Geodesic
Graphs in which neighborhoods of vertices are isomorphic to the Hoffman–Singleton graph
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 143-161
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Connected graphs are studied in which neighborhoods of vertices are isomorphic to the Hoffman—Singleton graph (i.e., the strongly regular graph with parameters (50,7,0,1)). It is proved that a distance-regular graph in which neighborhoods of vertices are isomorphic to the Hoffman—Singleton graph has $\mu=2$.
Keywords: Hoffman-–Singleton graph, distance-regular graph, locally $\mathcal F$-graph. 
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A. A. Makhnev. Graphs in which neighborhoods of vertices are isomorphic to the Hoffman–Singleton graph. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 143-161. http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a13/

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