K.S. Efimov. Automorphisms of an AT4(4,4,2)-graph and of the corresponding strongly regular graphs ... P. 119-127

A.A. Makhnev, D.V. Paduchikh, and M.M. Khamgokova gave a classification of distance-regular locally $GQ(5,3)$-graphs. In particular, there arises an $AT4(4,4,2)$-graph with intersection array $\{96,75,16,1;1,16,75,96\}$ on $644$ vertices. The same authors proved that an $AT4(4,4,2)$-graph is not a locally $GQ(5,3)$-graph. However, the existence of an $AT4(4,4,2)$-graph that is a locally pseudo $GQ(5,3)$-graph is unknown. The antipodal quotient of an $AT4(4,4,2)$-graph is a strongly regular graph with parameters $(322,96,20,32)$. These two graphs are locally pseudo $GQ(5,3)$-graphs. We find their possible automorphisms. It turns out that the automorphism group of a distance-regular graph with intersection array $\{96,75,16,1;1,16,75,96\}$ acts intransitively on the set of its antipodal classes.

Keywords: distance-regular graph, graph automorphism.

The paper was received by the Editorial Office on September 1, 2017

Konstantin Sergeevich Yefimov, Cand. Sci. (Phys.-Math.), Ural Federal University, Yekaterinburg, 620002 Russia;
Ural State University of Economics, 620144 Russia;
Krasovskii Institute of Mathematics and Mechanics,
Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990 Russia;
e-mail: konstantin.s.efimov@gmail.com

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