Neighbourhood total domination in graphs

Abstract

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 $\gamma {nt}(G)$. 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.