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Carbon nanorings are macrocyclic aromatic hydrocarbons that represent the segments of carbon nanotubes and have received considerable attention due to their novel nanoelectronic and photophysical capabilities. The cycloparaphenylene (CPP), a carbon nanoring with a ring-like structure comprising of only benzene units, has been the subject matter of several studies. The carbon nanoring structures bearing polycyclic aromatic hydrocarbons such as hexabenzocoronene and pyrene molecules are also found to exhibit exciting characteristics and applications. This in turn evolves a wide range of novel chemical structures whose behavior and attributes are to be studied and explored. Molecular descriptors help us to study such novel nanostructures by providing a greater understanding of their unique properties, whereas such characterization remains challenging due to their ring-shaped arrangement. In this study, we investigate cycloparaphenylene series and show that such structures are not bounded by the partial cube family. We also derive the exact analytic expressions of degree, distance and closeness-related descriptors. We have also computed the thermodynamic and kinetic stabilities of the three structures using the graph spectra, resonance energies, HOMO-LUMO gaps and Kekulé counts obtained from the graph spectra and combinatorial methods. Whereas the CPPhbc[5] structure is thermodynamically more stable, the CPPyr[9] is kinetically more stable. Furthermore, we have employed combinatorial generating function methods to compute the NMR and ESR spectra of the title compounds. [ABSTRACT FROM AUTHOR]

Low-dimensional graphene-based nanomaterials are interesting due to their cutting-edge electronic and magnetic properties. Their large surface area, strong mechanical resistance, and electronic properties have enabled potential pharmaceutical and opto-electronic applications. Graphene nanoribbons (GNRs) are graphene strips of nanometer size possessing zigzag and armchair edge geometries with tunable widths. Despite the recent developments in the characterization, design and synthesis of GNRs, the study of electronic, magnetic and topological properties, GNRs continue to pose a challenge owing to their multidimensionality. In this study, we obtain the topological and electronic properties of a series of wave-like nanoribbons comprising nanographene units with zigzag-shaped edges. The edge partition techniques based on the convex components are employed to compute the mathematical formulae of molecular descriptors for the wave-like zigzag GNRs. We have also obtained the spectral and energetic properties including HOMO-LUMO gaps, bond delocalization energies, resonance energies, 13 C NMR and ESR patterns for the GNRs. All of these computations reveal zero to very low HOMO-LUMO gaps that make these nanoribbons potential candidates for topological spintronics. [ABSTRACT FROM AUTHOR]

The advent of two‐dimensional transition metal dichalcogenides has triggered an interest in exploring a new class of high‐performance materials with intriguing physicochemical attributes. Molybdenum and tungsten disulfides have attracted significant attention due to surface excitons and trions and the large spin‐orbit effects of these compounds. Moreover, WS2 is especially intriguing due to large relativistic effects, which result in bound excitons at the edge and biexciton formation in the bilayers. Hence, we present a relativistic topological model for the characterization of these two types of metal disulfides. We have employed relativistically weighted graph‐theoretical methods for obtaining structural descriptors of these compounds through the inclusion of different shapes on the boundaries and employing the topological cut techniques. [ABSTRACT FROM AUTHOR]

Humanity has always benefited from an intercapillary study in the quantification of natural occurrences in mathematics and other pure scientific fields. Graph theory was extremely helpful to other studies, particularly in the applied sciences. Specifically, in chemistry, graph theory made a significant contribution. For this, a transformation is required to create a graph representing a chemical network or structure, where the vertices of the graph represent the atoms in the chemical compound and the edges represent the bonds between the atoms. The quantity of edges that are incident to a vertex determines its valency (or degree) in a graph. The degree of uncertainty in a system is measured by the entropy of a probability. This idea is heavily grounded in statistical reasoning. It is primarily utilized for graphs that correspond to chemical structures. The development of some novel edge-weighted based entropies that correspond to valency-based topological indices is made possible by this research. Then these compositions are applied to clay mineral tetrahedral sheets. Since they have been in use for so long, corresponding indices are thought to be the most effective methods for quantifying chemical graphs. This article develops multiple edge degree-based entropies that correlate to the indices and determines how to modify them in order to assess the significance of each type. [ABSTRACT FROM AUTHOR]