Neighborhood connected perfect domination in graphs - M.P., Kulandai Vel; P., Selvaraju; C., Sivagnanam (Tamkang Journal of Mathematics, 2012)
Let G = (V, E) be a connected graph. A set S of vertices in G is a perfect dominating set if every vertex v in V-S is adjacent to exactly one vertex in S. A perfect dominating set S is said to be a neighborhood connected perfect dominating set (ncpd-set) if the induced subgraph is connected. The minimum cardinality of a ncpd-set of G is called the neighborhood connected perfect domination number of G and is denoted by γ_ncp(G). In this paper we initiate a study of this parameter.