The Multipartite Property and the Cycle Structure of the Graph Associated with the Elements of Unequal Order in the Group (Zn,⊕)

Source abstract

The first two authors have introduced a new class of graphs associated with the elements of unequal order in the group of residue classes modulo , an integer. It is established that it is a connected graph and the vertex degree and size of the graph are determined. In this paper, it is shown that is Hamiltonian if is even. Further, it is proved that it is not a complete graph and it is a complete multipartite graph. The formula for the number of triangles in is determined.