New lower bounds for the Estrada and Signless Laplacian Estrada Index of a Graph

TL;DR

This paper introduces new lower bounds for the Estrada index of graphs, relating it to vertices, edges, and energy, and extends these bounds to non-negative Hermitian matrices.

Contribution

It provides novel lower bounds for the Estrada index using a different proof technique and extends the bounds to Hermitian matrices.

Findings

New lower bounds depend on vertices, edges, and energy.

Bounds are applicable to non-negative Hermitian matrices.

The results improve existing estimates for the Estrada index.

Abstract

Let $G$ be a graph on $n$ vertices and $\lambda_1,\lambda_2,\ldots,\lambda_n$ its eigenvalues. The Estrada index of $G$ is defined as $EE(G)=\sum_{i=1}^n e^{\lambda_i}.$ In this work, using a different demonstration technique, new lower bounds are obtained for the Estrada index, that depends on the number of vertices, the number of edges and the energy of the graph is given. Moreover, another lower bound for the Estrada index is obtained of an arbitrary non-negative Hermitian matrix are established.