山西大学学报（自然科学版）2025，Vol.48Issue(4)：705-712,8.DOI:10.13451/j.sxu.ns.2024128
一般超图规范化拉普拉斯张量的谱性质
The Properties of the Spectra of Normalized Laplace Tensor in General Hypergraphs
摘要
Abstract
The normalized Laplacian tensor of hypergraphs has a wide range of applications in multi class clustering problems involv-ing hypergraph models.In this paper,we prove that if H is a connected general hypergraph with rank(H)=m,then the spectrum of the adjacency tensor of H is symmetric if and only if m is even and H is odd-colorable.Furthermore,we give a characterization of the general hypergraphs with the normalized Laplace spectral radius 2 in terms of the odd-colorability of general hypergraphs.关键词
超图的谱/张量乘积/奇着色Key words
spectra of hypergraphs/tensor product/odd-colorable分类
数理科学引用本文复制引用
张磊,任海珍..一般超图规范化拉普拉斯张量的谱性质[J].山西大学学报（自然科学版）,2025,48(4):705-712,8.基金项目
湖南省自然科学基金(2023JJ40424) （2023JJ40424）
青海省自然科学基金(2022-ZJ-973Q) （2022-ZJ-973Q）
中国博士后基金(2023M741147) （2023M741147）
