Computation of Vertex Degree-Based Molecular Descriptors of Hydrocarbon Structure

Topological indices are such numbers or set of numbers that describe topology of structures. Nearly 400 topological indices are calculated so far. The prognostication of physical, chemical, and biological attributes of organic compounds is an important and still unsolved problem of computational chemistry. Topological index is the tool to predict the physicochemical properties such as boiling point, melting point, density, viscosity, and polarity of organic compounds. In this study, some degree-based molecular descriptors of hydrocarbon structure are calculated.

Computing Bounds for General Randic Coindex of Sum Graphs

The physical and structural properties of molecular structure or graph such as boiling point, melting point, surface tension, or solubility are studied using topological index (TI). Topological index is a mathematical formula that can be applied to any graph which models some molecular structures. The various operations play an important role in graph theory such as joining, union, intersection, products, and subdivision. In this paper, we computed the bounds for general Randic coindex of F -sum graphs such as ( S -sum, R -sum, Q -sum, and T -sum) in the form of their factor graphs. At the end, results are illustrated by numerical table for the particular F -sum graphs.

Connection-Based Multiplicative Zagreb Indices of Dendrimer Nanostars

The field of graph theory is broadly growing and playing a remarkable role in cheminformatics, mainly in chemistry and mathematics in developing different chemical structures and their physicochemical properties. Mathematical chemistry provides a platform to study these physicochemical properties with the help of topological indices (TIs). A topological index (TI) is a function that connects a numeric number to each molecular graph. Zagreb indices (ZIs) are the most studied TIs. In this paper, we establish general expressions to calculate the connection-based multiplicative ZIs, namely, first multiplicative ZIs, second multiplicative ZIs, third multiplicative ZIs, and fourth multiplicative ZIs, of two renowned dendrimer nanostars. The defined expressions just depend on the step of growth of these dendrimers. Moreover, we have compared our calculated for both type of dendrimers with each other.

Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

A topological index (TI) is a numerical descriptor of a molecule structure or graph that predicts its different physical, biological, and chemical properties in a theoretical way avoiding the difficult and costly procedures of chemical labs. In this paper, for two connected (molecular) graphs G 1 and G 2 , we define the generalized total-sum graph consisting of various (molecular) polygonal chains by the lexicographic product of the graphs T k G 1 and G 2 , where T k G 1 is obtained by applying the generalized total operation T k on G 1 with k ≥ 1 as some integral value. Moreover, we compute the different degree-based TIs such as first Zagreb, second Zagreb, forgotten Zagreb, and hyper-Zagreb. In the end, a comparison among all the aforesaid TIs is also conducted with the help of certain statistical tools for some particular families of generalized total-sum graphs under lexicographic product.

Magnetic particle-antiparticle creation and annihilation

A fundamental property of particles and antiparticles, such as electrons and positrons, is their ability to annihilate one another. Similar behavior is predicted for magnetic solitons~\cite{Kovalev_90}-- localized spin textures that can be distinguished by their topological index Q.Theoretically, magnetic topological solitons with opposite values of Q, such as skyrmions~\cite{Bogdanov_89} and their antiparticles -- antiskyrmions -- are expected to be able to merge continuously and to annihilate~\cite{Kuchkin_20i}. However, experimental verification of such particle-antiparticle pair production and annihilation processes has been lacking. Here, we report the creation and annihilation of skyrmion-antiskyrmion pairs in an exceptionally thin film of the cubic chiral magnet B20-type FeGe observed using transmission electron microscopy. Our observations are highly reproducible and are fully consistent with micromagnetic simulations. Our findings provide a new platform for fundamental studies of particles and antiparticles based on magnetic solids and open new perspectives for practical applications of thin films of isotropic chiral magnets.

QSPR Models for the Molar Refraction, Polarizability and Refractive Index of Aliphatic Carboxylic Acids Using the ZEP Topological Index

The molar refraction, polarizability, and refractive index for a series of monocarboxylic, dicarboxylic, and unsaturated monocarboxylic acids, having a symmetric or asymmetric structure, were investigated by the application of quantitative structure property relationship (QSPR) technique. We used a linear regression method and a single molecular descriptor, the ZEP topological index, calculated in a simple manner, with the help of weighted electronic distances, and also calculated on the basis of the chemical structure of the molecules. The high-quality performance and predictive ability of the QSPR models obtained were validated by means of specific validation techniques: y-randomization test, the leave-one-out cross validation procedure, and external validation. The investigated properties are well modeled (with r2 > 0.99) by the ZEP index, using the regression analysis as a statistical tool for developing reliable QSPR models. Our approach provides an alternative technique to the existing additive methods for predicting the molar refraction and polarizability of carboxylic acids, which is essentially based on the summation of atom and/or functional group contributions or bond contributions, and of some correction increments.

A Computational Approach on Acetaminophen Drug using Degree-Based Topological Indices and M-Polynomials

Topological index is a numerical representation of a chemical structure. Based on these indices, physicochemical properties, thermodynamic behavior, chemical reactivity, and biological activity of chemical compounds are calculated. Acetaminophen is an essential drug to prevent/treat various types of viral fever, including malaria, flu, dengue, SARS, and even COVID-19. This paper computes the sum and multiplicative version of various topological indices such as General Zagreb, General Randić, General OGA, AG, ISI, SDD, Forgotten indices M-polynomials of Acetaminophen. To the best of our knowledge, for the Acetaminophen drugs, these indices have not been computed previously.

HDR Degree Bassed Indices and Mhr-Polynomial for the Treatment of COVID-19

In this research work, We introduce topological indices, namely as an HDR version of Modified Zagreb topological index (HDRM*), HDR version of Modified forgotten topological index (HDRF*), and HDR version of hyper Zagreb index (HDRHM*). Then the relatively study depends on the structure-property regression analysis to test and compute the chemical applicability of these indices to predict the physicochemical properties of octane isomers. Also, we show these HDR indices have well degeneracy properties compared to other degree-based topological indices. Also, We defined and computed the Mhr-polynomial of the newly indices and applied it on COVID-19 treatments. Also, we discussed some mathematical properties of HDR indices.