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The Nordhaus–Gaddum type inequalities of Aα-matrix

Author

Listed:
  • Huang, Xing
  • Lin, Huiqiu
  • Xue, Jie

Abstract

For a real number α ∈ [0, 1], the Aα-matrix of a graph G is defined as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and diagonal degree matrix of G, respectively. The Aα-spectral radius of G, denoted by ρα(G), is the largest eigenvalue of Aα(G). In this paper, the Nordhaus–Gaddum type bounds for the Aα-spectral radius are considered.

Suggested Citation

  • Huang, Xing & Lin, Huiqiu & Xue, Jie, 2020. "The Nordhaus–Gaddum type inequalities of Aα-matrix," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    • Handle: RePEc:eee:apmaco:v:365:y:2020:i:c:s0096300319307088
    DOI: 10.1016/j.amc.2019.124716
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    Cited by:

    1. 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).

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