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Koolen-Riebeek Graph

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The Koolen-Riebeek graph is a weakly regular graph on 486 vertices with parameters (nu,k,lambda,mu)=(486,45,0,(0,9)).

It is distance-regular but not distance-transitive with intersection array {45,44,36,5;1,9,40,45} and has graph spectrum (-45)^1(-9)^(110)0^(264)9^(110)45^1.

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

The Koolen-Riebeek graph is implemented in the Wolfram Language as GraphData["KoolenRiebeekGraph"].

See also

Berlekamp-van Lint-Seidel Graph, Distance-Regular Graph, Weakly Regular Graph

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References

Bailey, R. F. and Hawtin, D. R. "On the 486-Vertex Distance-Regular Graphs of Koolen-Riebeek and Soicher." 12 Jul 2020. https://arxiv.org/abs/1908.07104.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 Maldeghem, H. Strongly Regular Graphs. Cambridge, England: Cambridge University Press, p. 333, 2022.DistanceRegular.org. "Koolen-Riebeek graph." https://www.distanceregular.org/graphs/koolenriebeek.html.

Cite this as:

Weisstein, Eric W. "Koolen-Riebeek Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Koolen-RiebeekGraph.html

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