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Kummer Graph

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KummerGraph

The Kummer graph is the name apparently first adopted here for the Levi graph of Kummer's 16_6 configuration (Coxeter 1950), corresponding to the folded 6-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 several order-2 LCF notation embeddings.

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

See also

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

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References

Brouwer, A. E. "Folded 6-Cube and Graphs with the Same Parameters." http://www.win.tue.nl/~aeb/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.

Cite this as:

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

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