Sierpiński Gasket Graphs
The Sierpiński gasket graphs form one of the most studied examples of self-similar structures in graph theory [1]. They provide a discrete analogue of the classical Sierpiński triangle fractal, preserving both its recursive construction and its combinatorial richness. The sequence begins with the complete graph on three vertices, $S_{1}$, and at each subsequent step, $S_{n+1}$ is obtained from $S_{n}$ by subdividing every triangular face. New vertices are placed at the midpoints of its edges, and these are joined to form a smaller triangle inside. Repeating this process yields a hierarchy of graphs whose geometry captures the recursive pattern of the underlying fractal. Figure 1. The first 4 Sierpiński gasket graphs. Taken from Bunimovich et. al (2016) [2] Given this sequence, what is the Global Clustering coefficient of $S_n$, for $n\geq2$ and its limit when $n \to \infty$? $$\textbf{a)}\quad \frac{3^n}{3^{n}-2}, \quad 1$$ $$\textbf{b)}\quad \frac{4\cdot 3^...