Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices
Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices
复制标题
具有割点的超图邻接张量的最小H特征值
DOI：
10.1007/s11464-020-0842-0
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发表时间：
2020
影响因子：
--
通讯作者：
Wang Yi
中科院分区：
文献类型：
--
作者：
Fan Yizheng;Zhu Zhu;Wang Yi
设GetGbe是一个连通的均匀连通超图，它包含割点。则G是两个非平凡的连通子超图(称为分支)在一个割点处的合并。设G的邻接张量为G。的最小H-特征值是指与实本征向量有关的最小实特征值。本文给出了当连接于一个顶点的分支重新定位到另一个顶点时的最小H-特征值的扰动结果，并刻画了在包含固定连通超图的一类超图中所有超图中最小H-特征值达到最小的唯一超图。
LetGbe a connected hypergraph with even uniformity, which contains cut vertices. ThenGis the coalescence of two nontrivial connected sub-hypergraphs (called branches) at a cut vertex. Letbe the adjacency tensor ofG. The least H-eigenvalue ofrefers to the least real eigenvalue ofassociated with a real eigenvector. In this paper, we obtain a perturbation result on the least H-eigenvalue ofwhen a branch ofGattached at one vertex is relocated to another vertex, and characterize the unique hypergraph whose least H-eigenvalue attains the minimum among all hypergraphs in a certain class of hypergraphs which contain a fixed connected hypergraph.