Volume :2 , Issue :4 ,Page :209-216

Abstract :A graph G is said to be domi nation dot stable ( DDS ) if  (G  uv) =  ( G ),  u, v  V(G), u adjacent to v. In this paper we introduce a DDS graph. We have obtained a necessary and sufficient condition for a graph to DDS. We have initiated a study on DDS gr aph. We have discussed the properties of graph that are excellent and DDS.