Geodesic
Amply Regular Graphs with $b_1=6$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 1, pp. 63-77 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The unnoriented graph with $v$ verteces of valency $k$, such that every edge belongs to $\lambda$ triangles, is called an edge regular graph with the parameters $(v,k,\lambda)$. Let $b_1=k-\lambda-1$. In [1] it is proved that a connected edge regular graph with $b_1=1$ is either a polygon or a complete multipart graph all of whose parts have order 2. Edge regular graphs with $b_1\le5$ have been studied in previous work. In the present paper we investigate amply regular graphs with $b_1=6$.
Keywords: amply regular graph, unoriented graph. 
@article{JSFU_2009_2_1_a5,
     author = {Konstantin S. Efimov and Alexander A. Makhnev},
     title = {Amply {Regular} {Graphs} with $b_1=6$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {63--77},
     year = {2009},
     volume = {2},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2009_2_1_a5/}
}
TY  - JOUR
AU  - Konstantin S. Efimov
AU  - Alexander A. Makhnev
TI  - Amply Regular Graphs with $b_1=6$
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2009
SP  - 63
EP  - 77
VL  - 2
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JSFU_2009_2_1_a5/
LA  - ru
ID  - JSFU_2009_2_1_a5
ER  - 
%0 Journal Article
%A Konstantin S. Efimov
%A Alexander A. Makhnev
%T Amply Regular Graphs with $b_1=6$
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2009
%P 63-77
%V 2
%N 1
%U http://geodesic.mathdoc.fr/item/JSFU_2009_2_1_a5/
%G ru
%F JSFU_2009_2_1_a5
Konstantin S. Efimov; Alexander A. Makhnev. Amply Regular Graphs with $b_1=6$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 1, pp. 63-77. http://geodesic.mathdoc.fr/item/JSFU_2009_2_1_a5/

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

[2] A. A. Makhnev, “O silnoi regulyarnosti nekotorykh reberno regulyarnykh grafov”, Izvestiya RAN. Ser. matem., 68:1 (2004), 159–182 | MR | Zbl

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

[4] A. A. Makhnev, D. V. Paduchikh, “Ob odnom klasse koreberno regulyarnykh grafov”, Izvestiya RAN. Ser. matem., 69:6 (2005), 95–114 | MR | Zbl

[5] A. A. Makhnev, D. V. Paduchikh, “Novaya otsenka dlya chisla vershin reberno regulyarnykh grafov”, Sib. matem. zhurn., 48:4 (2007), 817–832 | MR | Zbl

[6] I. N. Belousov, A. A. Makhnev, “O pochti khoroshikh parakh vershin v reberno regulyarnykh grafakh”, Izvestiya Uralskogo gosuniversiteta, 36:7 (2005), 35–48 | MR

[7] A. A. Makhnev, I. M. Minakova, “Ob odnom klasse reberno regulyarnykh grafov”, Izvestiya Gomelskogo gosuniversiteta. Voprosy algebry, 3:16 (2000), 145–154 | Zbl