A septic graph is a regular graph of degree seven. The numbers of (not necessarily connected) simple septic graphs on 
, 10, 12, ... vertices are 1, 5, 1547, 21609301, 733351105935,
... (OEIS A165628).
The numbers of connected septic graphs on 
, 10, 12, ... vertices are 1, 5, 1547,
21609301, 733351105934, ... (OEIS AA014377),
with the sole disconnected 16-vertex graph being 
.
Examples of septic graphs are illustrated above and summarized in the following table.
graph  |  |
| 8-complete graph | 8 |
| (7,5)-cone graph | 12 |
| complete bipartite graph (7,7) | 14 |
| 8-crown graph | 16 |
| 24-Klein graph | 24 |
| incidence graph (15,7,3) | 30 |
| Hoffman-Singleton graph | 50 |
| (7,6)-cage graph | 90 |
| 7-hypercube graph | 128 |
