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In this article, we discuss the dynamic and steady-state features of the absorption-dispersion of a graphene monolayer system, interacting with an elliptically polarized control and coherent pumping fields. We find that, under a proper condition of parameters selection, the absorption, dispersion and group index of the weakly probe field in a monolayer graphene system can be adjusted. We show that, under optimal conditions, the controlling of the group velocity can be possible to achieve the subluminal and superluminal light propagation. Moreover, we realize that the amplification of the probe light due to the presence and absence of population inversion can be obtained by the proper choice of controllable parameters. Our findings may be useful for high-speed optical communications based on a graphene monolayer system.