Berlekamp-van Lint-Seidel Graph

The Berlekamp-van Lint-Seidel graph is the Hamiltonian strongly regular graph on 243 vertices with parameters (243,22,1,2). It is also distance-regular with intersection array {22,20;1,2}, as well as distance-transitive.

It has graph spectrum 22^14^(132)(-5)^(110) and is therefore an integral graph.

The halved graph of the (bipartite) Koolen-Riebeek graph is the graph complement of the Berlekamp-van Lint-Seidel graph (Brouwer and van Maldeghem 2022, p. 333).

The Berlekamp-van Lint-Seidel graph is implemented the Wolfram Language as GraphData["BerlekampVanLintSeidelGraph"].

See also

Koolen-Riebeek Graph, Strongly Regular Graph

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Berlekamp, E R.; van Lint, J. H.; and Seidel, J. J. "A Strongly Regular Graph Derived from the Perfect Ternary Golay Code." In A Survey of Combinatorial Theory, Symp. Colorado State Univ., 1971 (Ed. J. N. Srivastava et al.) Amsterdam, Netherlands: North Holland, 1973.Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. §11.3B in Distance-Regular Graphs. New York: Springer-Verlag, p. 360, 1989.Brouwer, A. E.; Koolen, J. H.; and Riebeek, R. J. "A New Distance-Regular Graph Associated to the Mathieu Group M_(10)." J. Algebraic Combin. 8, 153-156, 1998.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.Brouwer, A. E. and van Maldeghem, H. "The Berlekamp-Van Lint-Seidel Graph." §10.55 in Strongly Regular Graphs. Cambridge, England: Cambridge University Press, p. 333, 2022.Delsarte, P. "An Algebraic Approach to the Association Schemes of Coding Theory." Philips Res. Reports Suppl. 10, "Berlekamp-Van Lint-Seidel Graph."

Referenced on Wolfram|Alpha

Berlekamp-van Lint-Seidel Graph

Cite this as:

Weisstein, Eric W. "Berlekamp-van Lint-Seidel Graph." From MathWorld--A Wolfram Web Resource.

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