Paired Triple Connected Domination Number of a Graph
Gopalakrishnan Mahadevan, Selvam Avadayappan, Thirumavalavan Subramanian · 2012
The concept of triple connected graphs with real life application was introduced in [10] by considering the existence of a path containing any three vertices of G and also they studied their properties. In [2, 4], the authors introduced the concept of triple connected domination number and complementary triple connected domination number of a graph. In this paper, we introduce another new concept called paired triple connected domination number of a graph. A subset S of V of a nontrivial connected graph G is said to be paired triple connected dominating set, if S is a triple connected dominating set and the induced subgraph has a perfect matching. The minimum cardinality taken over all paired triple connected dominating sets is called the paired triple connected domination number and is denoted by ptc. We determine this number for some standard classes of graphs and obtain some bounds for general graph. Its relationship with other graph theoretical parameters are investigated.