mediation of the sp hybridized carbon atoms and their coupling effects are similar with the case of TM-chain-GY will be discussed below. As for TM-chain-GY, from the band structures as shown in Fig.\[fig2\], one can see that the adsorption of TM chain on GY is an effective modulation approach to their electronic properties; and all TM-chain-GY systems show metallic characteristics. The TM-chain absorbed systems show similar band structures, which is derived from the quais-1D structural nature as the cases of carbon nanotubes[@46], graphene nanoribbons[@47], and Cr chain embedded graphene topological line defect[@48]. Although our previous investigation indicated that the GY sheet emerge magnetism by adsorption of single TM atom[@19], the existence of magnetic order of TM-chain-GY determined by the magnetic exchange coupling between TM atoms is deserved to be studied thoroughly. The results as listed in Tab.\[tab1\] indicate that ferromagnetic state for V, Mn, Fe and Co chains is 271 meV, 193 meV, 11 meV and 16 meV energetically more favorable than that of antiferromagnetic state, respectively. Especially, the V-chain-GY and Mn-chain-GY show considerable exchange energy suggesting that V and Mn TM chain adsorbed on GY behave as stable ferromagnetism hopping to be high $T_c$ temperature magnetic materials. However, Cr 