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We investigate the topological phase transitions in graphene under themodulation of circularly polarized light, by analyzing the changes of edgestates and its topological structures. A full phase diagram, with up to tendifferent topological phases, is presented in the parameter space spanned bythe driving frequency and light strength. We find that the high-Chern numberbehavior is very common in the driven system. While the one-photon resonancecan create the chiral edge states in the $\pi-$gap, the two-photon resonancewill induce the counter-propagating edge modes in the zero-energy gap. When thedriving light strength is strong, the number and even the chirality of the edgestates may change in the $\pi-$gap. The robustness of the edge states todisorder potential are also examined. We close by discussing the feasibility ofexperimental proposals.

Edge states and phase diagram for graphene under polarized light