Towards a definition of almost-equienergetic graphs

Abstract

The energy E(G) of a graph G, a quantity closely related to total Π-electron energy, is equal to the sum of absolute values of the eigenvalues of G. Two graphs Ga and Gb are said to be equienergetic if E(Ga) = E(Gb). In 2009 it was discovered that there are pairs of graphs for which the difference E(Ga) - E(Gb) is non-zero, but very small. Such pairs of graphs were referred to as almost equienergetic, but a precise criterion for almost-equienergeticity was not given. We now fill this gap. © 2013 Springer Science+Business Media New York.