Topological aspects of metal-organic structure with the help of underlying networks

Applications of magnesium iodide structure via modified-polynomials

A relatively recent approach in molecular graph theory for analyzing chemical networks and structures is called a modified polynomial. It emphasizes the characteristics of molecules through the use of a polynomial-based procedure and presents numerical descriptors in algebraic form. The Quantitative Structure-Property Relationship study makes use of Modified Polynomials (M-Polynomials) as a mathematical tool. M-Polynomials used to create connections between a material's various properties and its structural characteristics. In this study, we calculated several modified polynomials and gave a polynomial description of the magnesium iodide structure. Particularly, we computed first, second and modified Zagreb indices based M-polynomials. Randić index, and inverse Randić indices based M-polynomials are also computed in this work.

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.

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 .

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.

Chemical applicability and computation of K-Banhatti indices for benzenoid hydrocarbons and triazine-based covalent organic frameworks

The novel applications in chemistry include the mathematical models of molecular structure of the compounds which has numerous findings in this area that refers to mathematical chemistry. Topological descriptors play a major role in QSAR/QSPR studies that analyses the biological and physicochemical properties of the compounds. In the recent times, a new type of topological descriptors are proposed, called K-Banhatti indices. In this study the chemical applicability of K-Banhatti indices are examined for benzenoid hydrocarbons (derivatives of benzene). These indices have shown remarkable results through the study of statistical analysis. Subsequently, triazine-based covalent organic frameworks (CoF's) are studied for which [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and HB(G) of a graph G are computed.

Structural descriptors of anthracene using topological coindices through CoM-polynomial

Topological indices and coindices are numerical invariants that relate to quantitative structure property/activity connections. The purpose of topological indices and coindices were introduced to draw the data related to chemical graphs with respect to adjacent & non adjacent pairs of vertex degrees respectively. These indices equip the researchers with a lot of information related to the properties and structure of the chemical compound. In this article, CoM-polynomials for molecular graph of linear and multiple Anthracene are computed from which eleven degree based topological coindices are derived. Finally numerical and graphical comparisons of coindices for both forms of anthracene are drawn while conclusions are summarized based on the results obtained.

Some new results on the face index of certain polycyclic chemical networks

Silicate minerals make up the majority of the earth's crust and account for almost 92 percent of the total. Silicate sheets, often known as silicate networks, are characterised as definite connectivity parallel designs. A key idea in studying different generalised classes of graphs in terms of planarity is the face of the graph. It plays a significant role in the embedding of graphs as well. Face index is a recently created parameter that is based on the data from a graph's faces. The current draft is utilizing a newly established face index, to study different silicate networks. It consists of a generalized chain of silicate, silicate sheet, silicate network, carbon sheet, polyhedron generalized sheet, and also triangular honeycomb network. This study will help to understand the structural properties of chemical networks because the face index is more generalized than vertex degree based topological descriptors.

Vertex metric resolvability of COVID antiviral drug structures

In November of 2019 year, there was the first case of COVID-19 (Coronavirus) recorded, and up to 3rd of April of 2020, 1,116,643 confirmed positive cases, and around 59,158 dying were recorded. Novel antiviral structures of the 2019 pandemic disease Coronavirus are discussed in terms of the metric basis of their molecular graph. These structures are named arbidol, chloroquine, hydroxy-chloroquine, thalidomide, and theaflavin. Metric dimension or metric basis is a concept in which the whole vertex set of a structure is uniquely identified with a chosen subset named as resolving set. Moreover, the fault-tolerant concept of those structures is also included in this study. By this concept of vertex-metric resolvability of COVID antiviral drug structures are uniquely identified and help to study the structural properties of the structure.

Breast cancer chemical structures and their partition resolvability

Cancer is a disease that causes abnormal cell formation and spreads throughout the body, causing harm to other organs. Breast cancer is the most common kind among many of cancers worldwide. Breast cancer affects women due to hormonal changes or genetic mutations in DNA. Breast cancer is one of the primary causes of cancer worldwide and the second biggest cause of cancer-related deaths in women. Metastasis development is primarily linked to mortality. Therefore, it is crucial for public health that the mechanisms involved in metastasis formation are identified. Pollution and the chemical environment are among the risk factors that are being indicated as impacting the signaling pathways involved in the construction and growth of metastatic tumor cells. Due to the high risk of mortality of breast cancer, breast cancer is potentially fatal, more research is required to tackle the deadliest disease. We considered different drug structures as chemical graphs in this research and computed the partition dimension. This can help to understand the chemical structure of various cancer drugs and develop formulation more efficiently.

Comparative study of vertex-edge based indices for semi-capped carbon nanotubes

Manufacturing relatively inexpensive items in every area of engineering and science is the major focus of exploration resultant the world's contemporary economic setback. Making small-sized items that are inexpensive and lightweight while providing high quality is critical in today's and tomorrow's worlds. Nanotechnology has a significant role to play in this situation. Nano-objects or, in general, nanomaterials are especially preferred; nanotubes, especially those comprised of carbon, are one of the most popular types of nanostructures, and they are applied in a variety of chemical, biological and technical applications. This notion prompted us to investigate their many physical and chemical characteristics. We utilized topological descriptors to evaluate diverse nanotube structures such as armchair carbon and semi-capped nanotubes by using vertex-edge based indices to characterize distinct chemical structures via numerical quantitative analysis. Furthermore, we examined uncapped and semi-capped armchair carbon nanotubes and achieved adequate comparative findings.

Partition dimension of COVID antiviral drug structures

In November 2019, there was the first case of COVID-19 (Coronavirus) recorded, and up to 3$ ^{rd }$ of April 2020, 1,116,643 confirmed positive cases, and around 59,158 dying were recorded. Novel antiviral structures of the SARS-COV-2 virus is discussed in terms of the metric basis of their molecular graph. These structures are named arbidol, chloroquine, hydroxy-chloroquine, thalidomide, and theaflavin. Partition dimension or partition metric basis is a concept in which the whole vertex set of a structure is uniquely identified by developing proper subsets of the entire vertex set and named as partition resolving set. By this concept of vertex-metric resolvability of COVID-19 antiviral drug structures are uniquely identified and helps to study the structural properties of structure.