Let G = (V (G), E(G)) be a connected undirected graph. The closed neighborhood of any vertex v ∈ V (G) is NG[v] = {u ∈ V (G) : uv ∈ E(G)} ∪ {v}. For C ⊆ V (G), the closed neighborhood of C is N [C] = ∪v∈CNG[v]. A set S ⊆ V (G) is a total dominating set ofG if for each x ∈ V (G), there exists y ∈ S such that xy ∈ E(G), that is, N(S) = V (G). A total dominating set S ⊆ V (G) is a weakly connected total dominating set of a connected graph G if the subgraph 〈S〉w = (NG(S), Ew) weakly induced by S is… CONTINUE READING