On maximum Estrada indices of bipartite graphs with some given parameters

TL;DR

This paper characterizes the bipartite graphs with the highest Estrada index given specific parameters like matching number and connectivity, advancing understanding of spectral graph properties.

Contribution

It identifies the unique extremal bipartite graphs with maximum Estrada index under constraints of matching number and connectivity.

Findings

Identifies the bipartite graph with maximum Estrada index for given matching number.

Determines the extremal bipartite graph with maximum Estrada index for specified connectivity.

Provides a characterization of these extremal graphs.

Abstract

The Estrada index of a graph $G$ is defined as $EE(G)=\sum_{i=1}^ne^{\lambda_i}$, where $\lambda_1,$ $ \lambda_2,\ldots, \lambda_n$ are the eigenvalues of the adjacency matrix of $G$. In this paper, we characterize the unique bipartite graph with maximum Estrada index among bipartite graphs with given matching number and given vertex-connectivity, edge-connectivity, respectively.