Weakly connected domination stable trees
Magdalena Lemańska, Joanna Raczek · Czechoslovak Mathematical Journal · 2009
A dominating set D ⊆ V(G) is a weakly connected dominating set in G if the subgraph G[D] w = (N G [D], E w ) weakly induced by D is connected, where E w is the set of all edges having at least one vertex in D. Weakly connected domination number γw (G) of a graph G is the minimum cardinality among all weakly connected dominating sets in G. A graph G is said to be weakly connected domination stable or just γw -stable if γw (G) = γ w (G + e) for every edge e belonging to the complement Ḡ of G. We provide a constructive characterization of weakly connected domination stable trees.