In summary, the stability of fullerenes with different carbon atoms can be inferred from topological attributes such as atom, bond, and hexagon features, alongside geometric measures like d, κ, and A/V ratio. Furthermore, there is a notable correlation between the logP values across ODCB and water phases and the cage sizes of fullerenes. While these topological attributes and geometric measures (i.e., V and A) effectively illustrate trends from C 20 to C 60 fullerenes, they fall short in precisely predicting logP values for fullerenes of identical sizes. Nonetheless, accurately determining the E g through these topological features and geometric measures remains a challenge. Future work might benefit from employing more complex models beyond linear regression or incorporating additional properties, to enhance the prediction of E g values in fullerenes. This falls beyond the scope of our current paper.