Topological Insights into Nanostar Dendrimers by Computing the Augmented Zagreb Index.

Background: The field of nanobiotechnology uses precise nanofabrication techniques to advance our understanding and control of biological systems. Due to their remarkable properties, dendrimers, which are hyperbranched macromolecular structures with distinct and well-defined architectures, have emerged as pivotal entities within this field. They are gaining increasing attention for their potential to catalyze a paradigm shift in medical therapeutics, biotechnological applications, and advanced material sciences.

Objective: This paper focuses on a novel analytical expression and determines the precise value of the augmented Zagreb index, a topological descriptor, for eight classes of nanostar dendrimers.

Methods: The Zagreb index is a topological invariant to predict molecular behaviour and reactivity. In this paper, we have explored its application in characterizing the branching of nanostar dendrimers through computational modelling and mathematical rigor.

Results: Our research has measured the augmented Zagreb index for nanostar dendrimers, which fall into eight distinct classes. The results better explain the relationship between the dendrimers' topology and chemical properties. This correlation has implications for their structural stability and reactivity, potentially leading to new applications.

Conclusion: Developing the augmented Zagreb index for nanostar dendrimers is a significant breakthrough in nanobiotechnology. Based on the correlation between the calculated topological index and the corresponding molecular attributes, our analytical approach has opened up new possibilities for designing and synthesizing dendrimers tailored to specific functions in medical and material science applications. This precise topological quantification could significantly enhance the utility and functionalization of dendrimers in cutting-edge nanotechnological applications.