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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
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    References listed on IDEAS

    as
    1. 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).
    2. 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.
    3. 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.
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