  Single-layer and Bilayer of graphene are new classes of two-dimensional
electron systems with unconventional band structures and valley degrees of
freedom. The ground states and excitations in the integer and fractional
quantum Hall regimes are investigated on torus and spherical geometries with
the use of the density matrix renormalization group (DMRG) method. At nonzero
Landau level indices, the ground states at effective filling factors 1, 1/3,
2/3 and 2/5 are valley polarized both in single-layer and bilayer graphenes. We
examine the elementary charge excitations which could couple with the valley
degrees of freedom (so called valley skyrmions). The excitation gaps are
calculated and extrapolated to the thermodynamic limit. The largest excitation
gap at effective filling 1/3 is obtained in bilayer graphene, which is a good
candidate for experimental observation of fractional quantum Hall effect.
