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Some Nordhaus-Gaddum type results of Aα-eigenvalues of weighted graphs

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  • He, Changxiang
  • Wang, Wenyan
  • Li, Yuying
  • Liu, Lele

Abstract

Let Gω be a weighted graph, whose adjacency matrix and weighted degree diagnoal matrix are A(Gω) and D(Gω), respectively. For a given α∈[0,1], the matrix Aα(Gω)=αD(Gω)+(1−α)A(Gω) is the Aα-matrix of Gω. If all edge weights of Gω are belonging to (0,1), by defining the complement of Gω, we obtain some Nordhaus-Gaddum type bounds concerning Aα-eigenvalues of Gω.

Suggested Citation

  • He, Changxiang & Wang, Wenyan & Li, Yuying & Liu, Lele, 2021. "Some Nordhaus-Gaddum type results of Aα-eigenvalues of weighted graphs," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    • Handle: RePEc:eee:apmaco:v:393:y:2021:i:c:s0096300320307141
    DOI: 10.1016/j.amc.2020.125761
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    References listed on IDEAS

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    1. Huang, Xing & Lin, Huiqiu & Xue, Jie, 2020. "The Nordhaus–Gaddum type inequalities of Aα-matrix," Applied Mathematics and Computation, Elsevier, vol. 365(C).
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    Cited by:

    1. Chen, Ming-Zhu & Liu, A-Ming & Zhang, Xiao-Dong, 2023. "On the Aα-spectral radius of graphs without linear forests," Applied Mathematics and Computation, Elsevier, vol. 450(C).

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