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Eigenvectors of Laplacian or signless Laplacian of hypergraphs associated with zero eigenvalue.
- Source :
-
Linear Algebra & its Applications . Oct2019, Vol. 579, p244-261. 18p. - Publication Year :
- 2019
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *HYPERGRAPHS
*EIGENVECTORS
*MATRICES (Mathematics)
*NORMAL forms (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 579
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 137777121
- Full Text :
- https://doi.org/10.1016/j.laa.2019.06.001