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...
Saved in:
| Date: | 2018 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
|
| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/849 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| 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. |
|---|