On the power graphs which are Cayley graphs of some groups

TL;DR

This paper fully characterizes finite groups whose power graphs can be represented as Cayley graphs of some groups, resolving a problem posed in 2013.

Contribution

It provides a complete characterization of finite groups with power graphs that are Cayley graphs, answering an open problem from 2013.

Findings

Complete classification of such finite groups

Resolution of the 2013 posed problem

Clarification of the relationship between power graphs and Cayley graphs

Abstract

In 2013, Jemal Abawajy, Andrei Kelarev and Morshed Chowdhury [1] proposed a problem to characterize the finite groups whose power graphs are Cayley graphs of some groups. Here we give a complete answer to this question.