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ScienceAsia 50 (2024):ID 2024006 1-9 |doi: 10.2306/scienceasia1513-1874.2024.006


On the principal eigenvectors of general hypergraphs


Haifeng Lia, Chunli Dengb,*

 
ABSTRACT:     Let G be a connected general hypergraph of order n with rank r. The unique positive eigenvector x with Pn i=1 x r i = 1 corresponding to the spectral radius ?(G) is called the principal eigenvector of G. In this paper, the relation between each entry of the principal eigenvector of G and the vertex degree associated with this entry is presented. And some bounds for the extreme entries of the principal eigenvector are obtained. As applications, we give some bounds of the spectral radius of G.

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a School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006 China
b Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043 China

* Corresponding author, E-mail: chunlideng@163.com

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Received 28 Oct 2022, Accepted 29 Jul 2023