Metric properties of Sierpiński triangle graphs
| Autor: | Sara Sabrina Zemljič, Andreas M. Hinz, Caroline Holz auf der Heide |
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| Rok vydání: | 2022 |
| Předmět: |
Class (set theory)
Applied Mathematics 0211 other engineering and technologies 021107 urban & regional planning 0102 computer and information sciences 02 engineering and technology Center (group theory) Type (model theory) Base (topology) 01 natural sciences Sierpinski triangle Combinatorics Fractal 010201 computation theory & mathematics Metric (mathematics) Discrete Mathematics and Combinatorics Representation (mathematics) Mathematics |
| Zdroj: | Discrete Applied Mathematics. 319:439-453 |
| ISSN: | 0166-218X |
| DOI: | 10.1016/j.dam.2021.03.002 |
| Popis: | Sierpinski triangle graphs S n have often been mistaken for Sierpinski graphs S 3 n . 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 Sierpinski triangle fractal. Therefore, we present here a new labeling for them which shows the relation, but also the differences to the more famous Sierpinski 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 Sierpinski triangle graphs S p n which are related to the class of classical Sierpinski graphs S p n , p ≥ 2 . Some of the metric properties of S p n can now be investigated for S p n as well; e.g., we characterize center and periphery of S p n . |
| Databáze: | OpenAIRE |
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