On the extended Estrada index of some 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 show the extended Estrada index of the complete bipartite graphs and the friendship graphs. Also the relationship of the extended Estrada index between the m-splitting, m-shadow graphs and the original graphs are obtained.