Generalized graph theoretic indices in chemistry
Estrada, Ernesto and Matamala, A.R.; Gutman, I. and Furtula, B., eds. (2010) Generalized graph theoretic indices in chemistry. In: Theory and Applications II. Mathematical Chemistry Monographs No.9. University of Kragujevac, pp. 217230. ISBN 9788681829998
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In the development of any scientific theory, the initial stage based on the accumulation of observational facts is necessarily followed by the formalization and generalization of the concepts involved. Graph theoretic molecular descriptors, which are referred as topological indices (TI) have been around for more than half century [1]. During this time many TIs have been defined [1], their mathematical properties have been scrutinized [2, 3], and more importantly they have proved to be useful in predicting molecular properties beyond any reasonable doubt [4]. Then, the field is mature enough to jump to the next stage of development. That is, the formalization and generalization of concepts that permits the elaboration of a physical theory for topological indices in molecular sciences. In 2001 one of the current authors (EE) proposed a graph theoretic scheme that permitted the generalization of several of the best known TIs [5]. In a subsequent series of papers we have shown several of the principal characteristics of this generalized scheme for graph theoretic indices in chemistry, hereafter named GGTI [612]. Among the most relevant characteristics of GGTI we can mention the following ones: It groups the definition of many known TIs into one graph theoretic invariant, namely a quadratic form based on a generalized graph matrix and vectors [5, 10]. TIs are designed alacarte more than in ad hoc way to describe a particular experimental property, which improves significantly the predictability of the methods used [79]. The generalized graph matrix can be used to generalize quantum chemical concepts, such as the Hückel Molecular Orbital method or the LennardJones potentials for unitedatoms [6, 12]. The method permits the optimization of local vertex invariants (LOVIs) to account for atomic properties, which is an avenue to be explored for introducing heteroatoms in the GGTI scheme. The structural interpretation of the TIs can be carried out in a generalized way accounting for throughbonds and throughspace interatomic interactions in molecules [512]. The aim of the current work is to review the GGTI method with special emphasis in the methodological aspects of the method and its applications for predicting physicochemical properties. Our objective is twofold. First, that chemists interested in the prediction of molecular properties are aware of the generality and simplicity of the GGTI approach in such a way that they can use it in modelling physical, chemical pharmacological, toxicological and environmental properties of organic molecules. Secondly, that graph theorists, both mathematicians and chemists, explore more deeply the possibilities of GGTI for studying molecular graphs. We hope that this chapter be of interest for both communities.


Item type: Book Section ID code: 29306 Dates: DateEvent2010PublishedSubjects: Science > Chemistry Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 21 Jun 2011 09:44 Last modified: 08 Apr 2024 12:41 URI: https://strathprints.strath.ac.uk/id/eprint/29306