• 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)

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

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