Fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges

Sun-Yuan Hsieh () and Pei-Yu Yu
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Sun-Yuan Hsieh: National Cheng Kung University
Pei-Yu Yu: National Cheng Kung University

Journal of Combinatorial Optimization, 2007, vol. 13, issue 2, No 4, 153-162

Abstract: Abstract Two Hamiltonian paths are said to be fully independent if the ith vertices of both paths are distinct for all i between 1 and n, where n is the number of vertices of the given graph. Hamiltonian paths in a set are said to be mutually fully independent if two arbitrary Hamiltonian paths in the set are fully independent. On the other hand, two Hamiltonian cycles are independent starting at v if both cycles start at a common vertex v and the ith vertices of both cycles are distinct for all i between 2 and n. Hamiltonian cycles in a set are said to be mutually independent starting at v if any two different cycles in the set are independent starting at v. The n-dimensional hypercube is widely used as the architecture for parallel machines. In this paper, we study its fault-tolerant property and show that an n-dimensional hypercube with at most n−2 faulty edges can embed a set of fault-free mutually fully independent Hamiltonian paths between two adjacent vertices, and can embed a set of fault-free mutually independent Hamiltonian cycles starting at a given vertex. The number of tolerable faulty edges is optimal with respect to a worst case.

Keywords: Fault-tolerant embedding; Graph-theoretic interconnection networks; Hamiltonian; Hypercubes; Mutually independent Hamiltonian cycles (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10878-006-9018-4

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