Cayley graphs and G-graphs of gyro-groups

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.

کلیدواژه ها:

gyro-group ، Cayley graph ، G-graph