Degree-based Indices Research Articles

Computing Topological Invariants of Triangular Chandelier Lattice

A numerical parameter mathematically derived from the graph structure is a topological index. The topological index is the first actual choice in QSAR research and these indices are used to build the correlation model between the chemical structures of various chemicals compounds. Here, we investigate some old degree-based topological indices like Randic index, sum connectivity index, <i>ABC</i> index, <i>GA</i> index, 1^st and 2^nd Zagreb indices, modified second Zagreb index, redefined version of 1^st, 2^nd and 3^rd Zagreb indices, hyper and augmented Zagreb indices, forgotten index and symmetric division degree index, and some new degree-based indices like <i>SK</i> index, <i>SK</i>₁ index, <i>SK</i>₂ index, and <i>AG</i>₁ index of triangular chandelier-lattice (TCL). The results are generalized by using edge partition and closed formulas for topological indices of triangular chandelier-lattice are analysed.

Polynomials of Degree-Based Indices for Swapped Networks Modeled by Optical Transpose Interconnection System

The Optical Transpose Interconnection System (OTIS) has applications in parallel processing, distributed processing, routing, and networks. It is used for efficient usage of multiple parallel algorithms or parallel systems, with different global interconnections in a network as it is an optoelectronic (combination of light signals and electronics). In chemical graph theory, topological indices are used to study characteristics of the chemical structures or biological activities. Topological indices are sometimes studied with the assistance to their polynomial. In this article, polynomials of degree-based topological indices for OTIS and swapped networks have been studied. Results can be used to compute any degree-based topological polynomials for OTIS swapped network.

Polynomials of Degree-based Indices for Three-Dimensional Mesh Network

Polynomials of Degree-based Indices for Three-Dimensional Mesh Network

Zagreb Polynomials and redefined Zagreb indices of Dendrimers and Polyomino Chains

AbstractDendrimers have an incredibly strong potential because their structure allows multivalent frameworks, i.e. one dendrimer molecule has many possible destinations to couple to a functioning species. Researchers expected to utilize the hydrophobic conditions of the dendritic media to lead photochemical responses that make the things that are artificially tested. Carboxylic acid and phenol- terminated water-dissolvable dendrimers were joined to set up their utility in tranquilize conveyance and furthermore driving compound reactions in their inner parts. This may empower scientists to associate both concentrating on atoms and medication particles to the equivalent dendrimer, which could diminish negative manifestations of prescriptions on sound and health cells. Topological indices are numerical numbers associated with the graphs of dendrimers and are invariant up to graph isomorphism. These numbers compare certain physicochemical properties like boiling point, strain energy, stability, etc. of a synthetic compound. There are three main types of topological indices, i.e degree-based, distance-based and spectrum-based. In this paper, our aim is to compute some degree-based indices and polynomials for some dendrimers and polyomino chains. We computed redefined first, second and third Zagreb indices of PAMAM dendrimers PD1, PD2, and DS1 and linear Polyomino chain Ln , Zigzag Polyomino chain Zn, polyomino chain with n squares and of m segments $B_{n}^{1}$and $B_{n}^{2}$We also computed some Zagreb polynomials of understudy dendrimers and chains.

Computational aspects of line graph of carbon nanocones

Graph theory plays substantial role in mathematics, chemistry, QSAR and physical sciences. The basic layout of the graph theoretic model is a molecular structure in which vertices of the graph correspond to atoms, and edges correspond to chemical bonds. The study of this graph model provides information about the chemical structure. A line graph has many useful applications in physical chemistry. M-polynomial is rich in producing closed forms of many degree-based topological indices which correlates chemical properties of the material under investigation. This polynomial is used in computing closed formulas of many degree-based topological invariants of the molecular structures. The molecular graph of carbon nanocones has a conical structure with a cycle of length k at its core and n layers of hexagons placed at the conical surface around its centre. In this study, we transformed the molecular structure of carbon nanocones into graph theoretic model and produced its line graph. Thereafter, we determined closed formulas for M-polynomials of line graphs of nanocones. We also recovered important topological degree-based indices of the line graph of nanocones. Moreover, we provide different graphs of topological indices and their relations with the parameters of the line graph of nanocones. These graphs depict the actual dependencies of the topological indices on the parameters of the carbon nanocones.

On the M-polynomials and degree-based topological indices of an important class of graphs

M-polynomial of chemical compounds is a recent idea and it produces closed forms of many degree-based topological indices which correlate chemical properties of material under investigation. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules like boiling point, stability, strain energy etc. are correlated with their structures. In this paper, we determine general closed formulae for M-polynomials of the Sierpinski graph. We recover important topological degree-based indices. We also give different graphs of topological indices and their relations with the parameters of structures.

On Some New Neighborhood Degree-Based Indices for Some Oxide and Silicate Networks

Topological indices are numeric quantities that describes the topology of molecular structure in mathematical chemistry. An important area of applied mathematics is the chemical reaction network theory. Real-world problems can be modeled using this theory. Due to its worldwide applications, chemical networks have attracted researchers since their foundation. In this report, some silicate and oxide networks are studied, and exact expressions of some newly-developed neighborhood degree-based topological indices named as the neighborhood Zagreb index ( M N ), the neighborhood version of the forgotten topological index ( F N ), the modified neighborhood version of the forgotten topological index ( F N ∗ ), the neighborhood version of the second Zagreb index ( M 2 ∗ ), and neighborhood version of the hyper Zagreb index ( H M N ) are obtained for the aforementioned networks. In addition, a comparison among all the indices is shown graphically.

On Degree-Based Topological Indices of Symmetric Chemical Structures

A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randić index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.

Inequalities between degree- and distance-based graph invariants

Inequalities provide a way to study topological indices relatively. There are two major classes of topological indices: degree-based and distance-based indices. In this paper we provide a relative study of these classes and derive inequalities between degree-based indices such as Randić connectivity, GA, ABC, and harmonic indices and distance-based indices such as eccentric connectivity, connective eccentric, augmented eccentric connectivity, Wiener, and third ABC indices.

Degree-based topological indices of hexagonal nanotubes

There are several papers that determine one or a few chosen degree-based topological indices for hexagonal nanotubes. We present formulas, which can be used to compute any degree-based topological index for those nanotubes. Then we give exact values of the best-known degree-based indices for hexagonal nanotubes.

M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori

V-Phenylenic nanotubes and nanotori are most comprehensively studied nanostructures due to widespread applications in the production of catalytic, gas-sensing and corrosion-resistant materials. Representing chemical compounds with M-polynomial is a recent idea and it produces nice formulas of degree-based topological indices which correlate chemical properties of the material under investigation. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules like boiling point, stability, strain energy etc. are correlated with their structures. In this paper, we determine general closed formulae for M-polynomials of V-Phylenic nanotubes and nanotori. We recover important topological degree-based indices. We also give different graphs of topological indices and their relations with the parameters of structures.

Calculating of degree-based topological indices of nanostructures

A larger amount of studies reveal that there is strong inherent connection between the chemical characteristics of nanostructures and their molecular structures. Degree-based topological indices introduced on these chemical molecular structures can help material scientists better understand its chemical and biological features, thus they can make up for the lack of chemical experiments. In this paper, by means of edge dividing trick, we present several degree-based indices of special widely employed nanostructures: nanotubes, polyphenylene dendrimers, H-Naphtalenic nanotubes NPHX[m, n], nanotubes and PAMAM dendrimers.

M-Polynomials and Topological Indices of Titania Nanotubes

Titania is one of the most comprehensively studied nanostructures due to their widespread applications in the production of catalytic, gas sensing, and corrosion-resistant materials. M-polynomial of nanotubes has been vastly investigated, as it produces many degree-based topological indices, which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules, such as boiling point, stability, strain energy, etc., are correlated with their structure. In this report, we provide M-polynomials of single-walled titania (SW TiO2) nanotubes and recover important topological degree-based indices to theoretically judge these nanotubes. We also plot surfaces associated to single-walled titania (SW TiO2) nanotubes.

On molecular topological properties of benzenoid structures

The degree-based topological indices correlate certain physicochemical properties such as boiling point, strain energy, and stability, etc., of certain chemical compounds. Among the major classes of topological indices are the distance-based topological indices, degree-based topological indices, and counting-related polynomials and corresponding indices of graphs. Among all of the degree-based indices, namely the first general Zagreb index, general Rndić connectivity index, general sum-connectivity index, atom–bond connectivity index (ABC), and geometric–arithmetic index (GA), are most important due to their chemical significance. In this paper, we compute the first general Zagreb index, general Randić connectivity index, general sum-connectivity index, ABC, GA, ABC4, and GA5 indices of hexagonal parallelogram P(m,n) nanotubes, triangular benzenoid Gn, and zigzag-edge coronoid fused with starphene ZCS(k,l,m) nanotubes by using the line graphs of the subdivision of these chemical graphs.

Degree-Based Indices of Polyhex Nanotubes and Dendrimer Nanostar

Degree-Based Indices of Polyhex Nanotubes and Dendrimer Nanostar

Degree-based indices computation for special chemical molecular structures using edge dividing method

Abstract In computational chemistry, the molecular structures are modelled as graphs which are called the molecular graphs. In these graphs, each vertex represents an atom and each edge denotes covalent bound between atoms. It is shown that the topological indices defined on the molecular graphs can reflect the chemical characteristics of chemical compounds and drugs. In this paper, we report several degree based indices of some widely used chemical molecular structures by means of edge dividing technology.