Power Graph Classes and Overfullness

Abstract

In this paper, we investigate the edge-coloring number of the power graph of a finite group. We show that the power graph of a finite group $G$ is overfull if and only if the power graph of $G$ is of Class $2$ (has edge-coloring number one more than its maximum vertex degree) if and only if $G$ is a cyclic group of odd prime power order.