IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v461y2024ics0096300323004824.html
   My bibliography  Save this article

Computation of resistance distance and Kirchhoff index of chain of triangular bipyramid hexahedron

Author

Listed:
  • Sajjad, Wasim
  • Sardar, Muhammad Shoaib
  • Pan, Xiang-Feng

Abstract

The two point effective resistance in some electrical networks has been extensively studied by many mathematicians and physicists. The computation of the effective resistance among two points in a network is a well-known problem in electrical networks theory. To solve this problem, we can apply methods such as the series principle, parallel principle, star-mesh transformation and Delta-Y transformation. The resistance distance among vertices u and v in a graph G is the effective resistance among the corresponding points in the given electrical network obtained from G by converting each edge of G with resistor of 1 ohm. The Kirchhoff index is the sum of resistance distance between all pairs of vertices of graph G. Chain of triangular bipyramid hexahedron structure which is a polyhedral graph has many applications in the area of reticular chemistry. In our paper, we compute the resistance distance among all pairs of vertices in the chain of triangular bipyramid hexahedron. Also we compute the closed formula for Kirchhoff index.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:461:y:2024:i:c:s0096300323004824
    DOI: 10.1016/j.amc.2023.128313
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323004824
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128313?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. Jiang, Zhuozhuo & Yan, Weigen, 2017. "Resistance between two nodes of a ring network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 21-26.
    3. R. B. Bapat & Somit Gupta, 2010. "Resistance distance in wheels and fans," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(1), pages 1-13, February.
    4. Liu, Jia-Bao & Pan, Xiang-Feng, 2016. "Minimizing Kirchhoff index among graphs with a given vertex bipartiteness," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 84-88.
    5. 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).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    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. Yang, Yujun & Cao, Yuliang & Yao, Haiyuan & Li, Jing, 2018. "Solution to a conjecture on a Nordhaus–Gaddum type result for the Kirchhoff index," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 241-249.
    4. Faxu Li & Hui Xu & Liang Wei & Defang Wang, 2023. "RETRACTED ARTICLE: Identifying vital nodes in hypernetwork based on local centrality," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-13, January.
    5. Jia-Bao Liu & Muhammad Kashif Shafiq & Haidar Ali & Asim Naseem & Nayab Maryam & Syed Sheraz Asghar, 2019. "Topological Indices of m th Chain Silicate Graphs," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    6. Fei, Junqi & Tu, Jianhua, 2018. "Complete characterization of bicyclic graphs with the maximum and second-maximum degree Kirchhoff index," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 118-124.
    7. Wenyu Shi & Qiang Tang, 2023. "RETRACTED ARTICLE: Cost-optimized data placement strategy for social network with security awareness in edge-cloud computing environment," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-15, January.
    8. Jia-Bao Liu & S. N. Daoud, 2019. "Number of Spanning Trees in the Sequence of Some Graphs," Complexity, Hindawi, vol. 2019, pages 1-22, March.
    9. Lin, Wei & Li, Min & Zhou, Shuming & Liu, Jiafei & Chen, Gaolin & Zhou, Qianru, 2021. "Phase transition in spectral clustering based on resistance matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    10. Li Zhang & Jing Zhao & Jia-Bao Liu & Salama Nagy Daoud, 2019. "Resistance Distance in the Double Corona Based on R -Graph," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    11. Liu, Jia-Bao & Zhao, Jing & Cai, Zheng-Qun, 2020. "On the generalized adjacency, Laplacian and signless Laplacian spectra of the weighted edge corona networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    12. Praba, B. & Saranya, R., 2020. "Application of the graph cellular automaton in generating languages," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 111-121.
    13. Jian Lu & Shu-Bo Chen & Jia-Bao Liu & Xiang-Feng Pan & Ying-Jie Ji, 2019. "Further Results on the Resistance-Harary Index of Unicyclic Graphs," Mathematics, MDPI, vol. 7(2), pages 1-13, February.
    14. Huang, Guixian & He, Weihua & Tan, Yuanyao, 2019. "Theoretical and computational methods to minimize Kirchhoff index of graphs with a given edge k-partiteness," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 348-357.
    15. Sun, Wensheng & Yang, Yujun, 2023. "Extremal pentagonal chains with respect to the Kirchhoff index," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    16. Fang Gao & Xiaoxin Li & Kai Zhou & Jia-Bao Liu, 2018. "The Extremal Graphs of Some Topological Indices with Given Vertex k -Partiteness," Mathematics, MDPI, vol. 6(11), pages 1-11, November.
    17. Hong, Yunchao & Zhu, Zhongxun & Luo, Amu, 2018. "Some transformations on multiplicative eccentricity resistance-distance and their applications," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 75-85.
    18. Fan, Jiaqi & Zhu, Jiali & Tian, Li & Wang, Qin, 2020. "Resistance Distance in Potting Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    19. Jia Wei & Jing Wang, 2022. "Spectra of Complemented Triangulation Graphs," Mathematics, MDPI, vol. 10(17), pages 1-9, September.
    20. Li Zhang & Jing Zhao & Jia-Bao Liu & Micheal Arockiaraj, 2018. "Resistance Distance in H -Join of Graphs G 1 , G 2 , … , G k," Mathematics, MDPI, vol. 6(12), pages 1-10, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:461:y:2024:i:c:s0096300323004824. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.