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.