engleski

Zagreb indices: an overview and development of new variants

Topological indices, so-called degree-based topological indices, are defined as the sum (over all bonds/edges) of the contributions of valences of atoms/vertices forming chemical bonds in the molecular structure represented by a graph. They are a large family of molecular descriptors used in QSAR/QSPR (Quantitative Structure-Activity/Property Relationship) modelling. The development of new degree-based topological indices and the analysis of their mathematical properties belong to the field of mathematics (mathematical chemistry), while their chemical interpretation and application takes place in the field of chemical modelling, with applications in biology, pharmacy, toxicology or environmental protection. Among the degree-based topological indices, the Zagreb indices M1 and M2, introduced 50 years ago by Gutman and Trinajstić [1], stand out together with the Randić connectivity index [2]. They have recently attracted more and more attention and became the basis and motivation for the introduction of numerous new degree-based indices [3]. The application and suitability of these new topological descriptors for chemical modelling will be explained in terms of their (1) chemical-structural interpretation and (2) correlation with the chemical properties of molecules. To assess the statistical significance of the obtained relationships, more advanced validation methods used in the validation of models in chemistry, such as cross-validation and external predictivity, were used. The final results, based on more rigorous validation procedures, favour the original variants of the Zagreb indices and those based on the sum of the valences of the atoms. These results differ from those in the literature, which are based only on fit validation procedures. References [1] I. Gutman ; N. Trinajstić, Chem. Phys. Lett., 17 (1972) 535-538. [2] M. Randić, J. Am. Chem. Soc. 97 (1975) 6606–6615. [3] I. Gutman, Croat. Chem. Acta. 86 (2013) 351–361.

chemical graph, vertex-degree, topological descriptor, Zagreb index, modified Zagreb index M1, QSPR

Basic grant of MZO/RBI to Bono Lučić