On maximum Estrada indices of k-trees

The Estrada index of a graph G   is defined as EE(G)=∑i=1neλi, where λ1,λ2,…,λnλ1,λ2,…,λn are the eigenvalues of the adjacency matrix of G  . Let Tnk be the set of the k-trees of order n  . In this paper, we characterize the graphs among Tnk having the first (resp. the second) largest Estrada index.