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Neighbourhood total domination in graphs

Arumugam S., Sivagnanam C.

Opuscula Mathematica

2011

Vol. 31, no. 4

519-531

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 ϒnt(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.