Original scientific paper

Harary Index - Twelve Years Later

Bono Lučić
Ante Miličević
Sonja Nikolić orcid.org/0000-0003-3203-040X ; The Rugjer Bošković Institute, P. O. Box 180, HR-10002 Zagreb, Croatia
Nenad Trinajstić

Abstract

A modification of the Harary index, denoted by H and introduced twelve years ago, is proposed. Unlike the original index, this index, called the modified Harary index and denoted by mH, consists of two parts: the first relates to greater contributions of outer bonds and the second to smaller contributions of inner bonds of an alkane, which is in accordance with the chemists’ intuition. The Wiener index W, Harary index and modified Harary index are compared in the structure-property modeling of eight representative properties of lower alkanes. The models considered were linear, Wiener-like and linear and nonlinear multivariate. Multivariate models were obtained using our variable selection procedure CROMRsel (B. Lučić and N. Trinajstić, J. Chem. Inf Comput. Sci. 39 (1999) 121-132). Multivariate models represent considerable improvements over the other two kinds of models. For example, the standard error of estimate improves on going from the best linear structure-boiling point model involving mH (S = 7.6 °C) to the best Wiener-like model based on the reduced Wiener number W/N2 and the number of paths of the length of three p3 (S = 6.2 °C) to the best four-parameter multivariate model containing ln values of W, H and mH, and p₃ (S = 1.5 °C). Ali good models obtained in this work involve mH, suggesting that this index has a great potential to be used in QSPR. Its advantage over W and H is due to the fact that the main contribution to mH comes from the outer, more exposed, bonds, which is not the case of the other two indices.

Keywords

Harary index; lower alkanes; modified Harary index; structure-property modeling; Wiener index

Hrčak ID:

131738

URI

https://hrcak.srce.hr/131738

Publication date:

4.11.2002.

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