Archimedean graph
In this article we are going to delve into the world of Archimedean graph, exploring its origins, its relevance today and its possible implications for the future. Archimedean graph has captured the attention of a wide spectrum of audiences, from experts in the field to those who are just beginning to discover its importance. Along these lines, we will analyze the impact that Archimedean graph has had on different aspects of society, addressing its influence on culture, economy and technology. Likewise, we will delve into the various perspectives and opinions that emerged around Archimedean graph, with the aim of providing a comprehensive and enriching vision on this topic.
In the mathematical field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, and all of them are regular, polyhedral (and therefore by necessity also 3-vertex-connected planar graphs), and also Hamiltonian graphs.[1]
Along with the 13, the infinite sets of prism graphs and antiprism graphs can also be considered Archimedean graphs.[2]
| Name | Graph | Degree | Edges | Vertices | Automorphisms |
|---|---|---|---|---|---|
| truncated tetrahedral graph |  |
3 | 18 | 12 | 24 |
| cuboctahedral graph |  |
4 | 24 | 12 | 48 |
| truncated cubical graph |  |
3 | 36 | 24 | 48 |
| truncated octahedral graph |  |
3 | 36 | 24 | 48 |
| rhombicuboctahedral graph |  |
4 | 48 | 24 | 48 |
| truncated cuboctahedral graph (great rhombicuboctahedron) |
 |
3 | 72 | 48 | 48 |
| snub cubical graph |  |
5 | 60 | 24 | 24 |
| icosidodecahedral graph |  |
4 | 60 | 30 | 120 |
| truncated dodecahedral graph |  |
3 | 90 | 60 | 120 |
| truncated icosahedral graph |  |
3 | 90 | 60 | 120 |
| rhombicosidodecahedral graph |  |
4 | 120 | 60 | 120 |
| truncated icosidodecahedral graph (great rhombicosidodecahedron) |
 |
3 | 180 | 120 | 120 |
| snub dodecahedral graph |  |
5 | 150 | 60 | 60 |
See also
References
- Read, R. C. and Wilson, R. J. An Atlas of Graphs, Oxford, England: Oxford University Press, 2004 reprint, Chapter 6 special graphs pp. 261, 267–269.
External links
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