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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2017, Volume 14, Pages 1064–1077
DOI: https://doi.org/10.17377/semi.2017.14.090
(Mi semr847)
 

Mathematical logic, algebra and number theory

Automorphisms of graph with intersection array $\{64,42,1;1,21,64\}$

A. A. Makhnevab, M. P. Golubyatnikovb

a Krasovskii Institute of Mathematics and Mechanics, 16 S.Kovalevskaya Str. 620990, Yekaterinburg, Russia
b Ural Federal University, 620990, Yekaterinburg, Russia
References:
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 $\{63,60,1; 1,4, 63\}$. Let $G={\rm Aut}(\Gamma)$, $\bar G=G/S(G)$, $\bar T$ is the socle of $\bar G$. If $\Gamma$ is vertex-symmetric then the possible structure of $G$ is determined. In the case $\bar T\cong U_3(3)$ graph exist and is arc-transitive.
Keywords: distance-regular graph, automorphism.
Received September 6, 2017, published October 19, 2017
Bibliographic databases:
Document Type: Article
UDC: 519.17+512.54
MSC: 05C25
Language: Russian
Citation: A. A. Makhnev, M. P. Golubyatnikov, “Automorphisms of graph with intersection array $\{64,42,1;1,21,64\}$”, Sib. Èlektron. Mat. Izv., 14 (2017), 1064–1077
Citation in format AMSBIB
\Bibitem{MakGol17}
\by A.~A.~Makhnev, M.~P.~Golubyatnikov
\paper Automorphisms of graph with intersection array $\{64,42,1;1,21,64\}$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 1064--1077
\mathnet{http://mi.mathnet.ru/semr847}
\crossref{https://doi.org/10.17377/semi.2017.14.090}
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