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The Non-Collinearity Graph of the O+(8,2) Quadric Is Uniquely Geometrisable

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Abstract

The graph of the titlehas the points of the O+(8,2) polar space as itsvertices, two such vertices being adjacent iff the correspondingpoints are non-collinear in the polar space. We prove that, uptoisomorphism, there is a unique partial geometry pg(8,7,4)whose point graph is this graph. This is the partial geometryof Cohen, Haemers and Van Lint and De Clerck, Dye and Thas. Ouruniqueness proof shows that this geometry has a subgeometry isomorphicto the affine plane of order three, and the geometry is canonicallydescribeable in terms of this affine plane.

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  1. Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India

    Pratima Panigrahi

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  1. Pratima Panigrahi
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Panigrahi, P. The Non-Collinearity Graph of the O+(8,2) Quadric Is Uniquely Geometrisable. Designs, Codes and Cryptography 20, 307–317 (2000). https://doi.org/10.1023/A:1008378226142

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  • DOI: https://doi.org/10.1023/A:1008378226142

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