  Based on the standard tight-binding model of the graphene $\pi$-band
electronic structure, the extended H\"uckel model for the adsorbate and
graphene carbon atoms, and spin splittings estimated from density functional
theory (DFT), the Dirac point resonances due to a single cobalt atom on
graphene are studied. The relaxed geometry of the magnetic adsorbate and the
graphene is calculated using DFT. The system shows strong spin polarization in
the vicinity of the graphene Dirac point energy for all values of the gate
voltage, due to the spin-splitting of Co 3d orbitals. We also model the
differential conductance spectra for this system that have been measured in the
scanning tunneling microscopy (STM) experiments of Brar {\em et al.} [Nat.
Phys. {\bf 7}, 43 (2011)]. We interpret the experimentally observed behavior of
the S-peak in the STM differential conductance spectrum as evidence of
tunneling between the STM tip and a cobalt-induced Dirac point resonant state
of the graphene, via a Co 3d orbital. The cobalt ionization state which is
determined by the energy position of the resonance can be tuned by gate
voltage, similar to that seen in the experiment.
