Entropy and topological indices of nanostar dendrimers: a graph-theoretic approach

Nanostar dendrimers have received considerable attention due to their unique properties and various applications, such as drug delivery, nanomedicine, and materials science. A comprehensive analysis of their structural characteristics is essential for optimizing these capabilities. In this study, we consider infinite families of nanostar dendrimers to analyze and characterize their structural properties. Graph theory provides a mathematical framework to examine the connectivity and topological features of these complex nanostructures. Particularly, we compute several key topological indices, including the degree distance, Gutman, Wiener, and Wiener polarity indices, for this class of nanostar dendrimers. Furthermore, we present a graphical analysis to visually determine the results, providing a clearer understanding of the structural trends and patterns within the nanostar dendrimers. Additionally, we extend our analysis by determining the graph entropy, which serves as a measure of the structural complexity and the information embedded within the dendrimer structure.