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∖s is adjacent to some vertex in s and v∖s is a weakly convex set. the emph{outer-weakly convex domination number} of a graph g, denoted by γ˜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 γ˜wcon(g) and, for some particular families of graphs, we obtain closed formula.