Computing Certain Topological Indices of Silicate Triangle Fractal Network Modeled by the Sierpiński Triangle Network

Abstract

The study of Sierpiński triangle network and extended Sierpiński graph is quite interesting in the field of fractal networks. In nature, fractal networks (FN) and silicate structure networks (Sio₄) play vital roles and in architecture to analyze the dimension of the above-mentioned FN and Sio₄ networks it is necessary to identify the number of copies of the network. In this paper, we introduced a silicate triangle fractal network (Si_n) which is a planar fractal and it is created using a related sequence of graphs named (Si_n)_n≥0, where n is the n^th level of silicate triangle fractal network. We analyze the topological indices (TI) of the silicate triangle fractal network Si_n graph and compare the calculated topological indices to the number of copies of silicate structure (Sio₄) in each iteration of Si_n for a sequence of a graph.