Geodesic
On graphs in which neighborhoods of vertices are strongly regular with parameters (85,14,3,2) or (325,54,3,10)
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 137-143

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J. Koolen posed the problem of studying distance regular graphs in which neighborhoods of vertices are strongly regular graphs with nonprincipal eigenvalue at most $t$ for a given positive integer$t$. This problem was solved earlier for $t=3$. In the case $t=4$, a reduction to graphs in which neighborhoods of vertices have parameters (352,26,0,2), (352,36,0,4), (243,22,1,2), (729,112,1,20), (204,28,2,4), (232,33,2,5), (676,108,2,20), (85,14,3,2), or (325,54,3,10) was obtained. In the present paper, we prove that a distance regular graph in which neighborhoods of vertices are strongly regular with parameters $(85,14,3,2)$ or $(325,54,3,10)$ has intersection array $\{85,70,1;1,14,85\}$ or $\{325,270,1;1,54,325\}$. In addition, we find possible automorphisms of a graph with intersection array $\{85,70,1;1,14,85\}$.
Keywords: strongly regular graph, locally $\mathcal X$-graph, automorphism of a graph. 
M. M. Isakova; A. A. Makhnev; A. A. Tokbaeva. On graphs in which neighborhoods of vertices are strongly regular with parameters (85,14,3,2) or (325,54,3,10). Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 137-143. http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a12/
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