Tree dominating set

Tree dominating set --- древесное доминирующее множество. A dominating set [math]\displaystyle{ S }[/math] is called a connected (acyclic) dominating set if the induced subgraph [math]\displaystyle{ \langle S \rangle }[/math] is connected (acyclic). The connected (acyclic) domination number is the minimum cardinality taken over all minimal connected (acyclic) dominating sets of [math]\displaystyle{ G }[/math].

If [math]\displaystyle{ \langle S \rangle }[/math] is both connected and acyclic, then [math]\displaystyle{ \langle S \rangle }[/math] is a tree. A dominating set [math]\displaystyle{ S }[/math] is called a tree dominating set, if the induced subgraph [math]\displaystyle{ \langle S \rangle }[/math] is a tree. The tree domination number [math]\displaystyle{ \gamma_{tr}(G) }[/math] of [math]\displaystyle{ G }[/math] is the minimum cardinality taken over all minimal tree dominating sets of [math]\displaystyle{ G }[/math].