Global dominating-c-coloring number of a graph G is the maximum number of color classes which are global dominating sets of G, where the maximum is taken over all c colorings of G. In this paper, we obtain the global dominating-c-coloring number for middle graph of path, middle graph of cycle, total graph of path, total graph of cycle, Mycielski graph of path and Mycielski graph of cycle and also we obtain some general observation on global dominating-c-coloring number.

global dominating set, middle graph, total graph, graph coloring.