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GQ(4, 2)-extensions, strongly regular case

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Abstract

A strongly regular locallyGQ(4, 2)-graph is a graph with parameters either (126, 45, 12, 8) or (190, 45, 12, 10). The existence and the uniqueness of the corresponding locallyGQ(4, 2)-graph in the first case are well known. We prove that theGQ(4, 2)-hyperoval on ten vertices either is the Petersen graph, or is the Möbius 5-prism, or consists of two (2, 3)-subgraphs connected by three edges. We obtain homogeneousGQ(4, 2)-solutions with a strongly regular point graph; in particular, this implies the negative answer to the question of F. Buekenhout concerning the existence of a locallyGQ(4, 2)-graph with the parameters (190, 45, 12, 10).

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, USSR

    A. A. Makhnev

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  1. A. A. Makhnev
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Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 113–119, July, 2000.

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Makhnev, A.A. GQ(4, 2)-extensions, strongly regular case. Math Notes 68, 97–102 (2000). https://doi.org/10.1007/BF02674651

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  • DOI: https://doi.org/10.1007/BF02674651

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