Graph theory, already useful in understanding the cages themselves, is shown to help in prediction of the extent and pattern of addition to fullerenes. Maximum coverage patterns for bulky ligands are predicted by the (closed-shell) independence numbers of the fullerene graphs, rationalising the experimental structure of C_(60)Br_(24) and, for example, reducing an initial set of approx 10~(17) conceivable isomers to only 10 likely candidates for C_(70)Br_(26). Simple rule sets, in which incoming ligands alternately attack sites of maxmum free valence and maximum spin density, rationalise, for example, the experimental structures of C_(60)Br_6 and C_(60)Cl_(10).
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