Geodesic
On automorphisms of a distance-regular graph with intersection array $\{39,36,22;1,2,18\}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 638-647.

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Prime divisors of orders of automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a hypothetical distance-regular graph with intersection array $\{39,36,22;1,2,18\}$. Let $G={\rm Aut}(\Gamma)$ is nonsolvable group, $\bar G=G/S(G)$ and $\bar T$ is the socle of $\bar G$. If $\Gamma$ is vertex-symmetric then $\bar T=L\times M$ and $L, M\cong Z_5,A_5,A_6$ or $PSp(4,3)$.
Keywords: distance-regular graph
Mots-clés : automorphism. 
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     title = {On automorphisms of a distance-regular graph with intersection array  $\{39,36,22;1,2,18\}$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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A. A. Makhnev; M. M. Khamgokova. On automorphisms of a distance-regular graph with intersection array  $\{39,36,22;1,2,18\}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 638-647. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a67/

[1] A.E. Brouwer, A.M. Cohen, A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin–Heidelberg–New York, 1989 | MR | Zbl

[2] A. Jurišić, J. Vidali, “Extremal 1-codes in distance-regular graphs of diameter 3”, Des. Codes Cryptogr., 65 (2012), 29–47 | DOI | MR | Zbl

[3] A.A. Makhnev, M.S. Nirova, “On distance-regular graphs with $\lambda=2$”, Jornal of Siberian Federal Univ., 7:2 (2014), 188–194 | MR

[4] M. Behbahani, C. Lam, “Strongly regular graphs with nontrivial automorphisms”, Discrete Math., 311:2–3 (2011), 132–144 | DOI | MR | Zbl

[5] P.J. Cameron, Permutation Groups, London Math. Soc. Student Texts, 45, Cambridge Univ. Press, Cambridge, 1999 | MR | Zbl

[6] A.L. Gavrilyuk, A.A. Makhnev, “On automorphisms of distance-regular graphs with intersection array $\{56, 45, 1; 1, 9, 56\}$”, Doklady Mathematics, 81:3 (2010), 439–442 | DOI | MR | Zbl

[7] A.V. Zavarnitsine, “Finite simple groups with narrow prime spectrum”, Sibirean Electr. Math. Reports, 6 (2009), 1–12 | MR | Zbl