| 树的孤立点 |
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| 引用本文： | 李亮,龚世才.树的孤立点[J].安徽大学学报(自然科学版),2009,33(3). |
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| 作者姓名： | 李亮 龚世才 |
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| 作者单位： | 1. 安徽交通职业技术学院,文理科学系,安徽,合肥,230051;安徽大学,电子科学与技术学院,安徽,合肥,230039
2. 安徽理工大学,数理系,安徽,淮南,232001 |
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| 基金项目： | 国家自然科学基金资助项目(10601001) |
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| 摘 要： | 设G=(V,E)为连通图,L为它的Laplace矩阵,Y为L的对应于特征值λ的特征向量.相对于向量Y,顶点u∈V称为是G的孤立点,如果Yu]=0,并且对任意与u相邻的顶点v,均有Yv]=0.论文证明:对于树T,如果mLT-v](λ)=mL(λ),则对λ的任意特征向量Y,v都是孤立点.
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| 关 键 词： | 树 Laplace矩阵 孤立点 特征向量 |
The isolated vertices of trees |
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| LI Liang,GONG Shi-cai.The isolated vertices of trees[J].Journal of Anhui University(Natural Sciences),2009,33(3). |
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| Authors: | LI Liang GONG Shi-cai |
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| Institution: | 1.Department of Arts and Science;Anhui Communications Vocational and Technical College;Hefei 230051;China;2.School of Electronic Science and Technology;Anhui University;Hefei 230039;3.Department of Mathematics and Physics;Anhui University of Science and Technology;Huainan 232001;China |
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| Abstract: | Let G = (V,E) was a connected graph on n vertices, L was its Laplacian matrix, and Y was an eigenvector of L corresponding to the eigenvalue λ . Respecting to the vector Y , a vertex u ∈ V was called an isolated vertex of G , if Yu] = 0 , and for an arbitrary vertex v adjacent to u , Yv] = 0 . In the paper, we proved that each vertex v satisfied m_(LT-v]) (A) = m_L(λ) , which was an isolate vertex of T respected to any eigenvector corresponding to λ . |
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| Keywords: | tree Laplacian matrix isolated vertex eigenvector |
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