## Fundamentals of Domination in Graphs"Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination." |

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### Contents

Introduction | 15 |

Bounds on the Domination Number | 41 |

Domination Independence and Irredundance | 67 |

Efficiency Redundancy and Their Duals | 107 |

Changing and Unchanging Domination | 135 |

Conditions on the Dominating Set | 155 |

Varieties of Domination | 183 |

Multiproperty and Multiset Parameters | 219 |

Sums and Products of Parameters | 237 |

Dominating Functions | 255 |

Frameworks for Domination | 281 |

Domination Complexity and Algorithms | 299 |

### Common terms and phrases

adjacent algorithm bipartite graphs C. M. Mynhardt Chapter chordal graphs classes of graphs closed neighborhood complete graph Comput connected dominating set connected graph contradiction Corollary cycle defined deg(v denote diam(G Discrete Math domatic dominating function domination in graphs domination number dt(G E. J. Cockayne edge domination endvertex endvertices equals the minimum example exists a vertex graph G Graph Theory grid graphs Hence independence number independent dominating set induced subgraph interval graphs IR(G irredundance number irredundant set isolated vertices least one vertex Let G M. A. Henning maximal independent set minimal dominating set minimum cardinality minimum number NP-complete number of G number of vertices P-set partition path permutation graphs polynomial positive integer private neighbor problem Proof S. T. Hedetniemi sequence series-parallel graphs set in G set of G set of vertices subset T. W. Haynes Theorem total dominating set total domination number tree upper bound vertex set