Volume :8 , Issue :1 ,Page :1-16

Abstract : A set D of a graph G = (V, E) is a dominating se t, if every vertex in V-D is adjacent to some vertex in D. The domination number  (G) of G is the minimum cardinality of a dominating set. A dominating set D of a connected graph G is called a co mplementary tree nil dominating set if the induced sub graph is a tree and V-D is not a dominating set . The minimum cardinality of a complementary tree nil dominating set is called the co mplementary tree nil domination number of G and is denoted by  ctnd (G). In this pa per, bounds for  ctnd (G) and its exact values for some particular classes of graphs are found. Some results on complementar y tree nil domination number are also established.