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Journal articles on the topic 'Signed hypercubes'

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Author: Grafiati

Published: 20 April 2024

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1

Shi, Wei. "The signed (|G| –1)-subdomination number of balanced hypercubes." Journal of Physics: Conference Series 1978, no. 1 (July 1, 2021): 012040. http://dx.doi.org/10.1088/1742-6596/1978/1/012040.

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2

Lobov, Alexander A., and Mikhail B. Abrosimov. "About uniqueness of the minimal 1-edge extension of hypercube Q4." Prikladnaya Diskretnaya Matematika, no. 58 (2023): 84–93. http://dx.doi.org/10.17223/20710410/58/8.

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One of the important properties of reliable computing systems is their fault tolerance. To study fault tolerance, you can use the apparatus of graph theory. Minimal edge extensions of a graph are considered, which are a model for studying the failure of links in a computing system. A graph G* = (V*,α*) with n vertices is called a minimal k-edge extension of an n-vertex graph G = (V, α) if the graph G is embedded in every graph obtained from G* by deleting any of its k edges and has the minimum possible number of edges. The hypercube Qn is a regular 2n-vertex graph of order n, which is the Cartesian product of n complete 2-vertex graphs K2. The hypercube is a common topology for building computing systems. Previously, a family of graphs Q*n was described, whose representatives for n>1 are minimal edge 1-extensions of the corresponding hypercubes. In this paper, we obtain an analytical proof of the uniqueness of minimal edge 1-extensions of hypercubes for n≤4 and establish a general property of an arbitrary minimal edge 1-extension of a hypercube Qn for n>2: it does not contain edges connecting vertices, the distance between which in the hypercube is equal to 2.

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3

Mou, Gufang, and Qiuyan Zhang. "Signed zero forcing number and controllability for a networks system with a directed hypercube." MATEC Web of Conferences 355 (2022): 01012. http://dx.doi.org/10.1051/matecconf/202235501012.

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The controllability for complex network system is to find the minimum number of leaders for the network system to achieve effective control of the global networks. In this paper, the problem of controllability of the directed network for a family of matrices carrying the structure under directed hypercube is considered. The relationship between the minimum number of leaders for the directed network system and the number of the signed zero forcing set is established. The minimum number of leaders of the directed networks system under a directed hypercube is obtained by computing the zero forcing number of a signed graph.

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4

Seo, Jung-Hyun, and Hyeong-Ok Lee. "Design and Analysis of a Symmetric Log Star Graph with a Smaller Network Cost Than Star Graphs." Electronics 10, no. 8 (April 20, 2021): 981. http://dx.doi.org/10.3390/electronics10080981.

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Graphs are used as models to solve problems in fields such as mathematics, computer science, physics, and chemistry. In particular, torus, hypercube, and star graphs are popular when modeling the connection structure of processors in parallel computing because they are symmetric and have a low network cost. Whereas a hypercube has a substantially smaller diameter than a torus, star graphs have been presented as an alternative to hypercubes because of their lower network cost. We propose a novel log star (LS) that is symmetric and has a lower network cost than a star graph. The LS is an undirected, recursive, and regular graph. In LSn, the number of nodes is n! while the degree is 2log2n − 1 and the diameter is 0.5n(log2n)2 + 0.75nlog2n. In this study, we analyze the basic topological properties of LS. We prove that LSn is a symmetrical connected graph and analyzed its subgraph characteristics. Then, we propose a routing algorithm and derive the diameter and network cost. Finally, the network costs of the LS and star graph-like networks are compared.

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5

Tsai, Chang-Hsiung, and Shu-Yun Jiang. "Path bipancyclicity of hypercubes." Information Processing Letters 101, no. 3 (February 2007): 93–97. http://dx.doi.org/10.1016/j.ipl.2006.08.011.

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6

Gregor, Petr, and Tomáš Dvořák. "Path partitions of hypercubes." Information Processing Letters 108, no. 6 (November 2008): 402–6. http://dx.doi.org/10.1016/j.ipl.2008.07.015.

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7

Chen, Xie-Bin. "On path bipancyclicity of hypercubes." Information Processing Letters 109, no. 12 (May 2009): 594–98. http://dx.doi.org/10.1016/j.ipl.2009.02.009.

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8

Ma, Meijie, and Baodong Liu. "Cycles embedding in exchanged hypercubes." Information Processing Letters 110, no. 2 (December 2009): 71–76. http://dx.doi.org/10.1016/j.ipl.2009.10.009.

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9

Loh, P. K. K., W. J. Hsu, and Y. Pan. "The exchanged hypercube." IEEE Transactions on Parallel and Distributed Systems 16, no. 9 (September 2005): 866–74. http://dx.doi.org/10.1109/tpds.2005.113.

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10

Cybenko, George, David W. Krumme, and K. N. Venkataraman. "Fixed hypercube embedding." Information Processing Letters 25, no. 1 (April 1987): 35–39. http://dx.doi.org/10.1016/0020-0190(87)90090-1.

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11

LU, Xiao-Nan, and Tomoko ADACHI. "On Dimensionally Orthogonal Diagonal Hypercubes." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E103.A, no. 10 (October 1, 2020): 1211–17. http://dx.doi.org/10.1587/transfun.2019dmp0009.

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12

Tsai, Chang-Hsiung, Jimmy J. M. Tan, Tyne Liang, and Lih-Hsing Hsu. "Fault-tolerant hamiltonian laceability of hypercubes." Information Processing Letters 83, no. 6 (September 2002): 301–6. http://dx.doi.org/10.1016/s0020-0190(02)00214-4.

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13

Chang, Chung-Haw, Cheng-Kuan Lin, Hua-Min Huang, and Lih-Hsing Hsu. "The super laceability of the hypercubes." Information Processing Letters 92, no. 1 (October 2004): 15–21. http://dx.doi.org/10.1016/j.ipl.2004.06.006.

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14

Shih, Lun-Min, Jimmy J. M. Tan, and Lih-Hsing Hsu. "Edge-bipancyclicity of conditional faulty hypercubes." Information Processing Letters 105, no. 1 (December 2007): 20–25. http://dx.doi.org/10.1016/j.ipl.2007.07.009.

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15

Ma, Meijie, and Liying Zhu. "The super connectivity of exchanged hypercubes." Information Processing Letters 111, no. 8 (March 2011): 360–64. http://dx.doi.org/10.1016/j.ipl.2011.01.006.

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16

Klavžar, Sandi, and Meijie Ma. "The domination number of exchanged hypercubes." Information Processing Letters 114, no. 4 (April 2014): 159–62. http://dx.doi.org/10.1016/j.ipl.2013.12.005.

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17

Chen, Xie-Bin. "Hamiltonicity of hypercubes with faulty vertices." Information Processing Letters 116, no. 5 (May 2016): 343–46. http://dx.doi.org/10.1016/j.ipl.2015.09.018.

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18

Xu, Jun-Ming, Zheng-Zhong Du, and Min Xu. "Edge-fault-tolerant edge-bipancyclicity of hypercubes." Information Processing Letters 96, no. 4 (November 2005): 146–50. http://dx.doi.org/10.1016/j.ipl.2005.06.006.

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19

Tsai, Chang-Hsiung. "Cycles embedding in hypercubes with node failures." Information Processing Letters 102, no. 6 (June 2007): 242–46. http://dx.doi.org/10.1016/j.ipl.2006.12.016.

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20

Lai, Chia-Jui. "A note on path bipancyclicity of hypercubes." Information Processing Letters 109, no. 19 (September 2009): 1129–30. http://dx.doi.org/10.1016/j.ipl.2009.07.007.

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21

Yonta, Paulin Melatagia, Maurice Tchuente, and René Ndoundam. "Routing automorphisms of the hypercube." Information Processing Letters 110, no. 20 (September 2010): 854–60. http://dx.doi.org/10.1016/j.ipl.2010.07.002.

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22

Sabir, Eminjan, and Jixiang Meng. "Fault-tolerant Hamiltonicity of hypercubes with faulty subcubes." Information Processing Letters 172 (December 2021): 106160. http://dx.doi.org/10.1016/j.ipl.2021.106160.

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23

Ye, Deshi, and Guochuan Zhang. "Maximizing the throughput of parallel jobs on hypercubes." Information Processing Letters 102, no. 6 (June 2007): 259–63. http://dx.doi.org/10.1016/j.ipl.2007.01.005.

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24

Chen, Xie-Bin. "Some results on topological properties of folded hypercubes." Information Processing Letters 109, no. 8 (March 2009): 395–99. http://dx.doi.org/10.1016/j.ipl.2008.12.005.

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25

Chen, Xie-Bin. "Edge-fault-tolerant diameter and bipanconnectivity of hypercubes." Information Processing Letters 110, no. 24 (November 2010): 1088–92. http://dx.doi.org/10.1016/j.ipl.2010.09.012.

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26

Li, Xiang-Jun, and Jun-Ming Xu. "Generalized measures of fault tolerance in exchanged hypercubes." Information Processing Letters 113, no. 14-16 (July 2013): 533–37. http://dx.doi.org/10.1016/j.ipl.2013.04.007.

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27

Diaz de Cerio, L., M. Valero-Garcia, and A. Gonzalez. "Hypercube algorithms on mesh connected multicomputers." IEEE Transactions on Parallel and Distributed Systems 13, no. 12 (December 2002): 1247–60. http://dx.doi.org/10.1109/tpds.2002.1158263.

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28

Chen, Yu-wei. "A Comment on "The Exchanged Hypercube'." IEEE Transactions on Parallel and Distributed Systems 18, no. 4 (April 2007): 576. http://dx.doi.org/10.1109/tpds.2007.1006.

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29

Qian-Ping Gu and Shietung Peng. "Unicast in hypercubes with large number of faulty nodes." IEEE Transactions on Parallel and Distributed Systems 10, no. 10 (1999): 964–75. http://dx.doi.org/10.1109/71.808128.

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30

Trifonov, Dmitry I. "Flaws of hypercube-like ciphers." Prikladnaya Diskretnaya Matematika, no. 57 (2022): 52–66. http://dx.doi.org/10.17223/20710410/57/4.

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The class of block cryptographic XSLP-algorithms called "hypercube" is considered. For algorithms of this class, we obtain estimates for the dispersion index of a linear environment for any number of iterations. It is shown that when choosing a transformation P using generalized de Bruijn graphs for the algorithms under consideration, the avalanche effect may not occur, as a result of which the encryption key can be determined with laboriousness, which is significantly less than the laboriousness of total key testing.

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31

Narayanaswani, Chandrasekhar, and William Randolph Franklin. "Edge intersection on the hypercube computer." Information Processing Letters 41, no. 5 (April 1992): 257–62. http://dx.doi.org/10.1016/0020-0190(92)90169-v.

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32

Shankar, Ravi V., and Sanjay Ranka. "Hypercube algorithms for operations on quadtrees." Pattern Recognition 25, no. 7 (July 1992): 741–47. http://dx.doi.org/10.1016/0031-3203(92)90137-8.

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33

Bhandarkar, Suchendra M. "Parallelizing object recognition on the hypercube." Pattern Recognition Letters 13, no. 6 (June 1992): 433–41. http://dx.doi.org/10.1016/0167-8655(92)90050-a.

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34

Fang, Jywe-Fei, and Kuan-Chou Lai. "Embedding the incomplete hypercube in books." Information Processing Letters 96, no. 1 (October 2005): 1–6. http://dx.doi.org/10.1016/j.ipl.2005.05.026.

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35

Wu, Ruei-Yu, Gen-Huey Chen, Jung-Sheng Fu, and Gerard J. Chang. "Finding cycles in hierarchical hypercube networks." Information Processing Letters 109, no. 2 (December 2008): 112–15. http://dx.doi.org/10.1016/j.ipl.2008.09.007.

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36

Yang, Weihua, Shuli Zhao, and Shurong Zhang. "Strong Menger connectivity with conditional faults of folded hypercubes." Information Processing Letters 125 (September 2017): 30–34. http://dx.doi.org/10.1016/j.ipl.2017.05.001.

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37

MOROTA, Miya, Ryoichi HATAYAMA, and Yukio SHIBATA. "Cayley Graph Representation and Graph Product Representation of Hypercubes." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A, no. 3 (2011): 946–54. http://dx.doi.org/10.1587/transfun.e94.a.946.

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38

Dybizbański, Janusz, and Andrzej Szepietowski. "Hamiltonian cycles and paths in hypercubes with disjoint faulty edges." Information Processing Letters 172 (December 2021): 106157. http://dx.doi.org/10.1016/j.ipl.2021.106157.

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39

Fu, Jung-Sheng. "Fault-free cycles in folded hypercubes with more faulty elements." Information Processing Letters 108, no. 5 (November 2008): 261–63. http://dx.doi.org/10.1016/j.ipl.2008.05.024.

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40

Chen, Meirun, and Xiaofeng Guo. "Adjacent vertex-distinguishing edge and total chromatic numbers of hypercubes." Information Processing Letters 109, no. 12 (May 2009): 599–602. http://dx.doi.org/10.1016/j.ipl.2009.02.006.

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41

Du, Zheng-Zhong, and Jun-Ming Xu. "A note on cycle embedding in hypercubes with faulty vertices." Information Processing Letters 111, no. 12 (June 2011): 557–60. http://dx.doi.org/10.1016/j.ipl.2011.03.002.

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42

Shih, Jau-Der. "Fault-tolerant wormhole routing for hypercube networks." Information Processing Letters 86, no. 2 (April 2003): 93–100. http://dx.doi.org/10.1016/s0020-0190(02)00477-5.

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43

Li, Xiang-Jun, and Jun-Ming Xu. "Edge-fault tolerance of hypercube-like networks." Information Processing Letters 113, no. 19-21 (September 2013): 760–63. http://dx.doi.org/10.1016/j.ipl.2013.07.010.

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44

Tsai, Tsung-Han, Y.-Chuang Chen, and Jimmy J. M. Tan. "Topological Properties on the Wide and Fault Diameters of Exchanged Hypercubes." IEEE Transactions on Parallel and Distributed Systems 25, no. 12 (December 2014): 3317–27. http://dx.doi.org/10.1109/tpds.2014.2307853.

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45

Avresky, D. R., and K. M. Al-Tawil. "Correction to "Embedding and reconfiguration of spanning trees in faulty hypercubes"." IEEE Transactions on Parallel and Distributed Systems 10, no. 10 (October 1999): 1102. http://dx.doi.org/10.1109/tpds.1999.808160.

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46

Lee-Juan Fan, Chang-Biau Yang, and Shyue-Horng Shiau. "Routing algorithms on the bus-based hypercube network." IEEE Transactions on Parallel and Distributed Systems 16, no. 4 (April 2005): 335–48. http://dx.doi.org/10.1109/tpds.2005.49.

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47

Mei, A., and R. Rizzi. "Hypercube computations on partitioned optical passive stars networks." IEEE Transactions on Parallel and Distributed Systems 17, no. 6 (June 2006): 497–507. http://dx.doi.org/10.1109/tpds.2006.72.

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48

Hsieh, Sun-Yuan. "A note on cycle embedding in folded hypercubes with faulty elements." Information Processing Letters 108, no. 2 (September 2008): 81. http://dx.doi.org/10.1016/j.ipl.2008.04.003.

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49

Hsieh, Sun-Yuan, Che-Nan Kuo, and Hsin-Hung Chou. "A further result on fault-free cycles in faulty folded hypercubes." Information Processing Letters 110, no. 2 (December 2009): 41–43. http://dx.doi.org/10.1016/j.ipl.2009.10.003.

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50

Chen, Xie-Bin. "Hamiltonian paths and cycles passing through a prescribed path in hypercubes." Information Processing Letters 110, no. 2 (December 2009): 77–82. http://dx.doi.org/10.1016/j.ipl.2009.10.010.

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