On the inverse sum indeg index. (English) Zbl 1311.05201
Summary: Discrete Adriatic indices have been defined by D. Vukičević and M. Gašperov [“Bond aditive modelling. I: Ariatic indices”, Croat. Chem. Acta, 83, 243–260 (2010)], as a way of generalizing well-known molecular descriptors defined as the sum of individual bond contributions, such as the second Zagreb index or the Randić index. Among the 148 discrete Adriatic indices analyzed by Vukičević and Gašperov on the benchmark datasets of the International Academy of Mathematical Chemistry, 20 indices were selected as significant predictors of physicochemical properties.
Here we study graph-theoretical properties of the inverse sum indeg index, which was selected as a significant predictor of total surface area of octane isomers, and determine extremal values of this index across several graph classes, including connected graphs, chemical graphs, trees and chemical trees.
Here we study graph-theoretical properties of the inverse sum indeg index, which was selected as a significant predictor of total surface area of octane isomers, and determine extremal values of this index across several graph classes, including connected graphs, chemical graphs, trees and chemical trees.
MSC:
| 05C90 | Applications of graph theory |
Software:
MathchemReferences:
| [1] | Balaban, A. T., Highly discriminating distance based numerical descriptor, Chem. Phys. Lett., 89, 399-404 (1982) |
| [2] | Devillers, J.; Balaban, A. T., Topological Indices and Related Descriptors in QSAR and QSPR (1999), Gordon and Breach: Gordon and Breach Amsterdam |
| [3] | Gutman, I.; Trinajstić, N., Graph theory and molecular orbitals. Total \(\pi \)-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, 535-538 (1972) |
| [5] | Karelson, M., Molecular Descriptors in QSAR/QSPR (2000), Wiley-Interscience: Wiley-Interscience New York |
| [6] | Randić, M., On characterization of molecular branching, J. Am. Chem. Soc., 97, 6609-6615 (1975) |
| [7] | Todeschini, R.; Consonni, V., Handbook of Molecular Descriptors (2000), Wiley-VCH: Wiley-VCH Weinheim |
| [9] | Vasilyev, A.; Stevanović, D., Mathchem: a python package for calculating topological indices, MATCH Commun. Math. Comput. Chem., 71, 657-680 (2014) |
| [10] | Vukičević, D., Bond additive modeling 2. Mathematical properties of Max-Min Rodeg index, Croat. Chem. Acta, 83, 261-273 (2010) |
| [11] | Vukičević, D.; Gašperov, M., Bond aditive mdelling 1. Ariatic indices, Croat. Chem. Acta, 83, 243-260 (2010) |
| [12] | Wiener, H., Structural determination of paraffin boiling points, J. Am. Chem. Soc., 69, 17-20 (1947) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
