Discussiones Mathematicae Graph Theory 32(4) (2012)
677-683

doi: 10.7151/dmgt.1635

Houcine Boumediene Merouane and Mustapha Chellali
LAMDA-RO, Department of Mathematics |

**Keywords:** dominator coloring, domination, trees

**2010 Mathematics Subject Classification:** 05C69, 05C15.

[1] | M. Chellali and F. Maffray, Dominator colorings in some classes of graphs, Graphs Combin. 28 (2012) 97--107, doi: 10.1007/s00373-010-1012-z. |

[2] | R. Gera, On the dominator colorings in bipartite graphs in: Proceedings of the 4th International Conference on Information Technology: New Generations (2007) 947--952, doi: 10.1109/ITNG.2007.142. |

[3] | R. Gera, On dominator colorings in graphs, Graph Theory Notes of New York LII (2007) 25--30. |

[4] | R. Gera, S. Horton and C. Rasmussen, Dominator colorings and safe clique partitions, Congr. Numer. 181 (2006) 19--32. |

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

[6] | T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, Inc., New York, 1998). |

[7] | O. Ore, Theory of Graphs (Amer. Math. Soc. Colloq. Publ. 38, 1962). |

[8] | L. Volkmann, On graphs with equal domination and covering numbers, Discrete Appl. Math. 51 (1994) 211--217, doi: 10.1016/0166-218X(94)90110-4. |

Received 24 January 2011

Revised 11 August 2011

Accepted 19 December 2011