%A WU Ya-Rong
%T On limit points of the third largest Laplacian eigenvalues of graphs
%0 Journal Article
%D 2015
%J Journal of East China Normal University(Natural Science)
%R 10.3969/j.issn.1000-5641.2015.01.015
%P 126-130
%V 2015
%N 1
%U {https://xblk.ecnu.edu.cn/CN/abstract/article_25065.shtml}
%8 2015-01-25
%X 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