The first three largest Estrada indices for trees

Abstract

Let G be a simple graph with n vertices, and λ1, … λn, be the eigenvalues of its adjacent matrix. The Estrada index of G is a graph invariant, defined as , is proposed as a measure of branching in alkanes. In this paper, we prove that, among trees with n vertices, S(2; n – 2) and S(3; n – 2) have the second and the third largest EE, respectively.