  Landau level quantization in graphene reflects the Dirac nature of its
quasiparticles and has been found to exhibit an unusual integer quantum Hall
effect. In particular the lowest Landau level can be thought as shared equally
by electrons and holes and this leads to characteristic behaviour of the
magneto-optical conductivity as a function of frequency $\Omega$ for various
values of the chemical potential $\mu$. Particular attention is paid to the
optical spectral weight under various absorption peaks and its redistribution
as $\mu$ is varied. We also provide results for magnetic field $B$ as well as
chemical potential sweeps at selected fixed frequencies which can be
particularly useful for possible measurements in graphene. Both diagonal and
Hall conductivity are considered.
