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

32276

Lex-Max Vpar Forests Differences N=5

Kevin Ryde

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

Acyclic | No | Index | 4.546 |

Algebraic Connectivity | 0.461 | Laplacian Largest Eigenvalue | 8.556 |

Average Degree | 3.6 | Longest Induced Cycle | 6 |

Bipartite | No | Longest Induced Path | 10 |

Chromatic Index | 7 | Matching Number | 10 |

Chromatic Number | 4 | Maximum Degree | 7 |

Circumference | 15 | Minimum Degree | 1 |

Claw-Free | No | Minimum Dominating Set | 5 |

Clique Number | 4 | Number of Components | 1 |

Connected | Yes | Number of Edges | 36 |

Density | 0.189 | Number of Triangles | 14 |

Diameter | 4 | Number of Vertices | 20 |

Edge Connectivity | 1 | Planar | No |

Eulerian | No | Radius | 3 |

Genus | 1 | Regular | No |

Girth | 3 | Second Largest Eigenvalue | 3.072 |

Hamiltonian | No | Smallest Eigenvalue | -2.837 |

Independence Number | 9 | Vertex Connectivity | 1 |

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

Posted by Kevin Ryde at Dec 16, 2018 2:45 AM.

Each graph vertex is an unlabelled rooted forest of n=5 vertices (20 of them) represented by a labelled rooted forest in vertex parent array form (vpar). Labelling is chosen to give each the lexicographically greatest vpar array. Graph edges are between arrays differing in one position.

The 2 degree-1 vertices are vpar=[0,0,0,0,0] singletons and vpar=[5,5,4,2,0] path-5. The latter has the degree-6 neighbour.

The 2 degree-1 vertices are vpar=[0,0,0,0,0] singletons and vpar=[5,5,4,2,0] path-5. The latter has the degree-6 neighbour.

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