PreprintCC BY 4.0arXiv
Composing group automorphisms with colour-preserving automorphisms of Cayley graphs
Abstract
We show that if φ is a colour-permuting automorphism of a connected, finite Cayley graph, and the order of the Cayley graph is either odd or square-free, then φ is the composition of a group automorphism and a colour-preserving graph automorphism. Some analogous results are also established for isomorphisms between two different Cayley graphs.
Related
- Property R∞ for Artin and Coxeter groups whose outer automorphisms are length-preserving
- Linear maps preserving Kasparov cycles and the characterization of induced automorphisms
- Minimal Cayley graphs with large chromatic number
- Odd-ordered Cayley graphs satisfy Erdős--Gyárfás
- COLORING SEMIMINIMAL CAYLEY GRAPHS
BibTeX
@misc{morris2026composing,
title = {{Composing group automorphisms with colour-preserving automorphisms of Cayley graphs}},
author = {Dave Witte Morris},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09580},
eprint = {2609.09580},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09580},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Composing group automorphisms with colour-preserving automorphisms of Cayley graphs
AU - Dave Witte Morris
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09580
UR - https://arxiv.org/abs/2609.09580
AB - We show that if φ is a colour-permuting automorphism of a connected, finite Cayley graph, and the order of the Cayley graph is either odd or square-free, then φ is the composition of a group automorphism and a colour-preserving graph automorphism. Some analogous results are also established for isomorphisms between two different Cayley graphs.
ER -