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Gray Configuration


GrayConfiguration

The Gray configuration is a 27_3 configuration consisting of 27 points and 27 lines, with each point lying on exactly three lines and each line passing through exactly three points. It can be realized by taking the 27 points of a 3×3×3 grid graph P_3 square P_3 square P_3 and the 27 lines through these points that are parallel to one of the coordinate axes of the grid.

The Levi graph of the Gray configuration is the Gray graph.


See also

Configuration, Gray Graph, Grid Graph

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References

Boben, M. and Pisanski, T. "Polycyclic Configurations." European J. Combin. 24, 431-457, 2003.Hladnik, M.; Marušič, D.; and Pisanski, T. "Cyclic Haar Graphs." Discr. Math. 244, 137-152, 2002.Marušič, D.; Pisanski, T.; and Wilson, S. "The Genus of the GRAY [sic] Graph is 7." Europ. J. Combin. 26, 377-385, 2005.

Cite this as:

Weisstein, Eric W. "Gray Configuration." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GrayConfiguration.html

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