  Here we show that the Pfaffian state proposed for the $\frac52$ fractional
quantum Hall states in conventional two-dimensional electron systems can be
readily realized in a bilayer graphene at one of the Landau levels. The
properties and stability of the Pfaffian state at this special Landau level
strongly depend on the magnetic field strength. The graphene system shows a
transition from the incompressible to a compressible state with increasing
magnetic field. At a finite magnetic field of ~10 Tesla, the Pfaffian state in
bilayer graphene becomes more stable than its counterpart in conventional
electron systems.
