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

33736

21,3 Symmetric Configuration Incidence Graph

Kevin Ryde

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

Acyclic | No | Index | 3 |

Algebraic Connectivity | 0.706 | Laplacian Largest Eigenvalue | 6 |

Average Degree | 3 | Longest Induced Cycle | 30 |

Bipartite | Yes | Longest Induced Path | 28 |

Chromatic Index | 3 | Matching Number | 21 |

Chromatic Number | 2 | Maximum Degree | 3 |

Circumference | 42 | Minimum Degree | 3 |

Claw-Free | No | Minimum Dominating Set | 12 |

Clique Number | 2 | Number of Components | 1 |

Connected | Yes | Number of Edges | 63 |

Density | 0.073 | Number of Triangles | 0 |

Diameter | 6 | Number of Vertices | 42 |

Edge Connectivity | 3 | Planar | No |

Eulerian | No | Radius | 5 |

Genus | 5 | Regular | Yes |

Girth | 8 | Second Largest Eigenvalue | 2.294 |

Hamiltonian | Yes | Smallest Eigenvalue | -3 |

Independence Number | 21 | 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 Jul 3, 2019 10:40 AM.

Betten, Brinkmann and Pisanskic give this as an example 21,3 symmetric configuration incidence graph (their figure 2). It is triangle-free, point transitive, block intransitive, and they construct by subdivision and addition to the Heawood graph (which is the sole 7,3 incidence graph).

Anton Betten, Gunnar Brinkmann, Tomaž Pisanskic, "Counting Symmetric Configurations v₃", Discrete Applied Mathematics, volume 99, 2000, pages 331–338.

Anton Betten, Gunnar Brinkmann, Tomaž Pisanskic, "Counting Symmetric Configurations v₃", Discrete Applied Mathematics, volume 99, 2000, pages 331–338.

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