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1

On knowledge discovery and representations of molecular structures using topological indices

Alsaadi Fawaz E., Bokhary Syed Ahtsham Ul Haq, Shah Aqsa, Ali Usman, Cao Jinde, Alassafi Madini Obad, Rehman Masood Ur, Rahman Jamshaid Ul

Journal of Artificial Intelligence and Soft Computing Research

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2021

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Vol. 11, No. 1

21--32

EN

The main purpose of a topological index is to encode a chemical structure by a number. A topological index is a graph invariant, which decribes the topology of the graph and remains constant under a graph automorphism. Topological indices play a wide role in the study of QSAR (quantitative structure-activity relationship) and QSPR (quantitative structure-property relationship). Topological indices are implemented to judge the bioactivity of chemical compounds. In this article, we compute the ABC (atom-bond connectivity); ABC4 (fourth version of ABC), GA(geometric arithmetic) and GA5(fifth version of GA) indices of some networks sheet. These networks include: octonano window sheet; equilateral triangular tetra sheet; rectangular sheet; and rectangular tetra sheet networks.

2

Prediction of cohesion energy of polymers using topological indices

Xu J., Chen B., Liang H., Xu W., Cui W.

Polimery

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2009

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T. 54, nr 1

19-25

EN

The quantitative structure-property relationship (QSPR) study of the cohesion energy (Ecoh) values for a training set of 60 polymers was carried out using only topological indices as input parameters. A general four-parameter correlation was obtained to predict Ecoh values by stepwise multilinear regression analysis (MLRA), with squared correlation coefficient (R2) equal to 0.9775 and standard error of estimation (s) 2455J/mol. The mean relative error (MRE) of Ecoh prediction was 5.82%. The stability of the proposed model was validated using Leave-One-Out cross-validation, randomization experiments and external test set. The model requires only topological indices for the predictions and its advantage is relative ease in calculation of descriptors which makes it easy to apply.

PL

Dotyczącą energii kohezji (Ecoh) ilościową zależność struktura-właściwości (QSPR - quantitative structure-property relationship) wykorzystano do określenia wartości Ecoh wzorcowej serii 60 polimerów z zastosowaniem w charakterze parametrów wejściowych wyłącznie wskaźników topologicznych. Uzyskano ogólną czteroparametrową zależność [równanie (6)] pozwalającą na prognozowanie Ecoh metodą krokowej wieloliniowej analizy regresji (MLRA - stepwise multilinear regression analysis) z kwadratem współczynnika korelacji R2=0,9975 i ze standardowym błędem oznaczania s=2455J/mol (tabele 1 i 2, rys. 1). Średni błąd względny (MRE) tego oznaczania wynosił 5,82% (rys. 2). Trwałość omawianego modelu oceniono wykorzystując sposób walidacji krzyżowej w wariancie Leave-One-Out (LOO) (rys. 3, tabela 3) oraz testu prognozowania Ecoh serii polimerowych próbek zewnętrznych (tabela 5, rys. 4). Określono również istotność poszczególnych parametrów występujących w wyprowadzonej 4-parametrowej zależności (tabela 4). Pozwala ona na wiarygodne prognozowanie wartości Ecoh na podstawie wyłącznie wskaźników topologicznych a jej dodatkową zaletą użytkową jest możliwość uniknięcia skomplikowanych obliczeń.

3

Mathematical Chemistry: (3,g)-Cages with Girth g, Topological Indices, and Other Graph-Theoretical Problems

Balaban A.T.

Fundamenta Informaticae

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2005

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Vol. 64, nr 1-4

1-16

EN

This essay contains personal views about mathematical chemistry - mainly with non-numerical and non-quantum flavor. Similarities between mathematics and chemistry are pointed out, mainly based on the invention aspect of these two sciences, in contrast to discoveries characterizing most natural sciences. The author's involvement with chemical applications of graph theory needed a biographical background. Then five topics are reviewed: (1) enumerations of certain classes of chemical compounds initiated in collaboration with Professors Silviu Teleman and Frank Harary; (2) the (3,g)-cages with g = 10 and 11; (3) isoprenoid structures modeled in collaboration with Professor Solomon Marcus by cellular automata and picture grammars; (4) benzenoid polycyclic hydrocarbons described in collaboration with Professor Ioan Tomescu; and (5) topological indices.

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Indeksy topologiczne i ich znaczenie w badaniach chromatograficznych. Cz. 2

Pyka A.

Wiadomości Chemiczne

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1998

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[Z] 52, 9-10

727--754

EN

The prediction of physicochemical and toxicological properties of organic compounds with selected topological indices have been reviewed in monographs and in dedicated articles The first topological indices used to the prediction of selected physicochemical properties (boiling point, heat of formation, heat of vaporization, molar volume, molar refraction) were: Wiener index, polarity number and Platt's index. The Wiener index has been continuously modified In recent years topological indices have come prominently to the fore on several different fronts. The prime reason for wide publicity accorded to these indices has been the remarkable ability to correlate and predict the properties of a vast range of molecular species. Topological indices based on the adjacency matrix, on the distance matrix and on information theory were applicable to the calculation of many physicochemical properties and to the evaluation of biological and toxicological properties of organic compounds. The procedure for calculating the topological indices is illustrated in this work by the calculation of the topological indices based on the adjacency matrix (the Gutman index M1), ; the Randić connectivity indices (0X, 1X, 2X, 0Xv, 1Xv, 2Xv); on the distance matrix (the Wiener index W); the Pyka indices (A, 0B, 1B, 2B); the Balaban index (IB); the Schultz Molecular Topological Index (MTI) for pentamethylenediamine. It should be noted that none of these topological indices yet described differentiates between d and l isomers. The procedure for calculating the optical topological index (Iopt) for d and l isomers is illustrated in this work by the calculation of Iopt for d- and l-alanine. Applications of these topological indices for the correlation analysis are discussed. The TLC, the HPLC and the GC retention parameters of different organic compounds were calculated using equations with the topological indices. As examples, selected correlation equations for calculation retention parameters in TLC, in HPLC, and in GC were shown in this work Definitions of the three-dimensional Wiener number 3W and the mean square distance topological indices of the s-th order D(x) were presented.