Triple Connected Domination Number of Graph

Abstract

The concept of triple connected graphs with real life application was prefaced by considering the existence of a path containing any three vertices of a graph G. In this paper, we introduce a new domination parameter, called 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 sub graph is triple connected. The minimum cardinality undertake all triple connected dominating sets. Then which is called the triple connected domination number and is denoted by ?tc.