Bounds for the energy of graphs

Abstract

© 2016, Hacettepe University. All rights reserved. The energy of a graph G, denoted by E(G), is the sum of the absolute values of all eigenvalues of G. In this paper we present some lower and upper bounds for E(G) in terms of number of vertices, number of edges, and determinant of the adjacency matrix. Our lower bound is better than the classical McClelland’s lower bound. In addition, Nordhaus–Gaddum type results for E(G) are established.