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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Bibliographic Details
Date:2018
Main Authors: Protasov, I. V., Protasova, K. D.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/849
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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Summary: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.