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

Sib. Èlektron. Mat. Izv., 2019 Volume 16, Pages 1245–1253 (Mi semr1126)

This article is cited in 1 paper

Discrete mathematics and mathematical cybernetics

Automorphisms of small graphs with intersection array $\{nm-1, nm-n+m-1,n-m+1;1,1,nm-n+m-1\}$

M. P. Golubyatnikov

Krasovskii Institute of Mathematics and Mechanics, 16, S.Kovalevskaya str. Yekaterinburg, 620990, Russia.

Abstract: Let $\Gamma$ be a distance regular graph of diameter 3 for which the graph $\Gamma_3$ is a pseudo-network.
Previously, A.A. Makhnev, M.P. Golubyatnikov, Wenbin Guo found infinite series of admissible arrays of intersections of such graphs. In the case of $c_2 = 1$, we have the two-parameter series $\{nm-1,nm-n+m-1,n-m+1;1,1,nm-n+m-1\}$.
Possible automorphisms of such graphs were found by A.A. Makhnev, M.P. Golubyatnikov.
In this paper the author found automorphism groups of distance regular graphs with intersection arrays $\{90,84,7;1,1,84\}$ ($n=13,m=7$), $\{220,216,5;1,1,216\}$ ($n=17,m=13$), $\{272,264,9;1,1,264\}$ ($n=21,m=13$). In particular, this graphs are not arc transitive.

Keywords: distance-regular graph, automorphism.

UDC: 519.17+512.54

MSC: 05C25

Received August 27, 2019, published September 17, 2019

DOI: 10.33048/semi.2019.16.086



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