Affiliation:
1. School of Computer Science and Technology, Dalian University of Technology, Dalian 116024, P. R. China
2. Department of Computer Science, Zhongshan College of Dalian Medical University, Dalian 116085, P. R. China
Abstract
As one of the most fundamental networks for parallel and distributed computation, cycle is suitable for developing simple algorithms with low communication cost. A graph [Formula: see text] is called [Formula: see text]-fault-tolerant edge-pancyclic if after deleting any faulty set [Formula: see text] of [Formula: see text] vertices and/or edges from [Formula: see text], every correct edge in the resulting graph lies in a cycle of every length from [Formula: see text] to [Formula: see text], inclusively, where [Formula: see text] is the girth of [Formula: see text], the length of a shortest cycle in [Formula: see text]. The [Formula: see text]-dimensional crossed cube [Formula: see text] is an important variant of the hypercube [Formula: see text], which possesses some properties superior to the hypercube. This paper investigates the fault-tolerant edge-pancyclicity of [Formula: see text], and shows that if [Formula: see text] contains at most [Formula: see text] faulty vertices and/or edges then, for any fault-free edge [Formula: see text] and every length [Formula: see text] from [Formula: see text] to [Formula: see text] except [Formula: see text], there is a fault-free cycle of length [Formula: see text] containing the edge [Formula: see text]. The result is optimal in some senses.
Funder
National Natural Science Foundation of China
the National Key R&D Program of China
Natural Science Foundation of Liaoning Province
Publisher
World Scientific Pub Co Pte Lt
Subject
Computer Science (miscellaneous)
Cited by
1 articles.
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