一般超图规范化拉普拉斯张量的谱性质

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中图分类号：0436 文献标志码：A 文章编号：0253-2395（2025）04-0705-08

The Properties of the Spectra of Normalized Laplace Tensor in General Hypergraphs

ZHANG Lei 1，2，3* ，REN Haizhen1.2 （1.SchoolofathematicsandStatistics，QinghaiNormal UniversityXiningoo8，China; 2.The StateKeyLaboratoryofTbetan InformationProcessingandApplication，Xiningoo8，China; 3.SchoolofathematicsndStatistics，HunanNormalUniversityhangsha4ooo，ina）

Abstract：ThenormalizedLaplaciantensorofhypergraphshasawiderangeofappications inmulticlassclusteringproblemsnvolving 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 generalhypergraphs withthenormalizedLaplacespectralradius2intermsoftheodd-colorabilityofgeneralhypergraphs. Key words： spectra of hypergraphs; tensor product; odd-colorable

0 引言

1997年，Chung[1]首次引入了普通图的规范化拉普拉斯矩阵及其谱的概念。（剩余9943字）