The automorphism groups of small affine rank 3 graphs
Abstract
A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the classification of rank 3 graphs being complete, see, e.g., Chapter 11 of the recent monograph 'Strongly regular graphs' by Brouwer and Van Maldeghem, the full automorphism groups of these graphs (equivalently, the 2-closures of rank 3 groups) have not been explicitly described, though a lot of information on this subject is available. In the present note, we address this problem for the affine rank 3 graphs. We find the automorphism groups for finitely many relatively small graphs and show that modulo known results, this provides the full description of the automorphism groups of the affine rank 3 graphs, thus reducing the general problem to the case when the socle of the automorphism group is nonabelian simple.
Keywords
Cite
@article{arxiv.2406.04559,
title = {The automorphism groups of small affine rank 3 graphs},
author = {Jin Guo and Andrey V. Vasil'ev and Rui Wang},
journal= {arXiv preprint arXiv:2406.04559},
year = {2024}
}