Rimsha NoreenSP23-RMT-025Dr. Muhammad Kamran SiddiquiLHR TP 95682026-03-182024-03-18https://repository.cuilahore.edu.pk/handle/123456789/2925Graph theory has been widely utilized across various fields, with a significant rise in its application in molecular graph theory. In recent years, researchers have explored numerous new directions in this domain. A chemical graph is a labeled graph in which vertices represent atoms in a compound, and edges denote chemical bonds between these atoms. To determine the physical and chemical properties of molecular structures, the study of topological indices is crucial. This work focuses on topological indices, co-indices, and reverse degree-based indices of the Phenylacetone Monooxygenase Network (Pa3Mo). Subsequently, physical proper ties, such as the heat of formation for Pa3Mo are analyzed. Curve fitting techniques were employed to establish relationships between various indices and the corresponding heat of formation. These analyses were conducted using MATLAB, utilizing both linear and non-linear methods. Metrics such as Mean Squared Error (MSE), Sum of Squared Errors (SSE), and the coefficient of determination (R 2 ) were used to evaluate the performance of these methods. Graphical representations of these indices were also provided to aid inter pretation. These mathematical frameworks enable a detailed study of the thermodynamic characteristics of the chemical structure Pa3Mo. Additionally, machine learning techniques, particularly regression models, were ap plied to investigate the relationship between the indices and the corresponding volume of Pa3Mo. Models were developed using data from ten iterations of Pa3Mo, and their perfor mance was evaluated using metrics such as correlation coefficient (R), (R 2 ), and Standard Error (SE).enDepartment of MathematicsMathematicsSP23Graph theorymolecular graph theorytopological indicesMonooxygenase NetworkThesis