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 |
Klein graph | 24 |
incidence graph (15,7,3) | 30 |
Hoffman-Singleton graph | 50 |
(7,6)-cage graph | 90 |
7-hypercube graph | 128 |