## Trees with large paired-domination number.(English)Zbl 1112.05078

A paired-dominating set of a graph is a dominating set of vertices whose induced subgraph contains a perfect matching. If $$G$$ is a graph without isolated vertices, then it is easy to see that the paired-domination number of $$G$$ is bounded above by twice the domination number of $$G$$. The authors present a constructive characterization of those trees attaining this bound.

### MSC:

 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C05 Trees

### Keywords:

domination; paired-domination; tree