scholarly journals On Wiener Polarity Index and Wiener Index of Certain Triangular Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Mr. Adnan ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Muhammad Imran
Keyword(s):  
Chemical Compounds ◽  
Wiener Index ◽  
Topological Indices ◽  
Index Number ◽  
Graph Theoretic ◽  
Polarity Index ◽  
Boiling Points ◽  
Van Der Waals Surface ◽  
Density Surface ◽  
Quantitative Structure Activity Relationships

A topological index of graph G is a numerical quantity which describes its topology. If it is applied to the molecular structure of chemical compounds, it reflects the theoretical properties of the chemical compounds. A number of topological indices have been introduced so far by different researchers. The Wiener index is one of the oldest molecular topological indices defined by Wiener. The Wiener index number reflects the index boiling points of alkane molecules. Quantitative structure activity relationships (QSAR) showed that they also describe other quantities including the parameters of its critical point, density, surface tension, viscosity of its liquid phase, and the van der Waals surface area of the molecule. The Wiener polarity index has been introduced by Wiener and known to be related to the cluster coefficient of networks. In this paper, the Wiener polarity index W p G and Wiener index W G of certain triangular networks are computed by using graph-theoretic analysis, combinatorial computing, and vertex-dividing technology.

Topological characterization of dendrimer, benzenoid, and nanocone

2018 ◽  
Vol 74 (1-2) ◽  
pp. 35-43
Author(s):  
Wei Gao ◽  
Muhammad Kamran Siddiqui ◽  
Najma Abdul Rehman ◽  
Mehwish Hussain Muhammad
Keyword(s):  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Zagreb Index ◽  
Topological Characterization ◽  
Complex Molecules ◽  
Chemical Structures ◽  
Physico Chemical ◽  
Quantitative Structure Activity Relationships

Abstract Dendrimers are large and complex molecules with very well defined chemical structures. More importantly, dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core. Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity relationships. These topological indices correlate certain physico-chemical properties such as the boiling point, stability, strain energy, and others, of chemical compounds. In this article, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for hetrofunctional dendrimers, triangular benzenoids, and nanocones.

scholarly journals On the Wiener index and variants of the Szeged index of single-walled titania nanotubes TiO2(m,n)

2017 ◽  
Vol 95 (1) ◽  
pp. 68-86 ◽  
Author(s):  
Muhammad Imran ◽  
Sabeel-e Hafi
Keyword(s):  
Physicochemical Properties ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Exact Expression ◽  
Topological Indices ◽  
Titania Nanotubes ◽  
Graph Invariant ◽  
Szeged Index ◽  
Cut Method

Topological indices are numerical parameters of a graph that characterize its topology and are usually graph invariant. There are certain types of topological indices such as degree-based topological indices, distance-based topological indices, and counting-related topological indices. These topological indices correlate certain physicochemical properties such as boiling point, stability, and strain energy of chemical compounds. In this paper, we compute an exact expression of Wiener index, vertex-Szeged index, edge-Szeged index, and total-Szeged index of single-walled titania nanotubes TiO2(m, n) by using the cut method for all values of m and n.

scholarly journals New Bounds for Topological Indices on Trees through Generalized Methods

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1097 ◽  
Author(s):  
Álvaro Martínez-Pérez ◽  
José M. Rodríguez
Keyword(s):  
Large Class ◽  
Lower Bounds ◽  
Maximum Degree ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Topological Indices ◽  
Upper And Lower Bounds ◽  
Unified Approach ◽  
Wide Family ◽  
New Inequalities

Topological indices are useful for predicting the physicochemical behavior of chemical compounds. A main problem in this topic is finding good bounds for the indices, usually when some parameters of the graph are known. The aim of this paper is to use a unified approach in order to obtain several new inequalities for a wide family of topological indices restricted to trees and to characterize the corresponding extremal trees. The main results give upper and lower bounds for a large class of topological indices on trees, fixing or not the maximum degree. This class includes the first variable Zagreb, the Narumi–Katayama, the modified Narumi–Katayama and the Wiener index.

scholarly journals On the Degree-Based Topological Indices of Some Derived Networks

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 612 ◽  
Author(s):  
Haidar Ali ◽  
Muhammad Ahsan Binyamin ◽  
Muhammad Kashif Shafiq ◽  
Wei Gao
Keyword(s):  
Chemical Structure ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Topological Indices ◽  
Theoretical Chemistry ◽  
Zagreb Index ◽  
Entire Structure ◽  
Physical Chemical ◽  
Chemical Descriptors

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.

On vertex PI index of certain triangular tessellation networks

2021 ◽  
Vol 44 (1) ◽  
pp. 203-212
Author(s):  
Syed Ahtsham Ul Haq Bokhary ◽  
Adnan
Keyword(s):  
Biological Activities ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Theoretic Analysis ◽  
Complex Chemical ◽  
Chemical Graph ◽  
Graph Theoretic ◽  
Pi Index ◽  
Triangular Tessellation

Abstract The Wiener index, due to its many applications is considered to be one of very important distance-based index. But the Padmaker-Ivan (PI) index is kind of the only distance related index linked to parallelism of edges. The PI index like other distance related indices has great disseminating power. The index was firstly investigated by Khadikar et al. (2001), they have probed the chemical applications of the PI index. They proved that the proposed PI index correlates highly with the physicochemical properties and biological activities of a large number of diverse and complex chemical compounds and the Wiener and Szeged indices. Recently, the vertex Padmarkar-Ivan (PIv) index of a chemical graph G was introduced as the sum over all edges uv of a molecular graph G of the vertices of the graph that are not equidistant to the vertices u and v. In this paper, the vertex PIv index of certain triangular tessellation are computed by using graph-theoretic analysis, combinatorial computing, and edge-dividing technology.

scholarly journals Distance-Based Polynomials and Topological Indices for Hierarchical Hypercube Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Tingmei Gao ◽  
Iftikhar Ahmed
Keyword(s):  
Integral Equations ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Topological Indices ◽  
Harary Index ◽  
Hypercube Networks ◽  
Modified Wiener Index

Topological indices are the numbers associated with the graphs of chemical compounds/networks that help us to understand their properties. The aim of this paper is to compute topological indices for the hierarchical hypercube networks. We computed Hosoya polynomials, Harary polynomials, Wiener index, modified Wiener index, hyper-Wiener index, Harary index, generalized Harary index, and multiplicative Wiener index for hierarchical hypercube networks. Our results can help to understand topology of hierarchical hypercube networks and are useful to enhance the ability of these networks. Our results can also be used to solve integral equations.

scholarly journals M-Polynomials and Topological Indices of Titania Nanotubes

2016 ◽  
Author(s):  
Shin Min Kang ◽  
Mobeen Munir ◽  
Abdul Rauf Nizami ◽  
Shazia Rafique ◽  
Waqas Nazeer
Keyword(s):  
Tio2 Nanotubes ◽  
Strain Energy ◽  
Gas Sensing ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Structure Activity ◽  
Different Types ◽  
Quantitative Structure Activity Relationships ◽  
And Chemical Properties

Titania is one of the most comprehensively studied nanostructures due to its widespread applications in production of catalytic, gas- sensing and corrosion- resistance materials [1]. M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules are correlated with their structure like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine M-polynomials of single-walled titanium (SW TiO2) nanotubes and recover important topological degree based indices of them to theoretically judge these nanotubes. We also use Maple to plot surfaces associated to different types of single-walled titanium (SW TiO2) nanotubes.

scholarly journals Weighted Wiener Indices of Molecular Graphs with Application to Alkenes and Alkadienes

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 153
Author(s):  
Simon Brezovnik ◽  
Niko Tratnik ◽  
Petra Žigert Pleteršek
Keyword(s):  
Linear Regression Analysis ◽  
Chemical Properties ◽  
Wiener Index ◽  
Topological Indices ◽  
The Other ◽  
Multiple Bonds ◽  
Saturated Hydrocarbons ◽  
Simple Graphs ◽  
Boiling Points ◽  
Physico Chemical

There exist many topological indices that are calculated on saturated hydrocarbons since they can be easily modelled by simple graphs. On the other hand, it is more challenging to investigate topological indices for hydrocarbons with multiple bonds. The purpose of this paper is to introduce a simple model that gives good results for predicting physico-chemical properties of alkenes and alkadienes. In particular, we are interested in predicting boiling points of these molecules by using the well known Wiener index and its weighted versions. By performing the non-linear regression analysis we predict boiling points of alkenes and alkadienes.

Bounds on hyper-Wiener index of graphs

2017 ◽  
Vol 10 (03) ◽  
pp. 1750057
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Sadegh Rahimi
Keyword(s):  
Lower Bounds ◽  
Organic Molecules ◽  
Wiener Index ◽  
Upper And Lower Bounds ◽  
Pharmacological Properties ◽  
Graph Theoretic ◽  
Acyclic Graphs ◽  
Wiener Number ◽  
Number Formula ◽  
Cyclic Graphs

The Wiener number [Formula: see text] of a graph [Formula: see text] was introduced by Harold Wiener in connection with the modeling of various physic-chemical, biological and pharmacological properties of organic molecules in chemistry. Milan Randić introduced a modification of the Wiener index for trees (acyclic graphs), and it is known as the hyper-Wiener index. Then Klein et al. generalized Randić’s definition for all connected (cyclic) graphs, as a generalization of the Wiener index, denoted by [Formula: see text] and defined as [Formula: see text]. In this paper, we establish some upper and lower bounds for [Formula: see text], in terms of other graph-theoretic parameters. Moreover, we compute hyper-Wiener number of some classes of graphs.

scholarly journals M-polynomial-based topological indices of metal-organic networks

2021 ◽  
Vol 44 (1) ◽  
pp. 129-140
Author(s):  
Agha Kashif ◽  
Sumaira Aftab ◽  
Muhammad Javaid ◽  
Hafiz Muhammad Awais
Keyword(s):  
High Surface ◽  
Physical Stability ◽  
High Surface Area ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Energy Storage Devices ◽  
Storage Devices ◽  
Metal Organic ◽  
Relationship Of ◽  
Different Gases

Abstract Topological index (TI) is a numerical invariant that helps to understand the natural relationship of the physicochemical properties of a compound in its primary structure. George Polya introduced the idea of counting polynomials in chemical graph theory and Winer made the use of TI in chemical compounds working on the paraffin's boiling point. The literature of the topological indices and counting polynomials of different graphs has grown extremely since that time. Metal-organic network (MON) is a group of different chemical compounds that consist of metal ions and organic ligands to represent unique morphology, excellent chemical stability, large pore volume, and very high surface area. Working on structures, characteristics, and synthesis of various MONs show the importance of these networks with useful applications, such as sensing of different gases, assessment of chemicals, environmental hazard, heterogeneous catalysis, gas and energy storage devices of excellent material, conducting solids, super-capacitors and catalysis for the purification, and separation of different gases. The above-mentioned properties and physical stability of these MONs become a most discussed topic nowadays. In this paper, we calculate the M-polynomials and various TIs based on these polynomials for two different MONs. A comparison among the aforesaid topological indices is also included to represent the better one.

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