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

Venkatesan Maitreyi, Suresh Elumalai, Akbar Ali (), Selvaraj Balachandran, Hicham Saber and Adel A. Attiya
Additional contact information
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

Mathematics, 2024, vol. 12, issue 17, 1-11

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.

Keywords: topological index; atom-bond sum-connectivity index; tree graph; maximum degree (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/17/2704/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/17/2704/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:17:p:2704-:d:1467525

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().