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

33617

Binary Tree Rotate Right-Arm N=5

Kevin Ryde

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

Acyclic | No | Index | 3.255 |

Algebraic Connectivity | 0.075 | Laplacian Largest Eigenvalue | 7.055 |

Average Degree | 2.286 | Longest Induced Cycle | 4 |

Bipartite | Yes | Longest Induced Path | 12 |

Chromatic Index | 4 | Matching Number | 18 |

Chromatic Number | 2 | Maximum Degree | 4 |

Circumference | 16 | Minimum Degree | 1 |

Claw-Free | No | Minimum Dominating Set | 15 |

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 48 |

Density | 0.056 | Number of Triangles | 0 |

Diameter | 8 | Number of Vertices | 42 |

Edge Connectivity | 1 | Planar | Yes |

Eulerian | No | Radius | 4 |

Genus | 0 | Regular | No |

Girth | 4 | Second Largest Eigenvalue | 2.611 |

Hamiltonian | No | Smallest Eigenvalue | -3.255 |

Independence Number | 24 | 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 23, 2019 2:13 AM.

Each graph vertex represents a binary tree of N=5 vertices. There are Catalan(4)=14 such. Each graph edge is a "rotate" of an edge on the right arm of the tree. (Or equivalently mirror image and rotate from/to the left arm.)

J. M. Pallo, "Right-Arm Rotation Distance Between Binary Trees", Information Processing Letters, volume 87, number 4, 2003, pages 173-177.

Rik Sengupta and Warut Suksompong, "The Comb Poset and the Parsewords Function". The present graph is figure 11.

http://www-users.math.umn.edu/~reiner/REU/SenguptaSuksompong2010.pdf

J. M. Pallo, "Right-Arm Rotation Distance Between Binary Trees", Information Processing Letters, volume 87, number 4, 2003, pages 173-177.

Rik Sengupta and Warut Suksompong, "The Comb Poset and the Parsewords Function". The present graph is figure 11.

http://www-users.math.umn.edu/~reiner/REU/SenguptaSuksompong2010.pdf

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