Lower bounds for Estrada index and Laplacian Estrada index

Abstract

Let G be an n-vertex graph. If λ1, λ 2,⋯, λn and μ1, μ 2,⋯, μ n are the ordinary (adjacency) eigenvalues and the Laplacian eigenvalues of G, respectively, then the Estrada index and the Laplacian Estrada index of G are defined as EE (G) = Σni=1 eλi and LEE (G) = Σni=1 eλi, respectively. Some new lower bounds for EE and LEE are obtained and shown to be the best possible. © 2010 Elsevier Ltd. All rights reserved.