On sufficient spectral radius conditions for hamiltonicity of k-connected graphs

Abstract

In this paper, we present two new sufficient conditions on the spectral radius ρ(G) that guarantee the hamiltonicity and traceability of a k-connected graph G of sufficiently large order, respectively, unless G is a specified exceptional graph. In particular, if k≥2, n≥k3+k+2, and ρ(G)>n−k−1−1n, then G is hamiltonian, unless G is a specified exceptional graph. If k≥1, n≥k3+k2+k+3, and ρ(G)>n−k−2−1n, then G is traceable, unless G is a specified exceptional graph.