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Shortest Path Distance And Hausdorff Dimension Of Sierpinski Networks

Author

Listed:
  • JIAQI FAN

    (Department of Public Course Teaching, Ningbo Polytechnic, Ningbo 315800, P. R. China)

  • JIAJUN XU

    (School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China)

  • LIFENG XI

    (School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China)

Abstract

In this paper, we will study the geometric structure on the Sierpinski networks which are skeleton networks of a connected self-similar Sierpinski carpet. Under some suitable condition, we figure out that the renormalized shortest path distance is comparable to the planar Manhattan distance, and obtain the Hausdorff dimension of Sierpinski networks.

Suggested Citation

  • Jiaqi Fan & Jiajun Xu & Lifeng Xi, 2024. "Shortest Path Distance And Hausdorff Dimension Of Sierpinski Networks," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-8.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:03:n:s0218348x24500567
    DOI: 10.1142/S0218348X24500567
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