Geodesic
On amply regular graphs with $b_1\le5$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 1-11.

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

Regular graph of degree $k$ on $v$ vertices such that any edge is contained exactly in $\lambda$ triangles is called edge-regular graph with parameters $(v,k,\lambda)$. Edge-regular graph $\Gamma$ such that $|\Gamma(u)\cap\Gamma(w)|=\mu$ for any two vertices $u$, $w$ with $d(u,w)=2$ is called amply regular graph with parameters $(v,k,\lambda)$. It is obtained the description of amply regular graphs with $k-\lambda-1\le5$. 
@article{SEMR_2007_4_a0,
     author = {M. S. Nirova},
     title = {On amply regular graphs with $b_1\le5$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1--11},
     publisher = {mathdoc},
     volume = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a0/}
}
TY  - JOUR
AU  - M. S. Nirova
TI  - On amply regular graphs with $b_1\le5$
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2007
SP  - 1
EP  - 11
VL  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2007_4_a0/
LA  - ru
ID  - SEMR_2007_4_a0
ER  - 
%0 Journal Article
%A M. S. Nirova
%T On amply regular graphs with $b_1\le5$
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2007
%P 1-11
%V 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2007_4_a0/
%G ru
%F SEMR_2007_4_a0
M. S. Nirova. On amply regular graphs with $b_1\le5$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 1-11. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a0/

[1] A. A. Makhnev, I. M. Minakova, “Ob odnom klasse reberno regulyarnykh grafov”, Izvestiya Gomelskogo gosuniversiteta, Voprosy algebry, 3 (2000), 145–154 | Zbl

[2] S. R. Zaripov, A. A. Makhnev, I. P. Yablonko, “Reberno regulyarnye grafy diametra 2 s $\lambda\ge 2k/3-2$”, Trudy Ukrainskogo matem. kongressa, Kiev 2001, sektsiya 1: Algebra i teoriya chisel, Institut matematiki NAN Ukrainy, Kiev, 2003, 46–61 | MR

[3] A. A. Makhnev, “O rasshireniyakh chastichnykh geometrii, soderzhaschikh malye $\mu$-podgrafy”, Diskr. analiz i issled. operatsii, 3 (1996), 71–83 | MR | Zbl

[4] A. E. Brouwer, A. M. Cohen, A. Neumaier, Distance-regular graphs, Springer-Verlag, Berlin etc., 1989 | MR

[5] A. A. Makhnev, “O silnoi regulyarnosti nekotorykh reberno regulyarnykh grafov”, Izvestiya RAN, ser. matem., 68 (2004), 159–172 | MR

[6] A. A. Vedenev, A. N. Kuznetsov, A. A. Makhnev, V. V. Nosov, “O khoroshikh parakh v reberno regulyarnykh grafakh”, Diskret. matem., 15 (2003), 77–97 | MR | Zbl

[7] I. N. Belousov, E. I. Gurskii, A. S. Dergach, A. A. Makhnev, “O pochti khoroshikh parakh v reberno regulyarnykh grafakh”, Problemy teor. i priklad. matem., Trudy molodezhnoi konfer. (Ekaterinburg 2004), 9–11 | Zbl

[8] V. V. Kabanov, A. A. Makhnev, “Ob otdelimykh grafakh s nekotorymi usloviyami regulyarnosti”, Matem. sbornik, 187 (1996), 495–503 | MR

[9] I. N. Belousov, A. A. Makhnev, “O pochti khoroshikh parakh vershin v reberno regulyarnykh grafakh”, Izvestiya Ural. gos. un-ta, Ekaterinburg, 2005, no. 7, 35–48 | MR | Zbl

[10] V. I. Kazarina, A. A. Makhnev, “O reberno regulyarnykh grafakh s $b_1=5$”, Algebra, logika i kibernetika, Tez. dokl., Irkutsk, 2004, 159–161

[11] S. A. Vasilev, A. A. Makhnev, “O vpolne regulyarnykh grafakh s $b_1=4$”, Izvestiya Gomelskogo gos. un-ta, Gomel, 2006, 101–108