Circulant matrices and the spectrum of de Bruijn graphs
The block structure of $k$-circulant matrices $A$  of order $n(k\geq 2, k| n)$ is investigated and statements, enabling to reduce a series of problems with the matrices $A+A^T$  to analogous problems with matrices of lower order, namely the blocks of the matrices $A$ &a...
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| Date: | 1992 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
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Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8260 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513017434734592 |
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| author | Strok, V.V. Строк, В.В. |
| author_facet | Strok, V.V. Строк, В.В. |
| author_sort | Strok, V.V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-03-27T09:55:08Z |
| description | The block structure of $k$-circulant matrices $A$  of order $n(k\geq 2, k| n)$ is investigated and statements, enabling to reduce a series of problems with the matrices $A+A^T$  to analogous problems with matrices of lower order, namely the blocks of the matrices $A$  and $A^T$, are proved. The spectrum and the number of spanning trees of an undirected de Bruijn graph are obtained. |
| first_indexed | 2026-03-24T03:37:59Z |
| format | Article |
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| id | umjimathkievua-article-8260 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:37:59Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b5/0d8168a8ef6c86660f5cf8483b1835b5.pdf |
| spelling | umjimathkievua-article-82602024-03-27T09:55:08Z Circulant matrices and the spectrum of de Bruijn graphs Циркулянтные матрицы и спектр графов Де Брейна Strok, V.V. Строк, В.В. The block structure of $k$-circulant matrices $A$  of order $n(k\geq 2, k| n)$ is investigated and statements, enabling to reduce a series of problems with the matrices $A+A^T$  to analogous problems with matrices of lower order, namely the blocks of the matrices $A$  and $A^T$, are proved. The spectrum and the number of spanning trees of an undirected de Bruijn graph are obtained. Изучается блочное строение $k$-циркулянтных матриц $A$ порядка $n(k\geq 2, k| n)$ и доказаны утверждения, позволяющие ряд задач с матрицами $A+A^T$ сводить к аналогичным задачам с матрицами меньшего порядка — блоками матриц $A$ и $A^T$. Получен спектр и число остовных деревьев неориентированного графа де Брейна. Вивчається блочна структура $k$-циркулянтних матриць $A$  порядку $n(k\geq 2, k| n)$  та доведено твердження, що дозволяють ряд задач з матрицями $A+A^T$ зводити до аналогічних задач з матрицями меншого порядку — блоками матриць $A$  і $A^T$. Одержано спектр та число фактор-дерев неорієнтованого графа де Брьойна. Institute of Mathematics, NAS of Ukraine 1992-11-06 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8260 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 11 (1992); 1571-1579 Український математичний журнал; Том 44 № 11 (1992); 1571-1579 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/8260/9840 Copyright (c) 1992 V.V. Strok |
| spellingShingle | Strok, V.V. Строк, В.В. Circulant matrices and the spectrum of de Bruijn graphs |
| title | Circulant matrices and the spectrum of de Bruijn graphs |
| title_alt | Циркулянтные матрицы и спектр графов Де Брейна |
| title_full | Circulant matrices and the spectrum of de Bruijn graphs |
| title_fullStr | Circulant matrices and the spectrum of de Bruijn graphs |
| title_full_unstemmed | Circulant matrices and the spectrum of de Bruijn graphs |
| title_short | Circulant matrices and the spectrum of de Bruijn graphs |
| title_sort | circulant matrices and the spectrum of de bruijn graphs |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8260 |
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