Pancyclicity of Matching Composition Networks under the Conditional Fault Model

A graph G = (V, E) is said to be conditional k-edge-fault pancyclic if, after removing k faulty edges from G and provided that each node is incident to at least two fault-free edges, the resulting graph contains a cycle of every length from its girth to \V\ inclusive. In this paper, we sketch the common properties of a class of networks called Matching Composition Networks (MCNs), such that the conditional edge-fault pancyclicity of MCNs can be determined from the derived properties. We then apply our technical theorem to show that an m-dimensional hyper-Petersen network is conditional (2m 5)-edge-fault pancyclic.

[1]  D. West.  Introduction to Graph Theory , 1995 .

[2]  Hyeong-Seok Lim,et al.  Fault-Hamiltonicity of hypercube-like interconnection networks , 2005, 19th IEEE International Parallel and Distributed Processing Symposium.

[3]  Sabine R. Öhring,et al.  Embeddings Into Hyper Petersen Networks: Yet Another Hypercube-Like Interconnection Topology , 1995 .

[4]  David J. Evans,et al.  The locally twisted cubes , 2005, Int. J. Comput. Math..

[5]  Sun-Yuan Hsieh,et al.  Optimal fault-tolerant Hamiltonicity of star graphs with conditional edge faults , 2008, The Journal of Supercomputing.

[6]  Chang-Hsiung Tsai.  Linear array and ring embeddings in conditional faulty hypercubes , 2004, Theor. Comput. Sci..

[7]  Jun-Ming Xu,et al.  Weakly Edge-Pancyclicity of Locally Twisted Cubes , 2008, Ars Comb..

[8]  Cheng-Kuan Lin,et al.  Fault-tolerant hamiltonicity and fault-tolerant hamiltonian connectivity of the folded Petersen cube networks , 2009, Int. J. Comput. Math..

[9]  David J. Evans,et al.  Pancyclicity of Möbius cubes with faulty nodes , 2006, Microprocess. Microsystems.

[10]  Xiaohua Jia,et al.  Embedding of Cycles in Twisted Cubes with Edge-Pancyclic , 2008, Algorithmica.

[11]  Chun-Hua Chen,et al.  Pancyclicity on Möbius cubes with maximal edge faults , 2004, Parallel Comput..

[12]  Iain A. Stewart,et al.  Bipanconnectivity and Bipancyclicity in k-ary n-cubes , 2009, IEEE Transactions on Parallel and Distributed Systems.

[13]  Jung-Heum Park.  Panconnectivity and edge-pancyclicity of faulty recursive circulant G(2m, 4) , 2008, Theor. Comput. Sci..

[14]  Kyung-Yong Chwa,et al.  Recursive circulants and their embeddings among hypercubes , 2000, Theor. Comput. Sci..

[15]  Jung-Sheng Fu.  Fault-free Hamiltonian cycles in twisted cubes with conditional link faults , 2008, Theor. Comput. Sci..

[16]  Jun-Ming Xu,et al.  Panconnectivity and edge-fault-tolerant pancyclicity of augmented cubes , 2007, Parallel Comput..

[17]  Sun-Yuan Hsieh,et al.  Pancyclicity of Restricted Hypercube-Like Networks under the Conditional Fault Model , 2010, SIAM J. Discret. Math..

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

[19]  Jung-Sheng Fu,et al.  Edge-fault-tolerant Hamiltonicity of pancake graphs under the conditional fault model , 2008, Theor. Comput. Sci..

[20]  Fan Jian.  BC Interconnection Networks and Their Properties , 2003 .

[21]  Jung-Sheng Fu,et al.  Embedding Hamiltonian cycles in alternating group graphs under conditional fault model , 2009, Inf. Sci..

[22]  Sun-Yuan Hsieh,et al.  Hamiltonian path embedding and pancyclicity on the Mobius cube with faulty nodes and faulty edges , 2006, IEEE Transactions on Computers.

[23]  Jung-Heum Park,et al.  Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements , 2007, Theor. Comput. Sci..

[24]  Jimmy J. M. Tan,et al.  The diagnosability of the matching composition network under the comparison diagnosis model , 2004, IEEE Transactions on Computers.

[25]  Jung-Sheng Fu,et al.  Fault-free Hamiltonian cycles in crossed cubes with conditional link faults , 2007, Inf. Sci..

[26]  Mee Yee Chan,et al.  On the Existence of Hamiltonian Circuits in Faulty Hypercubes , 1991, SIAM J. Discret. Math..

[27]  Jung-Sheng Fu.  Conditional fault Hamiltonicity of the complete graph , 2008, Inf. Process. Lett..

[28]  Jun-Ming Xu,et al.  Edge-pancyclicity and Hamiltonian laceability of the balanced hypercubes , 2007, Appl. Math. Comput..

[29]  Yaagoub Ashir,et al.  Fault-Tolerant Embeddings of Hamiltonian Circuits in k-ary n-Cubes , 2002, SIAM J. Discret. Math..

[30]  Jun-Ming Xu,et al.  Fault-tolerant pancyclicity of augmented cubes , 2007, Inf. Process. Lett..

[31]  A. K. Banerjee,et al.  Hyper Petersen network: yet another hypercube-like topology , 1992, [Proceedings 1992] The Fourth Symposium on the Frontiers of Massively Parallel Computation.

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

[33]  Jung-Sheng Fu,et al.  Embedding fault-free cycles in crossed cubes with conditional link faults , 2009, The Journal of Supercomputing.

[34]  Fouad B. Chedid.  On the Generalized Twisted Cube , 1995, Inf. Process. Lett..

[35]  Sun-Yuan Hsieh,et al.  Conditional Edge-Fault Hamiltonicity of Matching Composition Networks , 2009, IEEE Transactions on Parallel and Distributed Systems.

[36]  Peter A. J. Hilbers,et al.  The Twisted Cube , 1987, PARLE.

[37]  Kemal Efe,et al.  The Crossed Cube Architecture for Parallel Computation , 1992, IEEE Trans. Parallel Distributed Syst..

[38]  Xiaohua Jia,et al.  Edge-pancyclicity and path-embeddability of bijective connection graphs , 2008, Inf. Sci..

[39]  Junming Xu,et al.  Survey on path and cycle embedding in some networks , 2009 .

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

[41]  Jun-Ming Xu,et al.  Edge-pancyclicity of Möbius cubes , 2005, Inf. Process. Lett..