Geodesic
The impact of 2-neighborhoods on graph structure
Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 892-897.

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Connected regular graphs of diameter greater than 2 with 2-neighborhoods isomorphic to a certain graph $\Delta$ of diameter 2 are studied. Regular graphs of diameter 2 with 2-neighborhoods isomorphic to the distance-regular graph $\Delta$ of diameter 3 are also studied. It is prowed that 2-locally Schrikhande graphs do not exist. 
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     author = {D. V. Paduchikh},
     title = {The impact of 2-neighborhoods on graph structure},
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D. V. Paduchikh. The impact of 2-neighborhoods on graph structure. Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 892-897. http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a9/

[1] Brouwer A. E., Cohen A. M., Neumaier A., Distance-Regular Graphs, Springer, Berlin, 1989

[2] Kabanov V. V., Makhnev A. A., “Koreberno regulyarnye grafy bez 3-lap”, Matem. zametki, 60:4 (1996), 495–503 | MR | Zbl