Geodesic
On automorphisms of a distance-regular graph with intersection array $\{27,24,1;1,8,27\}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 689-698.

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 $\{27,24,1;1,8,27\}$. It is shown, that there exists the unique (up to isomorphism) arc-transitive distance-regular graph with intersection array $\{27,24,1;1,8,27\}$. This graph is obtainable by the Cameron construction.
Keywords: distance-regular graph, arc-transitive graph
Mots-clés : automorphism, antipodal cover. 
@article{SEMR_2013_10_a19,
     author = {L. Yu. Tsiovkina},
     title = {On automorphisms of a distance-regular graph with intersection array $\{27,24,1;1,8,27\}$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {689--698},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a19/}
}
TY  - JOUR
AU  - L. Yu. Tsiovkina
TI  - On automorphisms of a distance-regular graph with intersection array $\{27,24,1;1,8,27\}$
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2013
SP  - 689
EP  - 698
VL  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2013_10_a19/
LA  - ru
ID  - SEMR_2013_10_a19
ER  - 
%0 Journal Article
%A L. Yu. Tsiovkina
%T On automorphisms of a distance-regular graph with intersection array $\{27,24,1;1,8,27\}$
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2013
%P 689-698
%V 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2013_10_a19/
%G ru
%F SEMR_2013_10_a19
L. Yu. Tsiovkina. On automorphisms of a distance-regular graph with intersection array $\{27,24,1;1,8,27\}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 689-698. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a19/

[1] Burichenko V. P., Makhnev A. A., “O vpolne regulyarnykh lokalno tsiklicheskikh grafakh”, Sovremennye problemy matematiki, Tezisy 42 Vserossiiskoi molodezhnoi konferentsii, IMM UrO RAN, Ekaterinburg, 2011, 181–183 | MR

[2] Makhnev A. A., Paduchikh D. V., “Ob avtomorfizmakh distantsionno regulyarnogo grafa s massivom peresechenii $ \{24,21,3;1,3,18\}$”, Doklady akademii nauk, 435:3 (2010), 1–4 | MR

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

[4] Cameron P. J., van Lint J. H., Designs, graphs, codes and their links, London Math. Soc. Student Texts, 22, Cambridge University Press, Cambridge, 1991 | MR | Zbl

[5] Cameron P. J., “Covers of graphs and EGQs”, Discrete Math., 97:1–3 (1991), 83–92 | MR | Zbl

[6] Gavrilyuk A. L., Makhnev A. A., “Ob avtomorfizmakh distantsionno regulyarnogo grafa s massivom peresechenii $\{56,45,1;1,9,56\}$”, Doklady akademii nauk, 432:5 (2010), 583–587 | MR | Zbl

[7] Makhnev A. A., Paduchikh D. V., Tsiovkina L. Yu., “Reberno simmetrichnye distantsionno regulyarnye nakrytiya klik: affinnyi sluchai”, Doklady akademii nauk, 449:6 (2013), 639–643 | MR | Zbl

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

[9] Godsil C. D., Liebler R. A., Praeger C. E., “Antipodal distance transitive covers of complete graphs”, Europ. J. Comb., 19:4 (1998), 455–478 | MR | Zbl

[10] Taylor D. E., “Two-graphs and doubly transitive groups”, J. Comb. Theory Ser. A, 61 (1992), 113–122 | MR | Zbl

[11] The GAP Group, 2013 http://www.gap-system.org