The Signless Laplacian Estrada Index of Unicyclic Graphs
نویسندگان
1 Department of Mathematics, Faculty of Science, University of Qom, Qom, I R Iran
2 Department of Mathematics, Faculty of Science, University of Qom, Qom, I R Iran
3 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kahsan, Kashan, Iran
4 Department of Mathematics, Faculty of Science, University of Qom, Qom, I R Iran
doi
10.22052/mir.2017.57775.1038چکیده
For a simple graph G, the signless Laplacian Estrada index is defined as SLEE(G)=∑ni=1eqi, 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.
