Topological Indices and New Graph Structures (original) (raw)
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Journal of Chemistry, 2021
In this research paper, we will compute the topological indices (degree based) such as the ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, first and second hyper-Gourava indices, general Randic´ index R γ G , for γ = ± 1 , ± 1 / 2 , harmonic index, general version of the harmonic index, atom-bond connectivity (ABC) index, SK, SK1, and SK2 indices, sum-connectivity index, general sum-connectivity index, and first general Zagreb and forgotten topological indices for various types of chemical networks such as the subdivided polythiophene network, subdivided hexagonal network, subdivided backbone DNA network, and subdivided honeycomb network. The discussion on the aforementioned networks will give us very remarkable results by using the aforementioned topological indices.
On Valency-Based Molecular Topological Descriptors of Subdivision Vertex-Edge Join of Three Graphs
Symmetry
In the studies of quantitative structure–activity relationships (QSARs) and quantitative structure–property relationships (QSPRs), graph invariants are used to estimate the biological activities and properties of chemical compounds. In these studies, degree-based topological indices have a significant place among the other descriptors because of the ease of generation and the speed with which these computations can be accomplished. In this paper, we give the results related to the first, second, and third Zagreb indices, forgotten index, hyper Zagreb index, reduced first and second Zagreb indices, multiplicative Zagreb indices, redefined version of Zagreb indices, first reformulated Zagreb index, harmonic index, atom-bond connectivity index, geometric-arithmetic index, and reduced reciprocal Randić index of a new graph operation named as “subdivision vertex-edge join” of three graphs.
On Degree-Based Topological Indices of Symmetric Chemical Structures
Symmetry
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 Randi c ´ , 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 Randi c ´ 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.
Role of Multiplicative Degree Based Topological Invariants in Chemical Graphs
A chemical graph is a mathematical representation of a chemical compound in which atoms and bonds are represented by nodes and lines respectively. Chemists have developed a number of useful tools from graph theory, such as topological index (TI) is structural descriptor or connectivity index used to express molecular size, branching, heat of formation, boiling points, strain energy, toughness and acyclicity. The Topological index is beneficial to establish an association between arrangement and chemical properties of chemical compounds without performing any testing. It is characterized into various categories like degree, distance, spectrum and eccentricity based. This paper consists of computation of multiplicative degree based topological indices namely multiplicative Zagreb indices, multiplicative atom bond connectivity index and generalized multiplicative geometric arithmetic index for SiC_3-I[j, k] and SiC_3-II[j, k].
TOPOLOGICAL INDICES OF MOLECULAR GRAPHS UNDER SPECIFIC CHEMICAL REACTIONS
Molecular graph serves as a convenient model for any real or abstract chemical compound. A topological index is the graph invariant number calculated from the graph representing the molecule. The advantage of topological indices is that it may be used directly as simple numerical descriptors in QSPR/QSAR models. Most of the topological descriptors are based either on atom-atom connectivity or on topological distances. A chemical reaction can be represented as the transformation of the chemical (Molecular) graph representing the reaction's substrate into another chemical graph representing the product. The type of chemical reaction where two substrates combine to form a single product (combination reaction) motivated us to study the effect of topological indices when a bridge is introduced between the respective vertices (of degree i, i=1, 2, 3) of two copies of the same graph. The graph obtained in this manner may or may not exist in reality, but it is the interest of the chemist to check the stability of the so obtained structure of the product. In this paper we present an algorithm to calculate the distance matrix of the resultant graph obtained after each iteration and thereby tabulate various topological indices. We also give the explicit formula for calculating Wiener index of the graph representing the resulting product.
Topological Indices of Certain Transformed Chemical Structures
Journal of Chemistry, 2020
Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.
Four New Topological Indices Based on the Molecular Path Code
Journal of Chemical Information and Modeling, 2007
The sequence of all paths p i of lengths i) 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Σ i p i 2 , and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q) Σ i p i 2 /(µ+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Σ i p i 1/2 , and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S) Σ i p i 1/2 /(µ+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D) Σ i {p i 1/2 /[i(µ+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A) Σ i {p i /[i(µ + 1)]}; and (v) the last TI with two square roots: Path-count index: P) Σ i {p i 1/2 / [i 1/2 (µ + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property. † Dedicated to Professor Nenad Trinajstić on the occasion of his 70th birthday.
Topological Indices of Molecular Graph and Drug Design
International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2022
The application of topology in molecular graph and drug design is covered in this article. On the basis of the most recent developments in this area, an overview of the use of topological indices (TIs) in the process of drug design and development is provided. The introduction of concepts used in drug design and discovery, graph theory, and topological indices is the primary goal of the first section of this book. Researchers can learn more about the physical characteristics, chemical reactivity, and biological activity of these chemical molecular structures by using topological indices. In order to compensate for the lack of chemical experiments and offer a theoretical foundation for the production of medications and chemical materials, topological indices on the chemical structure of chemical materials and drugs are studied. In this article, we concentrate on the family of smart polymers that are frequently utilised in the production of drugs.
Note on forgotten topological index of chemical structure in drugs
Applied Mathematics and Nonlinear Sciences, 2016
The forgotten topological index of a graph G is defined as the sum of the cube of the degrees of its vertices. In the recent paper [6], [W. Gao et al. (2016), Forgotten topological index of chemical structure in drugs, Saudi Pharmaceutical Journal, 24, 258-264], the forgotten topological index of some chemical structures has been obtained. In this note, we correct their result regarding triangular benzenoid. Also, we have given the expression for the forgotten topological index of graphene structure which is more compact than the one was obtained in the paper above.
Topological Indices of Some New Graph Operations and Their Possible Applications
2021
A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It’s found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index ”F-index”. Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.