A decreasing sequence of upper bounds for the Laplacian energy of a tree

Abstract

Let R be a nonnegative Hermitian matrix. The energy of R, denoted by E(R), is the sum of absolute values of its eigenvalues. We construct an increasing sequence that converges to the Perron root of R. This sequence yields a decreasing sequence of upper bounds for E(R). We then apply this result to the Laplacian energy of trees of order n, namely to the sum of the absolute values of the eigenvalues of the Laplacian matrix, shifted by -2(n-1)/n. © 2014 Elsevier Inc.