Cayley graphs of more than one abelian group
Keywords:
Cayley graph, Different Groups
Abstract
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.
Published
2021-01-29
Issue
Section
Bled 2019 – Polytopes, Configurations, and Symmetries (Grünbaum Issue)