## Abstract

For an arbitrary subset P of the reals, we define a function f. V → P to be a P-dominating function of a graph G = (V, E) if the sum of its function values over any closed neighbourhood is at least 1. That is, for every v ε V, f(N (v) U (v)) ≥ 1. The P-domination number of a graph G is defined to be the infimum of f(V) taken over all Pdominating functions f. When P = (0, 1) we obtain the standard domination number. When P = [0, 1], (-1, 0, 1) or (-1, 1) we obtain the fractional, minus or signed domination numbers, respectively. [n this chapter, we survey some recent results concerning dominating functions in which negative weights are allowed.

Original language | English |
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Title of host publication | Domination in Graphs |

Subtitle of host publication | Advanced Topics |

Publisher | CRC Press |

Pages | 31-60 |

Number of pages | 30 |

ISBN (Electronic) | 0824700341, 9781351454643 |

ISBN (Print) | 9780824700348 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics