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Electron correlation effects caused by the topological zero mode of ahydrogenated graphene vacancy, $V_{111}$, with three adsorbed hydrogen atoms isdiscussed theoretically. A Kondo model is derived from the multi-referencerepresentation of the density functional theory, where exchange scatteringprocesses between the zero mode and low-energy modes in the Dirac cones areestimated. Even when the Dirac cone is slightly off from the charge neutralpoint, a finite on-site correlation energy, $U_0$, for the zero mode of anisolated $V_{111}$ allows the half-filling of the localized level giving a spin$s=1/2$. The anti-ferromagnetic Kondo screening mediated by higher orderscattering processes becomes dominant in the dilute limit of the vacancies. Ourestimation of relevant two body interactions certifies appearance of the Kondoeffect at low temperatures.

Magnetic correlation effects by the topological zero mode in a hydrogenated graphene vacancy $V_{111}$