Fakhra MajidFA23-RMT-009Prof. Dr. Muhammad HussainLHR TP 97572026-01-072025https://repository.cuilahore.edu.pk/handle/123456789/335This thesis presents a comprehensive study of topological indices derived from graph theory, with a specific focus on the HourGlass System Carbon Nano Cone structures. By modeling these nano-scale carbon frameworks as simple, connected molecular graphs, we investigate a wide range of vertex degree-based and vertex neighborhood degree-based topological indices. The work explores indices such as the General Randic, General Inverse Randic, General Sombor, Harmonic, Geometric-Arithmetic, Hyper-Zagreb, Atomic Bond Connectivity, and numerous Kulli-Basava variants. These indices are computed analytically for HourGlass System Carbon Nano Cone configurations with both odd and even cycle lengths across varying dimensions. The results highlight the structural uniqueness and potential chemical properties of these networks, offering valuable insights for applications in nanotechnology, drug design, and chemical compound analysis. This research contributes to the advancement of chemical graph theory by establishing new mathematical formulations and expanding the predictive power of topological descriptors in nano-material science.enProf. Dr. Muhammad HussainMATHEMATICSChemical NetworksThesis