On the 486-vertex distance-regular graphs of Koolen--Riebeek and Soicher

2019/08/19 by Bailey, Robert F., Hawtin, Daniel R.
#05C25 #05E30 (primary) #20B25 #51E05 (secondary) #94B25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1908.07104

Abstract

This paper considers three imprimitive distance-regular graphs with 486 vertices and diameter 4: the Koolen--Riebeek graph (which is bipartite), the Soicher graph (which is antipodal), and the incidence graph of a symmetric transversal design obtained from the affine geometry AG(5,3) (which is both). It is shown that each of these is preserved by the same rank-9 action of the group 3⁵:(2× M₁₀), and the connection is explained using the ternary Golay code.

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