SHILLA GRAPHS WITH \(b=5\) AND \(b=6\)
A \(Q\)-polynomial Shilla graph with \(b = 5\) has intersection arrays \(\{105t,4(21t+1),16(t+1); 1,4 (t+1),84t\}\), \(t\in\{3,4,19\}\). The paper proves that distance-regular graphs with these intersection arrays do not exist. Moreover, feasible intersection arrays of \(Q\)-polynomial Shilla graphs...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2021-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/404 |
| _version_ | 1818018798302658560 |
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| author | Alexander A. Makhnev Ivan N. Belousov |
| author_facet | Alexander A. Makhnev Ivan N. Belousov |
| author_sort | Alexander A. Makhnev |
| collection | DOAJ |
| description | A \(Q\)-polynomial Shilla graph with \(b = 5\) has intersection arrays \(\{105t,4(21t+1),16(t+1); 1,4 (t+1),84t\}\), \(t\in\{3,4,19\}\). The paper proves that distance-regular graphs with these intersection arrays do not exist. Moreover, feasible intersection arrays of \(Q\)-polynomial Shilla graphs with \(b = 6\) are found. |
| first_indexed | 2024-04-14T07:44:36Z |
| format | Article |
| id | doaj.art-becc78a618674e87bf944b8d6599add7 |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-04-14T07:44:36Z |
| publishDate | 2021-12-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-becc78a618674e87bf944b8d6599add72022-12-22T02:05:24ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522021-12-017210.15826/umj.2021.2.004130SHILLA GRAPHS WITH \(b=5\) AND \(b=6\)Alexander A. Makhnev0Ivan N. Belousov1Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108; Ural Federal University, 19 Mira Str., Ekaterinburg, 620002Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108; Ural Federal University, 19 Mira Str., Ekaterinburg, 620002A \(Q\)-polynomial Shilla graph with \(b = 5\) has intersection arrays \(\{105t,4(21t+1),16(t+1); 1,4 (t+1),84t\}\), \(t\in\{3,4,19\}\). The paper proves that distance-regular graphs with these intersection arrays do not exist. Moreover, feasible intersection arrays of \(Q\)-polynomial Shilla graphs with \(b = 6\) are found.https://umjuran.ru/index.php/umj/article/view/404shilla graph, distance-regular graph, q-polynomial graph. |
| spellingShingle | Alexander A. Makhnev Ivan N. Belousov SHILLA GRAPHS WITH \(b=5\) AND \(b=6\) Ural Mathematical Journal shilla graph, distance-regular graph, q-polynomial graph. |
| title | SHILLA GRAPHS WITH \(b=5\) AND \(b=6\) |
| title_full | SHILLA GRAPHS WITH \(b=5\) AND \(b=6\) |
| title_fullStr | SHILLA GRAPHS WITH \(b=5\) AND \(b=6\) |
| title_full_unstemmed | SHILLA GRAPHS WITH \(b=5\) AND \(b=6\) |
| title_short | SHILLA GRAPHS WITH \(b=5\) AND \(b=6\) |
| title_sort | shilla graphs with b 5 and b 6 |
| topic | shilla graph, distance-regular graph, q-polynomial graph. |
| url | https://umjuran.ru/index.php/umj/article/view/404 |
| work_keys_str_mv | AT alexanderamakhnev shillagraphswithb5andb6 AT ivannbelousov shillagraphswithb5andb6 |