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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2017 Volume 14, Pages 1064–1077 (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

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.

UDC: 519.17+512.54

MSC: 05C25

Received September 6, 2017, published October 19, 2017

DOI: 10.17377/semi.2017.14.090



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