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arXiv · 1505.05771

Cayley graphs of more than one abelian group

Edward Dobson·Joy Morris
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Abstract

We show that for certain integers $n$, the problem of whether or not a Cayley digraph $Γ$ of $\mathbb Z_n$ is also isomorphic to a Cayley digraph of some other abelian group $G$ of order $n$ reduces to the question of whether or not a natural subgroup of the full automorphism group contains more than one regular abelian group up to isomorphism (as opposed to the full automorphism group). A necessary and sufficient condition is then given for such circulants to be isomorphic to Cayley digraphs of more than one abelian group, and an easy-to-check necessary condition is provided.

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Edward Dobson, Joy Morris. 2020-09-17. Cayley graphs of more than one abelian group. https://arxiv.org/abs/1505.05771

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