Equienergetic and almost-equienergetic trees

Abstract

The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G . Two graphs Ga and Gb are said to be equienergetic if E(Ga) = E(Gb) . Numerous families of non-cospectral equienergetic graphs have been reported so far. However, until now it was not noticed that there exist pairs of graphs whose energies differ insignificantly. We refer to such graphs as almost–equienergetic. A detailed study of almost–equienergetic trees is provided.