On the 486-Vertex Distance-Regular Graphs of Koolen-Riebeek and Soicher
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Published:2020-07-24
Issue:3
Volume:27
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Bailey Robert F.,Hawtin Daniel R.
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 $\mathrm{AG}(5,3)$ (which is both). It is shown that each of these is preserved by the same rank-$9$ action of the group $3^5:(2\times M_{10})$, and the connection is explained using the ternary Golay code.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics