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Strongly regular locally \(GQ(4,t)\)-graphs. (Russian, English) Zbl 1164.05467

Sib. Mat. Zh. 49, No. 1, 161-182 (2008); translation in Sib. Math. J. 49, No. 1, 130-146 (2008).
Summary: Amply regular with parameters \((v, k,\lambda, \mu)\) we call an undirected graph with \(v\) vertices in which the degrees of all vertices are equal to \(k\), every edge belongs to \(\lambda\) triangles, and the intersection of the neighborhoods of every pair of vertices at distance 2 contains exactly \(\mu\) vertices. An amply regular diameter 2 graph is called strongly regular. We prove the nonexistence of amply regular locally \(GQ(4,t)\)-graphs with \((t,\mu) = (4, 10)\) and \((8, 30)\). This reduces the classification problem for strongly regular locally \(GQ(4,t)\)-graphs to studying locally \(GQ(4, 6)\)-graphs with parameters \((726, 125, 28, 20)\).

MSC:

05E30 Association schemes, strongly regular graphs
05B25 Combinatorial aspects of finite geometries
51E12 Generalized quadrangles and generalized polygons in finite geometry
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