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# Quintic Graph

A quintic graph is a graph which is 5-regular. The only quintic graph on nodes is the complete graph . Quintic graphs exist only on even numbers of nodes, and the numbers of connected quintic graphs on , 4, 6, ... nodes are 0, 0, 1, 3, 60, 7848, 3459383, 2585136675, ... (OEIS A006821).

The following table gives some named quintic graphs.

 graph nodes symmetric complete graph 6 yes (5,3)-cone graph 8 no complete bipartite graph 10 yes icosahedral graph 12 yes 6-crown graph 12 yes 5-Andrásfai graph 14 yes Clebsch graph 16 yes graph Cartesian product 18 no (11,5,2)-Levi graph 22 yes snub cubical graph 24 no Foster cage 30 no Meringer graph 30 no Robertson-Wegner graph 30 no Wong graph 30 no Wells graph 32 yes hypercube graph 32 yes Sylvester graph 36 yes (5,6)-cage graph 42 yes snub dodecahedral graph 60 no 5-odd graph 126 yes (5,8)-cage graph 170 ? 6-permutation star graph 720 yes

Cubic Graph, Quartic Graph, Quasi-Quintic Graph, Quintic Symmetric Graph, 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. Sequence A006821/M3168 in "The On-Line Encyclopedia of Integer Sequences."

Quintic Graph

## Cite this as:

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