IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v333y2018icp435-442.html
   My bibliography  Save this article

On distances in vertex-weighted trees

Author

Listed:
  • Cai, Qingqiong
  • Cao, Fuyuan
  • Li, Tao
  • Wang, Hua

Abstract

The study of extremal problems on various graph invariants has received great attention in recent years. Among the most well known graph invariants is the sum of distances between all pairs of vertices in a graph. This is also known as the Wiener index for its applications in Chemical Graph Theory. Many interesting properties related to this concept have been established for extremal trees that maximize or minimize it. Recently a vertex-weighted analogue of sum of distances is introduced for vertex weighted trees. Some extremal results on (vertex-weighted) trees were obtained, by Goubko, for trees with a given degree sequence. In this note we first analyze the behavior of vertex-weighted distance sum in general, identifying the “middle part” of a tree analogous to that with respect to the regular distance sum. We then provide a simpler approach (than that of Goubko’s) to obtain a stronger result regarding the extremal tree with a given degree sequence. Questions and directions for potential future study are also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:435-442
    DOI: 10.1016/j.amc.2018.03.117
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318302984
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.03.117?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. Goubko, Mikhail, 2018. "Maximizing Wiener index for trees with given vertex weight and degree sequences," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 102-114.
    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. 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.
    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. Dobrynin, Andrey A., 2019. "Infinite family of 2-connected transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 1-4.
    2. Li, Shuchao & Wang, Hua & Wang, Shujing, 2019. "Some extremal ratios of the distance and subtree problems in binary trees," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 232-245.
    3. 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.
    4. 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. Yu, Guihai & Qu, Hui, 2018. "The coefficients of the immanantal polynomial," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 38-44.
    2. 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.
    3. 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.
    4. Tratnik, Niko, 2018. "On the Steiner hyper-Wiener index of a graph," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 360-371.
    5. Xiangxiang Liu & Ligong Wang & Xihe Li, 2020. "The Wiener index of hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 351-364, February.
    6. 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).
    7. Li, Fengwei & Ye, Qingfang & Broersma, Hajo & Ye, Ruixuan & Zhang, Xiaoyan, 2021. "Extremality of VDB topological indices over f–benzenoids with given order," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    8. 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.
    9. 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).
    10. 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.
    11. Al-Yakoob, Salem & Stevanović, Dragan, 2020. "On transmission irregular starlike trees," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    12. Li, Shuchao & Wang, Hua & Wang, Shujing, 2019. "Some extremal ratios of the distance and subtree problems in binary trees," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 232-245.
    13. 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).
    14. Dobrynin, Andrey A., 2019. "Infinite family of 2-connected transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 1-4.
    15. 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.

    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:333:y:2018:i:c:p:435-442. 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.