The Family of Generalized Variational Network of Cube-Connected Cycles

The RVCCCr is a kind of variant network of cube-connected cycle (CCC) network, which is constructed by replacing each vertex in the hypercube with a circle of length 2r, and the hypercube is r-dimensional. The RVCCCr is regular and vertex-symmetric, which makes its topological properties easy to be analyzed. However, the length of the circle in RVCCCr is fixed to 2r which makes RVCCCr is inflexible. This paper proposes the family of generalized variational CCC networks, named RVCCC(r,k), where r is the dimension of the underlying hypercube and the length of each cycle in RVCCC(r,k) is k×r. Same to RVCCCr, the RVCCC(r,k) is also regular and vertex-symmetry. Since the length of each circle in RVCCC(r,k) is k×r, the RVCCC(r,k) is more suitable to construct any scale interconnection network than RVCCCr. After calculating the shortest internode distance between any two vertices in the RVCCC(r,k), we obtained the exact diameter of this network and the optimal routing algorithm was developed.