Cycles embedding on folded hypercubes with faulty nodes

Let FF"v be the set of faulty nodes in an n-dimensional folded hypercube FQ"n with |FF"v|@?n-2. In this paper, we show that if n>=3, then every edge of FQ"n-FF"v lies on a fault-free cycle of every even length from 4 to 2^n-2|FF"v|, and if n>=2 and n is even, then every edge of FQ"n-FF"v lies on a fault-free cycle of every odd length from n+1 to 2^n-2|FF"v|-1.

[1]  N. Biggs.  Algebraic Graph Theory: COLOURING PROBLEMS , 1974 .

[2]  Jung-Sheng Fu.  Fault-free cycles in folded hypercubes with more faulty elements , 2008, Inf. Process. Lett..

[3]  Chang-Hsiung Tsai.  Cycles embedding in hypercubes with node failures , 2007, Inf. Process. Lett..

[4]  Jun-Ming Xu,et al.  Cycles in folded hypercubes , 2006, Appl. Math. Lett..

[5]  Meijie Ma,et al.  Path embedding in faulty hypercubes , 2007, Appl. Math. Comput..

[6]  Sun-Yuan Hsieh,et al.  Hamiltonian-connectivity and strongly Hamiltonian-laceability of folded hypercubes , 2007, Comput. Math. Appl..

[7]  S. Hsieh.  Some edge-fault-tolerant properties of the folded hypercube , 2008 .

[8]  Jun-Ming Xu,et al.  Edge-fault-tolerant properties of hypercubes and folded hypercubes , 2006, Australas. J Comb..

[9]  Franco P. Preparata,et al.  The cube-connected-cycles: A versatile network for parallel computation , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[10]  Xie-Bin Chen,et al.  Some results on topological properties of folded hypercubes , 2009, Inf. Process. Lett..

[11]  Sun-Yuan Hsieh,et al.  Pancyclicity and bipancyclicity of conditional faulty folded hypercubes , 2010, Inf. Sci..

[12]  Shahram Latifi,et al.  Properties and Performance of Folded Hypercubes , 1991, IEEE Trans. Parallel Distributed Syst..

[13]  Sun-Yuan Hsieh,et al.  Fault-tolerant path embedding in folded hypercubes with both node and edge faults , 2013, Theor. Comput. Sci..

[14]  Sun-Yuan Hsieh,et al.  Edge-bipancyclicity of a hypercube with faulty vertices and edges , 2008, Discret. Appl. Math..

[15]  Lionel M. Ni,et al.  The Twisted N-Cube with Application to Multiprocessing , 1991, IEEE Trans. Computers.

[16]  Dajin Wang.  Embedding Hamiltonian Cycles into Folded Hypercubes with Faulty Links , 2001, J. Parallel Distributed Comput..

[17]  Jimmy J. M. Tan,et al.  Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes , 2003, Inf. Process. Lett..

[18]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[19]  Sun-Yuan Hsieh,et al.  A further result on fault-free cycles in faulty folded hypercubes , 2009, Inf. Process. Lett..

[20]  Sun-Yuan Hsieh.  A note on cycle embedding in folded hypercubes with faulty elements , 2008, Inf. Process. Lett..

[21]  Sun-Yuan Hsieh,et al.  1-vertex-fault-tolerant Cycles Embedding on Folded Hypercubes , 2009, Discret. Appl. Math..

[22]  Selim G. Akl.  Parallel computation: models and methods , 1997 .