Bounds of distance Estrada index of graphs

Abstract

Let ${\lambda }_1,{\lambda }_2,\cdots ,{\lambda }_n$ be the eigenvalues of the distance matrix of a connected graph $G$. The distance Estrada index of $G$ is defined as $DEE(G)={\sum }_{i=1}^n{e}^{{\lambda }_i}$. In this note, we present new lower and upper bounds for $DEE(G)$. In addition, a Nordhaus-Gaddum type inequality for $DEE(G)$ is given.

arXiv commentTo appear in Ars Combin

References in corpus (1)

• On Distance Spectral Radius and Distance Energy of Graphs