Extended Fibonacci cubes

The Fibonacci cube (FC) is an interconnection network that possesses many desirable properties that are important in network design and application. However, most Fibonacci cubes (more than two third of all) are not Hamiltonian. In this paper, we propose a new network topology called extended Fibonacci cube (EFC₁) based on the same sequence F(i)=F(i-1)+F(i-2) as the regular Fibonacci sequence but with different initial values. We also propose a series of extended Fibonacci cubes with even number of nodes. Any extended Fibonacci cube (EFC_k, with k⩾1) in the series contains the node set of any other cube that precedes EFC_k in the series. We show that any extended Fibonacci cube maintains virtually all the desirable properties of the Fibonacci cube. EFC_k´s can be considered as flexible versions of incomplete hypercubes which eliminate the restriction on the number of nodes and thus makes it possible to construct parallel machines with arbitrary sizes