Geodesic
Strongly regular graphs with Hoffman's condition
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 3, pp. 54-60

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It is known that if the minimal eigenvalue of a graph is $-2$, then the graph satisfies Hoffman's condition; i.e., for any generated complete bipartite subgraph $K_{1,3}$ with parts $\{p\}$ and $\{q_1,q_2,q_3\}$, any vertex distinct from $p$ and adjacent to two vertices from the second part is not adjacent to the third vertex and is adjacent to $p$. We prove the converse statement, formulated for strongly regular graphs containing a 3-claw and satisfying the condition $gm>1$. 
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     author = {V. V. Kabanov and S. V. Unegov},
     title = {Strongly regular graphs with {Hoffman's} condition},
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     year = {2007},
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V. V. Kabanov; S. V. Unegov. Strongly regular graphs with Hoffman's condition. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 3, pp. 54-60. http://geodesic.mathdoc.fr/item/TIMM_2007_13_3_a4/