Anaesthesia is a fundamental aspect of modern medical practice, enabling surgical and diagnostic procedures to be performed without pain or distress by inducing a reversible loss of sensation or consciousness. Anaesthetic drugs exert their effect by interrupting neural signal transmission, thereby ensuring patient comfort and procedural safety. This study investigates the structural properties of selected anaesthetic agents through the application of topological indices derived from molecular graph theory. Both degree-based and neighborhood degree-based indices are computed to characterize the physical and chemical behavior of the drugs. Furthermore, a Quantitative Structure-Property Relationship (QSPR) analysis, utilizing quadratic regression models, demonstrates strong correlations between these topological descriptors and various physicochemical parameters. The results provide valuable theoretical insights into structure-property relationships, contributing to the advancement of drug discovery and molecular design in pharmaceutical research.