  We consider Upper Domination, the problem of finding the minimal dominating
set of maximum cardinality. Very few exact algorithms have been described for
solving Upper Domination. In particular, no binary programming formulations for
Upper Domination have been described in literature, although such formulations
have proved quite successful for other kinds of domination problems. We
introduce two such binary programming formulations, and show that both can be
improved with the addition of extra constraints which reduce the number of
feasible solutions. We compare the performance of the formulations on various
kinds of graphs, and demonstrate that (a) the additional constraints improve
the performance of both formulations, and (b) the first formulation outperforms
the second in most cases, although the second performs better for very sparse
graphs. Also included is a short proof that the upper domination number of any
generalized Petersen graph P(n,k) is equal to n.
