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Number of proper paths in edge-colored hypercubes

Author

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  • Xue, Lina
  • Yang, Weihua
  • Zhang, Shurong

Abstract

Given an integer 1 ≤ j < n, define the (j)-coloring of a n-dimensional hypercube Hn to be the 2-coloring of the edges of Hn in which all edges in dimension i, 1 ≤ i ≤ j, have color 1 and all other edges have color 2. Cheng et al. (2017) determined the number of distinct shortest properly colored paths between a pair of vertices for the (1)-colored hypercubes. It is natural to consider the number for (j)-coloring, j ≥ 2. In this note, we determine the number of different shortest proper paths in (j)-colored hypercubes for arbitrary j. Moreover, we obtain a more general result.

Suggested Citation

  • Xue, Lina & Yang, Weihua & Zhang, Shurong, 2018. "Number of proper paths in edge-colored hypercubes," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 420-424.
    • Handle: RePEc:eee:apmaco:v:332:y:2018:i:c:p:420-424
    DOI: 10.1016/j.amc.2018.03.063
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    References listed on IDEAS

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    1. Cheng, Eddie & Magnant, Colton & Medarametla, Dhruv, 2017. "Proper distance in edge-colored hypercubes," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 384-391.
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    Cited by:

    1. Yali Lv & Cheng-Kuan Lin & Lantao You, 2023. "A Novel Conditional Connectivity and Hamiltonian Connectivity of BCube with Various Faulty Elements," Mathematics, MDPI, vol. 11(15), pages 1-12, August.

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