Degree-based topological indices and polynomials of hyaluronic acid-curcumin conjugates

Curcumin-Conjugated PAMAM Dendrimers of Two Generations: Comparative Analysis of Physiochemical Properties Using Adriatic Topological Indices

Curcumin (C21H20O6) is a polyphenol found in the plant Curcuma longa. Even though it possesses many pharmacological effects, owing to its limited intestinal absorption, solubility, and oral bioavailability, it is more often used as a health supplement than as a lead chemical. The poly(amido)amine (PAMAM) dendrimer (nanostructure) is utilized to enhance the stability and targeted delivery of drugs. Recently, curcumin was conjugated with the PAMAM dendrimer and analyzed for its photostability. Further investigation into the physiochemical characteristics of different generations can facilitate curcumins' targeted delivery for many diseases, including cancer. However, many of these conjugates' physiochemical properties are not available in databases since they have not been explored theoretically or experimentally. In this article, QSAR/QSPR (quantitative structure-activity relationship/quantitative structure-property relationship) analysis of physiochemical properties was carried out for component structures, which produced encouraging results. Hence, 16 discrete adriatic topological indices and their associated entropy measures were evaluated to theoretically predict a few physiochemical properties of the conjugated structure. The predictions will aid the chemist in drug designing.

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.

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

In the past few years, two-dimensional (2D) layered nanomaterials have greatly attracted the scientific community. Among 2D nanomaterials, the porphyrin-based Naphtalenic nanosheets have been the subject of intense research due to their utilization in photo-dynamic therapy and nanodevices. New technologies based on nanomaterials or Naphtalenic nanosheet are advantageous in overcoming the problems in conventional drug delivery like poor solubility, toxicity and poor release pattern of drugs. In chemical network theory, various molecular descriptors are used to predict the chemical properties of molecules; these molecular descriptors are found to be very useful for Quantitative Structure–Activity/ Quantitative Structure–Property (QSAR/QSPR) relationship analysis in materials engineering, chemical and pharmaceutical industries. Researchers have computed the molecular descriptors for various nanostructures; however, despite intense research, the topology of nanostructures is not yet well understood. Specially, to our knowledge, the computation of topological indices for the line graph of subdivision graph of H-Naphtalenic nanosheet has not been discussed so far, which may open new perspectives for a more accurate and reliable topological characterization of this nanosheet.

In this article, we employed some important degree-based topological indices to study the chemical structure of Naphtalenic nanosheet as a chemical network for QSAR/QSPR analysis. We have computed these degree-based topological indices for the line graph of subdivision graph of H-Naphtalenic nanosheet and derived formulas for them. Based on the derived formulas, numerical results are obtained and the physical and chemical properties of the under study nanosheet are investigated.

On Hosoya Polynomial and Subsequent Indices of C4C8(R) and C4C8(S) Nanosheets

Chemical structures are mathematically modeled using chemical graphs. The graph invariants including algebraic polynomials and topological indices are related to the topological structure of molecules. Hosoya polynomial is a distance based algebraic polynomial and is a closed form of several distance based topological indices. This article is devoted to compute the Hosoya polynomial of two different atomic configurations (C4C8(R) and C4C8(S)) of C4C8 Carbon Nanosheets. Carbon nanosheets are the most stable, flexible structure of uniform thickness and admit a vast range of applications. The Hosoya polynomial is used to calculate distance based topological indices including Wiener, hyper Wiener and Tratch–Stankevitch–Zafirov Indices. These indices play their part in determining quantitative structure property relationship (QSPR) and quantitative structure activity relationship (QSAR) of chemical structures. The three dimensional presentation of Hosoya polynomial and related distance based indices leads to the result that though the chemical formula for both the sheets is same, yet they possess different Hosoya Polynomials presenting distinct QSPR and QSAR corresponding to their atomic configuration.

On Analysis of Banhatti Indices for Hyaluronic Acid Curcumin and Hydroxychloroquine

Topological indices are numerical numbers assigned to the graph/structure and are useful to predict certain physical/chemical properties. In this paper, we give explicit expressions of novel Banhatti indices, namely, first K Banhatti index $\left(B_1\left(G\right)\right)$ , second K Banhatti index $\left(B_2\left(G\right)\right)$ , first K hyper-Banhatti index $\left({\text{HB}}_1\left(G\right)\right)$ , second K hyper-Banhatti index $\left({\text{HB}}_2\left(G\right)\right)$ , and K Banhatti harmonic index $\left(H_b\left(G\right)\right)$ for hyaluronic acid curcumin and hydroxychloroquine. The multiplicative version of these indices is also computed for these structures.

Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index $\left(\text{GA}\right)$ , atom bond connectivity index $\left(\text{ABC}\right)$ , forgotten index $\left(F\right)$ , inverse sum indeg index $\left(\text{ISI}\right)$ , general inverse sum indeg index ${\text{ISI}}_{\left(\alpha ,\beta \right)}$ , first multiplicative-Zagreb index $\left({\text{PM}}_1\right)$ and second multiplicative-Zagreb index $\left({\text{PM}}_2\right)$ , fifth geometric arithmetic index $\left({\text{GA}}_5\right)$ , fourth atom bond connectivity index $\left({\text{ABC}}_4\right)$ of double graph, and strong double graph of Dutch Windmill graph $D_3^p$ .

Topological Characterization and Graph Entropies of Tessellations of Kekulene Structures: Existence of Isentropic Structures and Applications to Thermochemistry, Nuclear Magnetic Resonance, and Electron Spin Resonance

Tessellations of kekulenes and cycloarenes are of considerable interest as nanomolecular belts in trapping and transportation of heavy metal ions and chloride ions, as they possess optimal electronic features and pore sizes. A class of cycloarenes called kekulenes have been the focus of several experimental and theoretical studies from the stand point of aromaticity, superaromaticity, chirality, and novel electrical and magnetic properties. In the present study, we investigate the entropies and topological characterization of different tessellations of kekulenes through topological computations of superaromatic structures with pores. We introduce the self-powered vertex degree-based topological indices and then derive the graph entropy measures for three different tessellations (zigzag, armchair, and rectangular) via various molecular descriptors that we derive here. Several applications to computing the molecular properties are pointed out. We demonstrate the existence of isentropic and yet nonisomorphic tessellations of kekulenes for the first time. The two tessellations are predicted to be quite close in energy with comparable energy gaps. Graph theory-based PPP methods with parameters derived from higher levels of theory are proposed to be promising tools for the predictions of relative stabilities of kekulene tessellations. We show that the developed techniques can be applied in the general context of artificial intelligence for the machine generation of nuclear magnetic resonance and electron spin resonance spectroscopic patterns as well as in robust computations of thermochemistry of a large combinatorial libraries of tessellations of kekulenes through the generation of bond-equivalence classes.

On Ve-Degree and Ev-Degree Topological Properties of Hyaluronic Acid‐Anticancer Drug Conjugates with QSPR

The design of the quantitative structure-property/activity relationships for drug-related compounds using theoretical methods relies on appropriate molecular structure representations. The molecular structure of a compound comprises all the information required to determine its chemical, biological, and physical properties. These properties can be assessed by employing a graph theoretical descriptor tool widely known as topological indices. Generalization of descriptors may reduce not only the number of molecular graph-based descriptors but also improve existing results and provide a better correlation to several molecular properties. Recently introduced ve-degree and ev-degree topological indices have been successfully employed for development of models for the prediction of various biological activities/properties. In this article, we propose the general ve-inverse sum indeg index ${\text{ISI}}_{\left(\alpha ,\beta \right)}^{\text{ve}}\left(G\right)$ and general ve-Zagreb index $M_{\alpha }^{\text{ve}}\left(G\right)$ of graph $G$ and compute ${\text{ISI}}_{\left(\alpha ,\beta \right)}^{\text{ve}}\left(G\right),M_{\alpha }^{\text{ve}}\left(G\right)$ , and $M_{\alpha }^{\text{ev}}\left(G\right)$ (general ev-degree index) of hyaluronic acid-curcumin/paclitaxel conjugates, renowned for its potential anti-inflammatory, antioxidant, and anticancer properties, by using molecular structure analysis and edge partitioning technique. Several ve-degree- and ev-degree-based topological indices are obtained as a special case of ${\text{ISI}}_{\left(\alpha ,\beta \right)}^{\text{ve}}\left(G\right),M_{\alpha }^{\text{ve}}\left(G\right)$ , and $M_{\alpha }^{\text{ev}}\left(G\right)$ . Furthermore, QSPR analysis of ${\text{ISI}}_{\left(\alpha ,\beta \right)}^{\text{ve}}\left(G\right),M_{\alpha }^{\text{ve}}\left(G\right)$ , and $M_{\alpha }^{\text{ev}}\left(G\right)$ for particular values of $\alpha$ and $\beta$ is performed, which reveals their predicting power. These results allow researchers to better understand the physicochemical properties and pharmacological characteristics of these conjugates.