IDENTITY GRAPH OF GENERALIZED QUATERNION GROUP

Abstract

Identity graphs are graphs defined based on the relationship of group elements to identity elements. This study examines the relationship between the algebraic structure of the generalized quaternion group and the topological structure of the identity graph constructed from the group. Through a review of literature related to graph theory and group theory, this research identifies certain patterns in the identity graph of the generalized quaternion group. The results show that the identity graph formed has distinctive characteristics, such as a specific number of edges and cycles, as well as varying degrees of each vertex. Furthermore, this study proves that the identity graph on the generalized quaternion group is not eligible to be an Euler graph or a Hamiltonian graph. Moreover, based on the pattern formed, it can be identified that the identity graph on the group always forms a planar graph. The discussion is colosed with the identification of its girth and diameter.