  We propose a mechanism to control the interaction between adsorbates on
graphene. The interaction between a pair of adsorbates---the change in
adsorption energy of one adsorbate in the presence of another---is dominated by
the interaction mediated by graphene's pi-electrons and has two distinct
regimes. Ab initio density functional, numerical tight-binding, and analytical
calculations are used to develop the theory. We demonstrate that the
interaction can be tuned in a wide range by adjusting the adsorbate-graphene
bonding or the chemical potential.
