IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v329y2018icp297-314.html
   My bibliography  Save this article

Analyzing lattice networks through substructures

Author

Listed:
  • Lei, Hui
  • Li, Tao
  • Ma, Yuede
  • Wang, Hua

Abstract

Analyzing the topology of network structures is an important topic studied from many different aspects of science and mathematics. The Wiener polarity index (number of unordered pairs of vertices at distance 3 from each other) is one of the representative descriptors of graph structures. It was computed for several lattice networks by Chen et al. [11] in an effort to understand the properties of these networks. The Wiener polarity index is a variation of the classic distance-based graph invariant, the Wiener index (sum of distances between all pairs of vertices), which is known to be closely related to the number of substructures. In this paper we examine the numbers of various subgraphs of order 4 for these lattice networks. In addition to confirming their symmetric nature, comparing the numbers of various substructures leads to insights on other less trivial characteristics of these network structures of common interest.

Suggested Citation

  • Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:297-314
    DOI: 10.1016/j.amc.2018.02.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318301140
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.02.012?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. Cao, Shujuan & Dehmer, Matthias & Kang, Zhe, 2017. "Network Entropies Based on Independent Sets and Matchings," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 265-270.
    2. Zhang, Yanhong & Hu, Yumei, 2016. "The Nordhaus–Gaddum-type inequality for the Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 880-884.
    3. Yan, Weigen & Zhang, Zuhe, 2009. "Asymptotic energy of lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1463-1471.
    4. Yu, Guihai & Liu, Xin & Qu, Hui, 2017. "Singularity of Hermitian (quasi-)Laplacian matrix of mixed graphs," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 287-292.
    5. Hua, Hongbo & Das, Kinkar Ch., 2016. "On the Wiener polarity index of graphs," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 162-167.
    6. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "Asymptotic incidence energy of lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 193-202.
    7. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "A unified approach to the asymptotic topological indices of various lattices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 62-73.
    8. Liu, Jia-Bao & Pan, Xiang-Feng & Hu, Fu-Tao & Hu, Feng-Feng, 2015. "Asymptotic Laplacian-energy-like invariant of lattices," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 205-214.
    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. Liu, Xiaoxiao & Sun, Shiwen & Wang, Jiawei & Xia, Chengyi, 2019. "Onion structure optimizes attack robustness of interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    2. Li, Yinkui & Gu, Ruijuan, 2018. "Bounds for scattering number and rupture degree of graphs with genus," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 329-334.
    3. Noureen, Sadia & Bhatti, Akhlaq Ahmad & Ali, Akbar, 2021. "Towards the solution of an extremal problem concerning the Wiener polarity index of alkanes," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Lan, Yongxin & Li, Tao & Ma, Yuede & Shi, Yongtang & Wang, Hua, 2018. "Vertex-based and edge-based centroids of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 445-456.
    5. Ali, Akbar & Du, Zhibin & Ali, Muhammad, 2018. "A note on chemical trees with minimum Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 231-236.
    6. Sun, Chengbin & Luo, Chao, 2020. "Co-evolution of influence-based preferential selection and limited resource with multi-games on interdependent networks," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    7. Yu, Guihai & Qu, Hui, 2018. "The coefficients of the immanantal polynomial," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 38-44.
    8. Ma, Yuede & Cao, Shujuan & Shi, Yongtang & Dehmer, Matthias & Xia, Chengyi, 2019. "Nordhaus–Gaddum type results for graph irregularities," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 268-272.
    9. Cai, Qingqiong & Cao, Fuyuan & Li, Tao & Wang, Hua, 2018. "On distances in vertex-weighted trees," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 435-442.
    10. Tratnik, Niko, 2018. "On the Steiner hyper-Wiener index of a graph," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 360-371.

    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. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "A unified approach to the asymptotic topological indices of various lattices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 62-73.
    2. 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.
    3. Noureen, Sadia & Bhatti, Akhlaq Ahmad & Ali, Akbar, 2021. "Towards the solution of an extremal problem concerning the Wiener polarity index of alkanes," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Jia-Bao Liu & Mobeen Munir & Amina Yousaf & Asim Naseem & Khudaija Ayub, 2019. "Distance and Adjacency Energies of Multi-Level Wheel Networks," Mathematics, MDPI, vol. 7(1), pages 1-9, January.
    5. Ali, Akbar & Du, Zhibin & Ali, Muhammad, 2018. "A note on chemical trees with minimum Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 231-236.
    6. Lan, Yongxin & Li, Tao & Ma, Yuede & Shi, Yongtang & Wang, Hua, 2018. "Vertex-based and edge-based centroids of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 445-456.
    7. Ashrafi, Ali Reza & Ghalavand, Ali, 2017. "Ordering chemical trees by Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 301-312.
    8. Hua, Hongbo & Das, Kinkar Ch., 2016. "On the Wiener polarity index of graphs," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 162-167.
    9. Leurent, Martin & Jasserand, Frédéric & Locatelli, Giorgio & Palm, Jenny & Rämä, Miika & Trianni, Andrea, 2017. "Driving forces and obstacles to nuclear cogeneration in Europe: Lessons learnt from Finland," Energy Policy, Elsevier, vol. 107(C), pages 138-150.
    10. Wang, Juan & Li, Chao & Xia, Chengyi, 2018. "Improved centrality indicators to characterize the nodal spreading capability in complex networks," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 388-400.
    11. Shin, Kong Joo & Managi, Shunsuke, 2017. "Liberalization of a retail electricity market: Consumer satisfaction and household switching behavior in Japan," Energy Policy, Elsevier, vol. 110(C), pages 675-685.
    12. Ghorbani, Modjtaba & Dehmer, Matthias & Rajabi-Parsa, Mina & Emmert-Streib, Frank & Mowshowitz, Abbe, 2019. "Hosoya entropy of fullerene graphs," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 88-98.
    13. Liu, Xiaoyun & Yan, Weigen, 2013. "The triangular kagomé lattices revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5615-5621.
    14. Ma, Yuede & Cao, Shujuan & Shi, Yongtang & Dehmer, Matthias & Xia, Chengyi, 2019. "Nordhaus–Gaddum type results for graph irregularities," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 268-272.
    15. Bin Yang & Vinayak V. Manjalapur & Sharanu P. Sajjan & Madhura M. Mathai & Jia-Bao Liu, 2019. "On Extended Adjacency Index with Respect to Acyclic, Unicyclic and Bicyclic Graphs," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
    16. Li, Shuli & Yan, Weigen, 2016. "Dimers on the 33.42 lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 251-257.
    17. Wan, Pengfei & Tu, Jianhua & Dehmer, Matthias & Zhang, Shenggui & Emmert-Streib, Frank, 2019. "Graph entropy based on the number of spanning forests of c-cyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    18. Webber, Phil & Gouldson, Andy & Kerr, Niall, 2015. "The impacts of household retrofit and domestic energy efficiency schemes: A large scale, ex post evaluation," Energy Policy, Elsevier, vol. 84(C), pages 35-43.
    19. Das, Kinkar Ch. & Mojallal, Seyed Ahmad, 2016. "Extremal Laplacian energy of threshold graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 267-280.
    20. Yu, Guihai & Qu, Hui, 2018. "The coefficients of the immanantal polynomial," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 38-44.

    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:329:y:2018:i:c:p:297-314. 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.