<p>Predicting physicochemical properties of chemical compounds in a cost-effective and non-experimental manner is of great importance. This is often achieved using topological indices derived from graph theory. Topological index is the numerical value obtained from the structural property of the graph obtained by modeling the chemical structure with graph theory. Bipolar disorder is a mental health condition characterized by mood swings, including manic/hypomanic and depressive episodes. In this study, various Zagreb topological indices based on vertex degree, edge degree, and eccentricity are calculated for graphs of drugs used in the treatment of bipolar disorder. Furthermore, QSPR (quantitative structure property relationship) models are developed to predict the boiling point, enthalpy of vaporization, flash point, molar refractivity and polarizability of these drugs. This study determines the version of the Zagreb indices that best predict the physicochemical properties of bipolar drugs and the corresponding model. The findings demonstrate the potential of using mathematical descriptors in designing and evaluating pharmaceutical compounds.</p>