IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v6y2018i12p283-d185609.html
   My bibliography  Save this article

Resistance Distance in H -Join of Graphs G 1 , G 2 , … , G k

Author

Listed:
  • Li Zhang

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Jing Zhao

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Jia-Bao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Micheal Arockiaraj

    (Department of Mathematics, Loyola College, Chennai 600034, India)

Abstract

In view of the wide application of resistance distance, the computation of resistance distance in various graphs becomes one of the main topics. In this paper, we aim to compute resistance distance in H -join of graphs G 1 , G 2 , … , G k . Recall that H is an arbitrary graph with V ( H ) = { 1 , 2 , … , k } , and G 1 , G 2 , … , G k are disjoint graphs. Then, the H -join of graphs G 1 , G 2 , … , G k , denoted by ⋁ H { G 1 , G 2 , … , G k } , is a graph formed by taking G 1 , G 2 , … , G k and joining every vertex of G i to every vertex of G j whenever i is adjacent to j in H . Here, we first give the Laplacian matrix of ⋁ H { G 1 , G 2 , … , G k } , and then give a { 1 } -inverse L ( ⋁ H { G 1 , G 2 , … , G k } ) { 1 } or group inverse L ( ⋁ H { G 1 , G 2 , … , G k } ) # of L ( ⋁ H { G 1 , G 2 , … , G k } ) . It is well know that, there exists a relationship between resistance distance and entries of { 1 } -inverse or group inverse. Therefore, we can easily obtain resistance distance in ⋁ H { G 1 , G 2 , … , G k } . In addition, some applications are presented in this paper.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:283-:d:185609
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/6/12/283/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/6/12/283/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Frank Werner, 2019. "Discrete Optimization: Theory, Algorithms, and Applications," Mathematics, MDPI, vol. 7(5), pages 1-4, May.
    2. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. 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).
    9. 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.
    10. 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.
    11. 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).
    12. 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.
    13. 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.
    14. 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.
    15. Jia Wei & Jing Wang, 2022. "Spectra of Complemented Triangulation Graphs," Mathematics, MDPI, vol. 10(17), pages 1-9, September.
    16. 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.
    17. Wang, Daohua & Zeng, Cheng & Zhao, Zixuan & Wu, Zhiqiang & Xue, Yumei, 2023. "Kirchhoff index of a class of polygon networks," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

    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:gam:jmathe:v:6:y:2018:i:12:p:283-:d:185609. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.