# Vertex Cover without covering all edges

What would be the name of the problem of a vertex cover that covers all the vertices without the requirement of covering all the edges?

Vertex cover has to answer whether or not there is a set of $$k$$ vertices that covers all the edges of the graph, covering therefore, all the vertices. What is the name of the problem that, similarly to vertex cover, select a subset of $$k$$ vertices that has direct edges to all the vertices, but without necessarily covering all the edges of the graph?