Geodesic
On separated graphs with certain regularity conditions
Sbornik. Mathematics, Tome 187 (1996) no. 10, pp. 1487-1501

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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 $a$. 
@article{SM_1996_187_10_a3,
     author = {V. V. Kabanov and A. A. Makhnev},
     title = {On separated graphs with certain regularity conditions},
     journal = {Sbornik. Mathematics},
     pages = {1487--1501},
     publisher = {mathdoc},
     volume = {187},
     number = {10},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_10_a3/}
}
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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/