Studying toxic gases is more important because it is related to the health of humans. Therefore, it is appropriate to make some theoretical calculations to cover this topic. This study selectivity tunes the graphene derivatives’ ability to sense the most common gases in the atmosphere such as carbon monoxide, carbon dioxide, and oxygen. This involves a pristine and doped Gr-sheets complex with three gases. Density Functional Theory (DFT) was employed to investigate the electronic structures of 12 graphene-based sheets. The bandgap simulations demonstrate the effect of doping and complexing graphene sheets with different segments, that result in a sensing signature. The bandgap calculations also prove that the studied graphene derivatives selectively bind to different gases and this characteristic is in good agreement with the total energy calculations. Our results show that the electrical properties of graphene are improved with doping by Ni and As.