Problem: Weighted independent dominating set

Definition:
Input: A graph G in this class with weight function on the vertices and a real k.
Output: True iff G contains a set S of pairwise non-adjacent vertices, with the sum of the weights of the vertices in S at most k, such that every vertex in G is either in S or adjacent to a vertex in S.

Linear

Polynomial

GI-complete

NP-hard

NP-complete

coNP-complete

Open

Unknown to ISGCI