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

33640

Fibonacci Lattice to N=6

Kevin Ryde

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

Acyclic | No | Index | 4.253 |

Algebraic Connectivity | 0.267 | Laplacian Largest Eigenvalue | 9.431 |

Average Degree | 3.515 | Longest Induced Cycle | 14 |

Bipartite | Yes | Longest Induced Path | 18 |

Chromatic Index | 7 | Matching Number | 12 |

Chromatic Number | 2 | Maximum Degree | 7 |

Circumference | 24 | Minimum Degree | 1 |

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

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 58 |

Density | 0.11 | Number of Triangles | 0 |

Diameter | 6 | Number of Vertices | 33 |

Edge Connectivity | 1 | Planar | No |

Eulerian | No | Radius | 3 |

Genus | 2 | Regular | No |

Girth | 4 | Second Largest Eigenvalue | 3.182 |

Hamiltonian | No | Smallest Eigenvalue | -4.253 |

Independence Number | 21 | 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 Mar 17, 2019 1:19 AM.

Per Stanley, each vertex is a list of 1s and 2s with sum <= 6. There are Fibonacci(N+3)-1 = 33 such. Edges are by increasing one term 1->2 or append a new 1 to reach another list. The number of vertices with sum=k is Fibonacci(k+1).

Richard P. Stanley, "The Fibonacci Lattice", Fibonacci Quarterly, volume 13, number 3, October 1975, pages 215-232. The present graph is F1 page 227.

https://fq.math.ca/13-3.html

https://fq.math.ca/Scanned/13-3/stanley.pdf

Richard P. Stanley, "The Fibonacci Lattice", Fibonacci Quarterly, volume 13, number 3, October 1975, pages 215-232. The present graph is F1 page 227.

https://fq.math.ca/13-3.html

https://fq.math.ca/Scanned/13-3/stanley.pdf

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