Outer-weakly convex domination number of graphs

For a given simple graph G = (V;E), a set S ⊊ V is an outer-weakly convex dominating set if every vertex in V nS is adjacent to some vertex in S and V nS is a weakly convex set. The outer-weakly convex domination number of a graph G, denoted by e wcon(G), is the minimum cardinality of an outer-weakly convex dominating set of G. In this paper, we initiate the study of outer-weakly convex domination as a new variant of graph domination and we show the close relationship that exists between this novel parameter and other domination parameters of a graph. Furthermore, we obtain general bounds on e wcon(G) and, for some particular families of graphs, we obtain closed formula.