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.

I would be very happy to know the problem you are working which needed this data set. So if you could give me your name and email, I will be very happy to discuss it with you.
**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.