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

Sib. Èlektron. Mat. Izv., 2016 Volume 13, Pages 972–986 (Mi semr727)

Mathematical logic, algebra and number theory

Automorphisms of distance-regular graph with intersection array $\{117,80,18,1;1,18,80,117\}$

A. A. Makhnevab, D. V. Paduchikha, M. M. Khamgokovac

a Krasovskii Institute of Mathematics and Mechanics, ul. S.Kovalevskoi, 16, 620990, Ekaterinburg, Russia
b Uralskii Federalnii Universitet, ul. Mira, 19, 620002, Ekaterinburg, Russia
c Kabardino-Balkarskii University, ul. Mira, 16, 360000, Nalchik, Russia

Abstract: Distance-regular graph $\Gamma$ with intersection array $\{117, 80, 18, 1; 1, 18, 80, 117\}$ is an $AT4$-graph. Antipodal quotient $\bar \Gamma$ has parameters $(378, 117, 36, 36)$. Both graphs have strongly regular neighbourhoods with parameters $(117, 36, 15, 9)$. In the work automorphisms of the said graphs are found. In particular, there exist graphs of rank 3 with parameters $(117, 36, 15, 9)$ and $(378, 117, 36, 36)$, and graph with intersection array $\{117, 80, 18, 1; 1, 18, 80, 117\}$ is not arc-transitive.

Keywords: strongly regular graph, eigenvalue, automorphism of graph.

UDC: 519.17

MSC: 20C25

Received July 25, 2016, published November 8, 2016

Language: English

DOI: 10.17377/semi.2016.13.078



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© Steklov Math. Inst. of RAS, 2025