# example of planar graph with two different embeddings into the plane

Consider the following two plane graphs^{}:

The plane graph ${G}_{1}$.

The plane graph ${G}_{2}$.

Clearly the multigraph^{} associated with each of these plane graphs is the same, but the two plane graphs are not isomorphic^{}: in ${G}_{1}$, every face is adjacent to the central region, while in ${G}_{2}$ there is no face adjacent to every other. This also implies that their dual graphs are non-isomorphic.

Title | example of planar graph with two different embeddings into the plane |
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Canonical name | ExampleOfPlanarGraphWithTwoDifferentEmbeddingsIntoThePlane |

Date of creation | 2013-03-22 14:17:03 |

Last modified on | 2013-03-22 14:17:03 |

Owner | archibal (4430) |

Last modified by | archibal (4430) |

Numerical id | 5 |

Author | archibal (4430) |

Entry type | Example |

Classification | msc 05C10 |