Maximum Estrada Index of Bicyclic Graphs

Abstract

Let $G$ be a simple graph of order $n$, let $λ_1(G),λ_2(G),...,λ_n(G)$ be the eigenvalues of the adjacency matrix of $G$. The Esrada index of $G$ is defined as $EE(G)=\sum_{i=1}^{n}e^{λ_i(G)}$. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order.