Graphene has emerged as an exciting material because of its widespread applications resulting from its unique properties. Nano-scale engineering of graphene's structure is one of the most active research areas aimed at introducing functionalities to improve the performance or endow the graphene lattice with novel properties. In this regard, conversion between the hexagon and non-hexagon rings becomes an exciting tool to tune the electronic structure of graphene due to the distinct electronic structure and functionalities induced in graphene by each type of ring. This Density Functional Theory (DFT) study is an in-depth look at the adsorption-induced conversion of pentagon-octagon-pentagon rings to hexagon rings, and systematically investigates the possibility of the conversion of pentagon-octagon-pentagon rings to pentagon-heptagon pair rings. Moreover, the bottlenecks for these atomic-level conversions in the lattice structure of graphene and the influence of heteroatom doping on the mechanisms of these transformations are established.