  The topological properties of electronic edge states in time-periodically
driven spatially-periodic corrugated zigzag graphene nanoribbons are studied.
An effective one-dimensional Hamiltonian is used to describe the electronic
properties of graphene and the time-dependence is studied within the Floquet
formalism. Then the quasienergy spectrum of the evolution operator is obtained
using analytical and numeric calculations, both in excellent agreement.
Depending on the external parameters of the time-driving, two different kinds
(type I and type II) of touching band points are found, which have a Dirac-like
nature at both zero and $\pm\pi$ quasienergy. These touching band points are
able to host topologically protected edge states for a finite size system. The
topological nature of such edge states was confirmed by an explicit evaluation
of the Berry phase in the neighborhood of type I touching band points and by
obtaining the winding number of the effective Hamiltonian for type II touching
band points. Additionally, the topological phase diagram in terms of the
driving parameters of the system was built.
