The PageRank algorithm perturbs the adjacency matrix defined by a set of web pages and hyperlinks such that the resulting matrix is positive and row-stochastic. Applying the Perron-Frobenius theorem establishes that the eigenvector associated with the dominant eigenvalue exists and is unique. For some graphs, the PageRank algorithm may yield a canonical isomorph. We propose a ranking method bas...

Given V a finite set, a self–adjoint operator on C(V ), K, is called elliptic if it is positive semi–definite and its lowest eigenvalue is simple. Therefore, there exists a unique, up to sign, unitary function ω ∈ C(V ) satisfying K(ω) = λω and then K is named (λ, ω)–elliptic. Clearly, a (λ, ω)–elliptic operator is singular iff λ = 0. Examples of elliptic operators are the so–called Schrödinger...

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.