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The least H-eigenvalue of signless Laplacian of non-odd-bipartite hypergraphs
Discrete Mathematics ( IF 0.8 ) Pub Date : 2020-09-01 , DOI: 10.1016/j.disc.2020.111987
Jiang-Chao Wan , Yi-Zheng Fan , Yi Wang

Let $G$ be a connected non-odd-bipartite hypergraph with even uniformity. The least H-eigenvalue of the signless Laplacian tensor of $G$ is simply called the least eigenvalue of $G$ and the corresponding H-eigenvectors are called the first eigenvectors of $G$. In this paper we give some numerical and structural properties about the first eigenvectors of $G$ which contains an odd-bipartite branch, and investigate how the least eigenvalue of $G$ changes when an odd-bipartite branch attached at one vertex is relocated to another vertex. We characterize the hypergraph(s) whose least eigenvalue attains the minimum among a certain class of hypergraphs which contain a fixed non-odd-bipartite connected hypergraph. Finally we present some upper bounds of the least eigenvalue and prove that zero is the least limit point of the least eigenvalues of connected non-odd-bipartite hypergraphs.

中文翻译:

非奇二部超图的无符号拉普拉斯算子的最小H特征值

令 $G$ 是一个具有偶数一致性的连通的非奇二部超图。$G$的无符号拉普拉斯张量的最小H-特征值简称为$G$的最小特征值,对应的H-特征向量称为$G$的第一特征向量。在本文中,我们给出了包含奇二分枝的 $G$ 的第一个特征向量的一些数值和结构性质,并研究了当附着在一个顶点上的奇二分枝重新定位到 $G$ 的最小特征值时,$G$ 的最小特征值如何变化另一个顶点。我们在包含固定的非奇二部连通超图的某一类超图中表征其最小特征值达到最小值的超图。
更新日期:2020-09-01
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