Dominating cycle

Dominating cycle --- доминирующий цикл.

1. A cycle [math]\displaystyle{ C }[/math] in [math]\displaystyle{ G }[/math] is called a dominating cycle if the vertices of the graph [math]\displaystyle{ G - C }[/math] are independent.

2. A cycle [math]\displaystyle{ C }[/math] in [math]\displaystyle{ G }[/math] is called a dominating cycle if [math]\displaystyle{ V(C) }[/math] is a dominating set of [math]\displaystyle{ G }[/math].

3. In some papers, a dominating cycle is defined as a cycle such that every edge in [math]\displaystyle{ G }[/math] is incident with a vertex in [math]\displaystyle{ C }[/math].

Other name is Covering cycle.