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

33551

Tamari Lattice N=6

Kevin Ryde

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

Acyclic | No | Index | 5 |

Algebraic Connectivity | 0.617 | Laplacian Largest Eigenvalue | 8.913 |

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

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

Chromatic Index | Computation time out | Matching Number | 66 |

Chromatic Number | 3 | Maximum Degree | 5 |

Circumference | Computation time out | Minimum Degree | 5 |

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 | 7 | Number of Vertices | 132 |

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

Eulerian | No | Radius | 5 |

Genus | Computation time out | Regular | Yes |

Girth | 4 | Second Largest Eigenvalue | 4.383 |

Hamiltonian | Computation time out | Smallest Eigenvalue | -3.913 |

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 9, 2019 6:50 AM.

The Tamari lattice by Dov Tamari has graph vertices as parenthesizations of N+1 objects into pairs, and graph edges between those differing by one application of the associative law. Hence also called an associahedron. Here N=6 and there are Catalan(6) = 132 vertices.

Equivalently, binary tree rotation graph. Each vertex represents a binary tree of N=6 vertices and graph edges are between trees differing by one "rotation". Each tree edge can rotate, so degree N-1 regular (330 edges, OEIS A002054).

Equivalently, binary tree rotation graph. Each vertex represents a binary tree of N=6 vertices and graph edges are between trees differing by one "rotation". Each tree edge can rotate, so degree N-1 regular (330 edges, OEIS A002054).

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