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
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.
- 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.
