Topological characterization of dendrimer, benzenoid, and nanocone.

Dendrimers are large and complex molecules with very well defined chemical structures. More importantly, dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core. Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity relationships. These topological indices correlate certain physico-chemical properties such as the boiling point, stability, strain energy, and others, of chemical compounds. In this article, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for hetrofunctional dendrimers, triangular benzenoids, and nanocones.

Possibility of C38 and Si19Ge19 Nanocages in Anode of Metal Ion Batteries: Computational Examination.

In this study, the potential of C38 and Si19Ge19 as anode electrodes of Li-ion, Na-ion and K-ion batteries via density functional theory was investigated. Obtained results showed that Si19Ge19 as anode electrode in metal-ion batteries has higher potential than C38 ca 0.18 V. Calculated results illustrated that K-ion battery has higher cell voltage and higher performance than Li-ion and Na-ion batteries ca 0.15 and 0.31 V, respectively. Results showed that halogen adoption increased the cell voltage of studied metal-ion batteries ca 1.5-2.2 V. Results show that, Vcell values of studied metal-ion batteries in water are higher than gas phase ca 0.46 V. Finally it can be concluded that F-doped Si18Ge19 as anode electrode in K-ion battery has the highest performance and it can be proposed as novel metal-ion batteries with high performance.

Forgotten topological index of chemical structure in drugs.

A massive of early drug tests implies that there exist strong inner relationships between the bio-medical and pharmacology characteristics of drugs and their molecular structures. The forgotten topological index was defined to be used in the analysis of drug molecular structures, which is quite helpful for pharmaceutical and medical scientists to grasp the biological and chemical characteristics of new drugs. Such tricks are popularly employed in developing countries where enough money is lacked to afford the relevant chemical reagents and equipment. In our article, by means of drug molecular structure analysis and edge dividing technology, we present the forgotten topological index of several widely used chemical structures which often appear in drug molecular graphs.

Exploring the properties of antituberculosis drugs through QSPR graph models and domination-based topological descriptors.

Tuberculosis (TB) is a global health concern caused by the bacterium Mycobacterium tuberculosis. This infectious disease primarily affects the lungs but can also impact other organs. Effective TB control involves early diagnosis, appropriate treatment with a combination of antibiotics, and public health measures to prevent transmission. However, ongoing challenges include drug-resistant strains and socioeconomic factors influencing its prevalence. Drugs such as isoniazid, pyrazinamide, ethambutol, ethionamide, linezolid, and levofloxacin are approved for the treatment of drug-susceptible tuberculosis. The properties and other activities of the drug, can be analyzed by modelling its chemical structure in terms of a molecular graph [Formula: see text], by considering the atoms as the vertex set [Formula: see text] and the bonds between the two atoms as the edge set [Formula: see text]. A molecular descriptor or topological index of [Formula: see text] represents the corresponding chemical molecule as a numerical value. Domination is one of the key concepts in the molecular structure used to analyze the properties of atoms. In this article, the domination distance-based topological indices of the drugs isoniazid, pyrazinamide, ethambutol, ethionamide, linezolid, and levofloxacin are computed to conduct QSPR (Quantitative Structure-Property Relationship) analysis, exploring their physicochemical and ADMET (Absorption, Distribution, Metabolism, Excretion, and Toxicity) properties. Quadratic regression is then used in the QSPR analysis to examine the physicochemical and ADMET properties of these drugs. The results of this analysis indicate that the domination Schultz index and domination SM index are the indices most strongly correlated with the majority of the physicochemical and ADMET properties. The QSPR analysis can also be extended to analogs of these drugs and to other treatment drugs, such as rifampin and rifapentine, to further explore their properties.

Computation of molecular description of supramolecular Fuchsine model useful in medical data.

Supramolecular chemistry is a fascinating field that explores the interactions between molecules to create higher-order structures. In the case of the supramolecular chain of Fuchsine acid, which is a type of dye molecule, several chemical applications are possible. Fuchsine acid helps to make better medicine carriers that deliver drugs where they're needed in the body, making treatments more effective and reducing side effects. It also helps create smart materials like sensors and self-fixing plastics, which are useful in electronics, keeping our environment clean, and making new materials. In sensing and detection, the supramolecular chain of Fuchsine acid utilizes as a sensor or detector for specific analyzes. In drug delivery, the supramolecular chains of Fuchsine acid incorporated into drug delivery systems. In recent years, a common method is linking a graph to a chemical structure and using topological descriptors to study it. This technique is becoming increasingly important over time. Topological descriptors gives very useful information while studying the topology of chemical graph. In this paper, we have computed the 3D structure of supramolecular graph of Fuchsine acid. We have computed an explicit expressions of ABC index, GA index, General Randi c ´ index, first and second Zagreb index, hyper Zagreb index, H-index and F-index of supramolecular structure of Fushine acid.

On topological indices and entropy measures of beryllonitrene network via logarithmic regression model.

Chemical graph theory, a subfield of graph theory, is used to investigate chemical substances and their characteristics. Chemical graph analysis sheds light on the connection, symmetry, and reactivity of molecules. It supports chemical property prediction, research of molecular reactions, drug development, and understanding of molecular networks. A crucial part of computational chemistry is chemical graph theory, which helps researchers analyze and manipulate chemical structures using graph algorithms and mathematical models. Beryllonitrene , a compound of interest due to its potential applications in various fields, is examined through the lens of graph theory and mathematical modeling. The study involves the calculation and interpretation of topological indices and graph entropy measures, which provide valuable insights into the structural and energetic properties of Beryllonitrene's molecular graph. Logarithmic regression models are employed to establish correlations between these indices, entropy, and other relevant molecular attributes. The results contribute to a deeper understanding of Beryllonitrene's complex characteristics, facilitating its potential applications in diverse scientific and technological domains. In this study, degree-based topological indices TI are determined, as well as the entropy of graphs based on these TI .

On degree-based operators and topological descriptors of molecular graphs and their applications to QSPR analysis of carbon derivatives.

This work initiates a concept of reduced reverse degree based RR D M -Polynomial for a graph, and differential and integral operators by using this RR D M -Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using the RR D M -Polynomial. The topological descriptors, denoted as T D 's, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study.

On statistical evaluation of reverse degree based topological indices for iron telluride networks.

In the context of graph theory and chemical graph theory, this research conducts a detailed mathematical investigation of reverse topological indices as they relate to iron telluride networks, clarifying their complex interactions. Graph theory is a branch of abstract mathematics that carefully studies the connections and structural features of graphs made up of edges and vertices. These theoretical ideas are expanded upon in chemical graph theory, which models molecular architectures with atoms acting as vertices and chemical bonds as edges. By extending these concepts, this work investigates the reverse topological indices in the context of Iron Telluride networks and outlines their significant effects on chemical reactivity, molecular topology and statistical modeling. By navigating intricate mathematical formalisms and algorithmic approaches, the analysis provides profound insights into the reactivity patterns and structural dynamics of Iron Telluride compounds, enhancing our knowledge of solid-state chemistry and materials science.

On analysis of silicon dioxide based on topological indices and entropy measure via regression model.

The construction sector accounts for around 95% of the commercial usage of silicon dioxide (sand), for example, in the making of concrete. There are several uses for quartz, however in order to get a purer material, chemical processing is needed. Graph theory proved to be very beneficial for other research, especially in the applied sciences. In particular, graph theory has greatly influenced the field of chemistry. To do this, a transformation is needed to produce a graph with the vertices representing the atoms in the chemical compound and the edges indicating the bonds between the atoms. This graph then represents a chemical network or structure. In a graph, a vertex's valency (or degree) is determined by the number of edges that are incident to it. The entropy of a probability quantifies a system's level of uncertainty. In this article, we compute Zagreb-type indices and then compute the entropy measure. In order to evaluate the relevance of each kind, this article builds several edge degree-based entropies that link to the indices and establish how to adjust them. We also create the logarithmic regression model between indices and entropy.

On physical analysis of topological indices for iron disulfide network via curve fitting model.

In this study, we conduct a comprehensive physical analysis of topological indices for the Iron Disulfide (FeS 2 ) network using a curve-fitting model. Iron Disulfide is a cubic compound. In metamorphic rock, sedimentary rock, and quartz veins, it is typically found in combination with other sulfides or oxides. The numerical properties of molecular structures are referred to as topological indices. There are several different kinds of topological indices, including those that are based on distance, degree, or counting, among other factors. The real process of creating a topological index involves turning a chemical structure into a numerical value. In this paper, we calculate the iron disulfide network topological indices using the degrees of vertices in a chemical network of Iron Disulfide (FeS 2 ). Thereafter, we discovered the physical parameters of FeS 2 production, such as heat of formation. We then fitted curves between the thermodynamic properties and several indices. Several techniques based on rationality, linearity, and nonlinearity were used to fit curves in MATLAB. These quantitative results imply that a variety of thermodynamic characteristics of semiconducting materials may be accurately predicted by topological indices. These findings have significant ramifications as they provide the groundwork for the application of topological indices in semiconducting network design and optimization, which might result in more effective and economical material creation.

Topological indices and patterns in iron telluride networks.

This paper explores the complex interplay between topological indices and structural patterns in networks of iron telluride (FeTe). We want to analyses and characterize the distinct topological features of (FeTe) by utilizing an extensive set of topological indices. We investigate the relationship that these indicators have with the network's physical characteristics by employing sophisticated statistical techniques and curve fitting models. Our results show important trends that contribute to our knowledge of the architecture of the (FeTe) network and shed light on its physiochemical properties. This study advances the area of material science by providing a solid foundation for using topological indices to predict and analyses the behavior of intricate network systems. More preciously, we study the topological indices of iron telluride networks, an artificial substance widely used with unique properties due to its crystal structure. We construct a series of topological indices for iron telluride networks with exact mathematical analysis and determine their distributions and correlations using statistical methods. Our results reveal significant patterns and trends in the network structure when the number of constituent atoms increases. These results shed new light on the fundamental factors that influence material behavior, thus offering a deeper understanding of the iron telluride network and may contribute to future research and engineering of these materials.

On analysis of topological indices and heat of formation for benzyl sulfamoyl network via curve fitting model.

The study explores the intricate relationship between topological indices and the heat of formation in the benzyl sulfamoyl network. Topological indices of benzyl sulfamoyl networks are studied and also emphasize their properties statistically. The benzyl sulfamoyl has unique properties due to its crystalline structure and it is used in the form of artificial substance. We analyze the distributions and correlations of the benzyl sulfamoyl network with others by using statistical methods and also build a computational analysis for topological indices. The findings show a strong association between the variables, indicating that topological indices may be used to accurately predict thermodynamic characteristics and improve the effectiveness of molecular modelling and simulation procedures.

On characterization of entropy measure using logarithmic regression model for Copper(II) Fluoride.

The versatile uses of Copper(II) Fluoride (CuF2) are well known; these include its usage as a precursor in chemical synthesis as well as its contribution to the creation of sophisticated materials and electronics. There are interesting opportunities to study the interactions between these elements because of their unique crystal structure, which contains copper ions and fluoride anions. Its potential in optoelectronic devices and conductive qualities also make it a viable material for next-generation technologies. To better understand the structural properties of CuF2 and how they affect its entropy, we present new Zagreb indices in this study and use them to calculate entropy measures. We also build a regression model to clarify the relationship between the calculated indices and entropy levels. The findings of our investigation offer significant understanding regarding the ability of the suggested Zagreb indices to extract meaningful content and their correlation with entropy in the context of CuF2. This information is important for understanding CuF2 alloys and for exploring related complex materials.

Exploring topological indices and entropy measure via rational curve fitting models for calcium hydroxide network.

This work uses rational curve fitting models to investigate the complex link between topological indices and entropy metrics in calcium hydroxide ( C a ( O H ) 2 ) networks. Entropy measurements shed light on the complexity and disorder of these networks, whereas topological indices are essential instruments for comprehending the structural characteristics of chemical substances. Our goal is to find new patterns and connections by merging these two fields, improving materials science's prediction capacity. We calculate many topological indices, such as the Randic, Balaban, and Zagreb indices, and examine the relationship between them and entropy measurements obtained from ( C a ( O H ) 2 ) structural arrangement.

Analyzing boron oxide networks through Shannon entropy and Pearson correlation coefficient.

In the current age of chemical science, chemical graph theory has significantly advanced our understanding of the characteristics of chemical compounds. To simulate the mathematical, chemical, and physical aspects of networks, a topological index, a numerical measure obtained from the graph of a chemical network, employed. Recent work has explored the topological properties of boron oxide using chemical graph theory. In this work, we conduct a Pearson correlation analysis of boron oxide to assess the correlations between the Van and S indices and entropy metrics. We analyze the Pearson correlation coefficients between the entropy values and the calculated indices using a heatmap. In this article, a significant positive correlation between the Van, and S indices, and entropy values, which is represented by the heatmap of the strong linear correlations. To avoid duplication, a dimensionality reduction technique should be used for highly connected variables. Additionally, this study gives a detailed explanation of the link between the indices and entropy, which will form the basis of further statistical investigations.

On analysis of iron (II) chloride via graph entropy measures and statistical models.

The crystalline material that is greenish-white and dissolves in water is iron chloride. It is utilized in sewage treatment, dyeing, and medicine. Graph entropy plays a significant role in measuring the complexity of atoms, molecules, and structures in nature. It has specific chemical applications in biology, neuroscience, and chemistry. A compound's molecular structure consists of many atoms. Particularly, hydrocarbons are a chemical combination of hydrogen and carbon atoms. In this article, we discuss the entropy of the chemical structure Iron (II) Chloride. Additionally, we discuss the idea of degree-based indices and compute the Shannon entropy(ENT) using these indices. The linear regression(LR) of various indices and entropies for iron chloride, FeCl2, is also discussed. Also, we link the degree-based indices and entropies via line fit.

Statistical analysis of topological indices in linear phenylenes for predicting physicochemical properties using algorithms.

QSPR mathematically links physicochemical properties with the structure of a molecule. The physicochemical properties of chemical molecules can be predicted using topological indices. It is an effective method for eliminating costly and time-consuming laboratory tests. We established a QSPR between mev-degree and mve-degree-based indices and the physical properties of benzenoid hydrocarbons. To compute these indices, we designed a program using Maple software and the correlation between indices and physical properties was developed using the SPSS software. Our study reveals that the mve-degree-based sum-connectivity ( χ mve ) and atom bond connectivity ( A B C mve ) index, mev-degree-based Randic ( R mev ) and Zagreb ( M mev ) index are the three most significant parameters and have good prediction ability for the physicochemical properties. We examined that R mev predicts the molar refractivity and boiling point, χ mve predicts the LogP and enthalpy, A B C mve predicts the molecular weight, M mev predicts the Gibb's energy, Pie-electron energy and Henry's law. Moreover, we computed the indices for the linear [n]-phenylen.

On curve fitting between topological indices and Gibb's energy for semiconducting carbon nitrides network.

Quantitative structure relationships linked to a chemical structure that shed light on its properties and chemical reactions are called topological indices. This structure is upset by the addition of silicon (Si) doping, which changes the electrical and optical characteristics. In this article, we examine the connection between a chemical structure's Gibbs energy (GE) and K-Banhatti indices. In this article, we compute the K-Banhatti indices and then show the correlation between the indices and Gibb's energy of the molecule using curve fitting. Through the curve fitting, we see that there is a strong correlation between indices and Gibb's energy of a molecule. We use the polynomial curve fitting approach to see the correlation between indices and Gibb's energy.

On topological analysis of two-dimensional covalent organic frameworks via M-polynomial.

Covalent organic frameworks (ZnP-COFs) made of zinc-porphyrin have become effective materials with a variety of uses, including gas storage and catalysis. To simulate the structural and electrical features of ZnP-COFs, this study goes into the computation of polynomials utilizing degree-based indices. We gave a methodical study of these polynomial computations using Excel, illustrating the complex interrelationships between the various indices. Degree-based indices provide valuable insights into the connectivity of vertices within a network. M-polynomials, on the other hand, offer a mathematical framework for representing and studying the properties of 2D COFs. By encoding structural information into a polynomial form, M-polynomials facilitate the calculation of various topological indices, including the Wiener index, Zagreb indices, and more. The different behavior of ZnP-COFs based on degree-based indices was illustrated graphically, and this comparison provided insightful information for prospective applications and the construction of innovative ZnP-COF structures. Moreover, we discuss the relevance of these techniques in the broader context of materials science and the design of functional covalent organic frameworks.

On network construction and module detection for molecular graph of titanium dioxide.

Titanium dioxide is the most common and valuable oxide among four types of oxides of titanium. Its physicochemical properties make it a very valuable compound. The main objective of this article is to initially detect the modules based on highly connected links of the network of the degree-based topological indices. This information is lately integrated with different physical properties of the chemical compound of titanium dioxide to develop different mathematical frameworks based on master regulatory indices of the modules. This connection can be helpful in studying the physical measures at a deeper level in the form of different degree based topological indices.Communicated by Ramaswamy H. Sarma.