The paper discusses the magneto-optical conductivity of graphene, focusing on the unique properties of its quasiparticles due to the Dirac nature of its band structure. The authors derive analytical expressions for the optical conductivity tensor using the Kubo formula and consider both diagonal and Hall conductivities. They explore the impact of magnetic fields and chemical potential sweeps on the conductivity, providing numerical results for the real part of the diagonal conductivity at fixed frequencies and varying chemical potentials. The study also examines the redistribution of optical spectral weight under different conditions, including the presence of an excitonic gap. The results are useful for experimental measurements in graphene-based devices, particularly in field-effect transistors. The analysis is supported by detailed mathematical derivations and numerical simulations, highlighting the complex behavior of graphene's quasiparticles in magnetic fields and varying chemical potentials.The paper discusses the magneto-optical conductivity of graphene, focusing on the unique properties of its quasiparticles due to the Dirac nature of its band structure. The authors derive analytical expressions for the optical conductivity tensor using the Kubo formula and consider both diagonal and Hall conductivities. They explore the impact of magnetic fields and chemical potential sweeps on the conductivity, providing numerical results for the real part of the diagonal conductivity at fixed frequencies and varying chemical potentials. The study also examines the redistribution of optical spectral weight under different conditions, including the presence of an excitonic gap. The results are useful for experimental measurements in graphene-based devices, particularly in field-effect transistors. The analysis is supported by detailed mathematical derivations and numerical simulations, highlighting the complex behavior of graphene's quasiparticles in magnetic fields and varying chemical potentials.