  We have investigated the fractional quantum Hall states for the Dirac
electrons in a graphene layer in different Landau levels. The relativistic
nature of the energy dispersion relation of the electrons in the graphene
significantly modifies the inter-electron interactions. This results in a
specific dependence of the ground state energy and the energy gaps for
electrons on the Landau level index. For the valley-polarized states, i.e. at
\nu =1/m, m being an odd integer, the energy gaps have the largest values in
the n=1 Landau level. For the valley-unpolarized states, e.g., for the 2/3
state, the energy gaps are suppressed for the n=1 Landau level as compared to
the n=0 level. For both the n=1 and n=0 Landau levels the ground state of the
2/3 system is fully valley-unpolarized.
