On maximum signless Laplacian Estrada index of graphs with given parameters II

Ramin Nasiri (Department of Mathematics, Faculty of Science, University of Qom, Qom 37161-46611, I. R. Iran)
Hamid Reza Ellahi (Department of Mathematics, Faculty of Science, University of Qom, Qom 37161-46611, I. R. Iran)
Gholam Hossein Fath-Tabar (Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran.)
Ahmad Gholami (Department of Mathematics, Faculty of Science, University of Qom, Qom 37161-46611, I. R. Iran)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 6, No 1 (2018): Electronic Journal of Graph Theory and Applications

The signless Laplacian Estrada index of a graph G is defined as SLEE(G) = ∑ni = 1eqi where q1, q2, …, qn are the eigenvalues of the signless Laplacian matrix of G. Following the previous work in which we have identified the unique graphs with maximum signless Laplacian Estrada index with each of the given parameters, namely, number of cut edges, pendent vertices, (vertex) connectivity, and edge connectivity, in this paper we continue our characterization for two further parameters: diameter and number of cut vertices.