Cayley graphs and G-graphs of gyro-groups

Fath-Tabar, Gholam Hossein; Moradi, Neda; Bretto, Alain

doi:10.22061/jdma.2025.12144.1138

Cayley graphs and G-graphs of gyro-groups

Document Type : Full Length Article

Authors

¹ Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran;

² Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I.

³ Universite de Caen, GREYC CNRS UMR-6072, Campus II Bd Marechal Juin BP 5186, 14032 Caen cedex Caen, France

10.22061/jdma.2025.12144.1138

Abstract

The present paper investigates the structural properties of Cayley graphs and G-graphs associated with certain gyro-groups, providing rigorous proofs for several key characteristics. Additionally, we conduct a comprehensive review of specific classes of gyro-groups, including gyro-commutative gyro-groups, dihedral gyro-groups, and dihedralized gyro-groups. Subsequently, we derive and establish significant properties of the corresponding G-graphs. The study culminates in an examination of the symmetry properties exhibited by the Cayley graphs and G-graphs of selected gyro-groups, contributing to a deeper understanding of their algebraic and combinatorial structures.

Graphical Abstract