A complete solution for maximizing the general Sombor index of chemical trees with given number of pendant vertices

Sultan Ahmad and Kinkar Chandra Das

Applied Mathematics and Computation, 2025, vol. 505, issue C

Abstract: For a graph G, the general Sombor (SOα) index is defined as:SOα(G)=∑vivj∈E(G)(di2+dj2)α, where α≠0 is a real number, E(G) is the edge set and di denotes the degree of a vertex vi in G. A chemical tree is a tree in which no vertex has a degree greater than 4, and a pendant vertex is a vertex with degree 1. This paper aims to completely characterize the n− vertex chemical trees with a fixed number of pendant vertices (=p) that maximize the SOα index over α0<α<α1, where α0≈0.144 is the unique non-zero root of equation 4(32α−25α)+8α−13α+5α−10α=0 and α1≈3.335 is the unique non-zero solution of equation 3(17α−10α)+3(20)α−13α−2(25)α=0. Since SO1 and SO12 correspond to the classical forgotten and the Sombor indices of a graph G, respectively, our results apply to both indices. Moreover, Liu et al. [More on Sombor indices of chemical graphs and their applications to the boiling point of benzenoid hydrocarbons, Int. J. Quantum Chem. 121 (2021) #26689] addressed the problem of maximizing the Sombor index for chemical trees with even p≥6 only, which was later extended by Du et al. [On bond incident degree index of chemical trees with a fixed order and a fixed number of leaves, Appl. Math. Comput. 464 (2024) #128390] to include both even p≥6 and odd p≥9. This paper, in contrast, provides a more comprehensive solution, fully characterizing the problem for all p≥3 maximizing the general Sombor index for any α, where α0<α<α1. In addition, the chemical significance of the SOα index over the range −10≤α≤10 is explored by using the octane isomers dataset to predict their physicochemical properties. Promising results are obtained when the approximated values of α belong to the set {−1,1,8,10}.

Keywords: Chemical graph theory; Sombor index; General Sombor index; Extremal tree; Pendant vertex; Chemical tree (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300325002589
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:505:y:2025:i:c:s0096300325002589

DOI: 10.1016/j.amc.2025.129532

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().