Geodesic
Classification of Ryser Graphs
Matematičeskie zametki, Tome 86 (2009) no. 1, pp. 14-21 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The object of study is $(2,r_1,r_2)$-regular graphs in which the union of the neighborhoods of two different vertices $u$ and $w$ contains $r_1$ or $r_2$ vertices, depending on whether $u$ and $w$ are adjacent. It is proved that such graphs either are strongly regular or decompose into the direct sum of a complete multipartite graph and a clique. Earlier, the case $r_1=r_2$ was studied by other authors.
Mots-clés : Ryser graph, multipartite graph.
Keywords: strongly regular graph, distance-regular graph 
@article{MZM_2009_86_1_a1,
     author = {A. L. Gavrilyuk},
     title = {Classification of {Ryser} {Graphs}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {14--21},
     year = {2009},
     volume = {86},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a1/}
}
TY  - JOUR
AU  - A. L. Gavrilyuk
TI  - Classification of Ryser Graphs
JO  - Matematičeskie zametki
PY  - 2009
SP  - 14
EP  - 21
VL  - 86
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a1/
LA  - ru
ID  - MZM_2009_86_1_a1
ER  - 
%0 Journal Article
%A A. L. Gavrilyuk
%T Classification of Ryser Graphs
%J Matematičeskie zametki
%D 2009
%P 14-21
%V 86
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a1/
%G ru
%F MZM_2009_86_1_a1
A. L. Gavrilyuk. Classification of Ryser Graphs. Matematičeskie zametki, Tome 86 (2009) no. 1, pp. 14-21. http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a1/

[1] A. Khodkar, D. Leach, D. Robinson, “Every $(2,r)$-regular graph is regular”, Util. Math., 73 (2007), 169–172 | MR | Zbl

[2] H. J. Ryser, “A generalization of the Matrix equation $A^2=J$”, Linear Algebra and Appl., 3:4 (1970), 451–460 | DOI | MR | Zbl

[3] E. Bannai, T. Ito, Algebraicheskaya kombinatorika. Skhemy otnoshenii, Mir, M., 1987 | MR | Zbl

[4] C. D. Godsil, J. Shawe-Taylor, “Distance-regularised graphs are distance-regular or distance-biregular”, J. Combin. Theory Ser. B, 43:1 (1987), 14–24 | DOI | MR | Zbl