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Weight-Dependent Walks And Average Shortest Weighted Path On The Weighted Iterated Friendship Graphs

Author

Listed:
  • YAN LIU

    (School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China)

  • MEIFENG DAI

    (School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China)

  • YUANYUAN GUO

    (School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China)

Abstract

In this paper, we present the weighted iterated friendship graphs and study the trapping problem on the weighted iterated friendship graphs. It can be found that for 0 < r < 1 and r = 1, the relationship between the average trapping time (ATT) and network size is sublinear and linear, respectively. By controlling the parameters of the weighted iterated friendship graphs, the models are changed to the self-similar weighted networks. The average shortest weighted path (ASWP) in the self-similar weighted friendship graphs is studied. The results show that when 0 < r < 1, the ASWP is bounded, and when r = 1, the ASWP is linearly related to the order of the networks.

Suggested Citation

  • Yan Liu & Meifeng Dai & Yuanyuan Guo, 2022. "Weight-Dependent Walks And Average Shortest Weighted Path On The Weighted Iterated Friendship Graphs," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(06), pages 1-14, September.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:06:n:s0218348x22501092
    DOI: 10.1142/S0218348X22501092
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    Cited by:

    1. Lu, Ying & Xu, Jiajun & Xi, Lifeng, 2023. "Fractal version of hyper-Wiener index," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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