Discussiones Mathematicae Graph Theory 32(3) (2012)
461-471

doi: 10.7151/dmgt.1618

Seyed Mahmoud Sheikholeslami
Department of Mathematics | Lutz Volkmann
Lehrstuhl II für Mathematik |

**Keywords:** digraph, total *{k}*-dominating function, total *{k}*-domination number, total *{k}*-domatic number

**2010 Mathematics Subject Classification:** 05C69.

[1] | H. Aram, S.M. Sheikholeslami and L. Volkmann, On the total , Bull. Malays. Math. Sci. Soc. {k}-domination and {k}-domatic number of a graph {to appear}{}{}} (). |

[2] | J. Chen, X. Hou and N. Li, The total , J. Comb. Optim. {k}-domatic number of wheels and complete graphs {to appear}{}{}} (). |

[3] | E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211--219, doi: 10.1002/net.3230100304. |

[4] | E.J. Cockayne, T.W. Haynes, S.T. Hedetniemi, Z. Shanchao and B. Xu, Extremal graphs for inequalities involving domination parameters, Discrete Math. 216 (2000) 1--10, doi: 10.1016/S0012-365X(99)00251-4. |

[5] | T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in graphs (New York: Marcel Dekker, Inc., 1998). |

[6] | K. Jacob and S. Arumugam, Domatic number of a digraph, Bull. Kerala Math. Assoc. 2 (2005) 93--103. |

[7] | N. Li and X. Hou, On the total , J. Comb. Optim. {k}-domination number of Cartesian products of graphs 18 (2009) 173--178, doi: 10.1007/s10878-008-9144-2. |

[8] | S.M. Sheikholeslami and L. Volkmann, The total , J. Comb. Optim. {k}-domatic number of a graph 23 (2012) 252--260, doi: 10.1007/s10878-010-9352-4. |

Received 31 March 2011

Revised 29 August 2011

Accepted 30 August 2011