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Ukrainian Mathematical Journal

, Volume 54, Issue 7, pp 1137–1146 | Cite as

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

  • A. A. Makhnev
Article

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 pG2(5, 32), we conclude that the partial geometries pG2(5, 32) and pG2(32, 5) do not exist. Finally, a neighborhood of an arbitrary vertex of a pseudogeometric graph for pG3(6, 80) is a pseudogeometric graph for pG2(5, 32) and, therefore, a pseudogeometric graph for the partial geometry pG3(6, 80) [i.e., a strongly regular graph with parameters (1127, 486, 165, 243)] does not exist.

Keywords

Regular Graph Partial Geometry Arbitrary Vertex Pseudogeometric Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A. A. Makhnev
    • 1
  1. 1.Institute of Mathematics and MechanicsRussian Academy of Sciences, Ural DivisionEkaterinburgRussia

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