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Discrete mathematics and mathematical cybernetics
On automorphisms of a distance-regular graph with intersection array $\{44,30,5;1,3,40\}$
A. A. Makhnevab, V. V. Bitkinac a N.N. Krasovsky Institute of Mathematics and Meckhanics, 16, S. Kovalevskoy str., Ekaterinburg, 620990, Russia
b Ural Federal University named after the first President of Russia B.N.Yeltsin, 19, Mira str., Ekaterinburg, 620002, Russia
c North Ossetian State University after Kosta Levanovich Khetagurov, 46, Vatutina stк., Vladikavkaz, 362025, 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 $\{44,30,5;1,3,40\}$. Let $G={\rm Aut}(\Gamma)$ is nonsolvable group. If $\Gamma$ is arc-transitive then $G$ is is an extension of some group $P$ by $PGL_2(11)$, $|P:O_3(P)|=2$, $|G_a:P_a|=11$ and $|P:P_a|=9$.
Keywords:
distance-regular graph, automorphism.
Received April 11, 2019, published June 8, 2019
Citation:
A. A. Makhnev, V. V. Bitkina, “On automorphisms of a distance-regular graph with intersection array $\{44,30,5;1,3,40\}$”, Sib. Èlektron. Mat. Izv., 16 (2019), 777–785
Linking options:
https://www.mathnet.ru/eng/semr1094 https://www.mathnet.ru/eng/semr/v16/p777
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Abstract page: | 286 | Full-text PDF : | 172 | References: | 39 |
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