scholarly journals Topological Indices of Dendrimers used in Drug Delivery

2020 ◽  
Vol 12 (4) ◽  
pp. 645-655
Author(s):  
T. P. Jude ◽  
E. Panchadcharam ◽  
K. Masilamani
Keyword(s):  
Drug Delivery ◽  
Molecular Graph ◽  
Topological Indices ◽  
Vertex Degree ◽  
Numerical Representation ◽  
Chemical Bonds ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Carrier Vehicle

The topological index is a numerical representation of a molecular structure. In chemical graphs, the atoms and the chemical bonds between them are represented by vertices and edges respectively. Vertex degree based topological indices are the most studied and mostly used type of topological indices. The mostly used vertex degree based topological indices in the field of drug design and developments are the Zagreb index and the Randić index. The structural chemistry of dendrimers could be manipulated by their topological indices to get the specific structure with required properties to deliver the drugs to target carrier vehicle. In this work, topological indices of three types of dendrimers which are used as the drug delivery system were studied and their Zagreb index and the Randić index were calculated using molecular graph theory. Moreover, the other versions of these two indices were also calculated to these dendrimers.

Four New/Old Vertex-Degree-Based Topological Indices of HAC5C7[p, q] and HAC5C6C7[p, q] Nanotubes

2017 ◽  
Vol 14 (1) ◽  
pp. 796-799 ◽  
Author(s):  
Yingfang Li ◽  
Li Yan ◽  
Muhammad Kamran Jamil ◽  
Mohammad Reza Farahani ◽  
Wei Gao ◽  
...  
Keyword(s):  
Topological Indices ◽  
Vertex Degree ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Second Zagreb Index ◽  
Forgotten Index ◽  
Mathematical Literature

Recently, Gutman et al. presented some vertex-degree based topological indices, that earlier have been considered in the chemical and/or mathematical literature, but, evaded the attention of most mathematical chemists. These are the reciprocal Randic index (RR), the reduced reciprocal Randic index (RRR), the reduced second Zagreb index (RM2) and the forgotten index (F). In this paper, we compute these topological indices of HAC5C7[p, q] and HAC5C6C7[p, q] nanotubes.

scholarly journals Bounds on General Randić Index for F-Sum Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Xu Li ◽  
Maqsood Ahmad ◽  
Muhammad Javaid ◽  
Muhammad Saeed ◽  
Jia-Bao Liu
Keyword(s):  
Molecular Graph ◽  
Randić Index ◽  
Lower And Upper Bounds ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Structure Activity ◽  
General Randić Index ◽  
General Randic Index ◽  
The First Zagreb Index

A topological invariant is a numerical parameter associated with molecular graph and plays an imperative role in the study and analysis of quantitative structure activity/property relationships (QSAR/QSPR). The correlation between the entire π-electron energy and the structure of a molecular graph was explored and understood by the first Zagreb index. Recently, Liu et al. (2019) calculated the first general Zagreb index of the F-sum graphs. In the same paper, they also proposed the open problem to compute the general Randić index RαΓ=∑uv∈EΓdΓu×dΓvα of the F-sum graphs, where α∈R and dΓu denote the valency of the vertex u in the molecular graph Γ. Aim of this paper is to compute the lower and upper bounds of the general Randić index for the F-sum graphs when α∈N. We present numerous examples to support and check the reliability as well as validity of our bounds. Furthermore, the results acquired are the generalization of the results offered by Deng et al. (2016), who studied the general Randić index for exactly α=1.

scholarly journals On the Number of Spanning Trees of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Ş. Burcu Bozkurt ◽  
Durmuş Bozkurt
Keyword(s):  
Spanning Trees ◽  
Vertex Degree ◽  
Randić Index ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Connected Graphs ◽  
Randic Index ◽  
Number Of Spanning Trees

We establish some bounds for the number of spanning trees of connected graphs in terms of the number of vertices(n), the number of edges(m), maximum vertex degree(Δ1), minimum vertex degree(δ),…first Zagreb index(M1),and Randić index(R-1).

scholarly journals On Leap Reduced Reciprocal Randic and Leap Reduced Second Zagreb Indices of Some Graphs

2019 ◽  
Vol 3 (2) ◽  
pp. 27-35
Author(s):  
Fazal Dayan ◽  
Muhammad Javaid ◽  
Muhammad Aziz ur Rehman
Keyword(s):  
Topological Indices ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Second Degree

Naji et al. introduced the leap Zagreb indices of a graph in 2017 which are new distance-degree-based topological indices conceived depending on the second degree of vertices. In this paper, we have defined the first and second leap reduced reciprocal Randic index and leap reduced second Zagreb index for selected wheel related graphs.

scholarly journals Computation of General Zagreb Index of Nanotubes Covered by C5 and C7

2020 ◽  
Vol 11 (1) ◽  
pp. 8001-8008
Keyword(s):  
Carbon Nanotubes ◽  
Connected Graph ◽  
Molecular Graph ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Chemical Bonds ◽  
Graph Invariant ◽  
Zagreb Index ◽  
Physical And Chemical ◽  
Simple Connected Graph

A molecular graph is hydrogen deleted simple connected graph in which vertices and edges are represented by atoms and chemical bonds, respectively. Topological indices are numerical parameters of a molecular graph which characterize its topology and are usually graph invariant. In Mathematical chemistry, topological descriptors play an important role in modeling different physical and chemical activities of molecules. In this study, the generalized Zagreb index for three types of carbon nanotubes is computed. By putting some particular values to the parameters, some important degree-based topological indices are also derived.

scholarly journals Several Topological Indices of Two Kinds of Tetrahedral Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jia-Bao Liu ◽  
Lu-Lu Fang
Keyword(s):  
Finite Element ◽  
Network Model ◽  
Topological Indices ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Research Studies

Tetrahedral network is considered as an effective tool to create the finite element network model of simulation, and many research studies have been investigated. The aim of this paper is to calculate several topological indices of the linear and circle tetrahedral networks. Firstly, the resistance distances of the linear tetrahedral network under different classifications have been calculated. Secondly, according to the above results, two kinds of degree-Kirchhoff indices of the linear tetrahedral network have been achieved. Finally, the exact expressions of Kemeny’s constant, Randic index, and Zagreb index of the linear tetrahedral network have been deduced. By using the same method, the topological indices of circle tetrahedral network have also been obtained.

scholarly journals Comparing the molecular graph degeneracy of Wiener, Harary, Balaban, Randi´c and ZEP topological indices

2014 ◽  
Vol 23 (2) ◽  
pp. 165-174
Author(s):  
ZOITA-MARIOARA BERINDE ◽  
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Wiener Index ◽  
Topological Indices ◽  
Randić Index ◽  
Discrimination Power ◽  
Harary Index ◽  
Molecular Chemistry ◽  
Randic Index

The aim of this paper is to show that the ZEP topological index has better discrimination power than four well known topological indices in molecular chemistry: Balaban index, Harary index, Randic index, and Wiener index.

scholarly journals Study of Hardness of Superhard Crystals by Topological Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xiujun Zhang ◽  
Muhammad Naeem ◽  
Abdul Qudair Baig ◽  
Manzoor Ahmad Zahid
Keyword(s):  
Molecular Structure ◽  
Chemical Structure ◽  
Topological Indices ◽  
Connectivity Index ◽  
Chemical Bonds ◽  
Randić Index ◽  
Total Resistance ◽  
Randic Index ◽  
Atom Bond

Topological indices give immense information about a molecular structure or chemical structure. The hardness of materials for the indentation can be defined microscopically as the total resistance and effect of chemical bonds in the respective materials. The aim of this paper is to study the hardness of some superhard B C x crystals by means of topological indices, specifically Randić index and atom-bond connectivity index.

Sharp bounds for the general Randić index of transformation graphs

2020 ◽  
Vol 39 (5) ◽  
pp. 7787-7794
Author(s):  
Muhammad Imran ◽  
Shehnaz Akhter ◽  
Hani Shaker
Keyword(s):  
Graph Transformation ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Randić Index ◽  
Sharp Bounds ◽  
Randic Index ◽  
General Randić Index ◽  
General Randic Index ◽  
Total Point

Inequalities are a useful method to investigate and compare topological indices of graphs relatively. A large collection of graph associated numerical descriptors have been used to examine the whole structure of networks. In these analysis, degree related topological indices have a significant position in theoretical chemistry and nanotechnology. Thus, the computation of degree related indices is one of the successful topic of research. Given a molecular graph H , the general Randić connectivity index is interpreted as R α ( H ) = ∑ ℛ ∈ E ( H ) ( deg H ( a ) deg H ( b ) ) α , with α is a real quantity. Also a graph transformation of H provides a comparatively simpler isomorphic structure with an ease to work on different chemical properties. In this article, we determine the sharp bounds of general Randić index of numerous graph transformations, such that semi-total-point, semi-total-line, total and eight individual transformations H fgh , where f, g, h ∈ {+ , -} of graphs by using combinatorial inequalities.

scholarly journals M-Polynomials and Degree-Based Topological Indices of the Molecule Copper(I) Oxide

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Faryal Chaudhry ◽  
Iqra Shoukat ◽  
Deeba Afzal ◽  
Choonkil Park ◽  
Murat Cancan ◽  
...  
Keyword(s):  
Topological Indices ◽  
Randić Index ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Randic Index ◽  
Zagreb Indices ◽  
Symmetric Division ◽  
Augmented Zagreb Index ◽  
Physical And Chemical ◽  
Modified Zagreb Index

Topological indices are numerical parameters used to study the physical and chemical residences of compounds. Degree-based topological indices have been studied extensively and can be correlated with many properties of the understudy compounds. In the factors of degree-based topological indices, M-polynomial played an important role. In this paper, we derived closed formulas for some well-known degree-based topological indices like first and second Zagreb indices, the modified Zagreb index, the symmetric division index, the harmonic index, the Randić index and inverse Randić index, and the augmented Zagreb index using calculus.

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