中文摘要：

针对无爪图,将谱半径与稳定性相结合,得出了其关于可迹性判定的两个结论。此结论又利用图与补图的谱半径分别刻画无爪连通图是可迹图的充分条件,并利用一系列引理及代数方法加以证明,部分结论优于前人的成果。

英文摘要：

In this paper,two conclusions are obtained for the determination of the traceability of the claw-free graph,by the way of combining the method of spectral radius and stability. These conclusions are described as the sufficient condition of clawfree connected graph by the spectral radius of graph and complementary graph. Some lemmas are used to prove them,and some conclusions are better than the previous ones.