The multiplicity of the zero Laplacian eigenvalue of uniform hypertrees

2023/09/30 by Ge Lin, Changjiang Bu, Lin, Ge +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2310.00360

openalex publication_date 2023/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the Laplacian characteristic polynomial of uniform hypergraphs with cut vertices or pendant edges and the Laplacian matching polynomial of uniform hypergraphs are characterized.The multiplicity of the zero Laplacian eigenvalue of uniform hypertrees is given, which proves the conjecture in \citezheng2023zero (The zero eigenvalue of the Laplacian tensor of a uniform hypergraph, Linear and Multilinear Algebra, (2023) Doi:10.1080/03081087.2023.2172541).

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