Chemical Graph Theory Research Articles

Hex-Derived Molecular Descriptors via Generalized Valency-Based Entropies

Entropy is a thermodynamic function in chemistry that, based on the number of possible configurations for a given system or process, measures the randomness and disorder of molecules in that system or process. Many problems in arithmetic, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. A topological descriptor also connects certain physical aspects of the underlying chemical substances, in contrast to a topological index, which in chemical graph theory is a numerical representation of a chemical network. When building models for any chemical network, the graph is crucial. Simonraj et al. produced a brand-new category of graphs known as the third kind of hex-derived networks. In our work, we discuss the third class of hex-derived networks, which includes hex-derived networks ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {HDN}_{3}$ </tex-math></inline-formula> ), triangular hex-derived networks ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {THDN}_{3}$ </tex-math></inline-formula> ), rectangular hex-derived networks ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {RHDN}_{3}$ </tex-math></inline-formula> ), and chain hex-derived networks ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {CHDN}_{3}$ </tex-math></inline-formula> ). We compute exact results for newly defined entropies by utilizing their topological indices based on end vertex degrees.

Fuzzy topological analysis of pizza graph

&lt;abstract&gt;&lt;p&gt;Fuzzy topological indices are getting attention these days due to their vast applications in daily life. In crisp case, topological indices are beneficial in chemical graph theory but as far as fuzzy graph theory is concerned, fuzzy topological indices are useful in identifying human trafficking, and multi-criteria decision-making environments. In this paper, we have computed the fuzzy topological indices such as the first and second fuzzy Zagreb indices, Randic index, and Harmonic index for the $ Pz_{n} $ pizza graph. We have found generalized results for the above-mentioned structure.&lt;/p&gt;&lt;/abstract&gt;

Chemical Application of Topological Indices in Infertility Treatment Drugs and QSPR Analysis.

The main challenges faced by medical researchers while producing novel drugs are time commitment, amplified costs, creating a safety profile for the medications, reduced solubility, and a lack of experimental data. Chemical graph theory makes an important theoretical contribution to drug development and design by investigating the structural properties of molecules. To improve drug research and assess the effectiveness of treatments, topological indices aim to provide a mathematical representation of molecular structures. In this study, the author examined a number of recently used drugs, including tamoxifen, mesterolone, anastrozole, and letrozole which are used to treat infertility. We compute the topological descriptors with the limiting behaviors associated with these pharmaceutical drugs and offer degree-based topological parameters for them. We conducted a QSPR investigation on the prospective degree-based topological descriptors using quadratic, cubic, exponential, and logarithmic regression models.

On sombor index of m-shadow graph of some graphs

This new topological invariant is applied in the areas of chemical graph theory. In this paper we have obtained the Sombor index of m−shadow graphs of path graph Dm(Pn), cycle graph Dm(Cn), ladder graph Dm(Ln) and tadpole graph Dm(Tn,p). We have also concluded that, the Sombor index of m-shadow graph of any regular or finite connected graph G is SO(G)m3

Expressions for Mostar and weighted Mostar invariants in a chemical structure

Abstract The bond-additive topological invariants are largely employed to recognize the characteristics of chemical graphs. They provide quantitative measures of peripheral shapes of molecules and attract considerable attention, both in the context of complex networks and in more classical applications of chemical graph theory. In this article, we compute exact analytical expressions of Mostar and weighted Mostar invariants for a chemical structure.

SCHULTZ INDICES AND THEIR POLYNOMIALS OF MYCIELSKIAN GRAPHS

Topological indices are studied extensively due to its vibrant applica- bility in the field of chemical graph theory. These connectivity indices(topological indices) is a numerical value resulting in an unequivocal process based on the struc- ture of graph. Numerous topological indices are classified based on their distance and degree. The Schultz and modified Schultz indices considered in this paper have been expansively studied by various authors on different types of graphs. In this paper, we established the results on Schultz, modified Schultz indices and their polynomials for mycielskian graphs.

Some Novel Results Involving Prototypical Computation of Zagreb Polynomials and Indices for SiO4 Embedded in a Chain of Silicates.

A topological index as a graph parameter was obtained mathematically from the graph's topological structure. These indices are useful for measuring the various chemical characteristics of chemical compounds in the chemical graph theory. The number of atoms that surround an atom in the molecular structure of a chemical compound determines its valency. A significant number of valency-based molecular invariants have been proposed, which connect various physicochemical aspects of chemical compounds, such as vapour pressure, stability, elastic energy, and numerous others. Molecules are linked with numerical values in a molecular network, and topological indices are a term for these values. In theoretical chemistry, topological indices are frequently used to simulate the physicochemical characteristics of chemical molecules. Zagreb indices are commonly employed by mathematicians to determine the strain energy, melting point, boiling temperature, distortion, and stability of a chemical compound. The purpose of this study is to look at valency-based molecular invariants for SiO4 embedded in a silicate chain under various conditions. To obtain the outcomes, the approach of atom-bond partitioning according to atom valences was applied by using the application of spectral graph theory, and we obtained different tables of atom-bond partitions of SiO4. We obtained exact values of valency-based molecular invariants, notably the first Zagreb, the second Zagreb, the hyper-Zagreb, the modified Zagreb, the enhanced Zagreb, and the redefined Zagreb (first, second, and third). We also provide a graphical depiction of the results that explains the reliance of topological indices on the specified polynomial structure parameters.

Topological characterization and entropy measures of tetragonal zeolite merlinoites

Stimulated by QSAR and QSPR studies, bond additive topological indices have been investigated with physicochemical and structural properties of mineral networks. Through the use of molecular descriptors, the information entropy measures of such 3D complex networks are calculated. These structural descriptors find applications in many fields, such as chemical graph theory, drug delivery, nanomaterial characterizations and so on. This manuscript focuses on determining the generalized formulae to obtain degree and degree-sum based molecular descriptors of tetragonal zeolite merlinoites (MER). We have also presented a technique to compute the entropy measures of MER structures using Shannon’s entropy approach and a variation on that approach which provides greater discriminating power among the topological descriptors. In addition, the bondwise entropies reveal that the LTA zeolites exhibit greater bondwise entropies compared to the MER zeolites.

On neighborhood inverse sum indeg index of molecular graphs with chemical significance

Chemical graph theory is an interdisciplinary field that analyses the molecular structure of a chemical compound as a graph and investigates related mathematical queries by employing graph theoretical and computational techniques. The topological index is an important tool in this area that associates a numerical value with a graph structure. It can be interpreted as a real-valued function that represents the physico-chemical information of a chemical compound. One of the most recently reported neighbourhood degree sum-based indices is the neighbourhood inverse sum indeg index (NI). In this work, we first investigate the application potential of the NI index by exploring its predictive potential and isomer discrimination ability. Following that, some fascinating mathematical features of NI are revealed. Extremal values of NI are estimated for the class of all trees and unicyclic graphs. Furthermore, some crucial upper bounds on NI are set up in terms of well-known graph parameters, including graph order,independence number, and vertex connectivity. Associations between NI and existing indices are also demonstrated.

QSPR Analysis of Polycyclic Aromatic Hydrocarbons

Topological indices serve as a crucial component in chemical graph theory linked with some molecular structure. The First and Second Zagreb Indices are one among the earliest and extensively explored molecular descriptors. The study on equitable zagreb indices have been initiated earlier by Akram Alqesmah, Anwar Alwardi and R. Rangarajan based on the equitable degree of the vertices. In this paper, we introduce the first and second equitable and non-equitable zagreb polynomials and compute the exact values of the respective equitable and non-equitable zagreb indices for polycyclic aromatic hydrocarbons. We have also utilised certain formulations for the determination of the corresponding relative equitable and non-equitable zagreb indices of the chemical graph. Further, QSPR analysis is carried out for the topological indices with regard to the physico-chemical properties of the polycyclic hydrocarbon molecules.

Wiener Index of Some Brooms

In the field of chemical graph theory, a Wiener (topological) index is a type of a molecular descriptor that is calculated based on the molecular graph of alkanes. It gives the sum of geodesic distances (or shortest paths) between all pairs of vertices of the graph. We found and prove the Wiener indices of some Brooms, which are Caterpillars, giving several unknown sequences that are now added to the collection of the largest Online Encyclopedia of Integer Sequences.

Evaluation of some degree based topological indices of boron kagome lattice

The technique of securing information or data in the form of images, codes, merging words etc are closely related to the disciplines of cryptanalysis and cryptology. Analogous to this numerical encoding of chemical structure, connected to topological indices is also growing significantly in the field of chemical graph theory. One of the salient features of topological indices is to predict the characteristics prescribed by the molecule's chemical structure. In this paper, we calculate the topological indices of the two-dimensional Boron Kagome Lattice by M- polynomial. Further, the graphical representation of the 𝑀-polynomial and the topological indices are obtained.

The M-Polynomial and Nirmala index of Certain Composite Graphs

The M-Polynomial and Nirmala index are considered as two of the most recent found and important subjects in chemical graph theory. In this paper we drive and prove the computing formula of Nirmala index from the M-Polynomial, then compute the M-Polynomial for some certain composite graphs, and the Nirmala index via the computed M-Polynomial. The composite graphs are new defined graphs Kn(Pt)Km , Cn(e)Kn , and others obtained from simple graphs by certain graph operations such as join, corona, and cluster of any graph with some special graphs such as complete, path, …etc

Targeting highly resisted anticancer drugs through topological descriptors using VIKOR multi-criteria decision analysis.

The online version contains supplementary material available at 10.1140/epjp/s13360-022-03469-x.

On ve-Degree Irregularity Index of Graphs and Its Applications as Molecular Descriptor

Most of the molecular graphs in the area of mathematical chemistry are irregular. Therefore, irregularity measure is a crucial parameter in chemical graph theory. One such measure that has recently been proposed is the ve-degree irregularity index (irrve). Quantitative structure property relationship (QSPR) analysis explores the capability of an index to model numerous properties of molecules. We investigate the usefulness of the irrve index in predicting different physico-chemical properties by carrying out QSPR analysis. It is established that the irrve index is efficient to explain the acentric factor and boiling point of molecules with powerful accuracy. An upper bound of irrve for the class of all trees is computed with identifying extremal graphs. We noticed that the result is not correct. In this report, we provide a counter example to justify our argument and determine the correct outcome.

Study of Fractional Differential Equations Emerging in the Theory of Chemical Graphs: A Robust Approach

The study of the interconnections between chemical systems is known as chemical graph theory. Through the use of star graphs, a limited group of researchers has examined the space of possible solutions for boundary-value problems. They recognized that for their strategy to function, they needed a core node related to other nodes but not to itself; as a result, they opted to use star graphs. In this sense, the graphs of neopentane will be helpful in extending the scope of our technique. It has the CAS number 463-82-1 and the chemical formula C5H12, and it is a component of a petrochemical precursor. In order to determine whether or not the suggested boundary-value problems on these graphs have any known solutions, we use the theorems developed by Schaefer and Krasnoselskii on fixed points. In addition, we illustrate our preliminary results with the help of an example that we present.

Connecting SiO4 in Silicate and Silicate Chain Networks to Compute Kulli Temperature Indices.

A topological index is a numerical parameter that is derived mathematically from a graph structure. In chemical graph theory, these indices are used to quantify the chemical properties of chemical compounds. We compute the first and second temperature, hyper temperature indices, the sum connectivity temperature index, the product connectivity temperature index, the reciprocal product connectivity temperature index and the F temperature index of a molecular graph silicate network and silicate chain network. Furthermore, a QSPR study of the key topological indices is provided, and it is demonstrated that these topological indices are substantially linked with the physicochemical features of COVID-19 medicines. This theoretical method to find the temperature indices may help chemists and others in the pharmaceutical industry forecast the properties of silicate networks and silicate chain networks before trying.

A Paradigmatic Approach to Find the Valency-Based K-Banhatti and Redefined Zagreb Entropy for Niobium Oxide and a Metal-Organic Framework.

Entropy is a thermodynamic function in chemistry that reflects the randomness and disorder of molecules in a particular system or process based on the number of alternative configurations accessible to them. Distance-based entropy is used to solve a variety of difficulties in biology, chemical graph theory, organic and inorganic chemistry, and other fields. In this article, the characterization of the crystal structure of niobium oxide and a metal–organic framework is investigated. We also use the information function to compute entropies by building these structures with degree-based indices including the K-Banhatti indices, the first redefined Zagreb index, the second redefined Zagreb index, the third redefined Zagreb index, and the atom-bond sum connectivity index.

Computing the partition dimension of certain families of Toeplitz graph.

Let G = (V(G), E(G)) be a graph with no loops, numerous edges, and only one component, which is made up of the vertex set V(G) and the edge set E(G). The distance d(u, v) between two vertices u, v that belong to the vertex set of H is the shortest path between them. A k-ordered partition of vertices is defined as β = {β1, β2, …, βk}. If all distances d(v, βk) are finite for all vertices v ∈ V, then the k-tuple (d(v, β1), d(v, β2), …, d(v, βk)) represents vertex v in terms of β, and is represented by r(v|β). If every vertex has a different presentation, the k-partition β is a resolving partition. The partition dimension of G, indicated by pd(G), is the minimal k for which there is a resolving k-partition of V(G). The partition dimension of Toeplitz graphs formed by two and three generators is constant, as shown in the following paper. The resolving set allows obtaining a unique representation for computer structures. In particular, they are used in pharmaceutical research for discovering patterns common to a variety of drugs. The above definitions are based on the hypothesis of chemical graph theory and it is a customary depiction of chemical compounds in form of graph structures, where the node and edge represent the atom and bond types, respectively.

Sombor Leap Indices of Some Chemical Drugs

In Chemical Graph Theory, several degree-based topological indices were introduced and studied since 1972. In this paper, we introduce the Sombor leap index and modified Sombor leap index and compute these indices for some important nanostructures which appeared in nanoscience.