紧图的两个结果及其应用

双随机矩阵有许多重要的应用,紧图族可以看作是组合矩阵论中关于双随机矩阵的著名的Birkhoff定理的拓广,具有重要的研究价值.确定一个图是否紧图是个困难的问题,目前已知的紧图族尚且不多.给出了两个重要结果:任意紧图与任意多个孤立点的不交并是紧图;任意紧图的每一个顶点上各增加一条悬挂边的图是紧图.利用这两个结果,从已知紧图可构造出无穷多个紧图族.

Two results of the compact graph and its applications

Doubly stochastic matrix has many important applications, the family of compact graphs can be seen as the generalization of the famous Birkhoff theorem which is about doubly stochastic matrix, and is of important research value． Determine whether a graph is a compact graph is a difficult problem, at present there are only few compact graphs known． This paper gives two important results: the graph constructed by any compact graph combining some isolated points is a compact graph; the graph constructed by adding one pendant edge to each vertex of any compact graph is also a compact graph． By these two results, we can construct an infinite number of compact graph family from already known compact graph．