  Electron correlation effects caused by the topological zero mode of a
hydrogenated graphene vacancy, $V_{111}$, with three adsorbed hydrogen atoms is
discussed theoretically. A Kondo model is derived from the multi-reference
representation of the density functional theory, where exchange scattering
processes between the zero mode and low-energy modes in the Dirac cones are
estimated. Even when the Dirac cone is slightly off from the charge neutral
point, a finite on-site correlation energy, $U_0$, for the zero mode of an
isolated $V_{111}$ allows the half-filling of the localized level giving a spin
$s=1/2$. The anti-ferromagnetic Kondo screening mediated by higher order
scattering processes becomes dominant in the dilute limit of the vacancies. Our
estimation of relevant two body interactions certifies appearance of the Kondo
effect at low temperatures.
