%0 Journal Article %T On the difference between geometric-arithmetic index and atom-bond connectivity index for trees %A Zuki, Wan Nor Nabila Nadia Wan %A Hasni, Roslan %A Husin, Nor Hafizah Md. %A Du, Zhibin %A Raheem, Abdul %J Journal of Mathematics and Computer Science %D 2021 %V 22 %N 1 %@ ISSN 2008-949X %F Zuki2021 %X Let \(G\) be a simple and connected graph with vertex set \(V(G)\) and edge set \(E(G)\). The geometric-arithmetic index and atom-bond connectivity index of graph \(G\) are defined as \(GA(G)=\sum_{uv\in E(G)} \frac{2\sqrt{d_ud_v}}{d_u + d_v}\) and \(ABC(G)=\sum_{uv\in E(G)} \sqrt{\frac{d_u+d_v-2}{d_ud_v}}\), respectively, where the summation extends over all edges \(uv\) of \(G\), and \(d_u\) denotes the degree of vertex \(u\) in \(G\). Let \((GA-ABC)(G)\) denote the difference between \(GA\) and \(ABC\) indices of \(G\). In this note, we determine \(n\)-vertex binary trees with first three minimum \(GA-ABC\) values. We also present a lower bound for \(GA-ABC\) index of molecular trees with fixed number of pendant vertices. %9 journal article %R 10.22436/jmcs.022.01.05 %U http://dx.doi.org/10.22436/jmcs.022.01.05 %P 49--58