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.