A characterization of (2γ,γp)(2γ,γp)-trees

Let G=(V,E)G=(V,E) be a graph. A set S⊆VS⊆V is a dominating set of G if every vertex not in S is adjacent with some vertex in S. The domination number of G  , denoted by γ(G)γ(G), is the minimum cardinality of a dominating set of G  . A set S⊆VS⊆V is a paired-dominating set of G if S   dominates VV and 〈S〉〈S〉 contains at least one perfect matching. The paired-domination number of G  , denoted by γp(G)γp(G), is the minimum cardinality of a paired-dominating set of G. In this paper, we provide a constructive characterization of those trees for which the paired-domination number is twice the domination number.