Geodesic
On Terwilliger Graphs in Which the Neighborhood of Each Vertex is Isomorphic to the Hoffman--Singleton Graph
Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 673-685

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The Hoffman–Singleton graph is the only strongly regular graph with parameters $(50,7,0,1)$. A well-known hypothesis states that a distance-regular graph in which the neighborhood of each vertex is isomorphic to the Hoffman–Singleton graph has intersection array $\{50,42,1;1,2,50\}$ or $\{50,42,9;1,2,42\}$. In the present paper, we prove this hypothesis under the condition that a distance-regular graph is a Terwilliger graph and the graph diameter is at most $5$.
Keywords: distance-regular graph, Terwilliger graph.
Mots-clés : isomorphism 
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     author = {A. L. Gavrilyuk and A. A. Makhnev},
     title = {On {Terwilliger} {Graphs} in {Which} the {Neighborhood} of {Each} {Vertex} is {Isomorphic} to the {Hoffman--Singleton} {Graph}},
     journal = {Matemati\v{c}eskie zametki},
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A. L. Gavrilyuk; A. A. Makhnev. On Terwilliger Graphs in Which the Neighborhood of Each Vertex is Isomorphic to the Hoffman--Singleton Graph. Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 673-685. http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a3/