Embedding fault-free hamiltonian paths with prescribed linear forests into faulty ternary n-cubes

https://doi.org/10.1016/j.tcs.2018.09.020Get rights and content
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Highlights

  • Hamiltonian path embedding problem in ternary n-cubes with both faulty edges and prescribed linear forest was investigated.

  • Fault-free hamiltonian paths passing through prescribed linear forests in faulty 3-ary n-cubes were constructed.

  • Some known results were improved.

Abstract

The k-ary n-cube is an important underlying topology for large-scale multiprocessor systems. A linear forest in a graph is a subgraph each component of which is a path. In this paper, we investigate the problem of embedding hamiltonian paths passing through a prescribed linear forest in ternary n-cubes with faulty edges. Given a faulty edge set F with at most 2n3 edges and a linear forest L with at most 2n3|F| edges, for two distinct vertices in the ternary n-cube, we show that the ternary n-cube admits a fault-free hamiltonian path between u and v passing through L if and only if none of the paths in L has u or v as internal vertices or both of them as end-vertices.

Keywords

Multiprocessor systems
Interconnection networks
Fault tolerance
Prescribed linear forests
Hamiltonian paths

Cited by (0)

This work is supported by the Joint Fund of NSFC and Henan Province (U1304601).