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| 关于三圈图的拉普拉斯谱半径的一些结果 | |
| 引用本文： | 陈艳,袁西英,韩苗苗. 关于三圈图的拉普拉斯谱半径的一些结果[J]. 运筹学学报, 2011, 15(4): 1-8 |
| 作者姓名： | 陈艳 袁西英 韩苗苗 |
| 作者单位： | 上海大学数学系 |
| 基金项目： | supported by Graduate Innovation Foundation of Shanghai University(SHUCX 112013); the National Science Foundation of China(No.10926085); Shanghai Leading Academic Discipline Project(No.S30104) |
| 摘 要： | 边数等于点数加二的连通图称为三圈图.~设 ~$Delta(G)$~和~$mu(G)$~ 分别表示图~$G$~的最大度和其拉普拉斯谱半径,设${mathcal T}(n)$~表示所有~$n$~阶三圈图的集合,证明了对于~${mathcal T}(n)$~的两个图~$H_{1}$~和~$H_{2}$~,~若~$Delta(H_{1})> Delta(H_{2})$ ~且 ~$Delta(H_{1})geq frac{n+7}{2}$,~则~$mu (H_{1})> mu (H_{2}).$ 作为该结论的应用,~确定了~${mathcal T}(n)(ngeq9)$~中图的第七大至第十九大的拉普拉斯谱半径及其相应的极图. |
| 关 键 词： | 拉普拉斯谱半径 三圈图 最大度 |
| 收稿时间： | 2011-06-03 |
| 修稿时间： | 2011-07-16 |
Some Results on the Laplacian Spectral Radii of Tricyclic Graphs |
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| CHEN Yan YUAN Xiying HAN Miaomiao. Some Results on the Laplacian Spectral Radii of Tricyclic Graphs[J]. OR Transactions, 2011, 15(4): 1-8 | |
| Authors: | CHEN Yan YUAN Xiying HAN Miaomiao |
| Affiliation: | CHEN Yan YUAN Xiying HAN Miaomiao 1.Department of Mathematics,Shanghai University,Shanghai 200444,China |
| Abstract: | A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two. Let $Delta(G)$ and $mu(G)$ denote the maximum degree and the Laplacian spectral radius of a graph $G$, respectively. Let $mathcal {T}(n)$ be the set of tricyclic graphs on $n$ vertices.~In this paper,~it is proved that,~for two graphs $H_{1}$ and $H_{2}$ in $mathcal {T}(n)$,~if $Delta(H_{1})> Delta(H_{2})$ and $Delta(H_{1})geq frac{n+7}{2}$,~then $mu (H_{1})> mu (H_{2}).$ As an application of this result,~we determine the seventh to the nineteenth largest values of the Laplacian spectral radii among all the graphs in $mathcal {T}(n)(ngeq9)$ together with the corresponding graphs. |
| Keywords: | Laplacian spectral radius tricyclic graphs maximum degree |
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