Cayley graphs of more than one abelian group

Keywords: Cayley graph, circulant graph, group


We show that for certain integers n, the problem of whether or not a Cayley digraph Γ of ℤn 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.

Author Biography

Joy Morris, University of Lethbridge, Canada

Department of Mathematics and Computer Science, Professor

Bled 2019 – Polytopes, Configurations, and Symmetries (Grünbaum Issue)