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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.
Moradi et al. (Tue,) studied this question.