The concept of triple connected graphs with real life application was introduced in [7] by considering the existence of a path containing any three vertices of G. In [5], the authors introduced triple connected domination number of a graph. A subset S of V of a nontrivial graph G is said to be triple connected dominating set, if S is a dominating set and the induced subgraph  is triple connected. The minimum cardinality taken over all triple connected dominating sets is called the triple connected domination number of G and is denoted by  In this paper, we introduce a new domination parameter, called complementary triple connected domination number of a graph. A subset S of V of a nontrivial connected graph G is said to be complementary triple connected dominating set, if S is a dominating set and the induced subgraph  is triple connected. The minimum cardinality taken over all complementary triple connected dominating sets is called the complementary triple connected domination number of G and is denoted by  We determine this number for some standard classes of graphs and obtain bounds for general graphs. Its relationship with other graph theoretical parameters is also investigated.

domination number, triple connected graph, complementary triple connected domination number.