More on the relation between energy and laplacian energy of graphs

Abstract

I. Gutman et al. have recently conjectured that the energy of a graph does not exceed its Laplacian energy. We disprove this conjecture by giving a few small counterexamples and, in addition, an infinite set of counterexamples. Nevertheless, we do show that the standard deviation of eigenvalues of the adjacency matrix of every graph does not exceed the standard deviation of eigenvalues of its Laplacian matrix.