Topological Characterization of the Full k-Subdivision of a Family of Partial Cubes and Their Applications to α-Types of Novel Graphyne and Graphdiyne Materials

On degree-based operators and topological descriptors of molecular graphs and their applications to QSPR analysis of carbon derivatives

This work initiates a concept of reduced reverse degree basedRR D M -Polynomial for a graph, and differential and integral operators by using thisRR D M -Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using theRR D M -Polynomial. The topological descriptors, denoted as T D 's, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study.

On Certain Degree Based and Bond-additive Topological Indices of Dodeca-benzo-circumcorenene

BACKGROUND

Chemical graph theory has been used to mathematically model the various physical and biological aspects of chemical substances. A mathematical formulation that may be applied to any graph and can characterise a molecule structure is known as a topological index or molecular descriptor.

METHOD

It is convenient and efficient to analyse the mathematical values and further research on various physical properties of a molecule based on these molecular descriptors. They provide useful alternatives to lengthy, expensive, and labour-intensive laboratory experiments. The topological indices can be used to predict the chemical structures, physicochemical properties, and biological activities using quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs).

RESULT

In this study, the molecular descriptors of the Dodeca-benzo-circumcorenene compounds are derived based on their corresponding molecular structures.

CONCLUSION

The computed indices are then compared graphically to study their relationship with the molecular structure and with each other..

Topological and Spectral Properties of Wavy Zigzag Nanoribbons

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, 13C 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.

Symmetry and Combinatorial Concepts for Cyclopolyarenes, Nanotubes and 2D-Sheets: Enumerations, Isomers, Structures Spectra & Properties

This review article highlights recent developments in symmetry, combinatorics, topology, entropy, chirality, spectroscopy and thermochemistry pertinent to 2D and 1D nanomaterials such as circumscribed-cyclopolyarenes and their heterocyclic analogs, carbon and heteronanotubes and heteronano wires, as well as tessellations of cyclopolyarenes, for example, kekulenes, septulenes and octulenes. We establish that the generalization of Sheehan’s modification of Pólya’s theorem to all irreducible representations of point groups yields robust generating functions for the enumeration of chiral, achiral, position isomers, NMR, multiple quantum NMR and ESR hyperfine patterns. We also show distance, degree and graph entropy based topological measures combined with techniques for distance degree vector sequences, edge and vertex partitions of nanomaterials yield robust and powerful techniques for thermochemistry, bond energies and spectroscopic computations of these species. We have demonstrated the existence of isentropic tessellations of kekulenes which were further studied using combinatorial, topological and spectral techniques. The combinatorial generating functions obtained not only enumerate the chiral and achiral isomers but also aid in the machine construction of various spectroscopic and ESR hyperfine patterns of the nanomaterials that were considered in this review. Combinatorial and topological tools can become an integral part of robust machine learning techniques for rapid computation of the combinatorial library of isomers and their properties of nanomaterials. Future applications to metal organic frameworks and fullerene polymers are pointed out.

Surface Functionalization of Graphene-Based Materials: Biological Behavior, Toxicology, and Safe-By-Design Aspects

The increasing exploitation of graphene-based materials (GBMs) is driven by their unique properties and structures, which ignite the imagination of scientists and engineers. At the same time, the very properties that make them so useful for applications lead to growing concerns regarding their potential impacts on human health and the environment. Since GBMs are inert to reaction, various attempts of surface functionalization are made to make them reactive. Herein, surface functionalization of GBMs, including those intentionally designed for specific applications, as well as those unintentionally acquired (e.g., protein corona formation) from the environment and biota, are reviewed through the lenses of nanotoxicity and design of safe materials (safe-by-design). Uptake and toxicity of functionalized GBMs and the underlying mechanisms are discussed and linked with the surface functionalization. Computational tools that can predict the interaction of GBMs behavior with their toxicity are discussed. A concise framing of current knowledge and key features of GBMs to be controlled for safe and sustainable applications are provided for the community.

On Certain Topological Indices of Three-Layered Single-Walled Titania Nanosheets

AIM AND OBJECTIVE

Nanostructures are objects whose sizes are between microscopic and molecular. The most significant of these new elements are carbon nanotubes. These elements have extraordinary microelectronic properties and many other exclusive physiognomies. Recently, researchers have given the attention to the mathematical properties of these materials. The aim and objective of this research article is to investigate the most important molecular descriptors namely Wiener, edge-Wiener, vertex-edge-Wiener, vertex-Szeged, edge-Szeged, edge-vertex-Szeged, total-Szeged, PI, Schultz, Gutman, Mostar, edge-Mostar, and total-Mostar indices of three-layered single-walled titania nanosheets. By computing these topological indices, materials science researchers can have a better understanding of structural and physical properties of titania nanosheets, and thereby more easily synthesizing new variants of titania nanosheets with more amenable physicochemical properties.

METHODS

The cut method turned out to be extremely handy when dealing with distance-based graph invariants which are in turn among the central concepts of chemical graph theory. In this method, we use the Djokovic ́-Winkler relation to find the suitable edge cuts to leave the graph into exactly two components. Based on the graph theoretical measures of the components, we obtain the desired topological indices by mathematical computations.

RESULTS

In this paper, distance-based indices for three-layered single-walled titania nanosheets were investigated and given the exact expressions for various dimensions of three-layered single-walled titania nanosheets. These indices may be useful in synthesizing new variants of titania nanosheets and the computed topological indices play an important role in studies of Quantitative structure-activity relationship (QSAR) and Quantitative structure-property relationship (QSPR).

CONCLUSION

In this paper, we have obtained the closed expressions of several distance-based topological indices of three-layered single-walled titania nanosheet TNS_3 [m,n] molecular graph for the cases m≥ n and m < n. The graphical validations for the computed indices are done and we observe that the Wiener types, Schultz and Gutman indices perform in a similar way whereas PI and Mostar type indices perform in the same way.