The zero eigenvalue of the Laplacian tensor of a uniform hypergraph

In this paper, we study that the algebraic multiplicity of the zero Laplacian eigenvalue of a connected uniform hypergraph. We give the algebraic multiplicity of the zero Laplacian eigenvalue of a hyperstar. For a loose hyperpath, we characterize the algebraic multiplicity of the zero Laplacian eige...

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Bibliographic Details
Published in:Linear & multilinear algebra 2024-05, Vol.72 (7), p.1094-1111
Main Author: Zheng, Ya-Nan
Format: Article
Language:English
Subjects:
Algebra
algebraic multiplicity
Eigenvalues
Graph theory
hypergraph
Laplacian tensor
resultant
Tensors
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Summary:In this paper, we study that the algebraic multiplicity of the zero Laplacian eigenvalue of a connected uniform hypergraph. We give the algebraic multiplicity of the zero Laplacian eigenvalue of a hyperstar. For a loose hyperpath, we characterize the algebraic multiplicity of the zero Laplacian eigenvalue by the multiplicities of points in the affine variety defined by the Laplacian eigenvalue equations. We compute the algebraic multiplicities of the zero Laplacian eigenvalue of a loose hyperpath. We also show that the algebraic multiplicity of the zero Laplacian eigenvalue is not smaller than the number of irreducible components of the eigenvariety associated with the zero Laplacian eigenvalue for a loose hyperpath.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2023.2172541