Geodesic
Automorphisms of Coverings of Strongly Regular Graphs with Parameters (81,20,1,6)
Matematičeskie zametki, Tome 86 (2009) no. 1, pp. 22-36.

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

The possible orders and subgraphs of fixed points of the automorphisms of distance-regular graphs of diameter 4 which are $r$-coverings of a strongly regular graph with parameters (81,20,1,6) for $r\in\{2,3,6\}$ are found. It is proved that, if the automorphism group of a covering of the above type acts transitively on the set of vertices of the graph, then $r=3$.
Keywords: distance-regular graph, intersection array, adjacency maytix, covering of a graph, character of a finite group, Sylow subgroup.
Mots-clés : automorphism group, clique, coclique 
@article{MZM_2009_86_1_a2,
     author = {Guo Wenbin and A. A. Makhnev and D. V. Paduchikh},
     title = {Automorphisms of {Coverings} of {Strongly} {Regular} {Graphs} with {Parameters} (81,20,1,6)},
     journal = {Matemati\v{c}eskie zametki},
     pages = {22--36},
     publisher = {mathdoc},
     volume = {86},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a2/}
}
TY  - JOUR
AU  - Guo Wenbin
AU  - A. A. Makhnev
AU  - D. V. Paduchikh
TI  - Automorphisms of Coverings of Strongly Regular Graphs with Parameters (81,20,1,6)
JO  - Matematičeskie zametki
PY  - 2009
SP  - 22
EP  - 36
VL  - 86
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a2/
LA  - ru
ID  - MZM_2009_86_1_a2
ER  - 
%0 Journal Article
%A Guo Wenbin
%A A. A. Makhnev
%A D. V. Paduchikh
%T Automorphisms of Coverings of Strongly Regular Graphs with Parameters (81,20,1,6)
%J Matematičeskie zametki
%D 2009
%P 22-36
%V 86
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a2/
%G ru
%F MZM_2009_86_1_a2
Guo Wenbin; A. A. Makhnev; D. V. Paduchikh. Automorphisms of Coverings of Strongly Regular Graphs with Parameters (81,20,1,6). Matematičeskie zametki, Tome 86 (2009) no. 1, pp. 22-36. http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a2/

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

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

[3] 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

[4] A. A. Makhnev, V. V. Nosov, “Ob avtomorfizmakh silno regulyarnykh grafov s $\lambda=0$ i $\mu=3$”, Problemy teoreticheskoi i prikladnoi matematiki, Trudy 34-i Regionalnoi molodezhnoi konferentsii, IMM UrO RAN, Ekaterinburg, 2003, 30–33