Volume :8 , Issue :3 ,Page :119-125

Abstract :A set D of a graph G = (V, E) is a dominating se t, if every vertex in V(G) - D is adjacent to some vertex in D. The domination number γ (G) of G is the minimum cardinality of a dominating set. A dominating set D is called a complementary tree nil dominatin g set, if V(G) - D is not a dominating set and also the induced subgraph < V(G) - D > is a tree. The minimum cardinality of a complementary tree nil dominating set is called the complementary tree nil domination number of G and is denoted by ctnd γ (G). In this paper, some results regarding the complementary tree nil domination number of connecte d cubic graphs are found.