Calculation of topological indices from molecular structures and applications

Abstract

This mini review presents a brief description of the research efforts for new topological indices of organic molecular structures undertaken in the authors' laboratory at Changchun Institute of Applied Chemistry, Chinese Academy of Sciences. They were used for the processing of chemical information, as highly selective topological indices for uniqueness determination, as highly selective atomic chiral indices for chiral center recognition, in the exhaustive generation of isomers, in a stereo code for the exhaustive generation of stereoisomers, in the prediction of C-13 nuclear magnetic resonance spectra, and in studies on rare earth extractions. The topological indices A mi , 3D descriptors, and chiral descriptors are described, as well as their applications in quantitative structure activity/property relationship studies. KEYWORDShighly selective chiral indices, highly selective topological indices, processing of chemical information, QSAR/QSPR, structure generator 1 | OVERVIEW Among the myriad of available methods for the representation of molecular structures, graph theoretical (topological) indices are one of the most widely used techniques for processing chemical information, quantitative structure activity/property relationship (QSAR/QSPR) studies, and for searching combinatorial libraries to find structures that are most similar to a target structure. 1 However, not all indices can be used for the same tasks. For example, the Wiener index has been satisfactorily correlated with paraffin boiling points, but its uniqueness (selectivity) is not sufficient.For the administration of chemical information, databases are the important components, such as mass spectra, infrared spectra, nuclear magnetic resonance (NMR), rare earth (RE), and toxicological compound databases constructed from the early 1980s in China. Nuclear magnetic resonance and RE databases were built by the Changchun Institute of Applied Chemistry, Chinese Academy of Sciences (CIAC, CAS). Correspondingly, a large number of schemes for encoding molecules and extracting descriptors of structures were suggested, which were used for database searching

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“…Topological data analysis plays an important role in the use of chemometric methods such as principal component analysis, pattern recognition, cluster analysis, artificial neural networks, as well as in screening combinatorial libraries (ZHANG et al, 2018). The application of these multivariate data analysis methodologies requires the representation of chemical structures by a set of numbers called molecular descriptors, which contain information on the number and type of connections between the atoms that form the molecule.…”

On the extremal cactus graphs for variable sum exdeg index with a fixed number of cycles

“…In molecular graphs, vertices correspond to the atoms while edges represent the covalent bonds between atoms [9,12]. Among the various existing techniques for handling the issues of predicting physicochemical properties of chemical compounds and seeking combinatorial libraries to find molecular structures that are generally comparative to a target structure, the method involving topological indices is one of the simplest and most widely used such techniques [1,3,6,16,17]. Topological indices are actually those numerical quantities of (molecular) graph which remain same under graph isomorphism [8].…”

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“…In particular, many authors have worked on constructing graph-theoretic polynomials based on which some of these topological indices can be found [14][15][16][17][18][19][20][21]. For various applications of topological indices, we cite [22][23][24][25][26].…”