• TRIPLE CONNECTED.COM DOMINATION NUMBER OF A GRAPH

Abstract

In this paper we introduce new domination parameter called triple connected.com domination number of a graph with real life applications. A subset S of V of a nontrivial connected graph G is said to be a triple connected.com dominating set, if S is a triple connected dominating set and the induced subgraph <V – S> is connected. The minimum cardinality taken over all triple connected.com dominating sets is called the triple connected.com domination number and is denoted by _tc.com. We find the upper and lower bounds for the number and investigate this number for some standard graphs. We also investigate its relationship with other graph theoretical parameters.