Abstract
A strongly regular graph is called a Krein graph if, in one of the Krein conditions, an equality obtains for it. A strongly regular Krein graph Kre(r) without triangles has parameters ((r2 + 3r)2, r3 + 3r2 + r, 0, r2 + r). It is known that Kre(1) is a Klebsh graph, Kre(2) is a Higman-Sims graph, and that a graph of type Kre(3) does not exist. Let G be the automorphism group of a hypothetical graph Γ = Kre(5), g be an element of odd prime order p in G, and Ω = Fix(g). It is proved that either Ω is the empty graph and p = 5, or Ω is a one-vertex graph and p = 41, or Ω is a 2-clique and p = 17, or Ω is the complete bipartite graph K8,8, from which the maximal matching is removed, and p = 3.
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Supported by RFBR grant No. 05-01-00046.
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Translated from Algebra i Logika, Vol. 44, No. 3, pp. 335–354, May–June, 2005.
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Makhnyov, A.A., Nosov, V.V. Automorphisms of Strongly Regular Krein Graphs without Triangles. Algebr Logic 44, 185–196 (2005). https://doi.org/10.1007/s10469-005-0019-7
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DOI: https://doi.org/10.1007/s10469-005-0019-7