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. The cardinality of the smallest global dominating set of G, denoted by g(G), is called the global domination number of G. A unicyclic graph is a connected graph with exactly one cycle. In this paper we characterize the unicyclic graphs G for which g(G) = (G).
