The first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Dendrimer is a polimer molecule with a distinctive structure that resembles the crown of a tree. Dendrimers are key molecules in nanotechnology and can be put to good uses. In this paper we compute Zagreb indices of an infinite family of dendrimers nanostars. Copyright &cop...