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

  • A. A. Makhnev

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.
Published
25.07.2002
How to Cite
MakhnevA. A. “On the Nonexistence of Strongly Regular Graphs With Parameters (486, 165, 36, 66)”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 54, no. 7, July 2002, pp. 941-9, https://umj.imath.kiev.ua/index.php/umj/article/view/4130.
Section
Research articles