Composing group automorphisms with colour-preserving automorphisms of Cayley graphs

Dave Witte Morris

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arXiv · 2609.09580

Composing group automorphisms with colour-preserving automorphisms of Cayley graphs

Dave Witte Morris

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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.

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Dave Witte Morris. 2026-09-09. Composing group automorphisms with colour-preserving automorphisms of Cayley graphs. https://arxiv.org/abs/2609.09580

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