# Weakly Connected Domination in Graphs Resulting from Some Graph Operations

@inproceedings{Sandueta2011WeaklyCD, title={Weakly Connected Domination in Graphs Resulting from Some Graph Operations}, author={Elsie P. Sandueta and S. Canoy}, year={2011} }

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 dominating set C ⊆ V (G) is a weakly connected dominating set in G if the subgraph 〈C〉w = (NG[C], EW ) weakly induced by C is connected, where EW is the set of all edges with at least one vertex in C. The weakly connected domination number γw(G) of G is the minimum cardinality among all… CONTINUE READING

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