Geodesic
On extensions of exceptional strongly regular graphs with eigenvalue 3
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 169-184 Cet article a éte moissonné depuis la source Math-Net.Ru

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The study of distance regular graphs in which neighborhoods of vertices are strongly regular graphs with eigenvalue 3 was initiated in Makhnev's previous works. In particular, he reduced these graphs to graphs in which neighborhoods of vertices are exceptional graphs or pseudogeometric graphs for $pG_{s-3}(s,t)$. Makhnev and Paduchikh found parameters of exceptional graphs (see the Proposition). In the present paper, we study amply regular graphs in which neighborhoods of vertices are exceptional strongly regular graphs with eigenvalue 3 and parameters from conditions 3–6 of the Proposition.
Keywords: graph extensions, strongly regular graphs, amply regular graphs, distance regular graphs. 
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A. A. Makhnev; D. V. Paduchikh. On extensions of exceptional strongly regular graphs with eigenvalue 3. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 169-184. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a16/

[1] Makhnev A. A., “O silno regulyarnykh grafakh s sobstvennym znacheniem 3 i ikh rasshireniyakh”, Dokl. AN, 451:5 (2013), 475–478 | MR

[2] Gutnova A. K., Makhnev A. A., “Vpolne regulyarnye grafy, v kotorykh okrestnosti vershin psevdogeometricheskie grafy dlya $pG_{s-3}(s,t)$”, Dokl. AN, 454:2 (2014), 145–148 | DOI

[3] Makhnev A. A., Paduchikh D. V., “Isklyuchitelnye silno regulyarnye grafy s sobstvennym znacheniem 3”, Dokl. AN, 454:1 (2014), 27–30 | DOI

[4] Koolen J. H., Park J., “Distance-regular graphs with $a_1$ or $c_2$ at least half the valency”, J. Comb. Theory Ser. A, 119 (2012), 546–555 | DOI | MR | Zbl