  In this work we analyze impact of non-adiabatic effects on the
superconducting energy gap in the hole-doped graphene. By using the Eliashberg
formalism beyond the Migdal's theorem, we present that the non-adiabatic
effects strongly influence the superconducting energy gap in the exemplary
boron-doped graphene. In particular, the non-adiabatic effects, as represented
by the first order vertex corrections to the electron-phonon interaction,
supplement Coulomb depairing correlations and suppress the superconducting
state. In summary, the obtained results confirm previous studies on
superconductivity in two-dimensional materials and show that the corresponding
superconducting phase may be notably affected by the non-adiabatic effects.
