Under the assumptions that no two sp 3 carbon atoms are adjacent in the end product of bromination of a fullerene and that the residual π system is a closed shell, graph theory predicts maximum stoichiometries C 60 Br 24 , C 70 Br 26 , C 76 Br 28 , C 84 Br 32 and rules out all but 58 of the ~10 23 addition patterns conceivable for these molecules.