Quintic Graph
QuinticGraphs
A quintic graph is a graph which is 5-regular. The only quintic graph on n<=7 nodes is the complete graph K_6. Quintic graphs exist only on even numbers of nodes, and the numbers of connected quintic graphs on n=2, 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 K_6 6 yes
(5,3)-cone graph 8 no
complete bipartite
graph K_(5,5) 10 yes
icosahedral graph 12 yes
6-crown
graph 12 yes
5-Andrásfai graph 14 yes
Clebsch graph 16 yes
graph Cartesian product K_(3,3) square K_3 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 Q_5 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
See also
Cubic Graph, Quartic Graph, Quasi-Quintic Graph, Quintic Symmetric Graph, Regular GraphExplore with Wolfram|Alpha
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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."Referenced on Wolfram|Alpha
Quintic GraphCite this as:
Weisstein, Eric W. "Quintic Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/QuinticGraph.html