GENERALIZED 3 – COMPLEMENT OF SET DOMINATION

Abstract

Let G=(V,E) be a simple, undirected, finite nontrivial graph. A set S⊆V of vertices of a graph G = (V, E) is called a dominating set if every vertex v∈V is either an element of S or is adjacent to an element of S. 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 <RUT> is connected. The minimum cardinality of a set dominating set is called set domination number and it is denoted by γs (G).Let P=(V1,V2,V3) be a partition of V of order 3. Remove the edges between Vi and Vj where i≠j (1≤i,j≤3) in G and join the edges between Vi and Vjwhich are not in G. The graph G3p thus obtained is called 3-complement of G with respect to ‘P’.