Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (2): 161-170.doi: 10.13371/j.cnki.chin.q.j.m.2024.02.004

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Upper Bounds on the Aα Spectral Radius of Irregular Weighted Digraphs

XI Wei-ge, XU Tao   

  1. College of Science, Northwest A&F University, Shaanxi 712100, China
  • Received:2023-04-17 Online:2024-06-30 Published:2024-06-30
  • Contact: XI Wei-ge (1989-), female, native of Baoji, Shaanxi, associate professor of Northwest A&F University, engages in spectral graph theory; E-mail:xiyanxwg@163.com
  • About author: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.
  • 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+,...,wn+). In this paper, we study the matrix Aα(D), which is defined as Aα(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

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