Affine primitive symmetric graphs of diameter two
Abstract
Let be a positive integer, be a prime power, and be a vector space of dimension over . Let , where is an irreducible subgroup of which is maximal by inclusion with respect to being intransitive on the set of nonzero vectors. We are interested in the class of all diameter two graphs that admit such a group as an arc-transitive, vertex-quasiprimitive subgroup of automorphisms. In particular, we consider those graphs for which is a subgroup of either or and is maximal in one of the Aschbacher classes , where . We are able to determine all graphs which arise from with , and from with . For the remaining classes we give necessary conditions in order for to have diameter two, and in some special subcases determine all -symmetric diameter two graphs.
Cite
@article{arxiv.1601.07663,
title = {Affine primitive symmetric graphs of diameter two},
author = {Carmen Amarra and Michael Giudici and Cheryl E. Praeger},
journal= {arXiv preprint arXiv:1601.07663},
year = {2016}
}