Introduction
This is a database of graphs that are inequivalent with respect to pivot operations and isomorphism. See the paper [1] for more details.
^ TOPTables
inP: Number of pivot orbits of connected graphs on n vertices.
tnP: Total number of pivot orbits of graphs on n vertices.
inP,B: Number of pivot orbits of connected bipartite graphs on n vertices.
inP,B: Total number of pivot orbits of bipartite graphs on n vertices.
| n | inP | tnP | inP,B | tnP,B |
|---|---|---|---|---|
| 1 | 1 | 1 | 1* | 1 |
| 2 | 1 | 2 | 1 | 2 |
| 3 | 2 | 4 | 1* | 3 |
| 4 | 4 | 9 | 2 | 6 |
| 5 | 10 | 21 | 3* | 10 |
| 6 | 35 | 64 | 8 | 22 |
| 7 | 134 | 218 | 15* | 43 |
| 8 | 777 | 1,068 | 43 | 104 |
| 9 | 6,702 | 8,038 | 110* | 250 |
| 10 | 104,825 | 114,188 | 370 | 720 |
| 11 | 3,370,317 | 3,493,965 | 1,260* | 2,229 |
| 12 | 231,557,290 | 235,176,097 | 5,366 | 8,361 |
| 13 | 25,684* | 36,441 | ||
| 14 | 154,104 | 199,610 | ||
| 15 | 1,156,716* | 1,395,326+ |
* These numbers can be found by dividing the number of binary linear codes of length n [2] by two.
+ The orbits for 15 vertices have been generated by Sang-il Oum.
See [1] for more tables and information.
^ TOPFile formats
The graphs are stored in nauty's graph6 format. This compact representation can be transformed into Magma, Maple, or any other format by using the nauty package. The graph6 files can be used as input to all the utilities in the nauty package.
^ TOPFiles
Connected graphs
| n | Download |
|---|---|
| 1 | pivotorbits1.g6 |
| 2 | pivotorbits2.g6 |
| 3 | pivotorbits3.g6 |
| 4 | pivotorbits4.g6 |
| 5 | pivotorbits5.g6 |
| 6 | pivotorbits6.g6 |
| 7 | pivotorbits7.g6 |
| 8 | pivotorbits8.g6 |
| 9 | pivotorbits9.g6 |
| 10 | pivotorbits10.g6.gz |
| 11 | pivotorbits11.g6.gz |
| 12 | pivotorbits12.g6.gz* |
* The compressed file for length 12 is more than 2GB. Please send me an email me if you are interested in it.
Connected bipartite graphs
| n | Download |
|---|---|
| 1 | bipartite1.g6 |
| 2 | bipartite2.g6 |
| 3 | bipartite3.g6 |
| 4 | bipartite4.g6 |
| 5 | bipartite5.g6 |
| 6 | bipartite6.g6 |
| 7 | bipartite7.g6 |
| 8 | bipartite8.g6 |
| 9 | bipartite9.g6 |
| 10 | bipartite10.g6 |
| 11 | bipartite11.g6 |
| 12 | bipartite12.g6 |
| 13 | bipartite13.g6 |
| 14 | bipartite14.g6.gz |
References
[1] Lars Eirik Danielsen and Matthew G. Parker: Edge local complementation and equivalence of binary linear codes. Des. Codes Cryptogr. 49(1–3), 161–170, 2008. (doi:10.1007/s10623-008-9190-x) (arXiv:0710.2243)
[2] Harald Fripertinger: Isometry classes of codes.