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Aα-spectral radius of the second power of a graph

Author

Listed:
  • Chen, Yuanyuan
  • Li, Dan
  • Wang, Zhiwen
  • Meng, Jixiang

Abstract

The kth power of a graph G, denoted by Gk, is a graph with the same set of vertices as G such that two vertices are adjacent in Gk if and only if their distance in G is at most k. In this paper, we give upper and lower bounds on the Aα-spectral radius of G2. Furthermore, the first three largest Aα-spectral radius of the second power of trees are determined.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:418-425
    DOI: 10.1016/j.amc.2019.04.077
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    References listed on IDEAS

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    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. Kinkar Ch. Das & Ji-Ming Guo, 2016. "Eigenvalues of the k-th power of a graph," Mathematische Nachrichten, Wiley Blackwell, vol. 289(13), pages 1585-1593, September.
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    Cited by:

    1. Li, Dan & Chen, Yuanyuan & Meng, Jixiang, 2019. "The Aα-spectral radius of trees and unicyclic graphs with given degree sequence," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    2. 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).
    3. Hui, Hongxun & Ding, Yi & Shi, Qingxin & Li, Fangxing & Song, Yonghua & Yan, Jinyue, 2020. "5G network-based Internet of Things for demand response in smart grid: A survey on application potential," Applied Energy, Elsevier, vol. 257(C).

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