Eigenvectors of Laplacian or signless Laplacian of hypergraphs associated with zero eigenvalue
Eigenvectors of Laplacian or signless Laplacian of hypergraphs associated with zero eigenvalue
复制标题
与零特征值相关的超图的拉普拉斯或无符号拉普拉斯的特征向量
DOI：
10.1016/j.laa.2019.06.001
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发表时间：
2019
影响因子：
1.1
通讯作者：
Zhu Zhu
中科院分区：
文献类型：
--
作者：
Fan Yi Zheng;Wang Yi;Bao Yan Hong;Wan Jiang Chao;Li Min;Zhu Zhu
设G是连通的m-一致超图。本文主要考虑G的Laplacian或无符号Laplacian张量的与零特征值相关的特征向量，称为G的第一Laplacian或无符号Laplacian特征向量。利用G的关联矩阵，通过求解Zm（或Z2）上关联矩阵的Smith标准形，可以显式地得到第一Laplacian或无符号Laplacian（或H-）特征向量的个数.因此，我们证明了当零是无符号拉普拉斯张量的（H-）特征值时，第一拉普拉斯（H-）特征向量的数目等于第一无符号拉普拉斯（H-）特征向量的数目。建立了G的第一Laplacian（无符号Laplacian）H-特征向量与偶（奇）分划之间的联系。
Let G be a connected m-uniform hypergraph. In this paper we mainly consider the eigenvectors of the Laplacian or signless Laplacian tensor of G associated with zero eigenvalue, called the first Laplacian or signless Laplacian eigenvectors of G. By means of the incidence matrix of G, the number of first Laplacian or signless Laplacian (or H-) eigenvectors can be obtained explicitly by solving the Smith normal form of the incidence matrix over Z m (or Z 2). Consequently, we prove that the number of first Laplacian (H-) eigenvectors is equal to the number of first signless Laplacian (H-) eigenvectors when zero is an (H-) eigenvalue of the signless Laplacian tensor. We establish a connection between first Laplacian (signless Laplacian) H-eigenvectors and the even (odd) bipartitions of G.