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

34214

Cubic Integral G10

Kevin Ryde

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

Acyclic | No | Index | 3 |

Algebraic Connectivity | 1 | Laplacian Largest Eigenvalue | 6 |

Average Degree | 3 | Longest Induced Cycle | 12 |

Bipartite | Yes | Longest Induced Path | 13 |

Chromatic Index | 3 | Matching Number | 10 |

Chromatic Number | 2 | Maximum Degree | 3 |

Circumference | 20 | Minimum Degree | 3 |

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

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 30 |

Density | 0.158 | Number of Triangles | 0 |

Diameter | 5 | Number of Vertices | 20 |

Edge Connectivity | 3 | Planar | No |

Eulerian | No | Radius | 4 |

Genus | 2 | Regular | Yes |

Girth | 6 | Second Largest Eigenvalue | 2 |

Hamiltonian | Yes | Smallest Eigenvalue | -3 |

Independence Number | 10 | Vertex Connectivity | 3 |

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

Posted by Kevin Ryde at Dec 31, 2019 12:36 AM.

This graph is cubic and integral (regular of degree 3 and all roots of the characteristic polynomial of its adjacency matrix are integers). Bussemaker and Cvetković show there are 13 connected cubic integral graphs. This graph is G10 in their numbering of those graphs, and is cospectral with their G9 which is the Desargues graph.

F. C. Bussemaker and D. M. Cvetković, "There Are Exactly 13 Connected, Cubic, Integral Graphs", Publikacije Elektrotehničkog fakulteta, Serija Matematika i fizika, No. 544/576, 1976, pages 43-48, http://www.jstor.org/stable/43667961. Figure 1 graph G10.

F. C. Bussemaker and D. M. Cvetković, "There Are Exactly 13 Connected, Cubic, Integral Graphs", Publikacije Elektrotehničkog fakulteta, Serija Matematika i fizika, No. 544/576, 1976, pages 43-48, http://www.jstor.org/stable/43667961. Figure 1 graph G10.

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