Geodesic
On separated graphs with certain regularity conditions
Sbornik. Mathematics, Tome 187 (1996) no. 10, pp. 1487-1501 
V. V. Kabanov; A. A. Makhnev. On separated graphs with certain regularity conditions. Sbornik. Mathematics, Tome 187 (1996) no. 10, pp. 1487-1501. http://geodesic.mathdoc.fr/item/SM_1996_187_10_a3/
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_10_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Two theorems are proved in this paper. Theorem I describes the connected $\mu$-regular graphs without 3-claws. Necessary and sufficient conditions for a connected amply regular graph with $\mu >1$ to be separated are obtained in Theorem 2. A graph $\Gamma$ is said to be separated if for any vertex $a$ in $\Gamma$ the subgraph $\Gamma _2(a)$ contains vertices $b$ and $c$ at a distance 2 in $\Gamma _2(a)$, and the $\mu$-subgraph for any such pair does not intersect the neighbourhood of $a$.

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