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Metric properties of Sierpiński triangle graphs
Sierpiński triangle graphs Ŝn have often been mistaken for Sierpiński graphs S3n. Whereas the latter’s metric properties are by now well understood, the former graphs were mostly just considered as a pictorial representation of approximations to the Sierpiński triangle fractal. Therefore, we presen...
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Published in: | Discrete Applied Mathematics 2022-10, Vol.319, p.439-453 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | Sierpiński triangle graphs Ŝn have often been mistaken for Sierpiński graphs S3n. Whereas the latter’s metric properties are by now well understood, the former graphs were mostly just considered as a pictorial representation of approximations to the Sierpiński triangle fractal. Therefore, we present here a new labeling for them which shows the relation, but also the differences to the more famous Sierpiński graphs proper. On the base of this labeling we describe an algorithm to obtain individual distances between vertices. This type of algorithm can then be extended to base-p Sierpiński triangle graphs Ŝpn which are related to the class of classical Sierpiński graphs Spn, p≥2. Some of the metric properties of Spn can now be investigated for Ŝpn as well; e.g., we characterize center and periphery of Ŝpn. |
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ISSN: | 0166-218X 1872-6771 |
DOI: | 10.1016/j.dam.2021.03.002 |