Cayley graphs on non-isomorphic groups

TL;DR

This paper investigates conditions under which Cayley graphs on abelian groups can also be represented as Cayley graphs on generalized dihedral groups, exploring the relationship between different group structures for the same graph.

Contribution

It provides new criteria for when Cayley graphs on abelian groups can be represented on generalized dihedral groups and vice versa.

Findings

Identifies conditions for Cayley graphs on abelian groups to be represented on generalized dihedral groups

Establishes criteria for when such representations are possible in both directions

Advances understanding of the relationship between different group structures for Cayley graphs

Abstract

A number of authors have studied the question of when a graph can be represented as a Cayley graph on more than one nonisomorphic group. In this paper we give conditions for when a Cayley graph on an abelian group can be represented as a Cayley graph on a generalized dihedral group, and conditions for when the converse is true.