Extremal Laplacian Estrada Index of Threshold Graphs with Given Size

Abstract

Let \(G\) be a simple graph on \(n\) vertices. The Laplacian Estrada index of \(G\) is defined as \(LEE(G) = \sum_{i=1}^{n} e^{\mu_i}\), where \(\mu_1, \mu_2, \dots, \mu_n\) are the Laplacian eigenvalues of \(G\). In this paper, threshold graphs on \(n\) vertices and \(m\) edges having maximal and minimal Laplacian Estrada index are determined, respectively.