The cubic power graph of finite abelian groups

Abstract

Let G be a finite abelian group with identity 0. For an integer the additive power graph of G is the simple undirected graph with vertex set G in which two distinct vertices x and y are adjacent if and only if x + y = nt for some with When the additive power graph has been studied in the name of square graph of finite abelian groups. In this paper, we study the additive power graph of G with n = 3 and name the graph as the cubic power graph. The cubic power graph of G is denoted by More specifically, we obtain the diameter and the girth of the graph and its complement Using these, we obtain a condition for and its complement to be self-centered. Also, we obtain the independence number, the clique number and the chromatic number of and its complement and hence we prove that and its complement are weakly perfect. Also, we discuss about the perfectness of At last, we obtain a condition for and its complement to be vertex pancyclic.