Implied by the correlation between E b and logP, the solubility of fullerenes also exhibits a strong linear relationship with the atom, bond, and hexagon features, sharing an identical R 2 value of 0.996 (Table and Figure (i,j,l)). However, when exclusively considering C 60 isomers, the respective R 2 values drop to 0.297, 0.353, and 0.448 (Table and Figure (i,j,l). These findings underscore the notable relationship between logP values and fullerene cage size, which is well captured by topological features. Yet, within fullerene of the same size, logP values do not show a linear correlation with these topological features. Regarding pentagon features, the low R 2 value of 0.324 for logP in We further evaluated the relationships between logP and topological signatures. As illustrated in Figure ), the hexagon-derived signatures, H 1 and H 2 display a stronger correlation with logP compared to the pentagon-based signature P 1 across the C 20 -C 60 dataset, demonstrating that hexagon features are more adept at capturing the properties of fullerenes across different sizes than pentagon features. Nevertheless, among fullerenes of the same size, logP values do not exhibit a linear correlation with any of the topological signatures (see Figure )).