  The spin-orbit couplings (SOCs) of hydrogenated and fluorinated graphenes are
calculated from the first principles method. It is found that the SOC-induced
band splittings near their Fermi energies can be significantly enhanced to the
order of 10$^{-2}$ eV from the original about 10$^{-6}$ eV of the pure raphene,
which is comparable to those found in the diamond and even the archetypal
semiconductors. And two different mechanisms are proposed to explain the SOC
enhancements in these two systems. The huge SOC enhancements are found to come
not only from the sp$^3$ hybridization of carbon atoms, but also from the
larger intrinsic SOC of the fluorine atom than the carbon one. We hope many
interesting phenomena caused by the SOCs (e.g. the spin Hall effect) can be
observed experimentally in these systems.
