English

Cubic Graphical Regular Representations of $\mathrm{PSU}_3(q)$

Group Theory 2022-01-13 v1 Combinatorics

Abstract

A graphical regular representation (GRR) of a group GG is a Cayley graph of GG whose full automorphism group is equal to the right regular permutation representation of GG. Towards a proof of the conjecture that only finitely many finite simple groups have no cubic GRR, this paper shows that PSU3(q)\mathrm{PSU}_3(q) has a cubic GRR if and only if q4q\geq4. Moreover, a cubic GRR of PSU3(q)\mathrm{PSU}_3(q) is constructed for each of these qq.

Keywords

Cite

@article{arxiv.2201.04307,
  title  = {Cubic Graphical Regular Representations of $\mathrm{PSU}_3(q)$},
  author = {Jing Jian Li and Binzhou Xia and Xiao Qian Zhang and Shasha Zheng},
  journal= {arXiv preprint arXiv:2201.04307},
  year   = {2022}
}
R2 v1 2026-06-24T08:47:18.678Z