Fault-tolerant edge-pancyclicity of locally twisted cubes

The n-dimensional locally twisted cube LTQ n is a new variant of the hypercube, which possesses some properties superior to the hypercube. This paper investigates the fault-tolerant edge-pancyclicity of LTQ n , and shows that if LTQ n ( n ⩾ 3) contains at most n − 3 faulty vertices and/or edges then...

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Bibliographic Details
Published in:Information sciences 2011-06, Vol.181 (11), p.2268-2277
Main Authors: Xu, Xirong, Zhai, Wenhua, Xu, Jun-Ming, Deng, Aihua, Yang, Yuansheng
Format: Article
Language:English
Subjects:
Combinatorics
Cubes
Edge-pancyclic
Fault tolerance
Fault-tolerant
Hypercubes
Integers
Locally twisted cubes
Optimization
Proving
Recursive
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Summary:The n-dimensional locally twisted cube LTQ n is a new variant of the hypercube, which possesses some properties superior to the hypercube. This paper investigates the fault-tolerant edge-pancyclicity of LTQ n , and shows that if LTQ n ( n ⩾ 3) contains at most n − 3 faulty vertices and/or edges then, for any fault-free edge e and any integer ℓ with 6 ⩽ ℓ ⩽ 2 n − f v , there is a fault-free cycle of length ℓ containing the edge e, where f v is the number of faulty vertices. The result is optimal in some senses. The proof is based on the recursive structure of LTQ n .
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2011.01.031