Triple Connected Complementary Tree Domination Number of a Graph

Copyright © 2013 G. Mahadevan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The concept of triple connected graphs with real life application was introduced in [14] by considering the existence of a path containing any three vertices of a graph G. In [4], G. Mahadevan et. al., introduced triple connected domination number of a graph. A subset S of V of a nontrivial connected graph G is said to be triple connected dominating set, if S is a dominating set and the induced sub graph <S> is triple connected. The minimum cardinality taken over all triple connected dominating sets is called the triple connected domination number of G and is denoted by tc(G). A subset S of V of a nontrivial graph connected graph G is said to be a complementary tree dominating set, if S is a dominating set and the induced sub graph <V- S> is a tree. The minimum cardinality taken over all 660 G. Mahadevan et a