On Highly Discriminating Molecular Topological Index (original) (raw)
Related papers
Journal of Chemical Information and Computer Sciences, 2004
The structural interpretation is extended to the topological indices describing cyclic structures. Three representatives of the topological index, such as the molecular connectivity index, the Kappa index, and the atom-type EState index, are interpreted by mining out, through projection pursuit combining with a number theory method generating uniformly distributed directions on unit sphere, the structural features hidden in the spaces spanned by the three series of indices individually. Some interesting results, which can hardly be found by individual index, are obtained from the multidimensional spaces by several topological indices. The results support quantitatively the former studies on the topological indices, and some new insights are obtained during the analysis. The combinations of several molecular connectivity indices describe mainly three general categories of molecular structure information, which include degree of branching, size, and degree of cyclicity. The cyclicity can also be coded by the combination of chi cluster and path/cluster indices. The Kappa shape indices encode, in combination, significant information on size, the degree of cyclicity, and the degree of centralization/separation in branching. The size, branch number, and cyclicity information has also been mined out to interpret atom-type EState indices. The structural feature such as the number of quaternary atoms is searched out to be an important factor. The results indicate that the collinearity might be a serious problem in the applications of the topological indices.
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.
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.
Forgotten Topological Index of Chemical Structure in Drugs
Saudi Pharmaceutical Journal, 2016
A massive of early drug tests implies that there exist strong inner relationships between the bio-medical and pharmacology characteristics of drugs and their molecular structures. The forgotten topological index was defined to be used in the analysis of drug molecular structures, which is quite helpful for pharmaceutical and medical scientists to grasp the biological and chemical characteristics of new drugs. Such tricks are popularly employed in developing countries where enough money is lacked to afford the relevant chemical reagents and equipment. In our article, by means of drug molecular structure analysis and edge dividing technology, we present the forgotten topological index of several widely used chemical structures which often appear in drug molecular 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.
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.
The chemical meaning of topological indices
Chemometrics and Intelligent Laboratory Systems, 1992
Todeschini, R., Cazar, R. and Collina, E., 1992. The chemical meaning of topological indices. Chemometrics and Intelligent Laboratory Systems, 15: 51-59.
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 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.
Journal of Mathematics
In quantitative structure-property and structure-activity relationships studies, several graph invariants, namely, topological indices have been defined and studied due to their numerous applications in computer networks, biotechnology, and nanochemistry. Topological indices are numeric parameters that describe the biological, physical, and chemical properties depending on the structure and topology of different chemical compounds. In this article, we inaugurated some degree-based novel indices, namely, geometric-harmonic GHI , harmonic-geometric HGI , neighborhood harmonic-geometric NHGI , and neighborhood geometric-harmonic NGHI indices and verified their chemical applicability. Furthermore, an attempt is made to calculate analytical closed formulas for different variants of silicon carbides and analyze the obtained results graphically.