Power graph of finite abelian groups

Abstract

Let G be a group. The power graph ΓP(G) of G is a graph with vertex set V(ΓP(G)) = G and two distinct vertices x and y are adjacent in ΓP(G) if and only if either xˡ = y or yʲ = x, where 2 ≤ i, j ≤ n. In this paper, we obtain some fundamental characterizations of the power graph. Also, we characterize certain classes of power graphs of finite abelian groups.