@Article{Arumugam2011,
author = "Arumugam, S. and Sivagnanam, C.",
title = "Neighbourhood total domination in graphs",
journal = "Opuscula Math.",
year = "2011",
volume = "31",
number = "4",
pages = "519--531",
doi = "http://dx.doi.org/10.7494/OpMath.2011.31.4.519",
url = "http://dx.doi.org/10.7494/OpMath.2011.31.4.519",
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",
issn = "1232-9274"
}