Multiswapped networks and their topological and algorithmic properties

We generalise the biswapped network Bsw(G) to obtain a multiswapped network Msw(H ;G), built around two graphs G and H . We show that the network Msw(H ;G) lends itself to optoelectronic implementation and examine its topological and algorithmic. We derive the length of a shortest path joining any two vertices in Msw(H ;G) and consequently a formula for the diameter. We show that if G has connectivity κ ≥ 1 and H has connectivity λ ≥ 1 where λ ≤ κ then Msw(H ;G) has connectivity at least κ + λ, and we derive upper bounds on the (κ + λ)-diameter of Msw(H ;G). Our analysis yields distributed routing algorithms for a distributed-memory multiprocessor whose underlying topology is Msw(H ;G). We also prove that if G and H are Cayley graphs then Msw(H ;G) need not be a Cayley graph, but when H is a bipartite Cayley graph then Msw(H ;G) is necessarily a Cayley graph.