| ON THE κ-th LARGEST EIGENVALUE OF THE LAPLACIAN MATRIX OF A GRAPH |
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| 引用本文： | 张晓东 ,李炯生.ON THE κ-th LARGEST EIGENVALUE OF THE LAPLACIAN MATRIX OF A GRAPH[J].应用数学学报(英文版),2001(2). |
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| 作者姓名： | 张晓东 李炯生 |
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| 作者单位： | Department of Mathematics，University of Science and Technology of China，Hefei 230026，China |
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| 基金项目： | the National Natural Science Foundation of China (Grant No.19971086) and the Doctoral Program Foundation of State Education Depa |
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| 摘 要： | 1. IntroductionLet G be a simple graph with vertex set V = {yi, v2,', v.} and edge set E ~ E(G).Denote the degree of vertex yi by di. Let D(G) ~ diag (dl, d2,', da) and A(G) be thediagonal mains of vertex degrees and the adjacency matrix of G, respectively. Then L(G) D(G)-A(G) is the Laplacian matrix of G. It seems that L(G) first occurred in the celebratedMatriX-Thee Theorem:Theorem 1.1. If Li j is the submatrix of L(G) obtained by deleting its i-th row andj-th column, then (-…
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