@article {
author = {Ghalavand, Ali and Tavakoli, Mostafa},
title = {Another Approach to a Conjecture about the Exponential Reduced Sombor Index of Molecular Trees},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {13},
number = {2},
pages = {99-108},
year = {2022},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2022.246488.1632},
abstract = {For a graph G, the exponential reduced Sombor index (ERSI), denoted by eSored , is ∑uv∈E(G) e√(dG(v)-1)^2+(dG(u)-1)^2), where dG(v) is the degree of vertex v. The authors in [On the reduced Sombor index and its applications, MATCH Commun. Math. Comput. Chem. 86 (2021) 729–753] conjectured that for each molecular tree T of order n, eSored(T)≤(2/3) (n+1) e3 +(1/3) (n-5) e 3√2, where n≡2 (mod 3), eSored(T)≤(1/3) (2n+1) e3 +(1/3) (n-13) e3√2 + 3e√13 , where n≡1 (mod 3) and eSored(T)≤(2/3) ne3 +(1/3) (n-9) e3√2 + 2e√10 , where n≡0 (mod 3). Recently, Hamza and Ali [On a conjecture regarding the exponential reduced Sombor index of chemical trees. Discrete Math. Lett. 9 (2022) 107–110] proved the modified version of this conjecture. In this paper, we adopt another method to prove it. },
keywords = {Sombor index,Exponential reduced Sombor index,Degree,Tree},
url = {https://ijmc.kashanu.ac.ir/article_112031.html},
eprint = {https://ijmc.kashanu.ac.ir/article_112031_9a77b0a18799e9ef991fd52ef5f9359d.pdf}
}