▎ 摘　　要

Floquet theorem is widely used in the light-driven systems. But many 2D-materials models under the radiation are investigated with the high-frequency approximation, which may not be suitable for the practical experiment. In this work, we employ the non-perturbative Floquet method to strictly investigate the photo-induced topological phase transitions and edge states properties of graphene nanoribbons under the light irradiation of different frequencies (including both low and high frequencies). By analyzing the Floquet energy bands of ribbon and bulk graphene, we find the cause of the phase transitions and its relation with edge states. Besides, we also find the size effect of the graphene nanoribbon on the band gap and edge states in the presence of the light.