Estimating the distance Estrada index

Abstract

Suppose $G$ is a simple graph on $n$ vertices. The $D$-eigenvalues ${\mu }_1,{\mu }_2,\cdots ,{\mu }_n$ of $G$ are the eigenvalues of its distance matrix. The distance Estrada index of $G$ is defined as $DEE(G)={\sum }_{i=1}^n{e}^{{\mu }_i}$. In this paper, we establish new lower and upper bounds for $DEE(G)$ in terms of the Wiener index $W(G)$. We also compute the distance Estrada index for some concrete graphs including the buckminsterfullerene $C_{60}$.

8 pages, 2 figures