Opuscula Math. 31, no. 4 (2011), 519-531

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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  • S. Arumugam
  • Kalasalingam University, National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Anand Nagar, Krishnankoil-626190, India
  • The University of Newcastle, School of Electrical Engineering and Computer Science, NSW 2308, Australia
  • C. Sivagnanam
  • St. Joseph’s College of Engineering, Department of Mathematics, Chennai-600119, India
  • Received: 2009-10-21.
  • Revised: 2010-12-23.
  • Accepted: 2010-12-23.
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Cite this article as:
S. Arumugam, C. Sivagnanam, Neighbourhood total domination in graphs, Opuscula Math. 31, no. 4 (2011), 519-531, http://dx.doi.org/10.7494/OpMath.2011.31.4.519

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