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Platonic Graph


PlatonicGraphs

A polyhedral graph corresponding to the skeleton of a Platonic solid. The five platonic graphs, the tetrahedral graph, cubical graph, octahedral graph, dodecahedral graph, and icosahedral graph, are illustrated above. They are special cases of Schlegel graphs.

Platonic graphs are graceful (Gardner 1983, pp. 158 and 163-164).

The following table summarizes the Platonic graphs and some of their properties.

graph GregularityVE|Aut(G)|HamiltonianEulerianvertex-transitiveedge-transitive
cubical graphcubic81248yesnoyesyes
dodecahedral graphcubic2030120yesnoyesyes
icosahedral graphquintic1230120yesnoyesyes
octahedral graphquartic61248yesyesyesyes
tetrahedral graphcubic4624yesnoyesyes

See also

Archimedean Graph, Cubical Graph, Dodecahedral Graph, Icosahedral Graph, Octahedral Graph, Platonic Solid, Polyhedral Graph, Schlegel Graph, Tetrahedral Graph

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References

Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 234, 1976.Gardner, M. "Golomb's Graceful Graphs." Ch. 15 in Wheels, Life, and Other Mathematical Amusements. New York: W. H. Freeman, pp. 152-165, 1983.Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, pp. 263 and 266, 1998.

Referenced on Wolfram|Alpha

Platonic Graph

Cite this as:

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

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