Analyze the Sombor Index of Molecular Graphs Representing Antibiotic Drugs Using the ℳ Polynomial

Today's world is grappling with numerous infectious diseases and pandemics caused by bacteria, viruses, fungi, or parasites, which are affecting people at an alarming rate. Molecular topology, a field that significantly influences drug design and discovery, involves the algebraic description of chemical compounds, enabling their distinctive and straightforward characterization. Among various applications, the topological indices can be generated from ℳ-polynomial. ℳ-polynomial is a generating function that has been proposed to unify the computation of diverse topological indices. It contains degree-based topological data of molecular graphs and facilitates the derivation of multiple degree-based topological indices in an efficient manner. The ℳ-polynomial can be used to derive different degree-based topological indices by using different transformations. Computational efficiency offers a common method for calculating several topological indices. QSAR/QSPR Models are employed to examine molecular properties and biological activity in drug design. The Sombor index, a molecular descriptor, was studied in the context of several antibacterial medications, including Amoxicillin, Ampicillin, Tetracycline, Doxycycline, Cefalexin, and Ciprofloxacin. These drugs are commonly used to treat conditions such as bladder infections, rickettsial infections, pneumonia, bronchitis, and other respiratory tract infections. In this study, the edge partition technique is employed to derive the ℳ-polynomial for selected antibacterial drug molecules. The graphical representation of the respective molecular structures is calculated and discussed based on the derived ℳ-polynomial. To construct the ℳ -polynomial and derive the Sombor index for antibiotic drugs, then correlate them with the physicochemical properties of these drugs to analyze the regression models for the best fit.