Domination and edge domination in trees

Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is a dominating set if every vertex in $V \setminus S$ is adjacent to a vertex in $S$. The domination number of a graph $G$, denoted by $\gamma(G)$ is the minimum cardinality of a dominating set of $G$. A set $D \subseteq E$ is an edge dominating set if every edge in $E\setminus D$ is adjacent to an edge in $D$. The edge domination number of a graph $G$, denoted by $\gamma'(G)$ is the minimum cardinality of an edge dominating set of $G$. We characterize trees with domination number equal to twice edge domination number.