Maximum Estrada Index of Bicyclic Graphs

TL;DR

This paper identifies the bicyclic graph with the highest Estrada index among all graphs of a fixed size, providing a unique extremal structure based on spectral properties.

Contribution

It determines the unique maximum Estrada index graph within the class of bicyclic graphs of fixed order, advancing spectral graph theory understanding.

Findings

Identifies the unique bicyclic graph with maximum Estrada index

Provides explicit characterization of the extremal graph

Enhances understanding of spectral extremal problems

Abstract

Let $G$ be a simple graph of order $n$, let $\lambda_1(G),\lambda_2(G),...,\lambda_n(G)$ be the eigenvalues of the adjacency matrix of $G$. The Esrada index of $G$ is defined as $EE(G)=\sum_{i=1}^{n}e^{\lambda_i(G)}$. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order.