Title Locally s-arc-transitive graphs related to sporadic simple groups
Author Dimitri Leemans
Abstract We show that, up to isomorphism, there are ten locally (M_{11},2)-arc-transitive graphs. Then, using a series of Magma programs, we compute, up to conjugacy, the locally (G,s)-arc-transitive graphs for G = M_{11}, M_{12}, M_{22}, M_{23}, M_{24}, J_{1}, J_{2}, J_{3}, HS, McL, He, Ru, Suz and Co_3. We also obtain an almost complete classification for the O'Nan sporadic group O'N. We get some spectacular examples, like, for instance, locally (G,7)- and (G,9)-arc-transitive graphs for G= He and Ru. We also get some locally (G,7)-arc-transitive graphs for J_3 and O'N.

Download the Magma files containing the vertex-stabilizers of the graphs obtained in the paper.
M_11, M_12, M_22, M_23, M_24, J_1, J_2, J_3, HS, McL, He, Ru, Suz, Co3

Once you have dowloaded one of the files above, if you load it in Magma, a sequence geo will be created containing sequences of two subgroups that are the vertex-stabilizers of the graphs.

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