On separated graphs with certain regularity conditions

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 $a$.