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Gosset Graph

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The Gosset graph is a 27-regular graph on 56 vertices which is the skeleton of the Gosset polytope 3_(21).

The Gosset graph is implemented in the Wolfram Language as GraphData["GossetGraph"].

It is a distance-regular graph with intersection array {27,10,1;1,10,27}, and therefore also a Taylor graph. It is also distance-transitive.

It is an integral graph with graph spectrum (-3)^(21)(-1)^(27)9^727^1.

The graph distance-2 graph of the Gosset graph is itself a distance-transitive and distance-regular graph with intersection array {27,16,1;1,16,27} (and therefore another Taylor graph).

See also

Distance-Regular Graph, Taylor Graph

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References

Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance Regular Graphs. New York: Springer-Verlag, p. 103, 1989.Coxeter, H. S. M. "Extreme Forms." Canad. J. Math. 3, 391-441, 1951.DistanceRegular.org. "Gosset Graph." https://www.math.mun.ca/distanceregular/graphs/gosset.html.DistanceRegular.org. "Distance-2 Graph of Gosset Graph." https://www.math.mun.ca/distanceregular/graphs/gosset-dist2.html.Godsil, C. D. "Eigenpolytopes of Distance Regular Graphs." Canad. J. Math. 59, 739-755, 1998.House of Graphs. "Gosset Graph." https://houseofgraphs.org/graphs/1114.Miller, G. A.; Blichfeldt, H. F.; and Dickson, L. E. Part 3 in Theory and Applications of Finite Groups. New York: Dover, 1961.Taylor, D. E. "Regular 2-Graphs." Proc. London Math. Soc. 35, 257-274, 1977.

Referenced on Wolfram|Alpha

Gosset Graph

Cite this as:

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

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