Edge-Disjoint Hamiltonian Cycles in de Bruijn Networks

Abstract

We show that a slightly modified degree 2r de Bruijn graph can be decomposed into r Hamiltonian cycles when r is a power of a prime. Adjacent nodes in the de Bruijn graph remain adjacent in the modified graph, and the maximum degree does not increase. The presence of edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that requ.ire a ring structure by allowing message traflc to be spread evenly across the network. The changes also enhance fault tolerance.