Conjecture Involving Arithmetic-Geometric and Geometric-Arithmetic Indices

Abstract

The geometric-arithmetic (GA) index of a graph G is the sum of the ratios of geometric and arithmetic means of end-vertex degrees of edges of G . Similarly, the arithmetic-geometric (AG) index of G is defined. Recently, Vujošević et al. conjectured that a tree attaining the maximum value of the addition A G + G A or difference A G − G A of the AG and GA indices in the class of all n -vertex molecular trees must contain at most one vertex of degree 2 and at most one vertex of degree 3, but not both, for every fixed integer n ≥ 11 . In this paper, the aforementioned conjecture is p.