On sufficient spectral radius conditions for hamiltonicity

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 condition due to Chvátal, an operation edges is known as Kelmans’ transformation.