Computing two types of geometric-arithmetic indices of some benzenoid graphs

Abstract

The geometric-arithmetic index is a topological index was defined as $GA(G)=sum{uvin E(G)}frac{2sqrt{d_ud_v}}{d_u+d_v}}$, where d_u denotes the degree of vertex u in G. By replacing instead $delta_u=sum_{vcong u} d_v$ of d_u in GA(G), we have a new version of this index that defined as $GA(G)=sum{uvin E(G)}frac{2sqrt{delta_udelta_v}}{delta_u+delta_v}}$. In this paper, we present exact formulas of these indices for some benzenoid graphs.