Graph entropies of porous graphene using topological indices

Edge valency-based entropies of tetrahedral sheets of clay minerals

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.

Tetrahedral sheets of clay minerals and their edge valency-based entropy measures

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 to assess the significance of each type.

A study on anti-malaria drugs using degree-based topological indices through QSPR analysis

The use of topological descriptors is the key method, regardless of great advances taking place in the field of drug design. Descriptors portray the chemical characteristic of a molecule in numerical form, that is used for QSAR/QSPR models. The numerical values related with chemical constitutions that correlate the chemical structure with the physical properties refer to topological indices. The study of chemical structure with chemical reactivity or biological activity is termed quantitative structure activity relationship, in which topological index plays a significant role. Chemical graph theory is one such significant branch of science which plays a key role in QSAR/QSPR/QSTR studies. This work is focused on computing various degree-based topological indices and regression model of nine anti-malaria drugs. Regression models are fitted for computed indices values with 6 physicochemical properties of the anti-malaria drugs are studied. Based on the results obtained, an analysis is carried out for various statistical parameters for which conclusions are drawn.

Analysis of a Productive Topological Index Correlated to Fullerenes’ Physical Properties

Fullerene is a cage-like carbon allotrope admitting a vast range of applications. Some of the important fullerenes are C54,C58,C60,C70,C74,C76,C78,C80C82,C84,C86,C90. The physical properties of fullerenes can be exhibited using the degree-based topological indices. The sum based geometric arithmetic index is significant in this manner. The sum based atomic bond connectivity, Randic, first and second Zagreb indices are well known topological indices. We have determined the regression relation between each of these indices and the sum based geometric arithmetic index. Moreover, the correlation coefficient is also calculated. Correlation is a symmetric relation, as it provides association between two variables. On the basis of regression analysis and correlation coefficient, it was found that each of this index is strongly related to the sum based geometric arithmetic index. Moreover, we have computed the regression relations concerning the physical properties depending on the sum based geometric arithmetic index. The physical properties include binding energies, Ramsauer-Townsend minima, shape resonances and heat of formation of fullerene molecules. It was concluded that the sum based GA index is the best in presenting the heat of the formation of molecules.

Cyclic connectivity index of bipolar fuzzy incidence graph

In the performance characterization of chemical molecular structures, several uncertain properties are often encountered, and fuzzy theory is precisely the tool to characterize these uncertainties. When molecular structures are described by molecular graphs, the corresponding fuzzy graph theory is used to characterize the uncertainty of atoms and atomic bonds. In this study, there is introduced cyclic connectivity index and its average version for bipolar fuzzy incidence graph (BFIG), and several theoretical results are obtained in the light of graph theory and fuzzy theory. Finally, the given new fuzzy index is applied to the testing of anti-aging-related drugs yields average uncertainty data for the corresponding molecular structures.

Prediction of Exchange-Correlation Energy of Graphene Sheets from Reverse Degree-Based Molecular Descriptors with Applications

Over the past few years, the popularity of graphene as a potential 2D material has increased since graphene-based materials have applications in a variety of fields, including medicine, engineering, energy, and the environment. A large number of graphene sheets as well as an understanding of graphene’s structural hierarchy are critical to the development of graphene-based materials. For a variety of purposes, it is essential to understand the fundamental structural properties of graphene. Molecular descriptors were used in this study to investigate graphene sheets’ structural behaviour. Based on our findings, reverse degree-based molecular descriptors can significantly affect the exchange-correlation energy prediction. For the exchange-correlation energy of graphene sheets, a linear regression analysis was conducted using the reverse general inverse sum indeg descriptor, RGISI(p,q). From RGISI(p,q), a set of reverse topological descriptors can be obtained all at once as a special case, resulting in a model with a high correlation coefficient (R between 0.896 and 0.998). Used together, these reverse descriptors are graphed in relation to their response to graphene. Based on this study’s findings, it is possible to predict the exchange correlation energy as well as the geometric structures of graphene sheets with very little computational cost.