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Towards the Independent Spanning Trees in the Line Graphs of Interconnection Networks

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Algorithms and Architectures for Parallel Processing (ICA3PP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11336))

Abstract

Node/edge-Independent spanning trees (ISTs) have attracted a lot of attention in the past twenty years. Many results such as edge-disjoint Hamilton cycles, traceability, number of spanning trees, structural properties, topological indices, etc, have been obtained on line graphs, and researchers have applied the line graphs of some interconnection networks into data center networks, such as SWCube, BCDC, etc. However, node/edge conjecture is still open for n-node-connected interconnection network with \(n\ge \) 5. So far, results have been obtained on a lot of special interconnection networks, but few results are reported on the line graphs of them. In this paper, we consider the problem of constructing node-ISTs in a line graph G of an interconnection network \(G'\). We first give the construction of node-ISTs in \(G'\) based on the edge-ISTs in G. Then, an algorithm to construct node-ISTs in G based on the edge-ISTs in \(G'\) is presented. At the end, simulation experiments on the line graphs of hypercubes show that the maximal height of the constructed node-ISTs on the line graph of n-dimensional hypercube is \(n+1\) for \(n\ge 3\).

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Acknowledgment

This work is supported by National Natural Science Foundation of China (No. 61572337, No. 61502328, and No. 61602333), China Postdoctoral Science Foundation Funded Project (No. 2015M581858), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 18KJA520009), the Jiangsu Planned Projects for Postdoctoral Research Funds (No. 1501089B and No. 1701173B), Opening Foundation of Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks (No. WSNLBKF201701), and Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX17_2005 and No. KYCX18_2510).

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Authors and Affiliations

  1. School of Computer Science and Technology, Soochow University, Suzhou, 215006, China

    Baolei Cheng, Jianxi Fan, Xiaoyan Li, Guijuan Wang, Jingya Zhou & Yuejuan Han

  2. Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks, Nanjing, 21000, Jiangsu, China

    Baolei Cheng & Jianxi Fan

  3. Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou, China

    Baolei Cheng

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  1. Baolei Cheng
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  2. Jianxi Fan
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  3. Xiaoyan Li
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  4. Guijuan Wang
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  5. Jingya Zhou
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  6. Yuejuan Han
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Correspondence to Jianxi Fan .

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Editors and Affiliations

  1. Rutgers University–Newark, Newark, NJ, USA

    Jaideep Vaidya

  2. Guangzhou University, Guangzhou, China

    Jin Li

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Cheng, B., Fan, J., Li, X., Wang, G., Zhou, J., Han, Y. (2018). Towards the Independent Spanning Trees in the Line Graphs of Interconnection Networks. In: Vaidya, J., Li, J. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2018. Lecture Notes in Computer Science(), vol 11336. Springer, Cham. https://doi.org/10.1007/978-3-030-05057-3_27

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  • DOI: https://doi.org/10.1007/978-3-030-05057-3_27

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  • Online ISBN: 978-3-030-05057-3

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