IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i10p1151-d558285.html
   My bibliography  Save this article

Inequalities on the Generalized ABC Index

Author

Listed:
  • Paul Bosch

    (Facultad de Ingeniería, Universidad del Desarrollo, Ave. La Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago 7610658, Chile
    These authors contributed equally to this work.)

  • Edil D. Molina

    (Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54 Col. Garita, 39650 Acalpulco Gro., Mexico
    These authors contributed equally to this work.)

  • José M. Rodríguez

    (Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
    These authors contributed equally to this work.)

  • José M. Sigarreta

    (Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54 Col. Garita, 39650 Acalpulco Gro., Mexico
    These authors contributed equally to this work.)

Abstract

In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for A B C α improved, when α = 1 / 2 , known results on the A B C index. Moreover, in order to obtain our results, we proved a kind of converse Hölder inequality, which is interesting on its own.

Suggested Citation

  • Paul Bosch & Edil D. Molina & José M. Rodríguez & José M. Sigarreta, 2021. "Inequalities on the Generalized ABC Index," Mathematics, MDPI, vol. 9(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1151-:d:558285
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/10/1151/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/10/1151/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jair J. Pineda-Pineda & C. T. Martínez-Martínez & J. A. Méndez-Bermúdez & Jesús Muñoz-Rojas & José M. Sigarreta, 2020. "Application of Bipartite Networks to the Study of Water Quality," Sustainability, MDPI, vol. 12(12), pages 1-19, June.
    2. Shao, Zehui & Wu, Pu & Gao, Yingying & Gutman, Ivan & Zhang, Xiujun, 2017. "On the maximum ABC index of graphs without pendent vertices," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 298-312.
    3. Das, Kinkar Chandra & Rodríguez, José M. & Sigarreta, José M., 2020. "On the maximal general ABC index of graphs with given maximum degree," Applied Mathematics and Computation, Elsevier, vol. 386(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. Shaohui Wang & Zehui Shao & Jia-Bao Liu & Bing Wei, 2019. "The Bounds of Vertex Padmakar–Ivan Index on k -Trees," Mathematics, MDPI, vol. 7(4), pages 1-10, April.
    2. Muhammad Imran & Muhammad Kamran Siddiqui & Amna A. E. Abunamous & Dana Adi & Saida Hafsa Rafique & Abdul Qudair Baig, 2018. "Eccentricity Based Topological Indices of an Oxide Network," Mathematics, MDPI, vol. 6(7), pages 1-13, July.
    3. Lin, Wenshui & Chen, Jianfeng & Wu, Zhixi & Dimitrov, Darko & Huang, Linshan, 2018. "Computer search for large trees with minimal ABC index," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 221-230.
    4. Das, Kinkar Chandra & Rodríguez, José M. & Sigarreta, José M., 2020. "On the maximal general ABC index of graphs with given maximum degree," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    5. Frank Aangel Hernández-Mira & José Luis Rosas-Acevedo & Maximino Reyes-Umaña & Juan Violante-González & José María Sigarreta-Almira & Nodari Vakhania, 2021. "Multimetric Index to Evaluate Water Quality in Lagoons: A Biological and Geomorphological Approach," Sustainability, MDPI, vol. 13(9), pages 1-18, April.

    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:gam:jmathe:v:9:y:2021:i:10:p:1151-:d:558285. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.