The Second Hyper-Zagreb Index and Coindex of Chemical Nano-structures in Drugs

Abstract

Introduction: Various dendrimer nanoparticles have properties like multivalency, controlled size, and surface functionality that make them promising nanocarriers for targeted drug delivery and other applications in pharmaceutical sciences. The precise tunability of dendrimers is an advantage over other nanoparticles. The topological descriptors can be used to predict the physicochemical properties of dendrimers and optimize their branching pattern for specific applications. The second hyper-Zagreb index and co-index are computed for various chemical structures, including dendrimers, to facilitate the correlation between their structure and biological activity. Methods: In this study, the second Hyper-Zagreb index and second Hyper-Zagreb polynomials were calculated for various chemical structures, such as the molecular graph of poly(propyl) ether imine dendrimer PETIM, nanostar dendrimer (D3[p]), polypropylenimine octaamine dendrimer (NS1[p]) and (NS2[p]), polymer dendrimer (NS3[p]) and NS5[p]), fullerene dendrimer (NS4[p]), and other classes of dendrimers. Results: By computing formulae and analyzing data and figures, we obtained new insights into the features of structure-property connections for these types of compounds of nanostar dendrimers. Conclusion: The results can be used to optimize the properties of dendrimers for specific applications.