A distance-regular graph with the intersection array $\{8,7,5;1,1,4\}$ and its automorphisms
Trudy Instituta matematiki i mehaniki, Группы и графы, Tome 13 (2007) no. 1, pp. 44-56 Cet article a éte moissonné depuis la source Math-Net.Ru

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Possible orders and subgraphs of the fixed points of a distance-regular graph with the intersection array $\{8,7,5;1,1,4\}$ are found. It is shown that such a graph is not vertex-transitive.
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I. N. Belousov; A. A. Makhnev. A distance-regular graph with the intersection array $\{8,7,5;1,1,4\}$ and its automorphisms. Trudy Instituta matematiki i mehaniki, Группы и графы, Tome 13 (2007) no. 1, pp. 44-56. http://geodesic.mathdoc.fr/item/TIMM_2007_13_1_a2/

[1] Cameron P. J., Permutation groups, London Math. Soc. Student Texts, 45, Cambridge University Press, Cambridge, 1999 | MR | Zbl

[2] Makhnev A. A., Paduchikh D. V., “Ob avtomorfizmakh grafa Ashbakhera”, Algebra i logika, 40:2 (2001), 125–134 | MR | Zbl

[3] Makhnev A. A., Nosov V. V., “Ob avtomorfizmakh silno regulyarnykh grafov s $\lambda=0$, $\mu=2$”, Mat. sbornik, 195:3 (2004), 47–68 | MR | Zbl

[4] Makhnev A. A., Minakova I. M., “Ob avtomorfizmakh grafov s $\lambda=0$, $\mu=2$”, Diskret. matematika, 16:1 (2004), 95–104 | MR | Zbl

[5] Brouwer A. E., Cohen A. M., Neumaier A., Distance-regular graphs, Springer-Verlag, Berlin–New York–Heidelberg, 1989 | MR

[6] Cameron P. J., Lint J. van, Graphs, Codes and Designs, London Math. Soc. Student Texts, 22, Cambridge University Press, Cambridge, 1991 | MR | Zbl

[7] Kondratev A. S., Mazurov V. D., “Raspoznavanie znakoperemennykh grupp prostoi stepeni po poryadkam ikh elementov”, Sib. mat. zhurn., 41:2 (2000), 359–369 | MR

[8] Walter J., “The characterization of finite groups with abelian Sylow 2-subgroups”, Ann. Math., 89 (1969), 405–514 | DOI | MR | Zbl

[9] Bombieri E., “Thompson's problem ($\sigma^2=3$)”, Invent. Math., 58 (1980), 77–100 | DOI | MR | Zbl

[10] Gorenstein D., Walter J., “The characterization of finite groups with dihedral Sylow 2-subgroups, I–IV”, Ill. J. Math., 6 (1962), 553–593 ; J. Algebra, 2 (1965), 85–151 ; 218–270 ; 354–393 | MR | Zbl | DOI | MR | Zbl | MR | MR | Zbl