  We calculate the indirect charge carrier mediated
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities
for two selected graphene nanoflakes containing four hexagonal rings in their
structure, differing by their geometry. We describe the electronic structure of
either charge-neutral or doped nanoflakes using the tight-binding approximation
with the Hubbard term, which is treated within the molecular-field
approximation. We find pronounced differences in the RKKY coupling energies,
dependent on the placement of the pair of magnetic moments in the nanostructure
and on the edge form. For an odd total number of electrons in the structure, we
predict in some circumstances the existence of ferromagnetic coupling with
leading first-order perturbational contribution, while for an even number of
charge carriers the usual, second-order mechanism dominates. Therefore, doping
of the nanoflake with a single charge carrier is found to be able to change the
coupling from an antiferromagnetic to a ferromagnetic one for some geometries.
