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On the resistance diameter of hypercubes

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  • Sardar, Muhammad Shoaib
  • Hua, Hongbo
  • Pan, Xiang-Feng
  • Raza, Hassan

Abstract

The resistance distance among two vertices in some resistor networks has been widely considered by many physicists and mathematicians. The resistance diameter of a graph is defined by the maximum resistance distance among all pairs of vertices in the graph. The study of resistance diameter was initiated here. It seems to be possible that the resistance diameter of a graph could play a significant role in analyzing the efficiency of the interconnection networks for wave- or fluid-like communication. In order to improve the efficiency of wave- or fluid-like communication, we need to minimize the resistance diameter of graphs. The class of hypercubes is the most common, multipurpose and efficient topological structure class of interconnection networks. Hypercube networks satisfy most requirements for the basic principles of network design. The main result of this paper is to give a combinatorial formula for the resistance diameter of hypercubes. In addition, the minimum resistance distance among all pairs of vertices in hypercubes is also obtained. These two results are deduced via the electrical network approach and the hitting time of random walks, respectively.

Suggested Citation

  • Sardar, Muhammad Shoaib & Hua, Hongbo & Pan, Xiang-Feng & Raza, Hassan, 2020. "On the resistance diameter of hypercubes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317376
    DOI: 10.1016/j.physa.2019.123076
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    References listed on IDEAS

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    1. Jiabao Liu & Jinde Cao & Xiang-Feng Pan & Ahmed Elaiw, 2013. "The Kirchhoff Index of Hypercubes and Related Complex Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-7, December.
    2. Tu, Jianhua & Du, Junfeng & Su, Guifu, 2015. "The unicyclic graphs with maximum degree resistance distance," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 859-864.
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    Citations

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    Cited by:

    1. Sajjad, Wasim & Sardar, Muhammad Shoaib & Pan, Xiang-Feng, 2024. "Computation of resistance distance and Kirchhoff index of chain of triangular bipyramid hexahedron," Applied Mathematics and Computation, Elsevier, vol. 461(C).
    2. Sardar, Muhammad Shoaib & Pan, Xiang-Feng & Xu, Si-Ao, 2020. "Computation of resistance distance and Kirchhoff index of the two classes of silicate networks," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    3. Sardar, Muhammad Shoaib & Pan, Xiang-Feng & Xu, Shou-Jun, 2024. "Computation of the resistance distance and the Kirchhoff index for the two types of claw-free cubic graphs," Applied Mathematics and Computation, Elsevier, vol. 473(C).

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    1. Sardar, Muhammad Shoaib & Pan, Xiang-Feng & Xu, Si-Ao, 2020. "Computation of resistance distance and Kirchhoff index of the two classes of silicate networks," Applied Mathematics and Computation, Elsevier, vol. 381(C).

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