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Design and analysis of the rotational binary graph as an alternative to hypercube and Torus

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Abstract

Network cost is equal to degree × diameter and is one of the important measurements when evaluating graphs. Torus and hypercube are very well-known graphs. When these graphs expand, a Torus has an advantage in that its degree does not increase. A hypercube has a shorter diameter than that of other graphs, because when the graph expands, the diameter increases by 1. Hypercube Qn has 2n nodes, and its diameter is n. We propose the rotational binary graph (RBG), which has the advantages of both hypercube and Torus. RBGn has 2n nodes and a degree of 4. The diameter of RBGn would be 1.5n + 1. In this paper, we first examine the topology properties of RBG. Second, we construct a binary spanning tree in RBG. Third, we compare other graphs to RBG considering network cost specifically. Fourth, we suggest a broadcast algorithm with a time complexity of 2n − 2. Finally, we prove that RBGn embedded into hypercube Qn results in dilation n, and expansion 1, and congestion 7.

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Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A3B03032173).

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Authors and Affiliations

  1. Department of Multimedia Engineering, National University of Chonnam, Yeosu, Chonnam, 59626, Republic of Korea

    Jung-hyun Seo

  2. Department of Computer Education, National University of Sunchon, Jungang-ro 255, Sunchon, Chonnam, 57922, Republic of Korea

    HyeongOk Lee

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  1. Jung-hyun Seo
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  2. HyeongOk Lee
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Correspondence to HyeongOk Lee.

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Seo, Jh., Lee, H. Design and analysis of the rotational binary graph as an alternative to hypercube and Torus. J Supercomput 76, 7161–7176 (2020). https://doi.org/10.1007/s11227-019-03115-x

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