## Abstract

In this paper, we continue the study of neighborhood total domination in graphs first studied by Arumugam and Sivagnanam [S. Arumugam, C. Sivagnanam, Neighborhood total domination in graphs, Opuscula Math. 31 (2011) 519-531]. A neighborhood total dominating set, abbreviated NTD-set, in a graph G is a dominating set S in G with the property that the subgraph induced by the open neighborhood of the set S has no isolated vertex. The neighborhood total domination number, denoted by ^{γnt}(G), is the minimum cardinality of a NTD-set of G. Every total dominating set is a NTD-set, implying that γ(G)≤^{γnt}(G)≤^{γt}(G), where γ(G) and ^{γt}(G) denote the domination and total domination numbers of G, respectively. We show that if G is a connected graph on n≥3 vertices, then ^{γnt}(G)≤(n+1)/2 and we characterize the graphs achieving equality in this bound.

Original language | English |
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Pages (from-to) | 2460-2466 |

Number of pages | 7 |

Journal | Discrete Applied Mathematics |

Volume | 161 |

Issue number | 16-17 |

DOIs | |

Publication status | Published - Nov 2013 |

## Keywords

- Domination
- Neighborhood total domination
- Total domination

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics