SHORTEST PATH DISTANCE AND HAUSDORFF DIMENSION OF SIERPINSKI NETWORKS

Jiaqi Fan (), Jiajun Xu () and Lifeng Xi
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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

FRACTALS (fractals), 2024, vol. 32, issue 03, 1-8

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.

Keywords: Fractal Network; Sierpinski Network; Shortest Path Distance (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500567

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