Journal of Prime Research in Mathematics

Geometric arithmetic index of Alkanes and Unicyclic chemical graphs

Mohanad A. Mohammed\(^{a,*}\), Ahmed Abdulhussein Jabbar\(^{b}\)
\(^a\)Department of Mathematics, Open Educational College, Ministry of Education, Al Qadisiya Centre, Iraq.
\(^b\)Ministry of Education, Alnajaf Alashraf Education Directorate, Iraq.
Correspondence should be addressed to: Mohanad A. Mohammed at mohanadalim@gmail.com

Abstract

The geometric arithmetic \(GA\) index is one of the most investigated degree based molecular structure descriptors that have applications in chemistry. For a graph \(G\), the geometric arithmetic \(GA\) index is defined as \(GA(G)=\sum\limits_{uv\in E(G)}{\frac{2\sqrt{d_{u}d_{v}}}{d_{u}+d_{v}}}\), where d\(_{u}\) denotes the degree of a vertex \(u\) in \(G\). In this paper, we obtain the general formula for the geometric arithmetic \(GA\) index for certain trees and unicyclic graphs with application such as Alkanes, Isomerism of Alkanes and more classes of Cycloalkanes.

Keywords:

Degree of vertex, Graph, Geometric arithmetic index.