Upper Bounds on the Aα Spectral Radius of Irregular Weighted Digraphs

XI Wei-ge, XU Tao

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

Chinese Quarterly Journal of Mathematics >

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

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

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

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.

Received date: 2023-04-17

Online published: 2024-06-30

Supported by

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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Abstract

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.

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

Cite this article

XI Wei-ge, XU Tao . Upper Bounds on the Aα Spectral Radius of Irregular Weighted Digraphs[J]. Chinese Quarterly Journal of Mathematics, 2024 , 39(2) : 161 -170 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.004

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