Abstract
A new look on the problem of the molecular systems index description is presented. The capabilities of iterated line (edge) graphs in characterization of saturated hydrocarbons properties were investigated. It was demonstrated that single selected molecular (graph-theoretical (topological) or informational) descriptor calculated for the sequence of nested line graphs provides quite reliable progressive set of regression equations. Hence, the problem of descriptor set reduction is solved in the presented approach at list partially. Corresponding program complex (QUASAR) has been implemented with Python 3 program language. As the test example physico-chemical properties of octane isomers have been chosen. Among the properties under investigation there are boiling point, critical temperature, critical pressure, enthalpy of vaporization, enthalpy of formation, surface tension and viscosity. The corresponding rather simple linear regression equations which include one, two or three parameters correspondingly have been obtained. The predictive ability of the equations has been investigated using internal validation tests. The test by leave-one-out (LOO) validation and Y‑scrambling evaluate the obtained equations as adequate. For instance, for the regression model for boiling point the best equation characterizes by determination coefficients R2 = 0.943, with LOO procedure – Q2 = 0.918, while for the Y-scrambling test Q2y-scr<0.3 basically. It is shown that all the abovementioned molecular properties in iterated line graph approach can be effectively described by commonly used topological indices. Namely almost every randomly selected topological index can give adequate equation. Effectiveness is demonstrated on the example of Zagreb group indices. Also essential effectiveness and rather universal applicability of the so-called “forgotten” index (ZM3) was demonstrated.
Highlights
Development and investigation of new materials are strongly connected with building of corresponding mathematical models for target properties
Such tasks designated by widely known acronym QSAR – quantity structure-activity relationships (QSPR – quantity structure-property relationships) [1,2]
Information about predictive ability of regression equations based on ZM1, ZM2, and ZM3 indices is collected in the Table 3
Summary
Development and investigation of new materials are strongly connected with building of corresponding mathematical models for target properties. During the long history of QSAR investigations, the large set of so-called topological descriptors (TDs) based at chemical graph theory and information theory has been developed. By V(mol) we designate procedure of molecular vertex graph building, while G(k 1) E G(k) corresponds to building of line graph from previous one Adjacency matrix for such a sequence can be calculated using well-known matrix expression: Ak 1 Bk Bk 2I ,. In the present article we use the sequence of graphs for building QSAR models namely regression equations. Information about predictive ability of regression equations based on ZM1, ZM2, and ZM3 indices is collected in the Table 3 In this table di is ith vertex degree, tij is graph distance between i and j vertices,.
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