Author : Dr. A.Punitha Tharani 1
Date of Publication :6th February 2018
Abstract:
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. Mahadevan et. 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 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
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