Equitable Triple Connected Two Domination Number of a Graph

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. In this paper we introduce a new domination parameter called equitable triple connected two domination number of a graph. A two dominating set S S of V of a non-trivial graph G is said to be an equitable triple connected two domination set if <S> is triple connected and for every u  V – S there exists a v S such that uv is an edge of G and The minimum cardinality taken over all equitable triple connected two dominating sets is called the equitable triple connected two domination number and is denoted by  (G).  We find the upper and lower bounds and investigate this number for some standard graphs. We also investigate its relationship with other graph theoretical parameters.