Relation between second and third geometric–arithmetic indices of trees

The geometric–arithmetic indices ( GA ) are a recently introduced class of molecular structure descriptors found to be useful tools in QSPR/QSAR researches. We now establish a peculiar relation between the second ( GA 2 ) and the third ( GA 3 ) geometric–arithmetic indices of trees and chemical trees: for trees with a fixed number of vertices ( n ) and pendent vertices (ν), GA 2 and GA 3 are almost exactly linearly correlated. For various values of ν, the GA 3 / GA 2 lines are parallel, and their distance is proportional to ν. These findings are rationalized by deducing lower and upper bounds for GA 3 that are increasing linear functions of GA 2 and decreasing linear functions of ν. Copyright © 2010 John Wiley & Sons, Ltd.