This list is far from complete, and may include duplicates.
| Name (link) | degree | vertices |
|---|
| 1-cycle | 2 | 1 |
| K1 | 0 | 1 |
| K2 | 1 | 2 |
| K3 | 2 | 3 |
| 4-cycle | 2 | 4 |
| K4 | 3 | 4 |
| K5 | 4 | 5 |
| 5-cycle | 2 | 5 |
| K6 | 5 | 6 |
| 6-cycle | 2 | 6 |
| K3,3 | 3 | 6 |
| K2,2,2 | 4 | 6 |
| K7 | 6 | 7 |
| 7-cycle | 2 | 7 |
| K2,2,2,2 | 6 | 8 |
| K4,4 | 4 | 8 |
| K8 | 7 | 8 |
| 8-cycle | 2 | 8 |
| cubic graph | 3 | 8 |
| 9-cycle | 2 | 9 |
| K3,3,3 | 6 | 9 |
| K9 | 8 | 9 |
| K3 × K3 | 4 | 9 |
| K5 × K2 | 4 | 10 |
| Petersen graph | 3 | 10 |
| 10-cycle | 2 | 10 |
| 11-cycle | 2 | 11 |
| 12-cycle | 2 | 12 |
| K4,4,4 | 8 | 12 |
| icosahedron | 5 | 12 |
| K6 × K2 | 5 | 12 |
| K6,6 | 6 | 12 |
| cuboctahedron | 4 | 12 |
| C4 × K3 | 4 | 12 |
| 13-cycle | 2 | 13 |
| Paley order-13 graph | 6 | 13 |
| 13-circulant(1,5) | 4 | 13 |
| 14-cycle | 2 | 14 |
| Heawood graph | 3 | 14 |
| 15-circulant(1,4) | 4 | 15 |
| hemi-icosidodecahedron | 4 | 15 |
| rectification of C5:{5,5} | 4 | 15 |
| K5,5,5 | 10 | 15 |
| 10-regular Clebsch graph | 10 | 16 |
| C4 □ C4 | 4 | 16 |
| Shrikhande graph | 6 | 16 |
| Clebsch graph | 5 | 16 |
| Möbius-Kantor graph | 3 | 16 |
| torus-s-4-1 | 4 | 17 |
| Pappus graph | 3 | 18 |
| 6-cycle × 3-cycle | 4 | 18 |
| Desargues graph | 3 | 20 |
| 20-circulant(1,9) | 4 | 20 |
| dodecahedron | 3 | 20 |
| rectification of {3,6}(1,3) | 4 | 21 |
| 21-circulant(1,8) | 4 | 21 |
| Nauru graph | 3 | 24 |
| 7-valent Klein graph | 7 | 24 |
| 24-cell | 8 | 24 |
| icosahedron × K2 | 5 | 24 |
| torus-s-5-5 | 4 | 25 |
| torus-h-2-4 | 3 | 26 |
| rectification of {4,4}(3,2) | 4 | 26 |
| Schläfli graph | 16 | 27 |
| rectification of {3,6}(3,3) | 4 | 27 |
| rectification of C11:{6,6} | 4 | 27 |
| 28-circulant(1,13) | 4 | 28 |
| Coxeter graph | 3 | 28 |
| rectification of C7.2 | 4 | 28 |
| rectification of S4:{5,5} | 4 | 30 |
| rectification of the icosahedron | 4 | 30 |
| Tutte-Coxeter | 3 | 30 |
| rectification of C7:{4,6} | 4 | 30 |
| rectification of C5:{4,5} | 4 | 30 |
| rectification of N10.6 | 4 | 30 |
| rectification of {4,4}(4,0) | 4 | 32 |
| Dyck graph | 3 | 32 |
| 5-cube | 5 | 32 |
| rectification of {4,4}(4,1) | 4 | 34 |
| rectification of C10.3 | 4 | 36 |
| rectification of S4:{4,6} | 4 | 36 |
| rectification of {3,6}(0,4) | 4 | 36 |
| rectification of {4,4}(3,3) | 4 | 36 |
| torus-h-1-5 | 3 | 38 |
| rectification of {3,6}(2,4) | 4 | 39 |
| rectification of C6:{4,5} | 4 | 40 |
| rectification of {4,4}(4,2) | 4 | 40 |
| rectification of S5:{5,5} | 4 | 40 |
| F040A | 3 | 40 |
| torus-h-3-5 | 3 | 42 |
| rectification of N22.4 | 4 | 48 |
| rectification of {3,6}(4,4) | 4 | 48 |
| rectification of S3:{3,8} | 4 | 48 |
| rectification of N10.1 | 4 | 48 |
| F048A | 3 | 48 |
| rectification of S5:{4,6} | 4 | 48 |
| rectification of R9.17 | 4 | 48 |
| rectification of R9.18 | 4 | 48 |