IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v283y2016icp163-167.html
   My bibliography  Save this article

On Steiner degree distance of trees

Author

Listed:
  • Gutman, Ivan

Abstract

Let G be a connected graph, and u, v, w its vertices. By du is denoted the degree of the vertex u, by d(u, v) the (ordinary) distance of the vertices u and v, and by d(u, v, w) the Steiner distance of u, v, w. The degree distance DD of G is defined as the sum of terms [du+dv]d(u,v) over all pairs of vertices of G. As early as in the 1990s, a linear relation was discovered between DD of trees and the Wiener index. We now consider SDD, the Steiner–distance generalization of DD, defined as the sum of terms [du+dv+dw]d(u,v,w) over all triples of vertices of G. Also in this case, a linear relation between SDD and the Wiener index could be established.

Suggested Citation

  • Gutman, Ivan, 2016. "On Steiner degree distance of trees," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 163-167.
    • Handle: RePEc:eee:apmaco:v:283:y:2016:i:c:p:163-167
    DOI: 10.1016/j.amc.2016.02.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316301497
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.02.038?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. 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.
    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.
    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. Hongfang Liu & Jinxia Liang & Yuhu Liu & Kinkar Chandra Das, 2023. "A Combinatorial Approach to Study the Nordhaus–Guddum-Type Results for Steiner Degree Distance," Mathematics, MDPI, vol. 11(3), pages 1-19, February.
    2. Li, Shuchao & Liu, Xin & Sun, Wanting & Yan, Lixia, 2023. "Extremal trees of a given degree sequence or segment sequence with respect to average Steiner 3-eccentricity," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    3. Wu, Xiaoxia & Zhang, Lianzhu & Chen, Haiyan, 2017. "Spanning trees and recurrent configurations of a graph," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 25-30.
    4. Zhang, Jie & Wang, Hua & Zhang, Xiao-Dong, 2019. "The Steiner Wiener index of trees with a given segment sequence," Applied Mathematics and Computation, Elsevier, vol. 344, pages 20-29.
    5. 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. 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. 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).
    3. Wenjie Ning & Yuheng Song & Kun Wang, 2022. "More on Sombor Index of Graphs," Mathematics, MDPI, vol. 10(3), pages 1-12, January.
    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.
    5. 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.
    6. Das, Kinkar Ch., 2016. "On the Graovac–Ghorbani index of graphs," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 353-360.
    7. 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.
    8. 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.
    9. Ashrafi, Ali Reza & Ghalavand, Ali, 2017. "Ordering chemical trees by Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 301-312.

    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:283:y:2016:i:c:p:163-167. 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.