Strongly regular locally <Emphasis Type="Italic">GQ</Emphasis>(4,<Emphasis Type="Italic">t</Emphasis>)-graphs |
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Authors: | A A Makhnev |
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Institution: | (1) Institute of Mathematics and Mechanics, Ekaterinburg, Russia |
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Abstract: | Amply regular with parameters (v, k, λ, μ) we call an undirected graph with v vertices in which the degrees of all vertices are equal to k, every edge belongs to λ triangles, and the intersection of the neighborhoods of every pair of vertices at distance 2 contains exactly μ 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,μ) = (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). |
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Keywords: | strongly regular graph generalized quadrangle hyperoval |
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