There are multiple implications for topological indices (TIs) in the realm of anti-tumour, anti-cancer, anti-viral agents, anti-inflammatory, anti-microbial, anti-fungal, anti-oxidant, and enzyme inhibition potentials. One such utilisation involves predicting the effectiveness of compounds, where TIs shed light on these sulfonamides’ chemical structures and associated characteristics. Analysts can pinpoint the most suitable treatments for certain cancer types by examining the degree-based TIs of various compounds. This paper explores the functions of mathematical descriptors as TIs in estimating the anatomical and pharmacological features of emerging drugs utilised for chemotherapy for cancer. Analysing the compounds of sulfonamide is carried out utilising graph-based TIs computed by employing edge partitioning. The establishment of a QSPR model then follows using a linear regression approach. The conclusions highlight the significant capability of TIs as valuable assets in exploring and characterising compounds within the domains of anti-tumour, anti-cancer, anti-viral agents, anti-inflammatory, anti-microbial, anti-fungal, anti-oxidant, and enzyme inhibition.