K-Angulation Graphs Data

Simple k-Angulations

Simple *k*-Angulations is the family of simple 2-connected plane graphs such that all faces (including the outer face) have size equal to the *k*. This page contains the exhaustive list of *k*-angulations for *k=3,4,5,6,7,8,9,10* of small orders.

The graphs are in*planar code* **format**. A complete definition can be found in the plantri
manual (Appendix A). For the graphs on this page, the following should be adequate. Each graph is given as a sequence of bytes, starting with a byte containing the number of vertices. Then for each vertex, a list of the neighbours is given, one neighbour per byte in clockwise order, plus a zero byte to end the list. Vertices are numbered starting with 1. A graph with n vertices and e edges thus occupies exactly *1+2e+n* bytes.

**Reference:**

[1] M. Jooyandeh, Recursive Algorithms for Generation of Planar Graphs, PhD Thesis, College of Engineering and Computer Science, Australian National University, 2014.

[2] G. Brinkmann and B.D. McKay, Fast generation of planar graphs,*MATCH Commun. Math. Comput. Chem*, **58(2)** (2007) 323-357.

[3] G. Brinkmann and B.D. McKay, plantri (software).

[4] R. Bowen, S. Fisk, Generation of triangulations of the sphere,*Math. Comput.*, **21** (1967) 250–252.

[5] V. Batagelj, An improved inductive definition of two restricted classes of triangulations of the plane,*Combinatorics and Graph Theory*, **25** (1989) 11–18.

[6] G. Brinkmann, S. Greenberg, C. Greenhill, B.D. McKay, R. Thomas and P. Wollan, Generation of simple quadrangulations of the sphere,*Discrete Mathematics*, **305** (2005) 33-54.

The graphs are in

[1] M. Jooyandeh, Recursive Algorithms for Generation of Planar Graphs, PhD Thesis, College of Engineering and Computer Science, Australian National University, 2014.

[2] G. Brinkmann and B.D. McKay, Fast generation of planar graphs,

[3] G. Brinkmann and B.D. McKay, plantri (software).

[4] R. Bowen, S. Fisk, Generation of triangulations of the sphere,

[5] V. Batagelj, An improved inductive definition of two restricted classes of triangulations of the plane,

[6] G. Brinkmann, S. Greenberg, C. Greenhill, B.D. McKay, R. Thomas and P. Wollan, Generation of simple quadrangulations of the sphere,

Examples | ||

3-Angulations | 4-Angulations | 5-Angulations |

JavaScript must be enabled to display these example.

Count | File | ||

Vertex | Face | Graph | |

3 | 2 | 1 | 1KB |

4 | 4 | 1 | 1KB |

5 | 6 | 1 | 1KB |

6 | 8 | 2 | 1KB |

7 | 10 | 5 | 1KB |

8 | 12 | 14 | 1KB |

9 | 14 | 50 | 3KB |

10 | 16 | 233 | 14KB |

11 | 18 | 1,249 | 81KB |

12 | 20 | 7,595 | 542KB |

13 | 22 | 49,566 | 3.78MB |

14 | 24 | 339,722 | 3.82MB |

15 | 26 | 2,406,841 | 27.9MB |

16 | 28 | 17,490,241 | 208MB |

17 | 30 | 129,664,753 | 1.54GB |

18 | 32 | 977,526,957 |

Count | File | ||

Vertex | Face | Graph | |

4 | 2 | Comming Soon | |

5 | 3 | Comming Soon | |

6 | 4 | Comming Soon | |

7 | 5 | Comming Soon | |

8 | 6 | Comming Soon | |

9 | 7 | Comming Soon | |

10 | 8 | Comming Soon | |

11 | 9 | Comming Soon | |

12 | 10 | Comming Soon | |

13 | 11 | Comming Soon | |

14 | 12 | Comming Soon | |

15 | 13 | Comming Soon | |

16 | 14 | Comming Soon | |

17 | 15 | Comming Soon | |

18 | 16 | Comming Soon | |

19 | 17 | Comming Soon | |

20 | 18 | Comming Soon |

Count | File | ||

Vertex | Face | Graph | |

6 | 2 | 1 | 39B |

8 | 3 | 1 | 55B |

10 | 4 | 5 | 370B |

12 | 5 | 12 | 1.1KB |

14 | 6 | 89 | 10KB |

16 | 7 | 600 | 80.3KB |

18 | 8 | 6,139 | 949KB |

20 | 9 | 66,481 | 11.4MB |

22 | 10 | 792,680 | 15MB |

24 | 12 | 9,813,724 |