A wheel graph is a formed by connecting single vertex to all vertices of cycle. called wheel-free if it does not contain any as subgraph. In 2010, Nikiforov proposed Brualdi–Solheid–Turán type problem: what the maximum spectral radius order n that subgraphs particular kind. this paper, we study problem for graphs, and determine (signless Laplacian) n. Furthermore, characterize extremal graphs.

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) the Harary (also called matrix) while diag(RH(G)) represents diagonal of total vertices. In present work, some upper and lower bounds second-largest eigenvalue graphs in terms various parameters are investigated. Besides, all attaining these new characterized. Addi...

The signless Laplacian spectral radius of a graph G, denoted by q(G), is the largest eigenvalue its matrix. In this paper, we investigate extremal for graphs without short cycles or long cycles. Let G(m,g) be family on m edges with girth g and H(m,c) circumference c. More precisely, obtain unique maximal q(G) in H(m,c), respectively.