English

Detecting Graphical and Digraphical Regular Representations in groups of squarefree order

Combinatorics 2023-10-17 v1

Abstract

A necessary condition for a Cayley digraph Cay(R,S)(R,S) to be a regular representation is that there are no non-trivial group automorphisms of RR that fix SS setwise. A group is DRR-detecting or GRR-detecting if this condition is also sufficient for all Cayley digraphs or graphs on the group, respectively. In this paper, we determine precisely which groups of squarefree order are DRR-detecting, and which are GRR-detecting.

Keywords

Cite

@article{arxiv.2310.10243,
  title  = {Detecting Graphical and Digraphical Regular Representations in groups of squarefree order},
  author = {Joy Morris and Gabriel Verret},
  journal= {arXiv preprint arXiv:2310.10243},
  year   = {2023}
}

Comments

11 pages

R2 v1 2026-06-28T12:51:46.335Z