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The Kummer graph is the name apparently first adopted here for the Levi graph of the Kummer configuration (Coxeter 1950), corresponding to the 6-folded cube graph (Brouwer et al. 1989, p. 264). It is isomorphic to the graph formed from the 6-hypercube graph where vertices opposite to one other (i.e., at maximal graph distances from each other) are vertex-contracted together. It is illustrated above in a number of voltage graph drawings.

It is illustrated above in several order-2 LCF notation drawings.

The Kummer graph has graph crossing number and rectilinear crossing number of at most 128, as illustrated above (E. Weisstein, Sep. 13, 2026).

The Kummer graph has graph genus 9 (E. Weisstein, Jan. 13, 2026).

It is implemented in the Wolfram Language as GraphData["KummerGraph"].

See also

Clebsch Graph, Folded Cube Graph, Hypercube Graph, Kummer Configuration, Levi graph

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References

Brouwer, A. E. "Folded 6-Cube and Graphs with the Same Parameters." https://aeb.win.tue.nl/drg/graphs/Folded-6-cube.html.Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. "Halved and Folded Cubes." §9.2D in Distance-Regular Graphs. New York: Springer-Verlag, pp. 264-265, 1989.Coxeter, H. S. M. "Self-Dual Configurations and Regular Graphs." Bull. Amer. Math. Soc. 56, 413-455, 1950.House of Graphs. "Kummer Graph." https://houseofgraphs.org/graphs/1206.

Referenced on Wolfram|Alpha

Kummer Graph

Cite this as:

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

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