Triple Connected Domination Number of a Graph

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