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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A new area of applied chemistry called chemical graph theory uses combinatorial techniques to explain the complex interactions between atoms and bonds in chemical systems. This work investigates the use of edge partitions to decipher molecular connection patterns. The main goal is to use topological indices that capture important topological features to create a connection between the thermodynamic properties and structural characteristics of chemical molecules. We specifically examine the complex web of atoms and links that make up the Fe phthalocyanine chemical graph. Moreover, our study demonstrates a relationship between the calculated topological indices and the thermodynamic properties of Fe phthalocyanine (Phthalocyanine Iron (II)). This work offers insight into the thermodynamic consequences of molecule structures. It advances the subject of chemical graph theory, providing a useful perspective for future applications in catalysis and materials science. [ABSTRACT FROM AUTHOR]

In this research, the star gold structure with beta graphene is thoroughly examined. We mainly focus on computing degree-based topological indices, which provide information about the network's connectivity and complexity as well as structural features. In addition, we compute an entropy measure to represent the uncertainty, information richness, and degree of unpredictability in the network. Furthermore, this study explores the relationships between topological descriptors and entropy using regression models that are logarithmic, linear, and quadratic. By merging these regression models, we uncover hidden patterns and understand the underlying ideas governing the network's behaviour. Our findings shed light on the connection between topological indices and entropy. This work improves our understanding of star gold structure dynamics and provides a visual framework for interpreting their behaviour. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A correction to the article " On physical analysis of phthalocyanine iron (II) using topological descriptor and curve fitting models" in the Scientific Reports (August 10, 2024) issue is presented, which addresses inaccuracies in the authors' affiliations.

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., (© 2024. The Author(s).)

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., (© 2024. The Author(s).)

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., (© 2024. The Author(s).)

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., (© 2024. The Author(s).)