Bounds of the extended Estrada index of graphs.

Let G be a graph on n vertices and η1,η2,…,ηn the eigenvalues of its extended adjacency matrix. The extended Estrada index EEex is defined as the sum of the terms eηi,i=1,2,…,n. In this paper we establish lower and upper bounds for EEex in terms of the number of vertices and the number of edges and characterize the extremal graphs. Also the bounds for EEex of some special graphs are obtained.