Geodesic
Automorphism groups of small distance-regular graphs
Algebra i logika, Tome 56 (2017) no. 4, pp. 395-405

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We consider undirected graphs without loops and multiple edges. Previously, V. P. Burichenko and A. A. Makhnev [Modern Problems in Mathematics: Proc. 42nd All-Russian School–Conference of Young Scientists, Yekaterinburg, Institute of Mathematics and Mechanics, UB RAS, 2011, 181–183] found intersection arrays of distance-regular locally cyclic graphs with the number of vertices at most 1000. It is shown that the automorphism group of a graph with intersection array $\{15,12,1;1,2,15\}$, $\{35,32,1;1,2,35\}$, $\{39,36,1;1,2,39\}$ or $\{42,39,1;1,3,42\}$ (such a graph enters the above-mentioned list) acts intransitively on the set of its vertices.
Keywords: distance-regular graph, locally cyclic graph, intersection array
Mots-clés : automorphism group. 
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     author = {I. N. Belousov and A. A. Makhnev},
     title = {Automorphism groups of small distance-regular graphs},
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     pages = {395--405},
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     volume = {56},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_4_a0/}
}
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I. N. Belousov; A. A. Makhnev. Automorphism groups of small distance-regular graphs. Algebra i logika, Tome 56 (2017) no. 4, pp. 395-405. http://geodesic.mathdoc.fr/item/AL_2017_56_4_a0/