## On minimum cutsets in independent domination vertex-critical graphs

dc.contributor.author | Ananchuen, N. | |

dc.contributor.author | Ruangthampisan, S. | |

dc.contributor.author | Ananchuen, W. | |

dc.contributor.author | Caccetta, Louis | |

dc.date.accessioned | 2018-06-29T12:27:36Z | |

dc.date.available | 2018-06-29T12:27:36Z | |

dc.date.created | 2018-06-29T12:08:48Z | |

dc.date.issued | 2018 | |

dc.identifier.citation | Ananchuen, N. and Ruangthampisan, S. and Ananchuen, W. and Caccetta, L. 2018. On minimum cutsets in independent domination vertex-critical graphs. The Australasian Journal of Combinatorics. 71 (3): pp. 369-380. | |

dc.identifier.uri | http://hdl.handle.net/20.500.11937/68903 | |

dc.description.abstract |
© 2018, University of Queensland. All rights reserved. Let ? i (G) denote the independent domination number of G. A graph G is said to be k-? i -vertex-critical if ? i (G) = k and for each x ? V (G), ? i (G - x) < k. In this paper, we show that for any k-? i -vertex-critical graph H of order n with k = 3, there exists an n-connected k-? i -vertex-critical graph G H containing H as an induced subgraph. Consequently, there are infinitely many non-isomorphic connected k-? i -vertex-critical graphs. We also establish a number of properties of connected 3-? i -vertex-critical graphs. In particular, we derive an upper bound on ?(G-S), the number of components of G-S when G is a connected 3-? i -vertex-critical graph and S is a minimum cutset of G with |S| = 3. | |

dc.publisher | Centre for Discrete Mathematics & Computing | |

dc.title | On minimum cutsets in independent domination vertex-critical graphs | |

dc.type | Journal Article | |

dcterms.source.volume | 71 | |

dcterms.source.number | 3 | |

dcterms.source.startPage | 369 | |

dcterms.source.endPage | 380 | |

dcterms.source.issn | 1034-4942 | |

dcterms.source.title | The Australasian Journal of Combinatorics | |

curtin.department | School of Electrical Engineering, Computing and Mathematical Science (EECMS) | |

curtin.accessStatus | Fulltext not available |

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