论文标题
用切割顶点的超图的邻接张量最低的H元素值
The least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices
论文作者
论文摘要
令$ g $为具有均匀性的连接的超图，其中包含剪切的顶点。然后，$ g $是两个在剪切顶点上的两个非平凡连接的子杂志（称为分支）的合并。令$ \ mathcal {a}（g）$为$ g $的邻接张量。 $ \ Mathcal {a}（g）$的最低h-eigenvalue是指$ \ nathcal {a}（g）$的最小真实特征值。在本文中，我们获得了$ \ Mathcal {a}（g）$的最低h-eigenvalue的扰动结果。
Let $G$ be a connected hypergraph with even uniformity, which contains cut vertices. Then $G$ is the coalescence of two nontrivial connected sub-hypergraphs (called branches) at a cut vertex. Let $\mathcal{A}(G)$ be the adjacency tensor of $G$. The least H-eigenvalue of $\mathcal{A}(G)$ refers to the least real eigenvalue of $\mathcal{A}(G)$ associated with a real eigenvector. In this paper we obtain a perturbation result on the least H-eigenvalue of $\mathcal{A}(G)$ when a branch of $G$ attached 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.
