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GEODESIC DISTANCES ON SIERPINSKI-LIKE SPONGES AND THEIR SKELETON NETWORKS

YING LU

https://orcid.org/0009-0005-5871-8095

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

E-mail Address: 2211400027@nbu.edu.cn

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QINGCHENG ZENG

https://orcid.org/0009-0001-5196-0939

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

E-mail Address: 2111071003@nbu.edu.cn

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JIAJUN XU

https://orcid.org/0009-0002-3464-5168

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

E-mail Address: 2211400049@nbu.edu.cn

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, and

LIFENG XI

https://orcid.org/0000-0001-5867-185X

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

E-mail Address: xilifeng@nbu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0218348X24500063Cited by:1 (Source: Crossref)

Abstract

In this paper, we investigate the equivalence of connectedness for the Sierpinski-like sponge and skeleton networks, and find out the relation between the geodesic distance on the sponge and renormalized shortest path distance on the skeleton networks. Furthermore, under some assumption on the IFS, we obtain the comparability of the Manhattan distance and the geodesic distance on the sponge.

Keywords:

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