On maximum signless Laplacian Estrada indices of k-trees

Abstract The signless Laplacian Estrada index of a graph G is defined as S L E E ( G ) = ∑ i = 1 n e q i , 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 S L E E .