Degree Based Topological Indices of Isomers of Organic Compounds
IJSRP Journal
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
Let G(V,E) be a connected graph. The sets of vertices and edges of G are denoted by V=V (G) and E=E (G) respectively. In such a molecular graph, vertices represent atoms and edges represent bonds. The number of edges incident on a vi is called the degree d(vi) of vertex vi . The sum of degrees of all vertices in G is twice the number of edges in G [1]. In molecular graph we have many topological indices. In this research, we computing Randic index, Molecular topological index ,Augmented Zagreb index ,Geometric-Arithmetic index ,Atom– bond connectivity index, Harmonic index ,Sum-connectivity index of n-decane ,3,4,4-Trimethyl heptane and 2,4-dimethyl-4- ethyl hexane.
Figures (1)
Related papers
DEGREE BASED TOPOLOGICAL INDICES OF n-HEPTANE ISOMERS
A graphG = (V (G), E(G)) consists of the vertex set V(G) and the edge set E(G) such that each edge e in E is assigned an unordered pair of vertices (u, v), called the end vertices of e. The skeleton of an organic molecule (usually, of a hydrocarbon) represents simple graph. Thus the vertices of molecular graph represent the carbon atoms, and edges the carbon-carbon bonds. In molecular graph we have many topo-logical indices. In this paper, we are computing ABC index, GA index, AG index of n-heptane isomers.
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.
Three New/Old Vertex–Degree–Based Topological Indices
Three vertex-degree-based graph invariants are presented, that earlier have been considered in the chemical and/or mathematical literature, but that evaded the attention of most mathematical chemists. These are the reciprocal Randić index (RR), the reduced second Zagreb index RM 2 , and the reduced reciprocal Randić index (RRR). If d 1 , d 2 , . . . , d n are the degrees of the vertices of the graph G = (V, E), then
The Edge Version of Geometric–Arithmetic Index of Benzenoid Graph. [35]
Proceedings of the Romanian Academy - Series B: Chemistry
Topological Indices and New Graph Structures
2012
A topological representation of a molecule can be carried out through molecular graph. The descriptors are numerical values associated with chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. A topological index is the graph invariant number calculated from a graph representing a molecule. The most of the proposed topological indices are related either to a vertex adjacency relationship (atom-atom connectivity) in the graph G or to topological distances in G. In this paper we introduce an edge operation ˆ e on the graphs 1 G and 2 G such that resulting graph 12 ˆ Ge G has an edge introduced between arbitrary vertex of 1
On the Degree-Based Topological Indices of Some Derived Networks
Mathematics
There are numeric numbers that define chemical descriptors that represent the entire structure of a graph, which contain a basic chemical structure. Of these, the main factors of topological indices are such that they are related to different physical chemical properties of primary chemical compounds. The biological activity of chemical compounds can be constructed by the help of topological indices. In theoretical chemistry, numerous chemical indices have been invented, such as the Zagreb index, the Randić index, the Wiener index, and many more. Hex-derived networks have an assortment of valuable applications in drug store, hardware, and systems administration. In this analysis, we compute the Forgotten index and Balaban index, and reclassified the Zagreb indices, A B C 4 index, and G A 5 index for the third type of hex-derived networks theoretically.
Polynomial and Deficient Topological Indices of Identified Graphs
Journal of Interdisciplinary Mathematics, 2022
To study the properties such as physical and chemical of compounds, the topological indices are introduced in chemical graph theory. These indices provide qualitative structure activity relationship (QSAR). Degree based topological indices are commonly used invariant in chemical graph theory. However, in this article, a new degree of vertices is introduced, called "deficiency degree". Further, we have computed five topological indices based on the deficiency degree like "deficient first Zagreb index, deficient generalized Randić index, deficient harmonic index, deficient inverse sum index, deficient augmented Zagreb index" for identified graphs using the M-polynomial of graph.
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].
On Sum Degree-Based Topological Indices of Some Connected Graphs
Mathematical Problems in Engineering
In mathematical chemistry, molecular structure of any chemical substance can be expressed by a numeric number or polynomial or sequence of number which represents the whole graph is called topological index. An important branch of graph theory is the chemical graph theory. As a consequence of their worldwide uses, chemical networks have inspired researchers since their development. Determination of the expressions for topological indices of different derived graphs of graphs is a new and interesting problem in graph theory. In this article, some graphs which are derived from honeycomb structure are studied and obtained their exact results for sum degree-based indices. Additionally, a comparison is shown graphically among all the indices.
Topological indices of discrete molecular structure
Discrete & Continuous Dynamical Systems - S
Topological indices defined on molecular structures can help researchers better understand the physical features, chemical reactivity, and biological activity. Thus, the study of the topological indices on chemical structure of chemical materials and drugs can make up for lack of chemical experiments and can provide a theoretical basis for the manufacturing of drugs and chemical materials. In this paper, we focus on the family of smart polymer which is widely used in anticancer drugs manufacturing. In chemical graph theory, a topological index is a numerical representation of a chemical structure which correlates certain physico-chemical characteristics of underlying chemical compounds e.g., boiling point and melting point. More preciously, we focus on the family of smart polymer which is widely used in anticancer drugs manufacturing, and computed exact results for degree based topological indices.
Related topics
Related papers
Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges
Journal of Mathematical Chemistry, 2009
Research on the topological indices based on end-vertex degrees of edges has been intensively rising recently. Randić index, one of the best-known topological indices in chemical graph theory, is belonging to this class of indices. In this paper, we introduce a novel topological index based on the end-vertex degrees of edges and its basic features are presented here. We named it as geometrical-arithmetic index (GA).
The Atom Bond Connectivity Index of Some Trees and Bicyclic Graphs
Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015), 2016
The atom bond connectivity (ABC) index is one of the recently most investigated degree-based molecular structure descriptors that have applications in chemistry. For a graph G, the ABC index is defined as , where d u denotes the degree of a vertex u in G. In this paper, we obtain the general formula for ABC index of some special, chemical trees, and bicyclic graphs.
On Generalized Topological Indices for Some Special Graphs
Journal of Mathematics
Topological indices are numeric values associated with a graph and characterize its structure. There are various topological indices in graph theory such as degree-based, distance-based, and counting-related topological indices. Among these indices, degree-based indices are very interesting and studied well in literature. In this work, we studied the generalized form of harmonic, geometric-arithmetic, Kulli–Basava indices, and generalized power-sum-connectivity index for special graph that are bridge graph over path, bridge graph over cycle, bridge graph over complete graph, wheel graph, gear graph, helm graph, and square lattice graph. We found exact values for the stated indices and for the stated special graphs. We also investigated the generalized form of the indices for various properties of alkane isomers, from which we obtained interesting results which are closed to that of experimental obtained results.
On some degree based topological indices of mk-graph
Journal of Discrete Mathematical Sciences and Cryptography, 2020
A topological index is a real number which is same under graph isomorphism and it is derived from a graph by mathematically. In chemical graph theory, a molecular graph is a simple graph having no loops and multiple edges in which atoms and chemical bonds are represented by vertices and edges respectively. Topological indices defined on these chemical molecular structures can help researchers better understand the physical features, chemical reactivity, and biological activity. In this paper, we compute general expressions
On Certain Aspects of Topological Indices
Journal of Mathematics
A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index M r G , geometric arithmetic index GA G , harmonic index H G , general version of harmonic index H r G , sum connectivity index λ G , general sum connectivity index λ r G , forgotten topological index F G , and many more for the Robertson apex graph. Additionally, we calculated the newly developed topological indices such as the AG 2 G and Sanskruti index for the Robertson apex graph G.
Degree based Topological indices of Hanoi Graph
ArXiv, 2018
There are various topological indices for example distance based topological indices and degree based topological indices etc. In QSAR/QSPR study, physiochemical properties and topological indices for example atom bond connectivity index, fourth atom bond connectivity index, Randic connectivity index, sum connectivity index, and so forth are used to characterize the chemical compound. In this paper we computed the edge version of atom bond connectivity index, fourth atom bond connectivity index, Randic connectivity index, sum connectivity index, geometric-arithmetic index and fifth geometric-arithmetic index of Double-wheel graph and Hanoi graph. The results are analyzed and the general formulas are derived for the above mentioned families of graphs.
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.
Computing a New Connectivity Index for a Famous Molecular Graph of Benzenoid Family. [32]
Journal of Chemica Acta, 2013
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.
On Certain Degree Based and Bond-Additive Topological Indices of Dodeca-Benzo-Circumcorenene
Combinatorial Chemistry & High Throughput Screening,, 2023
Background: Chemical graph theory has been used to mathematically model the various physical and biological aspects of chemical substances. A mathematical formulation that may be applied to any graph and can characterise a molecule structure is known as a topological index or molecular descriptor. Method: It is convenient and efficient to analyse the mathematical values and further research on various physical properties of a molecule based on these molecular descriptors. They provide useful alternatives to lengthy, expensive, and labour-intensive laboratory experiments. The topological indices can be used to predict the chemical structures, physicochemical properties, and biological activities using quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs). Result: In this study, the molecular descriptors of the Dodeca-benzo-circumcorenene compounds are derived based on their corresponding molecular structures. Conclusion: The computed indices are then compared graphically to study their relationship with the molecular structure and with each other.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.