Geodesic
Amply regular graphs with Hoffman's condition
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 127-131 
V. V. Kabanov; S. V. Unegov. Amply regular graphs with Hoffman's condition. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 127-131. http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a10/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is known that, if the minimal eigenvalue of a graph is $-2$, then the graph satisfies Hoffman's condition: for any generated complete bipartite subgraph $K_{1,3}$ (a 3-claw) with parts $\{p\}$ and $\{q_1, q_2,q_3\}$, any vertex distinct from $p$ and adjacent to the vertices $q_1$ and $q_2$ is adjacent to $p$ but not adjacent to $q_3$. We prove the converse statement for amply regular graphs containing a 3-claw and satisfying the condition $\mu>1$.

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