On optimal molecular trees with respect to Sombor indices

Akbar Ali; Sadia Noureen; Akhlaq A. Bhatti; Abeer M. Albalahi; Akbar Ali; Sadia Noureen; Akhlaq A. Bhatti; Abeer M. Albalahi

doi:10.3934/math.2023270

AIMS Mathematics

2023, Volume 8, Issue 3: 5369-5390. doi: 10.3934/math.2023270

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On optimal molecular trees with respect to Sombor indices

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, Pakistan
3.
Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, Pakistan

Received: 27 September 2022 Accepted: 24 October 2022 Published: 15 December 2022
MSC : 05C09, 05C90, 05C92

The Sombor index and reduced Sombor index, introduced by mathematical chemist Ivan Gutman [MATCH Commun. Math. Comput. Chem. 86 (2021) 11–16], are the recently proposed degree-based graph invariants that attained a lot of attention from researchers in a very short time. In this paper, the best possible upper bounds on the both aforementioned indices for molecular trees are obtained in terms of order and number of branching vertices or vertices of degree 2. The optimal molecular trees achieving the obtained bounds are also completely characterized.
- topological index,
- Sombor indices,
- molecular trees,
- optimization
Citation: Akbar Ali, Sadia Noureen, Akhlaq A. Bhatti, Abeer M. Albalahi. On optimal molecular trees with respect to Sombor indices[J]. AIMS Mathematics, 2023, 8(3): 5369-5390. doi: 10.3934/math.2023270

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Abstract

The Sombor index and reduced Sombor index, introduced by mathematical chemist Ivan Gutman [MATCH Commun. Math. Comput. Chem. 86 (2021) 11–16], are the recently proposed degree-based graph invariants that attained a lot of attention from researchers in a very short time. In this paper, the best possible upper bounds on the both aforementioned indices for molecular trees are obtained in terms of order and number of branching vertices or vertices of degree 2. The optimal molecular trees achieving the obtained bounds are also completely characterized.

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