关于树和单圈图的第k大特征值

On the Largest kth Eigenvalues of Trees and Unicyclic Graphs

设T是kt＋l（k≥2，0＜l＜k）顶点树，G是n顶点单圈图。本文得到了l＝1时T的第k大特征值上界极图的某些性质，并且给出了G的第k（1＜k＜［n／2］）大特征值的一个上界和一个下界。

Let T be a tree with kt + 1 (k≥2, 0<1<k,) vertice, and G be a unicyclic connectedgraph with n vertices. In this paper, we give out some properties of the upper bound extremalgraphs of the largest kth eigenvalues of T. And we obtain a upper bound and a lower bound of thelargest k th (1<k<[2/n]) eigenvalue of G.