# uniformly locally finite graph

A is a locally finite graph^{} (http://planetmath.org/LocallyFiniteGraph) $(V,E)$ such that there exists an $M\in \mathbb{N}$ such that for every $x\in V$ we have that the degree of $x$, also denoted $\rho (x)$, is at most $M$. In other words there exists an $M\in \mathbb{N}$ such that for every $x\in V,\rho (x)\le M$.

Note that the examples provided in locally finite graph (http://planetmath.org/LocallyFiniteGraph) are also examples of a uniformly locally finite graph since both graphs are regular (http://planetmath.org/RegularGraph) and have finite degree (http://planetmath.org/Degree7) at each vertex.

Title | uniformly locally finite graph |
---|---|

Canonical name | UniformlyLocallyFiniteGraph |

Date of creation | 2013-03-22 16:00:54 |

Last modified on | 2013-03-22 16:00:54 |

Owner | sjm1979 (13837) |

Last modified by | sjm1979 (13837) |

Numerical id | 6 |

Author | sjm1979 (13837) |

Entry type | Definition |

Classification | msc 05C99 |

Related topic | LocallyFiniteGraph |