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Cubeplex Graph

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CubeplexGraph

The cubeplex graph is the cubic Hamiltonian graph on 12 nodes illustrated above in several drawings and corresponding to the graph Gamma_1 in Fischer and Little (2001). It has LCF notation [-6,-5,-3,-6,3,5,-6,-3,5,-6,-5,3].

The cubeplex graph is implemented in the Wolfram Language as GraphData["CubeplexGraph"].

CubeplexTwinplex

Norine and Thomas (2008) used the term "cubeplex graph" to describe one of the 12-vertex graphs Gamma_1 and Gamma_2 from Fischer and Little (2001). Unfortunately, in the figure supposedly giving drawings for the graphs termed cubeplex and twinplex in that paper (reproduced above), both drawings correspond to Fischer and Little's Gamma_1. However, since Robertson et al. (2019) identify the twinplex graph with a correct explicit figure, both graphs in Norine and Thomas (2008) can be identified as drawings of the cubeplex graph.

See also

Twinplex Graph

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References

Clancy, K.; Haythorpe, M.; Newcombe, A.; and Pegg, E. Jr. "There Are No Cubic Graphs on 26 Vertices with Crossing Number 10 or 11." Graphs Combin. 36, 1713-1721, 2020. https://doi.org/10.1007/s00373-020-02204-6.Fischer, I. and Little, C. H. C. "A Characterisation of Pfaffian Near Bipartite Graphs." J. Combin. Th., Ser. B 82, 175-222, 2001.House of Graphs. "Cubeplex." https://houseofgraphs.org/graphs/27407.Norine, S. and Thomas, R. "Minimally Non-Pfaffian Graphs." J. Combin. Th., Ser. B 98, 1038-1055, 2008.Robertson, N.; Seymour, P. D.; and Thomas, R. "Excluded Minors in Cubic Graphs." J. Combin. Th., Ser. B 138, 219-285, 2019. https://doi.org/10.1016/j.jctb.2019.02.002.

Referenced on Wolfram|Alpha

Cubeplex Graph

Cite this as:

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

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