  In this article we employ a simple nonrelativistic model to describe the low
energy excitation of graphene. The model is based on a deformation of the
Heisenberg algebra which makes the commutator of momenta proportional to the
pseudo-spin. We solve the Landau problem for the resulting Hamiltonian which
reduces, in the large mass limit while keeping fixed the Fermi velocity, to the
usual linear one employed to describe these excitations as massless Dirac
fermions. This model, extended to negative mass, allows to reproduce the
leading terms in the low energy expansion of the dispersion relation for both
nearest and next-to-nearest neighbor interactions. Taking into account the
contributions of both Dirac points, the resulting Hall conductivity, evaluated
with a $\zeta$-function approach, is consistent with the anomalous integer
quantum Hall effect found in graphene. Moreover, when considered in first order
perturbation theory, it is shown that the next-to-leading term in the
interaction between nearest neighbor produces no modifications in the spectrum
of the model while an electric field perpendicular to the magnetic field
produces just a rigid shift of this spectrum.
  PACS: 03.65.-w, 81.05.ue, 73.43.-f
