  We systematically investigate the magnetic and electronic properties of
graphene adsorbed with diluted 3d-transition and noble metal atoms using first
principles calculation methods. We find that most transition metal atoms (i.e.
Sc, Ti, V, Mn, Fe) favor the hollow adsorption site, and the interaction
between magnetic adatoms and \pi-orbital of graphene induces sizable exchange
field and Rashba spin-orbit coupling, which together open a nontrivial bulk gap
near the Dirac points leading to the quantum-anomalous Hall effect. We also
find that the noble metal atoms (i.e. Cu, Ag, Au) prefer the top adsorption
site, and the dominant inequality of the AB sublattice potential opens another
kind of nontrivial bulk gap exhibiting the quantum-valley Hall effect.
