On reliability of the folded hypercubes |
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| Affiliation: | 1. Department of Mathematics, XiDian University, Xi’an, Shanxi 710071, China;2. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China;3. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China;1. School of Information and Mathematics, Yangtze University, Jingzhou, Hubei, 434023, China;2. School of Mathematical Sciences, University of Science and Technology of China, Wentsun Wu Key Laboratory of CAS, Hefei, 230026, China;1. School of Mathematics and Statistics, Xidian University, Xi''an, Shaanxi, 710071, PR China;2. Department of Management Engineering, Chongqing aerospace polytechnic college, Chongqing, 400021, PR China;1. Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China;2. Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai 200237, China;3. School of Mathematics Science, Guangxi Teachers Education University, Nanning, Guangxi 530001, China |
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| Abstract: | In this paper, we explore the 2-extra connectivity and 2-extra-edge-connectivity of the folded hypercube FQn. We show that κ2(FQn) = 3n − 2 for n ⩾ 8; and λ2(FQn) = 3n − 1 for n ⩾ 5. That is, for n ⩾ 8 (resp. n ⩾ 5), at least 3n − 2 vertices (resp. 3n − 1 edges) of FQn are removed to get a disconnected graph that contains no isolated vertices (resp. edges). When the folded hypercube is used to model the topological structure of a large-scale parallel processing system, these results can provide more accurate measurements for reliability and fault tolerance of the system. |
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