Comparison Between Connection Based Modified Indices and Coindices for Product of Networks

Topological indices (TIs) are functional tools which correlate with a computational value through a undirected, finite and simple networks. Many physicochemical properties and chemical reactions are studied with the help of these TIs. Recently, they are commonly used in the behavior of quantitative structures activity as well as property relationships. In 1972, connection number based TIs are studied by Gutman and Trinajstić to calculate the entire $\pi $ -electron energy of the alternant hydrocarbons. Moreover, the data provided by the website https://www.moleculardescriptors.eu shows that the relations between Zagreb indices and connection based indices that provide the better absolute values of the correlation coefficients for the thirteen physicochemical properties of the octane isomers. In this paper, we discuss the two invariants which are modified indices and modified coindices based on connection number of the resultant networks obtained by the different operations of product such as lexicographic and corona. For the molecular networks such as fence, closed fence, alkene and cycloalkane are depicted in the consequences of the obtained results. The comparisons between two invariants of the aforemention molecular networks are also presented through tables and graphical depictions. In addition, the uses and significance related to product of networks are also included.