relation between the power graph of finite group and commutative elements

Let g be a finite group.## the power graph of a group g, with notation p(g) is a graph such that it’s vertex set is the group g and two distinct elements x, y are adjacent if and only if x = yn or y = xn for some positive integer n.## for a nonempety set x of g, the commuting graph c(g, x) is the graph with x as the vertex set and two distinct elements of x being joined by an edge if they are commuting elements of g. the purpose of this paper is study of groups with property p(g) = c(g, g).