Upper Bounds of Zagreb Connection Indices of Tensor and Strong Product on Graphs

Abstract

A topological index (TI) is a function from P to the set of real numbers, where P is the set of finite simple graphs. In fact, it is a final outcome of a logical, systematical and mathematical process that transforms feature encoded in a molecular graph to a fixed real number. Gutman and Trinajstic (1972) first time defined degree based TI named as first Zagreb index to compute the total π-electron energy of a molecular graph. They also exposed another TI that is renamed as modified first Zagreb connection index in [Ali and T rinajstic, Mol. Inform. 37(2018), 1 − 7]. In this paper, we compute the upper bounds for the Zagreb connection indices i.e. first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index of the resultant graphs which are obtained by applying the tensor and strong product of two graphs.