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

33638

Transpose Covers N=5

Kevin Ryde

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

Acyclic | No | Index | 7.714 |

Algebraic Connectivity | 0.852 | Laplacian Largest Eigenvalue | 15.806 |

Average Degree | 7.4 | Longest Induced Cycle | Computation time out |

Bipartite | Yes | Longest Induced Path | Computation time out |

Chromatic Index | Computation time out | Matching Number | 60 |

Chromatic Number | Computation time out | Maximum Degree | 9 |

Circumference | Computation time out | Minimum Degree | 4 |

Claw-Free | No | Minimum Dominating Set | Computation time out |

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 444 |

Density | 0.062 | Number of Triangles | 0 |

Diameter | 10 | Number of Vertices | 120 |

Edge Connectivity | Computation time out | Planar | Computation time out |

Eulerian | No | Radius | 5 |

Genus | Computation time out | Regular | No |

Girth | 4 | Second Largest Eigenvalue | 6.028 |

Hamiltonian | Computation time out | Smallest Eigenvalue | -7.714 |

Independence Number | Computation time out | 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 Mar 17, 2019 1:09 AM.

Each vertex is a permutation of integers 1..5, so 5!=120 vertices. Each edge is by swapping 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 444 is OEIS A002538.

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