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Algebra Logika, 2005, Volume 44, Number 3, Pages 335–354 (Mi al116)  

This article is cited in 2 scientific papers (total in 3 papers)

Automorphisms of Strongly Regular Krein Graphs without Triangles

A. A. Makhnev, V. V. Nosov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

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 $((r^2+3r)^2,r^3+3r^2+r,0,r^2+r)$. 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 $\Gamma=Kre(5)$, $g$ be an element of odd prime order $p$ in $G$, and $\Omega=\operatorname{Fix}(g)$. It is proved that either $\Omega$ is the empty graph and $p=5$, or $\Omega$ is a one-vertex graph and $p=41$, or $\Omega$ is a $2$-clique and $p=17$, or $\Omega$ is the complete bipartite graph $K_{8,8}$, from which the maximal matching is removed, and $p=3$.

Keywords: automorphism, Krein graph, Klebsh graph, Higman – Sims graph, $n$-clique, $n$-coclique

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English version:
Algebra and Logic, 2005, 44:3, 185–196

Bibliographic databases:

UDC: 519.14
Received: 05.01.2004
Revised: 12.01.2005

Citation: A. A. Makhnev, V. V. Nosov, “Automorphisms of Strongly Regular Krein Graphs without Triangles”, Algebra Logika, 44:3 (2005), 335–354; Algebra and Logic, 44:3 (2005), 185–196

Citation in format AMSBIB
\Bibitem{MakNos05}
\by A.~A.~Makhnev, V.~V.~Nosov
\paper Automorphisms of Strongly Regular Krein Graphs without Triangles
\jour Algebra Logika
\yr 2005
\vol 44
\issue 3
\pages 335--354
\mathnet{http://mi.mathnet.ru/al116}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2170690}
\zmath{https://zbmath.org/?q=an:1103.05090}
\transl
\jour Algebra and Logic
\yr 2005
\vol 44
\issue 3
\pages 185--196
\crossref{https://doi.org/10.1007/s10469-005-0019-7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-22344432285}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. L. Gavrilyuk, “Ob avtomorfizmakh silno regulyarnogo grafa s parametrami $(784,116,0,20)$”, Sib. elektron. matem. izv., 5 (2008), 80–87  mathnet  mathscinet
    2. A. A. Makhnev, “On automorphisms of distance-regular graphs”, J. Math. Sci., 166:6 (2010), 733–742  mathnet  crossref  mathscinet  elib
    3. “Makhnev Aleksandr Alekseevich (on his 60th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 1–11  mathnet  crossref  mathscinet
  • Алгебра и логика Algebra and Logic
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