The study aimed to obtain relationships between the omega invariants of a graph and its complement. We used some graph parameters, including the cyclomatic numbers, number of components, maximum number of components, order, and size of both graphs G and G. Also, we used triangular numbers to obtain our results related to the cyclomatic numbers and omega invariants of G and G. Several bounds for the above graph parameters have been obtained by the direct application of the omega invariant. We used combinatorial and graph theoretical methods to study formulae, relations, and bounds on the omega invariant, the number of faces, and the number of compo-nents of all realizations of a given degree sequence. Especially so-called Nordhaus-Gaddum type resulted in our calculations. In these calculations, the triangular numbers less than a given number play an important role. Quadratic equations and inequalities are intensively used. Several relations between the size and order of the graph have been utilized in this study. In this paper, we have obtained relationships between the omega invariants of a graph and its complement in terms of several graph parameters, such as the cyclomatic numbers, number of components, maximum number of components, order, and size of G and G, and triangular numbers. Some relationships between the omega invariants of a graph and its complement have been obtained.
This study aimed to prepare three imine derivatives (1, 2, and 3) via a condensation reaction of phenyl hydrazine, 2-hydrazino pyridine, and 4-methoxy aniline with 4-formyl pyridine. Electron impact mass spectrometry (EIMS), proton nuclear magnetic resonance (1H-NMR), ultraviolet-visible (UV-Vis) and Fourier transform infrared (FTIR) spectroscopy were utilized for the characterization. The chemosensing properties of [4((2-phenyl hydrazono)methyl) pyridine] (1), [2-(2-(pyridin-4-ylmethylene)hydrazinyl) pyridine] (2), and [4-methoxy-N-yl methylene) aniline] (3) imino bases have been explored for the first time in aqueous media. The photophysical properties of chemosensors (1, 2, and 3) were examined by various cations (Na+, NH4+, Ba+2, Ni+2, Ca+2, Hg+2, Cu+2, Mg+2, Mn+2, and Pd+2). The chemosensor (1) showed very selective binding capability with copper ions at low concentrations (20 μM) without the influence of any other mentioned ions. The maximum complexation was noted with Cu+2 and 1 at pH between 7 to 7.5. The stoichiometry binding ratio between chemosensor (1) and Cu+2 was determined by Job's plot and it was found to be 1:2. The current study explored the use of these Schiff bases for the first time as heterocyclic chemosensors. DPPH radical scavenging, urease enzyme inhibition activities, molecular docking simulation, and density functional theory (DFT) analysis of compounds 1, 2, and 3 were also conducted.
Background: Cheminformatics is a fascinating emerging subfield of chemical graph theory that studies quantitative structure-activity and property relationships of molecules and, in turn, uses these to predict the physical and chemical properties, which are extremely useful in drug discovery and optimization. Knowledge discovery can be put to use in pharmaceutical data matching to help in finding promising lead compounds.
Method: Topological descriptors are numerical quantities corresponding to the chemical structures that are used in the study of these phenomena.
Result: This paper is concerned with developing the generalized analytical expression of topological descriptors for zeolite ACO structures with underlying degree and degree-sum parameters.
Conclusion: To demonstrate improved discrimination power between the topological descriptors, we have further modified Shannon's entropy approach and used it to calculate the entropy measures of zeolite ACO structures.
Background: Topological indices (TIs) are mathematical formulas that are applied in mathematical chemistry to predict the physical and chemical properties of various chemical structures. In this study, three different types of polycyclic aromatic hydrocarbon structures (PAHs) (i.e., Hexa-peri-hexabenzocoronene, Dodeca-benzo-circumcoronene, and Hexa-cata- hexabenzocoronene) are studied with the help of the different connection number-based Zagreb indices.
Method: ϑ = (V(ϑ),E(ϑ)) is used as a graph, where V(ϑ) is a collection of vertices and E(ϑ) is a collection of edges. For a vertex y, ∈V(ϑ), the degree d_ϑ (y), is the number of those vertices that are at a distance of 1 from y and the connection number ρ_ϑ (y) is the number of such vertices that are at a distance of 2 from vertex y.
Results: Theoretical applications of topological indices were described in detail.
Conclusion: Finally, we obtained the first and second Zagreb connections as well as the modified first, second, third, and fourth Zagreb connection indices, which were calculated for three different types (Hexa-peri-hexabenzocorone, Dodeca-benzo-circumcoronene, and Hexa-cata-hexabenzocoronene) of polycyclic aromatic hydrocarbon structures.
Introduction: Pyrazolo-quinolinones (PQs) are a versatile class of Organic chemistry and it was found that they have very advanced functionally promising as selective compounds due to their scaffold and demonstrated low toxicity and considerable clinical promise. Moreover, these compounds have an important role in different applications such as analytical reagents, technical, pharmaceutical development, and biological markers. So, we aimed to synthesize and characterize new 4-(Het)aryl-substituted Pyrazole-quinolinones.
Method: Synthesis of One-Pot Multicomponent Reaction was carried out with the reaction of 5-amino-3-methyl-1H-pyrazole 1a, and 5-amino-3-phenyl-1H-pyrazole 1b and dimedone 2 with some (het)aryl aldehydes 3 using ethanol. Characterizations such as the linear structures and the regiospecificity of the reactions were determined by using NMR, GC-MS, IR, and UV measurements.
Conclusion: This research will be very useful for all methods and procedures using multi-one-point reactions which are very popular in the synthesis of heterocyclic systems for pyrazole- quinoline skeleton synthesis.
Background: The concept of Hückel molecular orbital theory is used to compute the graph energy numerically as well asnd graphically, on the base of the status of a vertex.
Objective: Our aim is to explore the graph energy of various graph families on the base of the status adjacency matirx matrix and its Laplacian version.
Method: We opt for the technique of finding eigenvalues of adjacency and Laplacian matrices constructed on the base of the status of vertices.
Results: We explore the exact status sum and Laplacian status sum energies of a complete graph, complete bipartite graph, star graphs, bistar graphs, barbell graphs and graphs of two thorny rings. We also compared the obtained results of energy numerically and graphically.
Conclusion: In this article, we extended the study of graph spectrum and energy by introducing the new concept of the status sum adjacency matrix and the Laplacian status sum adjacency matrix of a graph. We investigated and visualized these newly defined spectrums and energies of well-known graphs, such as complete graphs, complete bi-graphs, star graphs, friendship graphs, bistar graphs, barbell graphs, and thorny graphs with 3 and 4 cycles.
Background: The emergence of drug-resistant bacteria and multidrug-resistant diseases, both of which are associated with high mortality, has posed a serious global health issue. Thiazoles and coumarins were reported as antimicrobial agents.
Objective: This research paper aims to describe the synthesis of some novel thiazole derivatives bear-ing a coumarin residue as antibacterial agents Methods: The thiazole - coumarin hybrids were synthesized starting from the condensation of 3-acetyl coumarin (1) hydrazine carbothioamide (2) or thisemicarbazide then reacting the resulting products with different p-substituted phenacyl bromides (4a-e), hydrazonoyl chlorides (8a-e), and (11). In vitro antibacterial activity was studied in this work. In addition, molecular docking studies for the new compounds have also been carried out to investigate the binding mode of actions against the target DNA gyrase B.
Results: Some of the newly synthesized compounds such as compounds 10b, 7, and 6b showed pronounced activities against Gram (+ve) and Gram (-ve) bacteria compared to a reference antibacterial agent. Compounds 10b, 7, and 6b exhibited the best binding affinity against the target.
Conclusion: We could obtain a series of precious hitherto unknown thiazole derivatives with varied antibacterial activities from cheap laboratory-available starting material following rather simple environmentally friendly techniques avoiding the use of hazardous or heavy metal-containing catalysts.
Background: In connection with the study of chemical graph theory, it has been explored that a single number can capture the numerical representation of a molecular structure, and this number is known as a topological property (index).
Objective: This study aimed to explore a few Zagreb topological properties for four hexa organic molecular structures (hexagonal, honeycomb, silicate, and oxide) based on the valency and valency sum of atoms in the structure.
Methods: We employed the technique of partitioning the set of bonds according to the valency and valency-sum of end atoms of each bond and then performed the computation by using combinatorial rules of counting (that is, the rule of sum and the rule of product). The obtained results were also compared numerically and graphically.
Results and conclusion: Exact values of five valencies based and five valency-sum-based Zagreb topological properties were found for the underline chemical structures.
Fermentation is being utilized since ages as a safe process for food preservation. Fermentation in winemaking is the process which converts grapes juice into wine. Alcoholic fermentation is the principle for the manufacturing of alcoholic beverages like wine and beer. Several by-products are produced by the alcoholic fermentation of organic carbon sources by Saccharomyces cerevisiae. The secondary bacterial fermentation is malolactic fermentation which is carried out in most red and some kinds of white wines. Malolactic fermentation causes acid reduction, flavor modification, and also is accountable for microbial stability. The present searching was carried out by the keywords in major indexing systems including PubMed/MEDLINE, Scopus, Institute for Scientific Web of Science and the search engine of Google Scholar. The keywords were alcoholic fermentation, malolactic fermentation, bottle fermentation, carbonic maceration, Saccharomyces, Lactobacillus, Oenococcus oeni, aromatic substances, flavour quality, terpenes, esters, lactones, aldehydes, organic acid, pyrazines, mercaptans, and traditional fermented food. This review was done to highlight the significance, and introduce different kinds of fermentations carried out in wine-making process, specially alcoholic and malolactic fermentation, survey on aromatic substances, flavour quality, and organic acids, and introduce the most notable traditional fermented food in China.