By applying tight binding model of adatoms in graphene, we study theoretically the localized aspects of the interaction between transition metal atoms and graphene. Considering the electron-electron interaction by adding a Hubbard term in the mean-field approximation, we find the spin-polarized localized and total density of states. We obtain the coupled system of equations for the occupation number for each spin in the impurity and we study the fixed points of the solutions. By comparing the top site and hollow site adsorption, we show that the anomalous broadening of the latter allows to obtain magnetization for small values of the Hubbard parameter. Finally, we model the magnetic boundaries in order to obtain the range of Fermi energies at which magnetization starts.
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