Cube-connected modules: a family of cubic networks

A family of cubic networks, named cube-connected modules, is proposed in this paper. The cube-connected modules network consists of modules which are interconnected as a hypercube. Any connected graph, e.g., cycle, hypercube graph, and complete graph, can serve as a module. Topological properties are investigated, and the problems of routing, broadcasting, embedding, and finding parallel routing paths are studied. We show that the problem of determining the shortest routing path is NP-hard, and it can be transformed to the asymmetric traveling salesman problem. The broadcasting algorithms on cube-connected modules can be obtained by combining broadcasting algorithms on hypercubes and broadcasting algorithms on modules. We show that if the modules are hamiltonian, then the cube-connected modules are also hamiltonian. Moreover, a sufficient condition is given for the existence of maximum number of parallel paths between any two nodes of cube-connected modules