Degree-based Entropy Research Articles

Bicubic regression analysis a novel approach for estimation of physicochemical properties of skin cancer drugs through degree based entropy

Skin cancer poses a significant risk to the healthcare system worldwide and is projected to increase substantially over the next two decades, particularly if not detected in its early stages. The primary aim of this study is to construct a quantitative structure-property relationship (QSPR) by correlating calculated entropies with topological indices and specific physical-chemical properties of pharmaceuticals, in order to enhance their usefulness. The bicubic regression model is constructed through degree-based topological entropies to perform the QSPR analysis for the prediction of physiochemical properties like polar surface area, complexity, molar refractivity, boiling point, and polarity of skin cancer drugs. It is also examined that degree-based entropies provide best-fit models for skin cancer physiochemical properties. We inspected five physio-chemical properties of these anticancer drugs and found this methodology suitable for predicting best-fit approximations regarding R2 value. It is expected that this approach will be very favourable to examining problems related to mathematical chemistry.

On degree-based entropy measure for zero-divisor graphs

Let [Formula: see text] be a commutative ring with [Formula: see text] A zero-divisor graph [Formula: see text] is an undirected graph on the vertex set [Formula: see text] such that any two nonzero elements [Formula: see text] are adjacent whenever [Formula: see text] The concept of entropy measure is fundamental and has been the subject of interest in various fields. The purpose of this paper is to calculate the entropy measure of [Formula: see text] for various rings. We take into consideration the ring [Formula: see text] for [Formula: see text] where [Formula: see text] and [Formula: see text] are distinct prime numbers. Moreover, we also discussed the entropy measure of the zero-divisor graph for the rings [Formula: see text] and [Formula: see text] This study will help us further understand the algebraic structure of the commutative rings.

Retracted: On Computation of Degree-Based Entropy of Planar Octahedron Networks

Retracted: On Computation of Degree-Based Entropy of Planar Octahedron Networks

Entropy measures of the metal–organic network via topological descriptors

Abstract A family of chemical compounds known as metal–organic networks (MONs) is composed mainly of clusters of metal ions with organic ligands. It can increase volatility or make substances soluble in organic solvents. By using these salient features, organic compounds generate applications in material sciences for sol–gel processing. A graph’s entropy is utilized as a complexity indicator and is interpreted as the structural information content of the graph. Investigating the entropies of relationship systems is a common occurrence in discrete mathematics, computer science, information theory, statistics, chemistry, and biology. In this article, we investigated the degree-based entropies: geometric arithmetic entropy, atom bond connectivity entropy, general Randic′ entropy, and general sum connectivity entropy for MONs. Furthermore, we created tables for all expressions by using 1–10 values for the s s parameter of these entropies.

Retracted: On Topological Properties of Degree-Based Entropy of Hex-Derived Network of Type 3

Retracted: On Topological Properties of Degree-Based Entropy of Hex-Derived Network of Type 3

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.

Entropy Measures of Topological Indices Based Molecular Structure of Benzenoid Systems

Graph theory plays a significant role in the applications of chemistry, pharmacy, communication, maps, and aeronautical fields. A benzenoid is a class of chemical compounds with at least one benzene ring(hexagon as a graph) and resonance bonds in the benzene ring give increased stability in benzenoids. The molecules of chemical compounds are modeled as a graph to study the properties of the compounds. The geometric structure of the compound relates to a few physical properties such as boiling point, enthalpy, π-electron energy, and molecular weight. Entropy is a thermodynamic function in physics that measures the randomness and disorder of molecules in a particular system or process based on the diversity of configurations that molecules might take. Degree-based entropy is used to address a wide range of problems in the domains of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines. This paper focusses on computing analytical expressions of degree-based entropy measures for benzenoid systems.

On topological descriptor based heat of formation and entropy measure for actinium(III) fluoride

Silvery radioactive metallic element is known as actinium. Due to its high radioactivity and blue light, actinium glows in the dark. A recent discipline of applied chemistry is chemical graph theory. A topological index is a numerical value that links the thermodynamic properties of a chemical structure. Due to the importance of this structure, we computed the topological indices such as Randic, Zagreb Indices and so on. In this paper, we calculate topological indices of actinium(III) fluoride. A few degree-based entropies are computed from topological indices. Additionally, a connection has been made between the thermodynamic features of actinium(III) fluoride and Shannon entropy. The numerical and graphical representations of the computed data were combined with curve fitting between the calculated information entropies and the heat of formation.

QSPR Modeling with Curvilinear Regression on the Reverse Entropy Indices for the Prediction of Physicochemical Properties of Benzene Derivatives

Reverse entropies are the molecular descriptors that describe the structures of chemical compounds. They are used in isomer discrimination, structure-property relationship, and structure-activity relations. In this study, the QSPR models were designed using the reverse degree-based entropies to predict the physical properties of benzene derivatives. The relationship analyses between the physicochemical properties and the reverse entropies were done by using the curvilinear regression method. A Maple software based algorithm was designed to make the computation of reverse degree-based entropies easy. Analysis was performed using SPSS software. We analyzed that physical properties such as critical pressure, critical temperature, critical volume, Gibb’s energy, LogP, molar refractivity, and Henry’s law can be estimated by the QSPR model using reverse entropies. All the results were highly positive and significant.

Degree-Based Entropy of Some Classes of Networks

A topological index is a number that is connected to a chemical composition in order to correlate a substance’s chemical makeup with different physical characteristics, chemical reactivity, or biological activity. It is common to model drugs and other chemical substances as different forms, trees, and graphs. Certain physico-chemical features of chemical substances correlate better with degree-based topological invariants. Predictions concerning the dynamics of the continuing pandemic may be made with the use of the graphic theoretical approaches given here. In Networks, the degree entropy of the epidemic and related trees was computed. It highlights the essay’s originality while also implying that this piece has improved upon prior literature-based realizations. In this paper, we study an important degree-based invariant known as the inverse sum indeg invariant for a variety of graphs of biological interest networks, including the corona product of some interesting classes of graphs and the pandemic tree network, curtain tree network, and Cayley tree network. We also examine the inverse sum indeg invariant features for the molecular graphs that represent the molecules in the bicyclic chemical graphs.

On extremal cacti with respect to the first degree-based entropy

On extremal cacti with respect to the first degree-based entropy

Degree-Based Entropy Descriptors of Graphenylene Using Topological Indices

Graph theory plays a significant role in the applications of chemistry, pharmacy, communication, maps, and aeronautical fields. The molecules of chemical compounds are modelled as a graph to study the properties of the compounds. The geometric structure of the compound relates to a few physical properties such as boiling point, enthalpy, π-electron energy, molecular weight. The article aims to determine the practical application of graph theory by solving one of the interdisciplinary problems describing the structures of benzenoid hydrocarbons and graphenylene. The topological index is an invariant of a molecular graph associated with the chemical structure, which shows the correlation of chemical structures using many physical, chemical properties and biological activities. This study aims to introduce some novel degree-based entropy descriptors such as ENTSO, ENTGH, ENTHG, ENTSS, ENTNSO, ENTNReZ1 , ENTNReZ2 and ENTNSS using the respective topological indices. Also, the above-mentioned entropy measures and physico-chemical properties of benzenoid hydrocarbons are fitted using linear regression models and calculated for graphenylene structure.

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.

On Curve Fitting between Heat of Formation and Entropy Measures for Fe Phthalocyanine

The second-most significant category of colorants is phthalocyanines, and copper phthalocyanine is the single colorant with the highest sales volume. Phthalocyanine colorants have historically been used as blue and green pigments for printing inks and automobile paints as well as blue/cyan dyes for textiles and paper. To determine how complex the underlying graph was, we employed Shannon’s information entropy. Certain degree-based entropies derived from topological indices were estimated. Curve fitting between calculated information entropies and Heat of formation was combined with the numerical and graphical representation of computed results. The Fe Phthalocyanine is based on topological indices, which give a comprehensive picture of potentially significant aspects that could be useful in structurally changing (FePc) for particular applications.

Computing the Entropy Measures for the Line Graphs of Some Chemical Networks.

Chemical Graph entropy plays a significant role to measure the complexity of chemical structures. It has explicit chemical uses in chemistry, biology, and information sciences. A molecular structure of a compound consists of many atoms. Especially, the hydrocarbons is a chemical compound that consists of carbon and hydrogen atoms. In this article, we discussed the concept of subdivision of chemical graphs and their corresponding line chemical graphs. More preciously, we discuss the properties of chemical graph entropies and then constructed the chemical structures namely triangular benzenoid, hexagonal parallelogram, and zigzag edge coronoid fused with starphene. Also, we estimated the degree-based entropies with the help of line graphs of the subdivision of above mentioned chemical graphs.

The effect of graph operations on the degree-based entropy

The degree-based entropy Id(G) of a graph G on m>0 edges is obtained from the well-known Shannon entropy −∑i=1np(xi)logp(xi) in information theory by replacing the probabilities p(xi) by the fractions dG(vi)2m, where {v1,v2,…,vn} is the vertex set of G, and dG(vi) is the degree of vi. We continue earlier work on Id(G). Our main results deal with the effect of a number of graph operations on the value of Id(G). We also illustrate the relevance of these results by applying some of these operations to prove a number of extremal results for the degree-based entropy of trees and unicyclic graphs.

On Topological Properties of Degree-Based Entropy of Hex-Derived Network of Type 3

Hex-derived network has an assortment of significant applications in medicine store, equipment, and network organization. Graph entropy depends upon distribution probability of vertex set and on graph itself. There are numerous issues in discrete math, software engineering, statistics, and data innovation where graph entropies are utilized to portray the reasonable constructions. In this paper, we talk about hex-derived network of type 3 denoted as HDN 3 n . We likewise figure degree-based entropies, for example, Randic’, ABC, and GA entropy of HDN 3 n .

On Computation of Degree-Based Entropy of Planar Octahedron Networks

Chemical graph theory is the combination of mathematical graph theory and chemistry. To analyze the biocompatibility of the compounds, topological indices are used in the research of QSAR/QSPR studies. The degree-based entropy is inspired by Shannon’s entropy. The connectivity pattern such as planar octahedron network is used to predict physiochemical activity. In this article, we present some degree-based entropies of planar octahedron network.

Degree-based entropies of graphene, graphyne and graphdiyne using Shannon’s approach

Topological indices are graph-theoretically based parameters that enable the characterization of the underlying connectivity of a molecular structure. Many chemical properties have been linked to degree-based topological indices, which have been extensively studied. The study of entropy indices of graphs as a measure of complexity of the underlying connectivity and as a tool for the characterization of structural properties has also been gaining importance. Current work deals with certain substructures derived from hexagonal honeycomb graphite lattices such as graphene (GN), graphyne (GY) and graphdiyne (GDY). This paper investigates several degree-based topological indices of these structures by using the graph-theory based edge partition method. We have computed several topological indices including graph-based entropies of these structures as determined using Shannon’s entropy model.

On Rational Curve Fitting between Topological Indices and Entropy Measures for Graphite Carbon Nitride

Due to its metal-free and visible-light responsive nature, as well as attractive electrical band structure and excellent physicochemical stability, graphitic carbon nitride has become a new multidisciplinary research hot point. In the field of environmental remediation and energy applications, this interesting semiconductor conjugated polymer is regarded as a viable material for capturing clean and unlimited solar energy. We Used information entropy introduced by Shannon to measure the complexity of the underlying graph. Configuration entropy of glass-forming liquids or thermodynamic entropy of enzyme-substrate complexations are examples of thermodynamic entropy used in molecular dynamics investigations on complex chemical systems. In this article, we computed some degree-based entropies calculated from topological indices. The numerical and graphical depiction of computed results was combined with curve fitting between calculated information entropies and topological indices. The underlying framework is built on topological indices, which provide a full picture of potentially important features that could be beneficial in structural modification of (g-) for certain applications.