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This article is cited in 1 scientific paper (total in 1 paper)
Discrete mathematics and mathematical cybernetics
Automorphisms of graph with intersection array $\{289,216,1;1,72,289\}$
A. A. Makhnevab, M. P. Golubyatnikovb a Krasovskii Institute of Mathematics and Mechanics,
16 S.Kovalevskaya Str.,
620990, Yekaterinburg, Russia
b 620990, Yekaterinburg, Russia,
Ural Federal University
Abstract:
Prime orders automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a distance-regular graph with intersection array $\{289,216,1;1, 72,289\}$. Let nonsolvable automorphism group $G$ acts transitively on the vertex set of distance-regular graph $\Gamma$ with intersection array $\{289,216,1;1, 72,289\}$, $\bar T$ be a socle of $\bar G=G/S(G)$. Then either $\bar T\cong L_2(289)$ and $\Gamma$ is the Mathon graph or $\bar T\cong A_{29}$.
Keywords:
distance-regular graph, automorphism.
Received April 10, 2018, published May 18, 2018
Citation:
A. A. Makhnev, M. P. Golubyatnikov, “Automorphisms of graph with intersection array $\{289,216,1;1,72,289\}$”, Sib. Èlektron. Mat. Izv., 15 (2018), 603–611
Linking options:
https://www.mathnet.ru/eng/semr939 https://www.mathnet.ru/eng/semr/v15/p603
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