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 ${\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n$ are the eigenvalues of the adjacency matrix of $G$. In this paper, we characterize all pentacyclic graphs of order $n$ with maximal Estrada index.