A nonplanar graph is a graph that is not planar. The numbers of simple nonplanar graphs on , 2, ... nodes are 0, 0, 0, 0, 1, 14, 222, 5380, 194815, ... (OEIS A145269), with the corresponding number of simple nonplanar connected graphs being 0, 0, 0, 0, 1, 13, 207, 5143, 189195, ... (OEIS A145270).

The following table summarizes some named nonplanar graphs.

graph | |

pentatope graph | 5 |

utility graph | 6 |

16-cell graph | 8 |

Petersen graph | 10 |

Grötzsch Graph | 11 |

Chvatal graph | 12 |

Franklin graph | 12 |

uniquely three-colorable graph | 12 |

Heawood graph | 14 |

Clebsch graph | 16 |

Hoffman graph | 16 |

Möbius-Kantor graph | 16 |

tesseract graph | 16 |

first Blanuša snark | 18 |

second Blanuša snark | 18 |

Pappus graph | 18 |

Robertson graph | 19 |

Desargues graph | 20 |

flower snark | 20 |

Folkman graph | 20 |

McGee graph | 24 |

24-cell graph | 24 |

25-Grünbaum graph | 25 |

Doyle graph | 27 |

Coxeter graph | 28 |

double star snark | 30 |

Foster cage | 30 |

Tutte 8-cage | 30 |

Meringer graph | 30 |

Robertson-Wegner graph | 30 |

Wong graph | 30 |

Dyck graph | 32 |

Wells graph | 32 |

Thomassen graph | 34 |

Sylvester graph | 36 |

Hoffman-Singleton graph | 50 |

Szekeres snark | 50 |

Gray graph | 54 |

Gewirtz graph | 56 |

Balaban 10-cage | 70 |

Meredith graph | 70 |

Foster graph | 90 |

Biggs-Smith graph | 102 |

Balaban 11-cage | 112 |

600-cell graph | 120 |

Tutte 12-cage | 126 |

McLaughlin graph | 275 |

120-cell graph | 600 |