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Vertex-fault-tolerant cycles embedding on enhanced hypercube networks

Vertex-fault-tolerant cycles embedding on enhanced hypercube networks In this paper, we focus on the vertex-fault-tolerant cycles embedding on enhanced hypercube, which is an attractive variant of hypercube and is obtained by adding some complementary edges from hypercube. Let F v be the set of faulty vertices in the n-dimensional enhanced hypercube Q n,k (1 ≤ k ≤ n−1). When |F v | = 2, we showed that Q n,k − F v contains a fault-free cycle of every even length from 4 to 2 n −4 where n (n ≥ 3) and k have the same parity; and contains a fault-free cycle of every even length from 4 to 2 n − 4, simultaneously, contains a cycle of every odd length from n − k + 2 to 2 n − 3 where n(≥ 3) and k have the different parity. Furthermore, when |F v | = f v ≤ n − 2, we proof that there exists the longest fault-free cycle, which is of even length 2 n − 2f v whether n(n ≥ 3) and k have the same parity or not; and there exists the longest fault-free cycle, which is of odd length 2 n − 2f v − 1 in Q n,k − F v where n(≥ 3) and k have the different parity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Vertex-fault-tolerant cycles embedding on enhanced hypercube networks

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References (31)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-016-0547-z
Publisher site
See Article on Publisher Site

Abstract

In this paper, we focus on the vertex-fault-tolerant cycles embedding on enhanced hypercube, which is an attractive variant of hypercube and is obtained by adding some complementary edges from hypercube. Let F v be the set of faulty vertices in the n-dimensional enhanced hypercube Q n,k (1 ≤ k ≤ n−1). When |F v | = 2, we showed that Q n,k − F v contains a fault-free cycle of every even length from 4 to 2 n −4 where n (n ≥ 3) and k have the same parity; and contains a fault-free cycle of every even length from 4 to 2 n − 4, simultaneously, contains a cycle of every odd length from n − k + 2 to 2 n − 3 where n(≥ 3) and k have the different parity. Furthermore, when |F v | = f v ≤ n − 2, we proof that there exists the longest fault-free cycle, which is of even length 2 n − 2f v whether n(n ≥ 3) and k have the same parity or not; and there exists the longest fault-free cycle, which is of odd length 2 n − 2f v − 1 in Q n,k − F v where n(≥ 3) and k have the different parity.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Apr 5, 2016

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