Dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core (Ashrafi and Mirzargar, 2008 3; Chen et al., 2014 7; Klajnert and Bryszewska, 2001 26; Yamamoto et al., 2002 36). These are key molecules in nanotechnology and can be put to good use. Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity/property/toxicity relationships. These topological indices correlate certain physico-chemical properties like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index and Zagreb polynomials for some nanostar dendrimers.