• TRIPLE CONNECTED COMPLEMENTARY ACYCLIC DOMINATION OF A GRAPH

Abstract

Let G = (V, E) be a non trivial connected graph. A subset S of V(G) is called a triple connected dominating set if S is a dominating set and induced sub graph  is triple connected. The minimum cardinality taken over all triple connected dominating set is called the triple connected domination number of G and it is denoted by . A subset S of V of a non trivial connected graph G is said to be a triple connected complementary acyclic dominating set if S is a triple connected dominating set and induced subgraph  is acyclic .The minimum cardinality taken over all triple connected complementary acyclic dominating sets is called the triple connected complementary acyclic domination number of G and is denoted by  .We determine this number for some standard graphs and obtain bounds for general graphs. Its relationship with other graph theoretical parameters are also investigated.