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Relation between second and third geometric–arithmetic indices of trees
Author(s) -
Furtula Boris,
Gutman Ivan
Publication year - 2011
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1342
Subject(s) - mathematics , quantitative structure–activity relationship , relation (database) , combinatorics , class (philosophy) , arithmetic , geometric mean , discrete mathematics , stereochemistry , computer science , chemistry , statistics , artificial intelligence , data mining
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.