### Abstract

In this paper we consider the effect of edge contraction on the domination number and total domination number of a graph. We define the (total) domination contraction number of a graph as the minimum number of edges that must be contracted in order to decrease the (total) domination number. We show both of this two numbers are at most three for any graph. In view of this result, we classify graphs by their (total) domination contraction numbers and characterize these classes of graphs.

Original language | English (US) |
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Pages (from-to) | 431-443 |

Number of pages | 13 |

Journal | Ars Combinatoria |

Volume | 94 |

State | Published - Jan 2010 |

### Keywords

- Domination
- Domination contraction number
- Total domination

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Huang, J., & Xu, J. M. (2010). Domination and total domination contraction numbers of graphs.

*Ars Combinatoria*,*94*, 431-443.