超图的子图特征值的研究

Eigenvalues of Subgraphs for an Even Uniform Hypergraph

研究了偶一致超图的子图邻接张量的特征值,首先利用其最大特征值得到超图边割的下界,并证明这个界是紧的,指出当且仅当2个子图均为正则超图时下界成立,其次证明了k一致超图是正则超图的充要条件为全1向量是其邻接张量的H-特征向量,这是图谱理论中的相关性质在超图的推广.

In the report, the characteristic value of the subgraph adjacency tensors of an even uniform hyperg- raph was analyzed. Firstly, the maximal characteristic value of the subgraphs was used to obtain a lower bound on the cardinality of edge cuts and that the bound is tight was proved, of which a sufficient and necessary condi- tion was proposed; Secondly, that an uniform hypergraph is regular if and only if the all-1 vector is an H-eigen- vector of its adjacency tensor was proved; Lastly, the related characters of spectral graph theory were general- ized.