• Dr. A.Punitha Tharani
• A.Robina Tony

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.G. Mahadevan etc. al., introduced the concept of triple connected domination number of a graph. In this paper, we introduce a new domination parameter, called restrained triple connected two domination number of a graph. A subset S of V of a non – trivial graph G is said to be a restrained triple connected two dominating set, if S is a restrained two dominating set and the induced subgraph <S> is triple connected. The minimum cardinality taken over all restrained triple connected two dominating sets is called the restrained triple connected two domination number of G and is denoted by γ2rtc(G). Any restrained triple connected two dominating set with γ2rtc vertices is called a γ2rtc- set of G. We determine this number for some standard and special graphs and obtain bounds for general graph. Its relationship with other graph theoretical parameters is also investigated.

Triple connected graphs, restrained triple connected, restrained triple connected two domination Subject Classification: 05C69

"A Study on Restrained Triple Connected Two Domination Number of a Graph", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 3, page no.27-29, March-2019, Available :http://www.jetir.org/papers/JETIRAL06007.pdf

"A Study on Restrained Triple Connected Two Domination Number of a Graph", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 3, page no. pp27-29, March-2019, Available at : http://www.jetir.org/papers/JETIRAL06007.pdf