Spectral radius and traceability of connected claw-free graphs

Abstract

Let G be a connected claw-free graph on n vertices and G be its complement. Let μ(G) be the spectral radius of G. Denote by Nn−3,3 the graph consisting of Kn−3 and three disjoint pendent edges. In this note we prove that: (1) If μ(G) ≥ n − 4, then G is traceable unless G = Nn−3,3. (2) If μ(G) ≤ μ(Nn−3,3) and n ≥ 24, then G is traceable unless G = Nn−3,3. Our works are counterparts on claw-free graphs of previous theorems due to Lu et al., and Fiedler and Nikiforov, respectively.