Spectral radius and Hamiltonicity of graphs with large minimum degree

Abstract

Let G be a graph of order n and λ(G) the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in G. One of the main results of the paper is the following theorem

Let k ≥ 2, n ≥ k ³ + k + 4, and let G be a graph of order n, with minimum degree δ(G) ≥ k. If

$$\lambda \left( G \right) \geqslant n - k - 1$$

, then G has a Hamiltonian cycle, unless G = K ₁∨(K _n−k−1+K _k ) or G = K _k ∨(K _n−2k + ${\bar K_k}$ ).