AbstractDendrimers are profoundly extended natural macromolecules with successive layers of branch units encompassing a central core. Topological indicess are numbers related with graph of a compound to allow quantitative structureactivity/property/lethality connections. These topological indices relate certain physico-chemical properties like stability, boiling point, strain energy and so forth of a compound. In this report, there have been computed redefined first, second and third Zagreb indices of Nanostar dendrimers. The authors also analyzed some Zagreb polynomials of understudy dendrimers.