@article {
author = {Dehgardi, N. and Aram, H. and Khodkar, A.},
title = {The second geometric-arithmetic index for trees and unicyclic graphs},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {9},
number = {4},
pages = {279-287},
year = {2018},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2017.81079.1277},
abstract = {Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=\sum_{uv\in E(G)}\frac{2\sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree of the tree. We also find a sharp upper bound for $GA_2(G)$, where $G$ is a unicyclic graph, in terms of the order, maximum degree and girth of $G$. In addition, we characterize the trees and unicyclic graphs which achieve the upper bounds.},
keywords = {Second geometric-arithmetic index,Trees,Unicyclic graphs},
url = {http://ijmc.kashanu.ac.ir/article_81544.html},
eprint = {http://ijmc.kashanu.ac.ir/article_81544_d6ee54879d3b9af783c9e4a0e8b112b9.pdf}
}