Discussiones Mathematicae Graph Theory 32(4) (2012)
643-657

doi: 10.7151/dmgt.1633

Soufiane Khelifi
Laboratory LMP2M, Bloc of laboratories University of MEDEA | Mustapha Chellali
LAMDA-RO, Department of Mathematics |

**Keywords:** double domination, vertex removal critical graphs, vertex removal stable graphs.

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

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[3] | G. Chartrand and L. Lesniak, Graphs and Digraphs: Fourth edition (Chapman and Hall/CRC Inc., Boca Raton, Fl., 2005). |

[4] | M. Chellali and T.W. Haynes, Double domination stable graphs upon edge removal, Australas. J. Combin. 47 (2010) 157--164. |

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

[7] | S. Khelifi, M. Blidia, M. Chellali and F. Maffray, Double domination edge removal critical graphs, Australas. J. Combin. 48 (2010) 285--299. |

Received 20 May 2011

Revised 25 November 2011

Accepted 30 November 2011