Generalized 2-Complement Of Set Domination

Abstract Let GVE be a simple undirected finite nontrivial graph. A set SV of vertices of a graph G V E is called a dominating set if every vertex vV is either an element of S or is adjacent to an element of S. A set SV is a set dominating set if for every set TV-S there exists a non-empty set RS 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 26947s G.Let PV1V2 be a partition of Vfrom EG remove the edges between V1 and V2 in G and join the edges between V1 and V2 which are not in G. The graph G2p thus obtained is called 2-complement of G with respect to P.