Neighbourhood total domination in graphs

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 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 $gamma _{nt}(G)$. The maximum order of a partition of V into ntd-sets is called the neighbourhood total domatic number of G and is denoted by $d_{nt}(G)$. In this paper we initiate a study of these parameters.