LAUSR

The area of graph theory (GT) is rapidly expanding and playing a significant role in cheminformatics, mostly in mathematics and chemistry to develop different physicochemical, chemical structure, and their properties. The manipulation and study of chemical graphical details are made feasible by using numerical structure invariant. Investigating these chemical characteristics of topological indices (TIs) is made possible by the discipline of mathematical chemistry. In this article, we study with the Cartesian product of complete graphs, with path graphs, and find their general result of connection number (CN)-based TIs, namely, first connection- based Zagreb index (1st CBZI), second connection- based Zagreb index (2nd CBZI), and third CBZI (3rd CBZI) and then modified first connection- based Zagreb index (CBZI) and second and third modified CBZIs. We also express the general results of first multiplicative CBZI, second multiplicative CBZI, and third and fourth multiplicative CBZI, of two special types of graphs, namely, complete graphs and path graphs. More precisely, we arrange the graphical and numerical analysis of our calculated expressions for both of Cartesian product with each other.