Geodesic
A graph with intersection array 18, 15, 1; 1, 5, 18 is not vertex-symmetric
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 62-67 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : graph automorphism. 
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K. S. Efimov. A graph with intersection array 18, 15, 1; 1, 5, 18 is not vertex-symmetric. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 62-67. http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a6/

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