Investigation for metallic crystals through chemical invariants, QSPR and fuzzy-TOPSIS.

Chemical graph theory has revolutionary impacts in the field of mathematical chemistry when complex structures are investigated through various chemical invariants (topological indices). We have performed evaluations by considering alternatives as crystal structures, namely Face-Centered Cubic (FCC), hexagonal close-packed (HCP), Hexagonal (HEX), and Body Centered Cubic (BCC) Lattice structures, through the study of two-dimensional degree-based chemical invariants, which we considered criteria. QSPR modeling has been implemented for the targeted crystal structures to investigate the ability of targeted chemical invariants to predict targeted physical properties. Furthermore, the Fuzzy-TOPSIS technique provides the optimal structure HCP ranking as first among all structures when investigated under more than one criterion, which justifies further that the structure attaining dominant countable invariant values ranks high when investigated through physical properties and fuzzy TOPSIS.Communicated by Ramaswamy H. Sarma.

Multiple-Criteria Decision-Making (MCDM) techniques to study the behavior of dendrimers using topological indices.

Topological indices provide a mathematical language for capturing molecular structure, symmetry, and predicting properties. Dendrimers are microscopic bilaterally symmetrical molecules with a well-defined homogeneous nanoparticles structure, often consisting of a symmetric center, inner shell, and outer shell. In this work, first we compute some degree-based topological indices of Porphyrin (DnPn),Poly (Propyl) Ether Imine(PETIM), Zinc porphyrin (DPZn), and Polyamidoamine (PAMAM) dendrimers. Then, we use multi-criteria decision making (MCDM) techniques to establish the weighted evaluation of dendrimer classes based on certain topological indices. For weighted analysis we correlate the properties of benzene derivatives with topological invariants. Finally, based on the multi-criteria decision making techniques namely TOPSIS, SAW and MOORA method, we have ranked the dendrimer structures based on their properties.

QSPR Analysis of Drugs for Treatment of Schizophrenia Using Topological Indices.

Schizophrenia is a chronic psychotic disorder characterized primarily by cognitive deficits. Drugs and therapies are helpful in managing the symptoms, mostly with long-term compliance. There is a pressing need to design more efficient drugs with fewer adverse effects. Solubility, metabolic stability, toxicity, permeability, and transporter effects are important parameters in the efficacy of drug design, which in turn depend upon different physical and chemical characteristics of drugs. In recent years, there has been growing interest in developing computational tools for the discovery and development of drugs for schizophrenia. Some of these methods use machine learning algorithms to predict the efficacy and side effects of the potential drugs. Other studies have used computer simulations to understand the molecular mechanisms underlying the disease and identify new targets for drug development. Topological indices are numeric quantities linked to the chemical structure of drugs and predict the properties, reactivity, and stability of drugs through the quantitative structure-property relationship (QSPR). This work is aimed at using statistical techniques to link QSPR correlating properties with connectivity indices using linear regression. The QSPR model gives quite a better estimation of the properties of drugs, such as melting point, boiling point, enthalpy, flash point, molar refractivity, refractive index, complexity, molecular weight, and refractivity. Results are validated by comparing actual values to estimated values for the drugs.

Implementing QSPR modeling via multiple linear regression analysis to operations research: a study toward nanotubes.

Chemical graph theory significantly predicts multifarious physio-chemical properties of complex and multidimensional compounds when investigated through topological descriptors and QSPR modeling. The targeted compounds are widely studied nanotubes attaining exquisite nanostructures due to their distinguishable properties attaining numeric values. The studied nanotubes are carbon, naphthalene, boron nitride, V-phenylene, and titania nanotubes. In this research work, these nanotubes are characterized through their significance level by implementing highly applicable MCDM techniques. TOPSIS, COPRAS, and VIKOR are used to perform a comparative analysis between them through each optimal ranking. The criteria originated from multiple linear regression modeling established between degree-based topological descriptors and the physio-chemical properties of each nanotube.

Study the Behavior of Drug Structures via Chemical Invariants Using TOPSIS and SAW.

Every year, various experiments emerge in which a strong link between topological chemical structures and their properties is found. These properties are numerous such as melting point, boiling point, and drug toxicity. Topological index is the functional tool to determine these properties. This research paper will analyze some of the molecular drug structures, i.e., hyaluronic acid-paclitaxel conjugates G n , anticancer drug SP[n], polyomino chain of n-cycle Z n , triangular benzenoid T n , and circumcoronene benzenoid series H k using multicriteria decision-making techniques including TOPSIS and SAW. The topological indices used in this research paper include the Randic index for α = 1, -1, 1/2, the augmented Zagreb index and the forgotten topological index.

Targeting highly resisted anticancer drugs through topological descriptors using VIKOR multi-criteria decision analysis.

The disease cancer is expanding on high spans in virtually all over the world, and undoubtedly, the research through all the aspects of sciences for each of its perspective is a great cause in reducing its severeness and symptoms. Chemotherapy is itself a cure to cancer as it helps in controlling the formation of cancerous cells but leaving multiple side effects on a human body. In this research work, we targeted 21 anticancer drugs that are in taken by the patients in combinations during chemotherapies. We introduce another branch of mathematics named as OR (Operations Research) linking to the chemical graph theory. Chemical graph theory allows us to generate highly resistant research on any structure via quantitative structure property relationship (QSPR) modeling to explore and develop new compounds for drugs. In this research study, we visualized what else the QSPR could provide when it comes to ranking drugs. We visualized the results obtained for boiling points and enthalpy of vaporizations through QSPR as the values of correlation coefficients and the errors generated under unique QSPR modeling. The implementation of VIKOR provides the best ranking for each of anticancer drugs when keeping in concern the specified properties, and the conclusions from this research work show another path to biologist scientists to create best combinations keeping in concern the study generated from QSPR. Supplementary Information: The online version contains supplementary material available at 10.1140/epjp/s13360-022-03469-x.

Computing Topological Invariants of Deep Neural Networks.

A deep neural network has multiple layers to learn more complex patterns and is built to simulate the activity of the human brain. Currently, it provides the best solutions to many problems in image recognition, speech recognition, and natural language processing. The present study deals with the topological properties of deep neural networks. The topological index is a numeric quantity associated to the connectivity of the network and is correlated to the efficiency and accuracy of the output of the network. Different degree-related topological indices such as Zagreb index, Randic index, atom-bond connectivity index, geometric-arithmetic index, forgotten index, multiple Zagreb indices, and hyper-Zagreb index of deep neural network with a finite number of hidden layers are computed in this study.

On Trees with Greatest F-Invariant Using Edge Swapping Operations.

The F-index of a graph Q is defined as F(Q)=∑ t∈V(Q)(d t )3. In this paper, we use edge swapping transformations to find the extremal value of the F-index among the class of trees with given order, pendent vertices, and diameter. We determine the trees with given order, pendent vertices, and diameter having the greatest F-index value. Also, the first five maximum values of F index among the class of trees with given diameter are determined.

Study of HCP (Hexagonal Close-Packed) Crystal Structure Lattice through Topological Descriptors.

Chemical graph theory is a multidisciplinary field where the structure of the molecule is analyzed as a graphical structure. Chemical descriptors are one of the most important ideas employed in chemical graph theory; this is to associate a numerical value with a graph structure that often has correlation with corresponding chemical properties. In this paper, we investigate another very important closed-packed usual crystal structure defined as HCP (Hexagonal Close-Packed) crystal structure and its lattice formed by arranging its unit cells in a dimension for topological descriptors based on a neighborhood degree, reverse degree, and degree. Furthermore, we classify which descriptor is more dominating.