We continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks 32 (1998) 199-206). A paired-dominating set of a graph G with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G is the minimum cardinality of a paired-dominating set of G For k > 2, a fc-packing in G is a set S of vertices of G that are pair wise at distance greater than k apart The A;-packing number of G is the maximum cardinality of a fc-packing in G Haynes and Slater observed that the paired-domination number is bounded above by twice the domination number. We give a constructive characterization of the trees attaining this bound that uses labelings of the vertices. The key to our characterization is the observation that the trees with paired-domination number twice their domination number are precisely the trees with 2-packing number equal to their 3-packing number.
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