Weakly Convex 2-Domination in the Join of Two Graphs

For a nontrivial graph, a set of vertices of a graph is a weakly convex 2-dominating set if a set is weakly convex and for every vertex in its complement is adjacent to at least two vertices in the set. The weakly convex 2-domination number of a nontrivial graph is the cardinality of a minimum weakly convex 2-dominating set. In this paper, we characterize the weakly convex 2-dominating sets of the join of two graphs and derive the corresponding weakly convex 2-domination number.