Neighbourhood total domination in graphs

• Main Authors: S. Arumugam, C. Sivagnanam
• Format: Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 2011-01-01
• Series: Opuscula Mathematica
• Subjects: neighbourhood total domination; total domination; connected domination; paired domination; neighbourhood total domatic number
• Online Access: http://www.opuscula.agh.edu.pl/vol31/4/art/opuscula_math_3136.pdf

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.