@article {
author = {Dehgardi, Nasrin},
title = {Lower Bounds on the Entire Sombor Index},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {14},
number = {4},
pages = {195-205},
year = {2023},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2023.253281.1739},
abstract = {Let $G=(V,E)$ be a graph. The entire Sombor index of graph $G$, $ SO^\varepsilon(G) $ is defined as the sum of the terms$\sqrt{d_{G}^2(a)+d_{G}^2(b)}$, where $a$ is either adjacent to or incident with $b$ and$a,b\in V\cup E$.It is known that if $T$ is a tree of order $n$, then $SO^\varepsilon(T)\ge 6\sqrt{5}+8(n-3)\sqrt{2}$. We improve this result and establish best lower bounds on the entire Sombor index with given vertices number and maximum degree. Also, we determine the extremal trees achieve these bounds.},
keywords = {Sombor index,Entire Sombor index,tree},
url = {https://ijmc.kashanu.ac.ir/article_114100.html},
eprint = {https://ijmc.kashanu.ac.ir/article_114100_0165f87626c23140ed11b5b6803ea920.pdf}
}