Let G be a graph. A set D V (G) is a global dominating set of G if D is a dominating set of G and G. g(G) denotes global domination number of G. A set D V (G) is an outer independent global dominating set (OIGDS) of G if D is a global dominating set of G and V (G) D is an independent set of G. The cardinality of the smallest OIGDS of G, denoted by oi g (G), is called the outer independent global domination number of G. An outer independent global dominating set of cardinality oi g (G) is called a oi g -set of G. In this paper we characterize trees T for which oi g (T) = (T) and trees T for which oi g (T) = g(T) and trees T for which oi g (T) = oi(T) and the unicyclic graphs G for which oi g (G) = (G), and the unicyclic graphs G for which oi g (G) = g(G).
