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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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 319; pp. 439 - 453
Main Authors Hinz, Andreas M., Holz auf der Heide, Caroline, Zemljič, Sara Sabrina
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.10.2022
Subjects
Algorithm
Eccentricity
Graph distance
Sierpiński graph
Sierpiński triangle graph
Graph distance
Sierpiński triangle graph
Eccentricity
Algorithm
Sierpiński graph
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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.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2021.03.002