%0 Journal Article
%T The second geometric-arithmetic index for trees and unicyclic graphs
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Dehgardi, N.
%A Aram, H.
%A Khodkar, A.
%D 2018
%\ 12/01/2018
%V 9
%N 4
%P 279-287
%! The second geometric-arithmetic index for trees and unicyclic graphs
%K Second geometric-arithmetic index
%K Trees
%K Unicyclic graphs
%R 10.22052/ijmc.2017.81079.1277
%X Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, 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.
%U http://ijmc.kashanu.ac.ir/article_81544_d6ee54879d3b9af783c9e4a0e8b112b9.pdf