Please use this identifier to cite or link to this item:

`http://hdl.handle.net/10497/17693`

Title: | Lower bound on the weakly connected domination number of a cycledisjoint graph |

Authors: | Koh, Khee Meng Ting, T. S. Xu, Z. L. Dong, Fengming |

Issue Date: | 2010 |

Citation: | Koh, K. M., Ting, T. S., Xu, Z. L., & Dong, F. (2010). Lower bound on the weakly connected domination number of a cycledisjoint graph. Australasian Journal of Combinatorics, 46, 157-166. |

Abstract: | For a connected graph G and any non-empty S ⊆ V (G), S is called a weakly connected dominating set of G if the subgraph obtained from G by removing all edges each joining any two vertices in V (G) \ S is connected. The weakly connected domination number γw(G) is defined to be the minimum integer k with |S| = k for some weakly connected dominating set S of G. In this note, we extend a result on the lower bound for the weakly connected domination number γw(G) on trees to cycle-e-disjoint graphs, i.e., graphs in which no cycles share a common edge. More specifically, we show that if G is a connected cycle-e-disjoint graph, then γw(G) ≥ (|V (G)| − v1(G) − nc(G) − noc(G) + 1)/2, where nc(G) is the number of cycles in G, noc(G) is the number of odd cycles in G and v1(G) is the number of vertices of degree 1 in G. The graphs for which equality holds are also characterised. |

URI: | http://hdl.handle.net/10497/17693 |

ISSN: | 1034-4942 |

Website: | http://ajc.maths.uq.edu.au/pdf/46/ajc_v46_p157.pdf |

Appears in Collections: | Journal Articles |

###### Files in This Item:

File | Description | Size | Format | |
---|---|---|---|---|

AJC-46-157.pdf | 124.91 kB | Adobe PDF | View/Open |

Page view(s) 50

28
checked on Sep 25, 2017

Download(s)

13
checked on Sep 25, 2017