# realization of a graph

A *realization of a graph* $G$ in a topological space^{} $X$ is an injective map $\rho :G\to X$ such that $G$ with the graph topology is homeomorphic to $\rho (G)$ with the subspace topology. Of particular interest are realizations of $G$ in 3-dimensional Euclidean space^{}, where each of the edges is a line segment^{}, and where no 4 points of $G$ are coplanar^{}.

Title | realization of a graph |
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Canonical name | RealizationOfAGraph |

Date of creation | 2013-03-22 12:31:58 |

Last modified on | 2013-03-22 12:31:58 |

Owner | rmilson (146) |

Last modified by | rmilson (146) |

Numerical id | 7 |

Author | rmilson (146) |

Entry type | Definition |

Classification | msc 05C99 |

Related topic | Subdivision |

Related topic | GraphTopology |