Cayley graphs are a visual representation of finite groups bridging graph theory and algebraic structures. This study aims to analyze the algebraic properties appearing in Cayley graphs formed from cyclic and dihedral groups.

The method used in this research includes literature study and computational simulation using Python NetworkX to visualize graph structures. The results indicate that Cayley graphs of cyclic groups always form circulant graphs, while those of dihedral groups exhibit more complex symmetry depending on the chosen generating set.

This research provides new insights into the relationship between group order and the diameter of the resulting Cayley graph. It is hoped that these results can be applied in designing efficient interconnection network topologies.