Introduction
This is a database of circle graphs. One representative from each LC orbit of connected circle graphs is given. For a classification of all LC orbits, see the Database of Self-Dual Quantum Codes. For more details, see the paper [1].
^ TOPTables
Number of connected (cn) and total number (tn) of circle graphs on n vertices:
| n | cn | tn |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 1 | 2 |
| 3 | 2 | 4 |
| 4 | 6 | 11 |
| 5 | 21 | 34 |
| 6 | 110 | 154 |
| 7 | 789 | 978 |
| 8 | 8336 | 9497 |
| 9 | 117,283 | 127,954 |
| 10 | 2,026,331 | 2,165,291 |
| 11 | 40,302,425 | 42,609,994 |
| 12 | 892,278,076 | 937,233,306 |
Number of connected (cn) and total number (tn) of LC orbits containing circle graphs on n vertices:
| n | cn | tn |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 1 | 2 |
| 3 | 1 | 3 |
| 4 | 2 | 6 |
| 5 | 4 | 11 |
| 6 | 10 | 25 |
| 7 | 23 | 55 |
| 8 | 81 | 157 |
| 9 | 293 | 499 |
| 10 | 1403 | 2059 |
| 11 | 7968 | 10,543 |
| 12 | 55,553 | 68,281 |
Files
Graphs are stored in nauty's graph6 format. This compact representation can be transformed into Magma and Maple format by using the nauty package.
Each file contains one representative from each LC orbit of connected circle graphs on n vertices.
| n | Download |
|---|---|
| 1 | circle1.g6 |
| 2 | circle2.g6 |
| 3 | circle3.g6 |
| 4 | circle4.g6 |
| 5 | circle5.g6 |
| 6 | circle6.g6 |
| 7 | circle7.g6 |
| 8 | circle8.g6 |
| 9 | circle9.g6 |
| 10 | circle10.g6 |
| 11 | circle11.g6 |
| 12 | circle12.g6 |
References
[1] Lars Eirik Danielsen and Matthew G. Parker: Interlace polynomials: Enumeration, unimodality, and connections to codes. Submitted for publication, Apr. 2008. (arXiv:0804.2576)