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WU Ya-Rong. On limit points of the third largest Laplacian eigenvalues of graphs[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 126-130. doi: 10.3969/j.issn.1000-5641.2015.01.015
Citation:
WU Ya-Rong. On limit points of the third largest Laplacian eigenvalues of graphs[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 126-130. doi: 10.3969/j.issn.1000-5641.2015.01.015
WU Ya-Rong. On limit points of the third largest Laplacian eigenvalues of graphs[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 126-130. doi: 10.3969/j.issn.1000-5641.2015.01.015
Citation:
WU Ya-Rong. On limit points of the third largest Laplacian eigenvalues of graphs[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 126-130. doi: 10.3969/j.issn.1000-5641.2015.01.015
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
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.