Let G be a graph. For a given χ - colouring of a graph G, a dominating set S ⊆ V (G) is said to be a dom-colouring set if it contains atleast one vertex of each colour class of G. The dom chromatic number of a graph G is the minimal cardinality taken over all its dom-colouring sets and is denoted by γd-c (G). In this paper, we introduce algorithms to obtain the dom-colouring and dom-chromatic number of various classes of graphs.