This study examines the structural complexity of fullerene graphs using Hosoya entropy as a measure. The entropy values were calculated for various fullerene structures, including \(F^s_{3,1},\) \(F^s_{4,2}\) and fullerenes ranging from C20 to C100.The relationship between the size of the fullerenes and the entropy is intuitively clear: the larger the fullerenes, the higher the value of entropy because of increased structural complexity and diversity of equivalence classes. Smaller fullerenes, like C20, have lower entropy, a consequence of their simpler and more symmetrical molecular structure. These findings provide theoretical insights into structural intricacies of fullerenes and their possible applications in material science and nanotechnology.
