On the Power Graph of a Finite Group

M. Mirzargar, A. R. Ashrafi, M. J. Nadjafi-Arani

The power graph $P(G)$ of a group $G$ is the graph whose vertex set is the group elements and two elements are adjacent if one is a power of the other. We consider some graph theoretical properties of a power graph $P(G)$ that can be related to its group theoretical properties. As consequences of our results, simple proofs for some earlier results are presented.