THE LAPLACIAN SPECTRUM OF A GRAPH .2.
THE LAPLACIAN SPECTRUM OF A GRAPH .2.
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DOI：
10.1137/s0895480191222653
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发表时间：
1994-05-01
影响因子：
0.8
通讯作者：
MERRIS, R
中科院分区：
文献类型：
--
作者：
GRONE, R;MERRIS, R
设G是一个图。用D（G）表示其顶点度的对角矩阵，用A（G）表示其邻接矩阵。则L（G）= D（G）- A（G）是G的Laplacian矩阵.本文的第一部分致力于拉普拉斯整图的性质，那些拉普拉斯谱完全由整数组成。第二部分通过优化将度序列与Laplacian谱联系起来。第三节引入了d-簇的概念，用它来限制L（G）的谱中d的重数。
Let G be a graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then L(G) = D(G) - A(G) is the Laplacian matrix of G. The first section of this paper is devoted to properties of Laplacian integral graphs, those for which the Laplacian spectrum consists entirely of integers. The second section relates the degree sequence and the Laplacian spectrum through majorization. The third section introduces the notion of a d-cluster, using it to bound the multiplicity of d in the spectrum Of L(G).