## 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.)

### Keywords:

paired-domination number; tree
Full Text:

### References:

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