## A characterization of 3-i-critical graphs of connectivity two

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

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

dc.contributor.author | Caccetta, Louis | |

dc.date.accessioned | 2017-12-10T12:40:48Z | |

dc.date.available | 2017-12-10T12:40:48Z | |

dc.date.created | 2017-12-10T12:20:16Z | |

dc.date.issued | 2017 | |

dc.identifier.citation | Ananchuen, N. and Ananchuen, W. and Caccetta, L. 2017. A characterization of 3-i-critical graphs of connectivity two. Quaestiones Mathematicae. 40 (7): pp. 937-965. | |

dc.identifier.uri | http://hdl.handle.net/20.500.11937/59557 | |

dc.identifier.doi | 10.2989/16073606.2017.1336653 | |

dc.description.abstract |
A subset S of V (G) is an independent dominating set of G if S is independent and each vertex of G is either in S or adjacent to some vertex of S. Let i(G) denote the minimum cardinality of an independent dominating set of G. A graph G is k-i-critical if i(G) = k, but i(G + uv) < k for any pair of non-adjacent vertices u and v of G. The problem that arises is that of characterizing k-i critical graphs. In this paper, we characterize connected 3-i-critical graphs with minimum vertex cutset of size 2. More specifically, we show that if G is a connected 3-i-critical graph with minimum vertex cutset S of size 2 and the number of components of G - S is exactly two, then G is isomorphic to a graph in one of nine classes of connected 3-i-critical graphs. The results in this paper together with results in [1] and [2] provide a complete characterization of connected 3-i-critical graphs with a minimum cutset of size at most 3. | |

dc.title | A characterization of 3-i-critical graphs of connectivity two | |

dc.type | Journal Article | |

dcterms.source.volume | 40 | |

dcterms.source.number | 7 | |

dcterms.source.startPage | 937 | |

dcterms.source.endPage | 965 | |

dcterms.source.issn | 1607-3606 | |

dcterms.source.title | Quaestiones Mathematicae | |

curtin.department | Department of Mathematics and Statistics | |

curtin.accessStatus | Fulltext not available |

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