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

44107

Hanoi Exchanging Discs, 4 Discs

Kevin Ryde

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

Acyclic | No | Index | 3.214 |

Algebraic Connectivity | 0.035 | Laplacian Largest Eigenvalue | 6.472 |

Average Degree | 2.963 | Longest Induced Cycle | 42 |

Bipartite | No | Longest Induced Path | 45 |

Chromatic Index | Computation time out | Matching Number | 40 |

Chromatic Number | 3 | Maximum Degree | 4 |

Circumference | 81 | Minimum Degree | 2 |

Claw-Free | No | Minimum Dominating Set | 24 |

Clique Number | 3 | Number of Components | 1 |

Connected | Yes | Number of Edges | 120 |

Density | 0.037 | Number of Triangles | 27 |

Diameter | 13 | Number of Vertices | 81 |

Edge Connectivity | Computation time out | Planar | Computation time out |

Eulerian | No | Radius | 9 |

Genus | Computation time out | Regular | No |

Girth | 3 | Second Largest Eigenvalue | 3.13 |

Hamiltonian | Yes | Smallest Eigenvalue | -2.647 |

Independence Number | Computation time out | Vertex Connectivity | Computation time out |

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, 2021 8:45 AM.

Scorer, Grundy and Smith define a variation of the towers of Hanoi puzzle where the smallest disk moves freely and two disks can exchange positions when they differ in size by 1, are on different pegs, and each is top-most on its peg. Each vertex here is a configuration of discs on spindles. Each edge is a step (move or exchange) between configurations.

R. S. Scorer, P. M. Grundy and C. A. B. Smith, "Some Binary Games", The Mathematical Gazette, July 1944, volume 28, number 280, pages 96-103, http://www.jstor.org/stable/3606393. See section 4(iii).

Paul K. Stockmeyer et al, "Exchanging Disks in the Tower of Hanoi", International Journal of Computer Mathematics, volume 59, number 1-2, pages 37-47, 1995, http://www.cs.wm.edu/~pkstoc/gov.pdf, calculating the graph diameter (OEIS A341579).

R. S. Scorer, P. M. Grundy and C. A. B. Smith, "Some Binary Games", The Mathematical Gazette, July 1944, volume 28, number 280, pages 96-103, http://www.jstor.org/stable/3606393. See section 4(iii).

Paul K. Stockmeyer et al, "Exchanging Disks in the Tower of Hanoi", International Journal of Computer Mathematics, volume 59, number 1-2, pages 37-47, 1995, http://www.cs.wm.edu/~pkstoc/gov.pdf, calculating the graph diameter (OEIS A341579).

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