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Hamiltonian Properties of the Dragonfly Network

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New Trends in Computer Technologies and Applications (ICS 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1723))

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Abstract

The dragonfly network is a hierarchical network with a low diameter and high throughput, which uses a set of high-cardinality routers to increase the effective cardinality of the network. The Hamiltonian property is instrumental in communication networks. In this paper, we study the Hamiltonian properties of the logical graph of the dragonfly network, denoted by D(n, h, g), where n, h, and g represent the number of vertices in each group, the number of edges that each vertex connects to other groups, and the number of groups, respectively. Firstly, we show that there exists a Hamiltonian cycle and propose an O(g) algorithm for constructing a Hamiltonian cycle in D(n, h, g) when \(n \ge 2\) and \(h \ge 1\). Then, we prove that D(n, h, g) is Hamiltonian-connected for \(n \ge 4\) and \(h \ge 2\).

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 62172291, 62272333, U1905211), and Jiangsu Province Department of Education Future Network Research Fund Project (FNSRFP-2021-YB-39).

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Authors and Affiliations

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

    Suying Wu, Baolei Cheng, Yan Wang, Yuejuan Han & Jianxi Fan

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  1. Suying Wu
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  2. Baolei Cheng
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  3. Yan Wang
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  4. Yuejuan Han
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  5. Jianxi Fan
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Corresponding author

Correspondence to Jianxi Fan .

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Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Sun-Yuan Hsieh

  2. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  3. CNRS and University of Bordeaux, Talence, France

    Ralf Klasing

  4. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

  5. National Taipei University of Business, Taoyuan, Taiwan

    Sheng-Lung Peng

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Wu, S., Cheng, B., Wang, Y., Han, Y., Fan, J. (2022). Hamiltonian Properties of the Dragonfly Network. In: Hsieh, SY., Hung, LJ., Klasing, R., Lee, CW., Peng, SL. (eds) New Trends in Computer Technologies and Applications. ICS 2022. Communications in Computer and Information Science, vol 1723. Springer, Singapore. https://doi.org/10.1007/978-981-19-9582-8_15

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  • DOI: https://doi.org/10.1007/978-981-19-9582-8_15

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  • Online ISBN: 978-981-19-9582-8

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