The -path complement graph is the graph complement of the path graph . The first few are illustrated above.

Since is self-complementary, is isomorphic to . Special cases are summarized in the table below.

graph name | |

1 | singleton graph |

2 | empty graph |

3 | |

4 | path graph |

5 | house graph |

6 | tetragonal antiwedge graph |

has vertex count and edge count

where is the binomial coefficient.

is connected for and Hamiltonian for .