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arXiv · 2610.33692

On the isomorphism problem of Cayley digraphs

Péter P. Pálfy
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Abstract

A finite group $G$ is called a DCI-group provided any two Cayley digraphs $Cay(G,S)$ and $Cay(G,T)$ are isomorphic iff the two connection sets $S$ and $T$ are images of each other via automorphisms of the group $G$. Building on the vast literature on CI- and DCI-groups we present an updated list of possible DCI-groups. In addition, we give an alternative proof that does not rely on deep results from group theory. We also point out the three most important open problems related to the classification of DCI-groups.

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Péter P. Pálfy. 2026-10-24. On the isomorphism problem of Cayley digraphs. https://arxiv.org/abs/2610.33692

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