A sextic graph is a finite regular graph of positive graph order and vertex degree
six. The numbers of connected simple
sextic graphs on 
,
8, ... vertices are 1, 1, 4, 21, 266, 7849, 367860,
... (OEIS A006822). Examples are illustrated
above and summarized in the following table. The Hoffman-Singleton example is obtained
by deleting the closed neighborhood of one
vertex.
graph  |  |
| 7-complete graph | 7 |
16-cell
graph  | 8 |
| (6,4)-cone graph | 10 |
| 5-triangular graph | 10 |
| complete bipartite graph (6,6) | 12 |
| 13-Paley graph | 13 |
| 7-crown graph | 14 |
| generalized quadrangle (2,2) | 15 |
| Shrikhande graph | 16 |
| (16,6,2,2)-strongly regular graph 1 | 16 |
| (6,5)-cage graph | 40 |
| Hoffman-Singleton graph minus star graph | 42 |
| generalized hexagon (3,1) | 52 |
| Perkel graph | 57 |
| generalized hexagon (1,5) | 62 |
| 6-hypercube graph | 64 |
| (6,8)-cage graph | 312 |
| 6-odd graph | 462 |
