The Convex and Weak Convex Domination Number of Convex Polytopes

Abstract

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 An, Bn, Cn, Dn, En, Rn, R"n, Qn, Sn, S"n, Tn, T"n and Un. When n is up to 26, the values are confirmed by using the exact method, while for greater values of n theoretical proofs are given.