Computation of connection-based Zagreb indices in chain graphs and triangular sheets

Graph theory is a mathematical framework that can be used to model and analyze complex networks. Topology plays a key role in determining the compatibility of chemical graphs. Topological indices have been widely applied in a wide range of domains, such as chemistry, biological activity prediction, environmental risk assessment, and drug design. These indices can predict aqueous solubility, dipole moment, viscosity, boiling degree, refractive index, toxicity, and surface tension, among other physicochemical characteristics. Topological descriptors also assist us in the quantitative analysis and comparison of molecules by simplifying complicated molecular information. In this paper, we have computed the first Zagreb connection index ZC(1), the second Zagreb connection index ZC(2), and the first modified Zagreb connection index ZC(1)*. Further, a few recently introduced Zagreb connection indices like atom-bond connectivity, geomatric-arithmatic, and hyper-Zagreb connection indices are also calculated for the melem chain MC(m), the borophene chain B-36(m),, and the boron triangular sheet BTS(m, n). Our goal is to comprehend the molecular connections between these substances. Through the study of several mathematical methods, we discovered intriguing relationships and patterns within their structures. The primary objective of our research is to learn more about these compounds and the relationship between their molecular structures and properties. Every chemical, as we have seen, has distinct properties. The ability to predict the behavior of these molecules under different conditions might open up new research avenues and practical applications.