  The Dirac-like quasiparticles in honeycomb graphene lattice are taken to
possess a non-zero effective mass. The charge carriers involve to interact with
a femtosecond strong laser pulse. Due to the scattering time of electrons in
graphene ($\tau \approx 10-100 fs$), the one femtosecond optical pulse is used
to have coherence effect, and consequently, it is realized to use the
time-dependent Schr$\ddot{o}$dinger equation for coupling electron with strong
electromagnetic field. Generalized wavevector of relativistic electrons
interacting with electric field of laser pulse leads to obtain a time-dependent
electric dipole matrix element. Using the coupled differential equations of a
two-state system of graphene, the density of probability of population
transition between valence and conduction bands of gapped graphene is
calculated. In particular, the effect of bandgap energy on dipole matrix
elements in the Dirac points, and also on conduction band population is
investigated. The irreversible electron dynamics is achieved when the optical
pulse end. Increasing the energy gap of graphene results in a decreasing the
maximum conduction band population.
