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

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摘要： 对于任一自然数$b$,假设方程$b\mu(\mu-2)\!-\!(\mu-1)^2(\mu-3)\!=\!0$的第二大特征根分别为$l_G(b)$;假设方程$b\mu(\mu-2)\!-\!(\mu-1)^2(\mu-3)\!-\!(\mu-1)(\mu-2)\!=\!0$的第二大特征根分别为$l_T(b)$.\,本文首先证明了存在图序列$\{G_{n,b}\}$和$\{T_{n,b}\}$,其第三大拉普拉斯特征值的极限点分别为$l_G(b)$和$l_T(b)$,$(b\!=\!0,1,\cdots)$. 其次, 本文证明了$l_G(b)$,$l_T(b)$及$2$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 $l_G(b)$ denote the second largest root of $b\mu(\mu-2)\!-\!(\mu-1)^2(\mu-3)\!=\!0$ $(b\!=\!0,1,\cdots)$ and $l_T(b)$ denote the second largest root of $b\mu(\mu-2)\!-\!(\mu-1)^2(\mu-3)\!-\!(\mu-1)(\mu-2)\!=\!0$$(b\!=\!0,1,\cdots)$. Firstly, we will prove that there exist sequences of graphs  $\{G_{n,b}\}(b\!=\!0,1,\cdots)$ and $\{T_{n,b}\}(b\!=\!0,1,\cdots)$ such that their limit points of the third largest Laplacian eigenvalues are $l_G(b)$ and $l_T(b)$, respectively. Secondly, we will prove that $l_G(b)$, $l_T(b)$ 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

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