Let G be a graph. Among all X-colorings of G, a coloring with the maximum number of color classes that are global dominating sets in G is called a global dominating- X-coloring of G. The number of color classes that are global dominating sets in a global dominating-X-coloring of G is defined to be the global dominating -X- color number of G, denoted by gd_X (G). This concept was introduced in [5]. This paper extends the study of this notion.