  We study nxn honeycomb superlattices of defects in graphene. The considered
defects are missing p_z orbitals and can be realized by either introducing C
atom vacancies or chemically binding simple atomic species at the given sites.
Using symmetry arguments we show how it is possible to open a gap when
n=3m+1,3m+2 (m integer), and estimate its value to have an approximate
square-root dependence on the defect concentration x=1/n^2. Tight-binding
calculations confirm these findings and show that the induced-gaps can be quite
large, e.g. ~100 meV for x~10^{-3}. Gradient-corrected density functional
theory calculations on a number of superlattices made by H atoms adsorbed on
graphene are in good agreement with tight-binding results, thereby suggesting
that the proposed structures may be used in practice to open a gap in graphene.
