论文信息 - On weakly connected domination in graphs

On weakly connected domination in graphs

A dominating set D is a weakly connected dominating set of a connected graph G=(V,E) if (V,E@?(DxV)) is connected. The weakly connected domination number of G, denoted @c"w"c(G), is min{|S||S is a weakly connected dominating set of G}. We characterize graphs G for which @c(H)=@c"w"c(H) for every connected induced subgraph H of G, where @c is the domination number of a graph. We provide a constructive characterization of trees T for which @c(T)=@c"w"c(T). Lastly, we constructively characterize the trees T in which every vertex belongs to some weakly connected dominating set of cardinality @c"w"c(T).

Johannes H. Hattingh | Alice A. McRae | Jean E. Dunbar | Stephen T. Hedetniemi | Jerrold W. Grossman

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