  There is powerful relation between the chemical behaviour of chemical
compounds and their molecular structures. Topological indices defined on these
chemical molecular structures are capable to predict physical properties,
chemical reactivity and biological activity. In this article, a new topological
index named as Neighbourhood Zagreb index $(M_N)$ is presented. Here the
chemical importance of this newly introduced index is studied and some explicit
results for this index of different product graphs such as Cartesian, Tensor
and Wreath product is derived. Some of these results are applied to obtain the
Neighbourhood Zagreb index of several chemically important graphs and
nano-structures.
