A quintic graph is a graph which is 5-regular. The only quintic graph on nodes is the complete graph . Quintic graphs exist only on even numbers of nodes, and the numbers of connected quintic graphs on , 4, 6, ... nodes are 0, 0, 1, 3, 60, 7848, 3459383, 2585136675, ... (OEIS A006821).

The following table gives some named quintic graphs.

graph | nodes | symmetric |

complete graph | 6 | yes |

(5,3)-cone graph | 8 | no |

complete bipartite graph | 10 | yes |

icosahedral graph | 12 | yes |

6-crown graph | 12 | yes |

5-Andrásfai graph | 14 | yes |

Clebsch graph | 16 | yes |

graph Cartesian product | 18 | no |

(11,5,2)-Levi graph | 22 | yes |

snub cubical graph | 24 | no |

Foster cage | 30 | no |

Meringer graph | 30 | no |

Robertson-Wegner graph | 30 | no |

Wong graph | 30 | no |

Wells graph | 32 | yes |

hypercube graph | 32 | yes |

Sylvester graph | 36 | yes |

(5,6)-cage graph | 42 | yes |

snub dodecahedral graph | 60 | no |

5-odd graph | 126 | yes |

(5,8)-cage graph | 170 | ? |

6-permutation star graph | 720 | yes |