Topological indices of some families of nanostar dendrimers (original) (raw)
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On Topological Indices of Certain Families of Nanostar Dendrimers
Molecules (Basel, Switzerland), 2016
A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are used to predict the bioactivity of different chemical compounds. A dendrimer is an artificially manufactured or synthesized molecule built up from the branched units called monomers. In this paper, the fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated. We derive the analytical closed formulas for these families of nanostar dendrimers. The obtained results can be of use in molecular data mining, particularly in researching the uniqueness of tested (hyp...
Connection-Based Multiplicative Zagreb Indices of Dendrimer Nanostars
Journal of Mathematics, 2021
The field of graph theory is broadly growing and playing a remarkable role in cheminformatics, mainly in chemistry and mathematics in developing different chemical structures and their physicochemical properties. Mathematical chemistry provides a platform to study these physicochemical properties with the help of topological indices (TIs). A topological index (TI) is a function that connects a numeric number to each molecular graph. Zagreb indices (ZIs) are the most studied TIs. In this paper, we establish general expressions to calculate the connection-based multiplicative ZIs, namely, first multiplicative ZIs, second multiplicative ZIs, third multiplicative ZIs, and fourth multiplicative ZIs, of two renowned dendrimer nanostars. The defined expressions just depend on the step of growth of these dendrimers. Moreover, we have compared our calculated for both type of dendrimers with each other.
THE ( a , b )-ZAGREB INDEX OF NANOSTAR DENDRIMERS
2018
Let be a simple graph, where and are the vertex and edge sets of , and represent the number of vertices and edges of respectively. The degree of a vertex is defined as the number of adjacent vertices of in and is denoted as . A topological index is a real number related to a chemical constitution for correlation of a chemical structure with various physicochemical properties. Quantitative structure-activity relationships (QSAR) and quantitative structure-properties relationships (QSPR) are mathematical correlation between a specified biological activity and one or more physicochemical properties, known as descriptors as they describe the activity or property under examination. Different topological indices are correlate with biological and physicochemical properties of chemical compounds. Therefore, they are useful descriptors in QSAR and QSPR that are used for predictive purposes, such as prediction of the toxicity of a chemical or the potency of a drug for future release in the ma...
M-Polynomial and Related Topological Indices of Nanostar Dendrimers
Symmetry, 2016
Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.
Generalized Zagreb index of some dendrimer structures
Universal journal of mathematics and applications, 2018
Chemical graph theory, is a branch of mathematical chemistry which deals with the nontrivial applications of graph theory to solve molecular problem. A chemical graph is represent a molecule by considering the atoms as the vertices and bonds between them as the edges. A topological index is a graph based molecular descriptor, which is graph theoretic invariant characterising some physicochemical properties of chemical compounds. Dendrimers are generally large, complex, and hyper branched molecules synthesized by repeatable steps with nanometre scale measurements. In this paper, we study the (a, b)-Zagreb index of some regular dendrimers and hence obtain some vertex degree based topological indices.
Computing entire Zagreb indices of some dendrimer structures
Main Group Metal Chemistry, 2020
Topological indices are numerical numbers associated to molecular graphs and are invariant of a graph. In QSAR/QSPR study, Zagreb indices are used to explain the different properties of chemical compounds at the molecular level mathematically. They have been studied extensively due to their ease of calculation and numerous applications in place of the existing chemical methods which needed more time and increased the costs. In this paper, we compute precise values of new versions of Zagreb indices for two classes of dendrimers.
On Multiple Zagreb Indices of Dendrimer Nanostars [121]
In this paper, we focus on the structure of an infinite class of Dendrimer Nanostars D 3 [n] (n≥0 is infinite integer) and counting its First Multiple Zagreb index and Second Multiple Zagreb index. The Multiple Zagreb topological indices are equal to PM 1 (G)= ( )
Computing the Narumi-Katayama indices and its modified version of some nanostar dendrimers
Eurasian Chemical Communications
Dendrimers are the highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core. In mathematical chemistry, a particular attention has been given to degree-based graph invariant. The Narumi-Katayama index and its modified version of a graph G, denoted by NK(G) and NK * (G) are equal to the product of the degrees of the vertices of G. In this work we calculated the Narumi-Katayama Indices and its Modified version for some families of dendrimers such as NS1[n], NS2[n] and NS3[n]. The exact formulas of the Narumi-Katayama and Modified Narumi-Katayama indices of these dendrimers nano structures are presented in this paper.
International Journal of Engineering Science, Advanced Computing and Bio-Technology, 2018
Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity/property/toxicity relationships. These topological indices correlate certain Physico-Chemical properties like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine Multiplicative Sum connectivity, Multiplicative Randic and Multiplicative Harmonic index for some Nanostar Dendrimers