On automorphisms of distance-regular graphs
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 65-79.

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In this paper, we present a survey of results on automorphisms of distance-regular graphs obtained at the department of algebra and topology of IMM UB RAS in the last five years. Also, we explain the Higman method of application of the character theory to the investigation of automorphisms of distance-regular graphs.
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A. A. Makhnev. On automorphisms of distance-regular graphs. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 65-79. http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a4/

[1] Belousov I. N., “O silno regulyarnykh grafakh s $\mu=1$ i ikh avtomorfizmakh. II”, Tr. IMM UrO RAN, 13, no. 4, 2007, 27–33

[2] Belousov I. N., Makhnev A. A., “O silno regulyarnykh grafakh s $\mu=1$ i ikh avtomorfizmakh”, Dokl. RAN, 410:2 (2006), 151–155 | MR | Zbl

[3] Belousov I. N., Makhnev A. A., “Distantsionno regulyarnyi graf s massivom peresechenii $\{8,7,5;1,1,4\}$ i ego avtomorfizmy”, Tr. IMM UrO RAN, 13, no. 1, 2007, 44–56 | MR

[4] Belousov I. N., Makhnev A. A., “Ob avtomorfizmakh obobschënnogo vosmiugolnika poryadka $(2,4)$”, Dokl. RAN, 423:2 (2008), 151–154 | MR | Zbl

[5] Gavrilyuk A. L., “Ob avtomorfizmakh silno regulyarnogo grafa s parametrami $(784,116,0,20)$”, Sib. elektron. mat. izv., 2008, no. 5, 80–87 | MR | Zbl

[6] Gavrilyuk A. L., Go Venbin, Makhnev A. A., “Ob avtomorfizmakh grafov Tervilligera s $\mu=2$”, Algebra i logika, 47:5 (2008), 584–600 | MR | Zbl

[7] Gavrilyuk A. L., Makhnev A. A., “O grafakh Kreina bez treugolnikov”, Dokl. RAN, 403:6 (2005), 727–730 | MR | Zbl

[8] Gavrilyuk A. L., Makhnev A. A., “Vpolne regulyarnye grafy i blok-skhemy”, Sib. mat. zhurn., 47:4 (2006), 753–768 | MR | Zbl

[9] Gavrilyuk A. L., Makhnev A. A., “Ob avtomorfizmakh distantsionno regulyarnogo grafa s massivom peresechenii $\{60,45,8;1,12,50\}$”, Tr. IMM UrO RAN, 13, no. 3, 2007, 41–53

[10] Kabanov V. V., Tkachëva (Minakova) I. M., “Ob avtomorfizmakh grafov s parametrami $(115,18,1,3)$”, Tr. 35-i region. molod. konf., UrO RAN, Ekaterinburg, 2004, 30–32

[11] Kazarina V. I., Makhnev A. A., “Ob avtomorfizmakh silno regulyarnykh grafov s $\lambda=2$ i $\mu=3$”, Vestn. UGTU, 2005, no. 17(69), 174–194 | MR

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

[13] Makhnev A. A., Nirova M. S., “Uzkie chastichnye chetyrëkhugolniki i ikh avtomorfizmy”, Algebra i logika, 45:5 (2006), 603–619 | MR | Zbl

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

[15] Makhnev A. A., Nosov V. V., “Ob avtomorfizmakh grafov s $\lambda=0$, $\mu=3$”, Mezhdunar. algebr. konf. “Klassy grupp i algebr”, Tez. dokl., Izd-vo Gomelskogo un-ta, Gomel, 2005, 78–79

[16] Makhnev A. A., Nosov V. V., “Ob avtomorfizmakh silno regulyarnykh grafov Kreina bez treugolnikov”, Algebra i logika, 44:3 (2005), 335–354 | MR | Zbl

[17] Makhnev A. A., Paduchikh D. V., “Avtomorfizmy nakrytii silno regulyarnogo grafa s parametrami $(81,20,1,6)$”, Dokl. RAN, 423:1 (2008), 25–28 | MR | Zbl

[18] Makhnev A. A., Paduchikh D. V., “O nakrytiyakh grafa Khigmena–Simsa i ikh avtomorfizmakh”, Dokl. RAN, 422:1 (2008), 26–29 | MR | Zbl

[19] Makhnev A. A., Paduchikh D. V., “O gruppe avtomorfizmov grafa Ashbakhera”, Dokl. RAN, 426:3 (2009), 310–313 | MR | Zbl

[20] Nosov V. V., “Ob avtomorfizmakh grafa s parametrami $(704,37,0,2)$”, Problemy teoreticheskoi i prikladnoi matematiki, Tr. 36-i region. molod. konf., UrO RAN, Ekaterinburg, 2005, 55–60

[21] Paduchikh D. V., “Ob avtomorfizmakh silno regulyarnogo grafa s parametrami $(85,14,3,2)$”, Mezhdunar. algebr. konf. “Klassy grupp i algebr”, Tez. dokl., Izd-vo Gomelskogo un-ta, Gomel, 2005, 85–87

[22] Tkachëva (Minakova) I. M., “Ob avtomorfizmakh grafov s parametrami $(243,22,1,2)$”, Tr. 35-i region. molod. konf., UrO RAN, Ekaterinburg, 2004, 51–59

[23] Aschbacher M., “The nonexistence of rank three permutation groups of degree 3250 and subdegree 57”, J. Algebra, 19:3 (1971), 538–540 | DOI | MR | Zbl

[24] Brouwer A. E., Cohen A. M., Neumaier A., Distance-Regular Graphs, Springer, Berlin, 1989 | MR | Zbl

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

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

[27] Cooolsaet K., Degraer R., Spence E., “The strongly regular $(45,12,3,3)$ graphs”, Electron. J. Combin., 13:R32 (2006), 1–9 | MR