A quartic graph is a graph which is 4-regular . The unique quartic graph on five nodes is the complete
graph ,
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 .
A number of the Archimedean solids have skeletons
that are quartic.

The numbers of connected quartic graphs on , 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 , 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." Referenced
on Wolfram|Alpha 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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