  We compute the tunneling conductance of graphene as measured by a scanning
tunneling microscope (STM) with a normal/superconducting tip. We demonstrate
that for undoped graphene with zero Fermi energy, the first derivative of the
tunneling conductance with respect to the applied voltage is proportional to
the density of states of the STM tip. We also show that the shape of the STM
spectra for graphene doped with impurities depends qualitatively on the
position of the impurity atom in the graphene matrix and relate this
unconventional phenomenon to the pseudopsin symmetry of the Dirac
quasiparticles in graphene. We suggest experiments to test our theory.
