Reaction pathways are presented for hydrogen-mediated isomerization of a five- and six-member carbon ring complex on the zigzag edge of a graphene layer. A new reaction sequence that reverses the orientation of the ring complex, or "flips" it, was identified. Competition between the flip reaction and the "ring separation" was examined. Ring separation is the reverse of the five- and six-member ring complex formation reaction, previously reported as "ring collision". The elementary steps of the pathways were analyzed using density functional theory (I)FT). Rate coefficients were obtained by solution of the energy master equation and classical transition-state-theory utilizing the DFT energies, frequencies., and geometries. The results indicate that the flip reaction pathway dominates the separation reaction and should be competitive with other pathways important to the graphene zigzag edge growth in high-temperature environments.