2017
Том 69
№ 9

All Issues

On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66)

Makhnev A. A.

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Abstract

We prove that a strongly regular graph with parameters (486, 165, 36, 66) does not exist. Since the parameters indicated are parameters of a pseudogeometric graph for pG 2(5, 32), we conclude that the partial geometries pG 2(5, 32) and pG 2(32, 5) do not exist. Finally, a neighborhood of an arbitrary vertex of a pseudogeometric graph for pG 3(6, 80) is a pseudogeometric graph for pG 2(5, 32) and, therefore, a pseudogeometric graph for the partial geometry pG 3(6, 80) [i.e., a strongly regular graph with parameters (1127, 486, 165, 243)] does not exist.

English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 7, pp 1137-1146.

Citation Example: Makhnev A. A. On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66) // Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 941-949.

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