# neighborhood (of a vertex)

For a graph $G$, the set of vertices adjacent to a vertex $x\in G$, the *neighborhood ^{}* of $x$, is denoted by $\mathrm{\Gamma}(x)$. Occasionally one calls $\mathrm{\Gamma}(x)$ the

*open*neighborhood of $x$, and $\mathrm{\Gamma}\cup \{x\}$ the

*closed*neighborhood of $x$.

Adapted with permission of the author from *Modern Graph Theory ^{}* by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.

Title | neighborhood (of a vertex) |
---|---|

Canonical name | NeighborhoodofAVertex |

Date of creation | 2013-03-22 11:58:03 |

Last modified on | 2013-03-22 11:58:03 |

Owner | digitalis (76) |

Last modified by | digitalis (76) |

Numerical id | 10 |

Author | digitalis (76) |

Entry type | Definition |

Classification | msc 05C99 |

Synonym | neighborhood |

Related topic | Graph |