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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 638–647 (Mi semr1083)  

Discrete mathematics and mathematical cybernetics

On automorphisms of a distance-regular graph with intersection array $\{39,36,22;1,2,18\}$

A. A. Makhneva, M. M. Khamgokovab

a N.N. Krasovsky Institute of Mathematics and Meckhanics, 16, S. Kovalevskoy str., Ekaterinburg, 620990, Russia
b Kabardino-Balkarian State University named after H.M. Berbekov, 175, Chernyshevsky st., Nalchik, 360004, Russia

Abstract: Prime divisors of orders of automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a hypothetical distance-regular graph with intersection array $\{39,36,22;1,2,18\}$. Let $G=Aut(\Gamma)$ is nonsolvable group, $\bar G=G/S(G)$ and $\bar T$ is the socle of $\bar G$. If $\Gamma$ is vertex-symmetric then $\bar T=L\times M$ and $L, M\cong Z_5,A_5,A_6$ or $PSp(4,3)$.

Keywords: distance-regular graph, automorphism.

DOI: https://doi.org/10.33048/semi.2019.16.041

Full text: PDF file (177 kB)
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Bibliographic databases:

UDC: 519.17
MSC: 05C25
Received March 21, 2019, published May 17, 2019

Citation: A. A. Makhnev, M. M. Khamgokova, “On automorphisms of a distance-regular graph with intersection array $\{39,36,22;1,2,18\}$”, Sib. Èlektron. Mat. Izv., 16 (2019), 638–647

Citation in format AMSBIB
\Bibitem{MakKha19}
\by A.~A.~Makhnev, M.~M.~Khamgokova
\paper On automorphisms of a distance-regular graph with intersection array $\{39,36,22;1,2,18\}$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 638--647
\mathnet{http://mi.mathnet.ru/semr1083}
\crossref{https://doi.org/10.33048/semi.2019.16.041}


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