A set S V is a global dominating set of a graph G = (V;E) if S is a dominating set of G and G; where G is the complement graph of G. The global domination number g(G) equals the minimum cardinality of a global dominating set of G. The square graph G2 of a graph G is the graph with vertex set V and two vertices are adjacent in G2 if they are joined in G by a path of length one or two. In this paper we provide a characterization of all trees T whose global domination number equals the global domination number of the square of T.
