IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v282y2016icp53-64.html
   My bibliography  Save this article

Integral trees with diameter four

Author

Listed:
  • Wang, Ligong
  • Wang, Qi
  • Huo, Bofeng

Abstract

A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. In this paper, we investigate integral trees S(r;mi)=S(a1+a2+⋯+as;m1,m2,…,ms) of diameter 4 with s=3,4,5,6. Such integral trees are found by using a computer search or solving the Diophantine equations. New sufficient conditions for a construction of infinite families of integral trees S(r′;mi)=S(b1+⋯+bs;m1,…,ms) of diameter 4 from given integral trees S(r;mi)=S(a1+⋯+as;m1,…,ms) of diameter 4 are given. Further, using these conditions we construct infinitely many new classes of integral trees S(r′;mi)=S(b1+⋯+bs;m1,…,ms) of diameter 4 with s=3,4,5,6. Finally, we propose two basic open problems about integral trees of diameter 4 for further study.

Suggested Citation

  • Wang, Ligong & Wang, Qi & Huo, Bofeng, 2016. "Integral trees with diameter four," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 53-64.
    • Handle: RePEc:eee:apmaco:v:282:y:2016:i:c:p:53-64
    DOI: 10.1016/j.amc.2016.02.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316300868
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.02.002?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. Shi, Yongtang, 2015. "Note on two generalizations of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1019-1025.
    Full references (including those not matched with items on IDEAS)

    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. 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. 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.
    4. 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.
    5. Li, Fengwei & Ye, Qingfang & Sun, Yuefang, 2017. "On edge-rupture degree of graphs," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 282-293.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Milovanović, E.I. & Milovanović, I.Ž. & Dolićanin, E.Ć. & Glogić, E., 2016. "A note on the first reformulated Zagreb index," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 16-20.
    12. Yu, Guihai & Qu, Hui, 2015. "Hermitian Laplacian matrix and positive of mixed graphs," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 70-76.
    13. Borovićanin, Bojana & Furtula, Boris, 2016. "On extremal Zagreb indices of trees with given domination number," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 208-218.
    14. 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.
    15. Li, Fengwei & Broersma, Hajo & Rada, Juan & Sun, Yuefang, 2018. "Extremal benzenoid systems for two modified versions of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 14-24.
    16. Das, Kinkar Ch., 2016. "On the Graovac–Ghorbani index of graphs," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 353-360.
    17. Banerjee, Anirban & Mehatari, Ranjit, 2015. "Characteristics polynomial of normalized Laplacian for trees," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 838-844.
    18. Ghalavand, Ali & Reza Ashrafi, Ali, 2018. "Ordering chemical graphs by Randić and sum-connectivity numbers," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 160-168.
    19. Li, Jianxi & Guo, Ji-Ming & Shiu, Wai Chee & Altındağ, Ş. Burcu Bozkurt & Bozkurt, Durmuş, 2018. "Bounding the sum of powers of normalized Laplacian eigenvalues of a graph," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 82-92.
    20. Chen, Hanlin & Wu, Renfang & Deng, Hanyuan, 2016. "The extremal values of some topological indices in bipartite graphs with a given matching number," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 103-109.

    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:282:y:2016:i:c:p:53-64. 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.