The Hamiltonicity of swapped (OTIS) networks built of Hamiltonian component networks

A two-level swapped (also known as optical transpose interconnect system, or OTIS) network with n2 nodes is built of n copies of an n-node basis network constituting its clusters. A simple rule for intercluster connectivity (node j in cluster i connected to node i in cluster j for all i≠j) leads to regularity, modularity, packageability, fault tolerance, and algorithmic efficiency of the resulting networks. We prove that a swapped network is Hamiltonian if its basis network is Hamiltonian. This general closure property for Hamiltonicity under swap or OTIS composition replaces a number of proofs in the literature for specific basis networks and obviates the need for proving Hamiltonicity for many other basis networks of potential practical interest.