IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v335y2018icp231-236.html
   My bibliography  Save this article

A note on chemical trees with minimum Wiener polarity index

Author

Listed:
  • Ali, Akbar
  • Du, Zhibin
  • Ali, Muhammad

Abstract

The Wiener polarity index (usually denoted by Wp) of a graph G is defined as the number of unordered pairs of the vertices of G which are at distance 3. Denote by CTn the family of all n-vertex chemical trees. In a recent paper, Ashrafi and Ghalavand [1] determined the first three minimum Wp values of n-vertex chemical trees for n ≥ 7 and characterized the chemical trees attaining the first two minimum Wp values among all the members of CTn for n ≥ 4. In this note, the chemical trees with the third minimum Wp value are characterized from the graph family CTn for n ≥ 7, and the chemical trees from the family CTn,n ≥ 4, with the first two minimum Wp values are also obtained in an alternative but shorter way.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:335:y:2018:i:c:p:231-236
    DOI: 10.1016/j.amc.2018.04.051
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318303692
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.04.051?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. Hua, Hongbo & Das, Kinkar Ch., 2016. "On the Wiener polarity index of graphs," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 162-167.
    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. 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.
    4. Tsang, Eric W. K., 2014. "Old and New," Management and Organization Review, Cambridge University Press, vol. 10(03), pages 390-390, November.
    5. Ashrafi, Ali Reza & Ghalavand, Ali, 2017. "Ordering chemical trees by Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 301-312.
    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. 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).

    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. 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).
    2. 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.
    3. Ashrafi, Ali Reza & Ghalavand, Ali, 2017. "Ordering chemical trees by Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 301-312.
    4. Ali Shalizar Jalali, 2018. "Male Fertility as a Bull’s Eye for Mastocytosis," Global Journal of Reproductive Medicine, Juniper Publishers Inc., vol. 3(3), pages 58-60, February.
    5. Hui Yan & Guixiang Liu, 2021. "Fire’s Effects on Grassland Restoration and Biodiversity Conservation," Sustainability, MDPI, vol. 13(21), pages 1-15, October.
    6. Michal Plaček & Martin Schmidt & František Ochrana & Michal Půček, 2017. "Do the Selected Characteristics of Public Tenders Affect the Likelihood of Filing Petitions with the Regulators of Public Tenders?," Prague Economic Papers, Prague University of Economics and Business, vol. 2017(3), pages 317-329.
    7. Nikolov, Plamen & Adelman, Alan, 2019. "Do private household transfers to the elderly respond to public pension benefits? Evidence from rural China," The Journal of the Economics of Ageing, Elsevier, vol. 14(C).
    8. Dana Benešová & Viera Kubičková & Miroslava Prváková, 2020. "Open innovation model in the knowledge intensive business services in the Slovak Republic," Entrepreneurship and Sustainability Issues, VsI Entrepreneurship and Sustainability Center, vol. 8(2), pages 1340-1358, December.
    9. Holzmann, Robert & Alonso-García, Jennifer & Labit-Hardy, Heloise & Villegas, Andres M., 2017. "NDC Schemes and Heterogeneity in Longevity: Proposals for Redesign," IZA Discussion Papers 11193, Institute of Labor Economics (IZA).
    10. Selman, P., 2014. "Intercountry Adoption Agencies and the HCIA," ISS Working Papers - General Series 77404, International Institute of Social Studies of Erasmus University Rotterdam (ISS), The Hague.
    11. Martinho, Vítor João Pereira Domingues, 2019. "Historical records of wine: Highlighting the old wine world," EconStor Preprints 193461, ZBW - Leibniz Information Centre for Economics.
    12. Gabriella Garbarino & Giovanni Pampararo & Thanh Khoa Phung & Paola Riani & Guido Busca, 2020. "Heterogeneous Catalysis in (Bio)Ethanol Conversion to Chemicals and Fuels: Thermodynamics, Catalysis, Reaction Paths, Mechanisms and Product Selectivities," Energies, MDPI, vol. 13(14), pages 1-19, July.
    13. Zhongcheng Yan & Feng Wei & Xin Deng & Chuan Li & Qiang He & Yanbin Qi, 2022. "Feminization of Agriculture: Do Female Farmers Have Higher Expectations for the Value of Their Farmland?—Empirical Evidence from China," Agriculture, MDPI, vol. 12(1), pages 1-22, January.
    14. Hélène Laurell & Leona Achtenhagen & Svante Andersson, 2017. "The changing role of network ties and critical capabilities in an international new venture’s early development," International Entrepreneurship and Management Journal, Springer, vol. 13(1), pages 113-140, March.
    15. Hua, Hongbo & Das, Kinkar Ch., 2016. "On the Wiener polarity index of graphs," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 162-167.
    16. Trine Filges & Anu Siren & Torben Fridberg & Bjørn C. V. Nielsen, 2020. "Voluntary work for the physical and mental health of older volunteers: A systematic review," Campbell Systematic Reviews, John Wiley & Sons, vol. 16(4), December.
    17. Alexandru-Ionuţ Petrişor & Walid Hamma & Huu Duy Nguyen & Giovanni Randazzo & Anselme Muzirafuti & Mari-Isabella Stan & Van Truong Tran & Roxana Aştefănoaiei & Quang-Thanh Bui & Dragoş-Florian Vintilă, 2020. "Degradation of Coastlines under the Pressure of Urbanization and Tourism: Evidence on the Change of Land Systems from Europe, Asia and Africa," Land, MDPI, vol. 9(8), pages 1-43, August.
    18. repec:ers:journl:v:special_issue:y:2018:i:1:p:466-478 is not listed on IDEAS
    19. Sellami Sana & Verhaest Dieter & Nonneman Walter & Van Trier Walter, 2017. "The Impact of Educational Mismatches on Wages: The Influence of Measurement Error and Unobserved Heterogeneity," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 17(1), pages 1-20, February.
    20. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    21. Kenneth M. Johnson & Daniel T. Lichter, 2016. "Diverging Demography: Hispanic and Non-Hispanic Contributions to U.S. Population Redistribution and Diversity," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 35(5), pages 705-725, October.

    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:335:y:2018:i:c:p:231-236. 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.