Author

D. Morris

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Preprint Sep 2026

Isomorphisms of abelian Cayley graphs with their natural edge-colouring

We prove that if $\varphi$ is an isomorphism between two connected Cayley graphs of abelian groups, and $\varphi$ respects the natural edge-colourings of the Cayley graphs, then $\varphi$ is the composition of a group isomorphism and a colour-preserving graph automorphism. This implies that if every colour-preserving a...

Shirin Alimirzaei, D. Morris · 2 citations

Preprint Sep 2026

Composing group automorphisms with colour-preserving automorphisms of Cayley graphs

We show that if $\varphi$ 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 $\varphi$ is the composition of a group automorphism and a colour-preserving graph automorphism. Some analogous results are also established for isomorph...

D. Morris · 0 citations