On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66)
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 arbitrar...
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| Datum: | 2002 |
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| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4130 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510264630181888 |
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| author | Makhnev, A. A. Махнев, А. А. Махнев, А. А. |
| author_facet | Makhnev, A. A. Махнев, А. А. Махнев, А. А. |
| author_sort | Makhnev, A. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:23:13Z |
| description | 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. |
| first_indexed | 2026-03-24T02:54:14Z |
| format | Article |
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| id | umjimathkievua-article-4130 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:54:14Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/74/4f143c9676b82df3e1e2aa46d0f12374.pdf |
| spelling | umjimathkievua-article-41302020-03-18T20:23:13Z On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66) О несуществовании сильно регулярных графов с параметрами (486, 165, 36, 66) Makhnev, A. A. Махнев, А. А. Махнев, А. А. 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. Доведено, що регулярний граф із параметрами (486, 165, 36,66) не існує. Оскільки вказані параметри є параметрами псевдогсометричного графа для $pG_2(5, 32)$, то не існують часткові геометрії $pG_2(5,32)$ і $pG_2(32,5)$. Нарешті, окіл будь-якої вершини псевдогеометричного графа для $pG_3(6, 80)$ є псевдогеометричним графом для $pG_2(5,32)$, тому псевдогеометричний граф для часткової геометрії $pG_3(6, 80)$ (тобто сильно регулярний граф із параметрами (1127,486, 165, 243)) не існує. Institute of Mathematics, NAS of Ukraine 2002-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4130 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 7 (2002); 941-949 Український математичний журнал; Том 54 № 7 (2002); 941-949 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4130/4969 https://umj.imath.kiev.ua/index.php/umj/article/view/4130/4970 Copyright (c) 2002 Makhnev A. A. |
| spellingShingle | Makhnev, A. A. Махнев, А. А. Махнев, А. А. On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66) |
| title | On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66) |
| title_alt | О несуществовании сильно регулярных графов с параметрами (486, 165, 36, 66) |
| title_full | On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66) |
| title_fullStr | On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66) |
| title_full_unstemmed | On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66) |
| title_short | On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66) |
| title_sort | on the nonexistence of strongly regular graphs with parameters (486, 165, 36, 66) |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4130 |
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