On neighborhood Zagreb index of product graphs

Abstract

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.

Keywords: Cartesian product; Molecular descriptor; Molecular graph; Neighborhood Zagreb index; Tensor product; Wreath product.