This paper is devoted to solving the weakly convex dominating set problem and the convex dominating set problem for some classes of planar graphs-convex polytopes. We consider all classes of convex polytopes known from the literature and present exact values of weakly convex and convex domination number for all classes, namely

The recently introduced {k}-packing function problem is considered in this paper. Relationship between cases when k = 1, k ≥ 2 and linear programming relaxation are introduced with sufficient conditions for optimality. For arbitrary simple connected graph

The recently introduced {k}-packing function problem is considered in this paper. Special relation between a case when k = 1, k ≥ 2 and linear programming relaxation is introduced with sufficient conditions for optimality. For arbitrary simple connected graph G there is construction procedure for finding values of k for which L {k} (G) can be determined in the polynomial time. Additionally, relationship between {1}-packing function and independent set number is established. Optimal values for some special classes of graphs and general upper and lower bounds are introduced.