scholarly journals Analysis of SC5C7p,q and NPHXp,q Nanotubes via Topological Indices

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Ye-Jun Ge ◽  
Jia-Bao Liu ◽  
Muhammad Younas ◽  
Muhammad Yousaf ◽  
Waqas Nazeer
Keyword(s):  
Carbon Nanotube ◽  
Closed Form ◽  
Topological Indices ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Molecular Graphs ◽  
Boiling Points ◽  
Structure Activity ◽  
Electrical Voltage

Scientists are creating materials, for example, a carbon nanotube-based composite created by NASA that bends when a voltage is connected. Applications incorporate the use of an electrical voltage to change the shape (transform) of air ship wings and different structures. Topological indices are numbers related with molecular graphs to allow quantitative structure activity/property/poisonous relationships. Topological indices catch symmetry of molecular structures and give it a scientific dialect to foresee properties, for example, boiling points, viscosity, and the radius of gyrations. We compute M-polynomials of two nanotubes, SC5C7p,q and NPHXp,q. The closed form of M-polynomials for these nanotubes produces formulas of numerous degree-based topological indices which are functions relying on parameters of the structure and, in combination, decide properties of the concerned nanotubes. Moreover, we sketch our results by using Maple 2015 to see the dependence of our results on the involved parameters.

scholarly journals Useful Irregularity Indices in QSPR Study for Bismuth Tri-Iodide

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Abaid ur Rehman Virk ◽  
M. A. Rehman ◽  
Ce Shi ◽  
Waqas Nazeer
Keyword(s):  
Chemical Compound ◽  
Chemical Compounds ◽  
Quantitative Structure Activity Relationship ◽  
Molecular Structures ◽  
Mathematical Language ◽  
Quantitative Structure ◽  
Boiling Points ◽  
Structure Activity ◽  
Qspr Study ◽  
Single Number

Topological indices give us a mathematical language to study molecular structures. They convert a chemical compound into a single number which foresees properties, for example, boiling points, viscosity, and the radius of gyrations. Drugs and other chemical compounds are often modeled as various polygonal shapes, trees, and graphs. In this paper, we will compute some irregularity indices for bismuth tri-iodide chain and sheet that are useful in the quantitative structure-activity relationship.

scholarly journals Some Algebraic Polynomials and Topological Indices of Octagonal Network

2016 ◽  
Author(s):  
Young Chel Kwun ◽  
Waqas Nazeer ◽  
Mobeen Munir ◽  
Shin Min Kang
Keyword(s):  
Graphical Representation ◽  
Topological Indices ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Structure Property ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Structure Activity ◽  
Activity Structure ◽  
Augmented Zagreb Index

M-polynomial of different molecular structures helps to calculate many topological indices. 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 Zagreb indices, Randic index, Symmetric division index, Harmonic index, Inverse sum index, Augmented Zagreb index, multiple Zagreb indices etc. are correlated. In this report, we compute closed forms of M-polynomial, first Zagreb polynomial and second Zagreb polynomial of Octagonal network. From the M-polynomial we recover some degree-based topological indices for Octagonal network. Moreover, we give a graphical representation of our results.

scholarly journals General Fifth M-Zagreb Polynomials of Benzene Ring Implanted in the P-Type-Surface in 2D Network

2020 ◽  
Vol 10 (6) ◽  
pp. 6881-6892 ◽  
Keyword(s):  
Molecular Structure ◽  
Benzene Ring ◽  
Biological Properties ◽  
Topological Indices ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Structure Activity ◽  
Physical Chemical ◽  
P Type ◽  
2D Network

Constitutional formulae of molecules are molecular graphs consisting of atoms as vertices and bonds between them represented as edges. The various physical, chemical, and biological properties of molecules are dependent on their molecular structures. The molecular structure is most important, not only to chemists but also to all scientists. The molecular structure descriptors or topological indices of molecules are a mathematical number or a set of selected invariants of matrices that are used to Quantitative Structure-Activity (-Property) Relationships (QSAR/QSPR) studies. In this paper, we computed some new degree-based topological indices of benzene ring implanted in the P-type-surface in the 2D network and its line subdivision of graph.

Characteristic study of irregularity measures of some nanotubes

2019 ◽  
Vol 97 (10) ◽  
pp. 1125-1132 ◽  
Author(s):  
Zahid Iqbal ◽  
Adnan Aslam ◽  
Muhammad Ishaq ◽  
Muhammad Aamir
Keyword(s):  
Quantitative Structure ◽  
Structure Property ◽  
Know How ◽  
Molecular Graphs ◽  
Irregularity Index ◽  
Structure Property Relationships ◽  
Boiling Points ◽  
Quantitative Structure Property Relationships ◽  
Quantitative Structure Activity Relationships ◽  
Vertex Degrees

In many applications and problems in material engineering and chemistry, it is valuable to know how irregular a given molecular structure is. Furthermore, measures of the irregularity of underlying molecular graphs could be helpful for quantitative structure property relationships and quantitative structure-activity relationships studies, and for determining and expressing chemical and physical properties, such as toxicity, resistance, and melting and boiling points. Here we explore the following three irregularity measures: the irregularity index by Albertson, the total irregularity, and the variance of vertex degrees. Using graph structural analysis and derivation, we compute the above-mentioned irregularity measures of several molecular graphs of nanotubes.

scholarly journals Multiplicative Zagreb Indices of Molecular Graphs

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Xiujun Zhang ◽  
H. M. Awais ◽  
M. Javaid ◽  
Muhammad Kamran Siddiqui
Keyword(s):  
Mathematical Modeling ◽  
Vital Role ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Structure Properties

Mathematical modeling with the help of numerical coding of graphs has been used in the different fields of science, especially in chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitative structure properties relationship (QSPR) models. Todeshine et al. (2010) and Eliasi et al. (2012) defined two different versions of the 1st multiplicative Zagreb index as ∏Γ=∏p∈VΓdΓp2 and ∏1Γ=∏pq∈EΓdΓp+dΓq, respectively. In the same paper of Todeshine, they also defined the 2nd multiplicative Zagreb index as ∏2Γ=∏pq∈EΓdΓp×dΓq. Recently, Liu et al. [IEEE Access; 7(2019); 105479–-105488] defined the generalized subdivision-related operations of graphs and obtained the generalized F-sum graphs using these operations. They also computed the first and second Zagreb indices of the newly defined generalized F-sum graphs. In this paper, we extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs. At the end, some particular results as applications of the obtained results for alkane are also included.

scholarly journals Topological indices of rhombus type silicate and oxide networks

2017 ◽  
Vol 95 (2) ◽  
pp. 134-143 ◽  
Author(s):  
M. Javaid ◽  
Masood Ur Rehman ◽  
Jinde Cao
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Activity ◽  
Structure Property Relationship ◽  
Cartesian Coordinate ◽  
Atom Bond

For a molecular graph, a numeric quantity that characterizes the whole structure of a graph is called a topological index. In the studies of quantitative structure – activity relationship (QSAR) and quantitative structure – property relationship (QSPR), topological indices are utilized to guess the bioactivity of chemical compounds. In this paper, we compute general Randić, first general Zagreb, generalized Zagreb, multiplicative Zagreb, atom-bond connectivity (ABC), and geometric arithmetic (GA) indices for the rhombus silicate and rhombus oxide networks. In addition, we also compute the latest developed topological indices such as the fourth version of ABC (ABC4), the fifth version of GA (GA5), augmented Zagreb, and Sanskruti indices for the foresaid networks. At the end, a comparison between all the indices is included, and the result is shown with the help of a Cartesian coordinate system.

Some topological indices of dendrimers

2020 ◽  
pp. 2050018
Author(s):  
S. Alyar ◽  
R. Khoeilar ◽  
A. Jahanbani
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Topological Indices ◽  
Molecular Structures ◽  
Topological Properties ◽  
Zagreb Index ◽  
Zinc Porphyrin ◽  
Molecular Graphs

There are immense applications of graph theory in chemistry and in the study of molecular structures, and after that, it has been increasing exponentially. Molecular graphs have points (vertices) representing atoms and lines (edges) that represent bonds between atoms. In this paper, we study the molecular graph of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers and analyzed its topological properties. For this purpose, we have computed topological indices, namely the Albertson index, the sigma index, the Nano-Zagreb index, the first and second hyper [Formula: see text]-indices of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers.

scholarly journals M-Polynomials And Topological Indices Of Zigzag And Rhombic Benzenoid Systems

2018 ◽  
Vol 16 (1) ◽  
pp. 73-78 ◽  
Author(s):  
Ashaq Ali ◽  
Waqas Nazeer ◽  
Mobeen Munir ◽  
Shin Min Kang
Keyword(s):  
Closed Form ◽  
Significant Role ◽  
Chemical Compound ◽  
Molecular Graph ◽  
Topological Indices ◽  
Molecular Structures

AbstractM-polynomial of different molecular structures helps to calculate many topological indices. This polynomial is a new idea and its beauty is the wealth of information it contains about the closed forms of degree-based topological indices of molecular graph G of the structure. It is a well-known fact that topological indices play significant role in determining properties of the chemical compound [1, 2, 3, 4]. In this article, we computed the closed form of M-polynomial of zigzag and rhombic benzenoid systemsbecause of their extensive usages in industry. Moreover we give graphs of M-polynomials and their relations with the parameters of structures.

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