Current Organic Synthesis - Volume 21, Issue 3, 2024

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.

Background: Chemical graph theory is a sub-branch of mathematical chemistry, assuming each atom of a molecule is a vertex and each bond between atoms as an edge. Objective: Owing to this theory, it is possible to avoid the difficulties of chemical analysis because many of the chemical properties of molecules can be determined and analyzed via topological indices. Due to these parameters, it is possible to determine the physicochemical properties, biological activities, environmental behaviours and spectral properties of molecules. Nowadays, studies on the zero divisor graph of Zn via topological indices is a trending field in spectral graph theory. Methods: For a commutative ring R with identity, the prime ideal sum graph of R is a graph whose vertices are nonzero proper ideals of R and two distinctvertices I and J are adjacent if and only if I+J is a prime ideal of R . Results: In this study the forgotten topological index and Wiener index of the prime ideal sum graph of Zn are calculated for n=p^α ,pq, p²q, p²q², pqr, p³q, p²qr, pqrs where p, q, r and s are distinct primes and a Sage math code is developed for designing graph and computing the indices. Conclusion: In the light of this study, it is possible to handle the other topological descriptors for computing and developing new algorithms for next studies and to study some spectrum and graph energies of certain finite rings with respect to PIS-graph easily.

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. Materials and Methods: = (V(),E()) is used as a graph, where V() is a collection of vertices and E() is a collection of edges. For a vertex y, ∈V(), the degree d_ (y), is the number of those vertices that are at a distance of 1 from y and the connection number ρ_ (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.

In this work, we studied the problem of determining the values of the Zagreb indices of all the realizations of a given degree sequence. Methods: We first obtained some new relations between the first and second Zagreb indices and the forgotten index sometimes called the third Zagreb index. These relations also include the triangular numbers, order, size, and the biggest vertex degree of a given graph. As the first Zagreb index and the forgotten index of all the realizations of a given degree sequence are fixed, we concentrated on the values of the second Zagreb index and studied several properties including the effect of vertex addition. Results: In our calculations, we make use of a new graph invariant, called omega invariant, to reach numerical and topological values claimed in the theorems. This invariant is closely related to Euler char-acteristic and the cyclomatic number of graphs. Conclusion: Therefore this invariant is used in the calculation of some parameters of the molecular structure under review in terms of vertex degrees, eccentricity, and distance.

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. Materials and Methods: Topological descriptors are numerical quantities corresponding to the chemical structures that are used in the study of these phenomena. Results: 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: The concept of Hückel molecular orbital theory is used to compute the graph energy numerically and 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 matrix and its Laplacian version. Methods: 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 omega index has been recently introduced to identify a variety of topological and combinatorial aspects of a graph with a new viewpoint. As a continuing study of the omega index, by considering the incidence of edges and vertices to the adjacency of the vertices, in this paper, we have introduced the second omega index Ω2 and then computed it over some well-known graph classes. Methods: Many combinatorial counting methods have been utilized in the proofs. The edge partition is frequently used throughout the work. Naturally, some graph theoretical lemmas are also used. Results: In particular, trees having the smallest and largest Ω2 have been constructed. Finally, the second omega index of some derived graphs, such as line graphs, subdivision graphs, and vertex-semitotal graphs, has been presented. Conclusion: Omega invariant has already been explored in many papers. It has been defined in terms of vertex degrees. Vertices correspond to the atoms in a molecule and a calculation, which only depends on the atomic parameters, is not even comparable with a calculation containing both atoms and chemical bonds between them. With this idea in mind, we have evaluated some mathematical properties of the second omega index, which has great potential in chemical applications related to the number of cycles in the molecular graph.

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. Methods: 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- quin-oline skeleton synthesis.

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.

The synthesis of coumarin derivatives has been an essential topic since its discovery in 1820. In bioactive compounds, the coumarin moiety serves as a backbone, as many such bioactive compounds with the coumarin moiety play a significant role in their bioactivities. Given this moie-ty's relevance, several researchers are developing fused-coumarin derivatives to create new drugs. Mostly the approach done for this purpose was a multicomponent reaction based. Over the years, the multicomponent reaction has gained enormous popularity, and this approach has evolved as a replacement for conventional synthetic methods. Because of all these perspectives, we have reported the various fused-coumarin derivatives synthesized using multicomponent reactions in recent years.

A series of reactive disperse dyes bearing azo and cyanuric groups were synthesized, and their structures were established using spectral and elemental analyses. Methods: The IR, ¹H NMR, and DFT studies indicated that the prepared reactive disperse dyes predominately exist as hydrazone tautomers. The electronic absorption spectra in methanol were observed and compared to those computed using B3LYP/6-311G(d,p). The dyeing efficiency of the produced dispersed reactive dyes was examined on polyester, cotton, and polyester/cotton blended fabrics. Results: The degree of exhaustion and the fastness properties of the dyed samples in terms of perspiration, washing, scorch and light fastness were assessed. It was found that reactive disperse dyes under investigation have a higher affinity for dyeing polyester textiles than cotton textiles. Conclusion: Moreover, the reflectance and color strength of the synthesized dyes were measured and discussed.

Background: Bimetallic catalysis plays a major role in boosting the catalytic performance of monometallic counterparts due to the synergetic effect. Materials and Methods: In the present study, we have exploited ZrCl4:Mg(ClO4)2 as an efficient bimetallic catalyst for the synthesis of a few biologically relevant N-substituted decahydroacri-dine-1,8-diones and xanthene-1,8-diones under solvent-free conditions. The complete characterization data (XRD, SEM, BET, pH, TGA, and IR) of the bimetallic catalyst, ZrCl4: Mg(ClO4)2, are provided in the supporting information. Results: Among the compounds screened for anti-oxidant and anti-microbial activities, the ac-ridine derivatives with chloro and fluoro substitutions (compounds 4b, 4c, 4d, and 4j) have ex-hibited potent activities when compared to other compounds. Among the xanthene derivatives screened for anti-oxidant activity, compounds 5c, 5i, and 5j with chloro and nitro derivatives exhibited potent antioxidant activity, and the rest all showed moderately potent activity. Conclusion: Among the compounds screened for antibacterial activity, compound 5j with chloro substitution showed potent activity, followed by compounds 5c, 5d, 5h, and 5i against Gram +ve bacteria, and compounds 5h, 5f, and 5g with N,N-dimethyl, methoxy and hydroxy substitutions have shown potent activity against Gram -ve bacteria.