Pentacyclic Graphs with Maximal Estrada Index

Abstract

The Estrada index of a simple connected graph \(G\) of order \(n\) is defined as \(EE(G) = \sum_{i=1}^{n} e^{\lambda_i}\), where \(\lambda_1, \lambda_2, \ldots, \lambda_n\) are the eigenvalues of the adjacency matrix of \(G\). In this paper, we characterize all pentacyclic graphs of order \(n\) with maximal Estrada index.