Bounds of distance Estrada index of graphs

TL;DR

This paper establishes new bounds and inequalities for the distance Estrada index of connected graphs, enhancing understanding of its extremal properties and relationships.

Contribution

It introduces novel lower and upper bounds for the distance Estrada index and a Nordhaus-Gaddum type inequality, expanding theoretical insights into graph spectral measures.

Findings

New lower bounds for $DEE(G)$

New upper bounds for $DEE(G)$

A Nordhaus-Gaddum type inequality for $DEE(G)$

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 $DEE(G)=\sum_{i=1}^ne^{\lambda_i}$. 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.