  Recent experiments show that a substantial energy gap in graphene can be
induced via patterned hydrogenation on an iridium substrate. Here, we show that
the energy gap is roughly proportional to $\sqrt{N_{H}}/N_{C}$ when disorder is
accounted for, where $N_H$ and $N_C$ denote concentration of hydrogen and
carbon atoms, respectively. The dispersion relation, obtained through
calculation of the momentum-energy resolved density of states, is shown to
agree with previous angle-resolved photoemission spectroscopy results.
Simulations of electronic transport in finite size samples also reveal a
similar transport gap, up to 1eV within experimentally achievable
$\sqrt{N_{H}}/N_{C}$ value.
