Two families of graphs that are Cayley on nonisomorphic groups

Year 2021, Volume: 8 Issue: 1, 53 - 57, 15.01.2021

Joy Morris Josip Smolcic

https://doi.org/10.13069/jacodesmath.867644

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. The work to date has focussed on a few special situations: when the groups are $p$-groups; when the groups have order $pq$; when the Cayley graphs are normal; or when the groups are both abelian. In this paper, we construct two infinite families of graphs, each of which is Cayley on an abelian group and a nonabelian group. These families include the smallest examples of such graphs that had not appeared in other results.

Keywords

Cayley graphs , Nonisomorphic groups , Cayley on nonisomorphic groups

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