In an undirected graph G =(V, E), we say D ⊆ V is a dominating set if every v∈V is either...

In an undirected graph G =(V, E), we say D ⊆ V is a dominating set if every v∈V is either in D or adjacent to at least one member of D. In the DOMINATING SET problem, the input is a graph and a budget b, and the aim is to find a dominating set in the graph of size at most b, if one exists. Prove that this problem is NP-complete.