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

33543

Binomial Tree Order 6

Kevin Ryde

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

Acyclic | Yes | Index | 3.163 |

Algebraic Connectivity | 0.028 | Laplacian Largest Eigenvalue | 8.194 |

Average Degree | 1.969 | Longest Induced Cycle | undefined |

Bipartite | Yes | Longest Induced Path | 11 |

Chromatic Index | 6 | Matching Number | 32 |

Chromatic Number | Computation time out | Maximum Degree | 6 |

Circumference | undefined | Minimum Degree | 1 |

Claw-Free | No | Minimum Dominating Set | 32 |

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 63 |

Density | 0.031 | Number of Triangles | 0 |

Diameter | 11 | Number of Vertices | 64 |

Edge Connectivity | 1 | Planar | Yes |

Eulerian | No | Radius | 6 |

Genus | 0 | Regular | No |

Girth | undefined | Second Largest Eigenvalue | 2.689 |

Hamiltonian | No | Smallest Eigenvalue | -3.163 |

Independence Number | Computation time out | 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 Feb 9, 2019 6:22 AM.

An order N binomial tree has a root vertex and under it N sub-trees which are binomial trees orders 0 to N-1 inclusive. An order 0 tree is a single vertex. The number of vertices at depth d is binomial(N,d).

Equivalently, an order N tree is integers n=0 to n=2^N-1 inclusive with root n=0 and parent of n is n with its least significant 1-bit cleared to 0.

Equivalently, an order N tree is integers n=0 to n=2^N-1 inclusive with root n=0 and parent of n is n with its least significant 1-bit cleared to 0.

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