The Signless Laplacian Estrada Index of Unicyclic Graphs

‎For a simple graph G ‎, ‎the signless Laplacian Estrada index is defined as SLEE(G)=Σ^ n _i=1 e^ q^i‎, ‎where q1; q2; : : : ; qn are the eigenvalues of the signless Laplacian matrix of G ‎. ‎In this paper‎, ‎we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$’s and then determine the unique unicyclic graph with maximum $SLEE$ among all ‎unicyclic graphs on n vertices with a given diameter‎. ‎All extremal graphs‎, ‎which have been introduced in our results are also extremal with respect to the signless Laplacian ‎resolvent energy‎.