LINE SET TRIPLE CONNECTED DOMINATION NUMBER OF GRAPH

Abstract

The concept of triple connected graphs with real life application was introducedby Paul raj Joseph et.al.by considering the existence of a path containing any three vertices of a graphG.Mahadevan et.al. introduced the concept of triple connected domination number of a graph . Asubset S of V of a nontrivial connected graph G is said to be triple connected dominating set, if S is adominating set and the induced subgraph hSi is triple connected.A subset F of the edge set E(G) of agraph G is called line set dominating if for each subset S ⊆ E − F, there exists an edge eL such thatthe subgraph hS ∪ {e}i induced by S ∪ {e} is connected.In this paper, we introduce new dominationparameter line set triple connected domination number of a graph as follows,A subset L of the edgeset E(G) of a nontrivial connected graph G is said to be a line set triple connected dominating set,if L is a line set dominating set and the induced sub graph hLi is triple connected. The maximumcardinality taken over all line set triple connected dominating sets is called the line set triple connecteddomination number and is denoted by v0ltc(G). We determine this number for some standard graphsand obtain bounds for general graph.Its relationships with other domination parameters were found.