Abstract

We show that, up to isomorphism, there are ten locally (M_{11},2)arctransitive graphs.
Then, using a series of Magma programs, we compute, up to conjugacy, the locally (G,s)arctransitive 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)arctransitive graphs for G= He and Ru.
We also get some locally (G,7)arctransitive graphs for J_3 and O'N.
Download the Magma files containing the vertexstabilizers 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 vertexstabilizers of the graphs.
