Some Bounds on Estrada Index of Graphs

Let G be a simple graph on n vertices. The Estrada index of G, denoted by EE(G), is defined as \(EE(G)=\sum _{i=1}^ne^{\lambda _i}\) $EE(G)={\sum }_{i=1}^n{e}^{{\lambda }_i}$ , where \(\lambda _1,\ldots ,\lambda _n\) ${\lambda }_1,\dots ,{\lambda }_n$ are the eigenvalues (the eigenvalues of the adjacency matrix) of G. In this paper we find some sharp bounds on the Estrada index of graphs in terms of the number of vertices, the number of edges and the rank of graphs.