scholarly journals On the Computation of Some Topological Descriptors to Find Closed Formulas for Certain Chemical Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Muhammad Haroon Aftab ◽  
Muhammad Rafaqat ◽  
M. Hussain ◽  
Tariq Zia
Keyword(s):  
Research Paper ◽  
Topological Indices ◽  
Connectivity Index ◽  
Topological Descriptors ◽  
General Version ◽  
Harmonic Index ◽  
Chemical Graphs ◽  
Abc Index ◽  
Atom Bond ◽  
Honeycomb Network

In this research paper, we will compute the topological indices (degree based) such as the ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, first and second hyper-Gourava indices, general Randic´ index R γ G , for  γ = ± 1 , ± 1 / 2 , harmonic index, general version of the harmonic index, atom-bond connectivity (ABC) index, SK, SK1, and SK2 indices, sum-connectivity index, general sum-connectivity index, and first general Zagreb and forgotten topological indices for various types of chemical networks such as the subdivided polythiophene network, subdivided hexagonal network, subdivided backbone DNA network, and subdivided honeycomb network. The discussion on the aforementioned networks will give us very remarkable results by using the aforementioned topological indices.

scholarly journals Topological Indices of Certain Transformed Chemical Structures

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Xuewu Zuo ◽  
Jia-Bao Liu ◽  
Hifza Iqbal ◽  
Kashif Ali ◽  
Syed Tahir Raza Rizvi
Keyword(s):  
Carbon Nanotube ◽  
Line Graph ◽  
Topological Indices ◽  
Connectivity Index ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Chemical Structures ◽  
Augmented Zagreb Index ◽  
Carbon Nanotube Networks ◽  
Atom Bond

Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.

scholarly journals Topological Descriptors of M-Carbon M r , s , t

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hong Yang ◽  
Muhammad Naeem
Keyword(s):  
Crystal Structures ◽  
Topological Indices ◽  
Connectivity Index ◽  
Topological Descriptors ◽  
Chemical System ◽  
Zagreb Indices ◽  
Chemical Structures ◽  
The One ◽  
Atom Bond

We have studied topological indices of the one the hardest crystal structures in a given chemical system, namely, M-carbon. These structures are based and obtained by the famous algorithm USPEX. The computations and applications of topological indices in the study of chemical structures is growing exponentially. Our aim in this article is to compare and compute some well-known topological indices based on degree and sum of degrees, namely, general Randić indices, Zagreb indices, atom bond connectivity index, geometric arithmetic index, new Zagreb indices, fourth atom bond connectivity index, fifth geometric arithmetic index, and Sanskruti index of the M-carbon M r , s , t . Moreover, we have also computed closed formulas for these indices.

scholarly journals On Certain Aspects of Topological Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Tanweer Ul Islam ◽  
Zeeshan Saleem Mufti ◽  
Aqsa Ameen ◽  
Muhammad Nauman Aslam ◽  
Ali Tabraiz
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Topological Indices ◽  
Connectivity Index ◽  
General Version ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Degree Distance ◽  
Apex Graph ◽  
Structure Descriptor

A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index M r G , geometric arithmetic index GA G , harmonic index H G , general version of harmonic index H r G , sum connectivity index λ G , general sum connectivity index λ r G , forgotten topological index F G , and many more for the Robertson apex graph. Additionally, we calculated the newly developed topological indices such as the AG 2 G and Sanskruti index for the Robertson apex graph G.

On eccentricity-based topological descriptors of water-soluble dendrimers

2018 ◽  
Vol 74 (1-2) ◽  
pp. 25-33 ◽  
Author(s):  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Adnan Aslam ◽  
Wei Gao
Keyword(s):  
Molecular Structure ◽  
Chemical Properties ◽  
Topological Indices ◽  
Water Soluble ◽  
Connectivity Index ◽  
Topological Descriptors ◽  
Physical And Chemical Properties ◽  
Eccentric Connectivity Index ◽  
Physical And Chemical ◽  
And Chemical Properties

AbstractPrevious studies show that certain physical and chemical properties of chemical compounds are closely related with their molecular structure. As a theoretical basis, it provides a new way of thinking by analyzing the molecular structure of the compounds to understand their physical and chemical properties. The molecular topological indices are numerical invariants of a molecular graph and are useful to predict their bioactivity. Among these topological indices, the eccentric-connectivity index has a prominent place, because of its high degree of predictability of pharmaceutical properties. In this article, we compute the closed formulae of eccentric-connectivity–based indices and its corresponding polynomial for water-soluble perylenediimides-cored polyglycerol dendrimers. Furthermore, the edge version of eccentric-connectivity index for a new class of dendrimers is determined. The conclusions we obtained in this article illustrate the promising application prospects in the field of bioinformatics and nanomaterial engineering.

scholarly journals Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Asad Ali ◽  
Muhammad Shoaib Sardar ◽  
Imran Siddique ◽  
Dalal Alrowaili
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Vaporization Enthalpy ◽  
Zagreb Index ◽  
Graph Operations ◽  
Big Graphs ◽  
Physical And Chemical ◽  
Atom Bond

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1   and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

Atom Bond Connectivity Index of Molecular Graphs of Alkynes and Cycloalkynes

2016 ◽  
Vol 13 (10) ◽  
pp. 6698-6706
Author(s):  
Mohanad A Mohammed ◽  
K. A Atan ◽  
A. M Khalaf ◽  
R Hasni ◽  
M. R. Md Said
Keyword(s):  
Molecular Structure ◽  
Connectivity Index ◽  
Molecular Graphs ◽  
Degree Of A Vertex ◽  
Abc Index ◽  
Atom Bond

The atom-bond connectivity (ABC) index is one of the recently most investigated degree based molecular structure descriptors that have applications in chemistry. For a graph G, the ABC index is defined as ABC(G) = <inline-formula> <mml:math display="block"> <mml:msub> <mml:mo>∑</mml:mo> <mml:mrow> <mml:mi>u</mml:mi><mml:mi>v</mml:mi><mml:mo>∈</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msub> <mml:msqrt> <mml:mrow> <mml:mo stretchy="false">[</mml:mo><mml:msub> <mml:mi>d</mml:mi> <mml:mi>v</mml:mi> </mml:msub> <mml:mo>+</mml:mo><mml:msub> <mml:mi>d</mml:mi> <mml:mi>u</mml:mi> </mml:msub> <mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">]</mml:mo><mml:mo>/</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub> <mml:mi>d</mml:mi> <mml:mi>v</mml:mi> </mml:msub> <mml:mtext> </mml:mtext><mml:mo>·</mml:mo><mml:mtext> </mml:mtext><mml:msub> <mml:mi>d</mml:mi> <mml:mi>u</mml:mi> </mml:msub> <mml:mo stretchy="false">]</mml:mo><mml:mo>,</mml:mo> </mml:mrow> </mml:msqrt> </mml:math> </inline-formula> where du denotes the degree of a vertex u in G. In this paper, we establish the general formulas for the atom bond connectivity index of molecular graphs of alkynes and cycloalkynes.

scholarly journals The Atom-Bond Connectivity Index of Catacondensed Polyomino Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jinsong Chen ◽  
Jianping Liu ◽  
Qiaoliang Li
Keyword(s):  
Upper Bound ◽  
Connectivity Index ◽  
Zigzag Chain ◽  
Extremal Graphs ◽  
Degree Of A Vertex ◽  
Abc Index ◽  
Atom Bond

LetG=(V,E)be a graph. The atom-bond connectivity (ABC) index is defined as the sum of weights((du+dv−2)/dudv)1/2over all edgesuvofG, wheredudenotes the degree of a vertexuofG. In this paper, we give the atom-bond connectivity index of the zigzag chain polyomino graphs. Meanwhile, we obtain the sharp upper bound on the atom-bond connectivity index of catacondensed polyomino graphs withhsquares and determine the corresponding extremal graphs.

On degree-based topological descriptors of strong product graphs

2016 ◽  
Vol 94 (6) ◽  
pp. 559-565 ◽  
Author(s):  
Shehnaz Akhter ◽  
Muhammad Imran
Keyword(s):  
Physicochemical Properties ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Zagreb Indices ◽  
Strong Product ◽  
Product Graphs ◽  
Product Of Graphs ◽  
Atom Bond

Topological descriptors are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as Randić, atom–bond connectivity, and geometric–arithmetic are used to predict the bioactivity of different chemical compounds. There are certain types of topological descriptors such as degree-based topological indices, distance-based topological indices, counting-related topological indices, etc. Among degree-based topological indices, the so-called atom–bond connectivity and geometric–arithmetic are of vital importance. These topological indices correlate certain physicochemical properties such as boiling point, stability, strain energy, etc., of chemical compounds. In this paper, analytical closed formulas for Zagreb indices, multiplicative Zagreb indices, harmonic index, and sum-connectivity index of the strong product of graphs are determined.

scholarly journals Relating the ABC and harmonic indices

2014 ◽  
Vol 79 (5) ◽  
pp. 557-563 ◽  
Author(s):  
Ivan Gutman ◽  
Lingping Zhong ◽  
Kexiang Xu
Keyword(s):  
Molecular Structure ◽  
Topological Index ◽  
Molecular Graph ◽  
Vertex Degree ◽  
Harmonic Index ◽  
Abc Index ◽  
Atom Bond ◽  
Structure Descriptor

The atom-bond connectivity (ABC) index is a much-studied molecular structure descriptor, based on the degrees of the vertices of the molecular graph. Recently, another vertex-degree-based topological index - the harmonic index (H) - attracted attention and gained popularity. We show how ABC and H are related.

scholarly journals On Eccentricity-Based Topological Indices and Polynomials of Phosphorus Containing Dendrimers

2018 ◽  
Author(s):  
Shin Min Kang ◽  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Rabia Sarfraz ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Topological Indices ◽  
Connectivity Index ◽  
The Other ◽  
Topological Descriptors ◽  
Eccentric Connectivity Index ◽  
Important Place ◽  
Eccentricity Index ◽  
Phosphorus Containing ◽  
Pharmaceutical Properties ◽  
High Degree

In the study of QSAR/QSPR, due to high degree of predictability of pharmaceutical properties, the eccentric-connectivity index has very important place among the other topological descriptors, In this paper, we compute the exact formulas of eccentric-connectivity index and its corresponding polynomial, total eccentric-connectivity index and its corresponding polynomial, first Zagreb eccentricity index, augmented eccentric-connectivity index, modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

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