On Extremum Geometric-Arithmetic Indices of (Molecular) Trees

摘要

The geometric-arithmetic index (GA index for short) is a newly proposed graph invariant, based on the end-vertex degrees of all edges of a graph, in mathematical chemistry. Du et al. [On geometric arithmetic indices of (molecular) trees, unicyclic graphs and bicyclic graphs, MATCH Commun. Math: Comput. Chem. 66 (2011), 681-697] determined the first six maximum values for the GA indices of trees. In this paper, we will present a further ordering for the GA indices of trees, and determine the first fourteen maximum values. In particular, the trees with the first fourteen maximum GA indices are all molecular trees.