {22,39}, {21,43}, {11,36}, {26,35}, {25,31}, {24,42}, {13,24}, {16,23}, {17,20}, {8,19}, {11,13}, {16,26}, {17,25}, {19,24}, {23,33}, {20,36}, {8,35}, {22,40}, {21,39}, {6,38}, {20,22}, {8,21}, {6,9}, {8,18}, {7,17}, {2,29}, {15,32}, {27,30}, {29,37}, {10,44}, {9,44}, {8,44}, {7,44}, {23,29}, {25,32}, {26,30}, {12,29}, {2,31}, {15,42}, {27,42}, {33,37}, {17,34}, {19,36}, {28,31}, {9,33}, {1,31}, {24,35}, {23,34}, {25,28}, {24,27}, {1,15}, {23,37}, {25,34}, {24,36}, {1,33}, {10,31}, {13,35}, {16,34}, {3,33}, {7,29}, {20,32}, {23,30}, {25,29}, {12,44}, {11,44}, {28,29}, {27,32}, {15,30}, {3,29}, {12,16}, {11,14}, {11,15}, {3,26}, {14,25}, {4,5}, {4,6}, {21,22}, {21,41}, {38,41}, {22,38}, {4,39}, {6,43}, {18,43}, {17,40}, {16,43}, {14,40}, {15,43}, {3,40}, {14,43}, {13,40}, {4,35}, {6,34}, {21,34}, {36,41}, {27,41}, {22,37}, {4,19}, {21,28}, {37,38}, {28,38}, {13,39}, {25,36}, {10,42}, {19,39}, {13,16}, {14,16}, {3,17}, {33,42}, {31,33}, {35,36}, {34,35}, {34,40}, {36,39}, {33,38}, {31,38}, {3,22}, {2,21}, {35,39}, {34,43}, {34,36}, {31,42}, {2,16}, {17,18}, {17,19}, {9,42}, {23,35}, {6,13}, {35,41}, {22,34}, {4,34}, {6,36}, {19,43}, {18,40}, {2,43}, {15,40}, {4,40}, {6,39}, {21,38}, {22,41}, {5,6}, {18,23}, {2,20}, {8,15}, {2,22}, {15,21}, {6,27}, {5,37}, {20,34}, {8,36}, {8,10}, {7,9}, {8,12}, {7,11}, {29,30}, {29,32}, {30,45}, {29,45}, {44,45}, {29,44}, {32,44}, {8,23}, {7,25}, {12,26}, {20,24}, {24,26}, {12,23}, {7,20}, {22,26}, {12,21}, {6,7}, {5,20}, {20,26}, {1,20}, {8,42}, {7,33}, {12,36}, {11,35}, {30,36}, {29,35}, {31,45}, {42,45}, {38,45}, {29,39}, {32,43}, {1,8}, {7,10}, {30,40}, {39,44}, {43,44}, {40,44}, {1,25}, {31,34}, {36,42}, {18,37}, {17,28}, {1,23}, {6,25}, {5,24}, {13,37}, {16,28}, {13,17}, {16,19}, {33,35}, 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{28,42}, {11,39}, {24,39}, {3,35}, {2,34}, {12,34}, {10,33}, {9,31}, {9,39}, {1,43}, {24,40}, {23,39}, {9,25}, {1,24}, {10,23}, {13,42}, {17,35}, {19,34}, {34,37}, {1,40}, {24,43}, {23,40}, {25,43}, {10,40}, {6,11}, {10,21}, {9,41}, {10,41}, {9,22}, {4,8}, {35,37}, {28,34}, {13,34}, {16,36}, {37,42}, {19,42}, {25,39}, {7,34}, {15,36}, {8,39}, {2,15}, {13,32}, {16,30}, {4,31}, {6,42}, {21,42}, {33,41}, {14,42}, {13,33}, {18,19}, {2,37}, {10,27}, {9,37}, {7,18}, {14,29}, {41,43}, {21,32}, {30,41}, {27,36}, {8,38}, {7,38}, {22,29}, {29,41}, {22,32}, {4,30}, {18,44}, {2,44}, {15,44}, {31,40}, {39,42}, {38,42}, {17,22}, {19,21}, {6,37}, {9,20}, {1,22}, {1,21}, {8,45}, {7,45}, {11,32}, {8,30}, {12,45}, {11,45}, {21,45}, {41,45}, {8,26}, {7,12}, {11,20}, {20,45}, {21,33}, {5,35}, {1,42}, {1,38}, {10,38}, {16,39}, {17,38}, {19,38}, {13,38}, {16,38}, {17,39}, {9,38}, {1,41}, {10,22}, {4,11}, {6,26}, {19,20}, {14,38}, {38,40}, {38,39}, {38,43}, {5,39}, {1,17}, {10,19}, {11,37}, {26,28}, {4,28}, 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{26,44}, {2,24}, {1,18}, {10,17}, {2,39}, {27,40}, {8,40}, {7,39}, {9,29}, {1,32}, {24,30}, {10,30}, {39,41}, {15,39}, {3,43}, {9,19}, {30,34}, {9,32}, {27,38}, {1,14}, {10,13}, {20,43}, {21,36}, {9,16}, {5,19}, {4,18}, {16,31}, {3,31}, {17,33}, {26,42}, {12,33}, {6,14}, {5,13}, {11,41}, {4,25}, {6,24}, {4,24}, {6,23}, {7,31}, {20,42}, {2,33}, {3,39}, {22,35}, {32,34}, {3,24}, {2,40}, {27,43}, {18,27}, {7,27}, {12,15}, {3,11}, {5,40}, {8,32}, {7,30}, {12,32}, {11,30}, {15,45}, {2,26}, {26,29}, {20,29}, {39,43}, {40,43}, {39,40}, {3,41}, {6,17}, {19,23}, {18,25}, {20,38}, {5,15}, {3,4}, {14,22}, {13,21}, {17,24}, {5,23}, {3,20}, {14,23}, {13,25}, {4,16}, {2,41}, {18,41}, {23,45}, {25,45}, {5,12}, {10,14}, {14,41}, {38,44}, {9,18}, {30,31}, {29,42}, {16,24}, {1,10}, {9,10}, {8,11}, {7,26}, {28,37}, {13,19}, {16,18}, {12,20}, {1,9}, {8,34}, {11,31}, {8,33}, {11,34}, {14,17}, {5,25}, {32,33}, {5,7}, {26,38}, {19,22}, {18,21}, {2,6}, {5,27}, {4,37}, {23,26}, {12,25}, {7,23}, {20,25}, {5,45}, {11,24}, {10,34}, {27,44}, {9,30}, {1,29}, {9,34}, {6,28}, {8,24}, {17,41}, {2,17}, {3,16}, {16,41}, {10,32}, {18,36}, {14,35}, {24,45} } Symmetric graph 38 of order 45 Valency 32 Diameter 2 Girth 3 Automorphism group of order 43545600 Number of arcs = 1440 Number of 2-arcs = 44640 2-arc-transitive false Edge-set { {1,7}, {5,38}, {35,38}, {17,43}, {2,41}, {2,36}, {26,44}, {22,41}, {2,6}, {24,26}, {11,28}, {25,27}, {32,36}, {3,15}, {28,40}, {38,42}, {3,45}, {3,40}, {28,42}, {14,35}, {29,43}, {15,18}, {20,28}, {7,38}, {33,40}, {18,42}, {19,35}, {19,43}, {3,10}, {10,31}, {13,42}, {1,13}, {17,33}, {16,45}, {2,9}, {23,45}, {22,28}, {11,37}, {14,41}, {31,42}, {1,42}, {1,29}, {13,41}, {2,30}, {26,37}, {1,12}, {39,41}, {1,37}, {29,41}, {13,31}, {30,42}, {9,22}, {6,14}, {15,24}, {11,34}, {27,44}, {5,36}, {7,26}, {11,22}, {14,31}, {27,31}, {21,42}, {1,34}, {38,41}, {2,35}, {17,26}, {21,29}, {13,26}, {22,30}, {31,37}, {22,29}, {6,24}, {24,35}, {11,29}, {24,27}, {35,36}, {19,41}, {25,37}, {8,31}, {19,23}, {6,13}, {12,30}, {5,6}, {12,38}, {11,43}, {21,28}, {7,25}, {21,32}, {23,26}, {33,39}, {3,39}, {34,40}, {20,42}, {12,16}, {6,39}, {18,31}, {10,43}, {5,13}, {13,27}, {9,15}, {14,28}, {15,38}, {13,25}, {8,30}, {23,37}, {30,38}, {37,43}, {5,34}, {38,44}, {5,43}, {6,15}, {12,28}, {11,38}, {3,32}, {40,41}, {4,42}, {35,43}, {3,27}, {5,8}, {12,43}, {15,44}, {4,28}, {27,43}, {15,34}, {28,44}, {6,25}, {8,12}, {11,23}, {13,32}, {30,41}, {4,37}, {18,39}, {20,34}, {7,20}, {9,40}, {14,33}, {7,19}, {11,19}, {10,14}, {10,24}, {9,13}, {29,45}, {2,40}, {2,45}, {3,36}, {3,17}, {10,18}, {13,20}, {7,13}, {9,25}, {8,14}, {15,23}, {25,33}, {8,45}, {2,23}, {18,30}, {8,37}, {5,24}, {9,38}, {25,43}, {15,41}, {2,28}, {26,38}, {3,22}, {6,40}, {24,42}, {28,35}, {18,44}, {6,35}, {3,11}, {18,32}, {20,41}, {4,7}, {23,27}, {18,34}, {20,44}, {5,7}, {19,40}, {19,33}, {19,22}, {6,19}, {10,34}, {13,44}, {19,45}, {2,10}, {22,45}, {3,6}, {24,28}, {15,29}, {5,16}, {9,27}, {25,36}, {8,32}, {16,23}, {16,29}, {17,24}, {12,33}, {11,18}, {4,12}, {33,36}, {8,41}, {2,15}, {12,26}, {10,11}, {13,36}, {20,31}, {1,8}, {17,38}, {16,35}, {9,17}, {20,23}, {8,22}, {21,44}, {21,30}, {1,44}, {1,9}, {25,29}, {34,37}, {40,44}, {4,33}, {25,26}, {23,31}, {19,36}, {12,36}, {11,44}, {6,33}, {12,45}, {2,11}, {7,39}, {14,20}, {9,31}, {14,42}, {1,15}, {7,41}, {14,26}, {6,17}, {9,11}, {32,41}, {4,16}, {16,43}, {5,17}, {6,27}, {4,26}, {5,27}, {27,36}, {2,24}, {9,36}, {25,44}, {2,29}, {26,40}, {36,44}, {7,40}, {11,33}, {14,18}, {15,42}, {10,41}, {2,13}, {1,23}, {10,37}, {1,28}, {29,38}, {4,13}, {30,39}, {37,45}, {24,36}, {1,33}, {16,44}, {8,11}, {15,27}, {7,14}, {14,40}, {4,31}, {39,42}, {1,45}, {27,45}, {7,24}, {14,25}, {29,42}, {1,40}, {17,40}, {16,33}, {9,18}, {8,36}, {15,32}, {10,16}, {13,17}, {6,23}, {10,12}, {28,41}, {4,38}, {4,43}, {5,39}, {4,22}, {30,31}, {9,21}, {25,34}, {27,38}, {21,35}, {17,34}, {20,29}, {15,21}, {17,35}, {10,29}, {13,24}, {13,35}, {9,37}, {15,19}, {19,37}, {19,31}, {10,19}, {12,34}, {11,20}, {3,42}, {3,12}, {3,37}, {22,31}, {12,21}, {6,38}, {12,35}, {11,17}, {17,39}, {16,34}, {9,20}, {14,32}, {15,16}, {7,16}, {17,21}, {26,32}, {16,39}, {3,16}, {6,42}, {36,43}, {5,32}, {16,27}, {2,19}, {10,44}, {2,34}, {20,26}, {7,15}, {14,38}, {3,31}, {40,42}, {35,41}, {2,43}, {3,26}, {1,18}, {20,37}, {18,29}, {13,19}, {19,30}, {1,24}, {31,40}, {22,40}, {18,24}, {1,10}, {13,37}, {10,22}, {34,38}, {35,39}, {17,45}, {25,31}, {14,27}, {2,38}, {17,44}, {29,35}, {20,24}, {7,35}, {29,40}, {24,33}, {18,35}, {24,37}, {19,25}, {12,29}, {11,40}, {19,42}, {12,18}, {33,37}, {18,41}, {7,34}, {5,14}, {23,36}, {33,44}, {34,45}, {2,20}, {9,28}, {10,32}, {16,22}, {16,30}, {17,23}, {30,34}, {23,44}, {5,33}, {19,28}, {8,21}, {10,26}, {13,22}, {4,8}, {15,39}, {21,45}, {3,7}, {15,36}, {28,32}, {16,38}, {8,35}, {15,43}, {6,45}, {23,34}, {32,38}, {2,25}, {28,39}, {20,32}, {6,34}, {18,36}, {8,40}, {40,43}, {20,43}, {5,9}, {24,43}, {4,21}, {3,9}, {16,25}, {8,17}, {3,24}, {13,29}, {13,40}, {21,40}, {7,33}, {18,21}, {15,26}, {12,39}, {4,35}, {17,30}, {14,21}, {25,39}, {8,34}, {14,30}, {15,37}, {14,43}, {9,35}, {10,39}, {13,34}, {10,28}, {22,38}, {4,30}, {23,39}, {33,45}, {11,30}, {32,44}, {2,18}, {39,43}, {2,33}, {36,45}, {2,44}, {3,19}, {10,42}, {39,45}, {3,34}, {14,17}, {5,42}, {35,42}, {1,43}, {3,29}, {14,45}, {1,35}, {17,29}, {10,21}, {13,21}, {9,26}, {14,22}, {15,31}, {14,37}, {28,31}, {19,38}, {12,40}, {11,42}, {6,43}, {5,31}, {19,27}, {34,41}, {5,26}, {4,6}, {11,45}, {4,41}, {27,39}, {5,21}, {21,43}, {23,29}, {10,36}, {13,16}, {2,14}, {15,17}, {9,42}, {1,14}, {4,25}, {8,39}, {30,37}, {5,12}, {26,45}, {2,39}, {10,17}, {14,16}, {30,44}, {5,37}, {1,38}, {1,25}, {29,32}, {7,23}, {21,33}, {26,39}, {22,34}, {16,28}, {6,28}, {12,25}, {11,32}, {16,40}, {6,18}, {12,19}, {4,11}, {4,36}, {4,18}, {20,39}, {7,45}, {25,32}, {4,23}, {8,20}, {9,16}, {33,41}, {2,26}, {20,22}, {8,24}, {27,34}, {24,32}, {31,44}, {5,19}, {6,22}, {6,12}, {11,24}, {20,27}, {7,29}, {27,35}, {23,35}, {29,37}, {24,31}, {10,27}, {37,41}, {12,41}, {27,41}, {18,25}, {18,26}, {12,24}, {30,32}, {24,30}, {9,23}, {21,34}, {15,22}, {7,30}, {30,33}, {1,30}, {18,37}, {28,36}, {22,44}, {24,40}, {29,31}, {25,42}, {11,35}, {9,41}, {23,41}, {24,38}, {27,40}, {36,42}, {3,41}, {31,43}, {26,34}, {6,29}, {24,41}, {1,20}, {19,26}, {31,38}, {11,27}, {32,39}, {17,25}, {8,16}, {9,33}, {26,42}, {32,40}, {6,44}, {19,21}, {34,42}, {5,29}, {22,26}, {16,24}, {35,37}, {8,26}, {12,31}, {21,27}, {14,36}, {31,39}, {6,32}, {2,21}, {7,36}, {20,36}, {12,20}, {7,11}, {7,44}, {17,41}, {1,22}, {26,33}, {22,36}, {1,32}, {1,27}, {29,36}, {34,36}, {4,20}, {1,39}, {16,32}, {1,19}, {12,44}, {5,11}, {8,29}, {21,38}, {18,22}, {3,14}, {8,44}, {4,15}, {24,45}, {25,41}, {4,32}, {8,15}, {9,30}, {9,32}, {7,43}, {22,39}, {37,44}, {9,12}, {11,25}, {4,45}, {4,17}, {6,30}, {21,39}, {14,23}, {4,27}, {30,36}, {3,21}, {5,41}, {5,22}, {28,34}, {8,19}, {6,20}, {34,43}, {3,20}, {9,43}, {8,42}, {26,35}, {10,13}, {13,30}, {27,33}, {29,33}, {25,38}, {3,44}, {4,40}, {18,45}, {13,39}, {38,45}, {18,27}, {12,23}, {7,28}, {9,45}, {32,43}, {2,8}, {26,43}, {28,37}, {19,32}, {15,33}, {20,21}, {7,18}, {35,44}, {3,30}, {23,42}, {33,42}, {10,23}, {22,33}, {4,10}, {13,45}, {28,45}, {31,45}, {20,33}, {3,35}, {23,40}, {18,40}, {5,44}, {5,28}, {15,28}, {22,43}, {23,32}, {8,25}, {5,23}, {20,38}, {17,28}, {8,27}, {3,25}, {5,18}, {10,38}, {10,33}, {30,43}, {23,30}, {25,28}, {7,31}, {11,39}, {17,36}, {32,45}, {21,37}, {16,37}, {22,35}, {6,37}, {2,16}, {2,31}, {1,17}, {16,42}, {7,21}, {17,31} } Symmetric graph 39 of order 45 Valency 36 Diameter 2 Girth 3 Automorphism group of order 755085986637477121622016000000 Number of arcs = 1620 Number of 2-arcs = 56700 2-arc-transitive false Edge-set { {1,4}, {35,44}, {35,42}, {9,21}, {13,25}, {3,21}, {7,25}, {5,11}, {2,10}, {23,33}, {29,37}, {5,45}, {10,36}, {10,33}, {1,37}, {16,34}, {24,41}, {17,43}, {22,34}, {25,29}, {17,19}, {38,41}, {32,45}, {8,34}, {15,41}, {17,20}, {22,27}, {17,29}, {19,22}, {41,44}, {32,35}, {14,19}, {4,26}, {1,27}, {8,16}, {7,13}, {6,14}, {19,26}, {18,26}, {33,38}, {37,45}, {4,13}, {6,12}, {1,40}, {8,31}, {8,30}, {15,20}, {12,19}, {3,26}, {1,24}, {6,13}, {6,11}, {26,31}, {18,38}, {13,38}, {6,45}, {12,18}, {1,9}, {8,13}, {21,30}, {20,25}, {4,22}, {12,28}, {39,42}, {31,44}, {35,38}, {12,14}, {3,4}, {10,23}, {1,29}, {22,36}, {28,40}, {4,32}, {12,39}, {15,32}, {5,39}, {29,40}, {19,31}, {8,41}, {23,35}, {29,42}, {18,36}, {23,40}, {2,44}, {9,35}, {12,37}, {3,44}, {6,24}, {11,30}, {4,18}, {12,23}, {36,39}, {27,44}, {16,35}, {23,36}, {16,36}, {24,40}, {28,32}, {21,39}, {15,40}, {5,31}, {29,31}, {8,36}, {15,18}, {5,23}, {11,44}, {2,35}, {3,29}, {5,37}, {10,44}, {6,33}, {11,37}, {26,35}, {18,42}, {18,39}, {23,43}, {3,42}, {7,33}, {9,28}, {13,21}, {21,40}, {25,31}, {18,22}, {23,28}, {35,45}, {36,42}, {17,25}, {17,22}, {38,44}, {20,26}, {18,27}, {2,39}, {9,43}, {30,35}, {20,42}, {24,30}, {20,30}, {34,42}, {33,41}, {2,38}, {9,45}, {4,28}, {12,21}, {1,12}, {3,8}, {21,25}, {3,38}, 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{13,37}, {36,40}, {32,38}, {9,14}, {4,45}, {12,36}, {1,39}, {4,12}, {3,12}, {2,7}, {19,28}, {21,26}, {12,16}, {24,43}, {30,34}, {21,42}, {25,33}, {9,15}, {5,13}, {8,18}, {15,23}, {20,45}, {22,32}, {2,8}, {20,28}, {21,27}, {12,17}, {3,22}, {7,29}, {26,32}, {16,23}, {24,29}, {36,43}, {39,45}, {4,41}, {16,22}, {12,34}, {3,41}, {37,44}, {6,25}, {31,38}, {31,40}, {11,35}, {2,42}, {1,22}, {8,28}, {11,31}, {14,23}, {4,29}, {19,45}, {26,36}, {1,10}, {1,8}, {19,30}, {6,40}, {4,40}, {12,31}, {16,39}, {5,43}, {26,34}, {17,39}, {19,25}, {7,32}, {18,40}, {21,28}, {3,40}, {7,31}, {7,28}, {35,43}, {9,29}, {13,19}, {14,38}, {4,42}, {12,33}, {14,39}, {34,44}, {35,41}, {17,24}, {22,30}, {16,25}, {15,21}, {27,31}, {16,38}, {14,37}, {32,39}, {23,44}, {29,35}, {22,28}, {2,12}, {3,9}, {3,11}, {24,31}, {30,38}, {12,32}, {3,39}, {25,32}, {15,38}, {11,18}, {2,23}, {22,44}, {28,35}, {31,37}, {4,11}, {11,22}, {7,19}, {29,41}, {19,32}, {8,27}, {15,16}, {20,37}, {22,26}, {1,44}, {8,35}, {26,45}, {8,12}, {20,24}, {13,40}, {6,31}, {13,42}, {18,21}, {23,25}, {3,14}, {4,7}, {16,19}, {7,10}, {26,28}, {14,26}, {18,34}, {33,45}, {1,34}, {17,30}, {20,22}, {19,24}, {26,30}, {23,41}, {17,45}, {37,41}, {32,44}, {17,28}, {21,22}, {40,44}, {25,38}, {4,38}, {1,20}, {2,30}, {9,20}, {2,34}, {9,41}, {16,43}, {24,34}, {11,43}, {10,45}, {9,11}, {27,39}, {2,19}, {9,26}, {1,28}, {1,36}, {10,22}, {14,18}, {11,29}, {29,32}, {2,20}, {30,40}, {2,28}, {18,20}, {42,44}, {18,35}, {23,42}, {18,45}, {10,43}, {4,39}, {12,43}, {5,32}, {10,39}, {4,23}, {14,16}, {19,37}, {26,44}, {3,5}, {29,33}, {11,24}, {23,34}, {12,15}, {24,25}, {11,15}, {6,39}, {10,38}, {13,18}, {6,23}, {1,45}, {30,32}, {20,39}, {14,25}, {4,17}, {16,45}, {7,20}, {14,27}, {8,42}, {1,35}, {18,19}, {13,32}, {33,36}, {37,40}, {21,31}, {16,21}, {3,43}, {7,34}, {16,28}, {22,25}, {42,45}, {20,32}, {17,44}, {22,35}, {12,44}, {3,35}, {4,37}, {2,36}, {9,42}, {18,28}, {21,23}, {14,42}, {4,33}, {26,39}, {10,30}, {5,9}, {2,45}, {9,36}, {1,21}, {1,43}, {7,21}, {11,38}, {12,29}, {22,40}, {28,31}, {7,42}, {22,42}, {9,19}, {8,25}, {13,27}, {6,16}, {14,33}, {5,24}, {21,38}, {14,40}, {4,31}, {22,41}, {30,42}, {20,33}, {9,25}, {13,17}, {25,45}, {18,43}, {11,45}, {24,36}, {27,28}, {18,30}, {30,33}, {30,31}, {25,43}, {17,34}, {28,41}, {24,42}, {16,26}, {18,24}, {4,10}, {4,30}, {14,24}, {6,41}, {11,32}, {9,44}, {13,35}, {3,25}, {8,32}, {15,39}, {3,23}, {6,27}, {11,16}, {28,36}, {5,15}, {5,10}, {17,37}, {10,35}, {1,42}, {4,14}, {10,17}, {39,43}, {28,39}, {15,19}, {5,26}, {8,29}, {19,44}, {6,44}, {6,26}, {32,37}, {39,44}, {1,25}, {8,17}, {6,15}, {13,20}, {13,39}, {6,43}, {10,18}, {9,13}, {33,40}, {35,40}, {31,42}, {37,43}, {1,11}, {19,27}, {7,16}, {15,22}, {4,43}, {20,44}, {27,35}, {17,26}, {5,28}, {11,34}, {2,37}, {5,25}, {7,17}, {8,15}, {14,22}, {7,18}, {20,41}, {17,42}, {22,33}, {25,35}, {9,32}, {34,45}, {29,38}, {16,27}, {16,24}, {23,30}, {17,40}, {22,31}, {5,29}, {25,36}, {8,44}, {6,42}, {11,33}, {28,37}, {8,14}, {4,15}, {6,10}, {21,44}, {20,29}, {2,41}, {10,21}, {5,14}, {14,36}, {10,19}, {1,26}, {26,33}, {18,37}, {7,15}, {6,30}, {11,20}, {9,18}, {13,23}, {32,42}, {27,34}, {19,42}, {33,39}, {8,43}, {5,44}, {7,44}, {14,35}, {23,45}, {2,26}, {1,7}, {3,37}, {23,31}, {22,29}, {6,29}, {11,19}, {8,33}, {15,37}, {20,27}, {31,39}, {38,43}, {14,32}, {17,35}, {35,37}, {2,13}, {36,37}, {12,30}, {17,36}, {38,40}, {4,24}, {30,41}, {13,41}, {17,21}, {7,35}, {28,42}, {32,34}, {39,41}, {12,38}, {12,13}, {32,36}, {15,17}, {2,29}, {3,28}, {24,35}, {24,26}, {6,9}, {34,39}, {41,43}, {10,13}, {1,6}, {12,24}, {3,30}, {3,13}, {21,33}, {25,37}, {14,31}, {4,16}, {41,45}, {7,40}, {32,43}, {12,22}, {5,17}, {26,38}, {7,12}, {9,34}, {25,28}, {27,32}, {2,40}, {1,23}, {18,23}, {36,44} } Symmetric graph 40 of order 45 Valency 40 Diameter 2 Girth 3 Automorphism group of order 1872381094133760000000000 Number of arcs = 1800 Number of 2-arcs = 70200 2-arc-transitive false Edge-set { {1,6}, {7,11}, {25,31}, {12,23}, {17,32}, {4,17}, {2,24}, {9,18}, {18,26}, {2,30}, {10,26}, {23,30}, {3,8}, {10,21}, {14,27}, {26,34}, {27,41}, {26,38}, {8,45}, {21,37}, {15,41}, {35,38}, {2,45}, {9,37}, {9,13}, {22,33}, {5,15}, {7,35}, {21,42}, {20,39}, {20,41}, {4,38}, {33,42}, {39,41}, {12,38}, {13,32}, {33,45}, {5,38}, {16,41}, {16,39}, {5,12}, {8,32}, {21,45}, {14,38}, {11,34}, {14,25}, {19,34}, {1,19}, {6,22}, {16,24}, {12,16}, {5,32}, {5,34}, {7,42}, {29,40}, {13,28}, {29,33}, {28,41}, {10,39}, {3,42}, {33,40}, {13,41}, {24,39}, {12,18}, {18,25}, {2,19}, {19,32}, {3,45}, {6,39}, {12,24}, {30,33}, {29,41}, {30,40}, {13,29}, {6,24}, {18,24}, {13,18}, {2,33}, {7,45}, {21,39}, {12,20}, {20,23}, {4,21}, {6,20}, {20,28}, {4,27}, {7,28}, {25,27}, {1,11}, {8,31}, {3,30}, {10,29}, {24,30}, {18,29}, {6,18}, {4,24}, {12,34}, {32,42}, {36,44}, {14,36}, {25,43}, {19,40}, {19,44}, {3,36}, {33,43}, {40,41}, {15,40}, {13,35}, {9,34}, {22,42}, {19,36}, {3,14}, {25,33}, {19,41}, {3,40}, {10,13}, {24,27}, {6,26}, {8,28}, {21,27}, {18,28}, {2,27}, {9,32}, {22,45}, {11,40}, {13,31}, {3,24}, {10,18}, {19,45}, {3,37}, {33,44}, {36,41}, {36,45}, {14,37}, {25,44}, {3,11}, {10,31}, {3,27}, {19,26}, {8,19}, {3,21}, {12,32}, {32,45}, {5,40}, {7,13}, {24,29}, {2,29}, {9,28}, {5,10}, {7,23}, {11,29}, {28,31}, {29,43}, {28,40}, {10,42}, {23,39}, {12,43}, {32,40}, {4,42}, {17,25}, {13,17}, {1,33}, {9,45}, {22,37}, {15,44}, {35,36}, {10,37}, {27,44}, {26,36}, {11,27}, {26,31}, {3,10}, {10,23}, {20,24}, {4,18}, {18,34}, {2,42}, {31,37}, {15,20}, {4,35}, {6,43}, {28,36}, {15,22}, {19,35}, {3,43}, {33,36}, {14,41}, {22,36}, {14,16}, {16,25}, {5,19}, {14,20}, {4,34}, {1,34}, {8,42}, {28,37}, {15,27}, {9,21}, {20,22}, {4,19}, {3,6}, {28,33}, {9,36}, {14,22}, {15,25}, {11,41}, {31,38}, {13,43}, {5,42}, {7,39}, {27,43}, {26,40}, {14,18}, {2,34}, {1,32}, {23,36}, {14,17}, {3,9}, {10,22}, {26,35}, {28,32}, {27,45}, {9,38}, {11,22}, {19,31}, {3,44}, {33,37}, {32,37}, {15,45}, {21,38}, {11,20}, {4,31}, {6,44}, {9,23}, {17,22}, {15,17}, {1,35}, {9,42}, {22,39}, {27,38}, {27,33}, 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{4,39}, {37,45}, {38,44}, {18,44}, {2,36}, {10,11}, {23,28}, {25,34}, {17,29}, {1,28}, {22,28}, {13,33}, {33,41}, {1,39}, {1,24}, {8,18}, {18,30}, {35,43}, {26,45}, {30,37}, {14,45}, {34,37}, {19,22}, {15,19}, {3,35}, {12,41}, {32,38}, {4,44}, {12,17}, {24,38}, {11,18}, {18,22}, {2,16}, {3,31}, {10,44}, {30,39}, {17,24}, {11,19}, {30,34}, {34,39}, {12,42}, {23,40}, {6,25}, {19,24}, {12,19}, {3,32}, {8,40}, {13,21}, {2,9}, {9,41}, {18,35}, {2,43}, {32,36}, {10,43}, {27,36}, {14,26}, {27,34}, {26,42}, {15,21}, {20,35}, {5,43}, {7,40}, {15,18}, {2,35}, {2,32}, {14,28}, {6,37}, {14,44}, {34,36}, {7,21}, {13,27}, {6,45}, {12,45}, {3,19}, {19,25}, {13,19}, {3,33}, {24,37}, {12,44}, {30,36}, {14,29}, {14,19}, {27,40}, {11,26}, {15,24}, {29,38}, {10,25}, {19,23}, {25,37}, {4,7}, {18,23}, {2,17}, {8,39}, {12,21}, {1,9}, {30,44}, {16,35}, {18,31}, {10,38}, {11,23}, {3,18}, {10,24}, {19,21}, {3,17}, {26,41}, {25,40}, {4,43}, {28,44}, {11,28}, {27,31}, {18,33}, {5,18}, {6,41}, {14,42}, {32,39}, {5,31}, {10,40}, {31,39}, {26,44}, {8,37}, {15,23}, {7,43}, {3,41}, {38,45}, {20,45}, {20,38}, {4,11}, {16,27}, {9,16}, {5,22}, {24,26}, {10,12}, {8,26}, {9,17}, {3,26}, {17,27}, {20,40}, {3,28}, {24,28}, {2,22}, {13,36}, {14,33}, {8,14}, {21,34}, {34,41}, {21,43}, {37,42}, {15,39}, {20,42}, {16,29}, {5,28}, {6,35}, {12,36}, {22,27}, {20,44}, {20,37}, {4,15}, {7,32}, {31,45}, {6,27}, {19,27}, {3,22}, {9,27}, {9,26}, {5,24}, {37,44}, {12,35}, {10,35}, {22,30}, {4,36}, {23,43}, {40,44}, {17,40}, {17,42}, {11,33}, {31,41}, {15,36}, {14,35}, {29,39}, {30,42}, {14,30}, {29,34}, {29,36}, {9,43}, {22,40}, {20,33}, {5,20}, {5,35}, {34,38}, {11,42}, {28,42}, {1,45}, {15,16}, {34,43} } Symmetric graph 41 of order 45 Valency 42 Diameter 2 Girth 3 Automorphism group of order 614848852548510547968000 Number of arcs = 1890 Number of 2-arcs = 77490 2-arc-transitive false Edge-set { {1,4}, {10,40}, {29,38}, {7,21}, {15,16}, {24,39}, {6,8}, {17,26}, {1,19}, {2,32}, {32,36}, {30,37}, {5,40}, {16,41}, {20,39}, {3,6}, {10,31}, {10,27}, {3,29}, {12,45}, {25,30}, {14,45}, {22,25}, {22,38}, {4,7}, {21,42}, {15,37}, {2,19}, {13,32}, {25,37}, {2,5}, {11,41}, {28,39}, {7,44}, {16,27}, {5,7}, {11,16}, {11,24}, {8,28}, {9,34}, {17,44}, {4,22}, {7,12}, {31,34}, {34,44}, {4,28}, {12,42}, {6,42}, {17,40}, {19,38}, {20,26}, {1,14}, {32,38}, {4,36}, {12,27}, {3,30}, {33,45}, {25,35}, {4,38}, {4,12}, {8,19}, {13,18}, {23,37}, {5,9}, {17,35}, {19,43}, {11,32}, {17,42}, {19,37}, {2,8}, {18,32}, {8,30}, {18,40}, {16,23}, {9,20}, {21,23}, {3,35}, {31,43}, {28,40}, {38,42}, {9,17}, {17,19}, {13,44}, {23,27}, {13,35}, {23,43}, {23,40}, {9,38}, {14,17}, {20,41}, {14,39}, {3,21}, {15,31}, {27,39}, {6,25}, {2,10}, {29,34}, {39,45}, {14,40}, {11,17}, {11,22}, {7,28}, {34,43}, {26,44}, {4,15}, {12,24}, {39,40}, {6,38}, {9,40}, {17,38}, {3,20}, {1,33}, {33,35}, {4,41}, {18,42}, {21,37}, {3,15}, {24,31}, {27,36}, {3,45}, {8,45}, {18,25}, {14,31}, {27,38}, {3,4}, {12,16}, {20,30}, {1,45}, {25,33}, {16,22}, {7,20}, {1,21}, {15,33}, {2,29}, {32,41}, {2,21}, {26,29}, {1,41}, {11,15}, {24,28}, {36,44}, {27,45}, {9,15}, {6,14}, {3,18}, {21,31}, {3,27}, {3,31}, {35,43}, {5,29}, {24,35}, {29,36}, {41,45}, {21,29}, {15,41}, {18,39}, {6,21}, {19,25}, {2,13}, {31,37}, {5,34}, {11,26}, {1,28}, {32,44}, {5,37}, {5,11}, {12,39}, {16,30}, {13,24}, {8,23}, {34,37}, {5,44}, {15,34}, {3,8}, {18,31}, {17,23}, {9,19}, {13,36}, {23,45}, {6,35}, {10,43}, {32,40}, {36,38}, {9,30}, {5,15}, {39,41}, {6,39}, {18,21}, {15,21}, {3,39}, {6,31}, {11,25}, {2,28}, {15,43}, {24,26}, {19,40}, {13,38}, {1,20}, {14,33}, {26,38}, {28,36}, {30,44}, {27,40}, {5,14}, {11,34}, {28,44}, {16,34}, {20,44}, {12,33}, {31,44}, {27,34}, {5,39}, {6,11}, {11,40}, {28,38}, {2,9}, {17,32}, {2,7}, {10,34}, {29,44}, {4,43}, {12,26}, {32,42}, {17,25}, {10,26}, {1,29}, {32,43}, {26,36}, {19,45}, {13,25}, {1,30}, {6,24}, {8,10}, {10,19}, {13,29}, {8,32}, {18,36}, {23,30}, {14,35}, {22,43}, {11,44}, {21,36}, {31,41}, {34,39}, {1,11}, {28,33}, 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{19,29}, {33,40}, {6,15}, {10,39}, {6,29}, {6,33}, {11,20}, {9,23}, {20,22}, {7,14}, {3,34}, {6,17}, {30,32}, {12,30}, {30,40}, {21,24}, {8,15}, {25,32}, {2,36}, {8,34}, {19,28}, {12,41}, {7,15}, {24,36}, {37,45}, {10,42}, {18,26}, {9,36}, {15,27}, {3,24}, {12,13}, {40,45}, {25,38}, {9,14}, {17,22}, {19,23}, {9,13}, {20,37}, {20,43}, {31,39}, {6,34}, {15,38}, {4,24}, {35,38}, {8,16}, {39,44}, {7,31}, {6,20}, {1,40}, {14,41}, {15,32}, {25,39}, {2,6}, {26,31}, {3,19}, {13,31}, {23,34}, {28,35}, {17,37}, {5,19}, {2,37}, {5,32}, {8,27}, {13,23}, {1,23}, {9,33}, {3,14}, {22,31}, {5,31}, {13,26}, {24,32}, {8,36}, {13,40}, {8,44}, {4,19}, {22,34}, {30,36}, {14,42}, {22,37}, {18,44}, {13,33}, {31,40}, {34,38}, {2,27}, {3,32}, {2,35}, {10,32}, {10,45}, {25,29}, {14,43}, {24,38}, {19,42}, {6,28}, {38,43}, {11,18}, {21,28}, {27,31}, {11,42}, {1,34}, {35,41}, {39,43}, {27,32}, {18,35}, {21,43}, {3,5}, {11,31}, {27,37}, {2,45}, {7,19}, {2,30}, {16,25}, {2,20}, {23,38}, {9,35}, {17,43}, {9,45}, 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{29,41}, {21,26}, {28,34}, {42,44}, {13,28}, {7,22}, {20,31}, {4,42}, {33,43}, {26,35}, {21,44}, {13,39}, {6,23}, {24,30}, {7,34}, {16,44}, {31,36}, {34,45}, {6,40}, {20,27}, {9,39}, {23,26}, {23,29}, {15,19}, {5,45}, {1,15}, {28,37}, {5,38}, {12,22}, {12,32}, {29,39}, {6,41}, {3,36}, {18,34}, {32,34}, {12,21}, {17,34}, {21,40}, {17,21}, {15,17}, {19,24}, {2,31}, {7,10}, {8,26}, {5,35}, {11,43}, {8,31}, {3,13}, {10,36}, {4,17}, {10,44}, {24,29}, {8,17}, {4,26}, {1,12}, {9,21}, {16,21}, {12,19}, {5,25}, {6,27}, {3,10}, {28,31}, {34,42}, {28,42}, {21,38}, {9,41}, {14,37}, {5,22}, {32,37}, {13,45}, {6,37}, {12,20}, {1,13}, {3,17}, {26,28}, {1,42}, {4,9}, {22,28}, {2,33}, {32,35}, {3,33}, {15,42}, {10,41}, {1,31}, {33,34}, {7,18}, {36,43}, {9,28}, {8,11}, {1,43}, {30,38}, {5,42}, {19,33}, {22,39}, {3,11}, {25,44}, {9,42}, {5,8}, {11,39}, {11,14}, {23,33}, {33,37}, {23,44}, {24,37}, {1,17}, {3,26}, {27,30}, {3,40}, {10,20}, {31,38}, {9,10}, {9,27}, {7,11}, {18,19}, {29,35}, {12,43}, {14,36}, {18,20}, {5,18}, {11,21} } Symmetric graph 42 of order 45 Valency 44 Diameter 1 Girth 3 Automorphism group of order 119622220865480194561963161495657715064383733760000000000 Number of arcs = 1980 Number of 2-arcs = 85140 2-arc-transitive true Edge-set { {1,2}, {2,3}, {2,4}, {1,3}, {2,5}, {3,4}, {1,4}, {2,6}, {3,5}, {4,5}, {1,5}, {2,7}, {3,6}, {4,6}, {5,6}, {1,6}, {2,8}, {3,7}, {4,7}, {5,7}, {6,7}, {1,7}, {2,9}, {3,8}, {4,8}, {5,8}, {6,8}, {7,8}, {1,8}, {2,10}, {3,9}, {4,9}, {5,9}, {6,9}, {7,9}, {8,9}, {1,9}, {2,11}, {3,10}, {4,10}, {5,10}, {6,10}, {7,10}, {8,10}, {9,10}, {1,10}, {2,12}, {3,11}, {4,11}, {5,11}, {6,11}, {7,11}, {8,11}, {9,11}, {10,11}, {1,11}, {2,13}, {3,12}, {4,12}, {5,12}, {6,12}, {7,12}, {8,12}, {9,12}, {10,12}, {11,12}, {1,12}, {2,14}, {3,13}, {4,13}, {5,13}, {6,13}, {7,13}, {8,13}, {9,13}, {10,13}, {11,13}, {12,13}, {1,13}, {2,15}, {3,14}, {4,14}, {5,14}, {6,14}, {7,14}, {8,14}, {9,14}, {10,14}, {11,14}, {12,14}, {13,14}, {1,14}, {2,16}, {3,15}, {4,15}, 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{40,43}, {41,43}, {42,43}, {1,43}, {2,45}, {3,44}, {4,44}, {5,44}, {6,44}, {7,44}, {8,44}, {9,44}, {10,44}, {11,44}, {12,44}, {13,44}, {14,44}, {15,44}, {16,44}, {17,44}, {18,44}, {19,44}, {20,44}, {21,44}, {22,44}, {23,44}, {24,44}, {25,44}, {26,44}, {27,44}, {28,44}, {29,44}, {30,44}, {31,44}, {32,44}, {33,44}, {34,44}, {35,44}, {36,44}, {37,44}, {38,44}, {39,44}, {40,44}, {41,44}, {42,44}, {43,44}, {1,44}, {3,45}, {4,45}, {5,45}, {6,45}, {7,45}, {8,45}, {9,45}, {10,45}, {11,45}, {12,45}, {13,45}, {14,45}, {15,45}, {16,45}, {17,45}, {18,45}, {19,45}, {20,45}, {21,45}, {22,45}, {23,45}, {24,45}, {25,45}, {26,45}, {27,45}, {28,45}, {29,45}, {30,45}, {31,45}, {32,45}, {33,45}, {34,45}, {35,45}, {36,45}, {37,45}, {38,45}, {39,45}, {40,45}, {41,45}, {42,45}, {43,45}, {44,45}, {1,45} } ................................................................... Symmetric connected graphs of order 46 Symmetric graph 1 of order 46 Valency 2 Diameter 23 Girth 46 Automorphism group of order 92 Number of arcs = 92 Number of 2-arcs = 92 2-arc-transitive true Edge-set { {1,3}, {33,36}, {19,22}, {6,7}, {38,40}, {23,26}, {9,11}, {41,43}, {27,30}, {13,15}, {2,46}, {31,34}, {18,20}, {3,5}, {36,37}, {22,24}, {7,10}, {40,42}, {26,28}, {11,14}, {43,45}, {30,32}, {15,17}, {2,4}, {34,35}, {20,21}, {5,8}, {37,39}, {24,25}, {10,12}, {42,44}, {28,29}, {14,16}, {1,45}, {32,33}, {17,19}, {4,6}, {35,38}, {21,23}, {8,9}, {39,41}, {25,27}, {12,13}, {44,46}, {29,31}, {16,18} } Symmetric graph 2 of order 46 Valency 4 Diameter 11 Girth 4 Automorphism group of order 385875968 Number of arcs = 184 Number of 2-arcs = 552 2-arc-transitive false Edge-set { {1,3}, {11,13}, {34,35}, {21,23}, {43,46}, {43,45}, {20,21}, {31,33}, {7,10}, {8,10}, {29,32}, {8,9}, {29,31}, {30,31}, {5,7}, {41,44}, {18,19}, {17,20}, {39,42}, {18,20}, {40,42}, {16,17}, {40,41}, {39,41}, {16,18}, {15,18}, {37,39}, {28,30}, {27,29}, {3,6}, {4,5}, {4,6}, {25,27}, {27,30}, {3,5}, {26,27}, {25,28}, {1,4}, {26,28}, {2,3}, {2,4}, {23,25}, {37,40}, {13,15}, {38,39}, {14,16}, {35,38}, {36,37}, {14,15}, {36,38}, {11,14}, {38,40}, {13,16}, {35,37}, {12,14}, {34,36}, {12,13}, {33,35}, {33,36}, {10,11}, {23,26}, {2,46}, {24,25}, {1,45}, {21,24}, {22,23}, {24,26}, {2,45}, {1,46}, {22,24}, {44,45}, {20,22}, {44,46}, {19,21}, {19,22}, {42,43}, {10,12}, {32,33}, {9,11}, {31,34}, {7,9}, {9,12}, {32,34}, {30,32}, {5,8}, {6,7}, {6,8}, {42,44}, {17,19}, {41,43}, {15,17}, {28,29} } Symmetric graph 3 of order 46 Valency 11 Diameter 3 Girth 4 Automorphism group of order 506 Number of arcs = 506 Number of 2-arcs = 5060 2-arc-transitive false Edge-set { {1,3}, {13,34}, {22,27}, {11,42}, {11,25}, {29,43}, {7,36}, {22,45}, {4,5}, {22,24}, {1,5}, {17,20}, {10,13}, {28,31}, {32,40}, {29,39}, {16,36}, {8,33}, {28,33}, {4,29}, {36,41}, {8,13}, {22,33}, {10,35}, {23,29}, {2,42}, {11,46}, {38,44}, {8,20}, {25,37}, {19,44}, {17,26}, {13,43}, {15,31}, {18,32}, {12,27}, {26,39}, {12,44}, {8,26}, {17,33}, {13,28}, {31,46}, {3,32}, {27,42}, {11,39}, {12,29}, {26,36}, {2,32}, {3,17}, {13,42}, {14,45}, {4,21}, {22,40}, {5,15}, {5,19}, {9,38}, {10,27}, {6,24}, {1,37}, {9,19}, {9,30}, {23,35}, {2,23}, {20,42}, {10,11}, {16,38}, {36,37}, {19,24}, {21,43}, {6,7}, {23,26}, {2,43}, {19,21}, {6,9}, {23,27}, {2,39}, {12,35}, {42,44}, {8,11}, {38,40}, {15,20}, {34,37}, {19,27}, {43,45}, {4,7}, {22,26}, {5,43}, {17,21}, {6,13}, {23,31}, {14,37}, {34,35}, {42,45}, {4,11}, {39,41}, {12,16}, {30,33}, {28,35}, {25,29}, {36,44}, {8,16}, {8,9}, {38,45}, {7,46}, {34,41}, {22,37}, {1,9}, {30,45}, {1,18}, {31,42}, {3,14}, {21,42}, {10,45}, {2,22}, {5,46}, {18,38}, {6,31}, {32,37}, {4,9}, {30,41}, {20,30}, {7,28}, {34,40}, {3,23}, {14,20}, {10,21}, {30,35}, {1,7}, {34,45}, {3,43}, {7,42}, {14,26}, {21,32}, {19,45}, {5,39}, {5,25}, {10,16}, {17,29}, {6,11}, {9,43}, {7,30}, {20,39}, {28,40}, {2,36}, {10,33}, {11,34}, {3,38}, {6,41}, {12,37}, {11,32}, {25,31}, {39,45}, {4,16}, {5,28}, {26,46}, {15,21}, {6,18}, {12,18}, {32,44}, {8,31}, {17,24}, {1,13}, {19,31}, {9,32}, {15,27}, {18,39}, {1,27}, {15,40}, {3,25}, {6,29}, {14,16}, {13,36}, {4,20}, {4,35}, {16,46}, {14,29}, {21,36}, {8,40}, {15,33}, {5,36}, {24,38}, {7,38}, {20,34}, {6,37}, {19,37}, {1,33}, {28,45}, {18,46}, {10,18}, {28,44}, {25,44}, {3,34}, {10,41}, {2,30}, {35,46}, {14,31}, {16,25}, {4,40}, {23,41}, {2,12}, {30,37}, {19,35}, {9,39}, {16,30}, {33,43}, {8,24}, {2,15}, {17,35}, {13,23}, {7,22}, {5,34}, {1,20}, {18,28}, {14,40}, {10,26}, {8,44}, {11,22}, {27,38}, {6,21}, {16,43}, {23,40}, {24,34}, {7,17}, {24,43}, {17,44}, {15,41}, {28,29}, {32,33}, {15,18}, {17,41}, {12,13}, {30,31}, {32,35}, {25,27}, {39,44}, {38,41}, {36,40}, {15,24}, {24,46}, {2,46}, {3,46}, {14,18}, {14,21}, {12,20}, {25,33}, {3,42}, {1,26}, {4,27}, {22,29}, {25,41}, {9,23}, {19,26}, {12,24} } Symmetric graph 4 of order 46 Valency 22 Diameter 3 Girth 4 Automorphism group of order 51704033477769953280000 Number of arcs = 1012 Number of 2-arcs = 21252 2-arc-transitive true Edge-set { {1,3}, {20,23}, {26,36}, {9,18}, {17,37}, {21,41}, {4,7}, {5,35}, {1,41}, {6,45}, {2,39}, {7,14}, {20,27}, {24,31}, {6,25}, {27,42}, {3,15}, {7,20}, {20,36}, {16,28}, {16,46}, {4,19}, {30,35}, {31,44}, {6,22}, {9,25}, {37,44}, {17,34}, {18,24}, {22,28}, {8,16}, {8,25}, {19,44}, {1,23}, {11,26}, {9,31}, {6,37}, {9,41}, {4,37}, {2,26}, {12,43}, {2,15}, {12,45}, {10,24}, {25,38}, {30,42}, {3,33}, {12,34}, {13,28}, {22,35}, {8,41}, {10,39}, {2,14}, {5,17}, {1,18}, {13,26}, {28,43}, {2,32}, {5,12}, {22,32}, {5,8}, {10,12}, {10,38}, {18,20}, {17,36}, {21,40}, {7,32}, {34,35}, {24,41}, {28,45}, {16,39}, {7,35}, {20,41}, {24,45}, {25,39}, {19,21}, {11,39}, {1,19}, {11,35}, {31,46}, {18,42}, {22,46}, {8,40}, {8,30}, {19,33}, {23,38}, {37,39}, {14,31}, {26,43}, {21,43}, {13,42}, {3,28}, {5,20}, {4,36}, {6,27}, {1,36}, {7,21}, {9,43}, {23,35}, {27,39}, {15,31}, {13,33}, {23,28}, {27,32}, {5,15}, {36,39}, {31,42}, {36,46}, {40,42}, {5,9}, {1,37}, {6,41}, {2,4}, {3,14}, {27,29}, {31,33}, {6,23}, {37,42}, {7,17}, {16,26}, {43,46}, {12,30}, {3,6}, {7,9}, {20,37}, {16,17}, {18,46}, {4,22}, {10,14}, {27,38}, {4,40}, {30,32}, {10,20}, {36,38}, {3,32}, {15,34}, {13,15}, {5,29}, {5,33}, {13,38}, {17,40}, {4,45}, {30,39}, {34,44}, {22,24}, {11,21}, {11,14}, {9,27}, {8,43}, {23,26}, {15,37}, {4,25}, {25,28}, {16,44}, {3,17}, {30,44}, {1,34}, {11,24}, {38,43}, {13,21}, {18,26}, {17,43}, {25,33}, {23,44}, {1,27}, {11,15}, {4,41}, {4,30}, {8,34}, {19,24}, {15,41}, {3,8}, {19,29}, {27,35}, {20,45}, {7,28}, {16,20}, {25,35}, {22,26}, {25,29}, {34,38}, {13,24}, {18,28}, {8,45}, {19,39}, {6,31}, {2,6}, {2,21}, {7,12}, {9,45}, {31,35}, {2,12}, {1,45}, {36,44}, {22,42}, {25,46}, {40,44}, {3,24}, {30,33}, {23,33}, {9,36}, {41,46}, {1,43}, {2,29}, {16,24}, {12,37}, {13,17}, {14,40}, {41,44}, {11,32}, {18,21}, {10,33}, {14,36}, {18,32}, {11,46}, {9,40}, {14,43}, {21,27}, {5,21}, {1,7}, {6,11}, {2,9}, {22,38}, {8,13}, {12,18}, {10,17}, {20,25}, {1,40}, {7,24}, {24,30}, {32,37}, {5,14}, {18,38}, {11,20}, {23,32}, {5,26}, {10,29}, {25,42}, {3,44}, {9,16}, {37,46}, {26,31}, {6,43}, {22,29}, {16,32}, {5,46}, {4,10}, {30,38}, {28,34}, {19,28}, {16,35}, {14,19}, {31,39}, {34,42}, {12,41}, {15,22}, {3,12}, {17,23}, {35,41}, {7,15}, {2,17}, {39,45}, {33,40}, {15,40}, {32,45}, {3,35}, {29,41}, {11,44}, {9,22}, {14,25}, {27,44}, {14,27}, {15,27}, {20,31}, {6,36}, {28,40}, {19,35}, {13,46}, {32,43}, {5,39}, {1,31}, {2,42}, {8,37}, {3,20}, {29,36}, {17,31}, {6,18}, {17,30}, {18,33}, {33,45}, {23,39}, {8,22}, {8,19}, {12,23}, {10,26}, {2,35}, {15,45}, {21,34}, {11,28}, {13,29}, {2,33}, {24,36}, {30,46}, {26,37}, {10,44}, {4,34}, {7,39}, {1,13}, {7,42}, {6,19}, {4,16}, {3,38}, {11,29}, {16,33}, {23,46}, {23,42}, {3,26}, {7,29}, {20,34}, {12,40}, {10,32}, {13,35}, {28,41}, {22,44}, {12,25}, {25,44}, {1,25}, {9,34}, {24,37}, {29,43}, {10,42}, {15,43}, {21,45}, {11,33}, {9,23}, {4,27}, {15,30}, {6,34}, {2,24}, {5,28}, {1,16}, {6,30}, {5,38}, {16,38}, {4,18}, {13,32}, {18,39}, {21,36}, {19,42}, {14,37}, {26,40}, {19,38}, {17,41}, {12,36}, {4,31}, {20,43}, {8,31}, {10,28}, {29,40}, {32,34}, {2,38}, {12,13}, {15,18}, {17,45}, {8,18}, {17,19}, {21,23}, {7,26}, {29,31}, {9,37}, {3,39}, {33,36}, {42,43}, {3,21}, {22,39}, {12,22}, {8,10}, {20,22}, {8,36}, {35,37}, {14,41}, {1,11}, {9,11}, {14,16}, {27,46}, {38,40}, {18,35}, {24,25}, {1,30}, {28,37}, {26,27}, {2,20}, {28,30}, {2,46}, {5,24}, {33,43}, {4,5}, {44,45}, {10,46}, {6,7}, {39,41}, {24,34}, {3,29}, {29,34}, {33,37}, {14,23}, {19,46}, {35,40}, {39,43}, {21,31}, {1,5}, {6,16}, {5,32}, {6,10}, {14,18}, {17,27}, {35,45}, {4,23}, {26,30}, {38,41}, {4,13}, {8,11}, {9,19}, {13,39}, {28,31}, {32,36}, {5,42}, {9,13}, {32,41}, {42,45}, {7,44}, {20,40}, {2,44}, {15,25}, {3,46}, {17,22}, {20,30}, {26,45}, {21,25}, {15,19}, {11,38}, {24,27}, {12,16}, {15,36}, {23,29}, {26,34}, {29,37}, {14,34}, {38,45}, {18,44}, {10,15}, {3,42}, {4,11}, {9,30}, {2,28}, {27,33}, {15,23}, {28,36}, {16,42}, {5,44}, {1,22}, {17,25}, {21,30}, {7,33}, {7,46}, {24,43}, {32,40}, {10,35}, {4,43}, {33,41}, {8,27}, {35,43}, {12,31}, {3,9}, {12,19}, {6,13}, {16,21}, {14,22}, {1,10}, {40,46}, {18,29}, {21,37}, {29,45}, {34,39}, {11,42}, {8,23}, {19,26}, {24,40}, {25,32}, {13,44}, {11,17}, {26,41}, {2,8}, {12,27}, {13,20}, {14,30}, {31,38}, {36,42}, {7,38}, {14,45}, {16,29}, {34,46}, {19,32}, {10,21}, {22,33}, {6,40} } Symmetric graph 5 of order 46 Valency 23 Diameter 2 Girth 4 Automorphism group of order 1336653538935178044929642368586691379200000000 Number of arcs = 1058 Number of 2-arcs = 23276 2-arc-transitive true Edge-set { {1,24}, {5,35}, {13,43}, {9,46}, {4,33}, {17,31}, {10,36}, {13,34}, {18,46}, {8,44}, {14,24}, {21,42}, {1,26}, {22,32}, {17,45}, {9,36}, {22,34}, {18,35}, {12,32}, {5,37}, {13,45}, {2,30}, {15,39}, {3,43}, {19,25}, {21,33}, {23,26}, {13,24}, {22,46}, {3,45}, {9,25}, {4,35}, {16,43}, {19,27}, {17,33}, {23,36}, {6,41}, {6,29}, {7,31}, {10,38}, {2,44}, {14,39}, {4,37}, {3,34}, {17,35}, {13,36}, {18,25}, {7,33}, {23,38}, {8,46}, {4,24}, {20,31}, {10,40}, {21,44}, {14,26}, {10,29}, {20,42}, {11,42}, {1,28}, {6,32}, {5,29}, {18,27}, {7,45}, {8,25}, {17,24}, {9,38}, {21,46}, {4,26}, {22,36}, {8,35}, {11,44}, {14,28}, {12,34}, {18,37}, {1,42}, {1,30}, {2,32}, {5,39}, {14,40}, {11,32}, {15,30}, {15,41}, {10,43}, {19,42}, {9,40}, {11,33}, {22,38}, {21,35}, {23,28}, {12,36}, {8,37}, {13,26}, {12,46}, {2,34}, {18,39}, {3,24}, {22,25}, {15,32}, {5,41}, {16,45}, {9,27}, {5,30}, {15,43}, {6,43}, {19,29}, {18,28}, {2,45}, {19,41}, {6,31}, {14,31}, {10,32}, {23,30}, {15,44}, {13,28}, {2,46}, {14,41}, {3,26}, {12,25}, {4,39}, {16,34}, {16,24}, {22,27}, {17,37}, {3,36}, {6,45}, {9,29}, {7,35}, {13,38}, {19,43}, {19,31}, {20,33}, {23,40}, {9,41}, {6,33}, {10,31}, {10,42}, {22,39}, {16,35}, {23,29}, {20,44}, {18,42}, {1,45}, {14,43}, {19,32}, {4,41}, {6,34}, {5,31}, {17,39}, {16,36}, {18,29}, {20,45}, {7,37}, {3,38}, {8,27}, {7,24}, {20,35}, {13,40}, {21,25}, {17,26}, {10,33}, {23,42}, {11,46}, {4,28}, {23,31}, {10,44}, {1,44}, {14,30}, {13,29}, {20,46}, {14,42}, {1,32}, {3,27}, {7,25}, {4,40}, {11,34}, {22,30}, {15,35}, {5,33}, {23,43}, {18,31}, {10,45}, {19,44}, {8,29}, {20,24}, {9,42}, {1,33}, {21,27}, {7,26}, {22,40}, {11,35}, {11,25}, {17,28}, {12,38}, {21,37}, {1,46}, {4,30}, {2,36}, {8,39}, {14,44}, {14,32}, {15,34}, {18,41}, {4,42}, {1,34}, {5,32}, {5,43}, {17,40}, {11,36}, {18,30}, {15,45}, {7,38}, {21,38}, {8,28}, {2,24}, {3,41}, {6,25}, {19,46}, {4,31}, {9,44}, {14,33}, {10,34}, {22,42}, {1,35}, {23,32}, {5,44}, {12,40}, {11,37}, {13,30}, {15,46}, {2,38}, {21,39}, {3,28}, {2,25}, {15,36}, {8,41}, {16,26}, {12,27}, {5,34}, {18,43}, {6,24}, {22,29}, {18,32}, {5,45}, {19,45}, {9,31}, {8,30}, {15,24}, {9,43}, {19,33}, {21,28}, {2,26}, {22,41}, {6,35}, {11,26}, {12,28}, {12,39}, {16,37}, {7,29}, {20,38}, {8,42}, {23,34}, {18,44}, {13,32}, {5,46}, {14,45}, {9,32}, {3,30}, {15,25}, {4,43}, {19,34}, {16,28}, {2,27}, {17,41}, {6,36}, {6,26}, {12,29}, {7,39}, {16,38}, {19,24}, {22,31}, {20,37}, {3,40}, {9,45}, {9,33}, {10,35}, {13,42}, {22,43}, {19,35}, {23,33}, {23,44}, {12,41}, {6,37}, {13,31}, {10,46}, {2,39}, {16,39}, {3,29}, {20,25}, {15,37}, {16,27}, {7,27}, {11,40}, {11,28}, {12,30}, {4,45}, {9,34}, {17,43}, {19,36}, {18,33}, {23,45}, {7,41}, {6,38}, {8,31}, {10,24}, {20,39}, {16,40}, {21,29}, {20,26}, {10,37}, {3,42}, {11,27}, {7,28}, {23,35}, {13,44}, {1,25}, {17,30}, {13,33}, {23,46}, {14,46}, {4,32}, {3,31}, {10,25}, {4,44}, {14,34}, {16,29}, {20,27}, {17,42}, {1,36}, {6,27}, {7,40}, {11,38}, {21,40}, {15,28}, {2,41}, {16,41}, {8,33}, {23,24}, {21,31}, {10,26}, {22,44}, {14,35}, {11,29}, {20,28}, {12,42}, {1,37}, {1,27}, {7,30}, {2,40}, {11,39}, {14,25}, {17,32}, {15,38}, {21,41}, {4,46}, {4,34}, {5,36}, {8,43}, {17,44}, {14,36}, {18,34}, {18,45}, {7,42}, {1,38}, {8,32}, {5,24}, {20,40}, {21,30}, {15,26}, {2,28}, {19,39}, {16,31}, {20,29}, {12,44}, {14,37}, {2,42}, {1,39}, {3,32}, {5,25}, {15,40}, {11,41}, {16,30}, {15,27}, {5,38}, {21,43}, {6,28}, {2,29}, {18,36}, {8,45}, {19,26}, {12,31}, {8,34}, {18,24}, {9,24}, {22,33}, {21,32}, {5,26}, {22,45}, {9,35}, {11,30}, {12,43}, {19,37}, {6,39}, {23,27}, {7,44}, {1,40}, {16,32}, {5,27}, {6,30}, {15,29}, {7,43}, {19,38}, {19,28}, {2,31}, {20,41}, {6,40}, {9,26}, {12,33}, {10,39}, {16,42}, {22,24}, {22,35}, {23,37}, {3,44}, {12,45}, {9,37}, {13,35}, {13,46}, {2,43}, {3,33}, {23,25}, {10,27}, {4,38}, {21,34}, {5,28}, {20,43}, {19,40}, {10,41}, {6,42}, {11,31}, {10,28}, {23,39}, {16,44}, {1,29}, {20,30}, {13,37}, {3,46}, {14,27}, {7,32}, {3,35}, {13,25}, {4,25}, {17,34}, {16,33}, {17,46}, {4,36}, {14,38}, {8,26}, {12,24}, {9,39}, {1,31}, {10,30}, {14,29}, {20,32}, {15,42}, {1,41}, {4,27}, {7,34}, {5,40}, {11,43}, {17,25}, {17,36}, {18,38}, {21,45}, {7,46}, {8,36}, {8,24}, {18,26}, {12,37}, {3,37}, {13,27}, {5,42}, {1,43}, {18,40}, {11,45}, {19,30}, {15,31}, {8,38}, {21,24}, {9,28}, {2,33}, {21,36}, {22,26}, {12,35}, {22,37}, {16,25}, {17,27}, {17,38}, {9,30}, {15,33}, {22,28}, {2,35}, {23,41}, {6,44}, {12,26}, {13,39}, {16,46}, {3,25}, {20,36}, {8,40}, {21,26}, {13,41}, {6,46}, {3,39}, {4,29}, {20,34}, {7,36}, {2,37}, {17,29}, {11,24} } Symmetric graph 6 of order 46 Valency 44 Diameter 2 Girth 3 Automorphism group of order 216862434431944426122117120000 Number of arcs = 2024 Number of 2-arcs = 87032 2-arc-transitive false Edge-set { {1,3}, {10,36}, {13,32}, {22,37}, {40,44}, {27,32}, {8,29}, {18,40}, {9,16}, {3,44}, {23,33}, {26,32}, {8,18}, {6,41}, {22,36}, {33,44}, {20,33}, {7,21}, {1,39}, {3,36}, {23,32}, {11,20}, {25,28}, {32,45}, {8,45}, {33,41}, {20,22}, {15,24}, {3,6}, {37,40}, {9,44}, {3,11}, {23,25}, {11,14}, {25,38}, {39,42}, {10,21}, {10,43}, {13,34}, {36,37}, {32,44}, {20,32}, {8,28}, {1,14}, {11,38}, {25,46}, {17,46}, {29,32}, {8,41}, {29,41}, {22,41}, {11,24}, {6,25}, {14,40}, {9,38}, {8,19}, {2,27}, {15,36}, {3,32}, {18,44}, {16,33}, {3,21}, {23,39}, {1,36}, {11,32}, {20,46}, {28,46}, {1,28}, {11,30}, {15,46}, {23,43}, {5,34}, {22,39}, {10,40}, {4,22}, {24,40}, {12,27}, {26,29}, {18,37}, {16,44}, {8,23}, {14,32}, {8,38}, {25,41}, {17,22}, {10,28}, {13,30}, {1,17}, {11,15}, {30,46}, {42,46}, {30,34}, {19,42}, {6,32}, {8,36}, {24,41}, {6,22}, {6,24}, {6,36}, {6,9}, {1,19}, {11,27}, {3,46}, {28,44}, {30,33}, {17,21}, {15,39}, {13,41}, {9,26}, {14,18}, {8,37}, {2,44}, {32,36}, {8,32}, {3,33}, {20,23}, {7,11}, {1,25}, {36,39}, {10,32}, {20,43}, {28,34}, {10,37}, {13,44}, {1,32}, {8,11}, {14,30}, {38,42}, {25,30}, {17,42}, {10,25}, {13,17}, {1,5}, {11,35}, {8,30}, {2,42}, {4,20}, {24,28}, {12,16}, {4,26}, {40,43}, {9,34}, {22,44}, {33,40}, {35,40}, {9,31}, {19,44}, {27,33}, {2,26}, {12,18}, {6,45}, {36,45}, {18,33}, {16,20}, {3,7}, {1,23}, {20,41}, {22,28}, {28,32}, {17,41}, {15,22}, {24,46}, {6,46}, {34,40}, {9,19}, {22,25}, {17,40}, {5,27}, {29,35}, {10,34}, {13,19}, {1,8}, {2,11}, {5,30}, {35,42}, {23,30}, 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Symmetric connected graphs of order 47 Symmetric graph 1 of order 47 Valency 2 Diameter 23 Girth 47 Automorphism group of order 94 Number of arcs = 94 Number of 2-arcs = 94 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,12}, {12,13}, {13,14}, {14,15}, {15,16}, {16,17}, {17,18}, {18,19}, {19,20}, {20,21}, {21,22}, {22,23}, {23,24}, {24,25}, {25,26}, {26,27}, {27,28}, {28,29}, {29,30}, {30,31}, {31,32}, {32,33}, {33,34}, {34,35}, {35,36}, {36,37}, {37,38}, {38,39}, {39,40}, {40,41}, {41,42}, {42,43}, {43,44}, {44,45}, {45,46}, {46,47}, {1,47} } Symmetric graph 2 of order 47 Valency 46 Diameter 1 Girth 3 Automorphism group of order 258623241511168180642964355153611979969197632389120000000000 Number of arcs = 2162 Number of 2-arcs = 97290 2-arc-transitive true Edge-set { {1,2}, {2,3}, {3,25}, {3,4}, {3,28}, {4,26}, {14,28}, {4,5}, {6,28}, {4,29}, {28,42}, {5,27}, {6,39}, {15,29}, {21,42}, {5,6}, {6,31}, {7,29}, {9,42}, {5,30}, 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Total time: 15712.139 seconds,Total memory usage: 529.41MB