AVERAGE GEODESIC DISTANCE OF SIERPIŃSKI NETWORKS ON TORUS

Zixuan Zhao (), Yumei Xue (), Cheng Zeng and Lulu Peng ()
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Zixuan Zhao: School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China
Yumei Xue: School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China
Cheng Zeng: ��School of Mathematics and Information Science, Shandong Technology and Business University, Yantai, Shandong Province 264003, P. R. China
Lulu Peng: School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-13

Abstract: In this paper, we investigate the average geodesic distance on Sierpiński torus networks. We construct Sierpiński torus networks based on the classic Sierpiński carpet in an iterative way. By applying finite patterns on integrals, we deduce the exact value of the average geodesic distance of the Sierpiński torus. Furthermore, the asymptotic formula for the average geodesic distance of the corresponding networks can be obtained.

Keywords: Sierpiński Carpet; Sierpiński Torus Networks; Average Geodesic Distance; Manifold; Self-similar (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24501408

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