Degree-based Topological Indices Research Articles

Neighborhood degree sum-based molecular indices and their comparative analysis of some silicon carbide networks

Topological indices of a molecular graph are numeric quantities that characterize its numerous physico-chemical properties, chemical reactivities and biological activities. The neighborhood M-polynomial is productive for discovering neighborhood degree sum-based topological indices. This article deals with computing the neighborhood M-polynomial of silicon carbide networks Si 2 C 3-I[p, q], Si 2 C 3-II[p, q] and Si 2 C 3-III[p, q], and hence examining some standard neighborhood degree sum-based topological indices for the aforementioned networks. The obtained results are analyzed graphically. Moreover, a comparative study of the outcomes with some well-established degree-based topological indices of the silicon carbide networks is executed.

Investigating the properties of octane isomers by novel neighborhood product degree-based topological indices

A topological index is a real number calculated from the structure of a chemical compound to describe its topology. The use of molecular descriptors has been increasing in recent years, helping to determine the physicochemical and biological properties of drugs. The main purpose of this article is to investigate the properties of the octane isomers using the theoretical method. To study the structures of octane isomers, we have introduced a new approach called “neighborhood product degree” to calculate all the classical degree-based topological indices. The np-degree approach is applied to approximate eight properties of octane isomers, such as the acentric factor, density, refractive index, critical volume, molar volume, radius of curvature, critical pressure, and LogP. The np-degree-based topological indices are the estimated values of the properties of octane structures, so the linear and quadratic regression models and correlation coefficients are applied to check the validity of the estimated results. The quantitative structure property relation are obtained by using the linear, quadratic, exponential, logarithmic and sinusoidal regression methods with the help of SPSS. Two models are applied to all the compuations and three regression models are applied to the np-degree Randic index. The computation showed that quadratic regression model is suitable for study octane isomers and np-degree based graph invariants. If the values of the correlation coefficient r ⩾ 0.7, p-values ⩽ 0.05, and F-values ⩾ 2.5, then the results are significant. The results of np-degree-based topological indices satisfy all the criteria for being significant, so these newly introduced indices are valid to study octane isomers. The information determined in this article is beneficial for chemists and pharmacists.

Computing Topological Indices for Niobium Dioxide and Metal-Organic Frameworks via M-Polynomials

This paper investigates the topological properties of metal-organic frameworks and niobium dioxide using M-polynomials. The stability and wide range of bonding that the molecule exhibits make it a promising candidate for a number of uses, such as energy storage, gas detection, and catalysis. We use M-polynomials to calculate several degree-based topological indices for metal-organic frameworks and niobium dioxide. The M-polynomial is one such fundamental polynomial that provides a way to derive a multitude of degree-based topological indices. These indices are crucial for research in chemistry, biology, and physics and are derived from degree-based M-polynomials. This work develops a new M-polynomial algorithm for the computation and comparison of several degree-based molecular descriptors.

Sombor Index and Sombor Polynomial of the Noncommuting Graph Associated to Some Finite Groups

Sombor index is a newly developed degree-based topological index which involves the degree of the vertex in a simple connected graph. The Sombor index is known as the square root of the sum of the squared degrees of two adjacent vertices in a graph. Meanwhile, the noncommuting graph associated to a group is a graph where its vertices are the non-central elements of the group and two vertices are adjacent if and only if they do not commute. In this study, a new notion called the Sombor polynomial is introduced. Then, the general formula of the Sombor index and the Sombor polynomial of the noncommuting graph associated to some finite groups are determined by using their definitions and some preliminaries. The groups involved in this research are the dihedral groups, the quasidihedral groups, and the generalized quaternion groups. The results found can help the chemists and biologists to predict the chemical and physical properties of the molecules without involving any laboratory work.

On Ve-Degree and Ev-Degree Based Topological Invariants of Chemical Structures

In the realm of graph theory, recent developments have introduced novel concepts, notably the ν ε -degree and ε ν -degree, offering expedited computations compared to traditional degree-based topological indices (TIs). These TIs serve as indispensable molecular descriptors for assessing chemical compound characteristics. This manuscript aims to meticulously compute a spectrum of TIs for silicon carbide S i C 4 - I [ r , s ] , with a specific focus on the ε ν -degree Zagreb index, the ν ε -degree Geometric-Arithmetic index, the ε ν -degree Randić index, the ν ε -degree Atom-bond connectivity index, the ν ε -degree Harmonic index, and the ν ε -degree Sum connectivity index. This study contributes to the ongoing advancement of graph theory applications in chemical compound analysis, elucidating the nuanced structural properties inherent in silicon carbide molecules.

Comparative Analysis of M-polynomial Based Topological Indices Between Poly Hex-derived Networks and Its Subdivision

Topological indices are a vital class of structural descriptors that are extensively adopted in the innovation of structure-property models, virtual synthesis, drug design, and the assessment of similarity and diversity. Hex-derived networks have numerous applications in the pharmaceutical industry, as well as in hardware and system administration. In this paper, we first lay out the graph of subdivided poly Hex-derived networks of third type of dimension n (SPHDN3[n]) and then estimate the values of the degree-based topological indices using their precise formulas, which are related to their structure size. Additionally, with the help of the M-polynomials of SPHDN3[n] networks, we also compute and analyse its topological indices. Furthermore, we carry out a comparative graphical analysis between each of the calculated degree-based topological indices of the poly Hex-derived network of third type (PHDN3[n]) and SPHDN3[n] networks for better understanding and prediction of their physicochemical properties.

A QSPR analysis of physical properties of antituberculosis drugs using neighbourhood degree-based topological indices and support vector regression

Topological indices are molecular descriptors used in QSPR modelling to predict the physicochemical properties of molecules. Topological indices are used in numerous applications in drug design. In this work, we compute the neighbourhood degree-based topological indices of 15 antituberculosis drugs, we studied the QSPR analysis of these drugs using support vector regression. The efficiency of support vector regression is determined by comparing it with the classical linear regression. Our QSPR model further shows the superiority of the SVR model as a better predictive model in QSPR analysis of the physical properties of antituberculosis drugs. The findings in this study are a further contribution to the field of chemical graph theory and drug design, providing a deeper understanding of neighbourhood degree-based topological indices and their predictive capabilities in QSPR model.

A Computational Approach on Fenofibrate Drug Using Degree-Based Topological Indices and M-polynomials

Fenofibrate is a drug approved by FDA Food and Drugs Administration used to treat patients with Hypertrigly ceridemia primary hypercholesterolemia or mixed dyslipidemia. It reduces low-density lipoprotein cholesterol (LDL-c), total cholesterol, triglycerides, and apolipoprotein B and increases high -density lipoprotein cholesterol (HDL-C) in adults. The sum and multiplicative versions of several topological indices such as General Zagreb, General Randic, Arithmetic Geometric Index, Inverse sum (Indeg) Index, Symmetric Division (Deg) Index, Forgotten Indices M-polynomials of Fenofibrate are computed in this article.

Some inequalities between degree- and distance-based topological indices

hefirst Zagreb indexM1and the second Zagreb indexM2belongto the class of degree-based topological indices which are defined fora simple connected graphGwith vertex setV={υ1,υ2,···,υn}asM1(G)=Pn ̇ı=1d2 ̇ıandM2(G)=Pυ ̇ı∼υ ̇jd ̇ıd ̇j,whered ̇ıis the degreeof vertexυiandυ ̇ı∼υ ̇jrepresents the adjacency of verticesυ ̇ıandυ ̇jinG. The eccentric connectivity index (ECI) is a distance basedtopological index, denoted byξc,isdefined asξc(G)=Pni=1ε ̇ıd ̇ı,whereε ̇ıis the eccentricity ofυ ̇ıinG. The aim of this paper is toderive the inequalities between ECI and the Zagreb indices. Moreover,we establish the inequalities between some variants of ECI and theZagreb indices

Molecular insights into anti-Alzheimer’s drugs through predictive modeling using linear regression and QSPR analysis

The purpose of this paper is to discuss the use of topological indices (TIs) to anticipate the physical and biological aspects of innovative drugs used in the treatment of Alzheimer’s disease. Degree-based topological indices are generated using edge partitioning to assess the drugs Tacrine, Donepezil, Ravistigmine, Butein, Licochalcone-A and Flavokqwain-A. Furthermore, using linear regression, a quantitative structure–property relationship (QSPR) model is developed to predict the characteristics such as boiling point (BP), flash point (FP), molar volume (MV), molecular weight, complexity and polarizability. The findings show that topological indices have the potential to be used as a tool for drugs discovery and design in the field of Alzheimer’s disease treatment.

Degree-based topological indices and entropies of diamond crystals.

High hardness, low friction coefficient and chemical resistance are only a few of the exceptional mechanical qualities of diamond. Diamonds can be artificially created to have different levels of conductivity, or they can be single, micro or nanocrystalline and highly electrically insulating. It also has high biocompatibility and is famous for being mechanically robust. Due to its high hardness, lack of ductility and difficulty in welding, diamond is a challenging material to construct devices with. Diamonds have experienced a rise in attention as a biological material in recent decades due to new synthesis and fabrication techniques that have eliminated some of these disadvantages. In general, entropic measurements are used for investigating the chemical or biological properties of molecular structures. This study calculates several important -Banhatti entropies, redefined Zagreb entropies and atom-bond sum connectivity entropy for diamond crystals. We also present a numeric and graphical explanations of obtain indices.

On quantitative structure-property relationship (QSPR) analysis of physicochemical properties and anti-hepatitis prescription drugs using a linear regression model

Numerous studies demonstrate a strong intrinsic relationship between the boiling and melting temperatures, among other chemical properties, of chemical compounds and pharmaceutical and their molecular structures. Using topological indices, researchers can learn more about the physical traits, chemical stability, and bioactivities of these chemical molecular structures. Topological indices on the chemical structure of chemical materials and drugs are investigated in order to make up for the absence of chemical experiments and provide a theoretical basis for the manufacture of medications and chemical materials. According to well-known degree-based topological indices, the chemical structures of drugs used to treat hepatitis (A, B, C, D, and E) are assessed in this study. The atoms are thought of as the vertices of a graph, and the borders that separate them are thought of as the edges. Using degree-based topological indices, a quantitative structure-property relationship (QSPR) investigation was conducted to predict the physical properties of 16 hepatitis medications. These topological indices link the chemical structure to specific physical characteristics, such as the surface tension of hepatitis medication molecules and molecular weight, enthalpy, boiling point, density, vapor pressure, and logP. Using their molecular structures, the study's drugs are represented as molecular graphs, and 14 topological indices are computed.

Computation of reverse neighbourhood degree-based topological indices for the transition metal phthalocyanine polymers (poly-TMPc)

In this article, we discuss the reverse neighbourhood degree-based topological indices for the transition metal phthalocyanine polymers (poly- TMPc). Degree-based topological indices have been extensively studied and linked to a variety of chemical properties. An even more recently established methodology for assessing chemical systems and geometries is the use of numerical descriptors based on the degree of definition defined by the reverse-degree concept technique. It highlights molecular characteristics as numerical descriptors based on the reverse-degree concept’s degree of definition and delivers numerical descriptors in algebraic form. On the other hand, due to their high catalytic activity, photostability, resistance to severe environments, and adaptable properties, transition metal phthalocyanines are a fascinating class of organic semiconductors. Furthermore, different types of reverse neighbourhood topological indices, such as the augmented Zagreb index, first and second Zagreb indexes, and Randi ć indexes, are defined and used to assess the complexity, stability, and other properties of poly-TMPc(m,n).

Retracted: Study of Neighborhood Degree-Based Topological Indices via Direct and NM-Polynomial of Starphene Graph

Retracted: Study of Neighborhood Degree-Based Topological Indices via Direct and NM-Polynomial of Starphene Graph

Retracted: Degree-Based Topological Indices of Generalized Subdivision Double-Corona Product

Retracted: Degree-Based Topological Indices of Generalized Subdivision Double-Corona Product

Mathematically modeling of Ge-Sb-Te superlattice to estimate the physico-chemical characteristics

Superlattices are periodic arrangements of two or more different materials on a nanoscale. Ge-Sb-Te (Germanium-Antimony-Tellurium) superlattices are a type of material used in phase-change memory (PCM) technology. PCM is a non-volatile memory technology that relies on the reversible phase transition between amorphous and crystalline states in certain materials. This phase-change property, combined with the non-volatile nature of the material, makes it suitable for applications like phase-change memory in electronic devices. Topological and entropy indices are the mathematical tools that are helpful to estimate the physico-chemical characteristics of chemical compounds. In this article, we have calculated some reduced reverse degree-based topological indices and entropy indices for Ge-Sb-Te superlattice. Ravi et al. [32] examined the statistically significant relationship of reduced reverse degree-based topological indices with physico-chemical characteristics of drug structures and proposed regression models using entropy indices. In this context, our computed results can be helpful in predicting the physico-chemical characteristics of Ge-Sb-Te superlattices.

Reduced reverse degree-based topological indices of graphyne and graphdiyne nanoribbons with applications in chemical analysis

Graphyne and Graphdiyne Nanoribbons reveal significant prospective with diverse applications. In electronics, they propose unique electronic properties for high-performance nanoscale devices, while in catalysis, their excellent surface area and reactivity sort them valuable catalyst supports for numerous chemical reactions, contributing to progresses in sustainable energy and environmental remediation. The topological indices (TIs) are numerical invariants that provide important information about the molecular topology of a given molecular graph. These indices are essential in QSAR/QSPR analysis and play a significant role in predicting various physico-chemical characteristics. In this article, we present a formula for computing reduced reverse (RR) degree-based topological indices for graphyne and graphdiyne nanoribbons, including the RR Zagreb indices, RR hyper-Zagreb indices, RR forgotten index, RR atom bond connectivity index, and RR Geometric-arithmetic index. We also execute a graph-theoretical analysis and comparison to demonstrate the critical significance and validate the acquired results. Our findings provide insights into the structural and chemical properties of these nanoribbons and contribute to the development of new materials for various applications.

On Structure Sensitivity and Chemical Applicability of Some Novel Degree-Based Topological Indices

Numerous quantitative graph invariant-based topological indices have been developed in the literature and employed for correlation analysis in chemical graph theory. Among them, the degree-based topological indices are the most investigated molecular descriptors and have proven their usability in this area. Here, we focus on testing the structural properties and prediction potential of some novel degree-based topological indices. At the outset, computer testing for the considered topological indices is performed to calibrate their structure sensitivity and abruptness. After that, the correlation among the topological indices is also executed. In addition, QSPR analysis is performed for the octane isomers molecular database to investigate the physical and chemical significance of the considered topological indices.

Predictive modeling and regression analysis of diverse sulfonamide compounds employed in cancer therapy.

Topological indices (TIs) have rich applications in various biological contexts, particularly in therapeutic strategies for cancer. Predicting the performance of compounds in the treatment of cancer is one such application, wherein TIs offer insights into the molecular structures and related properties of compounds. By examining, various compounds exhibit different degree-based TIs, analysts can pinpoint the treatments that are most efficient for specific types of cancer. This paper specifically delves into the topological indices (TIs) implementations in forecasting the biological and physical attributes of innovative compounds utilized in addressing cancer through therapeutic interventions. The analysis being conducted to derivatives of sulfonamides, namely, 4-[(2,4-dichlorophenylsulfonamido)methyl]cyclohexanecarboxylic acid (1), ethyl 4-[(naphthalene-2-sulfonamido)methyl]cyclohexanecarboxylate (2), ethyl 4-[(2,5-dichlorophenylsulfonamido)methyl]cyclohexanecarboxylate (3), 4-[(naphthalene-2-sulfonamido)methyl]cyclohexane-1-carboxylic acid (4) and (2S)-3-methyl-2-(naphthalene-1-sulfonamido)-butanoic acid (5), is performed by utilizing edge partitioning for the computation of degree-based graph descriptors. Subsequently, a linear regression-based model is established to forecast characteristics, like, melting point and formula weight in a quantitative structure-property relationship. The outcomes emphasize the effectiveness or capability of topological indices as a valuable asset for inventing and creating of compounds within the realm of cancer therapy.

Some polynomials and degree-based topological indices of molecular graph and line graph of Titanium dioxide nanotubes

Graph polynomials based on distance and degree are helpful and necessary because they contain much information about topological indices. In this article, the general inverse sum indeg index and the generalized inverse sum indeg polynomials are calculated for the molecular graph and the line graph of the Titanium dioxide nanotubes. Then, with their help, some polynomials and some degree-based topological indices of the molecular graph and the line graph of Titanium dioxide nanotubes are obtained.