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This article is cited in 1 scientific paper (total 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.
Received August 27, 2019, published September 17, 2019
Citation:
M. P. Golubyatnikov, “Automorphisms of small graphs with intersection array $\{nm-1, nm-n+m-1,n-m+1;1,1,nm-n+m-1\}$”, Sib. Èlektron. Mat. Izv., 16 (2019), 1245–1253
Linking options:
https://www.mathnet.ru/eng/semr1126 https://www.mathnet.ru/eng/semr/v16/p1245
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