Zagreb Energy of Some Classes of Graphs

Abstract

Let G be a graph with n vertices and di is the degree of its ith vertex (d(i) is the degree of v(i)), then the Zagreb matrix of G is the square matrix of order n whose (i,j)entry is equal to d(i) + d(j) if the ith and jth vertex of G are adjacent, and zero otherwise. The Zagreb energy ZE(G) of a graph G is defined as the sum of the absolute values of the eigenvalues of the Zagreb matrix. In this paper, we compute the Zagreb energy for some of the specific graphs, edge deleted graphs and complements graphs. Moreover, some properties of the eigenvalues and bounds for Zagreb energy are also discussed.