  Due to their importance in practice, dominating set problems in graphs have
been greatly studied in past and different formulations of these problems are
presented in literature. This paper's focus is on two problems: weakly convex
dominating set problem (WCVXDSP) and convex dominating set problem (CVXDSP). It
introduces two integer linear programming (ILP) formulation for CVXDSP and one
ILP mode for WCVXDSP, as well as proof for equivalency between ILP models for
CVXDSP. The proof of correctness for all introduced ILP formulations is
provided by showing that optimal solution to the each ILP formulation is equal
to the optimal solution of the original problem.
