Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices

doi:10.1007/s11464-020-0842-0

Front. Math. China

2020, Vol. 15

Issue (3) : 451-465 https://doi.org/10.1007/s11464-020-0842-0

RESEARCH ARTICLE

Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices

Yizheng FAN(

), Zhu ZHU, Yi WANG

School of Mathematical Sciences, Anhui University, Hefei 230601, China

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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 $A$ (G) be the adjacency tensor of G. The least H-eigenvalue of $A$ (G) refers to the least real eigenvalue of $A$ (G) associated with a real eigenvector. In this paper, we obtain a perturbation result on the least H-eigenvalue of $A$ (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.

Keywords Hypergraph adjacency tensor least H-eigenvalue eigenvector perturbation

Corresponding Author(s): Yizheng FAN

Issue Date: 21 July 2020

Cite this article:

Yizheng FAN,Zhu ZHU,Yi WANG. Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices[J]. Front. Math. China, 2020, 15(3): 451-465.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0842-0
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I3/451

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