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Schläfli Graph

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SchlaefliGraph

The Schläfli graph is a strongly regular graph on 27 nodes which is the graph complement of the generalized quadrangle GQ(2,4). It is the unique strongly regular graph with parameters (27,16,10,8) (Godsil and Royle 2001, p. 259). It is illustrated above in two embeddings, the first one corresponding to an order-9 generalized LCF notation.

The Schläfli graph is implemented in the Wolfram Language as GraphData["SchlaefliGraph"].

It is distance-regular with intersection array {16,5;1,8}. It is also distance-transitive.

It is an integral graph with graph spectrum (-2)^(20)4^616^1.

See also

Generalized Quadrangle, Strongly Regular Graph

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References

Brouwer, A. E. "Schläfli Graph." https://aeb.win.tue.nl/drg/graphs/Schlaefli.html.Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance Regular Graphs. New York: Springer-Verlag, pp. 103-104 and 312, 1989.Brouwer, A. E. and van Lint, J. H. "Strongly Regular Graphs and Partial Geometries." In Enumeration and Design: Papers from the Conference on Combinatorics Held at the University of Waterloo, Waterloo, Ont., June 14-July 2, 1982 (Ed. D. M. Jackson and S. A. Vanstone). Toronto, Canada: Academic Press, pp. 85-122, 1984.DistanceRegular.org. "Schläfli Graph." https://www.math.mun.ca/distanceregular/graphs/schlafli.html.Godsil, C. and Royle, G. Algebraic Graph Theory. New York: Springer-Verlag, p. 259, 2001.House of Graphs. "Schlaefli Graph." https://houseofgraphs.org/graphs/1300.Seidel, J. J. "Strongly Regular Graphs with (-1,1,0) Adjacency Matrix Having Eigenvalue 3." Lin. Alg. Appl. 1, 281-298, 1968.

Referenced on Wolfram|Alpha

Schläfli Graph

Cite this as:

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

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