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

49225

n/a

Gunnar Brinkmann

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

Acyclic | No | Index | 4 |

Algebraic Connectivity | 0.619 | Laplacian Largest Eigenvalue | 6.798 |

Average Degree | 4 | Longest Induced Cycle | 14 |

Bipartite | No | Longest Induced Path | 13 |

Chromatic Index | 5 | Matching Number | 11 |

Chromatic Number | 4 | Maximum Degree | 4 |

Circumference | 22 | Minimum Degree | 4 |

Claw-Free | No | Minimum Dominating Set | 5 |

Clique Number | 3 | Number of Components | 1 |

Connected | Yes | Number of Edges | 44 |

Density | 0.19 | Number of Triangles | 15 |

Diameter | 4 | Number of Vertices | 22 |

Edge Connectivity | 4 | Planar | No |

Eulerian | Yes | Radius | 4 |

Genus | 1 | Regular | Yes |

Girth | 3 | Second Largest Eigenvalue | 3.381 |

Hamiltonian | Yes | Smallest Eigenvalue | -2.798 |

Independence Number | 8 | Vertex Connectivity | 4 |

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

Posted by Gunnar Brinkmann at Jun 3, 2022 9:53 AM.

A smallest (uniqueness not yest tested -- 03/06/2022) 4-regular 4-vertex-connected graph of even order that is class 2 -- that is: has chromatic index 5

Posted by Gunnar Brinkmann at Jun 7, 2022 1:05 PM.

It is not unique. Graph 49231 has the same properties. This graph as well as 49231 can be obtained from 48188 by replacing a vertex in the 3-cut by a K_5 with two independent edges broken open.

You need to be logged in to be able to add comments.