Using Variable and Fixed Topological Indices for the Prediction of Reaction Rate Constants of Volatile Unsaturated Hydrocarbons with OH Radicals

mVolatile organic compounds (VOCs) play an important role in differentphotochemical processes in the troposphere. In order to predict their impact on ozoneformation processes a detailed knowledge about their abundance in the atmosphere as wellas their reaction rate constants is required. The QSPR models were developed for theprediction of reaction rate constants of volatile unsaturated hydrocarbons. The chemicalstructure was encoded by constitutional and topological indices. Multiple linear regressionmodels using CODESSA software was developed with the RMSCV error of 0.119 log units.The chemical structure was encoded by six topological indices. Additionally, a regressionmodel using a variable connectivity index was developed. It provided worse cross-validation results with an RMSCV error of 0.16 log units, but enabled a structuralinterpretation of the obtained model. We differentiated between three classes of carbonatoms: sp2-hybridized, non-allylic sp3-hybridized and allylic sp3-hybridized. The structuralinterpretation of the developed model shows that most probably the most importantmechanisms are the addition to multiple bonds and the hydrogen atom abstraction at allylicsites

New Bounds for Topological Indices on Trees through Generalized Methods

This article belongs to the Special Issue Analytical and Computational Properties of Topological Indices.Topological indices are useful for predicting the physicochemical behavior of chemical compounds. A main problem in this topic is finding good bounds for the indices, usually when some parameters of the graph are known. The aim of this paper is to use a unified approach in order to obtain several new inequalities for a wide family of topological indices restricted to trees and to characterize the corresponding extremal trees. The main results give upper and lower bounds for a large class of topological indices on trees, fixing or not the maximum degree. This class includes the first variable Zagreb, the Narumi–Katayama, the modified Narumi–Katayama and the Wiener index.The first author was partially supported by a grant from Ministerio de Ciencia, Innovación y Universidades (PGC2018-098321-B-I00), Spain; the second author was partially supported by two grants from Ministerio de Economía y Competitividad, Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (MTM2016-78227-C2-1-P and MTM2017-90584-REDT), Spain

Topological indices and f-polynomials on some graph products

We Obtain Inequalities Involving Many Topological Indices In Classical Graph Products By Using The F-Polynomial. In Particular, We Work With Lexicographic Product, Cartesian Sum And Cartesian Product, And With First Zagreb, Forgotten, Inverse Degree And Sum Lordeg Indices.Gobierno de Españ

Inequalities on Topological Indices

Topological indices have been widely used in different fields associated with scientific research. They are recognized as useful tools in applied research in Chemistry, Ecology, Biology, Physics, among others. For many years, scientists have been trying to improve the predictive power of the famous Randi’c index. This led to the introduction and study of new topological descriptors that correlate or improve the level of prediction of the Randi’c index. Among the most commonly used descriptors are the Inverse index, the first general Zagreb index and the recently introduced Arithmetic- Geometric index. In this work we study the mathematical properties and relationships of the aforementioned topological indices.Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de MadridPresidente: Domingo de Guzmán Pestana Galván.- Secretaria: Ana Portilla Ferreira.- Vocal: Eva Tourís Loj