In this paper, we compute the general results in the form of the upper bounds of the Zagreb indices based on connection number called as rst Zagreb connection index, second Zagreb connection index and modi ed rst Zagreb connection index for the resultant graphs which are obtained by applying the product-related operations such as disjunction (co-normal product) and symmetric di erence. At the end, some applications of the obtained results with a comparison between exact and computed values of the aforesaid Zagreb connection indices for the particular classes of alkanes are also included.