  A novel type of one-dimensional (1D) photonic crystal formed by the array of
periodically located stacks of alternating graphene and dielectric stripes
embedded into a background dielectric medium is proposed. The wave equation for
the electromagnetic wave propagating in such structure solved in the framework
of the Kronig-Penney model. The frequency band structure of 1D graphene-based
photonic crystal is obtained analytically as a function of the filling factor
and the thickness of the dielectric between graphene stripes. The photonic
frequency corresponding to the electromagnetic wave localized by the defect of
photonic crystal formed by the extra dielectric placed on the place of the
stack of alternating graphene and dielectric stripes is obtained.
