Laplacian Estrada index of trees

Abstract

Let $G$ be a simple graph with $n$ vertices and let ${\mu }_1⩾{\mu }_2⩾...⩾{\mu }_{n-1}⩾{\mu }_n=0$ be the eigenvalues of its Laplacian matrix. The Laplacian Estrada index of a graph $G$ is defined as $LEE(G)=\sum _{i=1}^n{e}^{{\mu }_i}$. Using the recent connection between Estrada index of a line graph and Laplacian Estrada index, we prove that the path $P_n$ has minimal, while the star $S_n$ has maximal $LEE$ among trees on $n$ vertices. In addition, we find the unique tree with the second maximal Laplacian Estrada index.

8 pages, 1 figure

References in corpus (1)

• On sum of powers of Laplacian eigenvalues and Laplacian Estrada index of graphs