Conjecture Involving Arithmetic-Geometric and Geometric-Arithmetic Indices - Zainab Alsheekhhussain; Akbar Ali; Rabie A. Ramadan; Ahmed Y. Khedr (Discrete Dynamics in Nature and Society)
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.