Cayley graphs of more than one abelian group

2015/05/21 by Dobson, Edward, Morris, Joy
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1505.05771

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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