关于图的临界群的秩  

On the Rank of the Critical Group

作　　者：王健[1] 

机构地区：[1]浙江外国语学院理工学院,浙江杭州310012

出　　处：《浙江外国语学院学报》2011年第5期96-98,106,共4页Journal of Zhejiang International Studies University

摘　　要：图的临界群决定了其支撑树的内部结构,因而支撑树的很多性质可以通过研究图的临界群得到.作为顶点数有限的图,其临界群是一个有限生成的群.该群的生成元的数目显示了群结构的复杂性.所需要用到的生成元的最小数目即为临界群的秩.在不引起混淆的情况下,临界群的秩也被称为图的秩.秩越小,临界群的需要的生成元的数目也就越小,研究的难度也相应越小.有一部分图的秩的下界可以通过计算直接得到.The construct of the spanning tree of a graph depends on the corresponding critical group,so many properties of the spanning tree can be learned by studying the critical group.For a finite graph,the critical group is finitely generated.The number of the generators shows the complexity of a group.The minimum number of the generators is called rank.The rank of a critical group sometimes is also considered as the rank of a graph.Usually,a less rank will lead to a easier research.Some lower bound of a graph＇s rank is determined.

关 键 词：临界群 秩 生成元 

分 类 号：O175.5[理学—数学]