Independent sets and the prediction of addition patterns for higher fullerenes

Abstract

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.