Volume :2 , Issue :2 ,Page :88-103

Abstract :Let G be a simple graph with vertex set V and edge set E. A subset S of V is said to be a dom- chromatic set (or dc-set) if S is a dominating set and χ () = χ (G). The minimum cardinality of a dom-chromatic set in a graph G is called the dom-ch romatic number (or dc-number) and is denoted by γ ch (G). In this paper, bounds for the dom-chromatic numbers are found for standard graphs and some classes of graphs. Further, some Nordhaus Gaddum type of results are obtained.