Hamiltonian Cycles and Hamiltonian Paths in Faulty Burnt Pancake Graphs

Keiichi KANEKO

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E90-D    No.4    pp.716-721
Publication Date: 2007/04/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e90-d.4.716
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Algorithm Theory
Keyword: 
signed permutation,  interconnection network,  routing algorithm,  parallel processing,  

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Summary: 
Recently, research on parallel processing systems is very active, and many complex topologies have been proposed. A burnt pancake graph is one such topology. In this paper, we prove that a faulty burnt pancake graph with degree n has a fault-free Hamiltonian cycle if the number of the faulty elements is n-2 or less, and it has a fault-free Hamiltonian path between any pair of nonfaulty nodes if the number of the faulty elements is n-3 or less.

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