Metric properties of Sierpiski triangle graphs

Hinz, Andreas M.; Heide, Caroline Holz Auf Der and Zemljic, Sara Sabrina (2022): Metric properties of Sierpiski triangle graphs. In: Discrete Applied Mathematics, Vol. 319: pp. 439-453

Abstract

Sierpinski triangle graph (S) over cap (n) 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) over cap (n)(p) which are related to the class of classical Sierpinski graphs S-p(n), p >= 2. Some of the metric properties of Sn p can now be investigated for S-p(n) as well;e.g., we characterize center and periphery of S-p(n)

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0166-218X
• Language: English