Graph-Theoretical Modeling of Antipyretics: Stability and Reactivity via GA and ABC Indices
Antipyretic drugs such as Paracetamol, Ibuprofen, Aspirin, Metamizole, and Naproxen play a vital role in modern therapeutics, yet their reactivity and stability remain key factors in determining pharmacological performance. In this work, we explore these molecular properties through the lens of graph theory, employing two powerful topological descriptors: the Geometric–Arithmetic (GA) index and the Atom–Bond Connectivity (ABC) index. Rigorous theorems confirm the non-negativity of both indices, with proofs supported by illustrative graph structures. The GA index emphasizes balanced degree interactions, correlating with structural uniformity and stability, while the ABC index highlights degree disparity, offering insights into branching, reactivity, and thermodynamic behavior. Application of these indices to antipyretic drugs provides quantitative fingerprints that bridge molecular architecture with biological function. The findings demonstrate that GA and ABC indices serve as reliable, cost-effective, and predictive tools for QSAR/QSPR modeling, advancing the integration of mathematical chemistry into drug design and bioactivity prediction.