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

27042

twin alternate area tree level 4

Kevin Ryde

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

Acyclic | Yes | Index | 2.146 |

Algebraic Connectivity | 0.05 | Laplacian Largest Eigenvalue | 4.71 |

Average Degree | 1.875 | Longest Induced Cycle | undefined |

Bipartite | Yes | Longest Induced Path | 13 |

Chromatic Index | 3 | Matching Number | 8 |

Chromatic Number | 2 | Maximum Degree | 3 |

Circumference | undefined | Minimum Degree | 1 |

Claw-Free | No | Minimum Dominating Set | 6 |

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 15 |

Density | 0.125 | Number of Triangles | 0 |

Diameter | 13 | Number of Vertices | 16 |

Edge Connectivity | 1 | Planar | Yes |

Eulerian | No | Radius | 7 |

Genus | 0 | Regular | No |

Girth | undefined | Second Largest Eigenvalue | 1.835 |

Hamiltonian | No | Smallest Eigenvalue | -2.146 |

Independence Number | 8 | 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 26, 2017 5:23 AM.

Form a twin alternate curve by arranging four alternate paperfolding curves level 4 in a cycle (or two level 5 back-to-back). Graph vertices are the 2^4 unit squares inside. Edges connect squares beside consecutive curve segments, or equivalently if the curve is drawn with corners chamfered off leaving little gaps at corners then squares are connected through those gaps.

This is the first twin alternate area tree level which is not just a path. Diameter 13 is OEIS A053599.

This is the first twin alternate area tree level which is not just a path. Diameter 13 is OEIS A053599.

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