一般超图的张量谱性质  

Tensor spectral properties of general hypergraphs

作　　者：王蝶 康丽英[1] WANG Die;KANG Liying(College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院,上海200444

出　　处：《运筹学学报》2023年第1期138-148,共11页Operations Research Transactions

摘　　要：将一致超图的逆Perron值的概念推广到了一般超图上,并证明了超图G连通的充要条件为其逆Perron值大于0。同时给出了一般超图G的二分宽度、等周数、离心率基于逆Perron值的一些下界。最后,讨论了张量的可奇染色问题,得到非负对称弱不可约张量A可奇染色的充要条件为A的拉普拉斯张量和无符号拉普拉斯张量有相同的的谱。In this paper,we extend the concepts of inverse Perron values to general hypergraphs.We show that a general hypergraph G is connected if and only if any inverse Perron values is large than 0.We give some bounds on the bipartition width,isoperimetric number,eccentricities and degrees of a hypergraph G in terms of inverse Perron values.Finally,we obtain that a weakly irreducible,nonnegative,symmetric tensor A is odd-colorable if and only if its Laplacian tensor and the signless Laplacian tensor have the same spectral.

关 键 词：超图 分析连通度 逆Perron值 可奇染色 

分 类 号：O157.5[理学—数学]