关于树的代数连通度的Fiedler不等式的新证明(英文)

被引：3

作者：

范益政

机构：

[1] 南京师范大学数学系江苏南京安徽大学数学系,安徽合肥

来源：

数学研究 | 2003年 / 04期

关键词：

树; Laplace矩阵; 代数连通度;

D O I：

暂无

中图分类号：

O157.5 [图论];

学科分类号：

070104 ;

摘要：

设T为含n个顶点的树,L(T)为其Laplace矩阵.L(T)的次小特征值a(T)称为T的代数连通度.Fiedler给出如下关于a(T)的界的经典结论. a(Pn)≤a(T)≤a(Sn),其中Pn,Sn分别为含有n个顶点的路和星.Merris和Mass独立地证明了:a(T)=a(Sn)当且仅当T=Sn.通过重新组合由Fiedler向量所赋予的顶点的值,本文给出上述不等式的新证明,并证明了:a(T)=a(Pn)当且仅当T=Pn.

引用

页码：379 / 383

页数：5

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