During the last decade several research groups have published results on sufficient conditions for hamiltonicity of graphs in terms their spectral radius and signless Laplacian radius. Here we extend some these results. All our involve characterization exceptional graphs, i.e., all nonhamiltonian that satisfy condition. The proofs main are based Bondy–Chvátal closure, a degree sequence conditio...

Let K be an algebraically closed field, X a smooth projective variety over K and f : X → X a dominant regular morphism. Let N (X) be the group of algebraic cycles modulo numerical equivalence. Let χ(f) be the spectral radius of the pullback f∗ : H∗(X,Ql) → H ∗(X,Ql) on l-adic cohomology groups, and λ(f) the spectral radius of the pullback f∗ : N∗(X) → N∗(X). We prove in this paper, by using con...

In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.