Geodesic
Automorphisms of distance-regular graph with intersection array $\{25,16,1;1,8,25\}$
Ural mathematical journal, Tome 3 (2017) no. 1, pp. 27-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Makhnev and Samoilenko have found parameters of strongly regular graphs with no more than 1000 vertices, which may be neighborhoods of vertices in antipodal distance-regular graph of diameter 3 and with $\lambda=\mu$. They proposed the program of investigation vertex-symmetric antipodal distance-regular graphs of diameter 3 with $\lambda=\mu$, in which neighborhoods of vertices are strongly regular. In this paper we consider neighborhoods of vertices with parameters $(25,8,3,2)$.
Keywords: Strongly regular graph, Distance-regular graph. 
@article{UMJ_2017_3_1_a1,
     author = {Konstantin S. Efimov and Alexander A. Makhnev},
     title = {Automorphisms of distance-regular graph with intersection array $\{25,16,1;1,8,25\}$},
     journal = {Ural mathematical journal},
     pages = {27--32},
     year = {2017},
     volume = {3},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2017_3_1_a1/}
}
TY  - JOUR
AU  - Konstantin S. Efimov
AU  - Alexander A. Makhnev
TI  - Automorphisms of distance-regular graph with intersection array $\{25,16,1;1,8,25\}$
JO  - Ural mathematical journal
PY  - 2017
SP  - 27
EP  - 32
VL  - 3
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UMJ_2017_3_1_a1/
LA  - en
ID  - UMJ_2017_3_1_a1
ER  - 
%0 Journal Article
%A Konstantin S. Efimov
%A Alexander A. Makhnev
%T Automorphisms of distance-regular graph with intersection array $\{25,16,1;1,8,25\}$
%J Ural mathematical journal
%D 2017
%P 27-32
%V 3
%N 1
%U http://geodesic.mathdoc.fr/item/UMJ_2017_3_1_a1/
%G en
%F UMJ_2017_3_1_a1
Konstantin S. Efimov; Alexander A. Makhnev. Automorphisms of distance-regular graph with intersection array $\{25,16,1;1,8,25\}$. Ural mathematical journal, Tome 3 (2017) no. 1, pp. 27-32. http://geodesic.mathdoc.fr/item/UMJ_2017_3_1_a1/

[1] Makhnev A.A., Samoilenko M.S., “Automorphisms of distance-regular graph with intersection array $\{121,100,1;1,20,121\}$”, Proc. of the 47-th International Youth School-conference (Ekaterinburg, Russia, 2016), S21–S25 | MR

[2] Isakova M.M., Makhnev A.A., Tokbaeva A.A., “Automorphisms of distance-regular graph with intersection array $\{64,42,1;1,21,64\}$”, Intern. Conf. on applied Math. and Physics (Nalchik, 2017), 245—246 | MR

[3] Belousov I.N., “On automorphisms of distance-regular graph with intersection array $\{81,64,1;1,16,81\}$”, Proceedings of Intern. Russian – Chinese Conf. (Nalchik, 2015), 31–32 | MR

[4] Makhnev A.A., Isakova M.M., Tokbaeva A.A., “On graphs in which neighborhoods of vertices are strongly regular with parameters (85,14,3,2) or (325,54,3,10)”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 3, 2016, 137–143 | DOI | MR

[5] Ageev P.S., Makhnev A.A., “On automorphisms of distance-regular graphs with intersection array $\{99,84,1;1,14,99\}$”, Doklady Mathematics, 90:2 (2014), 525–528 | DOI | MR | Zbl

[6] Makhnev A.A., Paduchikh D.V., “Distance-regular graphs, in which neighbourhoods of vertices are strongly regular with the second eigenvalue at most 3”, Doklady Mathematics, 92:2 (2015), S568–S571 | DOI | MR

[7] Brouwer A.E., Cohen A.M., Neumaier A., Distance-Regular Graphs, Springer-Verlag, New York, 1989, 495 pp. | MR | Zbl

[8] Gavrilyuk A.L., Makhnev A.A., “On automorphisms of distance-regular graph with the intersection array $\{56,45,1;1,9,56\}$”, Doklady Mathematics, 81:3 (2010), S439–S442 | DOI | MR

[9] Makhnev A.A., Paduchikh D.V., Tsiovkina L.Y., “Edge-symmetric distance-regular covers of cliques with $\lambda=\mu$”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 2, 2013, 237–246 | MR

[10] Zavarnitsin A.V., “Finite simple groups with narrow prime spectrum”, Siberian electr. Math. Reports, 6 (2009), S1–S12. | MR