Asymptotic enumeration of graphical regular representations
Combinatorics
2023-08-01 v4 Group Theory
Abstract
We estimate the number of graphical regular representations (GRRs) of a given group with large enough order. As a consequence, we show that almost all finite Cayley graphs have full automorphism groups 'as small as possible'. This confirms a conjecture of Babai-Godsil-Imrich-Lovasz on the proportion of GRRs, as well as a conjecture of Xu on the proportion of normal Cayley graphs, among Cayley graphs of a given finite group.
Cite
@article{arxiv.2212.01875,
title = {Asymptotic enumeration of graphical regular representations},
author = {Binzhou Xia and Shasha Zheng},
journal= {arXiv preprint arXiv:2212.01875},
year = {2023}
}