Hamiltonian Cycle and Path Embeddings in 3-Ary n-Cubes Based on K1,2-Structure Faults

Yali Lv,Cheng-Kuan Lin,Jianxi Fan

doi:10.1109/trustcom.2016.0198

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 Q n 3 based on K 1,2 -structure faults, which means each faulty element is isomorphic to a connected graph K 1,2 or a connected subgraph of the connected graph. We show that for two arbitrary distinct healthy nodes of a faulty Q n 3 , 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 K 1,2 or a connected subgraph of K 1,2 . 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 K 1,2 or a connected subgraph of K 1,2 . These results mean that the 3-ary n-cube Q3n can tolerate up to 3(n - 2) faulty nodes such that Q n 3 - V (F) is still hamiltonian and hamiltonian-connected, where F denotes the faulty set of Q n 3 .

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