GENERALIZED 2-COMPLEMENT OF SET DOMINATION

Abstract

Let G=(V,E) be a simple, undirected, finite nontrivial graph and P= (V1,V2,….., VK) be a partition of V of order k>1.The k-complement Gk p of G (with respect to P) is defined as follows: For all Vi and Vj in P ij remove the edges between Vi and Vj in G and join the edges between Vi and Vj which are not in G. The graph thus obtained is called the kcomplement of G with respect to P. In this paper 2- complement is considered. Let G=(V,E) be a connected graph. A set SV is a set dominating set if for every set TV-S , there exists a non-empty set RS such that the subgraph is connected. The minimum cardinality of a set dominating set is called set domination number and it is denoted by γs (G). In the following example the set domination number γs is calculated..