非正则赋权有向图 Aa&nbsp;谱半径的上界

席维鸽, 许涛

doi:10.13371/j.cnki.chin.q.j.m.2024.02.004

数学季刊 >

2024 , Vol. 39 >Issue 2: 161 - 170

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.02.004

非正则赋权有向图 A_a谱半径的上界

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College of Science, Northwest A&F University, Shaanxi 712100, China

XI Wei-ge (1989-), female, native of Baoji, Shaanxi, associate professor of Northwest A&F University, engages in spectral graph theory; XU Tao (2001-), male, native of Yanan, Shaanxi, graduate student of Northwest A&F University.

收稿日期: 2023-04-17

网络出版日期: 2024-06-30

基金资助

Supported by the National Natural Science Foundation of China (Grant No. 12001434); The Natural Science Basic Research Program of Shaanxi Province (Grant No. 2022JM-006) and Chinese Universities Scientific Fund (Grant No. 2452020021).

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Upper Bounds on the Aα Spectral Radius of Irregular Weighted Digraphs

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College of Science, Northwest A&F University, Shaanxi 712100, China

Received date: 2023-04-17

Online published: 2024-06-30

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摘要

Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number. Let A(D) be the adjacency matrix of D and W(D) = diag(w₁⁺,w₂⁺,...,w_n⁺). In this paper, we study the matrix A_α(D), which is defined as A_α(D) =αW(D)+ (1−α)A(D), 0≤α≤1. The spectral radius of Aα(D) is called the Aα spectral radius of D, denoted by λα(D). We obtain some upper bounds on the Aα spectral radius of strongly connected irregular weighted digraphs.

关键词： Strongly connected; Irregular weighted digraph; Aα spectral radius; Upper bounds

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席维鸽, 许涛 . 非正则赋权有向图 A_a谱半径的上界[J]. 数学季刊, 2024 , 39(2) : 161 -170 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.004

Abstract

Key words： Strongly connected; Irregular weighted digraph; Aα spectral radius; Upper bounds

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