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Y[u]=0,并且对任意与u相邻的顶点v,均有Y[v]=0.论文证明:对于树T,如果mL[T-v](λ)=mL(λ),则对λ的任意特征向量Y,v都是孤立点.
Let G = （V,E） was a connected graph on n vertices, L was its Laplacian matrix, and Ywas an eigenvector of L corresponding to the eigenvalue A . Respecting to the vector Y, a vertex u ∈ V was called an isolated vertex of G, if Y[ u ] = 0 , and for an arbitrary vertex v adjacent to u, Y[v] = 0. In the paper, we proved that each vertex v satisfied mL[ T-v] （ λ ） = mL （ λ ）, which was an isolate vertex of T respected to any eigenveetor corresponding to λ.
出处
《安徽大学学报（自然科学版）》
CAS
北大核心
2009年第3期20-22,共3页
Journal of Anhui University(Natural Science Edition)
基金
国家自然科学基金资助项目(10601001)
