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 (GA2) and the third (GA3) geometric–arithmetic indices of trees and chemical trees: for trees with a fixed number of vertices (n) and pendent vertices (ν), GA2 and GA3 are almost exactly linearly correlated. For various values of ν, the GA3/GA2 lines are parallel, and their distance is proportional to ν. These findings are rationalized by deducing lower and upper bounds for GA3 that are increasing linear functions of GA2 and decreasing linear functions of ν. Copyright © 2010 John Wiley & Sons, Ltd.