▎ 摘　　要

In this letter, we show the possibility of controlling the optical bistability and group index switching in graphene under the action of strong magnetic and infrared laser fields. By using quantum-mechanical density matrix formalism, we obtain the equations of motion that govern the optical response of graphene in strong magnetic and optical fields. We found that by properly choosing the parameters of the system, the bistable behaviors and group velocity can be controlled. These results may have potential applications in telecommunication and optical information processing.