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 to be a regular representation is that there are no non-trivial group automorphisms of that fix 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}
}
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11 pages