| 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. 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. |
