Neighbourhood total domination in graphs
S. Arumugam, C. Sivagnanam · Opuscula Mathematica · 2011
Let G = (V, E) be a graph without isolated vertices.A dominating set S of G is called a neighbourhood total dominating set (ntd-set) if the induced subgraph N (S) has no isolated vertices.The minimum cardinality of a ntd-set of G is called the neighbourhood total domination number of G and is denoted by γnt(G).The maximum order of a partition of V into ntd-sets is called the neighbourhood total domatic number of G and is denoted by dnt(G).In this paper we initiate a study of these parameters.