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Topological indices for the iterations of Sierpiński rhombus and Koch snowflake

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Abstract

In fractal geometry, the study of Sierpiński rhombus and Koch snowflake is one of the important and interesting research topics. Sierpiński rhombus is a planar fractal which is created using a related sequence of graphs named \(\{\mathrm{SR}_n\}_{n\ge 0}\), where \(\mathrm{SR}_n\) is the \(n\mathrm{th}\) Sierpinski graph. Same as Sierpiński, Koch snowflake is also created using a sequence of graphs named \(\{\mathrm{KS}_n\}_{n\ge 0}\), where \(\mathrm{KS}_n\) is the \(n\mathrm{th}\) Koch snowflake graph. We can efficiently analyze their fractal structures by studying the topological indices for the graphs \(\mathrm{SR}_n\) and \(\mathrm{KS}_n\). In this paper, the topological indices for \(\mathrm{SR}_n\) and \(\mathrm{KS}_n\) are calculated and compared with the fractal dimension for a sequence of graphs.

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  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, India

    A. Divya & A. Manimaran

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  1. A. Divya
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  2. A. Manimaran
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Divya, A., Manimaran, A. Topological indices for the iterations of Sierpiński rhombus and Koch snowflake. Eur. Phys. J. Spec. Top. 230, 3971–3980 (2021). https://doi.org/10.1140/epjs/s11734-021-00338-z

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