On sufficient spectral radius conditions for hamiltonicity

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