  The generalized tight-binding model, with the exact diagonalization method,
is developed to investigate optical properties of graphene in five kinds of
external fields. The quite large Hamiltonian matrix is transferred into the
band-like one by the rearrangement of many basis functions; furthermore, the
spatial distributions of wave functions on distinct sublattices are utilized to
largely reduce the numerical computation time. The external fields have a
strong influence on the number, intensity, frequency and structure of
absorption peaks, and the selection rules. The optical spectra in a uniform
magnetic field exhibit plentiful symmetric absorption peaks and obey a specific
selection rule. However, there are many asymmetric peaks and extra selection
rules under the modulated electric field, the modulated magnetic field, the
composite electric and magnetic fields, and the composite magnetic fields.
