Let G = (V,E) be a connected undirected graph. For any vertex v ∈ V , the closed neighborhood of v is N [v] = {v} ∪ {u ∈ V | uv ∈ E }. For S ⊆ V , the closed neighborhood of S is N [S] = ⋃ v∈S N [v]. The subgraph weakly induced by S is 〈S〉w = (N [S], E ∩ (S × N [S])). A set S is a weakly-connected dominating set of G if S is dominating and 〈S〉w is connected. The weakly-connected domination numb...
