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Independent sets and the prediction of addition patterns for higher fullerenes

Under the assumptions that no two sp3 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 C60Br24, C70Br26, C76Br28, C84Br32 and rules out all but 58 of the ≈1023 addition patterns conceivable for these molecules.