Geodesic
Extensions of pseudogeometric graphs for~$pG_{s-5}(s,t)$
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 3, pp. 35-42

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J. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue $\leq t$ for a given positive integer $t$. This problem is reduced to the description of distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with non-principal eigenvalue $t$ for $t=1,2,\dots$ In the article by A. K. Gutnova and A. A. Makhnev "Extensions of pseudogeometrical graphs for $pG_{s-4}(s,t)$" the Koolen problem was solved for $t=4$ and for pseudogeometrical neighborhoods of vertices. In the article of A. A. Makhnev “Strongly regular graphs with nonprincipal eigenvalue 5 and its extensions” the Koolen problem for $t=5$ was reduced to the case where the neighborhoods of vertices are exceptional graphs. In this paper intersection arrays for distance-regular graphs whose local subgraphs are exceptional pseudogeometric graphs for $pG_{s-5}(s,t)$. 
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     author = {A. K. Gutnova and A. A. Makhnev},
     title = {Extensions of pseudogeometric graphs for~$pG_{s-5}(s,t)$},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {35--42},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a4/}
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A. K. Gutnova; A. A. Makhnev. Extensions of pseudogeometric graphs for~$pG_{s-5}(s,t)$. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 3, pp. 35-42. http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a4/