TY  - JOUR
ID  - Arumugam2011
LB  - Arumugam2011
AU  - Arumugam, S.
AU  - Sivagnanam, C.
TI  - Neighbourhood total domination in graphs
ST  - Neighbourhood total domination in graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2011
VL  - 31
IS  - 4
SP  - 519
EP  - 531
DO  - http://dx.doi.org/10.7494/OpMath.2011.31.4.519
UR  - http://dx.doi.org/10.7494/OpMath.2011.31.4.519
AB  - 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.
KW  - neighbourhood total domination
KW  - total domination
KW  - connected domination
KW  - paired domination
KW  - neighbourhood total domatic number
SN  - 1232-9274
ER  -