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On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66)

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Ukrainian Mathematical Journal Aims and scope

Abstract

We prove that a strongly regular graph with parameters (486, 165, 36, 66) does not exist. Since the parameters indicated are parameters of a pseudogeometric graph for pG 2(5, 32), we conclude that the partial geometries pG 2(5, 32) and pG 2(32, 5) do not exist. Finally, a neighborhood of an arbitrary vertex of a pseudogeometric graph for pG 3(6, 80) is a pseudogeometric graph for pG 2(5, 32) and, therefore, a pseudogeometric graph for the partial geometry pG 3(6, 80) [i.e., a strongly regular graph with parameters (1127, 486, 165, 243)] does not exist.

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  1. Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Division, Ekaterinburg, Russia

    A. A. Makhnev

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  1. A. A. Makhnev
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Makhnev, A.A. On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66). Ukrainian Mathematical Journal 54, 1137–1146 (2002). https://doi.org/10.1023/A:1022066425998

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  • DOI: https://doi.org/10.1023/A:1022066425998

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