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

33625

Dexter N=6

Kevin Ryde

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

Acyclic | No | Index | 5.718 |

Algebraic Connectivity | 0.491 | Laplacian Largest Eigenvalue | 12.514 |

Average Degree | 5 | Longest Induced Cycle | Computation time out |

Bipartite | No | Longest Induced Path | Computation time out |

Chromatic Index | 9 | Matching Number | 66 |

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

Circumference | Computation time out | Minimum Degree | 3 |

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

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 330 |

Density | 0.038 | Number of Triangles | 0 |

Diameter | 9 | Number of Vertices | 132 |

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

Eulerian | No | Radius | 5 |

Genus | Computation time out | Regular | No |

Girth | 4 | Second Largest Eigenvalue | 4.505 |

Hamiltonian | Computation time out | Smallest Eigenvalue | -5.611 |

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 Feb 23, 2019 2:28 AM.

Each graph vertex is a balanced binary string (Dyck word) of N pairs. There are Catalan(6)=132 such. Each graph edge is the "dexter" transform by Chapoton which shifts a block of 1s to raise their adjacent balanced substring. This is some multiple binary tree "rotates". Chapoton notes right-arm rotates are a subset of dexter.

F. Chapoton, "Some Properties of a New Partial Order on Dyck Paths", September 2018.

https://hal.archives-ouvertes.fr/hal-01878792

https://arxiv.org/abs/1809.10981

F. Chapoton, "Some Properties of a New Partial Order on Dyck Paths", September 2018.

https://hal.archives-ouvertes.fr/hal-01878792

https://arxiv.org/abs/1809.10981

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