## Adjacency matrix[Too large to display] |
## Adjacency list[Too large to display] |

34165

Keller N=3

Kevin Ryde

Invariant | Value | Invariant | Value |
---|---|---|---|

Acyclic | No | Index | 34 |

Algebraic Connectivity | 28 | Laplacian Largest Eigenvalue | 44 |

Average Degree | 34 | Longest Induced Cycle | 6 |

Bipartite | No | Longest Induced Path | 6 |

Chromatic Index | Computation time out | Matching Number | 32 |

Chromatic Number | Computation time out | Maximum Degree | 34 |

Circumference | 64 | Minimum Degree | 34 |

Claw-Free | No | Minimum Dominating Set | 4 |

Clique Number | 5 | Number of Components | 1 |

Connected | Yes | Number of Edges | 1088 |

Density | 0.54 | Number of Triangles | 5568 |

Diameter | 2 | Number of Vertices | 64 |

Edge Connectivity | 34 | Planar | Computation time out |

Eulerian | Yes | Radius | 2 |

Genus | Computation time out | Regular | Yes |

Girth | 3 | Second Largest Eigenvalue | 6 |

Hamiltonian | Yes | Smallest Eigenvalue | -10 |

Independence Number | 8 | Vertex Connectivity | Computation time out |

A table row rendered like this
indicates that the graph is marked as being *interesting* for that invariant.

Posted by Kevin Ryde at Nov 30, 2019 7:47 AM.

The Keller graph N has 4^N vertices numbered 0 to 4^N-1. These vertices are treated as base-4 integers. Edges are between vertices differing in 2 or more digit positions, at least one of which is difference = 2 mod 4.

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