IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v169y2023ics0960077923001431.html
   My bibliography  Save this article

On maximum Zagreb connection indices for trees with fixed domination number

Author

Listed:
  • Raza, Zahid
  • Akhter, Shehnaz

Abstract

The Zagreb connection indices of a graph are notable topological descriptors constructed from the connection number of every vertex (cardinality of set of vertices with distance two from that vertex). In 1972, these indices were presented to determine the total electron energy of the alternate hydrocarbons. The Zagreb connection indices give finer values for the correlation coefficient for the 13 physico-chemical characteristics of the octane isomers compared to basic Zagreb indices. For many years, all these connection indices have been ignored by researchers for further work. Recently, determining the extremal bounds for the topological indices in terms of graph parameters has turned out to be an interesting direction in extremal graph theory, and numerous related results have been acquired in the literature. This article presents sharp bounds on the first, second, and modified Zagreb connection indices of trees with a fixed domination number. These bounds are strict, and the trees which attained these bounds are characterized.

Suggested Citation

  • Raza, Zahid & Akhter, Shehnaz, 2023. "On maximum Zagreb connection indices for trees with fixed domination number," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001431
    DOI: 10.1016/j.chaos.2023.113242
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923001431
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113242?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. Sadia Noureen & Akhlaq Ahmad Bhatti & Akbar Ali, 2020. "Extremum Modified First Zagreb Connection Index of - Vertex Trees with Fixed Number of Pendent Vertices," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-6, April.
    2. 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.
    3. Jinde Cao & Usman Ali & Muhammad Javaid & Chuangxia Huang, 2020. "Zagreb Connection Indices of Molecular Graphs Based on Operations," Complexity, Hindawi, vol. 2020, pages 1-15, March.
    4. Haiying Wang & Jia-Bao Liu & Shaohui Wang & Wei Gao & Shehnaz Akhter & Muhammad Imran & Mohammad R. Farahani, 2017. "Sharp Bounds for the General Sum-Connectivity Indices of Transformation Graphs," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-7, December.
    5. Yousaf, Shamaila & Bhatti, Akhlaq Ahmad & Ali, Akbar, 2022. "On total irregularity index of trees with given number of segments or branching vertices," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    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. Wang, Yiqiao & Zheng, Lina, 2020. "Computation on the difference of Zagreb indices of maximal planar graphs with diameter two," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    2. Wang, Shaohui & Wang, Chunxiang & Liu, Jia-Bao, 2018. "On extremal multiplicative Zagreb indices of trees with given domination number," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 338-350.
    3. Bermudo, Sergio & Nápoles, Juan E. & Rada, Juan, 2020. "Extremal trees for the Randić index with given domination number," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    4. Ayu Ameliatul Shahilah Ahmad Jamri & Fateme Movahedi & Roslan Hasni & Rudrusamy Gobithaasan & Mohammad Hadi Akhbari, 2022. "Minimum Randić Index of Trees with Fixed Total Domination Number," Mathematics, MDPI, vol. 10(20), pages 1-13, October.
    5. 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.
    6. 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.
    7. Shuchao Li & Licheng Zhang & Minjie Zhang, 2019. "On the extremal cacti of given parameters with respect to the difference of zagreb indices," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 421-442, August.
    8. Lkhagva Buyantogtokh & Batmend Horoldagva & Kinkar Chandra Das, 2020. "On reduced second Zagreb index," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 776-791, April.
    9. Sun, Xiaoling & Du, Jianwei, 2022. "On Sombor index of trees with fixed domination number," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    10. Shaohui Wang & Chunxiang Wang & Lin Chen & Jia-Bao Liu & Zehui Shao, 2018. "Maximizing and Minimizing Multiplicative Zagreb Indices of Graphs Subject to Given Number of Cut Edges," Mathematics, MDPI, vol. 6(11), pages 1-10, October.
    11. 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.
    12. Walter Carballosa & José Manuel Rodríguez & José María Sigarreta & Nodari Vakhania, 2019. "f -Polynomial on Some Graph Operations," Mathematics, MDPI, vol. 7(11), pages 1-18, November.

    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:chsofr:v:169:y:2023:i:c:s0960077923001431. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.