Geodesic
Automorphisms of graph with intersection array $\{289,216,1;1,72,289\}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 603-611 Cet article a éte moissonné depuis la source Math-Net.Ru

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Prime orders automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a distance-regular graph with intersection array $\{289,216,1;1, 72,289\}$. Let nonsolvable automorphism group $G$ acts transitively on the vertex set of distance-regular graph $\Gamma$ with intersection array $\{289,216,1;1, 72,289\}$, $\bar T$ be a socle of $\bar G=G/S(G)$. Then either $\bar T\cong L_2(289)$ and $\Gamma$ is the Mathon graph or $\bar T\cong A_{29}$.
Keywords: distance-regular graph
Mots-clés : automorphism. 
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     title = {Automorphisms of graph with intersection array $\{289,216,1;1,72,289\}$},
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A. A. Makhnev; M. P. Golubyatnikov. Automorphisms of graph with intersection array $\{289,216,1;1,72,289\}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 603-611. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a67/

[1] A.A. Makhnev, M.S. Samoilenko, “On distance-regular covers of cliques with stromgly regular local subgraphs”, Trudy 46 Intern. Yang Conference, Yekaterinburg, 2015, 13–17

[2] Godsil C. D., Hensel A.D, “Distance regular covers of the complete graphs”, J. Comb. Theory Ser. B, 56:2 (1992), 205–238 | DOI | MR | Zbl

[3] M.M. Isakova, A.A. Makhnev, A.A. Tokbaeva, “On Graphs in Which Neighborhoods of Vertices Are Strongly Regular with Parameters $(85,14,3,2)$ or $(325,54,3,10)$”, Proceedings of the Steklov Institute of Mathematics, Suppl. 1, 299 (2017), S68–S74 | MR | Zbl

[4] V.V. Bitkina, A.K. Gutnova, A.A. Makhnev, “On Automorphisms of a Distance-Regular Graph with Intersection Array $\{243,220,1;1,22,243\}$”, Siberian Electronic Mathematical Reports, 13 (2016), 1040–1051 | MR | Zbl

[5] A. M. Kagazezheva, “Automorphisms of a distance-regular graph with intersection array $\{169,126,1;1,42,169\}$”, Siberian Electronic Mathematical Reports, 12 (2015), 318–327 | MR | Zbl

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

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

[8] A.L Gavrilyuk, A.A Makhnev, “On automorphisms of a distance-regular graph with intersection array $\{56,45,1;1,9,56\}$”, Doklady Akademii nauk, 432:5 (2010), 583–587 | MR | Zbl

[9] A.V Zavarnitsine, “Finite simple groups with narrow prime spectrum”, Siberian Electronic Mathematical Reports, 6 (2009), 1–12 | MR | Zbl