Volume :2 , Issue :3 ,Page :118-129

Abstract :Let G(V, E) be a nontrivial, simple, finite an d undirected graph. A dominating set of the graph G is a subset D of V such that every vertex not in D is adjacent to some vertex in D. The minimum cardinality of a dominatin g set is the domination number  (G). A dominating set D is called a complementary tree dominating set if the subg raph induced by V - D is a tree. The minimum cardinality of a complementary tree do minating set is called the complementary tree domination number of G and is denoted by  ctd (G). In this paper, we determin e the complementary tree domination numbers of some grid graphs (Cartesian product of two paths P m and P n ).