  The interlayer interaction in graphene/boron-nitride heterostructures is
studied using density functional theory calculations with the correction for
van der Waals interactions. It is shown that the use of the experimental
interlayer distance allows to describe the potential energy surface at the
level of more accurate but expensive computational methods. On the other hand,
it is also demonstrated that the dependence of the interlayer interaction
energy on the relative in-plane position of the layers can be fitted with high
accuracy by a simple expression determined by the system symmetry. The use of
only two independent parameters in such an approximation suggests that various
physical properties of flat graphene/boron-nitride systems are interrelated and
can be expressed through these two parameters. Here we estimate some of the
corresponding physical properties that can be accessed experimentally,
including the correction to the period of the Moir\'{e} superstructure for the
highly incommensurate ground state of graphene/boron-nitride bilayer coming
from the interlayer interaction, width of stacking dislocations in slightly
incommensurate systems of boron nitride on stretched graphene and shear mode
frequencies for commensurate graphene/boron-nitride systems, such as a flake on
a layer. We propose that the commensurate-incommensurate phase transition can
be observed in boron nitride on stretched graphene and experimental
measurements of the corresponding critical strain can be also used to get an
insight into graphene/boron-nitride interactions.
