Vertex minimal dominating graph

Vertex minimal dominating graph --- вершинно минимальный доминирующий граф.

A vertex minimal dominating graph [math]\displaystyle{ M_{v}D(G) }[/math] was introduced as the graph having [math]\displaystyle{ V(M_{v}(D(G)) = V(G) \cup S(G) }[/math], where [math]\displaystyle{ S(G) }[/math] is the set of all minimal dominating sets of [math]\displaystyle{ G }[/math], and two vertices [math]\displaystyle{ u }[/math] and [math]\displaystyle{ v }[/math] are adjacent, if they are adjacent in [math]\displaystyle{ G }[/math] or [math]\displaystyle{ v = D }[/math] is a minimal dominating set containing [math]\displaystyle{ u }[/math].