Abstract
The modified second Zagreb index, symmetric difference index, inverse symmetric index, and augmented Zagreb index are among the molecular descriptors which have good correlations with some physicochemical properties (such as formation heat, total surface area, etc.) of chemical compounds. By a random cyclooctane chain, we mean a molecular graph of a saturated hydrocarbon containing at least two rings such that all rings are cyclooctane, every ring is joint with at most two other rings through a single bond, and exactly two rings are joint with one other ring. In this article, our main purpose is to determine the expected values of the aforementioned molecular descriptors of random cyclooctane chains explicitly. We also make comparisons in the form of explicit formulae and numerical tables consisting of the expected values of the considered descriptors of random cyclooctane chains. Moreover, we outline the graphical profiles of these comparisons among the mentioned descriptors.
Highlights
Chemical graph theory is a branch of mathematics which deals with the mathematical modeling of graphs that is an essential branch of theoretical chemistry
We study the expected values of the modified Zagreb, symmetric difference, inverse symmetric, and augmented Zagreb indices in random cyclooctane chain
We are going to provide an expository comparison between the expected values for the modified Zagreb, symmetric difference, inverse symmetric, and augmented Zagreb indices for arbitrary cyclooctane chains with the same probabilities
Summary
Chemical graph theory is a branch of mathematics which deals with the mathematical modeling of graphs that is an essential branch of theoretical chemistry. Initial chemical research introduced the theory of chemical graphs. Chemists have confirmed that the physicochemical properties of a compound have been associated with molecular arrangement, with results derived from an enormous number of investigational data. The researchers considered the same topological index based on various chemical properties and applied it to QSR/QSPR learning. The features of a compound derived by chemical experiments are not very authentic. There are numerous topological indices in the literature of chemical graph theory. The first of its kind is the Wiener index [1]. The most important topological index is the class of the Zagreb indices and its variants [2]
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