Global 2-Point Set Domination Number of a Graph

A set D   of vertices in a graph G=(V,E)G=(V,E) is called a 2-point set dominating set of G   if for every set T⊆V−DT⊆V−D there exists a non-empty set S⊆DS⊆D containing at most two vertices such that the induced subgraph 〈S∪T〉〈S∪T〉 is connected. A set D⊆V(G)D⊆V(G) is called a global 2-point set dominating set of G if D is a 2-point set dominating set of both G   and G‾. The global 2-point set domination number (2-point set domination number) is the minimum cardinality of a global 2-point set dominating set (2-point set dominating set) in G. In this paper we determine bounds on the global 2-point set domination number of a graph in terms of other graph invariants. We have also given relation between global 2-point set domination number and 2-point set domination number for some classes of graphs.