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Quartic Graph


QuarticGraphs

A quartic graph is a graph which is 4-regular. The unique quartic graph on five nodes is the complete graph K_5, and the unique quartic graph on six nodes is the octahedral graph. There are two quartic graphs on seven nodes, one of which is the circulant graph Ci_(1,3)(7). A number of the Archimedean solids have skeletons that are quartic.

The numbers of connected quartic graphs on n=1, 2, ... nodes are 0, 0, 0, 0, 1, 1, 2, 6, 16, 59, ... (OEIS A006820), the numbers of not necessarily connected quartic graphs are 0, 0, 0, 0, 1, 1, 2, 6, 16, 60, ... (OEIS A033301), and the numbers of disconnected quartic graphs for n=10, 11, ... are 1, 1, 3, 8, 25, 88, ... (OEIS A033483; Read and Wilson 1998).

The following table gives a list of some named quartic graphs.


See also

120-Cell, Complete Graph, Cubic Graph, Cuboctahedral Graph, Doyle Graph, Grünbaum Graphs, Octahedral Graph, Quartic Symmetric Graph, Quintic Graph, Regular Graph

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References

Colbourn, C. J. and Dinitz, J. H. (Eds.). CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, p. 648, 1996.Faradzev, I. A. "Constructive Enumeration of Combinatorial Objects." In Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Paris: Centre Nat. Recherche Scient., pp. 131-135, 1978.Meringer, M. "Connected Regular Graphs." http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html#CRG.Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, 1998.Sloane, N. J. A. Sequences A006820/M1617, A033301, and A033483 in "The On-Line Encyclopedia of Integer Sequences."

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Quartic Graph

Cite this as:

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

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