Recursive circulant: a new topology for multicomputer networks (extended abstract)

We propose a new topology for multicomputer networks, called recursive cireulant. Recursive circulant G(N, d) is defined to be a ciwulant graph with N nodes and jumps of powers of d, d 2 2. G(N,d) is node symmetric, has a hamiltonian cycle unless N 5 2, and can be recursively constructed when N = cdm, 1 5 c < d. We analyze various network metrics of G(cdm, d) such as connectivity, diameter, mean internode distance, visit ratio, and develop a shortest path routing algorithm in G(cdm,d). G(2m,4), whose degree is m, compares favorably to the hypercube Qm. G(2m,4) has the mazimum connectivity, and its diameter is r(3m 1)/41. A simple bmdcasting algorithm in G(2m,4) as also presented.