The Signless Laplacian Estrada Index of Unicyclic Graphs

چکیده مقاله

For a simple graph G, the signless Laplacian Estrada index is defined as SLEE(G) is sum of e^q_i , where q_1; q_2; : : : ; q_n are the eigenvalues of the sign-less 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 Lapla-cian resolvent energy.