Structural and enumerative properties of the Fibonacci cubes

AbstractThe Fibonacci cube represents a new topology for the interconnection of multicomputers. It is a bipartite graph which can be embedded in the Boolean cube. We prove that it is a particular semilattice and determine its structural properties such as the partite sets, the radius, the center, the independence number of vertices. Furthermore, we obtain enumerative properties as a new formula for the Fibonacci numbers