华东师范大学学报(自然科学版) ›› 2015, Vol. 2015 ›› Issue (1): 126-130.doi: 10.3969/j.issn.1000-5641.2015.01.015

• 应用数学与基础数学 • 上一篇    下一篇

关于图的第三大拉普拉斯特征值的极限点(英)

吴雅容   

  1. 上海海事大学 文理学院, 上海 201306
  • 收稿日期:2014-04-01 出版日期:2015-01-25 发布日期:2015-03-29
  • 通讯作者: 吴雅容, 女, 博士, 研究方向为图论及其应用. E-mail:wuyarong1@163.com
  • 基金资助:

    国家自然科学基金(11226290, 11271315, 11401373)

On limit points of the third largest Laplacian eigenvalues of graphs

 WU  Ya-Rong   

  1. College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China
  • Received:2014-04-01 Online:2015-01-25 Published:2015-03-29

摘要: 对于任一自然数b,假设方程bμ(μ2)(μ1)2(μ3)=0的第二大特征根分别为lG(b);假设方程bμ(μ2)(μ1)2(μ3)(μ1)(μ2)=0的第二大特征根分别为lT(b).\,本文首先证明了存在图序列{Gn,b}{Tn,b},其第三大拉普拉斯特征值的极限点分别为lG(b)lT(b),(b=0,1,). 其次, 本文证明了lG(b),lT(b)2是第三大拉普拉斯特征值的所有小于等于2极限点

关键词: 拉普拉斯特征值, 特征多项式, 极限点

Abstract: For a different parameter b, let lG(b) denote the second largest root of bμ(μ2)(μ1)2(μ3)=0 (b=0,1,) and lT(b) denote the second largest root of bμ(μ2)(μ1)2(μ3)(μ1)(μ2)=0(b=0,1,). Firstly, we will prove that there exist sequences of graphs  {Gn,b}(b=0,1,) and {Tn,b}(b=0,1,) such that their limit points of the third largest Laplacian eigenvalues are lG(b) and lT(b), respectively. Secondly, we will prove that lG(b), lT(b) and 2 are all of the limit points of the third largest Laplacian eigenvalues which are no more than 2

Key words: Laplacian eigenvalue, characteristic polynomial, limit point

中图分类号: