On fixity of arc-transitive graphs

The relative fixity of a permutation group is the maximum proportion points fixed by non-trivial element group, and graph its automorphism viewed as on vertex-set graph. We prove in this paper that connected 2-arc-transitive graphs valence tends to 0 number vertices grows infinity. same result for class arc-transitive prime valence, more generally, any locally-L graphs, where L quasiprimitive graph-restrictive group.