# Cubical graph

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Cubical graph | |
---|---|

Elements | |

Vertices | 8 |

Edges | 12 |

Properties | |

Girth | 4 |

Radius | 3 |

Diameter | 3 |

Chromatic number | 2 |

Chromatic index | 3 |

Symmetry | |

Vertex transitive | Yes |

Edge transitive | Yes |

Flag transitive | Yes |

Distance transitive | Yes |

The **cubical graph** is the skeleton of the cube. It is distance-transitive cubic graph.

## Related polytopes[edit | edit source]

The cubical graph can be embedded on the sphere as the cube. It can also be embedded on a torus as the regular skew polyhedron the Petrial cube.

## Related graphs[edit | edit source]

The cubical graph is a graph in the infinite family of hypercube graphs. In that family it is Q 3 . The cubical graph is also the generalized Petersen graph GP (4, 1). It is one of seven symmetric generalized Petersen graphs.

### Duals[edit | edit source]

With respects to its spherical embedding, the dual graph of the cubical graph is the octahedral graph, K 2,2,2 . With respects to its toroidal embedding its dual is a double cover of K 4 .

## External links[edit | edit source]

- Wikipedia contributors. "Cubical graph".
- Weisstein, Eric W. "Cubical Graph" at MathWorld.