Shirin Alimirzaei

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...