Distance-based Topological Indices Research Articles

Some new version of resistance distance-based topological indices of complete bipartite networks

Some new version of resistance distance-based topological indices of complete bipartite networks

Some inequalities between degree- and distance-based topological indices

hefirst Zagreb indexM1and the second Zagreb indexM2belongto the class of degree-based topological indices which are defined fora simple connected graphGwith vertex setV={υ1,υ2,···,υn}asM1(G)=Pn ̇ı=1d2 ̇ıandM2(G)=Pυ ̇ı∼υ ̇jd ̇ıd ̇j,whered ̇ıis the degreeof vertexυiandυ ̇ı∼υ ̇jrepresents the adjacency of verticesυ ̇ıandυ ̇jinG. The eccentric connectivity index (ECI) is a distance basedtopological index, denoted byξc,isdefined asξc(G)=Pni=1ε ̇ıd ̇ı,whereε ̇ıis the eccentricity ofυ ̇ıinG. The aim of this paper is toderive the inequalities between ECI and the Zagreb indices. Moreover,we establish the inequalities between some variants of ECI and theZagreb indices

Study for Some Eccentricity-based Topological Indices of Second Type of Dominating David-derived Network.

Dominating David-derived networks are widely studied due to their fractal nature, with applications in topology, chemistry, and computer sciences. The use of molecular structure descriptors is a standard procedure that is used to correlate the biological activity of molecules with their chemical structures, which can be useful in the field of pharmacology. This article's goal is to develop analytically closed computing formulas for eccentricitybased descriptors of the second type of dominating David-derived network. Thermodynamic characteristics, physicochemical properties, and chemical and biological activities of chemical graphs are just a few of the many properties that may be determined using these computation formulas. Vertex sets were initially divided according to their degrees, eccentricities, and cardinalities of occurrence. The eccentricity-based indices are then computed using some combinatorics and these partitions. Total eccentricity, average eccentricity, and the Zagreb index are distance-based topological indices utilized in this study for the second type of dominating David-derived network, denoted as D2(m). These calculations will assist the readers in estimating the fractal and difficult-tohandle thermodynamic and physicochemical aspects of chemical structure. Apart from configuration and impact resistance, the D2(m) design has been used for fundamental reasons in a variety of technical and scientific advancements.

QSPR analysis of distance-based structural indices for drug compounds in tuberculosis treatment

Tuberculosis (TB) is one of the most contagious diseases that has a greater mortality rate than HIV/AIDS and the cases of TB are feared to rise as a repercussion of the COVID-19 pandemic. The pharmaceutical industry is constantly looking for ways to improve drug design processes in order to combat the growth of infections and cure newly identified syndromes or genetically based dysfunctions with the help of QSPR models. QSPR models are mathematical tools that establish relationships between a molecular structure and its physicochemical attributes using structural properties. Topological indices are such properties that are generated from the molecular graph without any empirically derived measurements. This work focuses on developing a QSPR model using distance-based topological indices for anti-tuberculosis medications and their diverse physicochemical features.

Bounds of Fibonacci-sum graph for some distancebased topological indices and an application on BFS algorithm

The aim of this study is to obtain the lower and upper bounds for the distance-based Wiener index, Hyper-Wiener index and Harary index of the Fibonacci-sum graph. Firstly, the shortest distance of the vertices in the Fibonacci-sum graph is characterized. Afterwards, the numbers of decision vertices and leaves are obtained by applying the BFS algorithm to the Fibonacci-sum graph.

Calculation of Topological Indices Based on the Distance of Polyacenes Without Edge Counting

Acenes or polyacenes are a group of organic compounds and polycyclic aromatic hydrocarbons consisting of benzene rings that are linearly fused. They are also the building blocks of nanotubes and graphene and follow the general molecular formula Due to the applications of polyacenes in optoelectronics, they are interesting for chemical and electrical engineering researchers. In this article, the general formulas for distance-based topological indices of Szeged, Mostar, and Padmakar-Ivan are determined by SMP-polynomials, which do not require edge counting and this formula work only by having the number of benzene rings in the composition of polyacenes.

On distance-based topological indices and co-indices of fractal-type molecular graphs and their respective graph entropies.

In graph theory, a topological index is a numerical value that is in good correlation with certain physical properties of a molecule. It serves as an indicator of how a chemical structure behaves. The Shannon's entropy describes a comparable loss of data in information transmission networks. It has found use in the field of information theory. Inspired by the concept of Shannon's entropy, we have calculated some topological descriptors for fractal and Cayley-type dendrimer trees. We also find the entropy that is predicted by these indices.

On the Distance Spectrum and Distance-Based Topological Indices of Central Vertex-Edge Join of Three Graphs

In this paper, we introduce a new graph operation based on a central graph called central vertex-edge join (denoted by $G_{n_1}^C \triangleright (G_{n_2}^V\cup G_{n_3}^E)$) and then determine the distance spectrum of $G_{n_1}^C \triangleright (G_{n_2}^V\cup G_{n_3}^E)$ in terms of the adjacency spectra of regular graphs $G_1$, $G_2$ and $G_3$ when $G_1$ is triangle-free. As a consequence of this result, we construct new families of non-D-cospectral D-equienergetic graphs. Moreover, we determine bounds for the distance spectral radius and distance energy of the central vertex-edge join of three regular graphs. In addition, we provide its results related to graph invariants like eccentric-connectivity index, connective eccentricity index, total-eccentricity index, average eccentricity index, Zagreb eccentricity indices, eccentric geometric-arithmetic index, eccentric atom-bond connectivity index, Wiener index. Using these results, we calculate the topological indices of the organic compounds Methylcyclobutane $(C_5H_{10})$ and Spirohexane $(C_6H_{10})$.

Algebraic approach to various chemical structures with new Banhatti coindices

Topological coindices are the numeric values, obtained by the complement graph of a molecular structure, which is used in Quantitative Structure Property/Activity Relationship (QSPR/QSAR) studies to evaluate the physicochemical and biological properties of compounds. In this article, we introduce new distance-based topological indices calculated with the C o M -polynomial approach. We present an application about the compatibility of these indices with some drugs that are candidates for use in the treatment of COVID-19 with QSPR analysis.

Graph Energy Variants and Topological Indices in Platinum Anticancer Drug Design: Mathematical Insights and Computational Analysis with DFT and QTAIM

In this paper, we present a new approach that explores the application of graph energy variants in chemistry, specifically in the development of platinum anticancer drugs. While previous energy variants have been proposed without considering their direct relevance to chemistry, our study focuses on two key aspects. First, we investigate the correlation between seven degree-based and four distance-based topological indices and their corresponding energies in platinum anticancer drugs. Furthermore, we mathematically analyze the properties of these energies, establishing upper and lower bounds that can be generalized to other structures. Second, we examine the possibility of utilizing the energies of these topological indices as structural descriptors. Our research showcases promising results, suggesting potential improvements in the future manufacturing of anticancer drugs. In addition, we employ density functional theory D F T calculations to optimize the molecular structures of platinum anticancer drugs and identify local reactive sites using Fukui functions. Quantum theory of atoms in molecules Q T A I M was carried out at the bond critical point B C P , to reveal the nature of the intermolecular interactions in the investigated ten Pt anticancer drugs, especially, the nature of bonds between Pt atoms and their bond atoms. Overall, this study presents an innovative approach that bridges graph energies, topological indices, and DFT with the properties (physical and chemical) of platinum anticancer drugs, offering insights into their molecular properties and potential for enhanced drug design.

Graph theoretic approach for calculation of new Banhatti indices VIA recent algebraic polynomials with a chemical application

In this article, we design new distance-based topological indices which are computed by a recent polynomial approach. Also, we present a chemical application on the suitability of these indices with some drugs used for the treatment of COVID-19 via QSPR analysis. Curvilinear regression models are obtained and analysed for the physico-chemical properties of the COVID-19 drugs. Our models and findings could aid in the development of new drugs for the treatment of COVID-19.

Computing the expected subtree number of random hexagonal and phenylene chains based on probability matrices

With structural analysis and probability matrix, this paper studies the subtree number index (number of non-labeled subtrees) of random hexagonal and phenylene chains, and presents exact recursive formulas for the expected values of subtree number index of the random hexagonal and phenylene chains in terms of probability matrices, as applications, we obtain the subtree number of hexagonal linear chain, hexagonal helicence chain, phenylene linear chain and phenylene helicence chain. Moreover, the proposed matrix method also builds a bridge to explore the deep correlation between structural-based and distance-based topological indices, and provides important theoretical support for prediction new properties of chemical compounds.

Application of the Caffeine in Antiviral Medications through Polynomials and Topological Descriptors

The two main sources of caffeine in the adult diet in North America are coffee (60 to 75%) and tea (15 to 30%), although caffeinated soft drinks and chocolate are primary sources of caffeine in kids’ diets. An algorithm can generate topological indices, which are mathematical representations of molecules that can be applied to their structure. The degree-based topological indices for the aforementioned antiviral medications have been examined in the current work using a polynomial technique. Caffeine is a significant component in various medications, with different prescription (30 to 100 milligrams per tablet), over-the-counter (15 to 200 milligrams per tablet or pill), and capsule dosages. Topological indices are employed to describe the biological and physico-chemical properties of diverse chemical compounds. The adult acute fatal dosage of caffeine has been calculated to be 10 grams per person. While 6.5 grams of caffeine have been reported to be fatal, there are cases of patients who purportedly consumed 24 grams of caffeine and survived. We have computed various polynomials including Hosoya and Harary, distance-based topological indices, and other important degree-based topological indices.

Distance-Based Topological Descriptors of Capra Operation on Some Graphs

The Capra operation is a graph theoretical operation that transforms the given graph into a structurally different and larger graph. It is commonly used in statistical analysis, data processing, and scientific research to compare and analyze data. The Capra operation involves subtracting the reference value from each numerical value, taking the absolute value of the resultand raising it to a specified power. This operation is used to create a new set of values that are more sensitive to differences between numerical values and can help to identify outliers and other anomalous data points. The Capra operation has numerous applications in fields such as finance, engineering, and biology, where it is used to analyze data and make predictions about future trends. Its ability to transform data and highlight differences between values makes it a valuable tool for researchers and analysts seeking to gain deeper insights into the patterns and structures within their data. In this paper, we studied the distance-based topological indices of some graphs under the Capra operation.

Topological Properties and Entropy Calculations of Aluminophosphates

Topological indices are invariant numerical quantities of a graph that give facts about the structure of graphs and are found to be very helpful in predicting the physical properties of aluminophosphates. The characteristics of aluminophosphates are similar to the characteristics of zeolites. Two examples of current applications are natural gas dehydration and humidity sensors. Researchers in chemistry and materials science are synthesizing new frameworks. There are many layers and holes in these substances. The technique used to predict natural behaviors among the physicochemical characteristics of chemical molecules in their basic network is known as topological indices. This study explains the vertex version of distance-based topological indices, the entropy of topological indices and their numerical analysis.

Hosoya polynomials and corresponding indices of aramids

Aramids are man-made high performance fibers admitting useful industrial applications. Aramids can be classified into para-aramids and meta-aramids. Kevlar is a para-aramid and Nomex is a meta-aramid. This work is devoted to compute the empirical formula for the Hosoya polynomial of these aramids. The closed form of a number of distance-related topological indices (TIs) is the famous distance-based Hosoya polynomial. These are Weiner, hyper-Weiner and Tratch–Stankevitch–Zafirov indices. Results exhibit that para-aramid and meta-aramid possess different Hosoya polynomials and corresponding distance-based TIs. Further, distance-related TIs derived from Hosoya polynomial for the para-aramid admit larger values as compared to those of the meta-aramid.

On Molecular Structural Characterization of Cyclen Cored Dendrimers

Macromolecules are gaining much attention in various fields today. Dendrimers are artificially synthesized macromolecules by convergent or divergent approach. They are compact regular structures with spherical dimension and has a vast number of application in disparate fields such as drug delivery, material science, and biology, magnetic resonance imaging, an organic light-emitting device, etc. Determining the pharmacological, chemical, and biological characteristics of a substance necessitates a significant amount of effort. From the chemical graph of the dendrimer structure, we can infer those characteristics with the help of numerical descriptors known as the topological index. The Wiener and Szeged indices are two important distance-based topological indices applicable in nanoscience. The degree-based topological indices also have great importance and huge applications in structural chemistry. These indices together with graph entropy are found to be more effective and have found application in different sciences. In this work, the Wiener index, Szeged indices, Mostar indices, and Padmakar Ivan index for cyclen cored dendrimers are evaluated by converting the original graph into quotient graphs using Θ * - classes. This technique is applied since the regular cut method is a lengthy process while moving on to higher generations and also due to the presence of odd cycles in the structure. The degree-based indices and the degree-based graph entropies for the cyclen cored dendrimers are further studied. The comparison graphs with respect to the topological indices as well as graph entropies are also presented.

Topological Indices, Graph Spectra, Entropies, Laplacians, and Matching Polynomials of n-Dimensional Hypercubes

We obtain a large number of degree and distance-based topological indices, graph and Laplacian spectra and the corresponding polynomials, entropies and matching polynomials of n-dimensional hypercubes through the use of Hadamard symmetry and recursive dynamic computational techniques. Moreover, computations are used to provide independent numerical values for the topological indices of the 11- and 12-cubes. We invoke symmetry-based recursive Hadamard transforms to obtain the graph and Laplacian spectra of nD-hypercubes and the computed numerical results are constructed for up to 23-dimensional hypercubes. The symmetries of these hypercubes constitute the hyperoctahedral wreath product groups which also pave the way for the symmetry-based elegant computations. These results are used to independently validate the exact analytical expressions that we have obtained for the topological indices as well as graph, Laplacian spectra and their polynomials. We invoke a robust dynamic programming technique to handle the computationally intensive generation of matching polynomials of hypercubes and compute all matching polynomials up to the 6-cube. The distance degree sequence vectors have been obtained numerically for up to 108-dimensional cubes and their frequencies are found to be in binomial distributions akin to the spectra of n-cubes.

Kirchhoff index of a class of polygon networks

The Kirchhoff index is a novel distance-based topological index corresponding to networks, which is the sum of resistance distances between all pairs of nodes. It plays an important role in describing the flow of a network. In this paper, we propose a polygon network model and derive the eigenvalue evolving rule between two generations of the network, and thus obtain the exact Kirchhoff index using the spectral graph theory.

Statistical Investigation for Some Classes of Alkanes Through Graph Indices

Topological indices are numerical descriptors that may be produced from a molecular graph to thoroughly analyze the medications. They are frequently employed in the analysis and forecasting of the physicochemical features of several pharmaceuticals. Numerous forms of polynomials and topological indices are computed, which serves as representations of chemical structure, and are crucial to chemical graph theory. The findings already obtained may be improved, and there may be a greater link to the various physical features of chemical substances, as a consequence of modifications and generalizations of the conventional topological indices. We suggest seven brand-new distance-based topological indices in this communication. We further investigate these suggested topological indices for several frequently occurring chemical structures from chemical graph theory.