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The concept of triple connected graphs with live application was introduced in by considering the available of roots containing any three vertices of a graph G. In this thesis, we introduce a new dominating parameter, called Smarandachely triple connected domination number of a graph. A subset S of V of a nontrivial G-graph is said to be Smarandachely triple connected dominated set, if S is a dominating set and the induced sub graph S is triple connected. The nominal cardinality take over all Smarandachely triple connected dominant sets is called the Smarandachely triple connected domination number and is denoted by γtc. We assumed this number for some standard graphs and obtain sustained bounds for general graphs. It’s have the relationship with other graph theoretical parameters also investigated.