In this paper we investigate the harmonious chromatic number for the central graph, middle graph, total graph and line graph of double star graph K1,n,n denoted by C(K1,n,n), M(K1,n,n), T (K1,n,n) and L(K1,n,n) respectively. We prove that for the line graph of double star graph, the harmonious chromatic number and the achromatic number are equal.