Topological indices for the iterations of Sierpiński rhombus and Koch snowflake

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 $$\{\mathrm{SR}_n\}_{n\ge 0}$$ { SR n } n ≥ 0 , where $$\mathrm{SR}_n$$ SR n is the $$n\mathrm{th}$$ n th Sierpinski graph. Same as Sierpiński, Koch snowflake is also created using a sequence of graphs named $$\{\mathrm{KS}_n\}_{n\ge 0}$$ { KS n } n ≥ 0 , where $$\mathrm{KS}_n$$ KS n is the $$n\mathrm{th}$$ n th Koch snowflake graph. We can efficiently analyze their fractal structures by studying the topological indices for the graphs $$\mathrm{SR}_n$$ SR n and $$\mathrm{KS}_n$$ KS n . In this paper, the topological indices for $$\mathrm{SR}_n$$ SR n and $$\mathrm{KS}_n$$ KS n are calculated and compared with the fractal dimension for a sequence of graphs.