  Small polaron behavior in a two dimensional honeycomb net is studied by
applying the strong coupling perturbative method to the Holstein molecular
crystal model. We find that small optical polarons can be mobile also if the
electrons are strongly coupled to the lattice. Before the polarons localize and
become very heavy, there is infact a window of {\it e-ph} couplings in which
the polarons are small and have masses of order $\simeq 5 - 50$ times the bare
band mass according to the value of the adiabaticity parameter. The 2D
honeycomb net favors the mobility of small optical polarons in comparison with
the square lattice.
