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On Cayley Graphs of Skew Braces and Their Distances
Abstract
We introduce the left and right Cayley graphs of a finite skew brace (A,·, ∘) with a connection set T⊂ A, as a directed multigraph with additive and multiplicative edges, depicting the operations · and ∘ respectively. We compute the distance from a to a∘ b in these Cayley graphs in terms of factorization lengths over T. As an application, we provide a characterization of the ideals of a skew brace in terms of their corresponding Cayley graphs.
Related
- Classification of skew left braces with additive group isomorphic to the infinite dihedral group
- Determinant characters and multiplicative solubility of finite skew braces
- Bisoluble and Binilpotent Skew Braces of Finite Morley Rank
- Skew braces whose left series is not generated by right-normed star products
- Classification of finite left-simple skew braces
BibTeX
@misc{ahdal2026cayley,
title = {{On Cayley Graphs of Skew Braces and Their Distances}},
author = {Ahmad Syarif Ahdal and Ryan Aziz and Denny Riama Silaban},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35388},
eprint = {2610.35388},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35388},
}
RIS
TY - UNPB
TI - On Cayley Graphs of Skew Braces and Their Distances
AU - Ahmad Syarif Ahdal
AU - Ryan Aziz
AU - Denny Riama Silaban
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35388
UR - https://arxiv.org/abs/2610.35388
AB - We introduce the left and right Cayley graphs of a finite skew brace (A,·, ∘) with a connection set T⊂ A, as a directed multigraph with additive and multiplicative edges, depicting the operations · and ∘ respectively. We compute the distance from a to a∘ b in these Cayley graphs in terms of factorization lengths over T. As an application, we provide a characterization of the ideals of a skew brace in terms of their corresponding Cayley graphs.
ER -