Geodesic
On automorphisms of a distance-regular graph with intersection array $\{44,30,5;1,3,40\}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 777-785.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\{44,30,5;1,3,40\}$. Let $G={\rm Aut}(\Gamma)$ is nonsolvable group. If $\Gamma$ is arc-transitive then $G$ is is an extension of some group $P$ by $PGL_2(11)$, $|P:O_3(P)|=2$, $|G_a:P_a|=11$ and $|P:P_a|=9$.
Keywords: distance-regular graph
Mots-clés : automorphism. 
@article{SEMR_2019_16_a68,
     author = {A. A. Makhnev and V. V. Bitkina},
     title = {On automorphisms of a distance-regular graph with intersection array $\{44,30,5;1,3,40\}$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {777--785},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a68/}
}
TY  - JOUR
AU  - A. A. Makhnev
AU  - V. V. Bitkina
TI  - On automorphisms of a distance-regular graph with intersection array $\{44,30,5;1,3,40\}$
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 777
EP  - 785
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a68/
LA  - ru
ID  - SEMR_2019_16_a68
ER  - 
%0 Journal Article
%A A. A. Makhnev
%A V. V. Bitkina
%T On automorphisms of a distance-regular graph with intersection array $\{44,30,5;1,3,40\}$
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 777-785
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a68/
%G ru
%F SEMR_2019_16_a68
A. A. Makhnev; V. V. Bitkina. On automorphisms of a distance-regular graph with intersection array $\{44,30,5;1,3,40\}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 777-785. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a68/

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

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

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

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

[5] 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

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