Let $G$ be a connected claw-free graph on $n$ vertices and $\overline{G}$ beits complement graph. Let $\mu(G)$ be the spectral radius of $G$. Denote by$N_{n-3,3}$ the graph consisting of $K_{n-3}$ and three disjoint pendent edges.In this note we prove that: (1) If $\mu(G)\geq n-4$, then $G$ is traceableunless $G=N_{n-3,3}$. (2) If $\mu(\overline{G})\leq \mu(\overline{N_{n-3,3}})$and $n\geq 24$, then $G$ is traceable unless $G=N_{n-3,3}$. Our works arecounterparts on claw-free graphs of previous theorems due to Lu et al., andFiedler and Nikiforov, respectively.
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机译：假设$ G $是$ n $顶点和$ \ overline {G} $ beits补图的连通无爪图。令$ \ mu（G）$为$ G $的光谱半径。用$ N_ {n-3,3} $表示由$ K_ {n-3} $和三个不相交的下垂边缘组成的图。在此注释中，我们证明：（1）如果$ \ mu（G）\ geq n -4 $，则除非$ G = N_ {n-3,3} $，否则$ G $是可追踪的。 （2）如果$ \ mu（\ overline {G}）\ leq \ mu（\ overline {N_ {n-3,3}}）$$和$ n \ geq 24 $，则除非$ G可以跟踪$ G $ = N_ {n-3,3} $。我们的工作分别对应于Lu等人，Fiedler和Nikiforov提出的先前定理的无爪图。
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