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.
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.