Maximal energy graphs

Abstract

Given a graph G, its energyE(G) is defined as the sum of the absolute values of the eigenvalues of G. The concept of the energy of a graph was introduced in the subject of chemistry by I. Gutman, due to its relevance to the total π-electron energy of certain molecules. In this paper, we show that if G is a graph on n vertices, then E(G)≤n21+n must hold, and we give an infinite family of graphs for which this bound is sharp. © 2001 Academic Press.