  We study the photoabsorption cross section and Fermi-edge singularities (FES)
in graphene. For fillings below one half, we find, besides the expected FES in
form of a peaked edge at the threshold (Fermi) energy, a second singularity to
arise at excitation energies that correspond to the Dirac point in the density
of states. We can explain this behaviour by comparing our results with the
photoabsorption cross section of a metal with a small central band gap where we
find a very similar signature. The existence of the second singularity might
prove useful for an experimental determination of the Dirac point. We also
demonstrate that the photoabsorption signal is enhanced by the zigzag edge
states due to their metallic-like character. Since the presence of the edge
states indicates a topological defect at the boundary, our study gives an
example for a Fermi-edge singularity in a system with a topologically
nontrivial electronic spectrum.
