recent results on the q-spectral moments of graphs

The k-th signless laplacian spectral moment (k-th q-spectral moment) of a graph g is t_k(g) =σ^n_{i=1} q^k_i ,where q1, q2, . . . , qn are signless laplacian eigenvalues of g. in this research, we investigate unique graph with the greatest q-spectral moments with a given number of cut edges, cut vertices, pendent vertices, (vertex) connectivity, edge connectivity, or diameter. also we show that there exist exactly two graphs with maximum q-spectral moments in the class of all n-vertex tricyclic graphs, for n ≥ 5. finally, we characterize the unicyclic graphs with the first two largest and smallest q-spectral moments and then determine the unique unicyclic graph with maximum q-spectral moments among all unicyclic graphs on n vertices with a given diameter.