应用数学与基础数学

关于图的第三大拉普拉斯特征值的极限点(英)

  • 吴雅容
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  • 上海海事大学 文理学院, 上海 201306

收稿日期: 2014-04-01

  网络出版日期: 2015-03-29

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
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  • College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China

Received date: 2014-04-01

  Online published: 2015-03-29

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

本文引用格式

吴雅容 . 关于图的第三大拉普拉斯特征值的极限点(英)[J]. 华东师范大学学报(自然科学版), 2015 , 2015(1) : 126 -130 . DOI: 10.3969/j.issn.1000-5641.2015.01.015

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

参考文献

HOFFMAN A J. On limit points on spectral radii of non-negative symmetric integral matrices [J]. Lecture Notes Math, 1972(303): 165-172.
BONDY J A, MURTY U S R. Graph Theory with Applications [M]. New York: The Macmillan Press LTD, 1976.
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