  We combine experimental observations by scanning tunneling microscopy (STM)
and density functional theory (DFT) to reveal the most stable edge structures
of graphene on Ni(111) as well as the role of stacking-driven activation and
suppression of edge reconstruction. Depending on the position of the outermost
carbon atoms relative to hollow and on-top Ni sites, zigzag edges have very
different energies. Triangular graphene nanoislands are exclusively bound by
the more stable zigzag hollow edges. In hexagonal nanoislands, which are
constrained by geometry to alternate zigzag hollow and zigzag top edges along
their perimeter, only the hollow edge is stable whereas the top edges
spontaneously reconstruct into the (57) pentagon-heptagon structure.
Atomically-resolved STM images are consistent with either top-fcc or top-hcp
epitaxial stacking of graphene and Ni sites, with the former being favored by
DFT. Finally, we find that there is a one-to-one relationship between the edge
type, graphene stacking, and orientation of the graphene islands.
