Opuscula Math. 31, no. 4 (2011), 519-531
http://dx.doi.org/10.7494/OpMath.2011.31.4.519

Opuscula Mathematica

# Neighbourhood total domination in graphs

S. Arumugam
C. Sivagnanam

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 $$\langle N(S)\rangle$$ 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.

Keywords: neighbourhood total domination, total domination, connected domination, paired domination, neighbourhood total domatic number.

Mathematics Subject Classification: 05C69.

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