Publication 1997 Issue No. 7 - July Abstract - Embedding of Generalized Fibonacci Cubes in Hypercubes with Faulty Nodes
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Embedding of Generalized Fibonacci Cubes in Hypercubes with Faulty Nodes
July 1997 (vol. 8 no. 7)
pp. 727-737
 ASCII Text x Feng-Shr Jiang, Shi-Jinn Horng, Tzong-Wann Kao, "Embedding of Generalized Fibonacci Cubes in Hypercubes with Faulty Nodes," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 7, pp. 727-737, July, 1997.
 BibTex x @article{ 10.1109/71.598347,author = {Feng-Shr Jiang and Shi-Jinn Horng and Tzong-Wann Kao},title = {Embedding of Generalized Fibonacci Cubes in Hypercubes with Faulty Nodes},journal ={IEEE Transactions on Parallel and Distributed Systems},volume = {8},number = {7},issn = {1045-9219},year = {1997},pages = {727-737},doi = {http://doi.ieeecomputersociety.org/10.1109/71.598347},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Parallel and Distributed SystemsTI - Embedding of Generalized Fibonacci Cubes in Hypercubes with Faulty NodesIS - 7SN - 1045-9219SP727EP737EPD - 727-737A1 - Feng-Shr Jiang, A1 - Shi-Jinn Horng, A1 - Tzong-Wann Kao, PY - 1997KW - Direct embeddingKW - fault-tolerantKW - generalized Fibonacci cubesKW - hypercubesKW - faulty hypercubeKW - second-order Fibonacci cube.VL - 8JA - IEEE Transactions on Parallel and Distributed SystemsER -

Abstract—The generalized Fibonacci cubes (abbreviated to GFCs) [4] were recently proposed as a class of interconnection topologies, which cover a spectrum ranging from regular graphs such as the hypercube to semiregular graphs such as the second-order Fibonacci cube in [1]. It has been shown that the kth order GFC of dimension n + k is equivalent to an n-cube for 0 ≤n < k; and it is a proper subgraph of an n-cube for nk [4]. Thus, a kth order GFC of dimension n + k can be obtained from the n-cube for all nk by removing certain nodes from an n-cube. This problem is very simple when no faulty node exists in an n-cube; but it becomes very complex if some faulty nodes appear in an n-cube. In this paper, we first consider the following open problem: How can a maximal (in terms of the number of nodes) generalized Fibonacci cube be distinguished from a faulty hypercube [3] which can also be considered as a Fault-tolerant embedding in hypercubes. Then, we shall show how to directly embed a GFC into a faulty hypercube and prove that if no more than three faulty nodes exist, then an $\left\lfloor {{\textstyle{n \over 2}}} \right\rfloor {\rm th}$ order GFC of dimension $n+\left\lfloor {{\textstyle{n \over 2}}} \right\rfloor$ can be directly embedded into an n-cube in the worst case, for n = 4 or n≥ 6.

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Index Terms:
Direct embedding, fault-tolerant, generalized Fibonacci cubes, hypercubes, faulty hypercube, second-order Fibonacci cube.
Citation:
Feng-Shr Jiang, Shi-Jinn Horng, Tzong-Wann Kao, "Embedding of Generalized Fibonacci Cubes in Hypercubes with Faulty Nodes," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 7, pp. 727-737, July 1997, doi:10.1109/71.598347