|
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.
Received September 6, 2017, published October 19, 2017
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
Linking options:
https://www.mathnet.ru/eng/semr847 https://www.mathnet.ru/eng/semr/v14/p1064
|
|