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# Septic Graph

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

Regular Graph

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## References

Meringer, M. "Connected Regular Graphs." http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html#CRG.Sloane, N. J. A. Sequences A014377 and AA165628 in "The On-Line Encyclopedia of Integer Sequences."

Septic Graph

## Cite this as:

Weisstein, Eric W. "Septic Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SepticGraph.html