New Results on Zagreb Energy of Graphs

摘要

Let G be a graph with vertex set V(G) = {v(1), ... , v(n)}, and let d(i) be the degree of v(i). 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 vertices v(i) and v(j) are adjacent, and zero otherwise. The Zagreb energy ZE(G) of G is the sum of the absolute values of the eigenvalues of the Zagreb matrix. In this paper, we determine some classes of Zagreb hyperenergetic, Zagreb borderenergetic, and Zagreb equienergetic graphs.