We expand a previous model developed for the study of the interaction of fullerenes with graphite planes to consider carbon, rings. The model assumes that the ring is rigid and the interaction energy arises from the cumulative effect of adding the pairwise interaction energies for all the pairs of the atoms in the ring and in the plane, respectively. We have seen that the preferred orientation of the ring with respect to the surface is parallel. This relative orientation has a binding energy five times larger than that of its corresponding perpendicular orientation. The calculated potential energy functions have been used to estimate the force constant and harmonic frequency of the rings on the graphite surface. Subsequently we have calculated and discussed the results of a feasible temperature-programmed desorption experiment.