  Ordered distributions of carbon and substitutional dopant (A) atoms over the
sites of a graphene lattice and problem of their stability are considered
theoretically. The ranges of values of interatomic-interaction parameters
providing the low-temperature stability of the graphene-based C7A, C3A, and CA
superstructures are determined within the framework of both the
third-nearest-neighbor Ising model and, more realistically, the
all-coordination-shell interaction model. The first model results in the
'omission' (instability) of some predicted superstructures, while the second
model shows that all predicted superstructures are stable at the certain values
of interatomic-interaction energies. Even short-range interatomic interactions
provide a stability of some superstructures, while only long-range interactions
stabilize others.
