Topological Analysis of Fractal Binary and Ternary Trees

Abstract

Fractals are complex geometric objects that seem the same at different scales and have self-similarity. Because of this special characteristic, fractals can be used to simulate intricate biological processes. Fractal binary and ternary trees are novel data types that combine the productiveness of tree architectures with the ideas of fractal geometry. In addition to self-similarity and scalability, these trees have potential across a range of computer science and medical applications. The main goal of the study is to identify and analyze topological indices and graph entropy for fractal binary and fractal ternary trees. By examining indices such as the Randić index, Zagreb indices, and entropy measurements, the study aims to obtain a comprehensive knowledge of the structural complexity and information-theoretic properties of these fractal graphs. The study starts with the vertex and edge partitioning of fractal binary and ternary trees in order to distinguish different structural classes. Using these partitions, we obtained topological indices and graph entropy values for the fractal trees. Also, this study compares the topological indices for each fractal tree with the number of copies in the fractal dimension for a succession of graphs.