Embedding Two Edge-Disjoint Hamiltonian Cycles and Two Equal Node-Disjoint Cycles into Twisted Cubes

The presence of edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the network. Edge-disjoint Hamiltonian cycles also provide the edge-fault tolerant Hamiltonicity of an interconnection network. Two node-disjoint cycles in a network are called equal if the number of nodes in the two cycles are the same and every node appears in one cycle exactly once. The presence of two equal node-disjoint cycles provides algorithms that require a ring structure to be preformed in the network simultaneously. The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. The n-dimensional twisted cube, an important variation of the hypercube, possesses some properties superior to the hypercube. In this paper, we present linear time algorithms to construct two edge-disjoint Hamiltonian cycles and two equal node-disjoint cycles in an n-dimensional twisted cube.