ABC index of cartesian product of some graphs

A topological index is a numerical value associated with a molecular graph that describes the correlation between molecular structure and physio-chemical properties. The atom-bond connectivity (ABC) index is a widely studied degree-based topological index in mathematical chemistry, leading to numerous results that incorporate both the structural properties and the computational aspects of various graph structures. The Cartesian product of graphs is an important structure in graph theory due to its ability to represent real-world complicated networks by simple subgraphs. This paper focuses on deriving a formula for ABC index as well as fourth atomic bond connectivity (ABC4) index of the Cartesian products of several graphs, including path graphs with path graphs, path graphs with cycle graphs, path graphs with regular graphs, path graphs with bipartite graphs and cycle graphs with cycle graphs.