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Diskr. Mat., 2004, Volume 16, Issue 1, Pages 95–104 (Mi dm144)  

This article is cited in 10 scientific papers (total in 11 papers)

On automorphisms of strongly regular graphs with the parameters $\lambda=1$ and $\mu=2$

A. A. Makhnev, I. M. Minakova


Abstract: Let $\Gamma$ be a strongly regular graph with parameters $(v,k,1,2)$. Then $k=u^2+u+2$ and $u=1,3,4,10$, or $31$. It is known that such graphs exist for $u$ equal to $1$ and $4$. They are the $(3\times 3)$-lattice and the graph of cosets of the ternary Golay code. If $u=3$, then $\Gamma$ has the parameters $(99,14,1,2)$. The question on existence of such graphs was posed by J. Seidel.
With the use of theory of characters of finite groups we find the possible orders and the structures of subgraphs of the fixed points of automorphisms of the graph $\Gamma$ with parameters $(99,14,1,2)$. It is proved that if the group $\operatorname{Aut}(\Gamma)$ contains an involution, then its order divides $42$.
This research was supported by the Russian Foundation for Basic Research, grant 02–01–00722.

DOI: https://doi.org/10.4213/dm144

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English version:
Discrete Mathematics and Applications, 2004, 14:2, 201–210

Bibliographic databases:

UDC: 519.14
Received: 18.12.2002

Citation: A. A. Makhnev, I. M. Minakova, “On automorphisms of strongly regular graphs with the parameters $\lambda=1$ and $\mu=2$”, Diskr. Mat., 16:1 (2004), 95–104; Discrete Math. Appl., 14:2 (2004), 201–210

Citation in format AMSBIB
\Bibitem{MakMin04}
\by A.~A.~Makhnev, I.~M.~Minakova
\paper On automorphisms of strongly regular graphs with the parameters $\lambda=1$ and $\mu=2$
\jour Diskr. Mat.
\yr 2004
\vol 16
\issue 1
\pages 95--104
\mathnet{http://mi.mathnet.ru/dm144}
\crossref{https://doi.org/10.4213/dm144}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2069991}
\zmath{https://zbmath.org/?q=an:1050.05118}
\transl
\jour Discrete Math. Appl.
\yr 2004
\vol 14
\issue 2
\pages 201--210
\crossref{https://doi.org/10.1515/156939204872374}


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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. A. Makhnev, M. S. Nirova, “Slender partial quadrangles and their automorphisms”, Algebra and Logic, 45:5 (2006), 344–352  mathnet  crossref  mathscinet  zmath
    2. V. I. Kazarina, “Ob avtomorfizmakh silno regulyarnykh grafov s $\lambda=2$ i $\mu=3$, II”, Sib. elektron. matem. izv., 3 (2006), 1–14  mathnet  mathscinet  zmath
    3. I. N. Belousov, A. A. Makhnev, “A distance-regular graph with the intersection array $\{8,7,5;1,1,4\}$ and its automorphisms”, Proc. Steklov Inst. Math. (Suppl.), 257, suppl. 1 (2007), S47–S60  mathnet  crossref  mathscinet  elib
    4. I. N. Belousov, A. A. Makhnev, “On Automorphisms of a Generalized Octagon of Order $(2,4)$”, Math. Notes, 84:4 (2008), 483–492  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. D. V. Paduchikh, “On the automorphisms of the strongly regular graph with parameters $(85, 14, 3, 2)$”, Discrete Math. Appl., 19:1 (2009), 89–111  mathnet  crossref  crossref  mathscinet  elib
    6. I. N. Belousov, A. A. Makhnev, “Оn automorphisms of the generalized hexagon of order (3,27)”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S33–S43  mathnet  crossref  isi  elib
    7. A. A. Makhnev, “On automorphisms of distance-regular graphs”, J. Math. Sci., 166:6 (2010), 733–742  mathnet  crossref  mathscinet  elib
    8. “Makhnev Aleksandr Alekseevich (on his 60th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 1–11  mathnet  crossref  mathscinet
    9. I. N. Belousov, “On automorphisms of a distance-regular graph with intersection array $\{99,84,1;1,12,99\}$”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 19–26  mathnet  crossref  crossref  mathscinet  isi  elib
    10. V. V. Nosov, “Ob avtomorfizmakh silno regulyarnogo grafa s parametrami $(1276,50,0,2)$”, Chebyshevskii sb., 17:3 (2016), 178–185  mathnet  elib
    11. K. S. Efimov, A. A. Makhnev, “On automorphisms of a distance-regular graph with intersection array $\{99,84,30;1,6,54\}$”, Discrete Math. Appl., 28:1 (2018), 23–27  mathnet  crossref  crossref  isi  elib
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