Automorphisms of a strongly regular graph with parameters $(1197,156,15,21)$
Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 2, pp. 5-11 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let a $3$-$(V,K,\Lambda)$ scheme $\mathscr E=(X,\mathscr B)$ is an extension of a symmetric $2$-scheme. Then either $\mathscr E$ is Hadamard $3$-$(4\Lambda+4,2\Lambda+2,\Lambda)$ scheme, or $V=(\Lambda+1)(\Lambda^2+5\Lambda+5)$ and $K=(\Lambda+1)(\Lambda+2)$, or $V=496$, $K=40$ and $\Lambda=3$. The complementary graph of a block graph of $3$-$(496,40,3)$ scheme is strongly regular with parameters $(6138,1197,156,252)$ and the neighborhoods of its vertices are strongly regular with parameters $(1197,156,15,21)$. In this paper automorphisms of strongly regular graph with parameters $(1197,156,15,21)$ are studied. We yet introduce the structure of automorphism groups of abovementioned graph in vetrex symmetric case.
@article{VMJ_2015_17_2_a0,
     author = {V. V. Bitkina and A. K. Gutnova and A. A. Makhnev},
     title = {Automorphisms of a~strongly regular graph with parameters $(1197,156,15,21)$},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {5--11},
     year = {2015},
     volume = {17},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2015_17_2_a0/}
}
TY  - JOUR
AU  - V. V. Bitkina
AU  - A. K. Gutnova
AU  - A. A. Makhnev
TI  - Automorphisms of a strongly regular graph with parameters $(1197,156,15,21)$
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2015
SP  - 5
EP  - 11
VL  - 17
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMJ_2015_17_2_a0/
LA  - ru
ID  - VMJ_2015_17_2_a0
ER  - 
%0 Journal Article
%A V. V. Bitkina
%A A. K. Gutnova
%A A. A. Makhnev
%T Automorphisms of a strongly regular graph with parameters $(1197,156,15,21)$
%J Vladikavkazskij matematičeskij žurnal
%D 2015
%P 5-11
%V 17
%N 2
%U http://geodesic.mathdoc.fr/item/VMJ_2015_17_2_a0/
%G ru
%F VMJ_2015_17_2_a0
V. V. Bitkina; A. K. Gutnova; A. A. Makhnev. Automorphisms of a strongly regular graph with parameters $(1197,156,15,21)$. Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 2, pp. 5-11. http://geodesic.mathdoc.fr/item/VMJ_2015_17_2_a0/

[1] Cameron P., Van Lint J., Designs, Graphs, Codes and their Links, London Math. Soc. Student Texts, 22, Cambridge Univ. Press, Cambridge, 1981, 240 pp. | MR

[2] Makhnev A. A., “Rasshireniya simmetrichnykh 2-skhem”, Tez. dokl. mezhdunar. konf. “Maltsevskie chteniya”, Novosibirsk, 2015, 112

[3] Brouwer A. E., Haemers W. H., “The Gewirtz graph: an exercize in the theory of graph spectra”, Europ. J. Comb., 14 (1993), 397–407 | DOI | MR | Zbl

[4] Behbahani M., Lam C., “Strongly regular graphs with non-trivial automorphisms”, Discrete Math., 311:2–3 (2011), 132–144 | DOI | MR | Zbl

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

[6] Gavrilyuk A. L., Makhnev A. A., “Ob avtomorfizmakh distantsionno regulyarnogo grafa s massivom peresechenii $\{56,45,1;1,9,56\}$”, Dokl. AN, 432:5 (2010), 512–515

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