The Construction of Distinct Circuits of Length Six for Complete Graph K-6

The emergent applications of complete graph in diverse domains have invited numerous works in this subject matter. Studies related to the decomposition of complete graph such as one-factor, several n-gons and Cartesian product have been solved. Yet, the decomposition of complete graph into distinct circuits still has not been done. Thus, this paper aims to investigate the structure of complete graph, and in particular, the decomposing of complete graph of length six. The decomposition algorithm will be presented to enumerate distinct circuits of length six. Along this process, the adjacency matrices will be used to clarify distinct structures of circuits in a complete graph of length six.