On computation of information entropy measures for certain fractal molecular architectures

Fractal molecular structures constitute a distinct category of systems characterized by self-similarity and hierarchical growth patterns, which can be effectively examined by graph-theoretical methods. This manuscript introduces a refined adaptation of Shannon's entropy calculation method by evaluating the degree-based topological indices for fractal molecular structures, specifically Kekulene $\left(K{E}_n\right)$ and Terpyridine Complex Sierpinski Triangle $\left(S{E}_n\right)$ systems, and examines their physicochemical implications. Builds upon previously reported hydrogen-bonded fractal architectures, we have generated graphical representations of these fractal molecular structures in the form of a Kekulene ring and a Sierpinski triangular system. Subsequent computational analysis enabled the determination of entropy values for degree-based topological descriptors. These calculations provide valuable insights into the structural complexity and molecular properties of the fractal systems, offering potential applications in quantitative structure-property relationship and quantitative structure-activity relationship analyses for advanced material design and synthesis.