The signless Laplacian Estrada index of tricyclic graphs

The signless Laplacian Estrada index of a graph G is defined as SLEE(G) = P n i=1 e q i where q1,q2,...,qn are the eigenvalues of the signless Laplacian matrix of G. In this paper, we show that there are exactly two tricyclic graphs with the maximal signless Laplacian Estrada index.