2020/04/30 by Raffaella Mulas, Dong Zhang
Computer Science · Mathematics · #Combinatorics #Discrete mathematics #Domain (mathematical analysis) #Eigenvalues and eigenvectors #Graph theory and applications #Hilbert space #Laplace operator #Laplace transform #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Pure mathematics #Spectral properties #Spectral theory #Spectrum (functional analysis) #Tensor decomposition and applications #Upper and lower bounds #math.CO #math.SP
paper · pdf · doi:10.1016/j.disc.2021.112372
published as Discrete Mathematics 344(6) (2021) 112372 · 39 pages
arxiv created 2021/02/18 · openalex publication_date 2021/03/19 · arxiv updated 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Several new spectral properties of the normalized Laplacian defined for oriented hypergraphs are shown. The eigenvalue 1 and the case of duplicate vertices are discussed; two Courant nodal domain theorems are established; new quantities that bound the eigenvalues are introduced. In particular, the Cheeger constant is generalized and it is shown that the classical Cheeger bounds can be generalized for some classes of hypergraphs; it is shown that a geometric quantity used to study zonotopes bounds the largest eigenvalue from below, and that the notion of coloring number can be generalized and used for proving a Hoffman-like bound. Finally, the spectrum of the unnormalized Laplacian for Cartesian products of hypergraphs is discussed.