The graphs of Hoffman-Singleton, Higman-Sims, and McLaughlin, and the Hermitian curve of degree 6 in characteristic 5

zbMATH Open1296.05207arXiv1405.4643MaRDI QIDQ2876036

Ichiro Shimada

Publication date: 15 August 2014

Abstract: We construct the graphs of Hoffman-Singleton, Higman-Sims, and McLaughlin from certain relations on the set of non-singular conics totally tangent to the Hermitian curve of degree 6 in characteristic 5. We then interpret this geometric construction in terms of the subgroup structure of the automorphism group of this Hermitian curve.

Full work available at URL: https://arxiv.org/abs/1405.4643

zbMATH Keywords

automorphism groupstrongly regular graph

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Planar graphs; geometric and topological aspects of graph theory (05C10)

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