一类非负张量的谱半径的上界及其应用

doi:10.15960/j.cnki.issn.1007-6093.2025.04.016

运筹学学报（中英文） ›› 2025, Vol. 29 ›› Issue (4): 205-218.doi: 10.15960/j.cnki.issn.1007-6093.2025.04.016

• • 上一篇

一类非负张量的谱半径的上界及其应用

王缘¹, 朱忠熏^1,†, 谭连生², 杨禹³

1 . 中南民族大学预科教育学院, 湖北武汉 430074;
2. 华中师范大学计算机学院, 湖北武汉 430079;
3. 云南警官学院心理健身教研中心, 云南昆明 650221

收稿日期:2022-08-02 发布日期:2025-12-11
通讯作者: 朱忠熏 E-mail:zzxun73@163.com
基金资助:
国家自然科学基金(No.62173157),中央高校基本科研业务费专项资金资助项目(No.CZY23009)

On the upper bound of spectral radius of a class of nonnegative general-tensors and its applications

WANG Yuan¹, ZHU Zhongxun^1,†, TAN Liansheng², YANG Yu³

1. College of Preparatory Education, South-Central Minzu University, Wuhan 430074, Hubei, China;
2. School of Computer Science, Central China Normal University, Wuhan 430079, Hubei, China;
3. Psychological Fitness Teaching and Research Center, Yunnan Police College, Kunming 650221, Yunnan, China

Received:2022-08-02 Published:2025-12-11

摘要/Abstract

摘要： 基于一类新的非负张量, 我们首先得到了一些与这类张量相关的组合恒等式。并利用这些组合恒等式, 得到了该类张量谱半径的紧上界及其对应的极值条件。最后作为应用, 得到了一些其他一般超图谱半径的紧上界, 并对其极值结构进行了刻画。

关键词: 非负张量, 弱不可约张量, 谱半径

Abstract: According to the nonnegative tensors defined in Xu et al. (2016), we first obtain some combinatorial identities related on these tensors. Then we attain a sharp upper bound on the spectral radius of this type tensors and its corresponding extremal conditions by these combinatorial identities. As its applications, some sharp upper bounds on the spectral radius of general hypergraphs are deduced and their corresponding extremal structure are characterized.

Key words: nonnegative general-tensor, weakly irreducible tensor, spectral radius

中图分类号:

O221

王缘, 朱忠熏, 谭连生, 杨禹. 一类非负张量的谱半径的上界及其应用[J]. 运筹学学报（中英文）, 2025, 29(4): 205-218.

WANG Yuan, ZHU Zhongxun, TAN Liansheng, YANG Yu. On the upper bound of spectral radius of a class of nonnegative general-tensors and its applications[J]. Operations Research Transactions, 2025, 29(4): 205-218.

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一类非负张量的谱半径的上界及其应用

On the upper bound of spectral radius of a class of nonnegative general-tensors and its applications

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