Neighborhood connected perfect domination in graphs

Abstract

LetG = (V,E) be a connected graph. A set S of vertices inG 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 〈. N(S) 〉 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 γncp(G). In this paper we initiate a study of this parameter.