Geodesic
Classification of Ryser Graphs
Matematičeskie zametki, Tome 86 (2009) no. 1, pp. 14-21

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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},
     publisher = {mathdoc},
     volume = {86},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a1/}
}
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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/