Affiliation:
1. School of Applied Science, Taiyuan University of Science and Technology Taiyuan, Shanxi 030024, P. R. China
2. School of Mathematics and Information Sciences, Henan Normal University Xinxiang, Henan 453007, P. R. China
Abstract
Low-dimensional Tori are regularly used as interconnection networks in distributed-memory parallel computers. This paper investigates the fault-Hamiltonicity of two-dimensional Tori. A sufficient condition is derived for the graph Row-Torus(m, 2n + 1) with two faulty edges to have a Hamiltonian cycle, where m ≥ 3 and n ≥ 1. By applying the fault-Hamiltonicity of Row-Torus to a two-dimensional torus, we show that Torus(m, n), m, n ≥ 5, with at most four faulty edges is Hamiltonian if the following two conditions are satisfied: (1) the degree of every vertex is at least two, and (2) there do not exist a pair of nonadjacent vertices in a 4-cycle whose degrees are both two after faulty edges are removed.
Publisher
World Scientific Pub Co Pte Lt
Subject
Computer Science (miscellaneous)
Cited by
2 articles.
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