| 引用本文： |
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张德龙,谭尚旺.树的邻接矩阵和Laplacian矩阵谱半径的新下界[J].广西科学,2005,12(4):250-254. [点击复制]
- Zhang Delong,Tan Shangwang.New Lower Bounds on the Spectral Radius of Adjacency Matrices and Laplacian Matrices of Trees[J].Guangxi Sciences,2005,12(4):250-254. [点击复制]
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| 摘要: |
| 利用代数方法、图的边变换,以及树的邻接矩阵谱与Laplacian谱的关系,研究树和完美树的邻接矩阵谱半径和Laplacian谱半径的下界,给出达到下界的所有极树,得到的新结果改进了文献[2]的结论. |
| 关键词: 树 完美树 下界 邻接矩阵 谱半径 Laplacian矩阵 |
| DOI： |
| 投稿时间：2005-08-09修订日期：2005-09-02 |
| 基金项目:广西自然科学基金项目(桂科自0131001)资助。 |
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| New Lower Bounds on the Spectral Radius of Adjacency Matrices and Laplacian Matrices of Trees |
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Zhang Delong1, Tan Shangwang2
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| (1.Department of Information and Computer Science, Guangxi Institute of Technology, Liuzhou, Guangxi, 545006, China;2.Department of Mathematics, University of Petroleum, Dongying, Shandong, 257061, China) |
| Abstract: |
| In this paper,lower bounds on the spectral radius of adjacency matrices of trees and perfect trees are discussed by algebraic method and edge switching of graph,and all trees which reach lower bounds on the spectral radius are obtained.Lower bounds on the spectral radius of Laplacian matrices of trees and perfect trees are discussed by the relation between spectra of adjacency matrices and spectra of Laplacian matrices,and all trees which reach lower bounds on the spectral radius are obtained. |
| Key words: trees perfect trees lower bounds adjacency matrices spectral radius Laplacian matrices |
