【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n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。更多还原

【Abstract】 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].更多还原