Cayley graphs

Objective: This research was carried out in order to investigate the Cayley graphs of the subgroups of the Euclidean group with compact quotient spaces. Material and Methods: Cayley graphs are directed graphs and the Cayley graph of a group depends on the set of generators. Each generator of the group corresponds to a different type of directed edge of the Cayley graph and they are denoted by different colours. Since the groups considered in this thesis are generated at most by four elements, their Cayley graphs contain at most four directed edges with different colours. Results: In this thesis, the Cayley graphs of the subgroups of the Euclidean group with compact quotient spaces, which are called wallpaper groups, have been determined and they have been visualized. The Cayley graphs of some finite groups such as cyclic, dihedral and symmetric groups have also been determined. Conclusion: In this thesis, the Cayley graphs of some finite groups such as cyclic, dihedral and symmetric groups and the subgroups of the Euclidean group with compact quotient spaces have been determined and it has been observed that different generating sets correspond to different Cayley graphs. Keywords: Cayley Graph, Directed Graph, Graph, Group