Hamiltonian cycle and path embeddings in 3-ary [formula omitted]-cubes based on [formula omitted]-structure faults

Abstract

The k-ary n-cube is one of the most attractive interconnection networks for parallel and distributed computing system. In this paper, we investigate hamiltonian cycle and path embeddings in 3-ary n-cubes Qn3 based on K1,3-structure faults, which means each faulty element is isomorphic to any connected subgraph of a connected graph K1,3. We show that for two arbitrary distinct healthy nodes of a faulty Qn3, there exists a fault-free hamiltonian path connecting these two nodes if the number of faulty element is at most n−2 and each faulty element is isomorphic to any connected subgraph of K1,3. We also show that there exists a fault-free hamiltonian cycle if the number of faulty element is at most n−1 and each faulty element is isomorphic to any connected subgraph of K1,3. Then, we provide the simulation experiment to find a hamiltonian cycle and a hamiltonian path in structure faulty 3-ary n-cubes and verify the theoretical results. These results mean that the 3-ary n-cube Qn3 can tolerate up to 4(n−2) faulty nodes such that Qn3−V(F) is still hamiltonian and hamiltonian-connected, where F denotes the faulty set of Qn3.