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


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.


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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


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