On fault-tolerant embedding of Hamiltonian cycles, linear arrays and rings in a Flexible Hypercube

Abstract The Hamiltonian cycle of a Flexible Hypercube graph network is investigated in this paper. The result can readily be used in the optimal embedding of a linear array (or a ring) of processors in a faulty Flexible Hypercube. There are embedding algorithms proposed in this paper. These embedding algorithms show a ring with any number of nodes that can be embedded into a faulty Flexible Hypercube with load 1, congestion 1 and dilation 3 such that O( n 2 −(⌊log 2 m ⌋) 2 ) faults can be tolerated, where n is the dimension of the Flexible Hypercube and m is the number of nodes of the ring.

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