Conjecture Involving Arithmetic-Geometric and Geometric-Arithmetic Indices

Zainab Alsheekhhussain, Akbar Ali, Rabie A. Ramadan, Ahmed Y. Khedr and Francisco R. Villatoro

Discrete Dynamics in Nature and Society, 2022, vol. 2022, 1-3

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:1188776

DOI: 10.1155/2022/1188776

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