## Graph Catalogs

### Interval graphs

The lists provide all nonisomorphic interval graphs of n vertices for n=1,2,...,12. The numbers of graphs are summarized as follows
 The number of vertices The number of interval graphs: The number of connected interval graphs: LIST, LIST, OEIS:A005975 OEIS:A005976 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 4 10 27 92 369 1807 10344 67659 491347 3894446 1 1 2 5 15 56 250 1328 8069 54962 410330 3317302
Each interval graph is represented in one line in a simple text format, e.g., 1 1 2 2 3 3 (independent set of three vertices), 1 2 1 3 2 3 (path of length 3), 1 2 3 3 2 1 (complete graph of size 3).

### Permutation graphs

The lists provide all nonisomorphic permutation graphs of n vertices for each of n=1,2,...,6. The numbers of graphs are summarized as follows
 The number of vertices The number of permutation graphs The number of connected permutation graphs 1 2 3 4 5 6 7 8 1 2 4 11 33 142 776 5699 1 1 2 6 20 99 600 4753
Each permutation graph represented in one line in a simple text format, e.g., 1 2 3 (independent set of three vertices), 2 3 1 (path of length 3), 3 2 1 (complete graph of size 3).

### Connected Proper Interval graphs

The list provides all nonisomorphic proper interval graphs of n vertices for n=1,2,...,23. The numbers of graphs are summarized as follows
 The number of vertices The number of connected proper interval graphs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 1 2 4 10 26 76 232 750 2494 8524 29624 104468 372308 1338936 4850640 17685270 64834550 238843660(608M) 883677784(2216M) 3282152588(8136MB) 12233309868(31GB) 45741634536(115GB)
Each interval graph is represented in one line in a simple text format, e.g., [[[]]] (complete graph of size 3), [[][]] (path of length 3).

### Histrory

• 2019/09/04: Update & Bug fix
• Permutation graphs (n≤8)
• Connected permutation graphs (n≤8) (Thanks to Kazuaki Yamazaki.)
• 2019/04/01-04/11: Update;
• Connected proper interval graphs (n=21,22,23) (Special thanks to Prof. Ryuichi SAKAI at Osaka Electro-Communication University. He made a nice program for enumeration of these graphs. Note that his program can compute for n=24, 25, but they are too huge to put on the Web site.)
• 2019/03/19: Update;
• Connected proper interval graphs (n=19,20) (Special thanks to Prof. Ryuichi SAKAI at Osaka Electro-Communication University. He made a nice program for enumeration of these graphs.)
• 2019/02/23: Update;
• Connected proper interval graphs (n=1,2,...,18)
• 2019/01/09: Update;
• We add the note about bugs for permutation graphs. (Many thanks to Prof. Yota Otachi.)
• 2017/10/16: Update;
• Interval graphs (n=12)
• Connected interval graphs (n=12)
• 2017/08/24: Update;
• Interval graphs (n=11)
• Connected interval graphs (n=11)
• 2017/08/08: Update;
• Interval graphs (n=10)
• Connected interval graphs (n=10)
• 2017/07/20: Update;
• Permutation graphs (n=6)
• Connected permutation graphs (n=6)
• 2017/06/30: Open for the following graph classes;
• Interval graphs (n=1,...,9)
• Connected interval graphs (n=1,...,9)
• Permutation graphs (n=1,...,6)
• Connected permutation graphs (n=1,...,6)

 Last modified: Fri Dec 24 20:14:43 JST 2010 by Ryuhei Uehara (uehara@jaist.ac.jp) 