  The X-ray edge problem of graphene with the Dirac fermion spectrum is
studied. At half-filling the linear density of states suppresses the singular
response of the Fermi liquid, while away from half-filling the singular
features of the Fermi liquid reappear. The crossover behavior as a function of
the Fermi energy is examined in detail. The exponent of the power-law
absorption rate depends both on the intra- and inter-valley scattering, and it
changes as a function of the Fermi energy, which may be tested experimentally.
