• TRIPLE CONNECTED EQUITABLE DOMINATION IN GRAPHS

Abstract

The concept of triple connected graphs with real life application was introduced in [5] by considering the existence of a path containing any three vertices of graph G. In [3] G. Mahadevan et.al., was introduced the concept of triple connected domination number of a graph. In this paper we introduce a new domination parameter called triple connected equitable domination number of a graph. A subset S of V of a nontrivial graph G is said to be triple connected equitable dominating set. If S is equitable dominating set and the induced subgraph áSñ is triple connected. The minimum cardinality taken over all triple connected equitable dominating sets is called the triple connected equitable domination number and is denoted by . We determine this number for some standard graphs and obtain bounds for general graph. Its relationship with other graph theoretical parameters are also investigated.