Makhnev, A. A. 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 \((726, 125, 28, 20)\). Cited in 1 Document MSC: 05E30 Association schemes, strongly regular graphs 05B25 Combinatorial aspects of finite geometries 51E12 Generalized quadrangles and generalized polygons in finite geometry Keywords:strongly regular graph; generalized quadrangle; hyperoval PDFBibTeX XMLCite \textit{A. A. Makhnev}, Sib. Mat. Zh. 49, No. 1, 161--182 (2008; Zbl 1164.05467); translation in Sib. Math. J. 49, No. 1, 130--146 (2008) Full Text: EuDML EMIS