# On the difference between geometric-arithmetic index and atom-bond connectivity index for trees

Volume 22, Issue 1, pp 49--58
Publication Date: June 29, 2020 Submission Date: April 16, 2020 Revision Date: April 28, 2020 Accteptance Date: May 16, 2020
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### Authors

Wan Nor Nabila Nadia Wan Zuki - Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia. Roslan Hasni - Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia. Nor Hafizah Md. Husin - Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia. Zhibin Du - School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong, P. R. China. Abdul Raheem - Department of Higher Education, Govt. Postgraduate College Asghar Mall Rawalpindi, Pakistan.

### Abstract

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.

### Share and Cite

##### ISRP Style

Wan Nor Nabila Nadia Wan Zuki, Roslan Hasni, Nor Hafizah Md. Husin, Zhibin Du, Abdul Raheem, On the difference between geometric-arithmetic index and atom-bond connectivity index for trees, Journal of Mathematics and Computer Science, 22 (2021), no. 1, 49--58

##### AMA Style

Zuki Wan Nor Nabila Nadia Wan, Hasni Roslan, Husin Nor Hafizah Md., Du Zhibin, Raheem Abdul, On the difference between geometric-arithmetic index and atom-bond connectivity index for trees. J Math Comput SCI-JM. (2021); 22(1):49--58

##### Chicago/Turabian Style

Zuki, Wan Nor Nabila Nadia Wan, Hasni, Roslan, Husin, Nor Hafizah Md., Du, Zhibin, Raheem, Abdul. "On the difference between geometric-arithmetic index and atom-bond connectivity index for trees." Journal of Mathematics and Computer Science, 22, no. 1 (2021): 49--58

### Keywords

• Atom-bond connectivity index
• geometric-arithmetic index
• trees

•  05C35
•  05C90

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