Automorphisms of Graphs with Intersection Arrays $\{60,45,8;1,12,50\}$ and~$\{49,36,8;1,6,42\}$
Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 823-831.

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

Automorphisms of distance-regular graphs are considered. It is proved that any graph with the intersection array $\{60,45,8;1,12,50\}$ is not vertex symmetric, and any graph with the intersection array $\{49,36,8;1,6,42\}$ is not edge symmetric.
Keywords: distance regular graph, vertex symmetric graph.
@article{MZM_2017_101_6_a2,
     author = {A. L. Gavrilyuk and A. A. Makhnev},
     title = {Automorphisms of {Graphs} with {Intersection} {Arrays} $\{60,45,8;1,12,50\}$ and~$\{49,36,8;1,6,42\}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {823--831},
     publisher = {mathdoc},
     volume = {101},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a2/}
}
TY  - JOUR
AU  - A. L. Gavrilyuk
AU  - A. A. Makhnev
TI  - Automorphisms of Graphs with Intersection Arrays $\{60,45,8;1,12,50\}$ and~$\{49,36,8;1,6,42\}$
JO  - Matematičeskie zametki
PY  - 2017
SP  - 823
EP  - 831
VL  - 101
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a2/
LA  - ru
ID  - MZM_2017_101_6_a2
ER  - 
%0 Journal Article
%A A. L. Gavrilyuk
%A A. A. Makhnev
%T Automorphisms of Graphs with Intersection Arrays $\{60,45,8;1,12,50\}$ and~$\{49,36,8;1,6,42\}$
%J Matematičeskie zametki
%D 2017
%P 823-831
%V 101
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a2/
%G ru
%F MZM_2017_101_6_a2
A. L. Gavrilyuk; A. A. Makhnev. Automorphisms of Graphs with Intersection Arrays $\{60,45,8;1,12,50\}$ and~$\{49,36,8;1,6,42\}$. Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 823-831. http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a2/

[1] A. E. Brouwer, A. M. Cohen, A. Neumaier, Distance-Regular Graphs, Ergeb. Math. Grenzgeb. (3), 18, Springer-Verlag, Berlin, 1989 | MR | Zbl

[2] P. J. Cameron, J. H. van Lint, Designs, Graphs, Codes and Their Links, London Math. Soc. Stud. Texts, 22, Cambridge Univ. Press, Cambridge, 1991 | MR | Zbl

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

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

[5] A. L. Gavrilyuk, A. A. Makhnev, “Ob avtomorfizmakh distantsionno regulyarnykh grafov s massivom peresechenii $\{56,45,1;1,9,56\}$”, Dokl. AN, 432:5 (2010), 583–587 | MR | Zbl

[6] A. V. Zavarnitsine, “Finite simple groups with narrow prime spectrum”, Sib. Èlektron. Mat. Izv., 6 (2009), 1–12 | MR | Zbl