Study on Weighted Sombor Indices and Its QSPR Analysis on Medical Drugs

Chemical Graph Theory has emerged as a vital tool in accelerating drug discovery by reducing costs and time frames while addressing critical challenges in bioavailability and toxicity during the early stages of development. This study introduces novel topological indices, namely Weighted Sombor indices and Reduced Weighted Sombor indices, derived from the M-Polynomial of the graph𝐺. These indices are evaluated for specific classes of graphs using their M-Polynomials. Additionally, Quantitative Structure-Property Relationship (QSPR) studies have been done on antiviral drugs utilized in COVID-19 medication, including Chloroquine, Hydroxychloroquine, Remdesivir, Lopinavir, Ritonavir, Arbidol, and Theaflavin. The predictive potential of the indices Reduced Sombor 𝑆𝑂𝑟, Weighted Sombor 𝑆𝑂𝑤, Reduced Weighted Sombor 𝑆𝑂𝑟𝑤 They are evaluated concerning physicochemical properties such as Boiling Point (BP), Surface Tension (T), Molar Volume (MV), and Polar Surface Area (PSA). These findings underscore the applicability of the proposed indices in Chemical Graph Theory and their relevance in computational drug discovery.