On the Maximum ABS Index of Fixed-Order Trees with a Given Maximum Degree
The ABS (atom-bond sum-connectivity) index of a graph G is denoted by ABS(G) and is defined as ∑xy∈E(G)(dx+dy)−1(dx+dy−2), where dx 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.
Authors
- Hicham Saber (ORCID: https://orcid.org/0000-0003-3453-9277)
- Suresh Elumalai (ORCID: https://orcid.org/0000-0001-7935-1644)
- Selvaraj Balachandran (ORCID: https://orcid.org/0000-0001-8498-3822)
- Venkatesan Maitreyi
- Akbar Ali (ORCID: https://orcid.org/0000-0001-8160-4196)
- Adel A. Attiya (ORCID: https://orcid.org/0000-0001-7135-7400)
Institutions
- SRM Institute of Science and Technology (IN)
- Mansoura University (EG)
- University of Ha'il (SA)
- SASTRA University (IN)
Publication Details
- Journal
- Mathematics
- Published
- 2024-08-30
- DOI
- https://doi.org/10.3390/math12172704
- Primary Topic
- Graph theory and applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00