University of KashanMathematics Interdisciplinary Research2538-36392220171201The Signless Laplacian Estrada Index of Unicyclic Graphs1551674667910.22052/mir.2017.57775.1038ENHamid RezaEllahiDepartment of Mathematics,
Faculty of Science,
University of Qom,
Qom, I R IranRaminNasiriDepartment of Mathematics,
Faculty of Science,
University of Qom,
Qom, I R IranGholam HosseinFath-TabarDepartment of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kahsan, Kashan, IranAhmadGholamiDepartment of Mathematics,
Faculty of Science,
University of Qom,
Qom, I R IranJournal Article20160714For a simple graph G, the signless Laplacian Estrada index is defined as SLEE(G)=∑<sup>n</sup><sub>i=1</sub>e<sup>qi</sup>, where q<sub>1</sub>, q<sub>2</sub>,..., q<sub>n</sub> 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.https://mir.kashanu.ac.ir/article_46679_9ebe519f917a721f6f9fd832c72a83d7.pdf