doiSerbia

On the power graph of a finite group

Mirzargar M. (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Kashan, Kashan, I. R. Iran)
Ashrafi A.R. (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Kashan, Kashan, I. R. Iran)
Nadjafi-Arani M.J. (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Kashan, Kashan, I. R. Iran)

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. In this paper, 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.

Keywords: power graph, clique number, EPPO-group, maximal cyclic subgroup