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Vertices contained in all or in no minimum paired-dominating set of a tree. (English) Zbl 1122.05071
Summary: A set \(S\) of vertices in a graph \(G\) is a paired-dominating set of \(G\) if every vertex of \(G\) is adjacent to some vertex in \(S\) and if the subgraph induced by \(S\) contains a perfect matching. We characterize the set of vertices of a tree that are contained in all, or in no, minimum paired-dominating sets of the tree.

MSC:
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
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