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arXiv · 2002.10288

The least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices

Yi-Zheng Fan·Zhu Zhu·Yi Wang
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Abstract

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.

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Yi-Zheng Fan, Zhu Zhu, Yi Wang. 2020-02-18. The least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices. https://doi.org/10.1007/s11464-020-0842-0

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