The forgotten index of complement graph operations and its applications of molecular graph

Abstract

A topological index of graph \(G\) is a numerical parameter related to graph which characterizes its molecular topology and is usually graph invariant. Topological indices are widely used to determine the correlation between the specific properties of molecules and the biological activity with their configuration in the study of quantitative structure-activity relationships (QSARs). In this paper some basic mathematical operations for the forgotten index of complement graph operations such as join \(\overline {G_1+G_2}\), tensor product \(\overline {G_1 \otimes G_2}\), Cartesian product \(\overline {G_1\times G_2}\), composition \(\overline {G_1\circ G_2}\), strong product \(\overline {G_1\ast G_2}\), disjunction \(\overline {G_1\vee G_2}\) and symmetric difference \(\overline {G_1\oplus G_2}\) will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.

Role of molecular descriptors in quantitative structure‐property relationship analysis of kidney cancer therapeutics

“…Alsharaf calculates a number of basic mathematical operations by the forgotten index of complement graph operations, including join, strong product, tensor product, composition, cartesian product, disjunction, and symmetric difference for nanotorus and titania nanotubes [23].…”

The Second Hyper-Zagreb Index and Coindex of Chemical Nano-structures in Drugs

“…In 1972, Gutman and Trinajsti'c [8,9] introduced the first degree-based structure descriptors, namely the first and second Zagreb indices. In 2015, Furtula et al [10][11][12][13] proposed a novel degreebased structure descriptor known as the forgotten index (F-index). Recently, in 2020, Alameri et al [14] defined another degree-based structure descriptor denoted as the Y-index.…”

The F-index and coindex of V-Phenylenic Nanotubes and Nanotorus and their molecular complement graphs

“…Many well-known topological indices of the V-Phenylenic nanotubes and nanotorus have been computed. The forgotten index one of the most important topological indices which preserve the symmetry of molecular structures and provide a mathematical formulation to predict their physical and chemical properties [2]. In this article, in view of structure analysis and mathematical derivation, we find the F-index and coindex of certain molecular graphs nanotubes and nanotorus that are interesting molecular graphs and nano-structures.…”

“…Since the forgotten topological index and coindex are considered among the most effective topological indices in analysis the QSPR/QSAR with high accuracy, so we intend to compute the F-index and F-coindex for some nanostructures such as V-Phenylenic Nanotube V P HX[m, n] and V-Phenylenic Nanotorus V P HY [m, n] and their polynomials which are useful for description of some characteristics of nanostructures. Topological indices are the molecular descriptors that describe the structures of chemical compounds and they help us to predict certain physicochemical properties [3]. The first and second Zagreb indices can be regarded as one of the oldest graph invariants which was defined in 1972 by Gutman and Trinajsti [4,5].…”