  We study graphene in a two-dimensional dynamical noncommutative space in the
presence of a constant magnetic field. The model is solved using perturbation
theory and to the second order of perturbation. The energy levels of the system
are calculated and the corresponding eigenstates are obtained. For all cases,
the energy shift depends on the dynamical noncommutative parameter {\tau}.
Using the accuracy of energy measurement we put an upper bound on the
noncommutativity parameter {\tau}. In addition, we investigate some of the
thermodynamic quantities of the system at zero temperature limit and extreme
relativistic case, which reveals interesting differences between commutative
and dynamical noncommutative spaces.
