Weakly-connected dominating set

Weakly-connected dominating set --- слабо связное доминирующее множество.

A weakly-connected dominating set, [math]\displaystyle{ {\mathcal W} }[/math], of a graph [math]\displaystyle{ G }[/math] is a domi\-nating set such that the subgraph consisting of [math]\displaystyle{ V(G) }[/math] and all edges incident with vertices in [math]\displaystyle{ {\mathcal W} }[/math] is connected. Define the minimum cardinality of all weakly-connected dominating sets of [math]\displaystyle{ G }[/math] as the weakly-connected domination number of [math]\displaystyle{ G }[/math] and denote this by [math]\displaystyle{ \gamma_{w}(G) }[/math].