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Crossed Dodecahedral Graph

CrossedDodecahedralGraphEmbeddings

The crossed dodecahedral graph is the crossed graph of the regular dodecahedron. It can therefore be constructed by adding edges in a pentagrammatic configuration to each face of a regular dodecahedron. It is also the graph square of the dodecahedral graph. This graph is 2-planar, does not admit a straight-line 2-planar drawing, and has the unique 2-planar graph embedding illustrated above (Bekos et al. 2017, Brandenburg 2021). It is implemented in the Wolfram Language as GraphData["CrossedDodecahedralGraph"].

See also

2-Planar Graph, Crossed Graph, Dodecahedral Graph, Graph Square, Local Crossing Number, Regular Dodecahedron

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References

Bekos, M. A.; Kaufmann, M.; and Raftopoulou, C. N. "On Optimal 2- and 3-Planar Graphs." In SoCG 2017 (Ed. B. Aronov and M. J. Katz). Vol. 77 of LIPIcs, Schloss Dagstuhl--Leibniz-Zentrum für Informatik, pp. 16:1-16:16, 2017.Brandenburg, F. J. "Straight-Line Drawings of 1-Planar Graphs." 3 Sep 2021. https://arxiv.org/abs/2109.01692.House of Graphs. "Crossed Dodecahedral Graph." https://houseofgraphs.org/graphs/56513.

Cite this as:

Weisstein, Eric W. "Crossed Dodecahedral Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CrossedDodecahedralGraph.html

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