Relation between geometric–arithmetic and arithmetic–geometric indices

Abstract

The paper is concerned with the two topological indices, GA and AG, constructed from the geometric and arithmetic means of the end-vertices of edges. Inequalities involving GA and AG are established. The two indices are linearly correlated, whereas for molecular graphs of benzenoid and similar polycyclic conjugated systems, the linear relation between GA and AG is exact. This indicates that introducing (in 2015) the index AG, after GA has already been conceived (in 2009), was fully unjustified.