On the signless Laplacian Estrada index of bicyclic graphs

Abstract The signless Laplacian Estrada index of a graph 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 . In this paper, we determine the unique bicyclic graph with maximum S L E E and the unique bipartite bicyclic graph with maximum S L E E , respectively.