Platonic Graph
المؤلف:
Bondy, J. A. and Murty, U. S. R.
المصدر:
Graph Theory with Applications. New York: North Holland
الجزء والصفحة:
...
23-3-2022
1839
Platonic Graph
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  |
regularity |
 |
 |
 |
Hamiltonian |
Eulerian |
vertex-transitive |
edge-transitive |
| cubical graph |
cubic |
8 |
12 |
48 |
yes |
no |
yes |
yes |
| dodecahedral graph |
cubic |
20 |
30 |
120 |
yes |
no |
yes |
yes |
| icosahedral graph |
quintic |
12 |
30 |
120 |
yes |
no |
yes |
yes |
| octahedral graph |
quartic |
6 |
12 |
48 |
yes |
yes |
yes |
yes |
| tetrahedral graph |
cubic |
4 |
6 |
24 |
yes |
no |
yes |
yes |
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.
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