The Schläfli graph is a strongly regular graph on 27 nodes which is the graph complement of the generalized quadrangle 
. It is the unique strongly regular graph with parameters 
(Godsil and Royle 2001, p. 259). It is illustrated above in two embeddings, the first one corresponding to an order-9 generalized LCF notation.
It is distance-regular with intersection array 
. It is also distance-transitive.
It is an integral graph with graph spectrum 
.
See also
Generalized Quadrangle,
Strongly Regular Graph Explore with Wolfram|Alpha
References
Brouwer, A. E. "Schläfli Graph." http://www.win.tue.nl/~aeb/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.Seidel, J. J. "Strongly Regular Graphs with 
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
Subject classifications
