A characterization of image-trees

Let image be a graph. A set image 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 image, is the minimum cardinality of a dominating set of G. A set image is a paired-dominating set of G if S dominates image and image contains at least one perfect matching. The paired-domination number of G, denoted by image, 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.