中文摘要：

利用图的移接变换与谱半径大小的关系，研究了树及其合成图的排序（按其谱半径从大到小）问题。首先，依据树的直径对”阶树的集合进行了分类，得到了树的一个排序。其次，研究了连通图与树的合成图的分类与排序问题，得到了一个排序及固定割边数的具有最大谱半径的极图。

英文摘要：

Using the relation of the spectral radii and the moving transformation of graphs, we have studied the order of the graphs combining trees with a connected graph by their largest eigenvalues. First, by the diameters of trees, we have classified the trees with n vertices, and have obtained an order of trees. This result is consistent with the result of Wenshui Lin and Xiaofeng Guo [Linear Algebra Appl. , 2006, 418]. Second we have described the classification and ordering of the graphs combining trees with a connected graph, and have obtained an order of the combinative graphs and a maximal graph with cut edges, the later is one main result of Huiqing Lin, Mei Lu and Feng Tian [Linear Algebra Appl. , 2004, 389].