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

We propose a new topology for multicomputer networks, called recursive circulant. Recursive circulant G(N, d) is defined to be a circulant graph with N nodes and jumps of powers of d, d⩾2. G(N, d) is node symmetric, has a hamiltonian cycle unless N⩽2, and can be recursively constructed when N=cd^m, 1⩽c⩽d. We analyze various network metrics of G(cd^m, d) such as connectivity, diameter, mean internode distance, visit ratio, and develop a shortest path routing algorithm in G(cd^m, d). G(2^m, 4), whose degree is m, compares favorably to the hypercube Q_m. G(2^m, 4) has the maximum connectivity, and its diameter is [(3m-1)/4]. A simple broadcasting algorithm in G(2^m, 4) is also presented