A new perspective on the modeling and topological characterization of H-Naphtalenic nanosheets with applications

Optimizing predictive models for evaluating the F-temperature index in predicting the π-electron energy of polycyclic hydrocarbons, applicable to carbon nanocones

In the fields of mathematics, chemistry, and the physical sciences, graph theory plays a substantial role. Using modern mathematical techniques, quantitative structure-property relationship (QSPR) modeling predicts the physical, synthetic, and natural properties of substances based only on their chemical composition. For a chemical graph, the temperature of a vertex is a local property introduced by Fajtlowicz (1988). A temperature-based graphical descriptor is structured based on temperatures of vertices. Involving a non-zero real parameter β , the general F-temperature index T β is a temperature index having strong efficacy. In this paper, we employ discrete optimization and regression analysis to find optimal value(s) of β for which the prediction potential of T β and the total π -electron energy E π of polycyclic hydrocarbons is the strongest. This, in turn, answers an open problem proposed by Hayat & Liu (2024). Applications of the optimal values for T β are presented a two-parametric family of carbon nanocones in predicting their E π with significantly higher accuracy.

Predictive potential of distance-related spectral graphical descriptors for structure-property modeling of thermodynamic properties of polycyclic hydrocarbons with applications

A distance-related spectral descriptor is a graphical index with defining structure built on eigenvalues of chemical matrices relying on distances in graphs. This paper explores the predictive ability of both existing and new distance-related spectral descriptors for estimating thermodynamic characteristics of polycyclic hydrocarbons (PHs). As a standard choice, the entropy and heat capacity are selected to represent thermodynamic properties. Furthermore, 30 initial members of PHs are considered as test molecules for this study. Three new molecular matrices have been proposed and our research demonstrates that distance-spectral graphical indices built by these novel matrices surpass in efficiency relative to famous distance-spectral indices. First, a novel computational method is put forwarded to evaluate distance-spectral indices of molecular graphs. The proposed methodology is utilized to compute both pre-existing and novel distance-related spectral descriptors, with an aim to assess their predictive efficacy using experimental data pertaining to two selected thermodynamic properties. Subsequently, we identify the five most promising distance-related spectral descriptors, comprising the degree-distance and Harary energies, the recently introduced second geometric-arithmetic energy along with its associated Estrada invariant, and 2[Formula: see text] atom-bond connectivity (ABC) Estrada index. Notably, the 2[Formula: see text] ABC Estrada index and Harary energy demonstrate correlation coefficients exceeding 0.95, while certain conventional spectral indices including the distance energy as well as its associated Estrada index, display comparatively lower performance levels. Moreover, we illustrate the practical implications of our findings on specific classes of one-hexagonal nanocones and carbon polyhex nanotubes. These outcomes hold potential for enhancing the theoretical determination of certain thermodynamic attributes of these nanostructures, offering improved accuracy and minimal margin of error.

Computational insights into zinc silicate MOF structures: topological modeling, structural characterization and chemical predictions

Metal-organic frameworks (MOFs) play a pivotal role in modern material science, offering unique properties such as flexibility, substantial pore space, distinctive structure, and large surface area. Recently, zinc-based MOFs have attracted significant attention, particularly in the biomedical arena, owing to their versatile applications in drug delivery, biosensing, and cancer imaging. However, there remains a crucial need to explore and understand the structural properties of zinc silicate-based MOFs to fully exploit their potential in various applications. The objective of this study is to address this need by employing topological modeling techniques to characterize zinc silicate networks. Utilizing connection number concept of chemical graph theory and novel AL molecular descriptors, we aim to investigate the structural intricacies of these MOFs. More precisely, zinc silicate-based MOF networks are topologically modeled via novel AL topological indices, and derived mathematical closed form formulae for them. By comparing experimental and calculated values and constructing linear regression models, the predictive capabilities of the proposed descriptors are evaluated. Specifically, the performance of derived topological indices against the physico-chemical properties of octane isomers is assessed, which provide valuable insights into their predictive potential. The findings of this study demonstrated the potential of novel AL indices in predicting a wide range of important physico-chemical properties, further enhancing their practicality in materials science and beyond.

Structure-property modeling of physicochemical properties of fractal trigonal triphenylenoids by means of novel degree-based topological indices

Trigonal triphenylenoids (TTPs) are a fascinating class of organic molecules with unique structural and electronic properties. Their diverse applications, ranging from organic electronics to nonlinear optics, have spurred significant research interest in understanding their physicochemical behavior. Topological indices, mathematical descriptors derived from the molecular graph, offer valuable insights into the structural complexity and potential properties of TTPs. This work focuses on exploring the utility of degree-based topological indices in characterizing and predicting the properties of trigonal triphenylenoids. We systematically calculate various degree-based topological indices, for a diverse set of TTPs with varying substituents and topologies. The relationships between these indices and key physicochemical properties, such as HOMO-LUMO energy gap, thermodynamic stability, and reactivity are investigated using statistical and machine learning approaches. We identify significant correlations between specific degree-based indices and different properties, allowing for potential prediction of these properties based solely on the topological information.

3D molecular structural modeling and characterization of indium phosphide via irregularity topological indices

Indium phosphide (InP) is a binary semiconductor composed of indium and phosphorus. It has a zinc blende crystal structure, which is a type of cubic lattice structure. This lattice is composed of indium and phosphorus atoms arranged in a lattice of cube-shaped cells, with each cell containing four indium atoms and four phosphorus atoms. This lattice structure is the same for all materials with a zinc blende crystal structure and is the most common type of lattice structure in semiconductors. Indium phosphide (InP) has several chemical applications. It is commonly used as a dopant in the production of semiconductors, where it helps control the electrical properties of the material. InP is also utilized in the synthesis various indium-containing compounds, which can have applications in catalysts and chemical reactions. Additionally, InP nanoparticles have been investigated for their potential use in biomedical imaging and drug delivery systems. The topological characterization of 3D molecular structures can be performed via graph theory. In graph theory, the connections between atoms are represented as edges and the atoms themselves are represented as nodes. Furthermore, graph theory can be used to calculate the topological descriptors of the molecule such as the degree-based and reverse degree-based irregularity toplogical indices. These descriptors can be used to compare the topology of different molecules. This paper deals with the modeling and topological characterization of indium phosphide ( InP ) via degree-based and reverse irregularity indices. The 3D crystal structure of the InP is topologically modeled via partition of the edges, and derived closed form expressions for its irregularity indices. Our obtained results will be surely be helpful in investigating the QSPR/QSAR analysis as well as understanding the deep irregular behavior of the indium phosphide ( InP ) .

Locating-dominating number of certain infinite families of convex polytopes with applications

A convex hull of finitely many points in the Euclidean space R d is known as a convex polytope. Graphically, they are planar graphs i.e. embeddable on R 2 . Minimum dominating sets possess diverse applications in computer science and engineering. Locating-dominating sets are a natural extension of dominating sets. Studying minimizing locating-dominating sets of convex polytopes reveal interesting distance-dominating related topological properties of these geometrical planar graphs. In this paper, exact value of the locating-dominating number is shown for one infinite family of convex polytopes. Moreover, tight upper bounds on γ l - d are shown for two more infinite families. Tightness in the upper bounds is shown by employing an updated integer linear programming (ILP) model for the locating-dominating number γ l - d of a fixed graph. Results are explained with help of some examples. The second part of the paper solves an open problem in Khan (2023) [28] which asks to find a domination-related parameter which delivers a correlation coefficient of ρ > 0.9967 with the total π-electronic energy of lower benzenoid hydrocarbons. We show that the locating-dominating number γ l - d delivers such a strong prediction potential. The paper is concluded with putting forward some open problems in this area.

Molecular structural modeling and physical characteristics of anti-breast cancer drugs via some novel topological descriptors and regression models

Research is continuously being pursued to treat cancer patients and prevent the disease by developing new medicines. However, experimental drug design and development is a costly, time-consuming, and challenging process. Alternatively, computational and mathematical techniques play an important role in optimally achieving this goal. Among these mathematical techniques, topological indices (TIs) have many applications in the drugs used for the treatment of breast cancer. TIs can be utilized to forecast the effectiveness of drugs by providing molecular structure information and related properties of the drugs. In addition, these can assist in the design and discovery of new drugs by providing insights into the structure-property/structure-activity relationships. In this article, a Quantitative Structure Property Relationship (QSPR) analysis is carried out using some novel degree-based molecular descriptors and regression models to predict various properties (such as boiling point, melting point, enthalpy, flashpoint, molar refraction, molar volume, and polarizability) of 14 drugs used for the breast cancer treatment. The molecular structures of these drugs are topologically modeled through vertex and edge partitioning techniques of graph theory, and then linear regression models are developed to correlate the computed values with the experimental properties of the drugs to investigate the performance of TIs in predicting these properties. The results confirmed the potential of the considered topological indices as a tool for drug discovery and design in the field of breast cancer treatment.

On Certain Degree Based and Bond-additive Topological Indices of Dodeca-benzo-circumcorenene

BACKGROUND

Chemical graph theory has been used to mathematically model the various physical and biological aspects of chemical substances. A mathematical formulation that may be applied to any graph and can characterise a molecule structure is known as a topological index or molecular descriptor.

METHOD

It is convenient and efficient to analyse the mathematical values and further research on various physical properties of a molecule based on these molecular descriptors. They provide useful alternatives to lengthy, expensive, and labour-intensive laboratory experiments. The topological indices can be used to predict the chemical structures, physicochemical properties, and biological activities using quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs).

RESULT

In this study, the molecular descriptors of the Dodeca-benzo-circumcorenene compounds are derived based on their corresponding molecular structures.

CONCLUSION

The computed indices are then compared graphically to study their relationship with the molecular structure and with each other..

Computational aspects of two important biochemical networks with respect to some novel molecular descriptors

Quantitative structure-activity relationship (QSAR) represents quantitative correlation of biological structural features (called as topological indices) and pharmacological activity as response endpoints. Topological index is a molecular descriptor extensively used to study QSAR of pharmaceutical to assess their molecular characteristics by numerical computation. Meanwhile, the topological indices are numerical functions which are used to predict the growth rate of microorganisms in biological networks. Theoretical assessment of microorganism, such as bacteria and viruses help to expedite the vaccine design and discovery process by rationalizing the lead identification, lead optimization and understanding their mechanism of actions. Hypertree, a network structure derived from graph theory, has a great importance in biological networks for growth of microorganisms, such as bacteria and viruses. In this article, some novel eccentric and degree based topological features of two important biological networks (hypertree and its corona product) are obtained on h-level and derived closed formulas for them. Based on the obtained topological features, the biological properties of these networks are investigated.Communicated by Ramaswamy H. Sarma.

Chemical Application of Topological Indices in Infertility Treatment Drugs and QSPR Analysis

The main challenges faced by medical researchers while producing novel drugs are time commitment, amplified costs, creating a safety profile for the medications, reduced solubility, and a lack of experimental data. Chemical graph theory makes an important theoretical contribution to drug development and design by investigating the structural properties of molecules. To improve drug research and assess the effectiveness of treatments, topological indices aim to provide a mathematical representation of molecular structures. In this study, the author examined a number of recently used drugs, including tamoxifen, mesterolone, anastrozole, and letrozole which are used to treat infertility. We compute the topological descriptors with the limiting behaviors associated with these pharmaceutical drugs and offer degree-based topological parameters for them. We conducted a QSPR investigation on the prospective degree-based topological descriptors using quadratic, cubic, exponential, and logarithmic regression models.

Mathematical modeling and topological graph description of dominating David derived networks based on edge partitions

Chemical graph theory is a well-established discipline within chemistry that employs discrete mathematics to represent the physical and biological characteristics of chemical substances. In the realm of chemical compounds, graph theory-based topological indices are commonly employed to depict their geometric structure. The main aim of this paper is to investigate the degree-based topological indices of dominating David derived networks (DDDN) and assess their effectiveness. DDDNs are widely used in analyzing the structural and functional characteristics of complex networks in various fields such as biology, social sciences, and computer science. We considered the FN*, [Formula: see text], and [Formula: see text] topological indices for DDDNs. Our computations' findings provide a clear understanding of the topology of networks that have received limited study. These computed indices exhibit a high level of accuracy when applied to the investigation of QSPRs and QSARs, as they demonstrate the strongest correlation with the acentric factor and entropy.

On the construction of some bioconjugate networks and their structural modeling via irregularity topological indices

Bioconjugate networks refer to networks that are formed by connecting different molecules or particles (such as proteins, enzymes, or nanoparticles) through covalent or non-covalent interactions. These networks are often used in various biological and biomedical applications, such as drug delivery, biosensors, and tissue engineering. The specific properties and behavior of these networks depend on the types of molecules used and the nature of their interactions, which can be studied using various computational and experimental techniques. Farnesyl and geranyl groups are types of isoprenoid chains that are commonly found in various biological molecules such as proteins, lipids, and pigments. The addition of these groups to penicillin molecules may alter their physical and chemical properties, such as solubility, stability, and bioavailability. To gain a better understanding of the structure-property relationships of these antibiotics, this study computes various irregularity indices such as the Albertson index, irregularity index, total irregularity index, Randić irregularity index, and other degree-based indices for two types of sensitive bonds of bioconjugate networks. Numerical results and graphical representations are used to illustrate these findings. The obtained results provide valuable insights into the structure-property relationships of penicillins, which will aid in a better understanding of their behavior and developing more effective antibiotics.

Derivation of mathematical closed form expressions for certain irregular topological indices of 2D nanotubes

A numeric quantity that characterizes the whole structure of a network is called a topological index. In the studies of QSAR and QSPR, the topological indices are utilized to predict the physical features related to the bioactivities and chemical reactivity in certain networks. Materials for 2D nanotubes have extraordinary chemical, mechanical, and physical capabilities. They are extremely thin nanomaterials with excellent chemical functionality and anisotropy. Since, 2D materials have the largest surface area and are the thinnest of all known materials, they are ideal for all applications that call for intense surface interactions on a small scale. In this paper, we derived closed formulae for some important neighborhood based irregular topological indices of the 2D nanotubes. Based on the obtained numerical values, a comparative analysis of these computed indices is also performed.

Structural modeling and topological characterization of three kinds of dendrimer networks

Dendrimers, also known as dendritic polymers, have various applications due to their unique properties, such as their monodisperse structure and their ability to be synthesized with precise control over their size, shape, and surface functionality. Dendrimers are used in drug delivery systems to improve drug solubility, bioavailability, and targeting. They can carry drugs to specific sites, such as cancer cells, and release them in a controlled manner, reducing side effects. Dendrimers can be used as gene delivery vehicles to deliver genetic material to cells in a controlled and targeted manner. Mathematical chemistry is useful to model chemical reactions and predict the behavior of chemical systems. It provides a quantitative understanding of chemical phenomena, which can aid in the design of new molecules and materials. It is used to develop molecular descriptors, which are mathematical representations of molecular structures that can be used to quantify the properties of molecules. These descriptors can be useful in structure-activity relationship studies to predict the biological activity of compounds. The topological descriptors are parameters of any molecular structure that gives a mathematical formula to model such molecular structures. In the current study, our concern is to calculate some useful topological indices for three kinds of dendrimer networks and derive closed mathematical formulas for them. The comparisons of these calculated topological indices are also investigated. Our obtained results will be helpful in investigating QSPRs/QSARs of such molecules in many fields of science, such as chemistry, physics and biochemistry. The dendrimer structure (left). From first (G0) to third (G3) generation, the dendrimer's increasing generations are shown schematically (right).

Mathematical analysis and molecular descriptors of two novel metal-organic models with chemical applications

Metal-Organic Networks (MONs) are made by chemical molecules that contain metal ions and organic ligands. A crystalline porous solid called Metal-Organic Networks (MONs) is made up of a [Formula: see text] metal network of ions held in place by a multidentate ligand. (MONs) can be used for gas storage, purification drug delivery, gas separation, catalysis, and sensing applications. There is enormous potential for effective integration and research of MONs in diverse applications. Molecular descriptors are arithmetic measures that reveal a chemical substance's physical and chemical characteristics in its foundational network in a natural relationship. They demonstrate an important role in theoretical and ecological chemistry, and in the field of medicine. In this research, we calculated various recently discovered molecular descriptors viz. the modified version of second zagreb index, harmonic index, reciprocal randic index, modified version of forgotten topological index, redefined first zagreb topological index, redefined second zagreb topological index and redefined third zagreb topological index for two separate metal-organic networks. The numerical and graphical comparative analysis of these considered molecular descriptors are also performed.

Network-Based Modeling of the Molecular Topology of Fuchsine Acid Dye with Respect to Some Irregular Molecular Descriptors

Fuchsine acid is one of the supramolecular dyes used in Masson’s trichrome stain and has enormous applications in histology. It is also used in Van Gieson’s method with picric acid to show red collagen fibers and in Masson’s trichrome to show smooth muscle in contrast to collagen. In addition to these, it has several other important applications in electronic fields and photonic devices as an organic semiconductor. Therefore, it is of utmost importance to investigate and predict the complex molecular topology of fuchsine acid, which serves as a foundation for the link with its physicochemical properties. In this article, the supramolecular sheet of fuchsine acid is modeled topologically based on the edge partition, and closed formulae are derived for some of its important irregular molecular descriptors, with the ultimate object of throwing some light on the effectiveness of the computed molecular descriptors for QSAR and QSPR analyses.