In this work first principles DFT calculation were carried out to identify the active center for 3d, 4d and 5d transition metal (TM) atoms adsorption on the surface of graphene (G) and single walled carbon nanotube (SWCNT) with mono (m)- and di-vacancy defects. The stability of TM atoms on the surface of pristine, defected G and SWCNT have been investigated by calculating binding energy of TM atoms at different sites. Inverse relationship was found among binding energy, bond distance and d-band center of TM atoms. When the binding energy increases, d-band center and bond distance experiences a decrease in their values; and more charge is transferred to the support from TM atoms and vice versa. Sc, Rh, and Ir have strongest binding energy among all kinds of TM elements while Au, Ag and Zn have smallest adsorption energy. Oxygen molecule (O-2) adsorbed on the surface of V, Nb and W TM atoms have stronger binding energy compared to Zn, Ag and Pt. Furthermore, O-2 adsorption and dissociation barrier is estimated to be small and is related with the binding energy of supported metal atoms. Our calculation sheds the light on the future applications of metal-carbon based catalysis.