The geometric arithmetic (GA) index of certain trees and bicyclic graphs

The geometric arithmetic (𝐺𝐴) index is one of the recently most investigated degree-based molecular structure descriptors that have applications in chemistry. For a graph 𝐺, the (𝐺𝐴) index is defined as 𝐺𝐴(𝐺)= Σ2√𝑑𝑢𝑑𝑣𝑑𝑢+𝑑𝑣𝑢𝑣∈𝐸(𝐺), where 𝑑𝑢 denotes the degree of a vertex 𝑢 in 𝐺. In this paper, we obtain the general formulas of geometric arithmetic 𝐺𝐴 index for two types of trees graphs. Also, we provide the general formulas to the bicyclic graphs after attaching branches of 𝐵𝑖 for all vertices. Finally, we computed the geometric arithmetic 𝐺𝐴 index to the molecular graph representing the molecular structure of the bicyclic chemical graphs.