Some New Lower Bounds for the Estrada Index

TL;DR

This paper introduces new lower bounds for the Estrada index of graphs, including bipartite graphs, based on various graph invariants such as vertices, edges, degrees, and diameter.

Contribution

It provides novel lower bounds for the Estrada index that depend on multiple graph parameters, expanding the understanding of this spectral invariant.

Findings

New lower bounds for Estrada index derived

Bounds specific to bipartite graphs

Results depend on graph invariants like degrees and diameter

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 an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. In this paper, we present some new lower bounds obtained for the Estrada Index of graphs and in particular of bipartite graphs that only depend on the number of vertices, the number of edges, Randi\'c index, maximum and minimum degree and diameter.