IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v280y2016icp162-167.html
   My bibliography  Save this article

On the Wiener polarity index of graphs

Author

Listed:
  • Hua, Hongbo
  • Das, Kinkar Ch.

Abstract

The Wiener polarity index Wp(G) of a graph G is the number of unordered pairs of vertices {u, v} in G such that the distance between u and v is equal to 3. Very recently, Zhang and Hu studied the Wiener polarity index in [Y. Zhang, Y. Hu, 2016] [38]. In this short paper, we establish an upper bound on the Wiener polarity index in terms of Hosoya index and characterize the corresponding extremal graphs. Moreover, we obtain Nordhaus–Gaddum-type results for Wp(G). Our lower bound on Wp(G)+Wp(G¯) is always better than the previous lower bound given by Zhang and Hu.

Suggested Citation

  • Hua, Hongbo & Das, Kinkar Ch., 2016. "On the Wiener polarity index of graphs," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 162-167.
    • Handle: RePEc:eee:apmaco:v:280:y:2016:i:c:p:162-167
    DOI: 10.1016/j.amc.2016.01.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316300431
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.01.043?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. 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.
    2. Su, Guifu & Tu, Jianhua & Das, Kinkar Ch., 2015. "Graphs with fixed number of pendent vertices and minimal Zeroth-order general Randić index," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 705-710.
    3. Shi, Yongtang, 2015. "Note on two generalizations of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1019-1025.
    4. Das, Kinkar Ch. & Gutman, Ivan & Nadjafi–Arani, Mohammad J., 2015. "Relations between distance–based and degree–based topological indices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 142-147.
    5. Li, Jing & Li, Yiyang, 2015. "The asymptotic value of the zeroth-order Randić index and sum-connectivity index for trees," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1027-1030.
    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. 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.
    2. Ashrafi, Ali Reza & Ghalavand, Ali, 2017. "Ordering chemical trees by Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 301-312.
    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. 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.

    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. Das, Kinkar Ch., 2016. "On the Graovac–Ghorbani index of graphs," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 353-360.
    2. Cui, Qing & Zhong, Lingping, 2017. "The general Randić index of trees with given number of pendent vertices," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 111-121.
    3. Das, Kinkar Ch. & Dehmer, Matthias, 2016. "Comparison between the zeroth-order Randić index and the sum-connectivity index," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 585-589.
    4. Zhang, Xin, 2019. "Upper bound on the sum of powers of the degrees of graphs with few crossings per edge," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 163-169.
    5. Gutman, Ivan, 2016. "On Steiner degree distance of trees," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 163-167.
    6. Lan, Yongxin & Li, Tao & Wang, Hua & Xia, Chengyi, 2019. "A note on extremal trees with degree conditions," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 70-79.
    7. Su, Guifu & Tu, Jianhua & Das, Kinkar Ch., 2015. "Graphs with fixed number of pendent vertices and minimal Zeroth-order general Randić index," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 705-710.
    8. Du, Zhibin, 2017. "Further results regarding the sum of domination number and average eccentricity," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 299-309.
    9. Ali, Akbar & Raza, Zahid & Bhatti, Akhlaq Ahmad, 2016. "Bond incident degree (BID) indices of polyomino chains: A unified approach," Applied Mathematics and Computation, Elsevier, vol. 287, pages 28-37.
    10. 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).
    11. Wang, Ligong & Wang, Qi & Huo, Bofeng, 2016. "Integral trees with diameter four," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 53-64.
    12. Li, Fengwei & Ye, Qingfang & Sun, Yuefang, 2017. "On edge-rupture degree of graphs," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 282-293.
    13. Sun, Qiang & Ikica, Barbara & Škrekovski, Riste & Vukašinović, Vida, 2019. "Graphs with a given diameter that maximise the Wiener index," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 438-448.
    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. Kinkar Ch. Das & M. J. Nadjafi-Arani, 2017. "On maximum Wiener index of trees and graphs with given radius," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 574-587, August.
    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. 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.
    18. Nadeem, Muhammad Faisal & Zafar, Sohail & Zahid, Zohaib, 2016. "On topological properties of the line graphs of subdivision graphs of certain nanostructures," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 125-130.
    19. 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.
    20. Ma, Gang & Bian, Qiuju & Wang, Jianfeng, 2019. "The weighted vertex PI index of (n,m)-graphs with given diameter," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 329-337.

    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:280:y:2016:i:c:p:162-167. 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.