Dominating set ($V=D\cup {\bigcup }_{v\in D}N(v)$)

A dominating set $D$ of a graph is a vertex subset such that every unselected vertex has a neighbour in $D$. Equivalently every vertex lies in $D$ or is adjacent to an element of $D$. This condition differs from vertex cover, which requires every edge to have an endpoint in the selected set.