Topological indices (TIs) have been found to be extensively useful in describing and simulating the chemical structure of diverse molecular compounds, including dendrimers, nanotubes, and neural networks. Dendrimers represent a distinct class of well-defined, highly branched macromolecules characterized by their symmetrical, tree-like architecture. This review provides a comprehensive overview of dendrimer synthesis, structure, properties, and diverse applications in nanoscience. Currently, the field of chemistry is actively exploring a mathematical approach that involves using topological techniques and numerical graph invariants to characterize molecular structures. Out of all the established descriptors, connection-based Zagreb indices are generally regarded as more efficient than the traditional indices. This manuscript presents the overarching outcome for calculating the Zagreb connection indices, specifically, harmonic connection index (HCI), augmented connection index (ACI), symmetric division connection index (SDCI), geometric arithmetic connection index (GACI), hyper Zagreb connection index (HZCI), inverse sum connection index (ISCI), and atom bond connectivity connection index (ABCCI). Furthermore, we compare the numerical and graphical values with each other to assess their relative superiority.
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