On the signless Laplacian Estrada index of cacti

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 cactus is a connected graph in which any two cycles have at most one common vertex. In this paper, we characterize the unique graph with maximum S L E E among all cacti with n vertices and k cycles. Also, the unique graph with maximum S L E E among all cacti with n vertices and k cut edges is determined.