Automorphisms of kaleidoscopical graphs
A regular connected graph \(\Gamma\) of degree \(s\) is called kaleidoscopical if there is a \((s+1)\)-coloring of the set of its vertices such that every unit ball in \(\Gamma\) has no distinct monochrome points. The kaleidoscopical graphs can be considered as a graph counterpart of the Hamming cod...
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-8492018-03-21T11:59:09Z Automorphisms of kaleidoscopical graphs Protasov, I. V. Protasova, K. D. kaleidoscopical graph, Hamming pair, kaleidoscopical tree 05C15, 05C25 A regular connected graph \(\Gamma\) of degree \(s\) is called kaleidoscopical if there is a \((s+1)\)-coloring of the set of its vertices such that every unit ball in \(\Gamma\) has no distinct monochrome points. The kaleidoscopical graphs can be considered as a graph counterpart of the Hamming codes. We describe the groups of automorphisms of kaleidoscopical trees and Hamming graphs. We show also that every finitely generated group can be realized as the group of automorphisms of some kaleidoscopical graphs. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/849 Algebra and Discrete Mathematics; Vol 6, No 2 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/849/379 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2018-03-21T11:59:09Z |
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OJS |
| language |
English |
| topic |
kaleidoscopical graph Hamming pair kaleidoscopical tree 05C15 05C25 |
| spellingShingle |
kaleidoscopical graph Hamming pair kaleidoscopical tree 05C15 05C25 Protasov, I. V. Protasova, K. D. Automorphisms of kaleidoscopical graphs |
| topic_facet |
kaleidoscopical graph Hamming pair kaleidoscopical tree 05C15 05C25 |
| format |
Article |
| author |
Protasov, I. V. Protasova, K. D. |
| author_facet |
Protasov, I. V. Protasova, K. D. |
| author_sort |
Protasov, I. V. |
| title |
Automorphisms of kaleidoscopical graphs |
| title_short |
Automorphisms of kaleidoscopical graphs |
| title_full |
Automorphisms of kaleidoscopical graphs |
| title_fullStr |
Automorphisms of kaleidoscopical graphs |
| title_full_unstemmed |
Automorphisms of kaleidoscopical graphs |
| title_sort |
automorphisms of kaleidoscopical graphs |
| description |
A regular connected graph \(\Gamma\) of degree \(s\) is called kaleidoscopical if there is a \((s+1)\)-coloring of the set of its vertices such that every unit ball in \(\Gamma\) has no distinct monochrome points. The kaleidoscopical graphs can be considered as a graph counterpart of the Hamming codes. We describe the groups of automorphisms of kaleidoscopical trees and Hamming graphs. We show also that every finitely generated group can be realized as the group of automorphisms of some kaleidoscopical graphs. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/849 |
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AT protasoviv automorphismsofkaleidoscopicalgraphs AT protasovakd automorphismsofkaleidoscopicalgraphs |
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2025-07-17T10:31:40Z |
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2025-07-17T10:31:40Z |
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1837890140693856256 |