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

48173

(5,5) cage

Sancuan Zhang

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

Acyclic | No | Index | 5 |

Algebraic Connectivity | 2.764 | Laplacian Largest Eigenvalue | 8.236 |

Average Degree | 5 | Longest Induced Cycle | 14 |

Bipartite | No | Longest Induced Path | 16 |

Chromatic Index | Computation time out | Matching Number | 15 |

Chromatic Number | 4 | Maximum Degree | 5 |

Circumference | 30 | Minimum Degree | 5 |

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

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 75 |

Density | 0.172 | Number of Triangles | 0 |

Diameter | 3 | Number of Vertices | 30 |

Edge Connectivity | 5 | Planar | Computation time out |

Eulerian | No | Radius | 3 |

Genus | Computation time out | Regular | Yes |

Girth | 5 | Second Largest Eigenvalue | 2.236 |

Hamiltonian | Yes | Smallest Eigenvalue | -3.236 |

Independence Number | 10 | Vertex Connectivity | 5 |

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

Posted by Sancuan Zhang at Jan 1, 2022 12:30 PM.

A 5-regular graph with girth 5 has at least 30 vertices; any graph attaining the minimum is called a (5,5) cage.

The graph has 30 automorphisms.

See the paper Exoo, G. , & Jajcay, R. . (2011). Dynamic cage survey. The Electronic Journal of Combinatorics electronic only. Link:https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS16/pdf

The graph has 30 automorphisms.

See the paper Exoo, G. , & Jajcay, R. . (2011). Dynamic cage survey. The Electronic Journal of Combinatorics electronic only. Link:https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS16/pdf

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