A subset S of V is called a dominating set in G, if every vertex in V- S is adjacent to at least one vertex in S. A Dominating set is said to be independent dominating set if the induced subgraph < V > is independent. The minimum cardinality taken over all, such independent dominating sets is called the independent domination number and is denoted by g_i(G). The minimum number of colours required to colour all the vertices such that adjacent vertices do not receive the same colour is the chromatic number c(G). It was already proved that g_i(G) + c(G) £ 2n-1 and corresponding extremal graphs were characterized of order up to 2n-5. In this paper we characterize the class of graphs for which g_i(G)+c(G) = 2n-6 for any n > 3.