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

33559

Kreweras Lattice N=5

Kevin Ryde

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

Acyclic | No | Index | 6.031 |

Algebraic Connectivity | 1.962 | Laplacian Largest Eigenvalue | 13.027 |

Average Degree | 5.714 | Longest Induced Cycle | 20 |

Bipartite | Yes | Longest Induced Path | 20 |

Chromatic Index | 10 | Matching Number | 20 |

Chromatic Number | 2 | Maximum Degree | 10 |

Circumference | Computation time out | Minimum Degree | 4 |

Claw-Free | No | Minimum Dominating Set | 7 |

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 120 |

Density | 0.139 | Number of Triangles | 0 |

Diameter | 4 | Number of Vertices | 42 |

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

Eulerian | No | Radius | 4 |

Genus | Computation time out | Regular | No |

Girth | 4 | Second Largest Eigenvalue | 3.295 |

Hamiltonian | Computation time out | Smallest Eigenvalue | -6.031 |

Independence Number | 22 | 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 8:18 AM.

Each graph vertex is one of the Catalan(5)=42 partitions of the integers 1..5 into non-crossing sets. Such a partition corresponds to an ordered rooted forest (its sets of siblings), and hence to a binary tree too.

Each graph edge is where one set in the partition splits into two to reach another partition (and hence is "graded" by number of sets in the partition).

G. Kreweras, "Sur les Partitions Non-Croisées d'Un Cycle", Discrete

Mathematics, volume 1, number 4, 1971, pages 333-350.

Each graph edge is where one set in the partition splits into two to reach another partition (and hence is "graded" by number of sets in the partition).

G. Kreweras, "Sur les Partitions Non-Croisées d'Un Cycle", Discrete

Mathematics, volume 1, number 4, 1971, pages 333-350.

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