Non-Triangle-Free Edge Regular Graphs
This is a complete enumeration up to N=20, and for N=21, we have an incomplete enumeration of (21,6,1) and a complete numeration of all other parameter sets.
You can download all the files here and find the source code here.
| N | K | \(\lambda\) | Number Of Graphs | Download Link | Notes |
|---|---|---|---|---|---|
| 3 | 2 | 1 | 1 | Download | K3 |
| 4 | 3 | 2 | 1 | Download | K4 |
| 5 | 4 | 3 | 1 | Download | K5 |
| 6 | 2 | 1 | 1 | Download | 2 K3s |
| 6 | 4 | 2 | 1 | Download | Complement is 3 K2s |
| 6 | 5 | 4 | 1 | Download | K6 |
| 7 | 6 | 5 | 1 | Download | K7 |
| 8 | 3 | 2 | 1 | Download | 2 K4s |
| 8 | 6 | 4 | 1 | Download | Complement is 4 K2s |
| 8 | 7 | 6 | 1 | Download | K8 |
| 9 | 2 | 1 | 1 | Download | 3 K3s |
| 9 | 4 | 1 | 1 | Download | Paley(9) |
| 9 | 6 | 3 | 1 | Download | Complement is 3 K3s |
| 9 | 8 | 7 | 1 | Download | K9 |
| 10 | 4 | 3 | 1 | Download | 2 K5s |
| 10 | 6 | 3 | 1 | Download | 5-triangular graph |
| 10 | 8 | 6 | 1 | Download | Complement is 5 K2s |
| 10 | 9 | 8 | 1 | Download | K10 |
| 11 | 10 | 9 | 1 | Download | K11 |
| 12 | 2 | 1 | 1 | Download | 4 K3s |
| 12 | 3 | 2 | 1 | Download | 3 K4s |
| 12 | 4 | 1 | 2 | Download | |
| 12 | 4 | 2 | 1 | Download | 2 ERG(6,4,2)s |
| 12 | 5 | 2 | 1 | Download | |
| 12 | 5 | 4 | 1 | Download | 2 K6s |
| 12 | 6 | 2 | 1 | Download | |
| 12 | 8 | 4 | 1 | Download | Complement is 3 K4s |
| 12 | 9 | 6 | 1 | Download | Complement is 4 K3s |
| 12 | 10 | 8 | 1 | Download | Complement is 6 K2s |
| 12 | 11 | 10 | 1 | Download | K12 |
| 13 | 6 | 2 | 1 | Download | Paley(13) |
| 13 | 12 | 11 | 1 | Download | K13 |
| 14 | 6 | 2 | 2 | Download | |
| 14 | 6 | 5 | 1 | Download | 2 K7s |
| 14 | 12 | 10 | 1 | Download | Complement is 6 K2s |
| 14 | 13 | 12 | 1 | Download | K14 |
| 15 | 2 | 1 | 1 | Download | 5 K3s |
| 15 | 4 | 1 | 6 | Download | |
| 15 | 4 | 3 | 1 | Download | 3 K5s |
| 15 | 6 | 1 | 1 | Download | |
| 15 | 6 | 2 | 1 | Download | |
| 15 | 8 | 3 | 1 | Download | |
| 15 | 8 | 4 | 1 | Download | 6-triangular graph |
| 15 | 10 | 5 | 1 | Download | Complement is 3 K5s |
| 15 | 12 | 9 | 1 | Download | Complement is 5 K3s |
| 15 | 14 | 13 | 1 | Download | K15 |
| 16 | 3 | 2 | 1 | Download | 4 K4s |
| 16 | 6 | 2 | 7 | Download | |
| 16 | 6 | 4 | 1 | Download | 2 ERG(8,6,4)s |
| 16 | 7 | 6 | 1 | Download | 2 K8s |
| 16 | 9 | 4 | 3 | Download | |
| 16 | 10 | 6 | 1 | Download | |
| 16 | 12 | 8 | 1 | Download | Complement is 4 K4s |
| 16 | 14 | 12 | 1 | Download | Complement is 8 K2s |
| 16 | 15 | 14 | 1 | Download | K16 |
| 17 | 6 | 1 | 1 | Download | |
| 17 | 6 | 2 | 1 | Download | |
| 17 | 8 | 3 | 1 | Download | Paley(17) |
| 17 | 16 | 15 | 1 | Download | K17 |
| 18 | 2 | 1 | 1 | Download | 6 K3s |
| 18 | 4 | 1 | 23 | Download | |
| 18 | 4 | 2 | 1 | Download | 3 ERG (6,4,2)s |
| 18 | 5 | 4 | 1 | Download | 3 K6s |
| 18 | 6 | 1 | 4 | Download | |
| 18 | 6 | 2 | 3 | Download | |
| 18 | 6 | 3 | 1 | Download | 2 ERG(9,6,3)s |
| 18 | 7 | 2 | 2 | Download | |
| 18 | 8 | 2 | 1 | Download | |
| 18 | 8 | 3 | 6 | Download | |
| 18 | 8 | 7 | 1 | Download | 2 K9s |
| 18 | 9 | 4 | 1 | Download | |
| 18 | 10 | 4 | 1 | Download | |
| 18 | 12 | 6 | 1 | Download | Complement is 3 K6s |
| 18 | 15 | 12 | 1 | Download | Complement is 6 K3s |
| 18 | 16 | 14 | 1 | Download | Complement is 9 K2s |
| 18 | 17 | 16 | 1 | Download | K18 |
| 19 | 6 | 1 | 14 | Download | |
| 19 | 6 | 2 | 2 | Download | |
| 19 | 6 | 3 | 1 | Download | |
| 19 | 18 | 17 | 1 | Download | K19 |
| 20 | 3 | 2 | 1 | Download | 5 K4s |
| 20 | 4 | 3 | 1 | Download | 4 K5s |
| 20 | 6 | 1 | 162 | Download | |
| 20 | 6 | 2 | 10 | Download | |
| 20 | 6 | 3 | 1 | Download | 2 ERG(10,6,3)s |
| 20 | 8 | 3 | 1 | Download | |
| 20 | 8 | 6 | 1 | Download | 2 ERG(10,8,6)s |
| 20 | 9 | 4 | 2 | Download | |
| 20 | 9 | 8 | 1 | Download | 2 K10s |
| 20 | 12 | 6 | 2 | Download | |
| 20 | 15 | 10 | 1 | Download | Complement is 4 K5s |
| 20 | 16 | 12 | 1 | Download | Complement is 5 K4s |
| 20 | 18 | 16 | 1 | Download | Complement is 10 K2s |
| 20 | 19 | 18 | 1 | Download | K20 |
| 21 | 2 | 1 | 1 | Download | 7 K3s |
| 21 | 4 | 1 | 112 | Download | |
| 21 | 6 | 1 | >4602 | Download | Incomplete Enumeration |
| 21 | 6 | 2 | 4 | Download | |
| 21 | 6 | 5 | 1 | Download | 3 K7s |
| 21 | 8 | 2 | 8 | Download | |
| 21 | 8 | 3 | 1 | Download | |
| 21 | 10 | 3 | 1 | Download | (7,2) Kneser Graph |
| 21 | 10 | 4 | 2 | Download | |
| 21 | 10 | 5 | 1 | Download | 7-triangular graph |
| 21 | 12 | 5 | 1 | Download | |
| 21 | 14 | 7 | 1 | Download | Complement is 3 K7s |
| 21 | 18 | 15 | 1 | Download | Complement is 7 K3s |
| 21 | 20 | 19 | 1 | Download | K21 |