On neighborhood Zagreb index of product graphs

The properties and activities of chemicals are strongly related to their molecular structures. Topological indices defined on these molecular structures are capable to predict those properties and activities. In this article, a new topological index named as neighborhood Zagreb index (M(N)) is presented. Here the chemical importance of the M(N) index is investigated and it is shown that the newly introduced index is useful in predicting physico-chemical properties with high accuracy compared to some well-established and often used indices. The isomer-discrimination ability of M(N) is also examined. To demonstrate how the computational formula of the novel index for chemical compounds is simple and convenient, the chemical structures of favipiravir and hydroxychloroquine are used. In addition, some explicit results for this index of different product graphs such as Cartesian, tensor and wreath product are derived. Some of these results are applied to obtain the M(N) index of some special structures.