Energi Detour pada Graf Invers dari Grup Quaternion Diperumum

A generalized quaternion group is a non-abelian group with a order constructed from the two elements that is denoted by defined as where the is the identity, . The inverse graph of a group is a graph which the vertices set are all elements of a finite group and two distinct vertices and are adjacent if and only if either or . Graph energy, especially detour energy, is an important aspect in graph theory that describes network stability and resistance. The method used in this research is a qualitative method. This study aims to determine the formula of the detour energy in the inverse graph of the quaternion group is announced with . Through algebra analysis methods and graph theory, it is found that detour energy can be calculated using the detour matrix and the resulting eigen value. The results showed that the detour energy formula in the inverse graph from the quaternion group was founded was for each .