On maximum signless Laplacian Estrada indices of k-trees

The signless Laplacian Estrada index of a graph G is defined as SLEE(G) = Sigma(n)(i=i) e(qi), where q(1), q(2), ... q(n) are the eigenvalues of the signless Laplacian matrix of G. A k-tree is either a complete graph on k vertices or a graph obtained from a smaller k-tree by adjoining a new vertex together with k edges connecting it to a k-clique. Denote by T-n(k) the set of all k-trees of order n. In this paper, we characterize the graphs among T-n(k) with the first (resp. the second) largest SLEE. (C) 2019 Elsevier B.V. All rights reserved.