2018/05/14 by Junjie Yue, Liping Zhang, Yue, Junjie +1
Computer Science · Mathematics · #Class (philosophy) #Combinatorics #Computer science #Conjecture #Convergence (economics) #Eigenvalues and eigenvectors #FOS: Mathematics #Graph theory and applications #Laplace operator #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Path (computing) #Physics #Pure mathematics #Quantum mechanics #Spectral Theory (math.SP) #Spectrum (functional analysis) #Tensor decomposition and applications #math.SP
paper · pdf · doi:10.48550/arxiv.1805.05798
published in arXiv (Cornell University) (Cornell University) · arXiv admin note: text overlap with arXiv:1304.6839, arXiv:1309.2163 by other authors
arxiv created 2018/05/14 · openalex publication_date 2018/05/14 · arxiv updated 2018/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The spectral theory of Laplacian tensor is an important tool for revealing some important properties of a hypergraph. It is meaningful to compute all Laplacian H-eigenvalues for some special k-uniform hypergraphs. For an odd-uniform loose path of length three, the Laplacian H-spectrum has been studied. However, all Laplacian H-eigenvalues of the class of loose paths have not been found out. In this paper, we compute all Laplacian H-eigenvalues for the class of loose paths. We show that the number of Laplacian H-eigenvalues of an odd(even)-uniform loose path with length three is 7(14). Some numerical results are given to show the efficiency of our method. Especially, the numerical results show that its Laplacian H-spectrum converges to \0,1,1.5,2\ when k goes to infinity. Finally, we establish convergence analysis for a part of the conclusion and also present a conjecture.