K.S. Efimov. A graph with intersection array {18, 15, 1; 1, 5, 18} is not vertex-symmetric

A.A. Makhnev and V.P. Burichenko found possible intersection arrays of distance-regular locally cyclic graphs with at most 1000 vertices. They proposed a program for studying arc-transitive graphs with these intersection arrays. The neighborhood of a vertex in such a graph is the union of isolated polygons. We study automorphisms of a hypothetical distance-regular graph with intersection array {18, 15, 1; 1, 5, 18}. In particular, we prove that the automorphism group of this graph acts intransitively on the vertex set.

Keywords: distance-regular graph, graph automorphism

The paper was received by the Editorial Office on June 26, 2018.

Funding Agency: This work was supported by the Russian Science Foundation (project no. 14-11-00061-П).

Konstantin Sergeevich Efimov, Cand. Sci. (Phys.-Math.), Ural Federal University, Yekaterinburg, 620002 Russia; Ural State University of Economics, Yekaterinburg, 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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