Cayley graphs and G-graphs of Gyro-groups

TL;DR

This paper investigates the structure and properties of Cayley graphs and G-graphs of gyro-groups, including special types like gyro-commutative and dihedral gyro-groups, focusing on their symmetry and graph characteristics.

Contribution

It introduces new analyses of Cayley and G-graphs for various gyro-groups, highlighting their properties and symmetries, which were not previously detailed.

Findings

Properties of Cayley graphs and G-graphs of gyro-groups are established.

Symmetry characteristics of these graphs are analyzed.

Special gyro-groups like gyro-commutative and dihedral are examined.

Abstract

In this paper the structure of the Cayley graphs and G-graphs of some gyro-groups are studied and some properties of them will be proved. Moreover we review some special gyro-groups including: gyro-commutative gyrogroups, dihedral gyro-groups and dihedralized gyro-groups. Then we try to establish some important properties of their associated G-graphs. Finally we will examine the symmetry of Cayley graphs and G-graphs of some gyro-groups.