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

35447

Binomial Both, order 4

Kevin Ryde

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

Acyclic | No | Index | 2.935 |

Algebraic Connectivity | 0.354 | Laplacian Largest Eigenvalue | 6.249 |

Average Degree | 2.75 | Longest Induced Cycle | 8 |

Bipartite | Yes | Longest Induced Path | 7 |

Chromatic Index | 4 | Matching Number | 8 |

Chromatic Number | 2 | Maximum Degree | 4 |

Circumference | 8 | Minimum Degree | 2 |

Claw-Free | No | Minimum Dominating Set | 4 |

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 22 |

Density | 0.183 | Number of Triangles | 0 |

Diameter | 4 | Number of Vertices | 16 |

Edge Connectivity | 2 | Planar | Yes |

Eulerian | No | Radius | 4 |

Genus | 0 | Regular | No |

Girth | 4 | Second Largest Eigenvalue | 2.303 |

Hamiltonian | No | Smallest Eigenvalue | -2.935 |

Independence Number | 8 | Vertex Connectivity | 2 |

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

Posted by Kevin Ryde at Jun 14, 2020 10:57 AM.

A "binomial both" order k is a binomial tree order k both up and down. Each vertex is an integer 0 to 2^k-1 written with k many bits. Each v>0 has an edge to v with its lowest 1-bit cleared (binomial tree parent). Each v<2^k-1 has an edge to v with its lowest 0-bit set to 1, which is a bit-flipped binomial tree. The result is a graded lattice.

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