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 AG + GA or difference AG − GA 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.