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On the Maximum ABS Index of Fixed-Order Trees with a Given Maximum Degree

Author

Listed:
  • Venkatesan Maitreyi

    (Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamil Nadu, India)

  • Suresh Elumalai

    (Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamil Nadu, India)

  • Akbar Ali

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2240, Saudi Arabia)

  • Selvaraj Balachandran

    (Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur 613401, Tamil Nadu, India)

  • Hicham Saber

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2240, Saudi Arabia)

  • Adel A. Attiya

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2240, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

The ABS (atom-bond sum-connectivity) index of a graph G is denoted by A B S ( G ) and is defined as ∑ x y ∈ E ( G ) ( d x + d y ) − 1 ( d x + d y − 2 ) , where d x represents the degree of the vertex x in G . In this paper, we derive the best possible upper bounds on the ABS index for fixed-order trees possessing a given maximum degree, which provides a solution to the open problem proposed quite recently by Hussain, Liu and Hua.

Suggested Citation

  • Venkatesan Maitreyi & Suresh Elumalai & Akbar Ali & Selvaraj Balachandran & Hicham Saber & Adel A. Attiya, 2024. "On the Maximum ABS Index of Fixed-Order Trees with a Given Maximum Degree," Mathematics, MDPI, vol. 12(17), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2704-:d:1467525
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