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On the Aα-spectral radius of graphs without linear forests

Author

Listed:
  • Chen, Ming-Zhu
  • Liu, A-Ming
  • Zhang, Xiao-Dong

Abstract

Let A(G) and D(G) be the adjacency and degree matrices of a simple graph G on n vertices, respectively. The Aα-spectral radius of G is the largest eigenvalue of Aα(G)=αD(G)+(1−α)A(G) for a real number α∈[0,1]. In this paper, for α∈(0,1), we obtain a sharp upper bound for the Aα-spectral radius of graphs on n vertices without a subgraph isomorphic to a linear forest for n large enough and characterize all graphs which attain the upper bound. As a result, we completely dertermine the maximum signless Laplacian spectral radius of graphs on n vertices without a subgraph isomorphic to a linear forest for n large enough.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:450:y:2023:i:c:s0096300323001741
    DOI: 10.1016/j.amc.2023.128005
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    References listed on IDEAS

    as
    1. Yu, Zhangqing & Kang, Liying & Liu, Lele & Shan, Erfang, 2019. "The extremal α-index of outerplanar and planar graphs," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 90-99.
    2. Chen, Yuanyuan & Li, Dan & Wang, Zhiwen & Meng, Jixiang, 2019. "Aα-spectral radius of the second power of a graph," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 418-425.
    3. 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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