A dominating set is called a global dominating set if it is a dominating set of a graph G and its complement  A set  is called a resolving set of G if for every  there exists  such that  A set D of G which is both a resolving and a dominating set is called a metro dominating set. A metro dominating set D of a graph G is a global metro dominating set if it is also a metro dominating set of the complement of G. The global metro domination number  is the minimum cardinality of a global metro dominating set of G. In this paper, we investigate global metro domination number  of graphs which satisfies the condition  and also characterize graphs of order n for which

domination, complement graph, metric dimension, metro dominating set, global dominating set, global metro dominating set, global metro domination number.