  A density-functional approach on the hexagonal graphene lattice is developed
using an exact numerical solution to the Hubbard model as the reference system.
Both nearest-neighbour and up to third nearest-neighbour hoppings are
considered and exchange-correlation potentials within the local density
approximation are parameterized for both variants. The method is used to
calculate the ground-state energy and density of graphene flakes and infinite
graphene sheet. The results are found to agree with exact diagonalization for
small systems, also if local impurities are present. In addition, correct
ground-state spin is found in the case of large triangular and bowtie flakes
out of the scope of exact diagonalization methods.
