  We consider an effective model for graphene with interface-induced spin-orbit
coupling and calculate the quantum Hall effect in the low-energy limit. We
perform a systematic analysis of the contribution of the different terms of the
effective Hamiltonian to the quantum Hall effect (QHE). By analysing the
spin-splitting of the quantum Hall states as a function of magnetic field and
gate-voltage, we obtain different scaling laws that can be used to characterise
the spin-orbit coupling in experiments. Furthermore, we employ a real-space
quantum transport approach to calculate the quantum Hall conductivity and
investigate the robustness of the QHE to disorder introduced by hydrogen
impurities. For that purpose, we combine first-principles calculations and a
genetic algorithm strategy to obtain a graphene-only Hamiltonian that models
the impurity.
