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

33636

Transpose Covers N=4

Kevin Ryde

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

Acyclic | No | Index | 5.008 |

Algebraic Connectivity | 1.087 | Laplacian Largest Eigenvalue | 10.25 |

Average Degree | 4.833 | Longest Induced Cycle | 12 |

Bipartite | Yes | Longest Induced Path | 12 |

Chromatic Index | 6 | Matching Number | 12 |

Chromatic Number | 2 | Maximum Degree | 6 |

Circumference | 24 | Minimum Degree | 3 |

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

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 58 |

Density | 0.21 | Number of Triangles | 0 |

Diameter | 6 | Number of Vertices | 24 |

Edge Connectivity | 3 | Planar | No |

Eulerian | No | Radius | 3 |

Genus | 4 | Regular | No |

Girth | 4 | Second Largest Eigenvalue | 3.171 |

Hamiltonian | Yes | Smallest Eigenvalue | -5.008 |

Independence Number | 12 | Vertex Connectivity | 3 |

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

Posted by Kevin Ryde at Mar 17, 2019 1:08 AM.

Each vertex is a permutation of integers 1..4, so 4!=24 vertices. Each edge is by swapping two elements to reach a lexicographically bigger permutation, and where not already reached by some longer chain of transpositions (so Hasse diagram, equivalent to number of "inversions" increase by 1). Number of edges 58 is OEIS A002538.

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